5.2.6: Cases
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Dischargeability of Student Loans under Chapter 7
In re Zygarewicz
423 B.R. 909 (Bkrtcy.E.D.Cal. 2010)
MCMANUS, BANKRUPTCY JUDGE.
Angela Zygarewicz, a chapter 7 debtor and the plaintiff in this adversary proceeding, borrowed 16 government-guaranteed student [sic] loans totaling $81,429. The loans have been assigned to Educational Credit Management Corporation (“ECMC”). By September 2009, the accrual of interest on these student loans had caused the debt to balloon to more than $146,000. The debtor asks the court to declare that these student loans were discharged in bankruptcy.
The Bankruptcy Code provides financially distressed debtors with a fresh start by discharging most of their pre-petition debts.…However, under 11 U.S.C. § 523(a)(8), there is a presumption that educational loans extended by or with the aid of a governmental unit or nonprofit institution are nondischargeable unless the debtor can demonstrate that their repayment would be an undue hardship. See [Citation]. This exception to a bankruptcy discharge ensures that student loans, which are typically extended solely on the basis of the student’s future earnings potential, cannot be discharged by recent graduates who then pocket all of the future benefits derived from their education. See [Citation].
The debtor bears the burden of proving by a preponderance of the evidence that she is entitled to a discharge of the student loan. See [Citation]. That is, the debtor must prove that repayment of student loans will cause an undue hardship.
The Bankruptcy Code does not define “the undue hardship.” Courts interpreting section 523(a)(8), however, have concluded that undue hardship [and] is something more than “garden-variety hardship.” [Citation.] Only cases involving “real and substantial” hardship merit discharges. See [Citation.]
The Ninth Circuit has adopted a three-part test to guide courts in their attempts to determine whether a debtor will suffer an undue hardship is required to repay a student loan:
- First, the debtor must establish “that she cannot maintain, based on current income and expenses, a ‘minimal’ standard of living for herself and her dependents if forced to repay the loans.”…
- Second, the debtor must show “that additional circumstances exist indicating that this state of affairs is likely to persist for a significant portion of the repayment period of the student loans.”…
- The third prong requires “that the debtor has made good faith efforts to repay the loans.…”
( Pena, citing Brunner v. N.Y. State Higher Educ. Servs. Corp ., [Citation]).
Debtor must satisfy all three parts of the Brunner test before her student loans can be discharged. Failure to prove any of the three prongs will defeat a debtor’s case.
When this bankruptcy case was filed in September 2005, the debtor was a single woman and had no dependents.
Schedule I reported that the debtor was unemployed. The debtor’s responses to the Statement of Financial Affairs revealed that she had received $5,500 in income during 2005 prior to the filing of the petition. Evidence at trial indicated that after the petition was filed, the debtor found work and earned a total of $9,424 in 2005. In 2004 and 2003, she earned $13,994 and $17,339, respectively.
Despite this modest income, the debtor did not immediately file an adversary proceeding to determine the dischargeability of her student loans. It was almost three years after the entry of her chapter 7 discharge ‘on January 3, 2006 that the debtor reopened her chapter 7 case in order to pursue this adversary proceeding.’
In her complaint, the debtor admits that after she received a discharge, she found part-time work with a church and later took a full-time job as a speech therapist. During 2006, the debtor earned $20,009 and in 2007 she earned $37,314. Hence, while it is clear the debtor’s income was very modest in the time period immediately prior to her bankruptcy petition, her financial situation improved during her bankruptcy case.
The court cannot conclude based on the evidence of the debtor’s financial circumstances up to the date of the discharge, that she was unable to maintain a minimal standard of living if she was required to repay her students [sic] loans.
However, in January 2007, the debtor was injured in an automobile accident. Her injuries eventually halted the financial progress she had been making and eventually prevented her from working. She now subsists on social security disability payments.
The circumstance creating the debtor’s hardship, the automobile accident, occurred after her chapter 7 petition was filed, indeed, approximately one year after her discharge was entered. The debtor is maintaining that this post-petition, post-discharge circumstance warrants a declaration that her student loans were discharged effective from the petition date.
When must the circumstances creating a debtor’s hardship arise: before the bankruptcy case is filed; after the case if filed but prior to the entry of a discharge; or at anytime, including after the entry of a discharge?
The court concludes that the circumstances causing a chapter 7 debtor’s financial hardship must arise prior to the entry of the discharge. If the circumstances causing a debtor’s hardship arise after the entry of a discharge, those circumstances cannot form the basis of a determination that repayment of a student loan will be an undue hardship.…
[T]here is nothing in the Bankruptcy Code requiring that a complaint under section 523(a)(8) [to discharge student loans] be filed at any particular point in a bankruptcy case, whether it is filed under chapter 7 or 13. [Relevant Federal Rules of Bankruptcy Procedure] permits such dischargeability complaints to be brought at any time, including after the entry of a discharge and the closing of the bankruptcy case.…
While a debtor’s decision to file an action to determine the dischargeability of a student loan is not temporally constrained, this does not mean that a debtor’s financial hardship may arise after a discharge has been entered.
[The] Coleman [case, cited by debtor] deals with the ripeness of a dispute concerning the dischargeability of a student loan. [The Ninth Circuit held that it] is ripe for adjudication at any point during the case. The Ninth Circuit did not conclude, however, that a debtor could rely upon post-discharge circumstances to establish undue hardship. In fact, the court in Coleman made clear that the debtor could take a snapshot of the hardship warranting a discharge of a student loan any time prior to discharge. [ Coleman was a Chapter 13 case.]
Here, the debtor was injured in an automobile accident on January 17, 2007, almost exactly one year after her January 3, 2006 chapter 7 discharge. Because the accident had no causal link to the misfortune prompting the debtor to seek bankruptcy relief in the first instance, the accident cannot be relied on to justify the discharge of the student loans because repayment would be an undue hardship.
To hold otherwise would mean that a bankruptcy discharge is a perpetual license to discharge student loans based on events that occur years after the bankruptcy discharge is granted. If a discharged debtor suffers later financial misfortune, that debtor must consider seeking another discharge subject to the limitations imposed by [the sections of the code stipulating how often a person can petition for bankruptcy]. In the context of a second case, the debtor could then ask that the student loan be declared dischargeable under section 523(a)(8).
In this instance, the debtor is now eligible for a discharge in a chapter 13 case. Her chapter 7 petition was filed on September 19, 2005. Section 1328(f)(1) bars a chapter 13 discharge when the debtor has received a chapter 7 discharge in a case commenced in the prior four years. She would not be eligible for a chapter 7 discharge until September 19, 2013.
This is not to say that post-discharge events are irrelevant. The second and third prongs of the Pena test require the court to consider whether the circumstances preventing a debtor from repaying a student loan are likely to persist, and whether the debtor has made good faith efforts to repay the student loan. Post-discharge events are relevant to these determinations because they require the court to look into the debtor’s financial future.
Unfortunately for the debtor, it is unnecessary to consider the second and third prongs because she cannot satisfy the first prong.
Case Questions
- What is the rationale for making the bankruptcy discharge of student loans very difficult?
- Petitioner argued that she should be able to use a postdischarge event (the auto accident) as a basis for establishing that she could not maintain a “minimal” standard of living, and thus she should get a retroactive discharge of her student loans. What benefit is there to her if she could successfully make the argument, given that she could—as the court noted—file for Chapter 13?
- The court cites the Coleman case. That was a Chapter 13 proceeding. Here were the facts: Debtor had not yet completed her payments under her five-year repayment plan, and no discharge order had yet been entered; one year into the plan, she was laid off work. She had been trying to repay her student loans for several years, and she claimed she would suffer hardship in committing to the five-year repayment plan without any guarantee that her student loan obligations would be discharged, since she was required to commit all of her disposable income to payments under the plan and would likely be forced to pursue undue hardship issue pro se upon completion of the plan.” In Coleman, the court held that Debtor could, postfiling but predischarge—one year into the five-year plan—bring up the hardship issue.Now, in the case here, after the auto accident, the petitioner “subsists” on Social Security disability payments, and she has almost $150,000 in debt, yet the court prohibited her from claiming a hardship discharge of student loans. Does this result really make sense? Is the court’s concern that allowing this postdischarge relief would mean “that a bankruptcy discharge is a perpetual license to discharge student loans based on events that occur years after the bankruptcy discharge is granted” well founded? Suppose it is scheduled to take thirty years to pay off student loans; in year 4, the student-borrower, now Debtor, declares Chapter 7 bankruptcy, student loans not being discharged; in year 6, the person is rendered disabled. What public policy is offended if the person is allowed to “reopen” the bankruptcy and use the postbankruptcy event as a basis for claiming a hardship discharge of student loans?
- The court suggests she file for Chapter 13. What if—because of timing—the petitioner was not eligible for Chapter 13? What would happen then?
Chapter 11 Bankruptcy
In re Johns-Manville Corp.
36 B.R. 727 (Bkrtcy. N.Y. 1984)
Lifland, Bankruptcy Judge.
Whether an industrial enterprise in the United States is highly successful is often gauged by its “membership” in what has come to be known as the “Fortune 500”. Having attained this measure of financial achievement, Johns-Manville Corp. and its affiliated companies (collectively referred to as “Manville”) were deemed a paradigm of success in corporate America by the financial community. Thus, Manville’s filing for protection under Chapter 11 of Title 11 of the United States Code (“the Code or the Bankruptcy Code”) on August 26, 1982 (“the filing date”) was greeted with great surprise and consternation on the part of some of its creditors and other corporations that were being sued along with Manville for injuries caused by asbestos exposure. As discussed at length herein, Manville submits that the sole factor necessitating its filing is the mammoth problem of uncontrolled proliferation of asbestos health suits brought against it because of its substantial use for many years of products containing asbestos which injured those who came into contact with the dust of this lethal substance. According to Manville, this current problem of approximately 16,000 lawsuits pending as of the filing date is compounded by the crushing economic burden to be suffered by Manville over the next 20–30 years by the filing of an even more staggering number of suits by those who had been exposed but who will not manifest the asbestos-related diseases until some time during this future period (“the future asbestos claimants”). Indeed, approximately 6,000 asbestos health claims are estimated to have arisen in only the first 16 months since the filing date. This burden is further compounded by the insurance industry’s general disavowal of liability to Manville on policies written for this very purpose.
