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## 9.2 The Banking System and Money Creation

### Learning Objectives

1. Explain what banks are, what their balance sheets look like, and what is meant by a fractional reserve banking system.
2. Describe the process of money creation (destruction), using the concept of the deposit multiplier.
3. Describe how and why banks are regulated and insured.

Where does money come from? How is its quantity increased or decreased? The answer to these questions suggests that money has an almost magical quality: money is created by banks when they issue loans. In effect, money is created by the stroke of a pen or the click of a computer key.

We will begin by examining the operation of banks and the banking system. We will find that, like money itself, the nature of banking is experiencing rapid change.

## Banks and Other Financial Intermediaries

An institution that amasses funds from one group and makes them available to another is called a financial intermediaryAn institution that amasses funds from one group and makes them available to another.. A pension fund is an example of a financial intermediary. Workers and firms place earnings in the fund for their retirement; the fund earns income by lending money to firms or by purchasing their stock. The fund thus makes retirement saving available for other spending. Insurance companies are also financial intermediaries, because they lend some of the premiums paid by their customers to firms for investment. Mutual funds make money available to firms and other institutions by purchasing their initial offerings of stocks or bonds.

Banks play a particularly important role as financial intermediaries. Banks accept depositors’ money and lend it to borrowers. With the interest they earn on their loans, banks are able to pay interest to their depositors, cover their own operating costs, and earn a profit, all the while maintaining the ability of the original depositors to spend the funds when they desire to do so. One key characteristic of banks is that they offer their customers the opportunity to open checking accounts, thus creating checkable deposits. These functions define a bankA financial intermediary that accepts deposits, makes loans, and offers checking accounts., which is a financial intermediary that accepts deposits, makes loans, and offers checking accounts.

Over time, some nonbank financial intermediaries have become more and more like banks. For example, some brokerage firms offer customers interest-earning accounts and make loans. They now allow their customers to write checks on their accounts.

As nonbank financial intermediaries have grown, banks’ share of the nation’s credit market financial assets has diminished. In 1972, banks accounted for nearly 30% of U.S. credit market financial assets. In 2007, that share had dropped to about 15%.

The fact that banks account for a declining share of U.S. financial assets alarms some observers. We will see that banks are more tightly regulated than are other financial institutions; one reason for that regulation is to maintain control over the money supply. Other financial intermediaries do not face the same regulatory restrictions as banks. Indeed, their freedom from regulation is one reason they have grown so rapidly. As other financial intermediaries become more important, central authorities begin to lose control over the money supply.

The declining share of financial assets controlled by “banks” began to change in 2008. Many of the nation’s largest investment banks—financial institutions that provided services to firms but were not regulated as commercial banks—began having serious financial difficulties as a result of their investments tied to home mortgage loans. As home prices in the United States began falling, many of those mortgage loans went into default. Investment banks that had made substantial purchases of securities whose value was ultimately based on those mortgage loans themselves began failing. Bear Stearns, one of the largest investment banks in the United States, required federal funds to remain solvent. Another large investment bank, Lehman Brothers, failed. In an effort to avoid a similar fate, several other investment banks applied for status as ordinary commercial banks subject to the stringent regulation those institutions face. One result of the terrible financial crisis that crippled the U.S. and other economies in 2008 may be greater control of the money supply by the Fed.

## Bank Finance and a Fractional Reserve System

Bank finance lies at the heart of the process through which money is created. To understand money creation, we need to understand some of the basics of bank finance.

Banks accept deposits and issue checks to the owners of those deposits. Banks use the money collected from depositors to make loans. The bank’s financial picture at a given time can be depicted using a simplified balance sheetA financial statement showing assets, liabilities, and net worth., which is a financial statement showing assets, liabilities, and net worth. AssetsAnything of value. are anything of value. LiabilitiesObligations to other parties. are obligations to other parties. Net worthAssets less liabilities. equals assets less liabilities. All these are given dollar values in a firm’s balance sheet. The sum of liabilities plus net worth therefore must equal the sum of all assets. On a balance sheet, assets are listed on the left, liabilities and net worth on the right.

The main way that banks earn profits is through issuing loans. Because their depositors do not typically all ask for the entire amount of their deposits back at the same time, banks lend out most of the deposits they have collected—to companies seeking to expand their operations, to people buying cars or homes, and so on. Banks keep only a fraction of their deposits as cash in their vaults and in deposits with the Fed. These assets are called reservesBank assets held as cash in vaults and in deposits with the Federal Reserve.. Banks lend out the rest of their deposits. A system in which banks hold reserves whose value is less than the sum of claims outstanding on those reserves is called a fractional reserve banking systemSystem in which banks hold reserves whose value is less than the sum of claims outstanding on those reserves..

Table 9.1 "The Consolidated Balance Sheet for U.S. Commercial Banks, October 2010" shows a consolidated balance sheet for commercial banks in the United States for October 2010. Banks hold reserves against the liabilities represented by their checkable deposits. Notice that these reserves were a small fraction of total deposit liabilities of that month. Most bank assets are in the form of loans.

Table 9.1 The Consolidated Balance Sheet for U.S. Commercial Banks, October 2010

Assets Liabilities and Net Worth
Reserves $1,040.2 Checkable deposits$1,792.0
Other assets 1,743.7 Other deposits 6,103.6
Loans 6,788.7 Borrowings 1,927.5
Securities 2,452.6 Other liabilities 855.8
Total assets $12,025.2 Total liabilities 10,678.9 Net worth 1,346.4 This balance sheet for all commercial banks in the United States shows their financial situation in billions of dollars, seasonally adjusted, on October 2010. In the next section, we will learn that money is created when banks issue loans. ## Money Creation To understand the process of money creation today, let us create a hypothetical system of banks. We will focus on three banks in this system: Acme Bank, Bellville Bank, and Clarkston Bank. Assume that all banks are required to hold reserves equal to 10% of their checkable deposits. The quantity of reserves banks are required to hold is called required reservesThe quantity of reserves banks are required to hold.. The reserve requirement is expressed as a required reserve ratioThe ratio of reserves to checkable deposits a bank must maintain.; it specifies the ratio of reserves to checkable deposits a bank must maintain. Banks may hold reserves in excess of the required level; such reserves are called excess reservesReserves in excess of the required level.. Excess reserves plus required reserves equal total reserves. Because banks earn relatively little interest on their reserves held on deposit with the Federal Reserve, we shall assume that they seek to hold no excess reserves. When a bank’s excess reserves equal zero, it is loaned upWhen a bank’s excess reserves equal zero.. Finally, we shall ignore assets other than reserves and loans and deposits other than checkable deposits. To simplify the analysis further, we shall suppose that banks have no net worth; their assets are equal to their liabilities. Let us suppose that every bank in our imaginary system begins with$1,000 in reserves, $9,000 in loans outstanding, and$10,000 in checkable deposit balances held by customers. The balance sheet for one of these banks, Acme Bank, is shown in Table 9.2 "A Balance Sheet for Acme Bank". The required reserve ratio is 0.1: Each bank must have reserves equal to 10% of its checkable deposits. Because reserves equal required reserves, excess reserves equal zero. Each bank is loaned up.

