USCA1 Opinion

                            UNITED STATES COURT OF APPEALS                            UNITED STATES COURT OF APPEALS                                FOR THE FIRST CIRCUIT                                FOR THE FIRST CIRCUIT                                 ____________________        No. 93-1404                 THE CONJUGAL PARTNERSHIP COMPRISED BY JOSEPH JONES                     AND VERNETA G. JONES, D/B/A STENOTYPE SYSTEMS,                               Plaintiffs, Appellants,                                          v.                        THE CONJUGAL PARTNERSHIP COMPRISED OF                             ARTHUR PINEDA AND TONI PINEDA,                                Defendants, Appellees.                                 ____________________                     APPEAL FROM THE UNITED STATES DISTRICT COURT                           FOR THE DISTRICT OF PUERTO RICO              [Hon. W. Arthur Garrity, Jr.,* Senior U.S. District Judge]                                             __________________________                                 ____________________                                        Before                                  Cyr, Circuit Judge,                                       _____________                            Bownes, Senior Circuit Judge,                                    ____________________                              and Stahl, Circuit Judge.                                         _____________                                 ____________________            Olga M. Shepard for appellants.            _______________            Maria H. Sandoval for appellees.            _________________                                 ____________________                                     May 4, 1994                                 ____________________        _____________________        *Of the District of Massachusetts, sitting by designation.                      BOWNES, Senior Circuit Judge.  This  is a breach of                      BOWNES, Senior Circuit Judge.                              ____________________            contract  action arising out  of a dispute  between two court            reporters  in  the  United  States  District  Court  for  the            District  of Puerto  Rico.    The  appeal involves  two  jury            trials.    In the  first  trial,  a jury  found  in favor  of            plaintiff, Joseph Jones, and awarded him $225,000 in damages.            The  district   court  granted   a  postjudgment   motion  by            defendant, Arthur Pineda,1 vacated the  judgment, and ordered            plaintiff  to  remit $140,000  or submit  to  a new  trial on            damages.   Plaintiff  refused to  accept the  remittitur, and            proceeded to trial.  This time around he was awarded $20,000.            He  appeals, challenging  the district  court's jurisdiction,            its decision  to vacate  the  original judgment  and order  a            partial remittitur or a new trial on damages, and the court's            admission of  evidence,  at  both  trials, on  the  issue  of            mitigation of damages.  We affirm.                                          I.                                          I.                                      BACKGROUND                                      BACKGROUND                                      __________                      The following  facts are  viewed in the  light most            favorable  to  the verdict  winner,  the  plaintiff, and  all            reasonable  inferences  are drawn  in  his  favor.   Lama  v.                                                                 ____                                            ____________________            1.  More  precisely, the  plaintiffs-appellants in  this case            are the conjugal partnership  comprising Joseph Jones and his            wife  Vernetta, who  worked together  as  Stenograph Systems,            Inc.   The defendants-appellees  are the conjugal partnership            comprising Arthur Pineda and his wife Toni.   Throughout this            opinion, we refer to the parties in the singular, meaning the            husband court reporter.                                         -2-                                          2            Borras, 16 F.3d 473,  477 (1st Cir. 1994).2   Plaintiff Jones            ______            came from New York State to Puerto Rico in March 1987 to work            as  the official  court reporter  for federal  district judge            Jose A. Fuste.  The position was offered for a one-year term,            and Jones  left Judge  Fuste's employ  as scheduled  in March            1988.   Shortly  thereafter, defendant  Pineda, the  official            court reporter for federal  district judge Raymond L. Acosta,            offered Jones a lucrative opportunity.  Judge  Acosta was the            presiding judge in the San Juan Dupont Hotel Fire Litigation,            a complex multi-plaintiff case which promised a lengthy trial            during which the attorneys would require daily transcripts.                      Pineda realized that he and his wife, who was not a            court  reporter  but  aided  her  husband  in  producing  the            transcripts,  would  be unable  to  handle  this task  alone.            After some preliminary discussions, Pineda  and Jones reached            an oral agreement  whereby Pineda agreed  to hire Jones  "for            the  entire length of  the Dupont  trial," during  which they                                       ______            would  split all  of  the court  reporting  duties and  fees.            Jones  agreed to remain in Puerto Rico until the trial ended,            and  further agreed to get  a letter of  reference from Judge            Fuste.  Subsequently, Pineda  sought Judge Acosta's approval,            which was  reluctantly given,  for hiring Jones.   Apparently                                            ____________________            2.  For a more thorough recitation of the facts of this case,            we  refer  you  to  the district  court's  thorough  opinion,            Conjugal   Partnership  Comprised   by   Jones  v.   Conjugal            ______________________________________________       ________            Partnership  Comprised by  Pineda, 798  F. Supp.  892 (D.P.R.            _________________________________            1992) ("Conjugal I").                    __________                                         -3-                                          3            Jones  had  transcribed several  pretrial conferences  in the            Dupont  case, and  Judge Acosta  was  not impressed  with his            reporting  skills.    Nonetheless,  given  Pineda's  repeated            assurances, Judge Acosta  acquiesced to Jones'  participation            for  "phase  I"  of the  Dupont  trial.    But, Pineda  never            informed  Jones  that  Judge  Acosta's  authorization  was  a            condition precedent to the  oral contract, or that revocation            of  the  judge's  approval  would result  in  the  contract's            termination.  And, Pineda never informed Judge Acosta that he            had hired Jones for the duration of the trial.                      The  Dupont  trial  was  scheduled  to  proceed  in            discrete  "phases."  Phase I  began in March  1989 and lasted            for thirty-three days.  Jones and Pineda shared the  workload            and the  fees generated by  phase I.   Phase II  commenced on            June 27, 1989,  and lasted  until December 1990.   The  trial            ended  in December 1991.  Pineda terminated Jones on June 30,            1989, and told Jones  that he made too many mistakes  and was            slowing things  down.   Earlier that  day  Pineda had  voiced            similar concerns about Jones to Judge  Acosta who agreed that            Jones should no longer work on the case and revoked his prior            authorization.  Pineda  told Jones that he  (Pineda), and not            Judge Acosta was responsible for Jones' discharge.  There was            evidence  that  on   June  29,  the  day   before  Jones  was            terminated, a  new system was  developed for linking  the in-            court stenograph machine to a computer located outside of the                                         -4-                                          4            courtroom,  enabling  one  reporter  (Pineda) to  handle  the            reporting work.                      For  his  work  on  phase I  of  the  trial,  Jones            received, $49,108.00, or approximately $1,500 for each of the            thirty-three  sessions.   This represents  half of  the total            fees paid  for reporting  services during phase  I, $112,083,            less  expenses.   The  entire  trial  generated  a  total  of            $465,787.75 in court reporting fees.                      The jury found that, under the  parties' agreement,            Pineda   was  obligated   to  pay   Jones  one-half   of  the            compensation  received for transcribing the trial, whether or            not Judge  Acosta continued  to authorize Jones'  presence in            the courtroom.   Consequently,  it awarded Jones  $225,000 in            damages.                        Pineda moved  for judgment as  a matter of  law, or            alternatively, for a new trial pursuant to Fed. R. Civ. P. 50            and 59.  In  a thoughtful opinion, the district  court denied            the motion for judgment as a matter of law:                      [T]he  jury  found  reasonably  that,  in                      exchange for plaintiff's promise to stay,                      the   defendant    promised   to   employ                      plaintiff  for the duration of the Dupont                      trial   and   to   divide   equally   the                      compensation  he  received;  and  further                      found    reasonably    that   defendant's                      obligation to pay  was not conditioned on                      Judge  Acosta's  continuing  approval  of                      plaintiff's       participation      and,                      alternatively,  that defendant  knowingly                      assumed the risk that Judge  Acosta would                      not approve  of plaintiff's participation                      after phase I. . . .                                          -5-                                          5            Conjugal I, 798 F. Supp. at 896.  The court  also declined to            __________            order  a  new trial  on  liability  because  "the verdict  on            liability, while by no means  inevitable, was not against the            clear weight of the evidence."  Id. at 899.  The court found,                                            ___            however,  that damages were a "different story."  Id. at 899.                                                              ___            The  court found  that  the jury's  award was  excessive, was            based on a  flawed analysis, and that a  new trial limited to            the issue  of damages  was necessary.   Id.  at 900-02.   The                                                    ___            court added that plaintiff  could avoid a retrial on  damages            by agreeing to  remit $140,000.   Id. at  902-03.   Plaintiff                                              ___            declined  the offer and proceeded  to trial.   He was awarded            $20,000 in damages.  This appeal ensued.                                         II.                                         II.                                      DISCUSSION                                      DISCUSSION                                      __________                      On appeal plaintiff argues primarily that:  (1) the            district  court lacked subject  matter jurisdiction;  (2) the            trial judge  abused his  discretion in vacating  the original            judgment and  ordering a  remittitur or alternatively,  a new            trial on damages; and  (3) the trial judge erred  in allowing            defendant to present  evidence, in both the first  and second            trials,  concerning mitigation  of damages  because defendant            had not pleaded mitigation as an affirmative defense.            A.  Jurisdiction            A.  Jurisdiction                ____________                      This action  was removed from  Puerto Rico Superior            Court  pursuant  to 28  U.S.C.    1442(a)(3).    See Conjugal                                                             ___ ________                                         -6-                                          6            Partnership   Comprised  by  Jones  v.  Conjugal  Partnership            __________________________________      _____________________            Comprised  by Pineda, 734 F. Supp. 41 (D.P.R. 1990) (granting            ____________________            defendant's removal  petition and denying  plaintiff's motion            to remand).  That statute provides:                      (a)   A   civil   action    or   criminal                      prosecution  commenced  in a  State court                      against any of  the following persons may                      be removed by them to the district  court                      of the United States for the district and                      division embracing the  place wherein  it                      is pending:                      . . .                            (3) Any officer of the courts of the                      United States, for any Act under color of                      office  or  in  the  performance  of  his                      duties.            28 U.S.C.    1442(a)(3).3  Plaintiff  contends that the  case            was improvidently  removed from superior court  and should be            remanded.  We disagree.                      The  statute guarantees  an officer of  the federal            courts the right to remove an action commenced against him in            state court when he can  allege a "colorable" federal defense            to  that action.    Mesa v.  California,  489 U.S.  121,  136                                ____     __________            (1989); American Policyholders  Ins. Co. v. Nyacol  Products,                    ________________________________    ________________            989 F.2d 1256,  1259 n.3 (1st Cir. 1993).   Although the Mesa                                                                     ____            court  was  concerned  principally  with     1442(a)(1),  the                                            ____________________            3.  