---
abstract: 'Single crystals of Na$_{0.5}$CoO$_2$ were obtained through a flux method followed by de-intercalation of sodium. The Na$_{0.5}$CoO$_2$ samples were found to be vulnerable to water in the air and a hydration process in which H$_2$O molecules fill oxygen vacancies in CoO$_2$ layers is suggested to be responsible for the unusual vulnerability to water. The transport properties, including resistivity (*$\rho$*), thermopower (*S*) and Hall coefficient (*R$_H$*), were studied in a temperature range of 5-300 K. The compound shows a weak localization of carriers just below 200 K and Co$^{3+}$-Co$^{4+}$ charge ordering at about 30 K, a relatively lower temperature than previously reported. The results seem to be quite different from those previously reported for this system \[Foo et al, Phys. Rev. Lett. 92 (2004) 247001\]. Possible mechanism underlying this kind of inconsistency is discussed.'
address:
- 'Department of Physics, Zhejiang University, Hangzhou 310027, P. R. China'
- 'Institute of Refrigeration and Cryogenic Engineering, Zhejiang University, Hangzhou 310027, P. R. China'
author:
- 'X. Z. Chen'
- 'Z. A. Xu'
- 'G. H. Cao'
- 'J. Q. Shen'
- 'L. M. Qiu'
- 'Z. H. Gan'
title: 'Preparation and transport properties of non-hydrated Na$_{0.5}$CoO$_2$ single crystals'
---

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71.27.+a; 74.25.Fy; 71.10.Hf; 71.30.+h A. Strongly correlated electrons; B. Metal-insulator transitions; C. Transport properties

Layered transition-metal oxide Na$_x$CoO$_2$ has attracted great interest for its unusual behaviors due to strongly correlated electrons in the past years. It has a crystal structure consisting of layers of edge shared CoO$_6$ octahedra, between which Na$^+$ ions are inserted. Early researches have found an unusually large thermoelectric power with Na content *x*=2/3 [@ref1]. Spin entropy carried by holes (Co$^{4+}$) hoping in a Co$^{3+}$ background has been regarded as the likely source of enhanced thermopower [@ref2]. Recently, superconductivity with a transition temperature *T$_c$* of about 5 K has been found in water-intercalated compound Na$_{0.35}$CoO$_2$-1.3H$_2$O [@ref3], which has been viewed as a breakthrough in search of exotic superconductors other than the copper oxides. Magnetic susceptibility studies [@ref4; @ref5] have showed that Na$_{0.35}$CoO$_2$-1.3H$_2$O is an extreme type II superconductor, just like high *T$_c$* cuprates, and extensive Co NMR/NQR studies [@ref6; @add1; @add2] have shown evidences for non-s-wave superconductivity. Besides the large thermopower and superconductivity, very recent research [@ref7] found that as the sodium concentration *x* increases from 0.30 to 0.75, non-hydrated Na$_x$CoO$_2$ goes from a paramagnetic metal to a charge ordered insulator (at *x*=0.5), and then to a Curie-Weiss metal. The sudden appearance of charge ordered state and unusual transport properties of Na$_{0.5}$CoO$_2$ have made it a focus of attention. The distinct properties of this compound have been determined to be related to the Na$^+$ ion-vacancy ordering and consequential Co$^{3+}$-Co$^{4+}$ charge ordering at low temperature.

In this paper, we prepared Na$_x$CoO$_2$ crystal samples with *x*=0.5 and studied the transport properties including resistivity, thermopower and Hall coefficient. The samples were found to be vulnerable to the water in the air and the reaction between crystals and water seemed to bring significant influence on transport properties of the samples. Furthermore, our results on the temperature dependence of thermopower, magnetic susceptibility and Hall coefficient were found quite different from those in Ref.[@ref7], which may throw further complications on this compound.

The starting crystals of Na$_x$CoO$_2$ were grown by a flux method following the procedure reported in Ref. [@ref8]. To remove Na content , the as-grown crystals were immersed in solutions obtained by dissolving different amounts I$_2$ in acetonitrile. After reacting for a month at ambient temperature, the samples were washed several times with acetonitrile and then dried. The crystal structure was characterized by X-Ray Diffraction (XRD). The measurements of in-plane electrical resistivity *$\rho$*, thermopower *S*, Hall coefficient *R$_H$* and magnetic susceptibility *M* were carried out using a Quantum-Design PPMS-9 system. Unless mentioned otherwise, the transport measurements were performed just after preparation procedure and different measurements of a sample were taken as soon as possible to ensure uniformity of the sample.

Fig. \[fig:fig1\] shows the typical XRD patterns for the as-grown crystal (a) and for de-intercalated crystal (b). From these patterns, the crystals are considered to be of single phase. The Na content *x* of starting crystals was determined to be 0.75 from the c-axis parameter, using the calibration of the relationship between c-axis parameter and Na content reported in Ref  [@ref7]. Na$_x$CoO$_2$ crystals with *x* content near 0.5 can be easily obtained by de-intercalation using I$_2$-CH$_3$CN solution with excess I$_2$ concentrations for 30 days. The long reaction time assures the uniformity of Na content of de-intercalated crystals. It should be mentioned that so long as there is enough I$_2$ in the solution, the Na content *x* of de-intercalated crystals is always near 0.5 despite the different I$_2$ concentrations, which means that formation of the composition with *x* near 0.5 is favored during the de-intercalation of Na.

![XRD patterns (Cu K¦Á radiation) for Na$_x$CoO$_2$ crystals. (a) As-grown crystals Na$_{0.75}$CoO$_2$, (b) de-intercalated crystal Na$_{0.5}$CoO$_2$.[]{data-label="fig:fig1"}](fig1.EPS){width="12cm"}

Na$_x$CoO$_2$ samples with low Na content (*x* $<$ 0.35) are easy to absorb water in the atmosphere and form hydrated Na$_{x}$CoO$_2$-yH$_2$O with H$_{2}$O molecules being inserted between CoO$_2$ layers. However, when *x* comes as high as 0.45, the inserting of inter-layer H$_2$O is not favored [@ref9]. Meanwhile, our results show that Na$_{0.5}$CoO$_2$ samples are vulnerable to the small content of water in air. We have studied the time dependence of resistivity of Na$_{0.5}$CoO$_2$ samples preserved in dry air as well as humid air, as shown in Fig. \[fig:fig2\]. The original samples (Sample A) were newly obtained by de-intercalation process mentioned above, with c-axis lattice constant of 11.131 Å, for which Na content *x* was estimated to be near 0.50. After each measurement, the samples were preserved in dry air (cabinet with humidity 35%, Sample B, C, D) and humid air (Sample E). As can be seen from Fig. \[fig:fig2\] (a), the fresh samples (Sample A) show a transition below 50 K and the resistivity increases quickly after this transition (The detailed behaviors of fresh samples will be discussed below). The transition broaden and becomes less evident and finally unobservable after the samples were kept in air for a long period of time, which is shown in Fig. \[fig:fig2\] (a) for Sample B, Sample C and Sample D. The same variation of resistivity occurs much more rapidly when the samples were put in humid air (Fig. \[fig:fig2\] (b), Sample E). Sample F and G were obtained by annealing Sample E at $100\,^{\circ}\mathrm{C}$ and $250\,^{\circ}\mathrm{C}$ respectively for an hour, and their resistivity curves were shown in Fig. \[fig:fig2\](b). It is very interesting that Sample F (annealed at $100\,^{\circ}\mathrm{C}$) shows little difference in resistivity with Sample E while Sample G has almost the same behaviors in resistivity as Sample A, which means sintering at $250\,^{\circ}\mathrm{C}$ has restore Sample E to its original state (Sample A). It should be mentioned that, according to our XRD studies, no observable structural changes corresponding to this resistivity variation can be found and all the samples remain single phase.

![Temperature dependence of resistivity for Na$_{0.5}$CoO$_2$ crystals with different water content. Sample A: newly prepared samples(no water content), Sample B: expose Sample A to dry air for 40 days, Sample C: expose Sample A to dry air for 80 days, Sample D: expose Sample A to dry air for 300 days, Sample E: expose Sample A to humid air for 5 hours, Sample F: anneal Sample E at 100 $\,^{\circ}\mathrm{C}$ for an hour, Sample G: anneal Sample E at 250 $\,^{\circ}\mathrm{C}$ for an hour. All the samples are of single phase, and no structural differences between samples can be observed from XRD studies.[]{data-label="fig:fig2"}](fig2.EPS){width="12cm"}

To give further insight into this process, we combined thermogravimetric (TG) and differential-thermal-analysis (DTA) studies with resistivity measurements. Fig. \[fig:fig3\] shows TG and DTA curves for Samples E. From Fig. \[fig:fig3\], two weight losses can be observed, one below $100\,^{\circ}\mathrm{C}$ and one at about $245\,^{\circ}\mathrm{C}$, and the later is accompanied by a negative peak in DTA curve. The first weight loss below $100\,^{\circ}\mathrm{C}$ may come from the release of water absorbed on the surface of samples and it makes no contribution to the variation in resistivity. We believe that the weight loss at $245\,^{\circ}\mathrm{C}$ is responsible for all resistivity variations. According to some previous reports on superconducting Na$_x$CoO$_{2}-y$H$_2$O, intercalation of water between CoO$_2$ layers will increasingly separate neighboring layers and thus affect resistivity [@SSC1]. This part of water will lose quickly when samples were put in dry even at room temperature and resistivity is restored [@SSC1]. However, it’s quite different in our case. First, the small portion of water accounting for resistivity variations in our samples will not be released from the sample until $245\,^{\circ}\mathrm{C}$, a much higher temperature than the usual temperature for releasing inter-layered water. Second, only a very small proportion of water (about 0.015 H$_2$O per formula unit estimated from the weight loss at $245\,^{\circ}\mathrm{C}$) can be absorbed into crystals even when they are put in humid atmosphere for a long time. Third, no structural changes were observed from XRD studies in spite of dramatic changes in resistivity. All these differences make the hydration process seem complicated. One of the probable mechanisms is that H$_2$O molecules are scattered in CoO$_2$ layers instead of being inserted between them [@Cond1]. In such model, the O$^{2-}$ ions of H$_2$O fill the oxygen vacancies in CoO$_2$ while leaving H$^+$ suspended. If this is the truth, only a small portion of water depending on the density of O$^{2-}$ vacancies can be absorbed and definitely it will modify the periodic potential, have influence on the Na$^+$ ion-Na vacancy ordering and consequently contribute to transport properties of the system. The density of O$^{2-}$ vacancies in CoO$_2$ layers can be created during de-intercalation of Na content [@CM1], depending on the preparation process. The special vulnerability of Na$_{0.5}$CoO$_2$ samples to water makes consistent studies on this system difficult, for instance, special care is required to preserve samples and all measurements should be taken as soon as possible to assure the uniformity of test samples.