It is the propriety of the filing by Manville which is the subject of the instant decision. Four separate motions to dismiss the petition pursuant to Section 1112(b) of the Code have been lodged before this Court.…
Preliminarily, it must be stated that there is no question that Manville is eligible to be a debtor under the Code’s statutory requirements. Moreover, it should also be noted that neither Section 109 nor any other provision relating to voluntary petitions by companies contains any insolvency requirement.…Accordingly, it is abundantly clear that Manville has met all of the threshold eligibility requirements for filing a voluntary petition under the Code.…
A “principal goal” of the Bankruptcy Code is to provide “open access” to the “bankruptcy process.” [Citation.] The rationale behind this “open access” policy is to provide access to bankruptcy relief which is as “open” as “access to the credit economy.” Thus, Congress intended that “there should be no legal barrier to voluntary petitions.” Another major goal of the Code, that of “rehabilitation of debtors,” requires that relief for debtors must be “timely.” Congress declared that it is essential to both the “open access” and “rehabilitation” goals that
[i]nitiating relief should not be a death knell. The process should encourage resort to it, by debtors and creditors, that cuts short the dissipation of assets and the accumulation of debts. Belated commencement of a case may kill an opportunity for reorganization or arrangement.
Accordingly, the drafters of the Code envisioned that a financially beleaguered debtor with real debt and real creditors should not be required to wait until the economic situation is beyond repair in order to file a reorganization petition. The “Congressional purpose” in enacting the Code was to encourage resort to the bankruptcy process. This philosophy not only comports with the elimination of an insolvency requirement, but also is a corollary of the key aim of Chapter 11 of the Code, that of avoidance of liquidation. The drafters of the Code announced this goal, declaring that reorganization is more efficient than liquidation because “assets that are used for production in the industry for which they were designed are more valuable than those same assets sold for scrap.” [Citation.] Moreover, reorganization also fosters the goals of preservation of jobs in the threatened entity. [Citation.]
In the instant case, not only would liquidation be wasteful and inefficient in destroying the utility of valuable assets of the companies as well as jobs, but, more importantly, liquidation would preclude just compensation of some present asbestos victims and all future asbestos claimants. This unassailable reality represents all the more reason for this Court to adhere to this basic potential liquidation avoidance aim of Chapter 11 and deny the motions to dismiss. Manville must not be required to wait until its economic picture has deteriorated beyond salvation to file for reorganization.
Clearly, none of the justifications for declaring an abuse of the jurisdiction of the bankruptcy court announced by these courts [in various cases cited] are present in the Manville case. In Manville, it is undeniable that there has been no sham or hoax perpetrated on the Court in that Manville is a real business with real creditors in pressing need of economic reorganization. Indeed, the Asbestos Committee has belied its own contention that Manville has no debt and no real creditors by quantifying a benchmark settlement demand approaching one billion dollars for compensation of approximately 15,500 pre-petition asbestos claimants, during the course of negotiations pitched toward achieving a consensual plan. This huge asserted liability does not even take into account the estimated 6,000 new asbestos health claims which have arisen in only the first 16 months since the filing date. The number of post-filing claims increases each day as “future claims back into the present.” …
In short, Manville’s filing did not in the appropriate sense abuse the jurisdiction of this Court and it is indeed, like the debtor in [Citation], a “once viable business supporting employees and unsecured creditors [that] has more recently been burdened with judgments [and suits] that threaten to put it out of existence.” Thus, its petition must be sustained.…
In sum, Manville is a financially besieged enterprise in desperate need of reorganization of its crushing real debt, both present and future. The reorganization provisions of the Code were drafted with the aim of liquidation avoidance by great access to Chapter 11. Accordingly, Manville’s filing does not abuse the jurisdictional integrity of this Court, but rather presents the same kinds of reasons that were present in [Citation] , for awaiting the determination of Manville’s good faith until it is considered…as a prerequisite to confirmation or as a part of the cadre of motions before me which are scheduled to be heard subsequently.
[A]ll four of the motions to dismiss the Manville petition are denied in their entirety.
Case Questions
- What did Manville want to do here, and why?
- How does this case demonstrate the fundamental purpose of Chapter 11 as opposed to Chapter 7 filings?
- The historical background here is that Manville knew from at least 1930 that asbestos—used in many industrial applications—was a deadly carcinogen, and it worked diligently for decades to conceal and obfuscate the fact. What “good faith” argument was raised by the movants in this case?
Chapter 13: What Debts Are Dischargeable?
In re Ryan
389 B.R. 710 9th Cir. BAP, (Idaho, 2008)
On July 13, 1995, Ryan was convicted of possession of an unregistered firearm under 26 U.S.C. § 5861(d) in the United States District Court for the District of Alaska. Ryan was sentenced to fifty-seven months in prison followed by three years of supervised release. In addition, Ryan was ordered to pay a fine of $7,500…, costs of prosecution in the amount of $83,420, and a special assessment of $50.00. Ryan served his sentence. He also paid the $7,500 fine. The district court, following an appellate mandate, ultimately eliminated the restitution obligation.
On April 25, 2003, Ryan filed a petition for bankruptcy relief under chapter 7 in the District of Idaho. He received his chapter 7 discharge on August 11, 2003. Shortly thereafter, Ryan filed a case under chapter 13, listing as his only obligation the amount of unpaid costs of prosecution owed to the United States (“Government”).…
Ryan completed payments under the plan, and an “Order of Discharge” was entered on October 5, 2006. The chapter 13 trustee’s final report reflected that the Government received $2,774.89 from payments made by Ryan under his plan, but a balance of $77,088.34 on the Government’s costs of prosecution claim remained unpaid. Ryan then renewed his request for determination of dischargeability. The bankruptcy court held that the unpaid portion of the Government’s claim for costs of prosecution was excepted from discharge by § 1328(a)(3). Ryan appealed.
Section 1328(a)(3) provides an exception to discharge in chapter 13 for “restitution, or a criminal fine.” It states, in pertinent part:
[A]s soon as practicable after the completion by the debtor of all payments under the plan, the court shall grant the debtor a discharge of all debts provided for by the plan or disallowed under section 502 of this title except any debt…
(3) for restitution, or a criminal fine, included in a sentence on the debtor’s conviction of a crime [.] [emphasis added].
The essential question, then, is whether these costs of prosecution constitute a “criminal fine.”
Statutory interpretation begins with a review of the particular language used by Congress in the relevant version of the law. [Citation.]
The term “criminal fine” is not defined in [Chapter 13] or anywhere else in the Bankruptcy Code. However, its use in § 1328(a)(3) implicates two important policies embedded in the Bankruptcy Code. First, in light of the objective to provide a fresh start for debtors overburdened by debts that they cannot pay, exceptions to discharge are interpreted strictly against objecting creditors and in favor of debtors. See, e.g. [Citations]. In chapter 13, this principle is particularly important because Congress adopted the liberal “superdischarge” provisions of § 1328 as an incentive to debtors to commit to a plan to pay their creditors all of their disposable income over a period of years rather than simply discharging their debts in a chapter 7 liquidation.
“[T]he dischargeability of debts in chapter 13 that are not dischargeable in chapter 7 represents a policy judgment that [it] is preferable for debtors to attempt to pay such debts to the best of their abilities over three years rather than for those debtors to have those debts hanging over their heads indefinitely, perhaps for the rest of their lives.” [Citations.]
A second, countervailing policy consideration is a historic deference, both in the Bankruptcy Code and in the administration of prior bankruptcy law, to excepting criminal sanctions from discharge in bankruptcy. Application of this policy is consistent with a general recognition that, “[t]he principal purpose of the Bankruptcy Code is to grant a ‘fresh start’ to the ‘ honest but unfortunate debtor.’” [Citation] (emphasis added [in original]).
The legislative history is clear that [in its 1994 amendments to the bankruptcy law] Congress intended to overrule the result in [of a 1990 Supreme Court case so that]:…“[N]o debtor with criminal restitution obligations will be able to discharge them through any bankruptcy proceeding.”…
The imposition on a defendant of the costs of a special prosecutor is different from ordering a defendant to pay criminal fines. Costs are paid to the entity incurring the costs; criminal fines are generally paid to a special fund for victims’ compensation and assistance in the U.S. Treasury.…
To honor the principle that exceptions to discharge are to be construed narrowly in favor of debtors, particularly in chapter 13, where a broad discharge was provided by Congress as an incentive for debtors to opt for relief under that chapter rather than under chapter 7, it is not appropriate to expand the scope of the [Chapter 13] exception beyond the terms of the statute. Congress could have adopted an exception to discharge in chapter 13 that mirrored [the one in Chapter 7]. It did not do so. In contrast, under [the 2005] BAPCPA, when Congress wanted to limit the chapter 13 “superdischarge,” it incorporated exceptions to discharge from [Chapter 7] wholesale.…
As a bottom line matter, Ryan served his time and paid in full the criminal fine that was imposed as part of his sentence for conviction of possession of an unregistered firearm. The restitution obligation that was included as part of his sentence was voided. Ryan paid the Government a total of $6,331.66 to be applied to the costs of prosecution awarded as part of his criminal judgment, including $2,774.89 paid under his chapter 13 plan, leaving a balance of $77,088.34. We determine that the unpaid balance of the costs of prosecution award was covered by Ryan’s chapter 13 discharge.
Based on the foregoing analysis, we conclude that the exception to discharge included in [Chapter 13] for “restitution, or a criminal fine, included in a sentence on the debtor’s conviction of a crime” does not cover costs of prosecution included in such a sentence, and we REVERSE.
Case Questions
- What is the rationale for making some things dischargeable under Chapter 13 that are not dischargeable under Chapter 7?
- What is the difference between “criminal restitution” (which in 1994 Congress said could not get discharged at all) and “the costs of prosecution”?
- Why did the court decide that Ryan’s obligation to pay “costs of prosecution” was not precluded by the limits on Chapter 13 bankruptcies imposed by Congress?


6.1: The Fundamental Theorem of Arithmetic
In the last few chapters, we have encountered all of the major proof techniques one needs in mathematics and enhanced our proof-writing skills. In this chapter, we put these techniques and skills to work to prove three famous theorems, as well as numerous intermediate results along the way. All of these theorems are ones you are likely familiar with from grade school, but perhaps these facts were never rigorously justified for you.
In the first section, we develop all of the concepts necessary to state and then prove the Fundamental Theorem of Arithmetic (Theorem 6.17), which you may not recognize by name. The Fundamental Theorem of Arithmetic states that every natural number greater than 1 is the product of a unique combination of prime numbers. To prove the Fundamental Theorem of Arithmetic, we will need to make use of the Division Algorithm (Theorem 6.7), which in turn utilizes the Well-Ordering Principle (Theorem 4.38). In the second section, we prove that √ 2 is irrational, which settles a claim made in Section 5.1. In the final section, we prove that there are infinitely many primes.