Table 9.2 A Balance Sheet for Acme Bank

Acme Bank
Assets Liabilities
Reserves $1,000 Deposits$10,000
Loans $9,000 We assume that all banks in a hypothetical system of banks have$1,000 in reserves, $10,000 in checkable deposits, and$9,000 in loans. With a 10% reserve requirement, each bank is loaned up; it has zero excess reserves.

Acme Bank, like every other bank in our hypothetical system, initially holds reserves equal to the level of required reserves. Now suppose one of Acme Bank’s customers deposits $1,000 in cash in a checking account. The money goes into the bank’s vault and thus adds to reserves. The customer now has an additional$1,000 in his or her account. Two versions of Acme’s balance sheet are given here. The first shows the changes brought by the customer’s deposit: reserves and checkable deposits rise by $1,000. The second shows how these changes affect Acme’s balances. Reserves now equal$2,000 and checkable deposits equal $11,000. With checkable deposits of$11,000 and a 10% reserve requirement, Acme is required to hold reserves of $1,100. With reserves equaling$2,000, Acme has $900 in excess reserves. At this stage, there has been no change in the money supply. When the customer brought in the$1,000 and Acme put the money in the vault, currency in circulation fell by $1,000. At the same time, the$1,000 was added to the customer’s checking account balance, so the money supply did not change.

Figure 9.3

Because Acme earns only a low interest rate on its excess reserves, we assume it will try to loan them out. Suppose Acme lends the $900 to one of its customers. It will make the loan by crediting the customer’s checking account with$900. Acme’s outstanding loans and checkable deposits rise by $900. The$900 in checkable deposits is new money; Acme created it when it issued the $900 loan. Now you know where money comes from—it is created when a bank issues a loan. Figure 9.4 Presumably, the customer who borrowed the$900 did so in order to spend it. That customer will write a check to someone else, who is likely to bank at some other bank. Suppose that Acme’s borrower writes a check to a firm with an account at Bellville Bank. In this set of transactions, Acme’s checkable deposits fall by $900. The firm that receives the check deposits it in its account at Bellville Bank, increasing that bank’s checkable deposits by$900. Bellville Bank now has a check written on an Acme account. Bellville will submit the check to the Fed, which will reduce Acme’s deposits with the Fed—its reserves—by $900 and increase Bellville’s reserves by$900.

Figure 9.5

Notice that Acme Bank emerges from this round of transactions with $11,000 in checkable deposits and$1,100 in reserves. It has eliminated its excess reserves by issuing the loan for $900; Acme is now loaned up. Notice also that from Acme’s point of view, it has not created any money! It merely took in a$1,000 deposit and emerged from the process with $1,000 in additional checkable deposits. The$900 in new money Acme created when it issued a loan has not vanished—it is now in an account in Bellville Bank. Like the magician who shows the audience that the hat from which the rabbit appeared was empty, Acme can report that it has not created any money. There is a wonderful irony in the magic of money creation: banks create money when they issue loans, but no one bank ever seems to keep the money it creates. That is because money is created within the banking system, not by a single bank.

The process of money creation will not end there. Let us go back to Bellville Bank. Its deposits and reserves rose by $900 when the Acme check was deposited in a Bellville account. The$900 deposit required an increase in required reserves of $90. Because Bellville’s reserves rose by$900, it now has $810 in excess reserves. Just as Acme lent the amount of its excess reserves, we can expect Bellville to lend this$810. The next set of balance sheets shows this transaction. Bellville’s loans and checkable deposits rise by $810. Figure 9.6 The$810 that Bellville lent will be spent. Let us suppose it ends up with a customer who banks at Clarkston Bank. Bellville’s checkable deposits fall by $810; Clarkston’s rise by the same amount. Clarkston submits the check to the Fed, which transfers the money from Bellville’s reserve account to Clarkston’s. Notice that Clarkston’s deposits rise by$810; Clarkston must increase its reserves by $81. But its reserves have risen by$810, so it has excess reserves of $729. Figure 9.7 Notice that Bellville is now loaned up. And notice that it can report that it has not created any money either! It took in a$900 deposit, and its checkable deposits have risen by that same $900. The$810 it created when it issued a loan is now at Clarkston Bank.

The process will not end there. Clarkston will lend the $729 it now has in excess reserves, and the money that has been created will end up at some other bank, which will then have excess reserves—and create still more money. And that process will just keep going as long as there are excess reserves to pass through the banking system in the form of loans. How much will ultimately be created by the system as a whole? With a 10% reserve requirement, each dollar in reserves backs up$10 in checkable deposits. The $1,000 in cash that Acme’s customer brought in adds$1,000 in reserves to the banking system. It can therefore back up an additional $10,000! In just the three banks we have shown, checkable deposits have risen by$2,710 ($1,000 at Acme,$900 at Bellville, and $810 at Clarkston). Additional banks in the system will continue to create money, up to a maximum of$7,290 among them. Subtracting the original $1,000 that had been a part of currency in circulation, we see that the money supply could rise by as much as$9,000.

Notice that when the banks received new deposits, they could make new loans only up to the amount of their excess reserves, not up to the amount of their deposits and total reserve increases. For example, with the new deposit of $1,000, Acme Bank was able to make additional loans of$900. If instead it made new loans equal to its increase in total reserves, then after the customers who received new loans wrote checks to others, its reserves would be less than the required amount. In the case of Acme, had it lent out an additional $1,000, after checks were written against the new loans, it would have been left with only$1,000 in reserves against $11,000 in deposits, for a reserve ratio of only 0.09, which is less than the required reserve ratio of 0.1 in the example. ## The Deposit Multiplier We can relate the potential increase in the money supply to the change in reserves that created it using the deposit multiplierThe ratio of the maximum possible change in checkable deposits (∆D) to the change in reserves (∆R). (md), which equals the ratio of the maximum possible change in checkable deposits (∆D) to the change in reserves (∆R). In our example, the deposit multiplier was 10: Equation 9.1 $md = ∆D ∆R = 10,000 1,000 = 10$ To see how the deposit multiplier md is related to the required reserve ratio, we use the fact that if banks in the economy are loaned up, then reserves, R, equal the required reserve ratio (rrr) times checkable deposits, D: Equation 9.2 $R=rrrD$ A change in reserves produces a change in loans and a change in checkable deposits. Once banks are fully loaned up, the change in reserves, ∆R, will equal the required reserve ratio times the change in deposits, ∆D: Equation 9.3 $∆R=rrr∆D$ Solving for ∆D, we have Equation 9.4 $1 rrr ∆R=∆D$ Dividing both sides by ∆R, we see that the deposit multiplier, md, is 1/rrr: Equation 9.5 $1 rrr = ∆D ∆R = md$ The deposit multiplier is thus given by the reciprocal of the required reserve ratio. With a required reserve ratio of 0.1, the deposit multiplier is 10. A required reserve ratio of 0.2 would produce a deposit multiplier of 5. The higher the required reserve ratio, the lower the deposit multiplier. Actual increases in checkable deposits will not be nearly as great as suggested by the deposit multiplier. That is because the artificial conditions of our example are not met in the real world. Some banks hold excess reserves, customers withdraw cash, and some loan proceeds are not spent. Each of these factors reduces the degree to which checkable deposits are affected by an increase in reserves. The basic mechanism, however, is the one described in our example, and it remains the case that checkable deposits increase by a multiple of an increase in reserves. The entire process of money creation can work in reverse. When you withdraw cash from your bank, you reduce the bank’s reserves. Just as a deposit at Acme Bank increases the money supply by a multiple of the original deposit, your withdrawal reduces the money supply by a multiple of the amount you withdraw. And just as money is created when banks issue loans, it is destroyed as the loans are repaid. A loan payment reduces checkable deposits; it thus reduces the money supply. Suppose, for example, that the Acme Bank customer who borrowed the$900 makes a $100 payment on the loan. Only part of the payment will reduce the loan balance; part will be interest. Suppose$30 of the payment is for interest, while the remaining $70 reduces the loan balance. The effect of the payment on Acme’s balance sheet is shown below. Checkable deposits fall by$100, loans fall by $70, and net worth rises by the amount of the interest payment,$30.