Although  Puerto  Rico is  not  a  "State," Congress  has            expressly  provided that  actions commenced  in the  Superior            Court  of Puerto Rico are removable under the federal removal            statutes.  48 U.S.C.   864; Camacho, 868 F.2d at 486 n.4.                                        _______                                         -7-                                          7            general provision of  the federal  officer removal  statute,4            the  Court noted that  "subsections (2)-(4) of    1442(a) are            largely the  `residue' of the pre-1948,  more limited removal            statutes  now  entirely encompassed  by  the general  removal            provision  of the first clause of subsection (1)."  Mesa, 489                                                                ____            U.S. at 134.   The  Court further noted  that subsection  (3)            should be interpreted consistently  with subsection (1).  Id.                                                                      ___            at 135.  Consequently, the present case  was properly removed            if defendant asserted a federal right or raised a question of            federal  law in his defense.  Id. at 126-27 (citing Tennessee                                          ___                   _________            v. Davis, 100 U.S. 257, 262 (1880)).                 _____                      In  his Answer,  defendant  alleged that  plaintiff            "served at  the pleasure  of  the [District]  Court," was  no            longer acceptable  to the court because  of poor performance,            and was  properly  dismissed  by  Judge Acosta.    Answer  to                                                               __________            Complaint at      A-C  & E.    Defendant's  removal  petition            _________            averred  that  the  dispute  arose  "out  of   the  laws  and            regulations of the United  States . . . which govern and  set                                            ____________________            4.  Section  1442(a)(1)  permits  removal  of  an  action  to            federal court by:                      Any officer  of the United States  or any                      agency  thereof,  or person  acting under                      him,  for any  act  under  color of  such                      office  or on account of any right, title                      or  authority claimed  under  any Act  of                      Congress   for    the   apprehension   or                      punishment of criminals or the collection                      of revenue.            28 U.S.C.   1442(a)(1).                                         -8-                                          8            the  relationship between  the United  States Courts  and the            court  reporters  [who]  perform  duties  for   said  courts,            including the  power to  dismiss or  terminate the  duties of            said  court  reporters."   Notice  of Removal  at    2.   The                                       __________________            removal petition also stated that,                      [i]n  order  to  determine   whether  the                      defendants are  or  [are] not  liable  in                      this civil action .  . . any court .  . .                      must construe the terms  [and] provisions                      of  those Acts  of Congress  dealing with                      the  United  States   Courts  and   those                      regulations issued  by the Administrative                      Office of the United States  dealing with                      court   reporters  and   the  supervisory                      powers of  the courts over  federal court                      reporters. . . .            Id.  Finally, in opposition  to plaintiff's motion to remand,            ___            defendant elaborated on the statutes and regulations adverted            to in his removal petition.   In particular, defendant argued            that court  reporting and  court reporters in  federal courts            are regulated by  28 U.S.C.    753 and  the Court  Reporter's            Manual  issued by  the  Administrative Office  of the  United            States Courts (AO).   Opposition to Motion to  Remand at   4.                                  _______________________________            Defendant  further maintained  that  he  was  not  personally            liable  to plaintiff,  that  Judge Acosta  was authorized  to            discharge plaintiff  under   753  and the AO  guidelines, and            that the judge did  so as a result of  plaintiff's inadequate            performance.  Id. at   5.                          ___                      We believe  that these allegations  were sufficient            to satisfy the  statutory requirements, and thus the case was                                         -9-                                          9            properly removed.  Venezia v. Robinson, 16 F.3d 209, 212 (7th                               _______    ________            Cir.  1994)  ("Once the  federal  defendant  has a  plausible            federal defense,  removal is appropriate so  that the federal            court may determine whether the defense succeeds.  A  federal            defendant need not  show that  he is entitled  to prevail  in            order  to have  access  to the  federal forum.").   Plaintiff            insists, however, that this is a state law breach of contract            action that was properly filed  in superior court and  should            have  remained there.  We  disagree.  By  raising a colorable            federal defense, a  defendant-official converts an  otherwise            nonremovable  state law action into one that falls within the            federal court's jurisdiction.   See Mesa 489  U.S. at 136-37.                                            ___ ____            The federal officer removal statute does not require that the            case  be one that could have originally been filed in federal            court.    Williams v. Brooks,  945 F.2d 1322, 1325  (5th Cir.                      ________    ______            1991) (citing cases); see Mesa, 489 U.S. at 136 ("The removal                                  ___ ____            statute . . . serves to overcome the `well-pleaded complaint'            rule which would otherwise preclude removal even if a federal            defense  is alleged.").  Moreover,  that this is  a breach of            contract  case arising under Puerto  Rico law is  not alone a            bar to removal.   See  Camacho v. Autoridad  de Telefonos  de                              ___  _______    ___________________________            Puerto Rico, 868  F.2d 482,  487 (1st Cir.  1989) (under  the            ___________            federal removal statute "the right  to remove is not vitiated            even   if  the   case   necessitates  the   construction  and            interpretation of state or local law").                                         -10-                                          10                      Finally,  although plaintiff  has  pointed  to  the            ultimate failure  of defendant's federal defense  as a ground            for  remand, it is irrelevant for purposes of removal under              1442(a) that  Pineda did not prevail on  his federal defense.            See 28 U.S.C.   1447(c); see  also Jamison v. Wiley, 14  F.3d            ___                      ___  ____ _______    _____            222, 239  (4th Cir. 1994)  ("Nothing in  the federal  removal            statutes authorizes  the  remand  of a  case  that  has  been            properly  removed under    1442(a)(1) on the  ground that the            federal employee's . . . defense is later rejected.").                      At oral  argument plaintiff argued  that our recent            decision  in American Policyholders  precludes application of                         ______________________            the federal removal  statute in  this case.   Our reading  of            that case leads us  to the opposite conclusion.   In American                                                                 ________            Policyholders we held  that a suit against  a federal officer            _____________            exclusively in his or her official capacity is a suit against            the  agency  for  purposes  of removal  under     1442(a)(1).            American  Policyholders, 989 F.2d  at 1260.   And, because an            _______________________            agency may not remove a case under the statute, id. at  1259,                                                            ___            "a  federal  officer  sued  solely  in his  or  her  official            capacity may not  remove a  suit to federal  court under  the            aegis of 28 U.S.C.   1442(a)(1)."  Id. at 1261.  Because this                                               ___            action was brought against defendant solely in his individual            and  not his  official capacity,  it was  subject to  removal            under   1442(a)(3).                                         -11-                                          11            B.  Remittitur or A New Trial on Damages            B.  Remittitur or A New Trial on Damages                ____________________________________                      Plaintiff  argues that the  district court erred in            vacating  the original  judgment of  $225,000 and  ordering a            remittitur  of $140,000  or,  alternatively, a  new trial  on            damages.  According to plaintiff,  the district court was not            entitled to substitute its judgment for that of the jury.                      Under Federal  Rule of Civil Procedure  59(a), "[a]            new trial may be granted  . . . on all or part  of the issues            . . . ."   Fed. R.  Civ. P. 59(a); Allen  v. Chance Mfg. Co.,                                               _____     _______________            873  F.2d 465, 474 (1st Cir. 1989).   On the issue of damages            the court found  that the "[d]amages awarded to  plaintiff by            the jury were  so clearly excessive . . . as to require a new            trial on  damages, unless  a remittitur would  be appropriate            and acceptable  to plaintiff .  . .  ."  Conjugal  I, 798  F.                                                     ___________            Supp. at 900.   We  have recognized that  a district  court's            discretion to grant a new trial extends to cases in which the            court  determines that the  damages awarded  by the  jury are            excessive.  See Perez-Perez  v. Popular Leasing Rental, Inc.,                        ___ ___________     ____________________________            993 F.2d 281,  283 (1st  Cir. 1993) ("`The  motion for a  new            trial may  invoke the discretion of the court in so far as it            is bottomed  on  the  claim  .  .  .  that  the  damages  are            excessive.'" (quoting  Montgomery Ward  & Co. v.  Duncan, 311                                   ______________________     ______            U.S. 243,  251 (1940))); McIsaac v.  Didriksen Fishing Corp.,                                     _______     _______________________            809 F.2d 129, 135 (1st Cir. 1987).                                         -12-                                          12                      "Under the practice of  remittitur . . .  the court            may also  condition the denial of a motion for a new trial on            the  filing by plaintiff of a remittitur in a stated amount."            Phelan v. Local 305, 973 F.2d 1050, 1064 (2d Cir. 1992);  see            ______    _________                                       ___            also  Catullo v. Metzner, 834 F.2d 1075, 1082 (1st Cir. 1987)            ____  _______    _______            ("Rule 59 empowers the trial court to order  remittitur where            a  damage award  is  not  supported  by  the  weight  of  the            evidence.").  The court must, however, hold out the option of            a new trial.  Phelan, 973 F.2d at 1064 (collecting cases).                          ______                      We  will reverse  a  district court's  decision  to            order a remittitur or a partial new trial due to an excessive            damage  award, only  where the  court abused  its discretion.            Quinones-Pacheco v. American Airlines,  Inc., 979 F.2d 1 (1st            ________________    ________________________            Cir. 1992); Catullo, 834 F.2d at 1082.  Here, we must analyze                        _______            the district  court's decision against the  proper measure of            damages under Puerto Rico  law.  The Supreme Court  of Puerto            Rico has held that,                      "the  measure  of  damages  sustained  by                      reason  of  failure  on  the part  of  an                      employer  to comply  with a  contract for                      services    is,    prima    facie,    the                      compensation stipulated  in the contract,                      subject  to reduction  upon proof  by the                      defendant as  to the amount  the employee                      did  gain or could have gained during the                      time the contract remained in force."            Villar  & Co.  v.  Conde, 30  F.2d 588,  590 (1st  Cir. 1929)            _____________      _____            (quoting  Hardouin v.  Krajawsky-Pesant  Co., 22  P.R.R.  641                      ________     _____________________                                         -13-                                          13            (1923)).    This standard  was  correctly  identified by  the            district court.  Conjugal I, 798 F. Supp. at 901.                             __________                      Here  the  district  court  engaged  in  a detailed            examination  of  the  evidence  pertaining  to  damages,  and            concluded that  the jury's excessive generosity was traceable            to two errors.  First, the court determined that the jury, in            computing  plaintiff's damages,  failed  to  deduct the  fees            generated  during phase I  of the Dupont  trial, $112,083 (of            which  plaintiff received  his  share), from  the total  fees            earned during the entire  trial, $465,787.75.  Therefore, the            jury  used  $465,787.75  as   a  starting  point  instead  of            $353,704.25 (i.e., $465,787.75 - $112,083).                         ____                      According to  the district court, the  jury's error            was  almost  certainly  attributable  to   counsels'  "casual            treatment of  the evidence pertaining to  damages."  Conjugal                                                                 ________            I,  798 F.  Supp. at  900.   The figures  show that  the jury            _            likely committed  this  oversight.   If  we take  the  higher            figure,   deduct  $15,000   for  expenses5  and   divide  the            difference   ($450,787.75)  by   two,  the   quotient  (i.e.,                                                                    ____            plaintiff's "prima  facie" loss)  comes out  to approximately            $225,000 -- the amount actually awarded by the jury.                      The second defect in the damage award identified by            the district court was the  jury's apparent failure to reduce                                            ____________________            5.  This  is the minimum amount of expenses, supported by the            record, incurred by defendant after plaintiff's discharge.                                         -14-                                          14            plaintiff's damages by the  amount plaintiff earned after his            discharge on June 30, 1989, and before the termination of the            Dupont  trial  in December  1991.    It was  undisputed  that            plaintiff earned approximately $50,000 in 1990 and $40,000 in            1991  from court  reporting  sources.   There  was no  direct            testimony as  to plaintiff's  court reporting income  for the            balance of 1989.   Because  Puerto Rico law  requires that  a            damage award be reduced by the amount of the plaintiff's gain            during the remaining life of the contract, the jury's failure            to do so here resulted in an excessive damage award.                      After scanning the trial  record, we agree with the            district court  that these  deficiencies infected the  jury's            damage calculation and resulted in an excessive damage award.            Therefore, a new trial or a partial remittitur was warranted.                      With  respect to  the remittitur,  plaintiff argues            that he was  willing to remit a  lesser amount, and  that the            court's remittitur was excessive.   The rule in this  circuit            for computing a remittitur is the "least intrusive" standard.            See  Catullo, 834  F.2d at  1083; see  also Earl  v. Bouchard            ___  _______                      ___  ____ ____     ________            Transp. Co., 917  F.2d 1320, 1328 (2d Cir.  1990) (explaining            ___________            three different  rules for computing remittitur  and adopting            the  least  intrusive  method).   Under  this  standard,  the            remittitur  amount should  reduce  the verdict  "only to  the            maximum  that would  be  upheld by  the  trial court  as  not            excessive."  Earl, 917 F.2d at 1330.  The district court used                         ____                                         -15-                                          15            this standard in calculating its remittitur.  Conjugal I, 798                                                          __________            F.  Supp. at 902-03.   We can  find nothing in  the record to            substantiate plaintiff's  claim that the  trial judge  abused            his discretion by remitting the amount that he did, $140,000.                      As our  discussion above  indicates, see supra,  p.                                                           ___ _____            14,  the  maximum  amount  of plaintiff's  prima  facie  loss            supported  by the  evidence  was  $169,350 (i.e.,  ($353,705-                                                        ____            $15,000)/2).   Under  Puerto Rico  law, this  figure must  be            reduced  by  the  minimum  amount  of  mitigation  proved  by            defendant  at trial,  approximately $90,000.6   Consequently,            we  are left  with a  maximum  damage award  of approximately            $80,000.  Plaintiff's attack  on the amount left in  place by            the district court, $85,000, is therefore without force.            C.  Mitigation of Damages            C.  Mitigation of Damages                _____________________                      Plaintiff maintains that he  is entitled to a third            trial  on  damages  because  the  district  court  improperly            admitted, at both trials, evidence pertaining to the issue of            mitigation   of  damages.     According  to   plaintiff  this            constituted  reversible error  because  the  defendant  never            pleaded mitigation as an affirmative defense.                                            ____________________            6.  Because plaintiff  was only  able to estimate  his annual            earnings for 1990 and 1991, the district court discounted the            figures  provided  by  plaintiff.     The  court   reasonably            concluded from the evidence that plaintiff  earned a total of            $85,000  from  court  reporting   between  the  time  he  was            terminated  until the end of  the Dupont trial.   Conjugal I,                                                              __________            798 F. Supp. at 903.                                         -16-                                          16                      It is true that  defendant did not plead mitigation            of damages as an  affirmative defense in his complaint.   Nor            does it appear that  the issue was addressed in  any pretrial            orders  prior to  the first trial.   Plaintiff  did, however,            include a  proposed jury instruction concerning mitigation of            damages in  his proposed charge submitted  in anticipation of            the first trial.7                      At  the first  trial, the  issue of  mitigation was            initially raised during  defense counsel's  cross-examination            of plaintiff, when he asked plaintiff about income from court            reporting sources subsequent to being discharged.  At no time            during  this line  of  questioning  did  plaintiff's  counsel                                            ____________________            7.  Plaintiff's proposed instruction number 25 states:                           The measure of damages  sustained by                      reason of  failure  on  the  part  of  an                      employer  to  comply  with   a  contract,                      subject  to reduction  upon proof  by the                      defendant as  to the amount  the employee                      did gain or could  have gained during the                      time  the  contract  remained  in  force.                      Hardouin  v.   Krajewski-Pesant  Co.,  22                      ________       _____________________                      P.R.R. 641.                           In an action  for damages for breach                      of  a contract  for services  it devolves                      upon  the defendant  to  prove  that  the                      plaintiff secured or  could have  secured                      another    position,   and    while   the                      discharged  employee is bound to look for                      other work or take the risk of having the                      amount  claimed  reduced  by  the  amount                      which he  could  have earned,  he is  not                      required to look for  work of a different                      nature, or in another locality, or in the                      service of an unsuitable employer.  Id.                                                          ___                                         -17-                                          17            object  on  the grounds  that the  defendant had  waived this            defense by failing  to plead  it in accordance  with Fed.  R.            Civ.  P. 8(c).   The  sole objections  raised by  plaintiff's            counsel  were that  the questions exceeded  the scope  of the            direct  examination, and  that  plaintiff's  income  was  not            pertinent to the case.  At the end of the trial, the district            court instructed the jury,  without objection from plaintiff,            on the doctrine of mitigation.                      After  the  district   court  granted   defendant's            postjudgment  motion,  plaintiff  moved  for  reconsideration            based in part  on defendant's failure to plead  mitigation of            damages as an affirmative defense.  The district court denied            the motion on  the ground that,  "mitigation was referred  to            repeatedly during  trial and  in the Court's  instructions to            the   Jury   without  any   objection  being   interposed  by            plaintiffs.  Plaintiffs' conduct during trial amounted in our            opinion to a waiver of the ground they now assert."                        Between  the  first  and second  trials,  defendant            engaged in extensive discovery on the  issue of mitigation of            damages.    Questions  concerning mitigation  were  posed  by            defendant  in  written  interrogatories  and  at  plaintiff's            deposition.  Both parties retained  experts (certified public            accountants) who authored reports on plaintiff's damages, and            later  testified  at  trial   on  the  issue  of  mitigation.            Additionally,  both  parties  submitted  trial  memoranda  in                                         -18-                                          18            which, at the court's direction, the  issue of mitigation was            briefed.   The parties also filed a joint trial memorandum in            which plaintiff included, among  his claims and defenses, the            statement  that "[p]laintiffs  made every effort  to mitigate            the damages caused  by the breach of  contract by defendants,            but were  set  back  by  the unilateral  termination  of  the            contract by defendants, which  affected plaintiffs' good name            and reputation in the industry."                      Furthermore,  in  the  opening statement  plaintiff            proposed that the  judge give  to the  jury, he  specifically            asked the court to address the issue of mitigation:                           Once the amount due to plaintiffs is                      determined,  then,  you  must  consider[]                      whether or not plaintiffs had the duty to                      mitigate  the  damages   suffered  as   a                      consequence of the breach of  contract by                      defendants.   Also, you must consider the                      steps  taken  by  plaintiffs to  mitigate                      these damages.  Then, you  must determine                      whether  an  amount  for   mitigation  of                      damages, if  any, is to be  deducted from                      plaintiffs' award.            Finally,  in a  proposed jury  charge submitted prior  to the            second   trial,   plaintiff   devoted    seven   instructions            exclusively to the  issue of  mitigation of damages.   At  no            time during the activities leading up to the second trial did            plaintiff  argue that  defendant  had waived  the defense  of            mitigation of damages by omitting it from his answer.                      On the  opening day of the  second trial, defendant            moved to amend his answer, pursuant to Fed. R. Civ. P. 15(b),                                         -19-                                          19            to include  mitigation of damages as  an affirmative defense.            Plaintiff   objected.     The  court   overruled  plaintiff's            objection and allowed the amendment:                           [O]n mitigation, the  law of  Puerto                      Rico and  every other jurisdiction  is so                      clear that prima facie damage  for breach                      of contract places  on the injured  party                      the obligation to mitigate.                           But  it is  more than  that.   It is                      that  part  of  plaintiffs'  proof  in  a                      breach  of  contract  case, as  in  every                      case,   is   causation,  liability,   and                      liability  causing  damage to  the extent                      that an injured  plaintiff can avoid that                      damage  by  working  himself.    To  that                      extent his  damage is not  caused by  the                      defendant,  but  is,  rather, caused,  if                      this  is  the  evidence,  by  plaintiffs'                      failure  to  exert  reasonable effort  to                      make up for this loss of income.                                        * * *                           Now, basically it is the defendants'                      burden to  prove mitigation.   In the way                      this  case stands  the defendant  will go                      forward  and  have the  burden  of proof.                      But  to  eliminate   from  the  case  the                      mitigation  issue,  and  implicitly,  the                      importance of  the plaintiff establishing                      causation  between  liability and  damage                      requires,  in my  view, the  amendment of                      the  pleading  that  the   defendant  has                      proposed.            Transcript of Second Trial,  Vol. I, pp. 34-35.  At the start            __________________________            of the  third  and final  day of  trial, after  the issue  of            mitigation had been litigated,  the court revisited its prior            ruling:                           [T]he   Court    now   vacates   its                      allowance . .  . [of] defendant's  motion                      to  amend   its  answer  by   adding  the                      affirmative  defense   of  mitigation  of                      damages.   This order does not affect the                      evidence  at this  trial or  the evidence                                         -20-                                          20                      that will go  to the  jury, but,  rather,                      the state of the pleadings.            Transcript  of Second Trial, Vol. III, p.  3.  