The goal of this section is to prove The Fundamental Theorem of Arithmetic. The Fundamental Theorem of Arithmetic (sometimes called the Unique Factorization Theorem) states that every natural number greater than 1 is either prime or is the product of prime numbers, where this product is unique up to the order of the factors. For example, the natural number 12 has prime factorization \(2^2\cdot 3\) , where the order in which we write the prime factors (i.e., 2, 2, and 3) is irrelevant. That is, \(2^2\cdot 3\) , \(2\cdot 3\cdot2\) , and \(3\cdot 2^2\) are all the same prime factorization of 12. The requirement that the factors be prime is necessary since factorizations containing composite numbers may not be unique. For example, \(12=2\cdot 6\) and \(12=3\cdot 4\) , but these factorizations into composite numbers are distinct. We have just thrown around a few fancy terms; we should make sure we understand their precise meaning.
Definition 6.1. Let \(n\in\mathbb{Z}\) .
- If \(a\in \mathbb{Z}\) such that \(a\) divides \(n\) , then we say that \(a\) is a factor of \(n\) .
- If \(n\in \mathbb{N}\) such that \(n\) has exactly two distinct positive factors (namely, 1 and \(n\) itself), then \(n\) is called prime .
- If \(n>1\) such that \(n\) is not prime, then \(n\) is called composite .
Problem 6.2. According to our definition, is 1 a prime number or composite number? Explain your answer. You may have heard prime numbers defined as something like, “a prime number is a natural number that is only divisible by 1 and itself." Does this definition agree with the one above?
The upshot is that according to our definition, 1 is neither prime nor composite. However, throughout history, this has not always been the case. There were times when and mathematicians for whom the number one was considered prime. Whether 1 is prime or not is a matter of definition, and hence a matter of choice. There are compelling reasons—that we will not elaborate on here—why 1 is intentionally excluded from being prime. However, if you would like to learn more, check out the excellent article “What is the Smallest Prime?" by Chris Caldwell and Yeng Xiong.
Problem 6.3. List the first 10 prime numbers.
Problem 6.4. Prove or provide a counterexample: For all \(n\in\mathbb{N}\) , if \(4^n-1\) is prime, then \(n\) is odd.
Problem 6.5. Prove or provide a counterexample: For all \(n\in\mathbb{N}\) , \(n^2-n+11\) is prime.
The next result makes up half of the Fundamental Theorem of Arithmetic. We provide a substantial hint for its proof. Let \(S\) be the set of natural numbers for which the theorem fails. For sake of a contradiction, assume \(S\neq \emptyset\) . By the Well-Ordering Principle (Theorem 4.38), \(S\) contains a least element, say \(n\) . Then \(n\) cannot be prime since this would satisfy the theorem. So, it must be the case that \(n\) has a divisor other than 1 and itself. This implies that there exists natural numbers \(a\) and \(b\) greater than 1 such that \(n=ab\) . Since \(n\) was our smallest counterexample, what can you conclude about both \(a\) and \(b\) ? Use this information to derive a counterexample for \(n\) .
Theorem 6.6. If \(n\) is a natural number greater than 1, then \(n\) can be expressed as a product of primes. That is, we can write \[n=p_1 p_2 \cdots p_k,\] where each of \(p_1, p_2, \ldots, p_k\) is a prime number (not necessarily distinct).
Theorem 6.6 states that we can write every natural number greater than 1 as a product of primes, but it does not say that the primes and the number of times each prime appears are unique. To prove uniqueness, we will need Euclid’s Lemma (Theorem 6.15). To prove Euclid’s Lemma, we will utilize a special case of Bézout’s Lemma (Theorem 6.13), the proof of which relies on the following result, known as the Division Algorithm. We include the proof of the Division Algorithm below, which makes use of the Well-Ordering Principle (Theorem 4.38).
Theorem 6.7. If \(n,d\in\mathbb{Z}\) such that \(d>0\) , then there exists unique \(q,r\in\mathbb{Z}\) such that \(n=dq+r\) with \(0\leq r<d\) .
Let \(n,d\in\mathbb{Z}\) such that \(d>0\) such that \(n>0\) . We have two tasks. First, we need to show that \(q\) and \(r\) exist, and then we need to show that both are unique.
If \(d=1\) , it is clear that we can take \(q=n\) and \(r=0\) , so that \(n=1\cdot n+0=dq+r\) , as desired. Now, assume that \(d>1\) and define \[S:= \{n-dk\mid k\in\mathbb{Z}\text{ and } n-dk\geq 0\}.\] If we can show that \(S\neq\emptyset\) , then we can apply the Well-Ordering Principle (Theorem 4.38) to conclude that \(S\) has a least element of S. This least element will be the remainder \(r\) we are looking for. There are two cases.
First, suppose \(n\geq 0\) . If we take \(k=0\) , then we get \(n-dk=n-d\cdot 0=n\geq 0\) , which shows that \(n\in S\) .
Now, suppose \(n<0\) . In this case, we can take \(k=n\) , so that \(n-dk=n-dn=n(1-d)\) . Since \(n<0\) and \(d>1\) , \(n(1-d)>0\) . This shows that \(n-dn\in S\) .
We have shown that \(S\neq\emptyset\) , and so \(S\) contains a least element \(r=n-dq\) for some \(q\in\mathbb{Z}\) . Then \(n=dq+r\) with \(r\geq 0\) . For sake of a contradiction, assume \(r\geq d\) . This implies that there exists \(r'\in \mathbb{Z}\) such that \(r=d+r'\) and \(0\leq r'<r\) . But then we see that \[n=dq+r=dq+d+r'=d(q+1)+r'.\] This implies that \(r' = n-d(q+1)\) . Since \(0\leq r'<r\) , we have produced an element of \(S\) that is smaller than \(r\) . This contradicts the fact that \(r\) is the least element of \(S\) , and so \(r<d\) .
It remains to show that \(q\) and \(r\) are unique. Suppose \(q_1,q_2, r_1,r_2\in\mathbb{Z}\) such that \(n=dq_1+r_1\) and \(n=dq_2+r_2\) and \(0\leq r_1,r_2<d\) . Without loss of generality, suppose \(r_2\geq r_1\) , so that \(0\leq r_2-r_1<d\) . Since \(dq_1+r_1=dq_2+r_2\) , we see that \(r_2-r_1=d(q_1-q_2)\) . But then \(d\) divides \(r_2-r_1\) . If \(r_2-r_1>0\) , then by Theorem 2.56, it must be the case that \(r_2-r_1\geq d\) . However, we know \(0\leq r_2-r_1<d\) , and so we must have \(r_2-r_1=0\) . Therefore, \(r_1=r_2\) , which in turn implies \(q_1=q_2\) . We have shown that \(q\) and \(r\) are unique.
In the Division Algorithm, we call \(n\) the dividend , \(d\) the divisor , \(q\) the quotient , and \(r\) the remainder . It is worth pointing out that the Division Algorithm holds more generally where the divisor \(d\) is not required to be positive. In this case, we must replace \(0\leq r<n\) with \(0\leq r<|n|\) .
Contrary to its name, our statement of the Division Algorithm is not actually an algorithm, but this is the theorem’s traditional name. However, there is an algorithm buried in this theorem. If \(n\) is nonnegative, repeatedly subtract \(d\) from \(n\) until we obtain an integer value that lies between 0 (inclusive) and \(d\) (exclusive). The resulting value is the remainder \(r\) while the number of times that \(d\) is subtracted is the quotient \(q\) . On the other hand, if \(n\) is negative, repeatedly add \(d\) to \(n\) until we obtain an integer value that lies between 0 (inclusive) and \(d\) (exclusive). Again, the resulting value is \(r\) . However, in this case, we take \(-q\) to be the number of times that \(d\) is added, so that \(q\) (a negative value) is the quotient.
Problem 6.8. Suppose \(n=27\) and \(d=5\) . Find the quotient and remainder that are guaranteed to exist by the Division Algorithm. That is, find the unique \(q,r\in\mathbb{Z}\) such that \(0\leq r<n\) and \(n=dq+r\) .
It is a little trickier to determine \(q\) and \(r\) when \(n\) is negative.
Problem 6.9. Suppose \(n=-26\) and \(d=3\) . Find the quotient and remainder that are guaranteed to exist by the Division Algorithm. That is, find the unique \(q,r\in\mathbb{Z}\) such that \(0\leq r<n\) and \(n=dq+r\) .
It is useful to have some additional terminology.
Definition 6.10. Let \(m,n\in\mathbb{Z}\) such that at least one of \(m\) or \(n\) is nonzero. The greatest common divisor (gcd) of \(m\) and \(n\) , denoted \(\gcd(m,n)\) , is the largest positive integer that divides both \(m\) and \(n\) . If \(\gcd(m,n)=1\) , we say that \(m\) and \(n\) are relatively prime .
Problem 6.11. Find \(\gcd(54,72)\) .
Problem 6.12. Provide an example of two natural numbers that are relatively prime.
The next result is a special case of a theorem known as Bézout’s Lemma (or Bézout’s Identity). Ultimately, we will need this theorem to prove Euclid’s Lemma (Theorem 6.15), which we then use to prove uniqueness for the Fundamental Theorem of Arithmetic (Theorem 6.17). To prove our special case of Bézout’s Lemma, consider the set \(S:= \{ps+at> 0\mid s,t\in \mathbb{Z}\}\) . First, observe that \(p\in S\) (choose \(s=1\) and \(t=0\) ). It follows that \(S\) is nonempty. By the Well-Ordering Principle (Theorem 4.38), \(S\) contains a least element, say \(d\) . This implies that there exists \(s_1,t_1\in \mathbb{Z}\) such that \(d=ps_1+at_1\) . Our goal is to show that \(d=1\) . Now, choose \(m\in S\) . Then there exists \(s_2,t_2\in \mathbb{Z}\) such that \(m=ps_2+at_2\) . By the definition of \(d\) , we know \(d\leq m\) . By the Division Algorithm, there exists unique \(q,r\in \mathbb{N}\cup\{0\}\) such that \(m=qd+r\) with \(0\leq r < d\) . Now, solve for \(r\) and then replace \(m\) and \(d\) with \(ps_1+at_1\) and \(ps_2+at_2\) , respectively. You should end up with an expression for \(r\) involving \(p, a, s_1, s_2, t_1\) , and \(t_2\) . Next, rearrange this expression to obtain \(r\) as a linear combination of \(p\) and \(a\) (i.e., a sum of a multiple of \(p\) and a multiple of \(a\) ). What does the minimality of \(d\) imply about \(r\) ? You should be able to conclude that \(m\) is a multiple of \(d\) . That is, every element of \(S\) is a multiple of \(d\) . However, recall that \(p\in S\) , \(p\) is prime, and \(p\) and \(a\) are relatively prime. What can you conclude about \(d\) ?