Similar to the process of money creation, the money reduction process decreases checkable deposits by, at most, the amount of the reduction in deposits times the deposit multiplier.

Figure 9.8

## The Regulation of Banks

Banks are among the most heavily regulated of financial institutions. They are regulated in part to protect individual depositors against corrupt business practices. Banks are also susceptible to crises of confidence. Because their reserves equal only a fraction of their deposit liabilities, an effort by customers to get all their cash out of a bank could force it to fail. A few poorly managed banks could create such a crisis, leading people to try to withdraw their funds from well-managed banks. Another reason for the high degree of regulation is that variations in the quantity of money have important effects on the economy as a whole, and banks are the institutions through which money is created.

## Deposit Insurance

2. Now suppose that an Acme Bank customer, planning to take cash on an extended college graduation trip to India, withdraws $1,000 from her account. Show the changes to Acme Bank’s balance sheet and Acme’s balance sheet after the withdrawal. By how much are its reserves now deficient? 3. Acme would probably replenish its reserves by reducing loans. This action would cause a multiplied contraction of checkable deposits as other banks lose deposits because their customers would be paying off loans to Acme. How large would the contraction be? ### Case in Point: A Big Bank Goes Under Figure 9.9 It was the darling of Wall Street—it showed rapid growth and made big profits. Washington Mutual, a savings and loan based in the state of Washington, was a relatively small institution whose CEO, Kerry K. Killinger, had big plans. He wanted to transform his little Seattle S&L into the Wal-Mart of banks. Mr. Killinger began pursuing a relatively straightforward strategy. He acquired banks in large cities such as Chicago and Los Angeles. He acquired banks up and down the east and west coasts. He aggressively extended credit to low-income individuals and families—credit cards, car loans, and mortgages. In making mortgage loans to low-income families, WaMu, as the bank was known, quickly became very profitable. But it was exposing itself to greater and greater risk, according to the New York Times. Housing prices in the United States more than doubled between 1997 and 2007. During that time, loans to even low-income households were profitable. But, as housing prices began falling in 2007, banks such as WaMu began to experience losses as homeowners began to walk away from houses whose values suddenly fell below their outstanding mortgages. WaMu began losing money in 2007 as housing prices began falling. The company had earned$3.6 billion in 2006, and swung to a loss of $67 million in 2007, according to the Puget Sound Business Journal. Mr. Killinger was ousted by the board early in September of 2008. The bank failed later that month. It was the biggest bank failure in the history of the United States. The Federal Deposit Insurance Corporation (FDIC) had just rescued another bank, IndyMac, which was only a tenth the size of WaMu, and would have done the same for WaMu if it had not been able to find a company to purchase it. But in this case, JPMorgan Chase agreed to take it over—its deposits, bank branches, and its troubled asset portfolio. The government and the Fed even negotiated the deal behind WaMu’s back! The then chief executive officer of the company, Alan H. Fishman, was reportedly flying from New York to Seattle when the deal was finalized. The government was anxious to broker a deal that did not require use of the FDIC’s depleted funds following IndyMac’s collapse. But it would have done so if a buyer had not been found. As the FDIC reports on its Web site: “Since the FDIC’s creation in 1933, no depositor has ever lost even one penny of FDIC-insured funds.” ### Answer to Try It! Problem 1. Acme Bank is loaned up, since$2,000/$10,000 = 0.2, which is the required reserve ratio. Acme’s balance sheet is: Figure 9.10 2. Acme Bank’s balance sheet after losing$1,000 in deposits:

Figure 9.11

Required reserves are deficient by $800. Acme must hold 20% of its deposits, in this case , as reserves, but it has only$1,000 in reserves at the moment.

3. The contraction in checkable deposits would be

∆D = (1/0.2) × (−$1,000) = −$5,000


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# Lyapunov spectral analysis of a nonequilibrium Ising-like transition

Journal Article

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length~$\xi_\delta$ are insensitive to the onset of long-range ferromagnetic order. As a function of lattice coupling constant~$g$ and for certain lattice maps, the Lyapunov dimension density and other dynamical order parameters go through a minimum. The occurrence of this minimum as a function of~$g$ depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry, on the lattice dimensionality or on the position of the Ising-like transition. In one-space dimension, the spatial correlation length associated with magnitude fluctuations and the length~$\xi_\delta$ are approximately equal, with both varying linearly with the radius of the lattice coupling.

### Cited Authors

• O'Hern, CS; Egolf, DA; Greenside, HS

• 9964646

### Digital Object Identifier (DOI)

• 10.1103/PhysRevE.53.3374

format: plain


text:
# American Institute of Mathematical Sciences

ISSN:
1551-0018

eISSN:
1547-1063

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## Mathematical Biosciences & Engineering