The court then            ___________________________            explained that defendant was not required to plead mitigation            of  damages as an affirmative defense, and that the court had            granted defendant's motion to amend because  it did not think            that  the amendment  had any  real  significance.   The court            added, however, that  it realized that there  was support for            the  position  that  mitigation was  an  affirmative defense.            Therefore, the court "un-amended"  defendant's answer so that            plaintiff could raise the present issue on appeal.                      After   the  jury  returned  its  $20,000  verdict,            plaintiff moved to set aside the judgment  based primarily on            the  trial court's  admission  of mitigation  evidence.   The            court denied the motion:                           At   the   first  trial   plaintiffs                      offered  evidence  of  damage   to  their                      reputation for having been "kicked out of                      Puerto Rico", which was relevant  only to                      mitigation   and   did   not  object   to                      instructions submitting the issue  to the                      jury.     The  retrial   on  damages  was                      preceded  by  abundant  discovery  as  to                      mitigation, at the Court's  direction the                      parties  briefed  the  law applicable  to                      this  issue  and   both  parties   called                      alleged   experts    to   testify   about                      plaintiffs'    actual    and    potential                      earnings.  In  our opinion  any error  in                      the  Court's  reception  of  evidence  on                      mitigation    could    not   have    been                      prejudicial.            Conjugal  Partnership   Comprised   by  Jones   v.   Conjugal            _____________________________________________        ________            Partnership Comprised  by Pineda, No. 90-1051  (D. Mass. Dec.            ________________________________                                         -21-                                          21            15, 1992) (order denying  motion to set aside  new judgment).            We review plaintiff's claim of error against this backdrop.                      There  is some  question as  to whether  or not  we            should  look  to  state  law  in  determining  if  failure to            mitigate damages is an affirmative defense under Fed. R. Civ.            P. 8(c),8  compare Sayre v.  Musicland Group, Inc.,  850 F.2d                       _______ _____     _____________________            350,  354   (8th  Cir.   1988)  (whether  mitigation   is  an            affirmative defense  under Rule 8(c) is  a federal procedural            matter and is  governed by  the federal rules),  with 999  v.                                                             ____ ___            C.I.T. Corp., 776 F.2d  866, 870 n.2 (9th Cir.  1985) (citing            ____________            California law for the proposition that mitigation of damages            is an affirmative  defense under  Rule 8(c)).   We need  not,            however,  dwell on this dilemma.   Failure to  mitigate is an            affirmative defense  as a  matter of federal  procedural law,            see  Lennon v. U.S. Theatre  Corp., 920 F.2d  996, 1000 (D.C.            ___  ______    ___________________            Cir. 1990); Modern  Leasing v. Falcon Mfg. of California, 888                        _______________    _________________________            F.2d 59,  62 (8th Cir. 1989), as well as Puerto Rico law, see                                                                      ___            Odriozola v.  S. Cosmetic Dist. Corp., 116 D.P.R. 485 (1985),            _________     _______________________            and therefore must be pleaded.                       Generally speaking, failure to plead an affirmative            defense  results in a waiver of the defense and the exclusion            of all evidence relevant to it.  See Federal Deposit Ins. Co.                                             ___ ________________________                                            ____________________            8.  Under  Rule 8(c), certain  enumerated defenses,  of which            mitigation is not one, and "any other matter  constituting an            avoidance  or an affirmative defense," must be pleaded by the            defendant.                                           -22-                                          22            v.  Ramirez-Rivera,  869  F.2d  624,  626  (1st  Cir.  1989);                ______________            Depositors Trust Co. v. Slobusky, 692 F.2d 205, 208 (1st Cir.            ____________________    ________            1982).   Nevertheless, it is settled that "[w]hen there is no            prejudice and when fairness  dictates, the strictures of [the            raise  or  waive]   rule  may  be  relaxed."     Jakobsen  v.                                                             ________            Massachusetts  Port Authority,  520 F.2d  810, 813  (1st Cir.            _____________________________            1975).   Under Fed.  R. Civ. P.  15(b),9 the trial  court may            and  should liberally  allow amendments  to the  pleadings if            prejudice  does  not  result.     Id.    Moreover,  when   an                                              ___            affirmative defense that has not been raised in the pleadings            has  actually been tried  by implied consent  of the parties,                                            ____________________            9.  Rule 15(b) provides as follows:                      When issues not  raised by the  pleadings                      are tried  by express or  implied consent                      of the parties, they shall be treated  in                      all respects  as if they had  been raised                      in  the pleadings.  Such amendment of the                      pleadings  as may  be necessary  to cause                      them to  conform to  the evidence and  to                      raise  these  issues  may  be  made  upon                      motion  of any  party  at  any time  even                      after judgment; but failure to do so does                      not  affect the  result of  the trial  of                      these issues.  If evidence is objected to                      at  trial on  the ground  that it  is not                      within the issues  made by the pleadings,                      the  court may allow  the pleadings to be                      amended and  shall do so freely  when the                      presentation of the  merits of the action                      will   be   subserved  thereby   and  the                      objecting  party  fails  to  satisfy  the                      court that the admission of such evidence                      would prejudice the party  in maintaining                      the  party's action  or defense  upon the                      merits.      The   court  may   grant   a                      continuance to enable the objecting party                      to meet such evidence.                                         -23-                                          23            the court must treat the defense as if it had  been raised in            the original responsive pleading.  Id.; Depositors Trust Co.,                                               ___  ____________________            692 F.2d at 208.                      With respect  to the first trial, it  is clear that            the issue  of mitigation was actually  tried with plaintiff's            implied consent.  "One sign of implied consent is that issues            not raised by  the pleadings are presented and argued without            proper objection  by opposing counsel."   Matter of Prescott,                                                      __________________            805 F.2d 719, 725 (7th Cir. 1986) (citing cases).  Under Rule            15(b), lack of consent  is manifested by an objection  on the            ground that the evidence  is not within the issues  raised by            the pleadings.  Id.;  Hardin v. Manitowoc-Forsythe Corp., 691                            ___   ______    ________________________            F.2d 449, 457 (10th Cir. 1982).  Here, defendant's mitigation            evidence   was  presented   without  relevant   objection  by            plaintiff.                      Furthermore,  implied  consent  is generally  found            where the  opposing party  actually produced evidence  on the            new issue.  See Law v. Ernst & Young, 956 F.2d  364, 375 (1st                        ___ ___    _____________            Cir. 1992); Lynch  v. Dukakis,  719 F.2d 504,  508 (1st  Cir.                        _____     _______            1983);  Hardin, 691 F.2d at  457; see generally  6 Charles A.                    ______                    ___ _________            Wright & Arthur  R. Miller, Federal Practice  and Procedure                                          _______________________________            1493  at 28  (1990) (citing  cases).   Here, as  the district            court noted, plaintiff's testimony concerning  alleged damage            to his reputation within court reporting circles was relevant                                         -24-                                          24            only to the issue  of mitigation.10  Moreover,  plaintiff did            ____            not  object to  that portion  of  the jury  charge concerning            mitigation of damages.   See Zappia v. Baltimore &  Ohio R.R.                                     ___ ______    ______________________            Co., 312 F.2d 62,  64 (6th Cir. 1962) (implied  consent found            ___            where party did  not object to jury  instruction on unpleaded            issue).  Finally, plaintiff never asked for a  continuance in            order to meet the  evidence of mitigation, nor did  he allege            any  prejudice resulting  from the  court's admission  of the            mitigation evidence at the  first trial.  Rhode Island  Educ.                                                      ___________________            v. Secretary U.S. Dep't of Educ., 929 F.2d 844, 855 (1st Cir.               _____________________________            1991) (unpleaded issue  properly raised where  opposing party            failed  to argue prejudice); George Cohen Sons & Co. v. Koch,                                         _______________________    ____            376  F.2d 629, 632-33 (1st Cir. 1967) (claim tried by implied            consent  of the parties where opposing party failed to seek a            continuance to meet evidence  on unpleaded issue).  Moreover,            in  light  of  the  fact  that  plaintiff,  prior  to  trial,            submitted  a proposed  jury  instruction on  the doctrine  of            mitigation,  we   can  reasonably  conclude   that  plaintiff            anticipated   that  the   issue  would   be   litigated,  and            consequently was not prejudiced when it was raised.                                             ____________________            10.  This testimony  was relevant to the  issue of mitigation            because  while a party is  under a duty  to mitigate damages,            "only those  who are able to  mitigate must do so."   Noble v                                                                  _____            Corporacion Insular de  Seguros, 738  F.2d 51,  55 (1st  Cir.            _______________________________            1984).   It was not  otherwise relevant  since only  economic            damages are  recoverable in  a breach of  contract action  in            Puerto Rico.  See P.R. Laws Ann. tit. 31,   3023 (1990).                          ___                                         -25-                                          25                      Turning our attention to the second trial, we reach            the same  conclusion.   We note, however,  that the  district            court erred as a matter of  law in holding that mitigation of            damages  is  not  an  affirmative defense  under  Rule  8(c).            Nevertheless, because  we affirm the court's  ruling that the            issue  of mitigation  was properly  litigated, its  error was            harmless.                      It is hornbook law that,  "`at the trial stage  the            case is to be heard on the merits, and is not to be hamstrung            by   faulty  pleadings,   unless  actual,   not  conjectural,            prejudice  results from  the  faulty pleadings.'"   Green  v.                                                                _____            United States, 629 F.2d 581, 584 n.1 (9th Cir. 1980) (quoting            _____________            2A James  W. Moore et al., Moore's Federal Practice   8.05 at                                       ________________________            8-34 (2d ed. 1979)).  Because the issue of mitigation was the            subject of substantial pretrial activity, plaintiff had ample            notice  that the defense of  mitigation would be litigated at            the  second  trial.    Consequently,  the  district   court's            decision to admit the mitigation evidence and allow the issue            to be litigated was proper.  See Pane v. RCA  Corp., 868 F.2d                                         ___ ____    __________            631, 637 (3d Cir.  1989) (where unpleaded affirmative defense            was referred to repeatedly in  pretrial motions and no unfair            surprise  resulted,  district   court  did   not  abuse   its            discretion in allowing the issue to be litigated).                      We  have  considered  plaintiff's other  claims  --            particularly those concerning the trial court's denial of his                                         -26-                                          26            motion  for sanctions under Fed.  R. Civ. P.  11, the court's            decision  to stay the  execution of judgment  after the first            trial,  and its  refusal to  compel discovery  of defendant's            personal financial  papers --  and  find them  to be  without            merit.                      The judgment of the district court is Affirmed.                                                            Affirmed.                                                            ________                                         -27-                                          27