Theorem 6.13. If \(p,a\in\mathbb{Z}\) such that \(p\) is prime and \(p\) and \(a\) are relatively prime, then there exists \(s,t\in\mathbb{Z}\) such that \(ps+at=1\) .
Problem 6.14. Consider the natural numbers 2 and 7, which happen to be relatively prime. Find integers \(s\) and \(t\) guaranteed to exist according to Theorem 6.13. That is, find \(s,t\in\mathbb{Z}\) such that \(2s+7t=1\) .
The following theorem is known as Euclid’s Lemma. Note that if \(p\) divides \(a\) , the conclusion is certainly true. So, assume otherwise. That is, assume that \(p\) does not divide \(a\) , so that \(p\) and \(a\) are relatively prime. Apply Theorem 6.13 to \(p\) and \(a\) and then multiply the resulting equation by \(b\) . Try to conclude that \(p\) divides \(b\) .
Theorem 6.15. Assume that \(p\) is prime. If \(p\) divides \(ab\) , where \(a,b\in\mathbb{N}\) , then either \(p\) divides \(a\) or \(p\) divides \(b\) .
In Euclid’s Lemma, it is crucial that \(p\) is prime as illustrated by the next problem.
Problem 6.16. Provide an example of integers \(a, b, d\) such that \(d\) divides \(ab\) yet \(d\) does not divide \(a\) and \(d\) does not divide \(b\) .
Alright, we are finally ready to tackle the proof of the Fundamental Theorem of Arithmetic. Let \(n\) be a natural number greater than 1. By Theorem 6.6, we know that \(n\) can be expressed as a product of primes. All that remains is to prove that this product is unique (up to the order in which they appear). For sake of a contradiction, suppose \(p_1 p_2 \cdots p_k\) and \(q_1 q_2 \cdots q_l\) are both prime factorizations of \(n\) . Your goal is to prove that \(k=l\) and that each \(p_i\) is equal to some \(q_j\) . Make repeated use of Euclid’s Lemma.
Theorem 6.17. Every natural number greater than 1 can be expressed uniquely (up to the order in which they appear) as the product of one or more primes.
The Fundamental Theorem of Arithmetic is one of the many reasons why 1 is not considered a prime number. If 1 were prime, prime factorizations would not be unique.


24.4: Summary
24.1 Cardiovascular System
The cardiovascular system is essential for maintaining continuous blood circulation and oxygen and nutrient delivery throughout the body. This intricate network of the heart, blood vessels, and blood works interdependently with other organ systems, such as the respiratory and immune systems, to sustain homeostasis . Nurses, pivotal in identifying and addressing cardiovascular issues such as hypertension and arrhythmias, must comprehend the dynamics of heart structures, assess cardiac function accurately, and intervene effectively. The myocardium’s intricate muscle pattern, particularly in the left ventricle, plays a critical role in efficient pumping of blood to ensure all tissues and cells receive adequate supplies of oxygen and nutrients. Understanding the cardiac cycle and how blood flows through various vessels is integral to understanding cardiac physiology and therefore promoting optimal cardiovascular health. Nurses must be prepared to identify and understand the ECG abnormalities that may herald a variety of cardiovascular abnormalities.
24.2 Peripheral Vascular System
The peripheral vascular system consists of arteries, veins, and capillaries. This system is responsible for the transportation of oxygen, nutrients, and waste products throughout the body, which is integral to maintaining homeostasis and overall health. Nursing professionals need a comprehensive understanding of this complex network of structures for effective assessment, diagnosis, and management of various health conditions, ranging from peripheral artery disease to venous insufficiency .
Nurses must understand the functions performed by the peripheral vascular system. This allows the nurse to effectively identify early signs of vascular dysfunction and implement interventions to resolve problems. Arteries, responsible for transporting oxygenated blood away from the heart, exhibit elasticity and respond to signals for dilation or constriction, affecting blood pressure regulation. Arterioles branch from arteries and respond to the sympathetic nervous system and hormones. Veins have thinner walls and rely on muscle contraction to return deoxygenated blood to the heart.
Abnormalities in the PVS can be occlusive or functional in nature. Characteristics of arterial and venous insufficiency result in insufficient blood supply, leading to symptoms such as intermittent claudication and critical limb ischemia . Other symptoms of PVD include edema, pain and cramping, temperature changes, and skin changes. Understanding these aspects is crucial for accurate diagnosis and effective nursing care in individuals with peripheral vascular disorders.
24.3 Nursing Assessment
Assessing the cardiovascular and peripheral vascular systems for potential CVD, heart disease, and stroke is a critical component of the nursing evaluation. Nurses should collect both subjective data (from the patient) and objective findings (from the examination) to create a thorough, well-planned nursing care plan. Subjective data include the patient’s medical and surgical history, social history, cardiac risk factors, symptoms, medications and other therapies, and family history to determine the potential causes and effects of CVD. Objective findings include the results of the physical examination, laboratory tests, and imaging studies. Nurses should ask clear and inquiry-based questions to clarify the patient’s condition and identify any signs of dysfunction. Nurses should also follow the PQRSTU model to assess chest pain.
The various modifiable and nonmodifiable risk factors for CVD (e.g., smoking, blood pressure, cholesterol, obesity, diabetes, age, gender, genetics) should be identified and modifiable risks addressed. Validated risk assessment tools (e.g., BE-FAST, RACE, CPSS, LAMS, MEND) help nurses estimate the likelihood of stroke or heart attack and guide the treatment options. One or more of these risk assessment tools should be performed in patients who are exhibiting signs and symptoms of heart disease, stroke, and peripheral vascular disease and who have a family history of cardiovascular or peripheral vascular dysfunction.


21.4B: Lobes, Fissures, and Lobules
The lungs are located on either side of the heart and are separated by fissures into lobes, three in the right and two lobes in the left.
- Distinguish between the right and left lungs based on their lobes, fissures, and lobules
Key Points
- Human lungs are located in two cavities on either side of the heart and are separated into lobes by fissures.
- The two lungs are not identical. The right lung has three lobes and left has two lobes. They are further divided into segments and then into lobules.
- Lobules are hexagonal divisions of the lungs that are the smallest subdivision visible to the naked eye.
- The right lung is divided by the oblique fissure, which separates the inferior lobe from the middle and superior lobes, and the horizontal fissure, which separates the superior from the middle lobe.
- The human left lung is divided into two lobes, an upper and a lower, by the oblique fissure. It has a cardiac notch, a concave impression molded to accommodate the shape of the heart.
- The lingula is not technically a lobe, but is the left lung equivalent of the right lung’s middle lobe.
- The hilium is the root of the lung and contains the structures involved in pulmonary circulation, as well as the pulmonary nerves and lymph vessels.
Key Terms
- hilium : The root of the lung that contains the pulmonary veins and arteries that supply blood to the lungs.
- cardiac notch : A concave impression molded into the left lung to accommodate the shape of the heart.
The lungs are located in two chambers of the thoracic cavity on either side of the heart. Though similar in appearance, the two lungs are not identical, nor wholly symmetrical.
Fissures are double folds of pleura that divide the lung into lobes. There are three lobes in the right lung and two in the left lung. The lobes are further divided into segments and then into lobules, which are hexagonal divisions of the lungs that are the smallest visible subdivision.
The lobes are further divided into segments and then into lobules, hexagonal divisions of the lungs that are the smallest subdivision visible to the naked eye.
The Right Lung
The lobes of the lungs : The right lung has three lobes and the left lung has two. ( Copyright Public Domain)
The right lung is five centimeters shorter than the left lung to accommodate the diaphragm, which rises higher on the right side over the liver; it is also broader. The volume, the total capacity, and the weight of the right lung is greater than that of the left. The right lung is divided into three lobes.
The Upper Lobe (Right Lung)
The upper lobe is the largest lobe of the right lung. It extends from the apex of the lung down to the horizontal and oblique fissures. It bears apical, anterior, and posterior bronchopulmonary segments.
The Middle Lobe (Right Lung)
The middle lobe is the smallest lobe of the right lung, located between the horizontal and oblique fissures. It bears medial and lateral bronchopulmonary segments.
The Lower Lobe (Right Lung)
The lower lobe is the bottom lobe of the right lung. It lies beneath the oblique fissure. It bears medial, lateral, superior, anterior, and posterior bronchopulmonary segments.
The Left Lung
The Left Lung : This has a concave depression that accommodates the shape of the heart, called the cardiac notch.
The human left lung is smaller and narrower that the right lung, and is divided into two lobes, an upper and a lower, by the oblique fissure. The left lung has only two formal lobes because of the space taken up in the left side of the chest cavity by the heart, though it does have the lingula, which is similar to a lobe.
The left lung has a depression on the medial side of its surface called the cardiac notch, a concave impression molded to accommodate the shape of the heart.
The Upper Lobe (Left Lung)
The upper lobe of the left lung contains anterior and apicoposterior bronchopulmonary segments. It is above the oblique fissure.
The Lower Lobe (Left Lung)
The lower lobe of the left lung contains superior, anterior, posterior, medial, and lateral bronchopulmonary segments.
The Lingula
The lingula is not formally considered to be a lobe. It is a small, tongue-like projection of the left lung that is analogous to the middle lobe of the right lung. It contains superior and inferior bronchopulmonary segments.
The Hilium
Above and behind the cardiac impression is a triangular depression named the hilum. The hilum is the root of the lung where that contains structures that supply the lungs with blood, lymph fluid, and innervation, such as the pulmonary vein, pulmonary artery, pulmonary nerves, and lymphatic vessels.
These structures are enclosed by pleura. There is a hilium for each of the lungs found in the mediastinum (backside) of the lungs. The hilium is thinner in the left lung compared to the right lung because it lies between the cardiac notch and the groove for the aorta.
The hilium is important because it is the primary way in which the respiratory system links with the cardiovascular and nervous systems.