![TG and DTA curves for water-incorperated Na$_{0.5}$CoO2 sample (Sample E). The arrows show the water loss at about 245 $\,^{\circ}\mathrm{C}$.[]{data-label="fig:fig3"}](fig3.EPS){width="12cm"}

The transport measurements of Na$_{0.5}$CoO$_2$, including resistivity *$\rho$*, Hall coefficient *R$_H$*, thermopower *S* and magnetic susceptibility *M/H* were carried out in newly prepared sample (Sample A) in a temperature range of 5-300 K. Fig. \[fig:fig4\] shows the in-plane resistivity *$\rho$* and Hall coefficient *R$_H$*, and Fig. \[fig:fig5\] shows thermopower *S* and magnetic susceptibility *M/H* (H$\parallel$c =1 T) as a function of temperature. *$\rho$* and *R$_H$* show quite similar temperature dependence. They both decreases gradually while temperature drops from room temperature. However, below 200 K, they start to increase slowly (see the enlargement of $\rho$-$T$ curve in the inset of Fig.\[fig:fig4\]). Correspondingly, *S* starts to decrease below 200K, as shown in Fig.\[fig:fig5\]. A sharp transition in transport properties can be observed at about 30 K. Below 30 K, the increasing trend of *$\rho$* and *R$_H$* become much rapid, associated with a quick increase in *M* which is similar to the result reported in Ref. [@Chou]. *S* drop linearly to zero below 30 K (Fig.\[fig:fig5\]). There is a tiny cusp below 50 K in magnetic susceptibility and no anomaly can be seen around 88 K.

![Temperature dependences of in-plane resistivity *$\rho$* and Hall coefficient *R$_H$* for Na$_{0.5}$CoO$_2$. The arrow show the transition at about 30 K. Inset is the enlarged plot for $T \geq$ 50 K.[]{data-label="fig:fig4"}](fig4.EPS){width="12cm"}

![Temperature dependences of thermopower *S* and magnetic susceptibility *M* (H $\parallel$ c) for Na$_{0.5}$CoO$_2$. The arrow shows the transition at 30 K .[]{data-label="fig:fig5"}](fig5.EPS){width="12cm"}

According to previous study [@ref7; @Ord1], superlattice of ordered Na$^+$ ion-Na vacancy has been observed by electron diffraction in Na$_{0.5}$CoO$_2$ even at room temperature and the long-range ordering of Na$^+$ ion-vacancy at low temperature are suggested for this compound by thermal conductivity measurement. We presume that the changes starting around 200 K in *$\rho$*, *R$_H$* and *S* result from the ordering of Na$^+$ ion-vacancy. The ordering of Na$^+$ ion-vacancy introduces potential fluctuation which modulates electronic state and consequently leads to Co$^{3+}$-Co$^{4+}$ charge ordering in CoO$_2$ conduction layers. In our case, the Hall density at 100 K for Na$_{0.5}$CoO$_2$ is 40 times smaller than that for Na$_{0.75}$CoO$_2$(not shown in the paper). Below 30 K, *$\rho$*, *R$_H$* and *M* start to grow quickly, these may come from Co$^{3+}$-Co$^{4+}$ charge ordering transition.

However, there are many apparent differences between our results and those reported in Ref. [@ref7]. First, no evident transition in *R$_H$* or *S* at 87 K is observed from our results. Second, the sharp transition in *$\rho$* in our case is around 30 K, while a sharp transition in *$\rho$* at 53 K is observed in Ref. [@ref7]. And third, the system in Ref [@ref7] shows evidence for electron-hole symmetry (Both *S* and *R$_H$* fall toward zero as $T \rightarrow$ 0), while in our case the system remains hole-like in the whole temperature investigated and Hall density (1/e*R$_H$*) instead of *R$_H$* goes to zero as $T \rightarrow$ 0. It should be noted that the behaviors of resistivity, thermopower and Hall coefficient of our parent crystals ($x$=0.75) are very similar to the those reported in Ref. [@ref7] (not shown here). Therefore the above differences for the samples with $x$=0.5 seem to be surprising. Recalled that the Na$_{0.5}$CoO$_2$ crystals are vulnerable to water, we suggested that the oxygen vacancies in the CoO$_2$ layers could account for these differences. For the ideal composition of Na$_x$CoO$_2$ with $x$=0.5, the ratio of Co$^{3+}$/Co$^{4+}$(eletron/hole) is 1. If a certain amount of oxygen vacancies are introduced into the CoO$_2$ layers during preparing process(this is quite likely to happen in Na$_{0.5}$CoO$_2$), it will destroy not only the electron-hole symmetry, but also translation symmetry of the periodic potential. Thus, we can expect that even a small number O$^{2-}$ vacancies will have great influence on the transport properties of the system. This is supported by the result that only 0.015 H$_2$O per formula unit filling into O$^{2-}$ vacancies will substantially change the resistivity of the system.

In summary, the single crystals of Na$_{0.5}$CoO$_2$ were prepared and the transport properties were investigated. The unusual vulnerability of the sample to water in the air was found and may result from filling oxygen vacancies in CoO$_2$ layers with H$_2$O molecules. The temperature dependence of resistivity, Hall coefficient, and thermopower shows a weak localization of carriers just below 200 K and Co$^{3+}$-Co$^{4+}$ charge ordering at about 30 K, a relatively lower temperature than previously reported. The differences in transport properties between our results and those reported in Ref. [@ref7] may be caused by the oxygen vacancies in CoO$_2$ layers. More studies are needed to discover the underlying mechanism for the novel transport properties of this system.

**Acknowledgements** This work was supported by the National Natural Science Foundation of China (Grant No. 10225417) and the Ministry of Science and Technology of China (project: NKBRSF-G1999064602).

[00]{} \[sec:reference\]

I. Terasaki, Y. Sasago, and K. Uchinokura, Phys. Rev. B 10 (1997) 12685. Y.Y. Wang , N.S. Rogabo, R.J. Cava and N.P. Ong, Nature 423 (2003) 425. K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R.A. Dilanian and T. Sasaki, Nature 422 (2003) 53. G.H. Cao, C.M. Feng , Y. Xu, W. Lu, J.Q. Shen, M.H. Fang and Z.A. Xu, J. Phys: Condens. Matt. 15 (2003) 519. H. Sakurai, K. Takada, S. Yoshii, T. Sasaki, K. Kindo and E. Takayama-Muromachi, Phys. Rev. B 68 (2003) 132507. Y Kobayashi, M Yokoi and Sato, J. Phys. Soc. Jpn., 72 (2003) 2161. K. Ishida, Y. Ihara, Y. Maeno, C. Michioka, M. Kato, K. Yoshimura, K. Takada, T. Sasaki, H. Sakurai and E. Takayama-Muromachi, J. Phys. Soc. Jpn. 72 (2003) 3041. T. Fujimoto, G. Zheng, Y. Kitaoka , R.L. Meng , J. Cmaidalka and C.W. Chu, Phys. Rev. Lett. 92 (2004) 047004. M. L. Foo, Y. Y. Wang, S. Watauchi, H.W. Zandbergen, T. He, R.J. Cava and N.P. Ong, Phys. Rev. Lett 92 (2004) 247001. M. Mikami, M. Yoshimura, Y. Mori, T. Sasaki, R. Funahashi and I. Matsubara, Jpn. J. Appl. Phys. 41 (2002) 777. R.E. Schaak, T. Klimczuk, M.L. Foo and R.J. Cava, Nature 424 (2003) 527. M.L. Foo, R.E. Schaaka, V.L. Millera, T. Klimczuk, N.S. Rogadoa, Y. Wang, G.C. Laua, C. Craleya, H.W. Zandbergen, N.P. Ong, and R.J. Cava, Solid State Communications 127 (2003) 33. F. Rivadulla, J.S. Zhou and J. B. Goodenough, Phys. Rev. B 68 (2003) 075108. K. Maarit, A.Isao, M. Teruki, and Y. Hisao, Chem. Mater. 16 (2004) 1693. W. Zandbergen, M.L. Foo, Q. Xu, V. Kumar and R.J. Cava, Preprint, cond-mat/0403206. F. C. Chou, J. H. Cho, and Y. S. Lee, Preprint, cond-mat/0404061.


September 2014 sees the grand unveiling of a new £45 million Thurrock Campus in Grays which will include restaurants, health facilities, shops and an advice centre. There will also be specialist workshop and studio spaces linked to courses for technology, media and creative arts, and facilities for art, design, logistics, engineering and IT courses.

There will also be key areas available for public and community use. Hair and beauty salons, a restaurant and coffee shop will also be open to the public and are destined to breathe new life back into Grays.


The East York Health Needs Study. I: Prevalence of DSM-III-R psychiatric disorder in a sample of Canadian women.
This study reports the prevalence of psychiatric disorder in women from a Canadian community. The GHQ and the CES-D were compared for their utility. A thousand women over the age of 18 were mailed the GHQ and the CES-D. Our return rate was 44.4%; 24% were personally interviewed by interviews blind to screening information. The CIDI was used to establish DSM-III-R diagnoses. Four versions of the GHQ and one version of the CES-D were calibrated against the CIDI. The prevalence of general psychiatric disorder was estimated as between 15% and 19%, anxiety disorders between 10% and 13%, and depression occurring with anxiety between 3% and 4%. The calibrated GHQ was the most reliable instrument. Prevalence of DSM-III-R psychiatric disorder can be reliably determined with the calibrated GHQ. Anxiety disorders are most prevalent in this community, and were best detected using calibrated versions of the longer form GHQ.


Percussion Instruction

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When teaching a student to play drum sets, perhaps some of the following issues should be covered:

Keep It Simple - The fact is that playing drums can be complex, but it essentially is a very simple instrument. Do not inundate students with too much information at one time. Start off teaching by assuming that the student knows absolutely nothing about drums. As lessons progress, the complexity of the jargon and practices can progress as well.

Encourage the right equipment - A teacher should encourage students to take good care of their drums. A double tom case will save a student time because he will have less that he needs to carry around. Likewise, a portable handcart is a nice item to have. This can help a person move the drums from the vehicle to the stage without injuring himself from trying to carry the equipment.

Encourage over learning - A student on a drum must know every piece of that set and every sound that the set makes so that it is simply second nature when he plays it. Every lick should be over learned so that playing the drum is done without even needing to think about it.

Help with cleaning - A good teacher will help his students not only be able to play the drum sets, but will also help a student know how to care for the equipment. Teachers can show students how to clean their sets by using a can of compressed air to get the dust out of the places that are hard to reach with a rag. Such places include areas such as in between the lugs and underneath the foot pedals.

Drums also often have dry duct tape residue on them. If there is residue on either the cymbals or on the drum stands, it can fairly easily be removed with a bottle of "Goo Gone."

Practice without drums - Even though a set is needed for performing, it is not always needed for practicing. A person who is working on learning a beat sometimes might be better off starting without the drums and then start using the set once he has become a little more comfortable with the lick that is to be played.

Encourage "heel up" play - Teaching a student about a technique to use when playing a drum set can make the student improve at a faster pace. It can also keep him from getting used to bad habits. By using the heel up method for playing a bass drum, a teacher can help his student know how to play with more power and more speed.

Play together - Playing a drum set alongside a student can help the student get a better idea of the positioning and posture he needs to have to play well. Playing together can also help a student better learn how to keep a beat on these sets.

A teacher who takes the time to properly explain and show his student how to play on drum sets is likely to increase his customer base thanks to the good reviews he will receive.