2009 , Volume 6 , Issue 4

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2009, 6(4): 683-700 doi: 10.3934/mbe.2009.6.683 +[Abstract](685) +[PDF](567.6KB)
Abstract:
In this paper we study a Lotka-Volterra predator-prey system with prey logistic growth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determine the subset of omega-limit set of the system and show out the existence of a stationary distribution. We also focus on persistence of the predator and thus we look for conditions that allow persistence of the predator and prey community. We show that the asymptotic behaviour highly depends on the value of some constant $\lambda$ which is useful to make suitable predictions about the persistence of the system.
2009, 6(4): 701-718 doi: 10.3934/mbe.2009.6.701 +[Abstract](702) +[PDF](238.6KB)
Abstract:
We consider a selection mutation predator-prey model for the distribution of individuals with respect to an evolutionary trait. Local stability of the equilibria of this model is studied using the linearized stability principle and taking advantage of the (assumed) asymptotic stability of the equilibria of the resident population adopting an evolutionarily stable strategy.
2009, 6(4): 719-742 doi: 10.3934/mbe.2009.6.719 +[Abstract](692) +[PDF](407.0KB)
Abstract:
Harvesting and predation occur through contact processes in which the rate at which the managed (prey) population can be found depends on the population size, usually saturating at high densities. Many models incorporate saturation in this process without considering the effects of the particular function used to describe it. We show that the sharpness with which this saturation occurs has an important effect upon the resulting population dynamics, with bistability (sometimes involving a stable equilibrium and a stable limit cycle) occurring for saturation that is any sharper than the commonly used Michaelis-Menten (Holling type II) functional response. This sharpness threshold occurs across a wide range of model types, from simple harvesting to density-dependent and ratio-dependent predation.
2009, 6(4): 743-752 doi: 10.3934/mbe.2009.6.743 +[Abstract](827) +[PDF](154.8KB)
Abstract:
For a time-delayed reaction-diffusion equation of age-structured single species population, the linear and nonlinear stability of the traveling wavefronts were proved by Gourley [4] and Li-Mei-Wong [8] respectively. The stability results, however, assume the delay-time is sufficiently small. We now prove that the wavefronts remain stable even when the delay-time is arbitrarily large. This essentially improves the previous stability results obtained in [4, 8]. Finally, we point out that this novel stability can be applied to the age-structured reaction-diffusion equation with a more general maturation rate.
2009, 6(4): 753-778 doi: 10.3934/mbe.2009.6.753 +[Abstract](536) +[PDF](598.9KB)
Abstract:
Type 1 diabetes (T1DM) is a chronic autoimmune disease with a long prodrome, which is characterized by dysfunction and ultimately destruction of pancreatic $\beta$-cells. Because of the limited access to pancreatic tissue and pancreatic lymph nodes during the normoglycemic phase of the disease, little is known about the dynamics involved in the chain of events leading to the clinical onset of the disease in humans. In particular, during T1DM progression there is limited information about temporal fluctuations of immunologic abnormalities and their effect on pancreatic $\beta$-cell function and mass. Therefore, our understanding of the pathoetiology of T1DM relies almost entirely on studies in animal models of this disease. In an effort to elucidate important mechanisms that may play a critical role in the progression to overt disease, we propose a mathematical model that takes into account the dynamics of functional and dysfunctional $\beta$-cells, regulatory T cells, and pathogenic T cells. The model assumes that all individuals carrying susceptible HLA haplotypes will develop variable degrees of T1DM-related immunologic abnormalities. The results provide information about the concentrations and ratios of pathogenic T cells and regulatory T cells, the timing in which $\beta$-cells become dysfunctional, and how certain kinetic parameters affect the progression to T1DM. Our model is able to describe changes in the ratio of pathogenic T cells and regulatory T cells after the appearance of islet antibodies in the pancreas. Finally, we discuss the robustness of the model and its ability to assist experimentalists in designing studies to test complicated theories about the disease.
2009, 6(4): 779-813 doi: 10.3934/mbe.2009.6.779 +[Abstract](944) +[PDF](574.6KB)
Abstract:
After two phases of AIDS control activities in India, the third phase of the National AIDS Control Programme (NACP III) was launched in July 2007. Our focus here is to predict the number of people living with HIV/AIDS (PLHA) in India so that the results can assist the NACP III planning team to determine appropriate targets to be activated during the project period (2007-2012). We have constructed a dynamical model that captures the mixing patterns between susceptibles and infectives in both low-risk and high-risk groups in the population. Our aim is to project the HIV estimates by taking into account general interventions for susceptibles and additional interventions, such as targeted interventions among high risk groups, provision of anti-retroviral therapy, and behavior change among HIV-positive individuals. Continuing the current level of interventions in NACP II, the model estimates there will be 5.06 million PLHA by the end of 2011. If 50 percent of the targets in NACP III are achieved by the end of the above period then about 0.8 million new infections will be averted in that year. The current status of the epidemic appears to be less severe compared to the trend observed in the late 1990s. The projections based on the second phase and the third phase of the NACP indicate prevention programmes which are directed towards the general and high-risk populations, and HIV-positive individuals will determine the decline or stabilization of the epidemic. Model based results are derived separately for the revised HIV estimates released in 2007. According to revised projections there will be 2.08 million PLHA by 2012 if 50 percent of the targets in NACP III are reached. We perform a Monte Carlo procedure for sensitivity analysis of parameters and model validation. We also predict a positive role of implementation of anti-retroviral therapy treatment of 90 percent of the eligible people in the country. We present methods for obtaining disease progression parameters using convolution approaches. We also extend our models to age-structured populations.
2009, 6(4): 815-837 doi: 10.3934/mbe.2009.6.815 +[Abstract](1091) +[PDF](856.5KB)
Abstract:
Tuberculosis (TB) is the leading cause of death among individuals infected with the human immunodeficiency virus (HIV). The study of the joint dynamics of HIV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. Furthermore, although there is overlap in the populations at risk of HIV and TB infections, the magnitude of the proportion of individuals at risk for both diseases is not known. Here, we consider a highly simplified deterministic model that incorporates the joint dynamics of TB and HIV, a model that is quite hard to analyze. We compute independent reproductive numbers for TB ($\R_1$) and HIV ($\R_2$) and the overall reproductive number for the system, $\R =\max \{\R_1, \R_2\}$. The focus is naturally (given the highly simplified nature of the framework) on the qualitative analysis of this model. We find that if $\R <1$ then the disease-free equilibrium is locally asymptotically stable. The TB-only equilibrium $E_T$ is locally asymptotically stable if $\R_1>1$ and $\R_2<1$. However, the symmetric condition, $\R_1<1$ and $\R_2>1$, does not necessarily guarantee the stability of the HIV-only equilibrium $E_H$, and it is possible that TB can coexist with HIV when $\R_2>1$. In other words, in the case when $\R_1<1$ and $\R_2>1$ (or when $\R_1>1$ and $\R_2>1$), we are able to find a stable HIV/TB coexistence equilibrium. Moreover, we show that the prevalence level of TB increases with $\R_2>1$ under certain conditions. Through simulations, we find that i) the increased progression rate from latent to active TB in co-infected individuals may play a significant role in the rising prevalence of TB; and ii) the increased progression rates from HIV to AIDS have not only increased the prevalence level of HIV while decreasing TB prevalence, but also generated damped oscillations in the system.
2009, 6(4): 839-854 doi: 10.3934/mbe.2009.6.839 +[Abstract](969) +[PDF](545.1KB)
Abstract:
Rubella is a highly contagious childhood disease that causes relatively mild symptoms. However, rubella can result in severe congenital defects, known as congenital rubella syndrome (CRS), if transmitted from a mother to a fetus. Consequently, women have higher incentive to vaccinate against rubella than men do. Within the population vaccination reduces transmission but also increases the average age of infection and possibly the risk of CRS among unvaccinated females. To evaluate how the balance among these factors results in optimal coverage of vaccination, we developed a game theoretic age-structured epidemiological model of rubella transmission and vaccination. We found that high levels of vaccination for both genders are most effective in maximizing average utility across the population by decreasing the risk of CRS and reducing transmission of rubella. By contrast, the demands for vaccines driven by self-interest among males and females are $0\%$ and $100\%$ acceptance, respectively, if the cost of vaccination is relatively low. Our results suggest that the rubella vaccination by males that is likely to be achieved on voluntary basis without additional incentives would have been far lower than the population optimum, if rubella vaccine were offered separately instead of combined with measles and mumps vaccination as the MMR vaccine.
2009, 6(4): 855-871 doi: 10.3934/mbe.2009.6.855 +[Abstract](859) +[PDF](483.9KB)
Abstract:
We study an eco-epidemic model with two trophic levels in which the dynamics are determined by predator-prey interactions as well as the vulnerability of the predator to a disease. Using the concept of generalized models we show that for certain classes of eco-epidemic models quasiperiodic and chaotic dynamics are generic and likely to occur. This result is based on the existence of bifurcations of higher codimension such as double Hopf bifurcations. We illustrate the emergence of chaotic behavior with one example system.
2009, 6(4): 873-887 doi: 10.3934/mbe.2009.6.873 +[Abstract](747) +[PDF](337.1KB)
Abstract:
As obesity and its related health problems grow around the world, efforts to control and manage weight is increasing in importance. It is well known that altering and maintaining weight is problematic and this has led to specific studies trying to determine the cause of the difficulty. Recent research has identified that the body reacts to forced weight change by adapting individual total energy expenditure. Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. Forward time simulations of the model compare well with mean data in both overfeeding and calorie restriction studies.