Introductions
=============

In the past 50 years, antibiotics became an important part of our everyday lives: we take them during routine visits to dental and doctor offices, but they are also invisibly present on supermarket produce shelves. If asked around, one would probably hear as many definitions of the word "antibiotic" as there are uses for these powerful drugs. However, this everyday presence was recently interrupted by more and more alarming news that these "miracle drugs" that saved millions of lives stopped working as expected. Antibiotic resistance became a matter of public news and executive orders of governments. The urgency of tackling antibiotic resistance requires actions from everyone. The new book "Antibiotics: Current Innovations and Future Trends" edited by Sergio Sanchez and Arnold L. Demain takes a fresh look at antibiotics as we know them and explores what we can do to preserve existing antibiotics and to secure the present and the future of modern medicine.

What are antibiotics?
=====================

The book comprises 21 articles written by leading scientists on various aspects of antibiotic uses, activities, discovery and alternatives. Although the articles are unrelated, they are assembled in such a way as to truly engage a reader into the world of antibiotics. The starting article by Joan Wennstrom Bennett follows the history of defining "antibiotics" beginning with the "comprehensive" definition by Selman Waxman that an antibiotic is "... a chemical substance produced by micro-organisms... to inhibit the growth of and even to destroy bacteria and other microorganisms...." The subsequent chapters effectively demonstrate that the field of antibiotics has over-grown this definition and that medical uses of antibiotics include not only infectious diseases caused by micro-organisms but also oncological diseases (Chapter 2 by Ren and co-authors) as well as diseases caused by multicellular parasites (Chapter 9 by Shiomi and Omura) and viruses (Chapter 18 by Veiga-Crespo et al.). Non-medical uses are even more diverse and sometimes are troubling for example, feeding animals for growth, spraying flowers and fruits to preserve freshness and water treatments (Chapter 8 by Kardos). Although microorganisms remain to be major suppliers of antibiotics, present days these microorganisms come from new sources such as endophytes, geyzers and caves (Chapters 10--12). Even un-culturable micro-organisms are successfully "hunted" for new antibiotics (Lewis et al, Chapter 6). Animal venoms and plants also proved to be rich sources of peptides and small molecules with antibiotic properties (Samy et al., Chapter 13).

How can we expand the diversity of antibiotics?
===============================================

The empirical search for natural products in new and diverse places yielded most of the antibiotics that are currently used in medical and non-medical applications. This approach continues to expand the chemical diversity and biological activities of antibiotics. In addition, the book analyzes how more analytical approaches impact the drug discovery process and what we can expect in the future from these newest trends. Advances in DNA sequencing and genomics as well as in basic sciences impacted the drug discovery process in several major ways: (i) drug screening is re-focused from phenotypes onto specific targets (Chapter 14 by Lynn Silver); (ii) silent secondary metabolic pathways are identified from genome analyses and there are several ways to activate them (Chapter 15 by Martin and Liras); (iii) among various genome treasures are new enzymatic activities needed for combinatorial biosynthesis to generate novel bioactive compounds (Chapter 16 by Park and Yoon). Although some of these newest trends did not live up to high expectations---e.g., target focused screening was largely unproductive---they also suggested alternatives and solutions. Significant number of new antibiotics are currently in the development and clinical pipelines (Chapter 21 by Park and Thomas). Novel screening approaches focused on identification of pro-drugs effective against persisters, compounds acting on several homologous enzymes or pathways, efflux pump inhibitors, anti-virulence targets and pathogen specific vaccines all have a strong potential to expand the diversity and effectiveness of antibiotics.

How can we preserve the existing activities?
============================================

The book does not specifically address the problem of resistance or mechanisms underlying the development and spread of antibiotic resistance. However, resistance affects and changes the entire field of antibiotics starting with the drug discovery process through the development and applications and is invariably present in almost all chapters. Undoubtedly, the misuse and overuse of antibiotics are major contributors to development and spread of resistance (Chapter 8 by Nelson Kardos). I would like to briefly re-cite for the readers the 2011 World Health Organization advises on interventions to address this growing problem: (i) lack of comprehensive national actions; (ii) lack of capacity and surveillance to choose adequate treatment for individual patients and make policy decisions; (iii) overuse of antibiotics for diseases that do not require them and underuse due to insufficient dosing and course durations; (iv) misuse of antibiotics in food-producing animals for growth promotion; (v) prevention of the spread of resistant bacteria in hospitals and their presence as environmental contaminants; (vi) inadequate momentum in research and development in the essential technologies. This book however demonstrates that we are gaining significant momentum in the essential technologies and many of these interventions are already in place. The major message is that only acting on a global basis, we can preserve antibiotics.

Conclusions {#s1}
===========

This book would be of interest to a broad community of scientists, clinicians and administrators working with antibiotics. It could also be recommended as a textbook for upper level undergraduate and graduate classes at colleges and professional schools.

Conflict of interest statement
------------------------------

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

[^1]: This article was submitted to Antimicrobials, Resistance and Chemotherapy, a section of the journal Frontiers in Microbiology.

[^2]: Edited by: Jose L. Martinez, Centro Nacional de Biotecnología, Spain

[^3]: Reviewed by: Antonio Oliver, Hospital Son Dureta, Spain


---
abstract: 'We give an appropriate version of the result in the paper by Dipierro, Savin, and Valdinoci for different, not necessarily fractional, powers of the Laplacian.'
address: '127 Vincent Hall, University of Minnesota, Minneapolis, MN, 55455'
author:
- 'N.V. Krylov'
title: 'On the paper “All functions are locally s-harmonic up to a small error" by Dipierro, Savin, and Valdinoci'
---

Introduction
============

Let ${\mathbb{R}}^{d}$ be a $d$-dimensional Euclidean space. Denote $B_{r}=\{x\in{\mathbb{R}}^{d}
:|x|<r\}$, and for integers $k=0,1,...$ let $C^{k}(\bar B_{r})$ be the set of $k$-times continuously differentiable functions on $\bar B_{r}$ provided with the usual norm $\|\cdot\|_{C^{k}(B_{r})}$ equal to the sum of maximal magnitudes of all derivatives up to the $k$-th order.

Here is Theorem 1.1 of [@DSV_17] in a slightly different form.

\[theorem 10.10.1\] For any $k\in\{0,1,...\}$, $s\in(0,1)$, $f\in C^{k}(\bar B_{r})$, and $\varepsilon>0$, there exists $u\in C^{\infty}_{0}({\mathbb{R}}^{d})$ such that $(-\Delta)^{s}u=0$ in $B_{1}$ and $$\|f-u\|_{C^{k}(  B_{1})}\leq\varepsilon.$$

Actually, Theorem \[theorem 10.10.1\] may look like a generalization of Theorem 1.1 of [@DSV_17] because the smoothness class of $u$’s in the latter is much wider. However, by using mollifications one easily deduces Theorem \[theorem 10.10.1\] from Theorem 1.1 of [@DSV_17].

Many interesting consequences are extracted in [@DSV_17], in particular, that $s$-harmonic functions in $B_{1}$ do not satisfy the Harnack inequality.

One can rewrite Theorem \[theorem 10.10.1\] in different terms. For real $n$ introduce $$K_{n}(x,y)=|x-y|^{n},\quad K_{n}g(y)=\int_{{\mathbb{R}}^{d}}K_{n}(x-y)g(x)\,dx.$$ Since the function $u$ from Theorem \[theorem 10.10.1\] has a representation $u=c_{d,s}K_{2s-d}g$, where $g=(-\Delta)^{s}u$ and $c_{d,s}$ is an appropriate constant, Theorem \[theorem 10.10.1\] is equivalent to the following.

\[theorem 10.10.2\] For any $k\in\{0,1,...\}$, $s\in(0,1)$, $f\in C^{k}(\bar B_{1})$, and $\varepsilon>0$, there exists $g\in C^{\infty} ({\mathbb{R}}^{d})$ having all bounded derivatives of any order such that $g=0$ in $B_{1}$, $K_{2s-d}g\in  C^{\infty}_{0}({\mathbb{R}}^{d})$, and $$\|f-K_{2s-d}g\|_{C^{k}(  B_{1})}\leq\varepsilon.$$

The goal of this paper is to almost extend this result from $n=2s-d$, $s\in(0,1)$, to arbitrary $n\in(-d,0)$ such that $n+d \not \in\{2,4,...\}$. By “almost” we mean that we will have $K_{n}g\in  C^{\infty} ({\mathbb{R}}^{d})$ with each derivative of any order tending to zero as $|x|\to\infty$ instead of $K_{2s-d}g\in  C^{\infty}_{0}({\mathbb{R}}^{d})$, but on the other hand we will have $g\in C^{\infty}_{0} (B_{4}\setminus\bar B_{3})$. Wider range of $n$ than $(-d,0)$ is also treated.

Main result
===========

Fix a real number $n$ such that $n+d \not \in\{2,4,...\}$ and fix a $k\in\{0,1,...\}$. Define $S $ as the set of functions $f$ on $B_{1}$ each of which has a representation on $B_{1}$ as $f=K_{n}g$, where $g\in   C^{\infty}_{0}(B_{4}\setminus\bar B_{3})$. Observe right away that if $n\in(-d,0)$, then $K_{n}g$ is well defined in ${\mathbb{R}}^{d}$ and is bounded along with each of its derivatives of any order, which, in addition, tend to zero at infinity. This justifies the last paragraph in the Introduction.

Here is our result.

\[theorem 9.10.1\] The set $S$ is everywhere dense in $C^{k}(\bar B_{1})$.