A Personal Note – It Won’t Be Long

As many of you are already aware, my wife and I are taking a very needed and important time away. So, you probably won’t see much of me here on my blog for the next few weeks; but no worries, I’ll be back to my normal writing soon after Labor Day.

In the mean time, I would ask you to pray for my beautiful bride and me. First and foremost, I believe that the Lord will not only refresh our bodies, but will also instill in us fresh vision for the ministry He has bestowed upon us. My heart is truly excited for not only the days to come, but the years and decades! I believe the message and ministry our Lord has placed in us must go to new levels. So, pray and believe with us. Let’s believe that all obstacles the enemy may place in our way will be ineffectual, and that the Word and Spirit He has given us will revive all who come in contact with it.

My heart longs to see the gospel of our Lord heard as it should be…unencumbered by the world and all its counterfeit agendas. I long to see every body healed and restored to their divine call as sons and daughters of the King. I long to see everyone come to know the goodness of our God under the power of His Spirit. I have no other agenda. To this end I shall live until I see him face to face.

I want to see us coming together in such spiritual care and love that every spiritual AND natural need is met! That we have storehouses full to even spill out beyond our church. Faith and works our testimony! I know it’s coming!

Gods mighty spirit and power BE upon you for refreshing. To know and hear your heart toward the saints draws ours toward “HIM”……sooooooo thsnkful for HIS. divine Story in the life of the two of you- a. peace-filled covering!!

Believing & longing with you; knowing His greater good is being accomplished; praying in agreement by the Spirit.
May you both know His strength, revelation, vision, and healing, as you rest & refresh. May your eyes see anew and hearts be inflamed (in greater measure) of His great love.


CHANGZHOU, China, Feb. 12, 2015 -- Trina Solar Limited (NYSE: TSL) ("Trina Solar" or the "Company"), a global leader in photovoltaic ("PV") modules, solutions and services, today announced that it has signed a framework investment agreement (the "Agreement") with PingAn Trust Co., Ltd. ("PingAn Trust") and Jiangsu Jiuzhou Investment Group ("Jiuzhou Investment," and together with PingAn Trust, the "Investors") to jointly develop selected photovoltaic power plants ("the Projects") in China, with a total capacity of 500MW-1,000MW over the next three years.

Under the terms of the agreement, the Investors will enter convertible loan arrangements with Trina Solar to support the development of downstream projects in China. The Investors are entitled to convert the loans into minority stake in the project companies at pre-determined time. The investors are also entitled to participate in the potential capital operation of the holding vehicle in the future. To capitalize on growing demand in China and to strengthen Trina Solar's efforts in the downstream business the Company established Jiangsu Trina Solar Power Investment & Development Co., Ltd. under the above-mentioned holding vehicle at the end of 2014.

In addition, the Investors will provide bridge loans after completing due diligence on the Projects in order to meet their funding needs during the construction phase. The convertible loans and the bridge loans will not prevent the project companies from applying for long-term loans from other financial institutions. The Company and Investors are actively evaluating the portfolio of projects that need to be financed.

"We are excited to partner with strategic investors such as PingAn Trust and Jiuzhou Investment," said Mr. Jifan Gao, Chairman and Chief Executive Officer of Trina Solar. "By leveraging their financial strengths with our proven expertise in manufacturing and power plant development, we have a unique ability to build a superior and professional downstream development and operation company. In recent years, China's demand for new energy has been growing quickly. According to the government's plan, China's photovoltaic power installation capacity will reach over 100GW by 2020. Ever since the full-scale launch of our downstream business in 2013, we have made a number of significant achievements. In 2015, we will use this strategic collaboration as an opportunity to further reinforce and expand our leading position in China's PV market."

"We are delighted to work with Trina Solar to jointly develop solar projects in China that will generate stable and recurring cash flows in line with our investment strategy and the Chinese government's objectives," said Mr. Yuhang Li, General Manager of Industry Department of PingAn Trust. "We are excited to work with the leading company in the solar industry, and we believe the combination of the financing from the investors along with Trina Solar's industry expertise will be a win-win for all parties."

Mr. Shijin Luo, President of Jiuzhou Investment, added, "Jiuzhou Investment was a first round PE investor in Trina Solar prior to its initial IPO and has witnessed the Company's development into a leading player in the global PV industry. We are pleased to team up with Trina again to develop this downstream business. China is now in a new era of energy reform as it looks to promote green energy including solar energy production and consumption. As the world's largest solar module manufacturer with an established global brand, Trina Solar has made steady progress in the downstream business in recent years. We view Trina as a trusted partner for our move into the solar energy business."

About Trina Solar Limited
Trina Solar Limited (NYSE: TSL) is a global leader in photovoltaic modules, solutions and services. Founded in 1997 as a PV system integrator, Trina Solar today drives smart energy together with installers, distributors, utilities and developers worldwide. The company's industry-shaping position is based on innovation excellence, superior product quality, vertically integrated capabilities and environmental stewardship. For more information, please visit www.trinasolar.com.

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// Copyright 2015-2020 Parity Technologies (UK) Ltd.
// This file is part of Open Ethereum.

// Open Ethereum is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// Open Ethereum is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with Open Ethereum.  If not, see <http://www.gnu.org/licenses/>.

//! Test implementation of miner service.

use std::sync::Arc;
use std::collections::{BTreeMap, BTreeSet, HashMap};

use bytes::Bytes;
use client_traits::{Nonce, StateClient, ForceUpdateSealing};
use engine::{Engine, signer::EngineSigner};
use ethcore::block::SealedBlock;
use ethcore::client::{PrepareOpenBlock, EngineInfo};
use ethcore::miner::{self, MinerService, AuthoringParams, FilterOptions};
use ethcore::test_helpers::TestState;
use ethereum_types::{H256, U256, Address};
use miner::pool::local_transactions::Status as LocalTransactionStatus;
use miner::pool::{verifier, VerifiedTransaction, QueueStatus};
use parking_lot::{RwLock, Mutex};
use txpool;
use types::{
	BlockNumber,
	block::Block,
	header::Header,
	errors::EthcoreError as Error,
	ids::BlockId,
	receipt::RichReceipt,
	transaction::{self, UnverifiedTransaction, SignedTransaction, PendingTransaction},
};

/// Test miner service.
pub struct TestMinerService {
	/// Imported transactions.
	pub imported_transactions: Mutex<Vec<SignedTransaction>>,
	/// Pre-existed pending transactions
	pub pending_transactions: Mutex<HashMap<H256, SignedTransaction>>,
	/// Pre-existed local transactions
	pub local_transactions: Mutex<BTreeMap<H256, LocalTransactionStatus>>,
	/// Pre-existed pending receipts
	pub pending_receipts: Mutex<Vec<RichReceipt>>,
	/// Next nonces.
	pub next_nonces: RwLock<HashMap<Address, U256>>,
	/// Minimum gas price
	pub min_gas_price: RwLock<Option<U256>>,
	/// Signer (if any)
	pub signer: RwLock<Option<Box<dyn EngineSigner>>>,

	authoring_params: RwLock<AuthoringParams>,
}

impl Default for TestMinerService {
	fn default() -> TestMinerService {
		TestMinerService {
			imported_transactions: Default::default(),
			pending_transactions: Default::default(),
			local_transactions: Default::default(),
			pending_receipts: Default::default(),
			next_nonces: Default::default(),
			min_gas_price: RwLock::new(Some(0.into())),
			authoring_params: RwLock::new(AuthoringParams {
				author: Address::zero(),
				gas_range_target: (12345.into(), 54321.into()),
				extra_data: vec![1, 2, 3, 4],
			}),
			signer: RwLock::new(None),
		}
	}
}

impl TestMinerService {
	/// Increments nonce for given address.
	pub fn increment_nonce(&self, address: &Address) {
		let mut next_nonces = self.next_nonces.write();
		let nonce = next_nonces.entry(*address).or_insert_with(|| 0.into());
		*nonce = *nonce + 1;
	}
}

impl StateClient for TestMinerService {
	// State will not be used by test client anyway, since all methods that accept state are mocked
	type State = TestState;

	fn latest_state_and_header(&self) -> (Self::State, Header) {
		(TestState, Header::default())
	}

	fn state_at(&self, _id: BlockId) -> Option<Self::State> {
		Some(TestState)
	}
}

impl EngineInfo for TestMinerService {
	fn engine(&self) -> &dyn Engine {
		unimplemented!()
	}
}

impl MinerService for TestMinerService {
	type State = TestState;

	fn pending_state(&self, _latest_block_number: BlockNumber) -> Option<Self::State> {
		None
	}

	fn pending_block_header(&self, _latest_block_number: BlockNumber) -> Option<Header> {
		None
	}

	fn pending_block(&self, _latest_block_number: BlockNumber) -> Option<Block> {
		None
	}

	fn authoring_params(&self) -> AuthoringParams {
		self.authoring_params.read().clone()
	}

	fn set_author<T: Into<Option<miner::Author>>>(&self, author: T) {
		let author_opt = author.into();
		self.authoring_params.write().author = author_opt.as_ref().map(miner::Author::address).unwrap_or_default();
		match author_opt {
			Some(miner::Author::Sealer(signer)) => *self.signer.write() = Some(signer),
			Some(miner::Author::External(_addr)) => (),
			None => *self.signer.write() = None,
		}
	}

	fn set_extra_data(&self, extra_data: Bytes) {
		self.authoring_params.write().extra_data = extra_data;
	}

	fn set_gas_range_target(&self, target: (U256, U256)) {
		self.authoring_params.write().gas_range_target = target;
	}

	/// Imports transactions to transaction queue.
	fn import_external_transactions<C: Nonce + Sync>(&self, chain: &C, transactions: Vec<UnverifiedTransaction>)
		-> Vec<Result<(), transaction::Error>>
	{
		// lets assume that all txs are valid
		let transactions: Vec<_> = transactions.into_iter().map(|tx| SignedTransaction::new(tx).unwrap()).collect();
		self.imported_transactions.lock().extend_from_slice(&transactions);

		for sender in transactions.iter().map(|tx| tx.sender()) {
			let nonce = self.next_nonce(chain, &sender);
			self.next_nonces.write().insert(sender, nonce);
		}

		transactions
			.iter()
			.map(|_| Ok(()))
			.collect()
	}

	/// Imports transactions to transaction queue.
	fn import_own_transaction<C: Nonce + Sync>(&self, _chain: &C, _pending: PendingTransaction)
		-> Result<(), transaction::Error> {
		// this function is no longer called directly from RPC
		unimplemented!();
	}

	/// Imports transactions to queue - treats as local based on trusted flag, config, and tx source
	fn import_claimed_local_transaction<C: Nonce + Sync>(&self, chain: &C, pending: PendingTransaction, _trusted: bool)
		-> Result<(), transaction::Error> {

		// keep the pending nonces up to date
		let sender = pending.transaction.sender();
		let nonce = self.next_nonce(chain, &sender);
		self.next_nonces.write().insert(sender, nonce);

		// lets assume that all txs are valid
		self.imported_transactions.lock().push(pending.transaction);