2017  Impact Factor: 1.23


text:
# 73 questions

Tagged
• x
58
views
1
vote
1

I have an example combining BLE, UART and SPI in which I use RTT to watch the startup process. The SoC is nRF52 (BLE Nano2); building with armgcc. This works ok when JLink is connected. However, if I unplug the ... (more)

45
views
2
1

## Multiple devices debug in RTT viewer

Hey, is there a possibility to connect two or more devices to RTT viewer?

62
views
no
no

## RTT viewer multiple windows

Hi,

It looks like system (laptop windows 7) is not supporting more than two windows of RTT viewer simultaneously. When I connect, third one, it disconnects, one of the two's.

Is there any way to connect four windows of ... (more)

34
views
no
2

## RTT message logging with power cycles

Greetings,

I've got an embedded project where a NRF52 is a "co-processor". The NRF52 used to output UART debug messages but I've since changed this to use RTT.

During operation, the main microcontroller frequently performs a power cycle ... (more)

54
views
no
3

## SDK14 52810 rtt log

I used the 52810 board, with the SDK14. I modified the 52810 according to the official website related to the relevant definition. I can run the code but it does not print. The same code is programmed on the 52832 ... (more)

35
views
no
no

## Radio not working when RTT is in use

We are using a nRF52840 (QIAAAA) on a custom board which replicates exactly the schematic used by the development kit (PCA10056). When using Segger RTT for debugging purposes, the board does not emit any BLE packets (no errors are reported ... (more)

25
views
no
1

## ble_app_buttonless_dfu use RTT log

Hi, I'm useing ble_app_buttonless_dfu to get log with UART is possibly. I want to change RTT log. How can I do? Board is nRF52-DK. SDK is nRF5_SDK_14.0.0_3bcc1f7.

95
views
no
1

## SEGGER RTT printf() problem

Hi, I have problem with using printf() in SEGGER RTT.

I've read tutorial and others about SEGGER RTT printf() problem, but they didn't work.

When I use printf() in RTT and compile I got error like this:

[._build ... (more)

102
views
1
vote
1

## NRF_LOG_DEBUG() doesn't output in SDK14

Hi, I am running the ble_app_uart example from nRF5_SDK_14.0.0_3bcc1f7, and found that NRF_LOG_DEBUG() doesn't cause any log output. Although I have set #define NRF_LOG_ENABLED 1 and #define NRF_LOG_DEFAULT_LEVEL 4.

However, it's OK in the ... (more)

44
views
no
1

## RTT logging with freeRTOS and nRF5 SDK for Thread

I am trying to test a combination of BLE central role, Thread with CoAP server and FreeRTOS on an nRF52840 using version 0.10.0 of nRF5-SDK-for-Thread.

I don't seem able to get RTT traces from any example based ... (more)

22
views
no
no

## RTT infinite loop over initial commands

Hi,

Under Keil debbuging the J-Link RTT Viewer (or client) shows the initialization commands in an infinite loop (one after the other starting from the first ... (more)

63
views
2
2

## gpiote interrupt cannot wake sd_app_evt_wait? [closed]

I have tried to use sd_app_evt_wait() to sleep cpu, and use gpiote interrupt to wake up cpu from sleep. However, gpiote interrupt cannot wake up cpu. When I use __WFE(), gpiote interrupt can wake up cpu. And even if I ... (more)

96
views
no
1

## Undefined reference to SEGGER_RTT_printf, why?

HEllo I am having an error saying

Undefined reference to SEGGER_RTT_printf

I have looked into this post and tried it, however I am not able to fix it,I have defined GLOBAL_DEBUG on my preprocessor settings but the linker seems ... (more)

107
views
no
2

## RTT & RTT disable sdk 12/13 nRF52832/nRF52840

Dear all,

Help please, I'm evaluating ble_app_uart (Central/Peripheral) but I don't understand how to disable the echo I have on the RTT USB VCP

When I send data from the UART, I got (PCA10056/10040) the data ... (more)

95
views
no
1

## How to print out the time stamp in nRF log [closed]

Currently developing on NRF52 sdk12

I want to be able to show time stamp minutes:seconds:miliseconds on my RTT viewer, when I print my data out from the uC. Any hits on how to do that?

I'm looking ... (more)

126
views
no
1

## How to add timestamp in RTT viewer using NRF log module

Currently developing on NRF52 sdk12 with a terminal

In my source code i have nrf_log_init(null), and this allows me to print stuff to the RTT viewer.

Now I want to be able to show time stamp minutes:seconds:miliseconds ... (more)

82
views
2
1

## Jlink RTT Viewer not detecting Target Device Automatically

Hi,

I installed the latest version of Jlink 6.16f. I connected my nrf52-dk and on opening the RTT viewer, I always need to specify the target device manually instead of it being detected automatically. I am also attaching a ... (more)

35
views
no
no

## RTT Viewer colours

Hi all,

I am finding that the RTT Viewer is very unreliable at changing colour when sent commands from two different nRF52-DK boards. The text is coming out correctly, but the colours only change intermittently. I've tried dropping the ... (more)

40
views
no
no

## Error: L6200E: Symbol SEGGER_RTT_WaitKey multiply defined (by segger_rtt_1.o and segger_rtt.o).

Hi,

I followed the RTT tutorial but When I try to BUILD the project I got this error. What is it?