5.5: Types of Research Studies - Ecological and Case-Control Studies
The two general types of research studies are either observational or experimental. Observational studies come in many forms, but the researcher is always recording and analyzing information on the subjects - never interfering in any way. This differs from an experimental study, in which the researcher’s primary goal is to determine whether a specific intervention causes a measurable outcome or not. Observational studies include ecological, cross-sectional, case-control and cohort (or longitudinal) studies. Experimental studies are often referred to as clinical trials, or randomized controlled trials (RCTs).
Ecological studies are very basic statistical analyses of incidence or prevalence of some disease, risk factor or protective factor within a population or group. These types of studies are helpful in identifying a potentially vulnerable population, and/or the need for more research for particular risk factors. A hypothetical ecological study might find that counties with more office workers also had higher rates of back pain. We couldn’t conclude any causation from this type of study though. It could be that office work causes back pain, or it could be that people with back pain change careers so that they can work in an office, or it could be that office workers have better healthcare plans and therefore go to the doctor more often for musculoskeletal issues like back pain… there could be many indirect ways these two things are associated, or there could be no association at all. What if the people who had back pain aren’t also those who work in offices? Ecological studies are helpful at generating ideas for populations of interest or possible relationships between risks or protective factors and health outcomes. See Fig 5.2 for a diagram of ecological studies.
Cross-sectional studies are those that take a snapshot of a population at one point in time. This can be imagined similarly to a cross-sectional view of a limb in anatomy; it’s almost like you’re taking a “slice” of the population and looking at their current prevalence of specific risks or protective factors and health outcomes. A lot of times we may want to do a cross-sectional study to identify a specific need in a population. For example, we might do a cross-sectional study to identify how many office workers in a particular area currently have low back pain. Perhaps we survey these workers or offer a screening at each office location. The difference between an ecological study and a cross-sectional study is that the ecological studylooks at prevalence statistics in groups, whereas a cross-sectional study uses individual data - so in our own hypothetical example we can be sure whether it’s the office workers who have the low back pain. See Fig 5.3 for a diagram of cross-sectional studies.


1.6: Lifelong learning and professional development
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Teachers engage in the process of lifelong learning as a way to meet the needs of their students, respond to best practices in the literature and research and try to integrate the newly acquired approaches to support student learning. Some examples of lifelong learning, also known as professional development, may be attendance at a conference, mentoring (either as the mentee or mentor), joining a professional organization and conducting research. As an undergraduate student pursuing your Bachelors Degree in education you are immersed in a constant environment of learning.
New York state has teacher induction requirements for first-year teachers. As a first-year teacher in New York State, you will be assigned a mentor in your district who will serve to support and guide you through the challenges, questions, and joys that your first year of teaching will offer. Strong mentor-mentee programs increase the development of a new teacher’s connection to the school community and reduce isolations (NYSED, 2013).
Think it, Ink it (5 minutes) and divide into groups of 4-5 students and share your answers.
Report out to the class the results of the group’s conversation.
At some level reflection on practice is something you must do for yourself, since only you have had your particular teaching experiences, and only you can choose how to interpret and make use of them. But this individual activity also may benefit from the stimulus and challenge offered by fellow professionals. Others’ ideas may differ from your own, and they can, therefore, help in working out your own thoughts and in alerting you to ideas that you may otherwise take for granted. These benefits of reflection can happen in any number of ways, but most fall into one of four general categories:
Many teacher education preparation programs follow the INTASC Standards developed by the Council of Chief State School Officers. Standard nine outlines professional learning and ethical practice. Below you will find the exact excerpt from Standard 9. Notice Some of the relevant aspects are using data and evidence to support and evaluate classroom practices. Another key component to lifelong learning is engaging in ongoing reflective practice. Reflection is a hallmark of instructional leaders and assists teachers in meeting a diverse range of student needs.
The teacher engages in ongoing professional learning and uses evidence to continually evaluate his/her practice, particularly the effects of his/her choices and actions on others (learners, families, other professionals, and the community, and adapts practice to meet the needs of each learner.
9(a) The teacher engages in ongoing learning opportunities to develop knowledge and skills in order to provide all learners with engaging curriculum and learning experiences based on local and state standards.
9(b) The teacher engages in meaningful and appropriate professional learning experiences aligned with his/her own needs and the needs of the learners, school, and system.
9(c) Independently and in collaboration with colleagues, the teacher uses a variety of data (e.g., systematic observation, information about learners, research) to evaluate the outcomes of teaching and learning and to adapt planning and practice.
9(d) The teacher actively seeks professional, community, and technological resources, within and outside the school, as supports for analysis, reflection, and problem-solving.
9(e) The teacher reflects on his/her personal biases and accesses resources to deepen his/her own understanding of cultural, ethnic, gender, and learning differences to build stronger relationships and create more relevant learning experiences.
9(f) The teacher advocates, models, and teaches safe, legal, and ethical use of information and technology including appropriate documentation of sources and respect for others in the use of social media.
9(g) The teacher understands and knows how to use a variety of selfassessment and problem-solving strategies to analyze and refl ect on his/her practice and to plan for adaptations/adjustments.
9(h) The teacher knows how to use learner data to analyze practice and differentiate instruction accordingly.
9(i) The teacher understands how personal identity, worldview, and prior experience affect perceptions and expectations, and recognizes how they may bias behaviors and interactions with others.
9(j) The teacher understands laws related to learners’ rights and teacher responsibilities (e.g., for educational equity, appropriate education for learners with disabilities, confi dentiality, privacy, appropriate treatment of learners, reporting in situations related to possible child abuse).
9(k) The teacher knows how to build and implement a plan for professional growth directly aligned with his/her needs as a growing professional using feedback from teacher evaluations and observations, data on learner performance, and school- and systemwide priorities.
9(l) The teacher takes responsibility for student learning and uses ongoing analysis and refl ection to improve planning and practice.
9(m) The teacher is committed to deepening understanding of his/her own frames of reference (e.g., culture, gender, language, abilities, ways of knowing), the potential biases in these frames, and their impact on expectations for and relationships with learners and their families.
9(n) The teacher sees him/herself as a learner, continuously seeking opportunities to draw upon current education policy and research as sources of analysis and reflection to improve practice.
9(o) The teacher understands the expectations of the profession including codes of ethics, professional standards of practice, and relevant law and policy
Activity: How do you plan to integrate reflection into your practice as a teacher? How does reflection connect to teacher induction and mentor programs?
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12.1: Prelude - Sour Patch Kids and International Spy Movies
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Sour Patch Kids are a soft candy with a coating of invert sugar and sour sugar. Its slogan, "Sour. Sweet. Gone.", refers to the sour-to-sweet taste of the candy.
Sour sugar is a food ingredient that is used to impart a sour flavor, made from citric or tartaric acid and sugar. It is used to coat sour candies like Sour Patch Kids. Eating large amounts of sour sugar can cause irritation of the tongue because of the acid. It can also cause irreversible dental erosion.
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Describe temperament and the goodness-of-fit model
Use Erikson’s theory to characterize psychosocial development during infancy
Temperament
Perhaps you have spent time with a number of infants. How were they alike? How did they differ? Or compare yourself with your siblings or other children you have known well. You may have noticed that some seemed to be in a better mood than others and that some were more sensitive to noise or more easily distracted than others. These differences may be attributed to temperament.
Temperament
is an inborn quality noticeable soon after birth. Temperament is not the same as personality but may lead to personality differences. Generally, personality traits are learned, whereas temperament is genetic. Of course, for every trait, nature and nurture interact.
According to Chess and Thomas (1996), children vary on nine dimensions of temperament. These include activity level, regularity (or predictability), sensitivity thresholds, mood, persistence or distractibility, among others. These categories include the following:[foodnote]Thomas, A., & Chess, S. (1977). Temperament and development. New York: Brunner/Mazel[/footnote].
Activity level. Does the child display mostly active or inactive states?
Rhythmicity or Regularity. Is the child predictable or unpredictable regarding sleeping, eating, and elimination patterns?
Approach-Withdrawal. Does the child react or respond positively or negatively to a newly encountered situation?
Adaptability. Does the child adjust to unfamiliar circumstances easily or with difficulty
Responsiveness. Does it take a small or large amount of stimulation to elicit a response (e.g., laughter, fear, pain) from the child?
Reaction Intensity. Does the child show low or high energy when reacting to stimuli?
Mood Quality. Is the child normally happy and pleasant, or unhappy and unpleasant?
Distractibility. Is the child’s attention easily diverted from a task by external stimuli?
Persistence and Attention Span. Persistence – How long will the child continue at an activity despite difficulty or interruptions? Attention span – For how long a period of time can the child maintain interest in an activity?
The New York Longitudinal Study was a long term study of infants, on these dimensions, which began in the 1950s. Most children do not have their temperament clinically measured, but categories of temperament have been developed and are seen as useful in understanding and working with children. Based on this study, babies can be described according to one of several profiles: easy or flexible (40%), slow to warm up or cautious (15%), difficult or feisty (10%), and undifferentiated, or those who can’t easily be categorized (35%).
Easy babies (40% of infants) have a positive disposition. Their body functions operate regularly and they are adaptable. They are generally positive, showing curiosity about new situations and their emotions are moderate or low in intensity. Difficult babies (10% of infants) have more negative moods and are slow to adapt to new situations. When confronted with a new situation, they tend to withdraw. Slow-to-warm babies (15% of infants) are inactive, showing relatively calm reactions to their environment. Their moods are generally negative, and they withdraw from new situations, adapting slowly. The undifferentiated (35%) could not be consistently categorized. These children show a variety of combinations of characteristics. For example, an infant may have an overall positive mood but react negatively to new situations.
No single type of temperament is invariably good or bad, however, infants with difficult temperaments are more likely than other babies to develop emotional problems, especially if their mothers were depressed or anxious caregivers (Garthus-Niegel et al., 2017).
[1]
Children’s long-term adjustment actually depends on the
goodness-of-fit
of their particular temperament to the nature and demands of the environment in which they find themselves. Therefore, what appears to be more important than child temperament is how caregivers respond to it.
Think about how you might approach each type of child in order to improve your interactions with them. An easy or flexible child will not need much extra attention unless you want to find out whether they are having difficulties that have gone unmentioned. A slow to warm up child may need to be given advance warning if new people or situations are going to be introduced. A difficult or feisty child may need to be given extra time to burn off their energy. A caregiver’s ability to accurately read and work well with the child will enjoy this
goodness-of-fit,
meaning their styles match and communication and interaction can flow. The temperamentally active children can do well with parents who support their curiosity but could have problems in a more rigid family.