		Ok(())
	}

	/// Called when blocks are imported to chain, updates transactions queue.
	fn chain_new_blocks<C>(&self, _chain: &C, _imported: &[H256], _invalid: &[H256], _enacted: &[H256], _retracted: &[H256], _is_internal: bool) {
		unimplemented!();
	}

	/// New chain head event. Restart mining operation.
	fn update_sealing<C>(&self, _chain: &C, _force: ForceUpdateSealing) {
		unimplemented!();
	}

	fn work_package<C: PrepareOpenBlock>(&self, chain: &C) -> Option<(H256, BlockNumber, u64, U256)> {
		let params = self.authoring_params();
		let open_block = chain.prepare_open_block(params.author, params.gas_range_target, params.extra_data).unwrap();
		let closed = open_block.close().unwrap();
		let header = &closed.header;

		Some((header.hash(), header.number(), header.timestamp(), *header.difficulty()))
	}

	fn transaction(&self, hash: &H256) -> Option<Arc<VerifiedTransaction>> {
		self.pending_transactions.lock().get(hash).cloned().map(|tx| {
			Arc::new(VerifiedTransaction::from_pending_block_transaction(tx))
		})
	}

	fn remove_transaction(&self, hash: &H256) -> Option<Arc<VerifiedTransaction>> {
		self.pending_transactions.lock().remove(hash).map(|tx| {
			Arc::new(VerifiedTransaction::from_pending_block_transaction(tx))
		})
	}

	fn pending_transactions(&self, _best_block: BlockNumber) -> Option<Vec<SignedTransaction>> {
		Some(self.pending_transactions.lock().values().cloned().collect())
	}

	fn local_transactions(&self) -> BTreeMap<H256, LocalTransactionStatus> {
		self.local_transactions.lock().iter().map(|(hash, stats)| (*hash, stats.clone())).collect()
	}

	fn ready_transactions<C>(&self, _chain: &C, _max_len: usize, _ordering: miner::PendingOrdering) -> Vec<Arc<VerifiedTransaction>> {
		self.queued_transactions()
	}

	fn ready_transactions_filtered<C>(
		&self,
		_chain: &C,
		max_len: usize,
		filter: Option<FilterOptions>,
		_ordering: miner::PendingOrdering
	) -> Vec<Arc<VerifiedTransaction>> {
		self.queued_transactions()
			.iter()
			.cloned()
			.filter(|tx| {
				filter.as_ref().map_or(true, |filter| {
					filter.matches(tx.signed())
				})
			})
			.take(max_len)
			.collect()
	}

	fn pending_transaction_hashes<C>(&self, _chain: &C) -> BTreeSet<H256> {
		self.queued_transactions().into_iter().map(|tx| tx.signed().hash()).collect()
	}

	fn queued_transactions(&self) -> Vec<Arc<VerifiedTransaction>> {
		self.pending_transactions.lock().values().cloned().map(|tx| {
			Arc::new(VerifiedTransaction::from_pending_block_transaction(tx))
		}).collect()
	}

	fn queued_transaction_hashes(&self) -> Vec<H256> {
		self.pending_transactions.lock().keys().cloned().map(|hash| hash).collect()
	}

	fn pending_receipts(&self, _best_block: BlockNumber) -> Option<Vec<RichReceipt>> {
		Some(self.pending_receipts.lock().clone())
	}

	fn next_nonce<C: Nonce + Sync>(&self, _chain: &C, address: &Address) -> U256 {
		self.next_nonces.read().get(address).cloned().unwrap_or_default()
	}

	fn is_currently_sealing(&self) -> bool {
		false
	}

	fn queue_status(&self) -> QueueStatus {
		QueueStatus {
			options: verifier::Options {
				minimal_gas_price: 0x1312d00.into(),
				block_gas_limit: 5_000_000.into(),
				tx_gas_limit: 5_000_000.into(),
				no_early_reject: false,
			},
			status: txpool::LightStatus {
				mem_usage: 1_000,
				transaction_count: 52,
				senders: 1,
			},
			limits: txpool::Options {
				max_count: 1_024,
				max_per_sender: 16,
				max_mem_usage: 5_000,
			},
		}
	}

	/// Submit `seal` as a valid solution for the header of `pow_hash`.
	/// Will check the seal, but not actually insert the block into the chain.
	fn submit_seal(&self, _pow_hash: H256, _seal: Vec<Bytes>) -> Result<SealedBlock, Error> {
		unimplemented!();
	}

	fn sensible_gas_price(&self) -> U256 {
		20_000_000_000u64.into()
	}

	fn sensible_gas_limit(&self) -> U256 {
		0x5208.into()
	}

	fn set_minimal_gas_price(&self, gas_price: U256) -> Result<bool, &str> {
		let mut new_price = self.min_gas_price.write();
		match *new_price {
			Some(ref mut v) => {
				*v = gas_price;
				Ok(true)
			},
			None => {
				let error_msg = "Can't update fixed gas price while automatic gas calibration is enabled.";
				Err(error_msg)
			},
		}
	}
}


The engine in your 2008 Chrysler Town and Country should be running when you perform a transmission fluid level check, otherwise it will be inaccurate. The video above shows where the transmission fluid dipstick is located in your Town and Country and how to check the transmission fluid level. If the transmission fluid level in your Town and Country is low, you need to add transmission fluid through the dipstick tube. When adding transmission fluid to your Town and Country, be sure to add it slowly as it will fill up quickly and is difficult to remove excess fluid if you overfill.

If you are having problems with the transmission in your Town and Country, such as clunky shifting or hesitation, check the fluid level first - it is amazing how many drivers pay thousands of dollars for transmission work when a half quart of transmission fluid would have fixed the problem.


Roman Bridge (Saint-Thibéry)

The Roman Bridge at Saint-Thibéry () was a Roman segmental arch bridge on the Via Domitia in southern France. The partly surviving structure crossed the river Hérault in Saint-Thibéry, 17 km east of Béziers.
__NOTOC__

Construction

The ancient bridge had nine arches with spans of 10–12 m. The roadway rested on wide piers, which were protected on both sides by arched floodways and large cutwaters. The original length of the structure is estimated as 150 m, its road width as 4 m. The missing spans are known to have been destroyed by flood some time before 1536.

The remaining arches, with a span to rise ratio of 3.3:1 (115°) or more, show a visibly flatter profile than the semi-circular arches usually preferred by Roman engineers (180°). The rib thickness varies between one-tenth to one-twentieth of the span, corresponding to a common ratio also observed at a number of other Roman stone bridges. The structure is dated to the reign of emperor Augustus (30 BC–14 AD). Immediately upstream an old water mill and its millrace is located.

See also
 List of Roman bridges
 Roman architecture
 Roman engineering

References

Sources

External links

 Traianus – Technical investigation of Roman public works

Category:Roman bridges in France
Category:Roman segmental arch bridges
Category:Deck arch bridges
Category:Stone bridges in France
Category:Buildings and structures in Hérault
Category:Transport in Occitanie
Category:Tourist attractions in Hérault


---
abstract: |
    The probability for quantum creation of an inflationary universe with a pair of black holes in $1/R$ - gravitational theory has been studied. Considering a gravitational action which includes a cosmological constant ($\Lambda$) in addition to $ \delta \; R^{- 1} $ term, the probability has been evaluated in a semiclassical approximation with Hartle-Hawking boundary condition. We obtain instanton solutions determined by the parameters $\delta$ and $\Lambda$ satisfying the constraint $ \delta \leq \frac{4 \Lambda^{2}}{3}$. However, we note that two different classes of instanton solutions exists in the region $0 < \delta < \frac{4 \Lambda^{2}}{3}$. The probabilities of creation of such configurations are evaluated. It is found that the probability of creation of a universe with a pair of black holes is strongly suppressed with a positive cosmological constant except in one case when $0 < \delta < \Lambda^{2}$. It is also found that gravitational instanton solution is permitted even with $\Lambda = 0$ but one has to consider $\delta < 0$. However, in the later case a universe with a pair of black holes is less probable.\
    PACS No(s). : 04.70.Dy, 98.80.Bp, 98.80.Cq.
author:
- |
    Dilip Paul[^1] and Bikash Chandra Paul[^2]\
    Department of Physics, North Bengal University,\
    Siliguri, Dist. Darjeeling, Pin : 734 013, India
title: 'PROBABILITY FOR PRIMORDIAL BLACK HOLES PAIR IN 1/R GRAVITY'
---

‘=11

[**I. INTRODUCTION :** ]{}

It is now generally believed from the recent observations that the present universe is accelerating \[1\]. It is also believed that our universe might have emerged from an inflationary era in the past. In the last two decades a number of literature appeared which explored early universe with an inflationary phase \[2\]. Inflation not only opens up new avenues in the interface of particle physics and cosmology but also solves some of the outstanding problems not understood in the standard bigbang cosmology. Most successful theory developed so far is based on the dynamics of scalar field with a suitable potential which behaves like a cosmological constant. In order to explain present acceleration in the universe a number of literature appeared with a new gravitational physics considering theories other than scalar field e.g., Chaplygin gas \[3\], phantom fields \[4\] etc.. Moreover, it has been realized that modification of the Einstein-Hilbert action with higher order terms in curvature invariants that are become effective in the high curvature region are important in cosmological model building. The modified theories permit inflation in the early epoch \[5\]. In the same way it is important to explore modification of the Einstein gravitational action with terms that might be important at extremely low curvature region to explain the present cosmic acceleration. There are attempts to explain the cosmic speed up with a modification of the Einstein Hilbert action. Recently, Carroll [*et al.*]{} \[6\] suggested a gravitational action of the form $$I = \frac{1}{2 \kappa^{2}} \int d^{4} x \sqrt{- g} \left[ R -  \; \frac{\mu^{4}}{R} \right],$$ where $R$ is the Ricci Scalar, $\kappa^{2} = 8 \pi G $, and $\mu$ is a mass scale of the order of Hubble scale. Cosmological models with a modification of the above action has been used to construct an alternative to dark energy and dark matter models \[7\]. It is also important to explore the cosmological issues in the framework of new theories which are important at the present epoch. The important astrophysical objects, for example black holes need to be investigated in this theory. The mass of these objects may be greater than the solar mass or even less. It is known in stellar physics that a blackhole is the ultimate corpse of a collapsing star when its mass exceeds twice the mass of the Sun. Another kind of black holes are important in cosmology which might have formed due to quantum fluctuations of matter distribution in the early universe. These are termed as topological blackholes having mass many times smaller than the the solar mass. In particular these are important from the view point of Hawking radiation \[8\]. Bousso and Hawking \[9\] (in short, BH) calculated the probability of the quantum creation of a universe with a pair of primordial black holes in (3 + 1) dimensional universe. In the paper they considered two different Euclidean space-time : (1) a universe with space-like sections with $S^{3}$ - topology and (2) a universe with space-like section with $ S^{1} \times S^{2}$- topology, as is obtained in the Schwarzschild- de Sitter solution. The first kind of spatial structure describes an inflationary (de Sitter) universe without black hole while the second kind describes a Nariai universe \[10\], an inflationary universe with a pair of black holes. BH considered in their paper a theory with a massive scalar field which provided an effective cosmological constant for a while through a slow-rolling potential (mass-term). Chao \[11\] has studied the creation of a primordial black hole and Green and Malik \[12\] studied the primordial black holes production during reheating. Paul [*et al.*]{} \[13\] following the approach of BH studied the probability of creation of PBH including $R^{2}$-term in the Einstein action and found that the probability is very much suppressed in the $R^{2}$ -theory. Paul and Saha \[14\] studied probability of creation of a pair of black hole with higher order Lagrangian i.e., considering higher loop contributions into the effective action that are higher than quadratic in $R$. In this paper we investigate a pair of black holes in the modified gravity given by action (1) in the presence of a cosmological constant.