To prove the theorem we need rather rough estimates from the following lemma proved in Section \[section 10.9.1\].

\[lemma 9.10.1\] Take $r\in\{0,1,...\}$ such that $2r>k$. Then there exist a constant $N=N(d,k,r)$ such that, for any $x\in B_{4}\setminus\bar B_{3}$ and real $m$, we have $$\label{9.10.1}
\|K_{m}(x,\cdot)\|_{C^{ k}(B_{1})}
\leq N^{r}(m^{2r}+N^{r}).$$

[**Proof of Theorem \[theorem 9.10.1\]**]{}. Let $\bar S$ be the closure of $S$ in $C^{k}(\bar B_{1})$. Then $K(x,\cdot)\in \bar S$ for any $x\in B_{4}\setminus\bar  B_{3}$, which is seen from the formula $$K_{n}(x,y)=\lim_{m\to\infty}\int_{{\mathbb{R}}^{d}}K_{n}(x+z/n,y)\zeta
(z )\,dz$$ $$=\lim_{m\to\infty}\int_{B_{4}\setminus\bar  B_{3}}
K_{n}(z,y)\zeta_{m}
(z-x)\,dz,$$ where $\zeta_{m}(z)=m^{d}\zeta(mz)$ and $\zeta$ is any $C^{\infty}_{0}({\mathbb{R}}^{d})$ function which integrates to one.

Now, since partial derivatives are limits of finite differences, $\Delta^{m}_{x}K_{n}(x,\cdot)\in \bar S$ for any $m=0,1,...$ and $x\in B_{4}\setminus \bar B_{3}$, where $\Delta_{x}$ is the Laplacian applied with respect to the $x$ variable. Observe that $K_{n}(x-y)$ is a radial function if the origin is taken to be $y$. We know how the Laplacian looks on radial functions, so that, for $m\geq1$, $$\label{9.10.2}
\Delta _{x}K_{n} =n(n-1)  K_{n-2}+(d-1)n
 K_{n-2}=
n(n+d-2) K_{n-2}.$$ It follows that $\Delta^{m}_{x}K_{n}(x,\cdot)=c_{m}K_{n-2m}(x,\cdot)$, where $c_{m}$ are some constants, and our assumption that $n+d \not \in\{2,4,...\}$ implies that $c_{m}\ne0$. Thus $$K_{n-2m}(x,\cdot)\in \bar S\quad m=0,1,....$$

Next, owing to Lemma \[lemma 9.10.1\], for any $x\in B_{4}\setminus \bar B_{3}$, $r\in\{0,1,...\}$, and real $t$, the series $$\sum_{m=0}^{\infty}\frac{1}{m!}t^{m}K_{n-2r-2m}(x,\cdot)$$ converges in $C^{k}(\bar B_{1})$. Thus, for any $t$ and $x\in B_{4}\setminus \bar B_{3}$, $$K_{n-2r}(x-\cdot)\exp(-t/|x-\cdot|^{2})\in \bar S.$$ Obviously, the integral $$\int_{0}^{\infty}t^{m}K_{n-2r}(x-\cdot)\exp(-t/|x-\cdot|^{2})\,dt$$ converges in $C^{k}(\bar B_{1})$ for any $x\in B_{4}\setminus \bar B_{3}$ and $m>-1$. Thus, $$K_{n-2r+2m-2}(x-\cdot)\in \bar S.$$ For any real $j $ it is possible to find (many) $r\in\{0,1,...\}$ and real $m>-1$ such that $n-2r+2m-2=j$. Hence, for any $x\in B_{4}\setminus \bar B_{3}$ $$K_{j}(x-\cdot)\in \bar S\quad \forall j\in{\mathbb{R}}.$$ For $j\in\{0,1,...\}$ the functions $K_{j}(x-y)$ are polynomials with respect to $x$ with the coefficients depending on $y$. These coefficients can be found by differentiating $K_{j}(x-y)$ with respect to $x\in B_{4}\setminus\bar B_{3}$ and it follows that they belong to $\bar S$. But then, for any $x$, $K_{j}(x-\cdot)$ is in $\bar S$ being just a linear combination of elements of $\bar S$. Thus, $$K_{j}(x-\cdot)\in \bar S\quad \forall j=0,1,..., x\in{\mathbb{R}}^{d}.$$

Furthermore, clearly the series of polynomials $$\sum_{m=0}^{\infty}\frac{1}{m!}t^{-m}K_{2m}(x-\cdot)$$ converges in $C^{k}(\bar B_{1})$ for any $x\in {\mathbb{R}}^{d}$ and $t>0$. It follows that $$\exp(-|x-\cdot|^{2}/t)\in \bar S.$$

The rest is routine. Take an $f\in C^{k}(\bar B_{1})$, continue it to the whole ${\mathbb{R}}^{d}$ preserving its class and making it vanish outside $B_{2}$, and for $t>0$ define $$f_{t}(y)= t^{-d/2}\int_{{\mathbb{R}}^{d}}
f(x)\exp(-|x-y|^{2}/t)\,dx.$$ Obviously the integral converges in $C^{k}(\bar B_{1})$, so that $f_{t}\in \bar S$. We know that, if a constant $c$ is chosen appropriately, then $cf_{t}\to f$ in $C^{k}(\bar B_{1})$ as $t\downarrow 0$. Since $cf_{t}\in \bar S$, $f \in \bar S$ and the theorem is proved.

Proof of Lemma \[lemma 9.10.1\]
===============================

\[section 10.9.1\]

Take $p\in(1,\infty)$ and $u\in W^{2}_{p}(B_{2})$. By representing it as $h+v$, where $h$ is harmonic and $v=0$ on $\partial B_{2}$ it is easy to conclude that $\|u\|_{W^{2}_{p}(B_{1})}\leq N(\|u\|_{L_{p}(B_{2})}
+\|\Delta u\|_{L_{p}(B_{2})})$, where and below by $N$ we denote generic constants $\geq1$ depending only on $d$, $p$, and $r$ (which is coming later). This fact also holds for $B_{\rho_{1}}\subset \bar B_{\rho_{1}}\subset   B_{\rho_{2}}$ in place of $B_{1}$ and $B_{2}$ with a constant, this time, also depending on $\rho_{1}$ and $\rho_{2}$. By applying these estimates to the derivatives of $u$, we see that, for any $r=0,1,...$, $$\|u\|_{W^{2r}_{p}(B_{1})}
\leq N\sum_{i=0}^{r}\|\Delta^{i} u\|_{L_{p}(B_{2})}.$$

Then and the estimate $|n(n+d-2)|\leq N(n^{2}+1)$ show that, for $|y|\leq2$ and $3\leq|x|\leq4$, $$|\Delta^{i} K_{m}(x,y)|\leq c^{i}(m^{2}+1)((m-2)^{2}+1)
\cdot...\cdot((m-2i+2)^{2}+1)K_{m-2i}(x,y)$$ $$\leq c^{i}(m^{2}+1)((m-2)^{2}+1)
\cdot...\cdot((m-2i+2)^{2}+1).$$ Since, for $j=0,...,r$, we have $(m-2j)^{2}+1\leq 2m^{2}+N$, it holds that $$\|K_{m}(x,\cdot)\|_{W^{2r}_{p}(B_{1})}
\leq N^{r}(2m^{2}+N)^{r}.$$

Finally, by embedding theorems $W^{2r}_{p}(B_{1})\subset C^{k}(\bar B_{1})$ if $(2r-k)p>d$, which holds indeed for large enough $p$. This proves the lemma.

We conclude the paper with the following.

In [@DSV_17] the authors prove that the set of polynomials is dense in $C^{k}(\bar B_{1})$. Actually, this fact follows from Lemma 3 and Theorem 3 in Section 3 of an old paper [@Gr_41]. By using Bernstein’s polynomials this fact is also follows from Section 3.8 of [@Kr_95].

[10]{}

S. Dipierro, O. Savin, and E.Valdinoci, [*All functions are locally s-harmonic up to a small error*]{}, J. Eur. Math. Soc., Vol. 19 (2017), 957–955.

L.M. Graves, [*Some general approximation theorems*]{}, Annals of Mathematics, Second Series, Vol. 42, No. 1 (Jan., 1941), 281–292.

N.V. Krylov, “Introduction to the theory of diffusion processes”, Amer. Math. Soc., Providence, RI, 1995.


Survival after cardiopulmonary resuscitation in an urban Indian hospital.
Survival after cardiopulmonary resuscitation depends upon the quality of pre-hospital support, availability of resuscitation equipment and the competence of the resuscitator. There are few data on the prognosis of patients undergoing such resuscitation in India. In a retrospective analysis of 215 resuscitations done in a 125-bed community hospital between January 1995 and November 1997, return of spontaneous circulation and survival to discharge were evaluated. Multivariate methods were used to identify the predictors of successful outcome. Of all the patients, 14.4% were alive at discharge. Survival after a cardiorespiratory arrest in the hospital was 18.4%, which was significantly better than survival after pre-hospital events (5.9%; p = 0.027). Multivariate predictors of survival at discharge were resuscitation duration of less than 20 minutes [odds ratio (95% confidence limit): 32.6 (6.5-164.3)], presentation with ventricular tachycardia or fibrillation [odds ratio: 18.5 (4.4-77.9)], in-hospital cardiorespiratory arrest [odds ratio: 5.2 (1.2-21.6)] and female sex [odds ratio: 3.2 (1.1-9.6)]. Bystander resuscitation, though rarely provided, increased survival at discharge (p = 0.026). With 5.5 resuscitation attempts needed for one live discharge after in-hospital cardiorespiratory arrest and 17 attempts to save a life after pre-hospital events, our outcomes are comparable to those reported from developed nations. A return of pulse after shorter durations of cardiopulmonary resuscitation, ventricular fibrillation or tachycardia as the abnormal presenting rhythm, in-hospital location of cardiorespiratory (CR) arrest and female sex were independent predictors of live discharge. Age and aetiology of CR arrest did not influence the outcome.


---
abstract: |
    In this paper, we consider one dimensional adiabatic quasi-periodic Schr[ö]{}dinger operators in the regime of strong resonant tunneling. We show the emergence of a level repulsion phenomenon which is seen to be very naturally related to the local spectral type of the operator: the more singular the spectrum, the weaker the repulsion.