It is this goodness-of-fit between child temperament and parental demands and expectations that can cause struggles. Rather than believing that discipline alone will bring about improvements in children’s behavior, our knowledge of temperament may help a parent, teacher or other caregiver gain insight to work more effectively with a child. Viewing temperamental differences as varying styles that can be responded to accordingly, as opposed to ‘good’ or ‘bad’ behavior. For example, a persistent child may be difficult to distract from forbidden things such as electrical cords, but this persistence may serve her well in other areas such as problem-solving. Positive traits can be enhanced and negative traits can be subdued. The child’s style of reaction, however, is unlikely to change. Temperament doesn’t change dramatically as we grow up, but we may learn how to work around and manage our temperamental qualities. Temperament may be one of the things about us that stays the same throughout development.
Erikson maintained that the first year to year and a half of life involves the establishment of a sense of trust. Infants are dependent and must rely on others to meet their basic physical needs as well as their needs for stimulation and comfort. A caregiver who consistently meets these needs instills a sense of trust or the belief that the world is a safe and trustworthy place. The caregiver should not worry about overindulging a child’s need for comfort, contact, or stimulation.
Consider the implications for establishing trust if a caregiver is unavailable or is upset and ill-prepared to care for a child, or if a child is born prematurely, is unwanted, or has physical problems that could make them less desirable to a parent. However, keep in mind that children can also exhibit strong resiliency to harsh circumstances. Resiliency can be attributed to certain personality factors, such as an easy-going temperament and receiving support from others. A positive and strong support group can help a parent and child build a strong foundation by offering assistance and positive attitudes toward the newborn and parent.
Autonomy vs. shame and doubt
As the child begins to walk and talk, an interest in independence or autonomy replaces their concern for trust. The toddler tests the limits of what can be touched, said, and explored. Erikson believed that toddlers should be allowed to explore their environment as freely as safety allows and, in doing so, will develop a sense of independence that will later grow to self-esteem, initiative, and overall confidence. If a caregiver is overly anxious about the toddler’s actions for fear that the child will get hurt or violate others’ expectations, the caregiver can give the child the message that they should be ashamed of their behavior and instill a sense of doubt in their abilities. Parenting advice based on these ideas would be to keep your toddler safe, but let them learn by doing. A sense of pride seems to rely on doing rather than being told how capable one is (Berger, 2005).
Erikson’s second crisis of psychosocial development, during which toddlers strive to gain a sense of self-rule over their actions and their bodies
goodness-of-fit
the notion that development is dependent on the degree of match between children’s temperament and the nature and demands of the environment in which they are being raised
temperament
inborn differences between one person and another in emotions, activity, and self-regulation, typically measured by the person’s responses to the environment
trust vs. mistrust
Erikson’s first crisis of psychosocial development, during which infants learn basic trust if the world is a secure place where their needs (food, comfort, attention) are met
Garthus-Niegel, S., Ayers, S., Martini, J., von Soest, T. & Eberhard-Gran, M. (2017). The impact of postpartum post-traumatic stress disorder symptoms on child development: A population based, 2-year follow-up study. Psychological Medicine, 47(1), 161-170.
mailto:/Sandboxes/lhrli@ucdavis.edu


2.2: A Small Planar Truss
We return once again to the biaxial testing problem, introduced in the uniaxial truss module. It turns out that singular matrices are typical in the biaxial testing problem. As our initial step into the world of such planar structures let us consider the simple truss in the figure of a simple swing.
We denote by \(x_{1}\) and \(x_{2}\) the respective horizontal and vertical displacements of \(m_{1}\) (positive is right and down). Similarly, \(f_{1}\) and \(f_{2}\) will denote the associated components of force. The corresponding displacements and forces at \(m_{2}\) will be denoted by \(x_{3}, x_{4}\) and \(f_{3}, f_{4}\) In computing the elongations of the three springs we shall make reference to their unstretched lengths, \(L_{1}, L_{2}\) and \(L_{3}\)
Now, if spring 1 connects \(\{0, -L_{1}\}\) to \(\{0, 1\}\) when at rest and \(\{0, -L_{1}\}\) to \(\{x_{1}, x_{2}\}\) when stretched then its elongation is simply
\[e_{1} = \sqrt{2x_{1}^{2}+(x_{2}+L_{1})^2}-L_{1} \nonumber\]
The price one pays for moving to higher dimensions is that lengths are now expressed in terms of square roots. The upshot is that the elongations are not linear combinations of the end displacements as they were in the uniaxial case. If we presume, however, that the loads and stiffnesses are matched in the sense that the displacements are small compared with the original lengths, then we may effectively ignore the nonlinear contribution in Equation. In order to make this precise we need only recall the Taylor development of the square root of \((1+t)\)
The Taylor development of \(\sqrt{21+t}\) about \(t = 0\) is
\[\sqrt{21+t} = 1+\frac{t}{2}+O(t^2) \nonumber\]
where the latter term signifies the remainder.
With regard to \(e_{1}\) this allows
\[e_{1} = \sqrt{2x_{1}^{2}+x_{2}^{2}+2x_{2}L_{1}+L_{1}^2}-L_{1} \nonumber\]
\[= L_{1} \sqrt{21+\frac{x_{1}^{2}+x_{2}^{2}}{L_{1}^{2}}+\frac{2x_{2}}{L_{1}}}-L_{1} \nonumber\]
\[e_{1} = L_{1}+\frac{x_{1}^{2}+x_{2}^{2}}{2L_{1}^{2}}+x_{2}+L_{1}O((\frac{x_{1}^{2}+x_{2}^{2}}{L_{1}^{2}}+\frac{2x_{2}}{L_{1}})^{2})-L_{1} \nonumber\]
\[= \frac{x_{1}^{2}+x_{2}^{2}}{2L_{1}^{2}}+x_{2}+L_{1}O((\frac{x_{1}^{2}+x_{2}^{2}}{L_{1}^{2}}+\frac{2x_{2}}{L_{1}})^{2}) \nonumber\]
If we now assume that
\(\frac{x_{1}^{2}+x_{2}^{2}}{L_{1}^{2}}\) is small compared with \(x_{2}\)
then, as the O term is even smaller, we may neglect all but the first terms in the above and so arrive at
\[e_{1} = x_{2} \nonumber\]
To take a concrete example, if \(L_{1}\) is one meter and \(x_{1}\) and \(x_{2}\) are each one centimeter, then \(x_{2}\) is one hundred times \(\frac{x_{1}^{2}+x_{2}^{2}}{L_{1}^{2}}\).
With regard to the second spring, arguing as above, its elongation is (approximately) its stretch along its initial direction. As its initial direction is horizontal, its elongation is just the difference of the respective horizontal end displacements, namely,
\[e_{2} = x_{3}-x_{1} \nonumber\]
Finally, the elongation of the third spring is (approximately) the difference of its respective vertical end displacements, i.e.,
\[e_{3} = x_{4} \nonumber\]
We encode these three elongations in
\[\begin{array}{ccc} {\textbf{e} = A \textbf{x}}&{where}&{A = \begin{pmatrix} {0}&{1}&{0}&{0}\\ {-1}&{0}&{1}&{0}\\ {0}&{0}&{0}&{1} \end{pmatrix}} \nonumber \end{array}\]
Hooke's Law is an elemental piece of physics and is not perturbed by our leap from uniaxial to biaxial structures. The upshot is that the restoring force in each spring is still proportional to its elongation, i.e., \(y_{j} = k_{j}e_{j}\) where \(k_{j}\) is the stiffness of the jth spring. In matrix terms,
\[\begin{array}{ccc} {\textbf{y} = K \textbf{e}}&{where}&{K = \begin{pmatrix} {k_{1}}&{0}&{0}\\ {0}&{k_{2}}&{0}\\ {0}&{0}&{k_{3}} \end{pmatrix}} \nonumber \end{array}\]
Balancing horizontal and vertical forces at \(m_{1}\) brings
\[(-y_{2})-f_{1} = 0 \nonumber\]
and
\[y_{1}-f_{2} = 0 \nonumber\]
while balancing horizontal and vertical forces at \(m_{2}\) brings
\[y_{2}-f_{3} = 0 \nonumber\]
and
\[y_{3}-f_{4} = 0 \nonumber\]
We assemble these into
\[\begin{array}{ccc} {\textbf{B}y = \textbf{f}}&{where}&{\begin{pmatrix} {0}&{-1}&{0}\\ {1}&{0}&{0}\\ {0}&{1}&{0}\\ {0}&{0}&{1} \end{pmatrix}} \nonumber \end{array}\]
and recognize, as expected, that BB is nothing more than \(A^{T}\). Putting the pieces together, we find that \(\textbf{x}\) must satisfy \(S \textbf{x} = \textbf{f}\) where
\[S = A^{T} KA = \begin{pmatrix} {k_{2}}&{0}&{-k_{2}}&{0}\\ {0}&{k_{1}}&{0}&{0}\\ {-k_{2}}&{0}&{k_{2}}&{0}\\ {0}&{0}&{0}&{k_{3}} \end{pmatrix} \nonumber\]
Applying one step of Gaussian Elimination brings
\[\begin{pmatrix} {k_{2}}&{0}&{-k_{2}}&{0}\\ {0}&{k_{1}}&{0}&{0}\\ {0}&{0}&{0}&{0}\\ {0}&{0}&{0}&{k_{3}} \end{pmatrix} \begin{pmatrix} {x_{1}}\\ {x_{2}}\\ {x_{3}}\\ {x_{4}} \end{pmatrix} = \begin{pmatrix} {f_{1}}\\ {f_{2}}\\ {f_{1}+f_{3}}\\ {f_{4}} \end{pmatrix} \nonumber\]
and back substitution delivers
\[x_{4} = \frac{f_{4}}{k_{3}} \nonumber\]
\[0 = f_{1}+f_{3} \nonumber\]
\[x_{2} = \frac{f_{2}}{k_{1}} \nonumber\]
\[x_{1}-x_{3} = \frac{f_{1}}{k_{2}} \nonumber\]
The second of these is remarkable in that it contains no components of \(\textbf{x}\). Instead, it provides a condition on \(\textbf{f}\). In mechanical terms, it states that there can be no equilibrium unless the horizontal forces on the two masses are equal and opposite. Of course one could have observed this directly from the layout of the truss. In modern, three--dimensional structures with thousands of members meant to shelter or convey humans one should not however be satisfied with the `visual' integrity of the structure. In particular, one desires a detailed description of all loads that can, and, especially, all loads that can not, be equilibrated by the proposed truss. In algebraic terms, given a matrix \(S\), one desires a characterization of
- all those \(\textbf{f}\) for which \(S \textbf{x} = \textbf{f}\) possesses a solution
- all those \(\textbf{f}\) for which \(S \textbf{x} = \textbf{f}\) does not possess a solution
We will eventually provide such a characterization in our later discussion of the column space of a matrix.