Consequently it is also important to study the effects of these terms to study quantum creation of a universe with a pair of PBH. We calculate the probabilities for the creation of a universe with two types of topology namely, $ R \times S^{3} $ - topology and $R \times S^{1} \times S^{2}$ - topology, where the later accommodates a pair of primordial black holes. To calculate the probabilities for these spatial topologies, we use a semiclassical approximation for the evaluation of the Euclidean path integrals. The condition that a classical spacetime should emerge, to a good approximation, at a large Lorentzian time was selected by a choice of the path of the time parameter $\tau$ along the $\tau^{Re}$ axis from 0 to $\frac{\pi}{2H}$ and then continues along the $\tau^{im}$ axis. The wave-function of the universe in the semiclassical approximation is given by $$\Psi_{o} [ h_{ij}  , \Phi_{\partial  M} ]   \approx \sum_{n} A_{n}
 e^{- I_{n}}$$ where the sum is over the saddle points of the path integral, and $I_{n}$ denotes the corresponding Euclidean action. The probability measure of the creation of PBH is $$P[ h_{ab} , \Phi_{\partial M} ] \sim  e^{ - 2 \;  I^{Re}}$$ where $h_{ab}$ is the boundary metric and $I^{Re}$ is the real part of the action corresponding to the dominant saddle point, i.e. the classical solution satisfying the Hartle-Hawking (henceforth, HH) boundary conditions \[15\]. It was believed that all inflationary models lead to $ \Omega_{o} \sim 1$ to a great accuracy. This view was modified after it was discovered that there is a special class of inflaton effective potentials which may lead to a nearly homogeneous open universe with $ \Omega_{o} \leq 1$ at the present epoch. Cornish [*et al.*]{} \[16, 17\] studied the problem of pre-inflationary homogeneity and outlines the possibility of creation of a small, compact, negatively curved universe. We show that a universe with $S^{3}$-topology may give birth to an open inflation similar to that obtained in [*Ref.*]{} 18.

The paper is organised as follows : in sec. II we write the gravitational action for a higher derivative theories and obtain gravitational instanton solutions and in sec. III we use the action to estimate the relative probability of the two types of the universes and in sec. IV we give a brief discussion.

[**II. GRAVITATIONAL INSTANTON SOLUTIONS WITH OR WITHOUT A PAIR OF PRIMORDIAL BLACK HOLES :** ]{}

We consider a Euclidean action which is given by $$I_{E} =  - \frac{1}{16\pi} \int d^{4} x \sqrt{g} \;   f(R)  -
\frac{1}{8\pi} \int_{\partial M} d^{3} x \sqrt{h}\;  K f'(R)$$ where $g$ is the 4-dimensional Euclidean metric, $f(R) = R +  \frac{\delta}{ R  }
 - 2 \Lambda $, $R $ is the Ricci scalar, $\delta$ is a dimensional parameter and $\Lambda$ is the 4-dimensional cosmological constant. In the gravitational surface term, $h_{ab}$ is the boundary metric and $K = h^{ab} K_{ab}$ is the trace of the second fundamental form of the boundary $\partial M$ in the metric. The second term is the contribution from $\tau = 0$ back in the action. It vanishes for a universe with $S^{3}$ topology, but gives a non vanishing contribution for $S^{1} \times S^{2}$-topology, with the gravitational instanton discussed here.

[**(A) Topology $S^{3}$, the de Sitter spacetime :**]{}

In this section we study vacuum solution of the modified Euclidean Einstein action with a cosmological constant in four dimensions. We now look for a solution with spacelike section having $S^{3}$ - topology and the corresponding four dimensional metric ansatz which is given by $$\;
ds^{2} = d\tau^{2} + a^{2} (\tau) \left[ dx_{1}^{2} + sin^{2} x_{1} \;
d\Omega_{2}^{2} \right]$$ where $a(\tau)$ is the scale factor of a four dimensional universe and $ d\Omega_{2}^{2} $ is a line element on the unit two sphere. The scalar curvature is given by $$R = -  6 \left[ \frac{\ddot{a}}{a} + \left(
    \frac{\dot{a}^{2}}{a^{2}} - \frac{1}{a^{2}} \right) \right] .$$ where an overdot denotes differentiation with respect to $\tau$. We rewrite the action (3), including the constraint through a Lagrangian multiplier $\beta$ and obtain $$I_{E} = -  \frac{\pi}{8}  \int
         \left[ f(R) a^{3} - \beta \left( R + 6 \frac{\ddot{a}}{a} +
6 \frac{\dot{a}^{2} -1}{a^{2}} \right) \right] d \tau
- \frac{1}{8 \pi} \int_{\partial M} d^{3} x \sqrt{h} K f'(R).$$ Varying the action w.r.t. R, we determine $$\beta = a^{3} f'(R).$$ Substituting the above equation, treating $a$ and $R$ as independent variables we get $$I_{E} = -  \frac{\pi}{8}  \int_{\tau = 0}^{\tau_{\frac{\pi}{2 H}} }
         \left[ a^{3} f(R) - f'(R) \left( a^{3} R - 6  a \dot{a}^{2} - 6 a
\right)  + 6 a^{2} \dot{a} \dot{R} f''(R)  \right] d \tau$$ $$-  \frac{3 \pi}{4} \left[  \dot{a} a^{2} f'(R) \right]_{\tau = 0},$$ here we have eliminated $\ddot{a}$ term in the action by integration by parts. The field equations are now obtained by varying the action with respect to $a$ and $R$ respectively, giving $$f''(R) \left[ R + 6  \frac{ \ddot{a}}{a}    +
6 \frac{\dot{a}^{2} - 1}{a^{2}} \right]  = 0 ,$$ $$2 f'''(R) \dot{R}^{2} + 2 f''(R) \left[ \ddot{R} + 2 \frac{\dot{a}}{a}
\dot{R} \right] + f'(R) \left[ 4 \frac{ \ddot{a}}{a} + 2
\frac{ \dot{a}^{2}}{a^{2}} - \frac{2}{a^{2}} + R \right] - f(R)  = 0.$$ We now consider $f(R) = R + \frac{\delta}{R}  - 2 \Lambda $ and obtain an instanton solution which is given by $$a = \frac{1}{H} \; \sin  H \tau$$ where $ R = 12 H^{2} $ and $H$ is determined from the constraint equation $$48  H^{4} - 16 \Lambda H^{2} + \delta = 0.$$ We note that (i) two unequal values of $H$ are permitted when $0 < \delta < \frac{4 \Lambda^{2}}{3}$, (ii) $H
^{2} = \frac{\Lambda}{3}$ for $\delta = 0$, and (iv)$\Lambda = 0$ permits a real value for $H^{2} $ when $\delta < 0$. It is evident that the instanton solution obtained here satisfies the HH no boundary conditions viz., $a(0) = 0 $, $ \dot{a} (0) = 1$. One can choose a path along the $\tau^{Re}$ axis to $\tau = \frac{\pi}{2 H}$, the solution describes half of the Euclidean de Sitter instanton $S^{3}$. Analytic continuation of the metric (3) to Lorentzian region, $x_{1} \rightarrow \frac{\pi}{2} + i \sigma $, gives $$ds^{2} = d \tau^{2} + a^{2}(\tau) \left[ - d\sigma^{2} + \cosh^{2} \sigma
\;  d \Omega_{2}^{2} \right]$$ which is a spatially inhomogeneous de Sitter like metric. However, if one sets $\tau = i t $ and $ \sigma = i \frac{\pi}{2} + \chi $, the metric becomes $$ds^{2} = -  dt^{2} + b^{2}(t) \;  [ d\chi^{2} + \sinh^{2} \chi
 \;
 d \Omega_{2}^{2} ]$$ where $b(t) = - \; i \;  a( it )$. The line element (12) now describes an open inflationary universe. The real part of the Euclidean action corresponding to the solution calculated by following the complex contour of $\tau $ suggested by BH is given by $$I^{Re}_{S^{3}} = - \frac{2 \pi}{3  H^{2}} \left[ \frac{ 12 \Lambda H^{2} -  \delta }{ 16 \Lambda H^{2} - \delta } \right].$$ With the chosen path for $\tau $, the solution describes half the de Sitter instanton with $S^{4}$ topology, joined to a real Lorentzian hyperboloid of topology $R^{1} \times S^{3}$. It can be joined to any boundary satisfying the condition $a_{\partial M} > 0$ . For $a_{\partial M} > H^{- 1}$ , the wave function oscillates and predicts a classical space-time. We note the following cases :

$\bullet$ $\delta = 0$, the action reduces to that obtained by BH.

$\bullet$ $0 < \delta < \frac{4 \Lambda^{2}}{3}$, a realistic solution corresponds to $H_{o}^{2} > \frac{\delta}{12 \Lambda} $.

$\bullet$ $\Lambda = 0$, the action is decided by $\delta$ which is $I = - \frac{8 \pi}{\sqrt{- 3 \; \delta}}$, it is real for $\delta < 0$.