    .5cm

    R[é]{}sum[é]{}. Dans cet article, nous [é]{}tudions une famille d’op[é]{}rateurs quasi-p[é]{}riodiques adiabatiques dans un cas d’effet tunnel r[é]{}sonant fort. Nous voyons l’apparition d’un ph[é]{}nom[è]{}ne de r[é]{}pulsion de niveaux fort qui est reli[é]{} au type spectral local de l’op[é]{}rateur : plus le spectre est singulier, plus la r[é]{}pulsion est faible.
address:
- 'Department of Mathematical Physics, St Petersburg State University, 1, Ulianovskaja, 198904 St Petersburg-Petrodvorets, Russia'
- 'LAGA, Institut Galil[é]{}e, U.M.R. 7539 C.N.R.S, Universit[é]{} Paris-Nord, Avenue J.-B. Cl[é]{}ment, F-93430 Villetaneuse, France'
author:
- Alexander Fedotov
- 'Fr[é]{}d[é]{}ric Klopp'
title: 'Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic [Schr[ö]{}dinger]{} operators'
---

[10]{}

V. S. Buslaev and A. A. Fedotov. Bloch solutions for difference equations. , 7(4):74–122, 1995.

M. Eastham. . Scottish Academic Press, Edinburgh, 1973.

A. Fedotov and F. Klopp. Weakly resonant tunneling interactions for adiabatic quasi-periodic [Schr[ö]{}dinger]{} operators. Preprint math-ph/0408006, 2004. [](http://arxiv.org/abs/math-ph/0408006).

A. Fedotov and F. Klopp. Geometric tools of the adiabatic complex [WKB]{} method. , 39:309–357, 2004.

A. Fedotov and F. Klopp. On the singular spectrum of one dimensional quasi-periodic [Schr[ö]{}dinger]{} operators in the adiabatic limit. , 5:929–978, 2004.

A. Fedotov and F. Klopp. A complex [WKB]{} method for adiabatic problems. , 27(3-4):219–264, 2001.

A. Fedotov and F. Klopp. Anderson transitions for a family of almost periodic [S]{}chr[ö]{}dinger equations in the adiabatic case. , 227(1):1–92, 2002.

N. E. Firsova. On the global quasimomentum in solid state physics. In [*Mathematical methods in physics (Londrina, 1999)*]{}, pages 98–141. World Sci. Publishing, River Edge, NJ, 2000.

D. Gilbert and D. Pearson. On subordinacy and analysis of the spectrum of one-dimensional [S]{}chr[ö]{}dinger operators. , 128:30–56, 1987.

B. Helffer and J. Sj[ö]{}strand. Multiple wells in the semi-classical limit [I]{}. , 9:337–408, 1984.

M. Herman. Une m[é]{}thode pour minorer les exposants de [L]{}yapounov et quelques exemples montrant le caract[è]{}re local d’un th[é]{}or[è]{}me d’[A]{}rnol’d et de [M]{}oser sur le tore de dimension $2$. , 58(3):453–502, 1983.

A. R. Its and V. B. Matveev. Hill operators with a finite number of lacunae. , 9(1):69–70, 1975.

V. Marchenko and I. Ostrovskii. A characterization of the spectrum of [H]{}ill’s equation. , 26:493–554, 1975.

H. McKean and P. van Moerbeke. The spectrum of [Hill’s]{} equation. , 30:217–274, 1975.

H. P. McKean and E. Trubowitz. Hill’s surfaces and their theta functions. , 84(6):1042–1085, 1978.

S. Novikov, S. V. Manakov, L. P. Pitaevskiĭ, and V. E. Zakharov. . Contemporary Soviet Mathematics. Consultants Bureau \[Plenum\], New York, 1984. The inverse scattering method, Translated from the Russian.

L. Pastur and A. Figotin. . Springer Verlag, Berlin, 1992.

L. Pastur and A. Figotin. , volume 297 of [*Grundlehren der Mathematischen Wissenschaften \[Fundamental Principles of Mathematical Sciences\]*]{}. Springer-Verlag, Berlin, 1992.

B. V. Shabat. . “Nauka”, Moscow, third edition, 1985. Funktsii odnogo peremennogo. \[Functions of a single variable\].

B. Simon. Instantons, double wells and large deviations. , 8(2):323–326, 1983.

E. Sorets and T. Spencer. Positive [L]{}yapunov exponents for [S]{}chr[ö]{}dinger operators with quasi-periodic potentials. , 142(3):543–566, 1991.

E.C. Titschmarch. . Clarendon Press, Oxford, 1958.


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  <!-- Glass -->

  <GlassBatch.label>Lote de vidrio</GlassBatch.label>
  <GlassBatch.description>Lote de vidrio crudo que se hizo de arena. Es más útil cuando se refina en planchas de vidrio.</GlassBatch.description>

  <Glass.label>Vidrio</Glass.label>
  <Glass.description>Un material transparente que es muy popular a pesar de ser frágil. El vidrio se produce a partir del lote de vidrio, que está hecho de arena.</Glass.description>
  <Glass.stuffProps.stuffAdjective>vidrio</Glass.stuffProps.stuffAdjective>

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  <ReinforcedGlass.description>Una versión más fuerte de Marcos de vidrio que es más difícil de trabajar, pero tiene más usos potenciales.</ReinforcedGlass.description>
  <ReinforcedGlass.stuffProps.stuffAdjective>Vidrio reforzado</ReinforcedGlass.stuffProps.stuffAdjective>

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INTRODUCTION {#sec1-1}
============

Plant materials have been used for treatments of diseases in the Eastern countries, especially East Asia, for thousands of years. In the specific tribes in Thailand, *Kaempferia parviflora*, a Zingiberaceae plant, has been used a folk medicine called "Krachai Dum." The rhizome and tincture of *K. parviflora* has been applied as medicine for general pain, colic gastrointestinal disorders, and male impotence. These various pharmacological activities of *K. parviflora* prompted researchers to elucidate its activities scientifically using the *in vivo* and *in vitro* assays. Among them, inhibition of P-glycoprotein function,\[[@ref1]\] anti-plasmodial, anti-fungal and anti-mycobacterial effects,\[[@ref2]\] cytotoxicity against various cancer cell lines,\[[@ref3]\] anti-cholinesterase activity,\[[@ref4]\] anti-allergic activity,\[[@ref5]\] modulation of the function of multidrug resistance associated-proteins,\[[@ref6]\] anti-gastric ulcer effect,\[[@ref7]\] anti-obese activity,\[[@ref8]\] anti-diabetes activity,\[[@ref9][@ref10]\] and inhibition of fat absorption\[[@ref11]\] have been demonstrated. These multi-functional effects of *K. parviflora* makes it an attractive potential treatment for life-style-related diseases. Thus, continuous research to discover novel effects of *K. parviflora* on life-style-related diseases has been performed in our laboratory.

Among various life-style-related diseases, we first focused on anti-hyperuricemia activity based on inhibition on xanthine oxidase. Xanthine oxidase has been recognized as a key enzyme for producing uric acid and a treatment for gout. *K. parviflora* extract showed potent inhibitory activity compared to other Zingiberaceae plants used as crude drugs and the active principles were determined as 3,5,7,3΄,4΄-pentamethoxyflavone and 5,7,3΄,4΄-tetramethoxyflavone.\[[@ref12]\] In addition, we focused on an improvement effect on blood fluidity. Stagnation of blood causes a loss of metabolism, obesity, and poor circulation. *K. parviflora* has been shown to have fibrinolysis activity and improved the blood fluidity in disseminated intravascular coagulation model rats.\[[@ref13]\] Thus, we have been demonstrated some novel *K. parviflora* function and believe that other novel functions are yet to be revealed.

Benign prostate hyperplasia (BPH) is life-style-related illnesses caused by inappropriate diet habits and the social stress leading to hormone imbalance. The incidence of BPH is approximately 50-60% in males 40-60 years old and greater than 90% in men over 80 years.\[[@ref14]\] It also causes urinary tract obstruction and infection.\[[@ref15]\] Androgen plays an important role in the growth, and maintenance of normal prostate gland, function as well as in the development of BPH. The androgens testosterone and dihydrotestosterone (DHT) contribute to the onset of BPH.\[[@ref16]\] Testosterone is converted to DHT by 5α-reductase (5αR).\[[@ref17]\] DHT is a potent androgen whose and its action is mediated through binding to the androgen receptor (AR) in the prostate, which induces protein synthesis and abnormal growth of the prostate.\[[@ref17][@ref18]\] Therefore, inhibition of 5αR could help prevent BPH. Finasteride, a potent 5αR inhibitor and flutamide, a binding inhibitor to AR are used as effective agents in BPH treatment. These drugs, however, are known to produce side-effects including impaired liver function, diarrhea, and headache. Alternatively, functional foods including natural products that show 5αR inhibitions may be useful in the prevention of BPH.

Some 5αR inhibitors from natural products have been discovered by our group, i.e., 12-methoxycarnosic acid in *Rosmarinus officinalis* leaf,\[[@ref19]\] ginsenoside Ro in the rhizome of red ginseng,\[[@ref20]\] kaikasaponin and soyasaponin in flowers of *Pueraria thomsonii*\[[@ref21]\] and fatty acids and ethinylestradiol in spores of *Lygodium japonicum*.\[[@ref22]\]

In the present study, extract from *K. parviflora* rhizome was subjected to the inhibitory assay against 5αR along with other Zingiberaceae plants. *K. parviflora* showed potent activity and the active principle was revealed. Furthermore, a result on the improvement of BPH by *K. parviflora* using *in vivo* BPH model is described.

MATERIALS AND METHODS {#sec1-2}
=====================

Materials {#sec2-1}
---------

Rhizomes of *K. parviflora* were purchased from Aoba trading Co. (Tokyo, Japan). Voucher specimens were deposited at the Faculty of Pharmacy, Kinki University. Reagents used in this study were of analytical grade and were purchased from Wako Pure Chemicals Industries (Osaka, Japan) or Nacalai Tesque (Kyoto, Japan) unless otherwise stated.