Error: L6200E: Symbol SEGGER_RTT_WaitKey multiply defined (by segger_rtt_1.o and segger_rtt.o).
Error: L6200E: Symbol SEGGER_RTT_WriteString multiply defined (by ...
(more)

62
views
no
no

## could not connect with RTT

hi team,

i have tried to connect my device with RTT. i could not connect. i just followed the instruction as below link

https://devzone.nordicsemi.com/tutori...

if i insert the function( SEGGER_RTT_WriteString(0, "Hello World!\n"); ) in main ... (more)

100
views
no
2

## How to use RTT in bootloader project

Hi,I want to use RTT in bootloader project. First,i add all files(SEGGER_RTT.c ,SEGGER_RTT_printf.c,RTT_Syscalls_KEIL.c) to my bootloader project(Picture 1). Second,I add nrf_log.c to my bootloader project and define NRF_LOG_USES_RTT(Picture 2 ... (more)

34
views
no
no

## free RTOS with RTT view

SEGGER_RTT_printf(0, "Hello World from SEGGER! %d\r\n", i); <== It not working.

But before execute vTaskStartScheduler() function. SEGGER_RTT_printf(0, "Hello World from SEGGER! %d\r\n ... (more)

114
views
no
1

## NRF_LOG_INF didn't show in RTT

I use SDK12.2, and I have enabled NRF_LOG_BACKEND_SERIAL_USES_RTT and NRF_LOG_ENABLED. But there was nothing show in J-link RTT and don't know why.

206
views
no
3

## RTT logging from application started by bootloader

Hello, Is it possible to get logs (RTT) from an application started by a bootloader? As of now I don't get anything after the bootloader has jumped to the application start address.

If I run the application separately it ... (more)

377
views
1
vote
1

## SEGGER_RTT works but NRF_LOG not

Hi, can you help me out please: I have followed https://devzone.nordicsemi.com/questi... and have configured as it shows.

But NRF_LOG_INFO does not work however SEGGER_RTT_printf does. What should i do? Thanks

367
views
2
2

## Connect to multiple Segger J-Link debuggers

Hello!

I need to interact with two J-Link debuggers, connected to the same PC at the same time. I would then read and write data to the devices connected to the debuggers.

To send/receive the data, I was thinking ... (more)

138
views
1
vote
1

## What are the right memory mapping for nrf52 & SEGGER Embedded Studiov3?

HEllo,

I am trying to compile for the nrf52 one of the examples that are included in its SDK12.2, to be precies, I am using experimental_ble_app_blinky_pca10040_s132, I have been able to compile it with KEIL but now I would ... (more)

260
views
5
1

## SEGGER RTT printf not printing all the lines.

I want to read whole flash memory using for loop and see how long it takes. What i have noticed is that it does not print all the lines. On the other side i ask myself: Does it read all ... (more)

525
views
no
no

## How to print float values using SEGGER RTT

Hi, My question is similar to this https://devzone.nordicsemi.com/questi... but I can't get it to work.

I am using SEGGER_RTT_WriteString and sprintf for debugging, but I am not able to print a float value such as ... (more)

297
views
1
vote
1

## "SEGGER_RTT_CONFIG" problem

Hey! I was trying to modify s132 ble_beacon example to s140 for my nRF52840 DK but I couldn't build it in Segger Embeded Studio. What is the problem with "SEGGER_RTT_CONFIG"?

#### Statistics

• Total users: 24465
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## Recent blog posts

• ### 6 Things to Know about Bluetooth Beacons

Posted 2017-09-22 08:27:00 by Rose Martin
• ### Creating a Keil project for a Bluetooth Mesh example

Posted 2017-09-19 12:08:11 by Kristian Skordal
• ### Using millis() like in Arduino.

Posted 2017-09-18 11:58:04 by schef
• ### Flashing nRF5x firmware using any dumb terminal program via standard serial COM port

Posted 2017-09-18 03:53:40 by Nguyen Hoan Hoang
• ### How to Debug the nRF52 Interrupts — Useful Tips

Posted 2017-09-13 15:15:22 by Yaniv Nis

## Recent questions

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Posted 2017-09-24 20:25:18 by michael
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• ### Can not find Nordic dongle from my application

Posted 2017-09-24 14:23:37 by ofer
• ### Can’t program BT832 Module using NRF52-DK

Posted 2017-09-24 10:47:56 by Alexey
• ### Is there any Dc offset on nRF52840 RF port ?

Posted 2017-09-24 09:43:40 by Artak


text:
# [dev-context] regression testing Makefile

Taco Hoekwater taco at elvenkind.com
Mon Feb 5 19:25:05 CET 2007

```Hans Hagen wrote:
> Sanjoy Mahajan wrote:
>
>>
>>  systems         : begin file test-001-20070123 at line 19
>>  (/tmp/a/ctxtrees/20070123/tex/context/base/unic-run.tex)kpathsea: Running mktextfm UnicodeRegular25
>>  /usr/share/texmf/web2c/mktexnam: Could not map source abbreviation U for UnicodeRegular25.
>>  /usr/share/texmf/web2c/mktexnam: Need to update /usr/share/texmf-texlive/fonts/map/fontname/special.map?
>>  mktextfm: Running mf-nowin -progname=mf \mode:=ljfour; mag:=1; nonstopmode; input UnicodeRegular25
>>  This is METAFONT, Version 2.71828 (Web2C 7.5.5)
>>  kpathsea: Running mktexmf UnicodeRegular25
>>
>>  ! I can't find file `UnicodeRegular25'.
>>
>

> ok, this comes because UnicodeRegular is not mapped onto a real font; such unicode things assume
> a font split up in ranges, so, best ask the author of the test what was meant to be

The author of the test may well have been me, I think I wrote a set for
each of the (at that point in time) existing Unicode blocks.

If the macros in unic-037 do not map to a real font and therefore raises
an error, then the test 'works', in my view.

Taco
```


text:
Why isn't the associated sheaf transformation onto?

What is an example of a presheaf $F$ such that the usual morphism $F\to \tilde F$ to the associated sheaf is not onto on all sections, i.e. there exists an $X$ and $F(X)\to \tilde F(X)$ is not onto?

-

3 Answers

Let $X$ be a topological space with enough open sets and points (say, a Hausdorff space with infinitely many points). Take any non-trivial sheaf $\mathscr{F}$ you like on $X$, and define $\mathscr{P}(U) = \mathscr{F}(U)$ if $U \ne X$ and $\mathscr{P}(X) = 0$. It is easy to check that this defines a presheaf $\mathscr{P}$, and that $\mathscr{P}$ has the same stalks as $\mathscr{F}$, so the sheafification $\tilde{\mathscr{P}}$ of $\mathscr{P}$ is isomorphic to $\mathscr{F}$. But obviously the canonical map $\mathscr{P} \to \tilde{\mathscr{P}}$ is not surjective on sections.

Exercise. Modify the above example so that $\mathscr{P} \to \tilde{\mathscr{P}}$ is not injective on sections either.