Supposing now that \(f_{1}+f_{3} = 0\) we note that although the system above is consistent it still fails to uniquely determine the four components of \(\textbf{x}\). In particular, it specifies only the difference between \(x_{1}\) and \(x_{3}\) As a result both
\[\begin{array}{ccc} {\textbf{x} = \begin{pmatrix} {\frac{f_{1}}{k_{2}}}\\ {\frac{f_{2}}{k_{1}}}\\ {0}\\ {\frac{f_{4}}{k_{3}}} \end{pmatrix}}&{and}&{\textbf{x} = \begin{pmatrix} {0}\\ {\frac{f_{2}}{k_{1}}}\\ {-\frac{f_{1}}{k_{2}}}\\ {\frac{f_{4}}{k_{3}}} \end{pmatrix}} \nonumber \end{array}\]
satisfy \(S \textbf{x} = \textbf{f}\)
\[\begin{pmatrix} {1}\\ {0}\\ {1}\\ {0} \end{pmatrix} \nonumber\]
and still have a solution of \(S \textbf{x} = \textbf{f}\). Searching for the source of this lack of uniqueness we observe some redundancies in the columns of S. In particular, the third is simply the opposite of the first. As S is simply \(A^{T}KA\), where again, the first and third columns are opposites. These redundancies are encoded in \(\textbf{z}\) in the sense that
\[A \textbf{z} = \textbf{0} \nonumber\]
Interpreting this in mechanical terms, we view \(\textbf{z}\) as a displacement and \(A \textbf{z}\) as the resulting elongation. In
\[A \textbf{z} = \textbf{0} \nonumber\]
we see a nonzero displacement producing zero elongation. One says in this case that the truss deforms without doing any work and speaks of \(\textbf{z}\) as an unstable mode . Again, this mode could have been observed by a simple glance at Figure. Such is not the case for more complex structures and so the engineer seeks a systematic means by which all unstable modes may be identified. We shall see later that all these modes are captured by the null space of \(A\).
From
\[S \textbf{z} = \textbf{0} \nonumber\]
one easily deduces that \(S\) is singular. More precisely, if \(S^{-1}\) were to exist then \(S^{-1}S \textbf{z}\) would equal \(S^{-1} \textbf{0}\) i.e. \(\textbf{z} = \textbf{0}\), contrary to Equation. As a result, Matlab will fail to solve \(S \textbf{x} = \textbf{f}\) even when \(\textbf{f}\) is a force that the truss can equilibrate. One way out is to use the pseudo-inverse , as we shall see in the General Planal Truss module.


3.3: Anomalous dispersion
The 'anomalous' dispersion corrections, which are not in fact anomalous, take into account the effect of absorption in the scattering of phonons by electrons. In the classic picture the electron is approximated by a damped harmonic oscillator. The scattering factor of the electron is then complex and the atomic scattering factor, or atomic form factor, is given by:
f + f' + i f"
where f' and f" are the real and imaginary parts of the anomalous dispersion correction. Their importance increases as one gets closer to an absorption edge (resonant scattering). Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and relativistic approaches, see Section 4.2.6 of International Tables of Crystallography, Volume C .


11.7: Urinary System
The urinary system includes the kidneys, ureters, bladder, and urethra. It has many functions including filtering the blood and eliminating wastes, regulating blood and urine pH levels, and working in collaboration with the cardiovascular system to regulate blood pressure. The urinary system also provides reproductive functions in the prostate for males. The kidneys also release a hormone that stimulates red blood cell production and synthesizes vitamin D to assist in bone health. Each of these functions is vital to well-being and survival. [1] See Figure 11.10 [2] for an illustration of the structures of the urinary system.
Blood is filtered through the kidneys, and the filtrate is transformed into urine at a relatively constant rate throughout the day. The urine travels from the kidneys through the ureters to the bladder. The bladder stores urine and signals the brain when full (around 300 mL). It stores urine until a convenient time for elimination or voiding, and then the brain allows the urethra to release the urine. [3]
Urine is a fluid of variable composition. Urine characteristics change depending on influences such as water intake, exercise, environmental temperature, nutrient intake, and other factors. Characteristics such as color and odor provide a rough estimate of a person’s state of hydration. For example, after exercising or working outside on a hot day and sweating heavily, urine will become darker with a slight odor. [4] See Figure 11.11 [5] for ranges of urinary color related to hydration status. Review the subsection “ Observation and Documentation of Urinary Output ” in Chapter 5.8 for other characteristics that nursing assistants should document when assisting clients to void.
Urine volume varies considerably. The normal range of urine output for an adult is one to two liters per day. The kidneys must produce a minimum urine volume of about 500 mL/day to adequately eliminate wastes from the body. Output below this level can be caused by severe dehydration or kidney disease. [6]
The effects of failure of various parts of the urinary system can range from incontinence to kidney disease with a life-threatening loss of the ability to eliminate wastes. When the kidneys begin to fail, several symptoms may occur such as weakness, shortness of breath, widespread edema (swelling), rising potassium levels, and heart arrhythmias. [7]
Failure of voluntary control of urination is called incontinence . Incontinence may occur if the connection between the brain and the urethra is disrupted or there is loss of muscle tone in the urinary system. There are several types of incontinence. Incontinence in small amounts (i.e., leaking or dribbling) can occur from coughing, laughing, or moving when the bladder is full. Some people feel an urge to void and then must go immediately or incontinence may occur if they are not near a restroom. Some people have total loss of control of urination, resulting in the entire contents of their bladder being released involuntarily. [8] Refer to section Chapter 5.8, “ Assisting With Toileting ” to review appropriate interventions to help prevent incontinence.
The prostate gland encompasses the urethra in males. As males age, the prostate gland grows, known as benign prostate enlargement (BPE). Because prostate enlargement puts pressure on the urethra, the urine may become blocked. Older men may experience difficulty starting the stream of urine or become unable to completely empty their bladder. If the blockage becomes significant, it can cause infection when urine remains in the bladder for long periods of time. In these cases, a urinary catheter may be placed to reduce the retention of urine, or a surgical procedure may be completed to reopen the urethra.
See Table 11.7 for common chronic conditions, symptoms to report, and interventions nursing assistants can provide to promote urinary health.
Table 11.7 Common Chronic Conditions of the Urinary System and Related Interventions [9] , [10] , [11] , [12]
| Diagnosis | Definition | Symptoms to Report | Nursing Assistant Interventions |
|---|---|---|---|
| Urinary Incontinence | Inability to control the elimination of urine. | Change in the frequency or amount of incontinence. |
|
| Urinary Tract Infection (UTI) | Infection of any part of the urinary system. | Increased frequency of voiding; pain, itching, or burning with voiding; voiding in small amounts; strong odor; dark or cloudy urine; and/or sediment or blood in the urine. A sudden increase in confusion can also indicate infection. |
|
| Kidney Stones | Deposits of minerals from concentrated urine that form a mass in the kidneys. | Increased pain in the abdomen or pain with voiding. |
|
| Chronic Kidney Failure | Kidneys are unable to adequately filter and remove wastes and fluids from the body. | Puffiness around the eyes, frequent urge to urinate, urination in increasingly smaller amounts, dry and itchy skin, and/or fatigue. |
|
- This work is a derivative of Human Nutrition by University of Hawai‘i at Mānoa Food Science and Human Nutrition Program and is licensed under CC BY NC SA 4.0 ↵
- “ llu_urinary_system.svg ” by Thstehle is in the Public Domain ↵
- This work is a derivative of Human Nutrition by University of Hawai‘i at Mānoa Food Science and Human Nutrition Program and is licensed under CC BY NC SA 4.0 ↵
- This work is a derivative of Human Nutrition by University of Hawai‘i at Mānoa Food Science and Human Nutrition Program and is licensed under CC BY NC SA 4.0 ↵
- “ 2601_Urine_Color_Chart.jpg ” by OpenStax College is licensed under CC BY 3.0 ↵
- This work is a derivative of Human Nutrition by University of Hawai‘i at Mānoa Food Science and Human Nutrition Program and is licensed under CC BY NC SA 4.0 ↵
- This work is a derivative of Human Nutrition by University of Hawai‘i at Mānoa Food Science and Human Nutrition Program and is licensed under CC BY NC SA 4.0 ↵
- This work is a derivative of Human Nutrition by University of Hawai‘i at Mānoa Food Science and Human Nutrition Program and is licensed under CC BY NC SA 4.0 ↵
- Mayo Clinic Staff. (2021, December 17). Urinary incontinence . https://www.mayoclinic.org/diseases-conditions/urinary-incontinence/symptoms-causes/syc-20352808 ↵
- Mayo Clinic Staff. (2021, April 23). Urinary tract infection (UTI). https://www.mayoclinic.org/diseases-conditions/urinary-tract-infection/symptoms-causes/syc-20353447 ↵
- Mayo Clinic Staff. (2022, June 3). Kidney stones. https://www.mayoclinic.org/diseases-conditions/kidney-stones/symptoms-causes/syc-20355755 ↵
- Mayo Clinic Staff. (2021, September 3). Chronic kidney disease. https://www.mayoclinic.org/diseases-conditions/chronic-kidney-disease/symptoms-causes/syc-20354521 ↵


3.9: Putting It All Together
Patient Scenario
Mrs. Rosas is a 76-year-old patient admitted to the cardiology floor with an exacerbation of congestive heart failure. The patient’s primary language is Spanish, and she has a limited understanding of English. The patient’s daughter reports that the patient has been experiencing increased swelling in her ankles and increased shortness of breath over the last three weeks. Her daughter also reports that the patient has noted unexplained weight gain. During the admission assessment the nurse attempts to collect additional information related to current symptoms, diet, and history. The patient nods in response to questions and converses quietly in Spanish with her daughter.
Applying the Nursing Process
Assessment: The nurse notes that the patient does not respond to questions appropriately and is unable to converse in English. She defers to her daughter to provide interpretation of questions and relay information.
Based on the assessment information that has been gathered, the following nursing care plan is created for Mrs. Rosas.
Nursing Diagnosis: Impaired Verbal Communication related to cultural incongruence as evidenced by inability to speak the language of the caregiver.
Overall Goal: The patient will use effective communication techniques.