[**(B) Topology $ S^{1} \times S^{2} $ :**]{}

In this section we consider Euclidean Einstein equation and look for a universe with $S^{1} \times
S^{2}$ -spacelike sections as this topology accommodates a pair of black holes. The corresponding ansatz for (1 + 1 + 2) dimensions is given by $$ds^{2} = d \tau^{2} + a^{2}(\tau) \; dx^{2} + b^{2}(\tau) \;  d \Omega_{2}^{2}$$ where $a( \tau ) $ is the scale factor of $S^{1}$-surface and $b( \tau )$ is the scale factor of the two sphere. The metric for the two-sphere is given by the metric $$d\Omega_{2}^{2} = d \theta^{2} + sin^{2} \theta \; d \phi^{2}$$ The scalar curvature is given by $$R = - \left[ 2 \frac{\ddot{a}}{a} +  4 \frac{\ddot{b }}{b}
     + 2 \left( \frac{\dot{b}^{2}}{b^{2}} -
   \frac{1}{b^{2}} \right) + 4 \frac{\dot{a} \dot{b}}{a b} \right] .$$ The Euclidean action (3) becomes $$I_{E} = - \frac{\pi}{2} \int
 \left[  f(R) a b^{2} - \beta \left(R + 2 \frac{\ddot{a}}{a} + 4
\frac{\ddot{b}}{b} + 4 \frac{\dot{a} \dot{b}}{ab} + 2
\frac{\dot{b}^{2}}{b^{2}} - \frac{2}{b^{2}}\right) \right] d\tau$$ $$- \frac{1}{8 \pi} \int_{\partial M} \sqrt{h} \;  d^{3}x \;  K f'(R).$$ One can determine $\beta$ as is done before and obtains $$I_{S^{1} \times S^{2}} = - \frac{\pi}{2}
\int_{\tau = 0}^{\tau_{\partial M}}
 \left[  f(R) - f'(R) \left( R - 4  \frac{\dot{a} \dot{b}}{ab} -
2 \frac{\dot{b}^{2}}{b^{2}} - \frac{2}{b^{2}}\right) + 2 f''(R)
\dot{R} \left( \frac{\dot{a}}{a} + 2 \frac{\dot{b}}{b} \right) \right]$$ $$a b^{2} d \tau - \pi \left[ \left( \dot{a} b^{2}  + 2 a b \dot{b} \right) f'(R)
\right]_{\tau = 0}.$$ Variation of the action with respect to $R $, $a$ and $b$ respectively are given by the following equations $$f''(R) \left[  R + 2 \frac{\ddot{a}}{a}
  + 4 \frac{\ddot{b}}{b} + 4 \frac{\dot{a} \dot{b}}{ab}
+ 2 \frac{\dot{b}^{2}}{b^{2}} - \frac{2}{b^{2}} \right] = 0,$$ $$2  f'''(R) \dot{R}^{2} + 2 f''(R) \left[ \ddot{R} + 2 \dot{R}
\frac{\dot{b}}{b}
\right] + f'(R) \left[ R + 4
\frac{\ddot{b}}{b}  +
2 \frac{ \dot{b}^{2} - 1}{b^{2}} \right] - f(R)  = 0,$$ $$2 f'''(R) \dot{R}^{2} + 2 f''(R) \left[ \dot{R} \left(\frac{\dot{a}}{a} +
\frac{\dot{b}}{b}\right)  + \ddot{R} \right] + f'(R)
\left[  R + 2  \frac{\ddot{a}}{a} +
 2 \frac{\ddot{b}}{b}  + 2 \frac{\dot{a} \dot{b}}{ab} \right]$$ $$- \; f(R)   = 0.$$ Let us now consider $f(R) = R + \frac{\delta}{R}  - 2 \Lambda $. Equations (18)-(20) admit an instanton solution which is given by $$a = \frac{1}{H_{o}} \; sin ( H_{o} \tau ) , \; \; \;
b =  H_{o}^{- 1},$$ $$R = 4 H_{o}^{2},$$ where $H_{o}$ satisfies the constraint equation $$16  H_{o}^{4} - 16 \Lambda  H_{o}^{2} + 3 \delta  = 0.$$ We note the following : (i) $\delta = 0$, one gets $H_{o}^{2} = \Lambda$, (ii) $ 0  < \delta < \frac{4 \Lambda^{2}}{3}$, one obtains two unequal real values of $H_{o}^{2}$ are permitted, (iii) $\delta =  \frac{4}{3} \Lambda^{2}$ leads to $H_{o}^{2} = \frac{\Lambda}{2}$ and (iv) $\Lambda  = 0$, gives $H_{o}^{2} = \sqrt{ - \; \frac{3 \delta}{16} }$ which is real if $\delta < 0$. The above instanton solution satisfies the HH boundary conditions $a(0) = 0 $, $ \dot{a} (0) = 1,  b(0) = b_{o} $, $ \dot{b} (0) = 0$. Analytic continuation of the metric (14) to Lorentzian region, i.e., $\tau \rightarrow it $ and $ x \rightarrow \frac{\pi}{2} + i \sigma $ yields $$ds^{2} = -  dt^{2} + c^{2}(t) \; d\sigma^{2} + H_{o}^{-2} \; d \Omega_{2}^{2},$$ where $c(t) = - \;  i \;  a( i t )$. In this case the analytic continuation of time and space do not give an open inflationary universe. The corresponding Lorentzian solution is given by $$a(\tau^{Im}) |_{\tau^{Re} \;  = \frac{\pi}{2H_{o}}} = H_{o}^{-1} \cosh H_{o} \tau^{Im} ,$$ $$b(\tau^{Im}) |_{\tau^{Re} \;  = \frac{\pi}{2H_{o}}} = H_{o}^{-1}$$ Its space like sections can be visualised as three spheres of radius $H_{o}^{-1}$ with a [*hole*]{} of radius $b = H_{o}^{-1}$ punched through the north and south poles. The physical interpretation of the solution is that of two - spheres containing two black holes at opposite ends. The black holes have the radius $H_{o}^{-1}$ which accelerates away from each other with the expansion of the universe. The real part of the action can now be determined following the contour suggested by BH \[2\], and it is given by $$I^{Re}_{S^{1} \times S^{2}} = - \frac{4 \pi}{  H_{o}^{2}} \left[ \frac{4 \Lambda
  H_{o}^{2} - \delta}{16 \Lambda H_{o}^{2} - 3 \delta} \right].$$ The solution (24) describes a universe with two black holes at the poles of a two sphere. It may be pointed out here that the contribution of the integrand in (17) for the instanton vanishes and the non-zero contribution of the action here arises from the boundary term only. We note the following :

$\bullet $ $\delta = 0$, the action reduces to that obtained by BH.

$\bullet$ $\Lambda = 0$, the action is decided by $\delta$ which is $I = - \frac{16 \pi}{3 \sqrt{- 3 \; \delta}}$, it is real for $\delta < 0$.

$\bullet$ $\delta = \frac{4 \Lambda^{2}}{3}$, the action becomes $I = - \frac{4 \pi}{3\Lambda}$.

$\bullet$ $\delta < \frac{4 \Lambda^{2}}{3} $, either $ H_{o}^{2} > \frac{\delta}{4 \Lambda}$ or $ H_{o}^{2} < \frac{3 \delta}{16 \Lambda}$ allows a negative definite action corresponding to the instanton solution.

[**III. PRIMORDIAL BLACK HOLES PAIR CREATION PROBABILITY :**]{}

In the previous section we have calculated the actions for inflationary universe with or without a pair of black holes. We now compare the probability measure in the two cases. The probability for creation of a de Sitter universe is determined from the action (7). The probability for nucleation of an inflationary universe without a pair of Black holes is given by $$P_{S^{3}} \sim \; e^{ \frac{\pi}{36 H^{6}} \left[ 12 \Lambda  H^{2} - \delta \right] }.$$ However for an inflationary universe with a pair of black holes the corresponding probability of nucleation can be obtained from the action (17). The corresponding probability is $$P_{S^{1} \times S^{2}} \sim e^{ \frac{ \pi}{2 H_{o}^{6}} \left[
 4 \Lambda  H_{o}^{2} - \delta \right] }$$ We now describe spacial cases :

$\bullet$ $\delta = 0$, one recovers the result obtained by Bousso and Hawking \[9\] $$P_{S^{3}} \sim e^{\frac{3 \pi}{\Lambda}} , \; \; \; P_{S^{1}
\times S^{2}} \sim e^{\frac{2 \pi}{\Lambda}}.$$ Thus with a positive cosmological constant the probability for a universe with PBH is less than that without PBH.

$\bullet$ $\delta \neq  0$, since eqs. (11) and (22) are quadratic in $H^{2}$ and $H_{o}^{2}$, there are two branches of solutions admitting two different instanton solutions. In one case the probabilities are given by $$P_{S^{3}} \sim e^{\frac{6 \pi}{ \left( \Lambda +  \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)^{3}} \left[  2  \Lambda  \left(  \Lambda  + \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)  - \delta \right]}
,  \; \; \;
P_{S^{1} \times S^{2}}
\sim e^{\frac{4 \pi}{ \left( \Lambda +  \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)^{3}} \left[  2  \Lambda  \left(  \Lambda  + \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)  - \delta \right]}$$ for $\delta < \frac{4 \Lambda^{2}}{3}$, and in the other case the probabilities are $$P_{S^{3}} \sim e^{\frac{6 \pi}{ \left( \Lambda -  \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)^{3}} \left[  2  \Lambda  \left(  \Lambda  - \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)  - \delta \right]}
,  \; \; \;
P_{S^{1} \times S^{2}}
\sim e^{\frac{4 \pi}{ \left( \Lambda -  \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)^{3}} \left[  2  \Lambda  \left(  \Lambda  - \sqrt{ \Lambda^{2} - \frac{3 \delta}{4}} \right)  - \delta \right]}$$ when $0 < \delta < \frac{4 \Lambda^{2}}{3}$.

It may be pointed out here that the values of $H^{2}$ and $H_{o}^{2}$ corresponding to the probability measure given by eq.(28) are higher than that in eq.(29). It is evident from eqs. (28) and (29) that the creation of a universe without PBH is more probable than with PBH for $\delta < \frac{4 \Lambda^{2}}{3} \; $ with a positive cosmological constant. It admits negative $\delta$ also. However, the probability of creation of a universe with a pair of PBH is favoured in the first case when one considers a negative cosmological constant. In the second case, the probability of creation of a universe with a pair of PBH is favoured with a positive cosmological constant for $0 < \delta < \Lambda^{2}$, but it is suppressed for $ \Lambda^{2} < \delta < \frac{4 \Lambda^{2}}{3}$. In the second case no instanton solution exists with a negative cosmological constant.

$\bullet$ $\delta = \frac{4 \Lambda^{2}}{3}$, the probabilities are given by $$P_{S^{3}} \; \sim  \; e^{\frac{4 \pi}{\Lambda}},  \; \; \; \;  P_{S^{1} \times  S^{2}} \; \sim  \;  e^{\frac{8 \pi}{ 3 \Lambda}}.$$ In the above only one kind of instanton solution is permitted with $H = \sqrt{ \frac{\Lambda}{6}}$ in the $S^{3}$-topology and $H_{o} = \sqrt{ \frac{\Lambda}{2}}$ in the $S^{1} \times S^{2}$ -topology.

$\bullet$ $\Lambda = 0$, the probabilities are given by $$P_{S^{3}} \; \sim  \; e^{\frac{16 \pi}{\sqrt{- 3 \delta}}},  \; \;  \; \; P_{S^{1} \times S^{2}} \; \sim  \; e^{\frac{32 \pi}{ 3 \sqrt{- 3 \delta}}}.$$ in this case only negative values are permitted for the parameter $\delta$ in the action which reduces to the action that considered by Carrol [*et al.*]{} \[6\].