-

Let $X$ be a topological space on which there exists an unbounded continuous function$f:X\to \mathbb R$.
Take for $\mathcal F(U)$ the group $\mathcal C_b(U)$ of bounded real continuous functions on the open subset $U$.
Then $\tilde {\mathcal F}=\mathcal C$ is the sheaf of all continuous functions on $X$ and $f$ is not in the image of $\mathcal C_b (X) \to \mathcal C(X)$ .

-
A nice natural example! And the strange thing is that continuous functions $f : X \to \mathbb{R}$ are automatically locally bounded because the codomain is locally compact... –  Zhen Lin Mar 20 '12 at 19:45
Ah yes, I hadn't thought of the role of local compactness of the codomain. Thanks for this insightful remark, @Zhen. –  Georges Elencwajg Mar 20 '12 at 20:50

Your question comes up naturally when one tries to intuitively define the structure sheaf of an affine scheme. Basically, if you try to define the structure sheaf of $X=\DeclareMathOperator{\Spec}{Spec}\Spec R$, your thought process could go something like this:

Any open subset $U\subset\Spec R$ is the complement of the vanishing set of an ideal $I$ of elements of $R$, which means that the set $S=\{f\in R\colon$ f does not vanish anywhere on $U\}$ could potentially include more than just the units of $R$ (it contains $\DeclareMathOperator{\rad}{rad}\rad f$, for example, if $I=\langle f\rangle$). Therefore I will try to set $\mathscr F_X(U)=S^{-1}R$, the localization of $R$ at $S$ (note that $S$ is multiplicative), which will guarantee the only ''function'' vanishing on an open set $U$ is the zero function.

More formally, let $R_f=S^{-1}R$ where $S=\{1,f,f^2,\dots\}$. Then we have defined $\mathscr F_X(U)=\displaystyle\varinjlim_{V(f)\subset X\setminus U} R_f$.

Is the above, however, a sheaf? Let's check! Let the structure sheaf be the sheaffification $\mathscr O_X$ of $\mathscr F_X$. What is true is that the distinguished open sets $X_f=X\setminus V(\left<f\right>)$ with associated rings $S^{-1}R=R_f$ as in above form a $\mathscr B$-sheaf, that is, they form a topological basis for $X$, and satisfy the sheaf axioms for coverings by distinguished open sets, i.e. after sheaffification we would have $\mathscr O_X(X_f)=\mathscr F_X(X_f)=R_f$.

The sheaffifcation then gives that $\mathscr O_X(U)=\varprojlim_{X_g\subset U}\mathscr O_X(X_g)=\displaystyle\varprojlim_{X\setminus U\subset V(g)}R_g$.

Since $R_f$ injects into $R_g$ whenever $V(f)\subset V(g)$ (i.e. $\rad g\subset\rad f$ i.e. $g^n=fh$ for some $h\in R$, so both $g$ a unit implies $f$ a unit), we have that there exists a unique a injection $\displaystyle\varinjlim_{V(f)\subset X\setminus U} R_f\to\displaystyle\varprojlim_{X\setminus U\subset V(g)}R_g$, i.e. a unique injection $\mathscr F_X(U)\to\mathscr O_X(U)$.

Here then comes your question: is this sheaffifiction surjective? This it turns out is not an easy question to answer, especially when one is beginning to study this. I had the same question some months back, and Georges Elencwajg gave a very nice, instructive example of a ring $R$ and a Zariski open subset $U$ of $\Spec R$ where this sheaffification is NOT surjective.

-


text:
# Maximum permissible conductor temperature rise

Value of the conductor temperature rise above ambient in the steady-state due to Joule losses, i.e. the standard maximum permissible temperature rise.

Symbol
$\Delta \theta_{R,\infty}$
Unit
°C
Formulae
$\theta_{cmax}-\theta_a-\Delta \theta_d$
Related
$\Delta \theta_d$
$\theta_a$
$\theta_{cmax}$
Used in
$I_2$


text:
# Modeling viral growth

I'm trying to forecast the viral growth for a website I'm developing. I've arrived at some monthly growth rates I can expect per month, the difficulty is I'd like to model my growth per week instead.

Lets say I have these figures

            Growth Rate
Month 1             0.2
Month 2             0.1
Month 3            0.05
Month 4           0.025

What this means is that for every 5 new users to the site; they will invite another 1 new user in the first month. For every 10 new users, they will invite another user in their second month, etc. Looking at the pattern you can see that the growth rate decline is 50% each month. For the sake of simplicity we'll say the viral growth rate is 0 from month 5 onwards therefor a lifetime growth rate would be the sum of the first 4 months.

How does that translate to weekly growth rates, it's ok to make the assumption there's 4 weeks in a month.

Short version of the question (wrong)

I think what I need to calculate is (could be wrong), using month 1 as an example, how can I split 0.2 into four values where each is half (50%) the value of the previous but the sum of all four totals 0.2?

Short version findings

My theory towards approaching it in the short version is flawed, using that method I end up with results that look like this.

Growth           Week 1    Week 2    Week 3    Week 4     Total
Month 1            0.11      0.05      0.03      0.01       0.2
Month 2            0.05      0.03      0.01      0.01       0.1
Month 3            0.03      0.01      0.01         0      0.05
Month 4            0.01      0.01         0         0     0.025

(The values are rounded to 2dp)

This says that in week 4 there would be a viral growth rate of 0.01 whereas in week 5 there would be a growth rate of 0.05. Logically it shouldn't increase, each week should slowly decrease as if on a curve.

Would much appreciate any help on this, thanks.

If the growth rate falls by half every month, you don't want it to fall by half every week. As David Mitra says, that leads to $\frac {0.2}{15}=.0013333$ the last week of the first month. It would also give $8\cdot \frac {0.1}{15}=.005333333$ the first week of the second month, which doesn't make sense.
A more reasonable approach would be to multiply by $\frac 1{2^{1/4}}\approx 0.84$ every week. This retains the drop of a factor $2$ after four weeks. We follow the same approach. If the first week is $a$, we want $a(1+0.84+0.84^2+0.84^3)=0.2$, which gives $a=0.0637$, so you have $0.0637$ the first week, $0.0535$ the second week, $0.0450$ the third week, and $0.0378$ the fourth week, which nicely total to $0.2$ Now for the next month, divide each by $2$


text:
# japan oxygen can be found within two

Production Environment

Cooperation partner

Minimum Oxygen Concentration for Human Breathing | Sciencing- japan oxygen can be found within two ,Mar 10, 2018·Humans need oxygen to live, but not as much as you might think. The minimum oxygen concentration in the air required for human breathing is 19.5 percent. The human body takes the oxygen breathed in from the lungs and transports it to the other parts of the body via the body's red blood cells. Each cell uses and requires oxygen to thrive.Should Japan dump radioactive water from Fukushima into ...Oct 23, 2020·Around 1.2 million tonnes of water contaminated by radioactive substances from the 2011 Fukushima disaster will be dumped in the Pacific ocean, under …

### Oxygen Transport - Haemoglobin - Bohr Shift ...

May 20, 2021·Transport of Oxygen. Oxygen is transported in the blood in two ways: Dissolved in the blood (1.5%).; Bound to haemoglobin (98.5%).; Bound to Haemoglobin. Once oxygen has entered the blood from the lungs, it is taken up by haemoglobin (Hb) in the red blood cells.. Haemoglobin is a protein found in red blood cells that is comprised of four subunits: two alpha subunits and two beta subunits.