Preparations of extracts and methoxyflavones {#sec2-2}
--------------------------------------------

Preparations of extracts from rhizomes of *K. parviflora*, *Curcuma zedoaria* and *Zingiber officinale*, and methoxyflavones were performed according to the methods previously reported.\[[@ref12]\]

Inhibitory assay for 5αR {#sec2-3}
------------------------

The enzyme 5αR was prepared according to the method reported\[[@ref23]\] with modifications. Rats (Wistar, 9 weeks, 270-290 g) were purchased from Shimizu Laboratory Supplies Co., Ltd. (Kyoto, Japan), and were maintained at a constant temperature and humidity under a 12 h light/dark cycle for 11 days. Water and pellet chow (Labo MR stock, Nosan Corporation, Tokyo, Japan) were freely available. The epididymis was removed from 100 rats and homogenized with a blender in cooled physiological saline containing 0.25 M sucrose and protease inhibitor cocktail. Homogenates were filtered and centrifuged at 300 ×g for 10 min, and the supernatants were centrifuged again under the same conditions to obtain crude enzyme the protein assay method (Bio-Rad Laboratories, Inc., Hercules, CA) and crude enzyme solution was diluted to 10 mg/ml and stored at −85°C until use.

The 5αR inhibition assay was performed as reported previously\[[@ref24][@ref25]\] with minor modifications. The reaction solution containing 50% ethanol (50 μl) with various concentrations of test compounds, 600 μl of 100 mM Mcllvaine buffer (pH 5.0), 20 μl of testosterone (0.4 mM in propylene glycol \[PG\]-citrate/phosphate buffer, pH 5.0 \[1:1 v/v\]) and 110 μl of enzyme solution.\[[@ref26]\] Reactions were initiated by the addition of 20 μl of 34 mM nicotinamide adenine dinucleotide phosphate reduced form. The mixture was incubated at 37°C for 30 min. After addition of 1.0 ml of dichloromethane and 20 μl of *p*-hydroxybenzoate *n*-hexyl ester as an internal standard (IS), the organic layer was obtained by centrifugation (3000 × *g* for 3 min), and transferred to another tube and air dried. The residue was dissolved in 0.2 ml of methanol, and an aliquot of 30 μl was injected into an high performance liquid chromatography (HPLC) system under the following conditions: Column, YMC-Park ODS-AM302 (4.6 i.d. × 150 mm); column temperature, 40°C; mobile phase, methanol/water (65:35, v/v); flow rate, 1.0 ml/min; detection, UV at 254 nm, *t*~R~; testosterone, 7 min, *t*~R~; IS, 14 min. The control-0-min tube received 1.0 ml of dichloromethane before addition of the enzyme solution, whereas, the control-30-min tube received 50 μl of methanol instead of the test sample. A similar procedure to that described previously was carried out for these control tubes. The 5αR inhibitory activity was determined from the following equation using the peak-area ratios (*r* = testosterone/IS). Finasteride (Tokyo Chemical, Tokyo, Japan) was used as a reference drug.

Inhibition (%) = 100 × (C~sample~/C~control~)

C: Conversion rate (%) of testosterone to DHT

C~sample~ (C for sample groups) = *r* of the test sample -- *r* of control-30 min

C~control~ (C for control groups) = *r* of control-0 min -- *r* of control-30 min.

Animals {#sec2-4}
-------

Male Crj: CD Sprague-Dawley (SD) rats, which castrated at 6 weeks age and normal (not castrated) SD rats (7 weeks age) were purchased from Shimizu Laboratory Supplies (Kyoto, Japan). The rats were acclimatized for 1 week in an animal room, which is maintained by air-conditioning with lighting from 7 a.m. to 7 p.m. The temperature and humidity were controlled automatically. Laboratory pellet chow (Labo MR stock, Nihon Nosan Kogyo, Tokyo, Tokyo, Japan) and water were freely available. All experimental protocols using animals were approved by the Committee for the Care and Use of Laboratory Animals at Kinki University.

Animal treatments {#sec2-5}
-----------------

The growth suppression assay of prostates and seminal vesicles in castrated rats was performed based on the Hershberger\'s method.\[[@ref27][@ref28]\] The castrated rats were randomized to four groups of 6 rats: (1) A negative control group receiving intraperitoneal administration (i.p.) of olive oil and oral administration (p.o.) of 100 μl of 50% PG, (2) testosterone propionate (TP) (2 mg/kg, i.p.) and 100 μl of PG (p.o.), (3) TP (2 mg/kg, i.p.) and *K. parviflora* ext in PG (200 mg/kg, p.o.) and (4) TP (2 mg/kg, i.p.) and finasteride in PG (2 mg/kg, p.o.). Non-treatment group (not castrated rats) was also prepared. The administrations were performed once a daily for 14 days.

Sacrifice and evaluation of prostates and seminal vesicles weights {#sec2-6}
------------------------------------------------------------------

The day after the last treatment (at the day 15 from the starting of administration), rats were sacrificed under anesthesia with pentobarbital (35 mg/kg). Their prostates and seminal vesicles were removed and weighted.

Statistical analysis {#sec2-7}
--------------------

Data were evaluated statistically by Bonferroni/Dunn multiple range tests using a Microsoft Excel add-in software Statcel (Ver. 3, OMS publishing, Saitama, Japan). Significant differences were detected at *P* \< 0.05 and 0.01.

RESULTS AND METHODS {#sec1-3}
===================

Effects of *K. parviflora*, *C. zedoaria* and *Z. officinale* extracts on 5αR inhibition {#sec2-8}
----------------------------------------------------------------------------------------

Firstly, the inhibitory activity (conversion rate of testosterone to DHT) of the *K. parviflora* extract was studied compared with those of *C. zedoaria* and *Z. officinale* extracts on 5αR. The results are shown in [Table 1](#T1){ref-type="table"}. *K. parviflora* extract showed enzyme inhibition of 75.8% at 500 μg/ml while the values for the *C. zedoaria* and *Z. officinale* extracts were 28.2% and 21.1%, respectively. This result suggested that *K. parviflora* has the most potent activity and may be effective in the treatment of BPH.

######

Inhibitory effects of crude Zingiberaceae extracts on 5αR

![](PR-5-309-g001)

Effects of methoxyflavones from *K. parviflora* on 5αR {#sec2-9}
------------------------------------------------------

Secondly, the inhibitory activities of methoxyflavones from *K. parviflora* were examined since methoxyflavones are known to be multi-potential active compounds. The results are shown in [Table 2](#T2){ref-type="table"}. Among the compounds tested, 3, 5, 7, 3΄, 4΄-pentamethoxyflavone and 5, 7, 3΄,4΄-tetramethoxyflavone showed the most potent inhibitory activities of 55.9% at 50 μM ([Figure 1](#F1){ref-type="fig"}). Their IC~50~ values were 46.6 and 48.7 μM for 3, 5, 7, 3΄, 4΄-pentamethoxyflavone and 5, 7, 3΄, 4΄-tetramethoxyflavone, respectively. These results indicated that these two methoxyflavones were the most potent among the nine methoxyflavones.

######

Inhibitory effects of methoxyflavones on 5αR

![](PR-5-309-g002)

![Chemical structures of 3,5,7,3',4'-pentamethoxyflavone and 5,7,3',4'-tetramethoxyflavone](PR-5-309-g003){#F1}

Effects of *K. parviflora* extract on rat prostate and seminal vesicle weights {#sec2-10}
------------------------------------------------------------------------------

The effects of *K. parviflora* extract on the growth of rat prostates and seminal vesicles were studied. The results are shown in [Figure 2](#F2){ref-type="fig"}. The mean prostate weight/body weight of the group, which received PG (control group) was 145.0 ± 30.7 mg/kg \[[Figure 2a](#F2){ref-type="fig"}\]. The mean prostate weight/body weight of the group with BPH induced by TP injection was 1898.0 ± 325.2 mg/kg, which was significantly higher than that of the control group (*P* \< 0.01). The mean prostate weight/body weight of the rats that received the *K. parviflora* extract (200 mg/kg) was 986.1 ± 124.6 mg/kg. Compared with the BPH group, *K. parviflora* showed a significant reduction in prostate weight (*P* \< 0.05). The mean prostate weight/body weight of the finasteride-administered (2 mg/kg) rats was 742.3 ± 84.0 mg/kg, which was significantly lower than the BPH group (*P* \< 0.01). The mean prostate weight/body weight of the non-castrated and treated rats was 397.0 ± 61.9 mg/kg \[[Figure 2a](#F2){ref-type="fig"}\].

![Suppression of testosterone propionate-induced hyperplasia of prostates (a) and seminal vesicles (b) in castrated rats by *Kaempferia parviflora* extract. Values represent mean ± SE of *n* = 6. Significantly different from control group at \#*P* \< 0.01. Significantly different from negative control group at \*\**P* \< 0.01](PR-5-309-g004){#F2}

The mean seminal vesicles weight/body weight of the group, which received PG (control group) was 78.7 ± 16.7 mg/kg \[[Figure 2b](#F2){ref-type="fig"}\]. The mean seminal vesicles weight/body weight of the group with BPH induced by TP injection was 1099.1 ± 73.9 mg/kg, which was significantly higher than that of the control group (*P* \< 0.01). The mean seminal vesicles weight/body weight of the rats that received *K. parviflora* extract (200 mg/kg) was 737.2 ± 85.4 mg/kg. Compared with the BPH group, *K. parviflora* showed a significant reduction in seminal vesicle weight (*P* \< 0.05). The mean seminal vesicles weight/body weight of the finasteride (2 mg/kg)-administered rats was 415.2 ± 36.0 mg/kg, which was significantly lower than that of the BPH group (*P* \< 0.01). The mean seminal vesicles weight/body weight of the non-castrated and treated rats was 477.7 ± 28.3 mg/kg \[[Figure 2b](#F2){ref-type="fig"}\].

In the present study, *K. parviflora* extract treatment resulted in a significant decrease in the weights of prostates and seminal vesicles in TP injected-castrated rats. These effects can be attributed to the inhibitory activity against 5αR exhibited by *K. parviflora* extract as shown in this manuscript.

Search for effective plant resources for the improvement of BPH has been performed extensively. Among them, *Serenoa repens*\[[@ref29][@ref30]\] *Ganoderma lucidum*,\[[@ref31]\] *Lepidium meyenii* (Red Maca),\[[@ref32]\] banana peel,\[[@ref33]\] and *Echinacea purpurea*\[[@ref34]\] showed significant improvements of BPH. The results obtained in this study could have successfully presented that *K. parviflora* is a novel entry from Zigiberaceae plant and *K. parviflora* would be a promising candidate. Further, studies on the mode of action of *K. parviflora* extract are now underway.

**Source of Support:** Nil

**Conflict of Interest:** None declared.


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