[**IV. DISCUSSIONS :** ]{}

In this paper we have evaluated the probability for primordial black holes pair creation in a modified theory of gravity. In section II, we have obtained the gravitational instanton solutions in the two cases : (i) a universe with $R \times S^{3}$ - topology and (ii) a universe with $ R \times S^{1} \times S^{2} $ - topology respectively. The Euclidean action is then evaluated corresponding to the instanton solutions. For a non zero $\delta$ in the gravitational action, we obtain two classes of instanton solutions differing in the values of the radius of the sphere $H^{ - 1}$ and $H_{o}^{- 1}$ respectively. We found that the probability of a universe with $R \times S^{3} $ topology turns out to be much lower than a universe with topology $ R \times S^{1} \times S^{2} $ in the modified theory unless $0 < \delta < \frac{4 \Lambda^{2}}{3}$ with a positive cosmological constant in the case of lower instantonic radius ($H^{- 1}, H_{o}^{- 1}$) and in the case of higher instantonic radius ($H^{- 1}, H_{o}^{- 1}$) with $ \Lambda^{2} < \delta < \frac{4 \Lambda^{2}}{3} $ with a positive cosmological constant. It may be mentioned here that one gets a regular instanton in $S^{4} $ - topology if there are no black holes. The existence of black holes restricts such a regular topology. The results obtained here on the probability of creation of a universe with a pair of primordial black holes are found to be strongly suppressed depending on the parameter $\delta$ determined by the cosmological constant in some cases which are presented here. We note an interesting solution here in the framework of the modified gravitational action with inverse power of $R$ -theory, which admits de Sitter instantons with $S^{3}$ and $S^{1} \times S^{2}$ topologies even without a cosmological constant. In this case the action is similar to that considered by Carroll [*et al.*]{} \[6\]. It is interesting to note here that analytic continuation of a $R \times S^{3}$ metric considered here to Lorentzian region leads to an open 3 - space. One obtains Hawking-Turok \[18\] type open inflationary universe in this case. In the other type of topology an open inflation section of the universe is not permitted. A detail study of an open inflationary universe will be discussed elsewhere. Thus in a modified Lagrangian with inverse power in $R$-theory, quantum creation of PBH seems to be suppressed in the minisuperspace cosmology for some values of the parameters in the action, which are determined here. Another new result obtained here is that gravitational instanton solution may be obtained even with a negative cosmological constant which is not permitted in the case considered by BH \[9\].

[**[*Acknowledgement :*]{}**]{} BCP gratefully acknowledges valuable discussions with Naresh Dadhich. DP would like to thank S. Mukherjee for providing facilities of the IUCAA Reference Centre at North Bengal University to carry out a part of the work. This work is partially supported by University Grants Commission, New Delhi.

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[^1]: permanent address : Khoribari H.S. School, Khoribari, Dist. : Darjeeling

[^2]: e-mail : bcpaul@nbu.ernet.in


Flavor production from edible oils and their constituents by Penicillium corylophilum.
Production of volatile substances from edible oils and their constituents by Penicillium corylophilum was studied to clarify the mechanism of flavor production from a non-stick oil by the organism in a rice cake system. First, edible oils from plant and animal origins were tested for flavor production. Among the oils tested, coconut oil was the only one from which the flavor was produced. Second, triacylglycerols consisting of fatty acids with various lengths of carbon chain (C6 to C13) were studied for flavor production. Among the triacylglycerols tested, flavors were produced from those consisting of fatty acids with carbon chains of C6 to C11. The flavors consisted of methylketones and secondary alcohols, whose carbon chains were one carbon shorter than the precursor fatty acid molecules of the triacylglycerols. Flavors similar to that from the non-stick oil were produced from tricaprylin (C8), trinonanoin (C9), and tridecanoin (C10) among the triacylglycerols tested. Formation of mould spores was more strongly suppressed by triacylglycerols with shorter chain fatty acids. Third, fatty acids with various lengths of carbon chain (C7 to C15) were studied for flavor production. Among the fatty acids tested, flavors were produced from decanoic (C10) and undecanoic (C11) acids only. The flavors also consisted of methylketones and secondary alcohols one carbon shorter than the precursor fatty acids. Fatty acids with short carbon chains (C7 to C9) completely inhibited the mould growth. Our study showed that the range of carbon chain length of fatty acids capable of the flavor production (C10 to C11) was narrower than that of triacylglycerols (C6 to C11). It was also found that the non-stick oil and coconut oil contain tricaprylin and tridecanoin as triacylglycerols and decanoic acid as fatty acid.


Tour a Modern Mountain Retreat in Tahoe by John Maniscalco Architects

By Marisa Marcantonio | Photographs by Joe Fletcher

Surrounded by a seemingly endless expanse of white fir and sugar pines and nestled amidst mountains and lakes sits a minimalist retreat. Engaged by a client to build their dream home in a secluded Tahoe spot, San Francisco’s John Maniscalco Architecture drew inspiration from the rugged landscape to create a modern getaway: a long, low, refined rustic home beautifully integrated with its site.

“The client came to us with the best client brief ever: ‘We want the smallest house possible that sleeps 16,’” notes Maniscalco. “It was obviously tongue-in-cheek, but it was also a very clear statement of their intentions.”

The homeowners, an active family with their primary residence on the Peninsula, wanted a getaway where they could entertain friends and family and take advantage of every outdoor activity possible. Says Maniscalco, “The house is nestled into the slope as it descends—all the spaces spill directly into the landscape. We made sure there was a direct relationship between the interior uses and the elements of the landscape that the clients had come to love.”

Climate and site also drove the solutions for the nearly 6,300-square-foot house. Maniscalco, known for refined, urban Bay Area homes as well as mountain getaways, had already designed four residences in the area and knew how to design for local conditions. “The extremes of the weather directly affect the structural design, the materials used, and the configuration of the houses,” he notes. He situated the home so that it is optimized for the best natural light at all times of day, and the sunset can be appreciated from the outdoor gathering areas. “The home is based around an idea of framing and reframing nature,” says the architect.

“When you come back in from outdoors, natural assets are reframed: A tall slot window profiles a single tree; the master bedroom is suspended above the valley floor that slopes away below you.” In harsher weather, the sloping and cantilevered roof in painted zinc is able to withstand the elements and shed snow easily. “The experience of being in this master bedroom floating over the snow-covered valley floor as it drops away from you is a magical experience,” says Maniscalco.

One outstanding element of a site can often capture the imagination, and here, a sculptural, rocky outcropping on the property captivated the clients. It became the key natural element around which the L-shaped house was built. “At the early site meetings, the interior designer, the client and I started gathering branches, rocks and different materials. We said, ‘This is the palette of the house. It should have the qualities already here, just enhanced and multiplied,’” explains Maniscalco. “We took our cues from these colors, materials and textures.” The home was clad in dark-stained cedar, painted zinc panels, bronzed aluminum doors and windows, and polished and board-formed concrete, all in carefully proportioned dimensions.

The home’s layout is an open plan centered around a great room—with a double-height walnut and steel fireplace—and extends into two sleeping wings. “When used by the family alone, the house is concentrated on a single occupied floor,” says Maniscalco. “But when they have visitors, the house ‘expands’ to include the lower floor. This maintains a comfortable scale for smaller family use and an extended scale for larger groups.”

Maniscalco collaborated on the project with Dovetail Design Works founder Katy Chudacoff, an interior designer who had worked with the clients on two previous residences. Soothing, honest materials—including polished concrete and warm walnut floors—bring the expansive, light-filled space together, while pops of burnt orange and brown echo the landscape.

After a long ski day, a sheltered patio that overlooks a meadow and the Pacific Crest range invites lounging. Designed for entertaining, it’s complete with a dining table, barbecue area and built-in pizza oven. Whether gathered around the fire, restoring themselves in the sauna or taking a dip in the cold plunge pool, the clients are always connected to life’s essential elements.

A version of this article appeared in the February/March 2017 issue of SFC&G (San Francisco Cottages & Gardens) with the headline: Natural Assets.


BEIRUT, Lebanon — King Salman of Saudi Arabia on Sunday named his son Prince Abdulaziz bin Salman as energy minister, putting a member of the royal family for the first time in one of the kingdom’s most important roles, as part of a wider shake-up of top energy-sector jobs.

The appointment of Prince Abdulaziz, an older half brother of the Saudi crown prince, Mohammed bin Salman, brings to an end a long line of commoner technocrats charged with overseeing energy policy for the world’s largest oil exporter.

“It is a momentous change to place a royal atop the oil ministry,” said Ellen R. Wald, the president of Transversal Consulting and author of a book about the Saudi oil industry. “That said, Prince Abdulaziz is experienced in Saudi oil policy and well known on the oil scene.”

Prince Abdulaziz, who has been minister of state for energy affairs since 2017, replaces Khalid al-Falih, who was removed last week as board chairman of Saudi Aramco, the state-owned oil company that he once ran as chief executive. The move announced on Sunday is likely to surprise oil market participants, who had mostly assumed that the departing energy minister would retain that portfolio, which includes sway over Saudi production policy.


Q:

display confirmed products for purchase in purchase order openerp

I have added new statuses(PENDING,CONFIRMED) for products. I need to display only CONFIRMED products for purchase in the purchase order. I have tried, however, not getting clear idea on this.

A:

You can inherit the view and use domain [('status','=','confirmed')]
<field name="product_id" on_change="onchange_product_id(parent.pricelist_id,product_id,0,False,parent.partner_id, parent.date_order,parent.fiscal_position,date_planned,name,price_unit,context)" domain="[('state','=','confirmed')]" />


My hometown as I see it

28/03/2014

:: WP Word Press Weekly Photo Challenge: Street Life

It was quite early in a weekend morning when I woke up with the strong sound of the firefighter’s truck siren. Immediately I smelled smoke and hurried to the window. Fortunately nobody was in risk. But there it was: some stupid one had set fire to the rubble container in next block infecting all the neighborhood air.
See more interpretations of the challenge here.
…
Era muito cedo em uma manhã de fim de semana, quando acordei com o alto som da sirene do caminhão dos bombeiros. Imediatamente senti cheiro de fumaça e corri para a janela. Felizmente ninguém estava em risco. Mas lá estava: algum estúpido colocou fogo na caçamba de entulho no quarteirão seguinte empesteando todo o ar da vizinhança.
Veja mais interpretações desse desafio aqui.