SMART Expected Outcome: Mrs. Rosas will utilize interpreter services in order to receive information and express needs throughout her hospitalization.
Planning and Implementing Nursing Interventions:
The nurse will provide patient with interpreter services in order to facilitate patient communication. In-person interpreter or language line telephone services will be utilized to ensure that the patient receives information about her care. The nurse will eliminate distractions such as the television, hallway noise, etc., to decrease sources of additional stimuli in the communication experience. The nurse will communicate directly with the patient, utilizing appropriate eye contact, and nonverbal cues to enhance the communication experience.
Sample Documentation
Mrs. Rosas has impaired verbal communication due to limited English proficiency. She requires education regarding cardiac diet, fluid restriction, and exacerbation warning signs. Interpreter services have been utilized to ensure that communication and education needs are appropriate. Mrs. Rosas communicates freely through the interpreter and acknowledges understanding of the education that has been provided.
Evaluation
During the patient’s hospitalization, Mrs. Rosas engages with staff through the use of interpreter services and actively participates in her own care.


15.5: Prokaryotic Transcription - Elongation and Termination in Prokaryotes
- Explain the process of elongation and termination in prokaryotes
Elongation in Prokaryotes
The transcription elongation phase begins with the release of the σ subunit from the polymerase. The dissociation of σ allows the core RNA polymerase enzyme to proceed along the DNA template, synthesizing mRNA in the 5′ to 3′ direction at a rate of approximately 40 nucleotides per second. As elongation proceeds, the DNA is continuously unwound ahead of the core enzyme and rewound behind it. Since the base pairing between DNA and RNA is not stable enough to maintain the stability of the mRNA synthesis components, RNA polymerase acts as a stable linker between the DNA template and the nascent RNA strands to ensure that elongation is not interrupted prematurely.
Termination in Prokaryotes
Once a gene is transcribed, the prokaryotic polymerase needs to be instructed to dissociate from the DNA template and liberate the newly-made mRNA. Depending on the gene being transcribed, there are two kinds of termination signals: one is protein-based and the other is RNA-based.
Rho-dependent termination is controlled by the rho protein, which tracks along behind the polymerase on the growing mRNA chain. Near the end of the gene, the polymerase encounters a run of G nucleotides on the DNA template and it stalls. As a result, the rho protein collides with the polymerase. The interaction with rho releases the mRNA from the transcription bubble.
Rho-independent termination is controlled by specific sequences in the DNA template strand. As the polymerase nears the end of the gene being transcribed, it encounters a region rich in C–G nucleotides. The mRNA folds back on itself, and the complementary C–G nucleotides bind together. The result is a stable hairpin that causes the polymerase to stall as soon as it begins to transcribe a region rich in A–T nucleotides. The complementary U–A region of the mRNA transcript forms only a weak interaction with the template DNA. This, coupled with the stalled polymerase, induces enough instability for the core enzyme to break away and liberate the new mRNA transcript.
Upon termination, the process of transcription is complete. By the time termination occurs, the prokaryotic transcript would already have been used to begin synthesis of numerous copies of the encoded protein because these processes can occur concurrently in the cytoplasm. The unification of transcription, translation, and even mRNA degradation is possible because all of these processes occur in the same 5′ to 3′ direction and because there is no membranous compartmentalization in the prokaryotic cell. In contrast, the presence of a nucleus in eukaryotic cells prevents simultaneous transcription and translation.
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- amino acid. Provided by : Wiktionary. Located at : http://en.wiktionary.org/wiki/amino_acid . License : CC BY-SA: Attribution-ShareAlike
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- Structural Biochemistry/Genetic code. Provided by : Wikibooks. Located at : en.wikibooks.org/wiki/Structu...y/Genetic_code . License : CC BY-SA: Attribution-ShareAlike
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Key Points
- The transcription elongation phase begins with the dissociation of the σ subunit, which allows the core RNA polymerase enzyme to proceed along the DNA template.
- Rho-dependent termination is caused by the rho protein colliding with the stalled polymerase at a stretch of G nucleotides on the DNA template near the end of the gene.
- Rho-independent termination is caused the polymerase stalling at a stable hairpin formed by a region of complementary C–G nucleotides at the end of the mRNA.
Key Terms
- elongation : the addition of nucleotides to the 3′-end of a growing RNA chain during transcription


27.4: Tropical Deciduous Forest
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- Kammy Algiers
- Norco College
Learning Objective
Recognize distinguishing characteristics of tropical deciduous rainforests & plant adaptations of the biome.
This biome is distinguished by seasonal rainfall and a constant warm temperature throughout the year. There are two seasons in this biome, are often referred to as the dry season (with no to little rain) and the wet season (with heavy rain). This biome receives up to 80 inches of rain per year and temperatures range between 68°F to 77°F.
One would find this biome on the north and south ends of tropical rainforests, generally between 10° and 20°. Parts of South America, including parts of amazon and southern Mexico, as well as parts of south east Asia and India contain tropical deciduous forests. This biome is also sometimes called Monsoon forest or mixed deciduous forest, depending on its location and slight variations.
Adaptations
Though there is less biodiversity in this biome than tropical rainforests, there are still a large number of species, including many endemic species that reside here. Deciduous trees lose their leaves during the dry season and re-grow them during the rainy season. This allows the plants to save energy when liquid water is not as available. During the rainy season, the forest is lush and full of foliage, whereas the dry season creates an open canopy, allowing plants under the canopy to access sunlight. You can still see the various layers of vegetation in this biome, including lianas (woody vines) and epiphytes such as bromeliads and orchids. The canopy contains tall trees above and smaller trees and shrubs underneath. Though most of the tall trees are often deciduous, there are still plenty of evergreen plants that retain their leaves throughout the year. Many birds and mammals live in this biome and use the vegetation as habitat and food.


6.5: The Behavioral Side of Curriculum
Rather than thinking of children’s behavior as occurring separately from everything else that goes on in the classroom, it can be helpful to recognize that it is a part of everything else. As we plan interactions and experiences that are meaningful, we take into account a variety of factors that affect behavior. Part of every plan should be an understanding of who children are and intentionally planning for them. Just as with other skills that children are learning, they are learning to control their bodies, use their words, self-regulate, wait their turn, be patient, and a host of other social and emotional skills the will help them be able to manage themselves in social situations. Learning these life skills is no different from any other concept they will learn by exploring, repeated exposure, and having it make sense to them. As will other concepts, they need teachers who develop relationships with them, focus on what they CAN do, and maintain a positive attitude.
There is no magic approach to helping children learn to manage their behavior and no secret book with all of the answers. Instead, there are a variety of factors to consider and approaches to try to guide behaviors in the ways we prefer. This will be expanded upon in the ECE 104 Introduction to Curriculum in Early Childhood Education, so what follows here is an abridged version of considerations as we plan for the children in our programs.
As early childhood professionals, we have an ethical obligation to understand how behavior is affected by the following factors and to plan accordingly. Just as we started Chapter 4 (Observation and Assessment) with looking at the “why”, understanding why a child might be behaving in a certain way can assist in planning appropriately:
The “whys” of children’s behavior teachers should consider :
- Development – what to expect at various ages and stage for the “whole” child
- Environment – the physical space, routine and interpersonal tone
- Family & Cultural Influences – influences and variations in expectations
- Temperament – individual personality styles, approaches, and ways of interpreting events
- Motivation – purpose (communicating, relating, attention, control, revenge, inadequacy, fear of failure,…)
Often teachers will use a web like the one previously described to consider the “why” of a behavior. They place the behavior in the center and then web out the various factors to consider.
How might you use the information above when planning interactions and experiences for children?
Once we have an understanding of the “whys” of behavior, we can plan interactions that foster the behavior we desire. We will introduce you to guidance techniques in the ECE 104 Introduction to Curriculum in Early Childhood Education. Here we have highlighted the following Interactive Strategies to consider.
Useful teacher interactions when planning for children’s behavior (in addition to the interactive considerations posed earlier) :
- Consistency
- Clarity
- Realistic limits and expectations
- Calmness
- Focus on the behavior, not the child
- Focus on what the child can do and is doing appropriately
- Positive direction (for example instead of “don’t run” say “use walking feet”)
- Reflection and logic rather than immediate response and emotion
Some strategies to try include :
- Ignore – can be effective if a behavior is annoying rather than dangerous.
“If you choose to continue using a whining voice I will choose not to listen. As soon as you use your talking voice, I would like to hear what you have to say”
- Redirect – directing the child to a more positive way of using that behavior.
“Inside we use our walking feet, when you go outside you can run” or “We don’t throw things at other people, if you would like to throw let’s find the target and beanbags”
- Active Listening to understand – validating what the child is saying.
“I hear you saying that you want a turn, you sound very sad” or “you worked very hard on that block structure and you are angry it got knocked over”
- Give Choices – state what needs to be done and then give 2 options for how it can be done.

- Logical Consequences – as children behave in certain ways (both “positively” and “negatively”) consequences will logically happen.
“If you talk to your friends in that tone, they may continue not to want to play with you. If you want to play with them, what can you do differently?” or “We are having snack now; if you choose not to eat you will probably be very hungry by lunchtime”
- Problem Solving/Conflict Resolution – helping children to solve their own issues with support as needed.
“What can you do about that?” or “How might you solve that problem” or “it sounds like you both want to play with the same toy, I wonder how you will work that out?”
- Short removal with reflection and return – taking a moment to leave a situation to gain composure and return more successfully.
“It seems to be hard for you to keep the sand in the sandbox right now. I’m going to ask you to leave the sandbox for a few moments and think about how you can be respectful to the others that are sharing this space with you. Where will you go to think?”)A very brief time later) “what can you do differently next time you enter the sandbox? Great, would you like to try out your solution? Come on back and show me”. “You did it!” [79]
How might you use the information above when planning interactions and experiences for children? What makes sense? What feels comfortable to try?


1: Scattering Theory
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- 1.7: The Green's Function for a Free Particle
- We have defined the free-particle Green’s function as the operator G^0=(E−H^0)−1 . Its representation in the position basis, ⟨r|G^0|r′⟩ , is called the propagator. As we have just seen, when the Born series is written in the position basis, the propagator appears in the integrand and describes how the particle “propagates” between discrete scattering events.
Thumbnail: Collimated homogeneous beam of monoenergetic particles, long wavepacket which is approximately a planewave, but strictly does not extend to infinity in all directions, is incident on a target and subsequently scattered into the detector subtending a solid angle. The detector is assumed to be far away from the scattering center. (Department of Physics Wiki @ Florida State University).