From U.S. Pat. No. 4,338,327 triazolyldioxolanes are known, having the general formula: ##STR2## wherein: R.sup.1, R.sup.2, R.sup.3 are, independently, H, alkyl, alkoxy, halogen, NO.sub.2, CN, CF.sub.3 ;
n=0, 1; PA1 X=O, S; PA1 R.sup.4 is alkyl, mono-, di- and tri-haloalkyl, alkyloxyalkyl, mono-, di- and tri-haloalkyloxyalkyl, lower alkenyl, 2-propynyl, 3-halo-2-propynyl, cycloalkyl, aryl, arylalkyl, or arylalkenyl. PA1 m=0, also n=0; PA1 p=0, 1; q=1, 2; PA1 X is either oxygen or sulphur; PA1 A=N, CH; PA1 R is H, CH.sub.3, F; PA1 R.sub.1 is selected from chlorine, bromine, fluorine, CF.sub.3, phenyl, C.sub.1 -C.sub.2 -alkoxy, C.sub.1 -C.sub.2 -haloalkoxy, alkylthio, haloalkylthio, wherein the halogen is Cl, Br, F; PA1 R.sub.2 is selected from H, chlorine, bromine, fluorine; PA1 R.sub.f is selected from the group formed by alkyls containing from 2 to 4 carbon atoms, and containing at least 4 atoms of halogen selected from F, Cl and Br, of which at least 3 are F atoms; alkenyls and alkynyls containing up to 4 carbon atoms, containing at least 2 F atoms and, optionally, other halogens selected between Cl and Br. PA1 alkyls: --CF.sub.2 --CF.sub.3, --CF.sub.2 --CF.sub.2 H, --CFH--CF.sub.3, --CCl.sub.2 --CF.sub.3, --CF.sub.2 --CFHCl, --CF.sub.2 --CF.sub.2 --CF.sub.3, --CF.sub.2 --CF.sub.2 --CF.sub.2 --CF.sub.3, --CF.sub.2 --CFH--CF.sub.3, CF.sub.2 --C(CF.sub.3).sub.2 ; PA1 alkenyls: --CF.dbd.CF.sub.2, --CF.dbd.CF--CF.sub.3. --CH.dbd.CF--CF.sub.3, --CH.dbd.CCl--CF.sub.3, --CH.dbd.CBr--CF.sub.3, --CH.dbd.C(CF.sub.3).sub.2 ; PA1 alkynyls --C.tbd.C--CF.sub.3. PA1 the salts of the compounds having general formula (I) derived from an inorganic acid, such as a hydrogen e.g., hydriodic, hydrobromic, hydrochloric acid; sulphuric, nitric, thiocyanic and phosphoric acid; or from an organic acid, such as acetic, propanoic, hydroxyacetic, 2-hydroxypropanoic, 2-oxopropanoic, ethanedioic, propanedioic, butanedioic, benzoic, methanesulphonic, 4-methylbenzenesulphonic acid, etc.; PA1 the metal complexes obtained by the reaction of complexation between the derivatives of type (I) with an organic or inorganic salt of a metal, such as halide, nitrate, sulphate, phosphate of, e.g., copper, manganese, zinc or iron. PA1 1) Direct treatment of carbinol with zinc in acetic acid; PA1 2) Conversion of the carbinol into acetate or into dihalophosphite and subsequent treatment with zinc in a dipolar aprotic solvent, such as DMF, in particular by the reduction of the acylated compound having the formula: ##STR19## 3) Replacement of the hydroxy group of carbinol with a halogen atom, and subsequent dehalogenation by zinc.
In the patent, however, no examples are reported wherein R.sup.4 is either a di- or a tri-haloalkyl, or a di- or a tri-halo-alkyloxyalkyl. Furthermore, no such indications are reported on the trend of the fungicidal activity, as to demonstrate a superiority of the compounds wherein R.sup.4 contains a halogen atom, relative to the other compounds wherein R.sup.4 is not halogenated.


Nitto Trail Grappler M/T 40X15.50 R24

The Nitto Trail Grappler MT combines the exciting off-road capabilities of a mud terrain tire with the comfort and smooth, quiet ride of the Nitto Terra Grappler. Designed for the driver who likes off-road fun but has to hit the highway every now and then, this tire is the ideal combination of rugged performance and street comfort.


Protein kinase C stimulates HuD-mediated mRNA stability and protein expression of neurotrophic factors and enhances dendritic maturation of hippocampal neurons in culture.
HuD protein is an RNA-binding protein involved in post-transcriptional regulation of gene expression for synaptogenesis, neuronal differentiation, and learning and memory, and is up-regulated and redistributed by a protein kinase C (PKC)-dependent pathway in neurons. Here, we show a PKC-regulated mechanism on HuD-mediated mRNA stability and expression of several neurotrophic factors (NTFs) in cultured hippocampal neurons. HuD pull-down assays showed that HuD is associated with brain-derived neurotrophic factor (BDNF), nerve growth factor (NGF), and neurotrophin (NT)-3 mRNAs. Reduction of HuD expression with short hairpin RNAs decreased BDNF, NGF, and NT-3 mRNAs and NTFs expression. Bryostatin, a PKC activator, treatment enhanced their association with HuD and increased these transcripts' stability. Bryostatin induced HuD phosphorylation, which was inhibited by Ro 32-0432, a specific PKC inhibitor. Activated PKC specifically phosphorylated coactivator-associated arginine methyltransferase 1 (CARM1), which methylates HuD and negatively modulates HuD-mRNA interactions during neuronal differentiation, and inhibited its methyltransferase activity, resulting in decrease in CARM1-mediated HuD methylation. Furthermore cotreatment of bryostatin and AMI-1, a specific CARM1 inhibitor, potentiated PKC-dependent HuD-mRNA interactions and enhanced dendritic arborization. These results demonstrate that PKC may play an important role in neuronal differentiation and synaptogenesis via stimulating HuD-mediated mRNA stability and inhibiting CARM1 in hippocampal neurons.


[Detection of hepatitis G virus RNA in sera in non A-E hepatitis patients using polymerase chain reaction with multiple set primers].
A double polymerase chain reaction, involoving nested primers deduced from NS3-5 regions of the hepatitis G virus (GBV-c/HGV) genome, was developed for a sensitive and specific detection of GBV-C (HGV) RNA. With this method, 10 anti-HGV positive patients with non A-E hepatitis and 10 healthy subjects were tested. Among 10 patients, GBV-C RNA was detected in 9, 8, 4, 9 patients by the NS-3 (1) primers, the NS3(2) primers, the NS4 primers, the NS5(1) primers and the NS5(2) primers respectively. Control sera from 10 healthy subjects did not reveal GBV-C (HGV) RNA by any set of the primers. These data suggest that the detection rate of GBV-C (HGV) RNA is different in various set of primers, the NS3(1) and the NS5(2) primers are superior to other primers and are more suitable for RT-PCR of GBV-C (HGV) RNA.


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2.6.27-stable review patch. If anyone has any objections, please let us know.

------------------

From: fangxiaozhi <huananhu@huawei.com>

commit 1460e5e44cc5ecad7704f63b10dcb3a59d0e008b upstream.

In this patch, we want to do one thing: add more Huawei product IDs into theUSB driver. Then it can support more Huawei data card devices. So to declarethe unusual device for new Huawei data card devices in unusual_devs.h and todeclare more new product IDs in option.c.

To modify the data value and length in the function ofusb_stor_huawei_e220_init in initializers.c That's because based on the USBstandard, while sending SET_FETURE_D to the device, it requires thecorresponding data to be zero, and its sending length also must be zero. Inour old solution, it can be compatible with our WCDMA data card devices, butcan not support our CDMA data card devices. But in this new solution, it canbe compatible with all of our data card devices.


Q:

Are typedef and #define the same in c?

I wonder if typedef and #define are the same in c?

A:

typedef obeys scoping rules just like variables, whereas define stays valid until the end of the compilation unit (or until a matching undef).
Also, some things can be done with typedef that cannot be done with define.
For example:
typedef int* int_p1;
int_p1 a, b, c;  // a, b, c are all int pointers

#define int_p2 int*
int_p2 a, b, c;  // only the first is a pointer, because int_p2
                 // is replaced with int*, producing: int* a, b, c
                 // which should be read as: int *a, b, c

typedef int a10[10];
a10 a, b, c;  // create three 10-int arrays

typedef int (*func_p) (int);
func_p fp;  // func_p is a pointer to a function that
            // takes an int and returns an int

A:

No.
#define is a preprocessor token: the compiler itself will never see it.
typedef is a compiler token: the preprocessor does not care about it.
You can use one or the other to achieve the same effect, but it's better to use the proper one for your needs
#define MY_TYPE int
typedef int My_Type;

When things get "hairy", using the proper tool makes it right
#define FX_TYPE void (*)(int)
typedef void (*stdfx)(int);

void fx_typ(stdfx fx); /* ok */
void fx_def(FX_TYPE fx); /* error */

A:

No, they are not the same.  For example:
#define INTPTR int*
...
INTPTR a, b;

After preprocessing, that line expands to
int* a, b;

Hopefully you see the problem; only a will have the type int *; b will be declared a plain int (because the * is associated with the declarator, not the type specifier).
Contrast that with
typedef int *INTPTR;
...
INTPTR a, b;

In this case, both a and b will have type int *.
There are whole classes of typedefs that cannot be emulated with a preprocessor macro, such as pointers to functions or arrays:
typedef int (*CALLBACK)(void);
typedef int *(*(*OBNOXIOUSFUNC)(void))[20];
...
CALLBACK aCallbackFunc;        // aCallbackFunc is a pointer to a function
                               // returning int
OBNOXIOUSFUNC anObnoxiousFunc; // anObnoxiousFunc is a pointer to a function
                               // returning a pointer to a 20-element array
                               // of pointers to int

Try doing that with a preprocessor macro.


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Macclesfield Town midfielder Courtney Richards knows exactly how hard it can be to fulfil your dream of becoming a professional footballer. He began his career at Phoenix United and despite all the obstacles which threatened to dilute his ambitions, he turned his dreams into reality by never losing sight of his goal. Now Courtney is…

With Sir John’s side having another blank Saturday this weekend, we will be carrying on our renovation work on the Club’s Memorial Garden. We have already made great progress on this, but we are eager to finish the job and create a really special place where we can all remember those who have passed. The…

Macclesfield Town are under transfer embargo, which prevents them from bringing any new players into the club, according to Sir John. Speaking to Alistair Pattrick after today’s game at Dover, Askey stated – We have an embargo on us, so we can’t sign anyone but we know the restrictions at the Football Club. But the…

Butch’s Bar will be opening their doors this afternoon, allowing you to join with fellow Silkmen fans ahead of two fascinating games. First up will be the mighty Silkmen, who travel down to Dover in what is another crucial match in the promotion run in. Full commentary will be broadcast in the bar, which opens…

You still have time to purchase your 2018/19 season ticket at the cheapest price, with the first phase of sales ending at midnight tonight. Tickets can be bought online here right up until the deadline. Here is how much you could save – CATEGORY SEASON TICKET PRICE IN FIRST PHASE MATCH TICKET PRICE PRICE BY PAYING…

Macclesfield Town Head Groundsman Gary Lewis will be interviewed live on BBC Radio Manchester at around 18:30 this evening. Having been nominated for the prestigious Groundsman of the Year Award last year, Gary has continued in the same vein this year as he has battled against the elements to ensure that all of our games…

The first phase of the early bird season ticket offers ends this evening and as such the club will stay open until 18:30 tonight. Speaking to the Official Site, Chairman Mark Blower stated – The supporters have played a massive part in our success this season and we have seen attendances rise throughout the campaign. “Hopefully…

Sir John has paid tribute to the belief of his Macclesfield Town squad, as they prepare for another crucial National league fixture at Dover on Saturday. Speaking to Nick Bianchi following the victory over Barrow, the Manager stated – At one stage you start to think it could be one of those games, but the…

Butch’s Bar will be opening their doors this Saturday, as they are set to hold a very special St Patrick’s Day celebration. Starting from 14:00 fans will be able to come down and enjoy a fully stocked bar, together with live commentary of Macclesfield Town’s crucial National League clash against Dover Athletic. Following on from…

Steve Watson’s Gateshead will visit the Moss Rose on Tuesday March 27th, the club have revealed. The original tie was scheduled for the previous Saturday, but due to The Heed’s progression in the FA Trophy a new date had to be found. The match will kick off at 19:45 and we will bring you all…

As many of you will know, I have set myself the task of renovating the club’s Memorial Garden which is situated behind the John Askey Terrace. We have already made a great start with this and now we are set to complete the job by providing everyone with a vibrant place which we can all…

Mitch Hancox and Keith Lowe have both been named in the National League Team of the Week, after resounding performances against Barrow last Saturday. Mitch fired a majestic equaliser for Sir John’s side late in the first half, yet his all round play throughout the game oozed defiance and valour. Keith also had another rock…