### Clarification of OSHA's requirement for breathing air to ...

Apr 02, 2007·At oxygen levels of 10 to 14 percent, faulty judgment, intermittent respiration, and exhaustion can be expected even with minimal exertion (Exs. 25-4 and 150). Breathing air containing 6 to 10 percent oxygen results in nausea, vomiting, lethargic movements, and perhaps unconsciousness.

### 3 Ways to Increase Oxygen Levels in Your Home - wikiHow

Oct 22, 2019·There are 20 references cited in this article, which can be found at the bottom of the page. This article has been viewed 90,236 times. If you’re struggling with a chronic illness like COPD, heart failure, or sleep apnea, increasing your oxygen at home can help improve your symptoms. [1]

### What Causes Ocean "Dead Zones"? - Scientific American

Sep 25, 2012·The cause of such “hypoxic” (lacking oxygen) conditions is usually eutrophication, an increase in chemical nutrients in the water, leading to excessive blooms of …

### How to Make Oxygen and Hydrogen from Water Using Electrolysis

Apr 13, 2020·The process of splitting water (H 2 O) into its atomic components (hydrogen and oxygen) using electricity is known as electrolysis. This experiment has significant implications in terms of what these 2 gases can be used for in their own right, with hydrogen being one of the cleanest sources of energy we have access to.

### Polyethylene terephthalate - Wikipedia

Plastic bottles made from PET are widely used for soft drinks (see carbonation).For certain specialty bottles, such as those designated for beer containment, PET sandwiches an additional polyvinyl alcohol (PVOH) layer to further reduce its oxygen permeability.. Biaxially oriented PET film (often known by one of its trade names, "Mylar") can be aluminized by evaporating a thin film of metal ...

### 10 Uses for Oxygen | Sciencing

Jan 28, 2020·Oxygen makes up about 21 percent of the atmosphere. It is vital in industrial, medical and engineering settings. It is needed in home oxygen therapy, aerospace and metallurgy applications. The many functions of oxygen are often masked by the fact that most people regard it …

### Mammalian enteral ventilation ameliorates respiratory ...

May 14, 2021·O 2-PFD can be recycled after collection into an outlet bag (Argyle TM Dennis TM colorectal tube, CardinalHealth TM, Tokyo, Japan) placed in the rectum of the pig. Blood pressure, peripheral arterial oxygen saturation (SpO 2), endo tidal carbon dioxide (EtCO 2) and arterial blood gas analysis were estimated during the experiments. We used iSTAT ...

### Transport of Oxygen in the Blood | Biology for Majors II

The oxygen-carrying capacity of hemoglobin determines how much oxygen is carried in the blood. In addition to $\text{P}_{\text{O}_2}$, other environmental factors and diseases can affect oxygen carrying capacity and delivery. Carbon dioxide levels, blood pH, and body temperature affect oxygen-carrying capacity (Figure 2).

### Clarification of OSHA's requirement for breathing air to ...

Apr 02, 2007·At oxygen levels of 10 to 14 percent, faulty judgment, intermittent respiration, and exhaustion can be expected even with minimal exertion (Exs. 25-4 and 150). Breathing air containing 6 to 10 percent oxygen results in nausea, vomiting, lethargic movements, and perhaps unconsciousness.

### COVID-19 Strategy: The Japan Model – The Diplomat

Apr 24, 2020·According to Ministry of Health, Labour and Welfare statistics, 11,772 Japanese had been infected with the COVID-19 coronavirus as of April 23, with 287 total deaths. These numbers have been ...

### Japan researchers say ozone effective in neutralising ...

Aug 26, 2020·Ozone, a type of oxygen molecule, is known to inactivate many pathogens, and previously experiments have shown that high concentrations, between 1-6 ppm, were effective against the coronavirus but ...

### Obligate anaerobe - Wikipedia

Oxygen can also damage obligate anaerobes in ways not involving oxidative stress. Because molecular oxygen contains two unpaired electrons in the highest occupied molecular orbital, it is readily reduced to superoxide (O − 2) and hydrogen peroxide (H 2 O 2) within cells.

### Molecular oxygen - Energy Education

Molecular oxygen (O 2) is a diatomic molecule that is composed of two oxygen atoms held together by a covalent bond. Molecular oxygen is essential for life, as it is used for respiration by many organisms. It's also essential for fossil fuel combustion.. Molecular oxygen is very chemically reactive, and tends to form oxides by reaction with other elements and compounds quite easily.

### Anal oxygen supply to treat worst-case breathing woes ...

May 15, 2021·COVID-19 Update. Visit this page for the latest news on Japan’s battle with the novel coronavirus pandemic. Reporter’s COVID-19 Notebook. A mother of two …

### Hydrogen fuel - Wikipedia

Hydrogen fuel is a zero carbon fuel burned with oxygen. It can be used in fuel cells or internal combustion engines.It has begun to be used in commercial fuel cell vehicles, such as passenger cars, and has been used in fuel cell buses for many years. It is also used as a fuel for spacecraft propulsion.. As of 2018, the majority of hydrogen (∼95%) is produced from fossil fuels by steam ...

### How oxygen is made - material, manufacture, making ...

Worldwide the five largest oxygen-producing areas are Western Europe, Russia (formerly the USSR), the United States, Eastern Europe, and Japan. Raw Mcatericals Oxygen can be produced from a number of materials, using several different methods.

### Fig 2. Remarkable improvement of fatal hypoxemia by ...

May 14, 2021·Tokyo, Japan - Oxygen is crucial to many forms of life. Its delivery to the organs and tissues of the body through the process of respiration is vital for most biological processes. Now ...

### Transport of Oxygen in the Blood | Biology for Majors II

The oxygen-carrying capacity of hemoglobin determines how much oxygen is carried in the blood. In addition to $\text{P}_{\text{O}_2}$, other environmental factors and diseases can affect oxygen carrying capacity and delivery. Carbon dioxide levels, blood pH, and body temperature affect oxygen-carrying capacity (Figure 2).

### Japan's battery startups take the world beyond lithium ion ...

Aug 02, 2020·Now Japan's hopes to remain among the global heavyweights in a market expected to be worth more than 2.7 trillion yen (\$25 billion) by 2035 rest on the ability of its engineers.

### oxygen | Discovery, Symbol, Properties, Uses, & Facts ...

Oxygen, a colorless, odorless, tasteless gas essential to living organisms, being taken up by animals, which convert it to carbon dioxide; plants, in turn, utilize carbon dioxide as a source of carbon and return the oxygen to the atmosphere. Oxygen forms compounds by reaction with practically any other element.

### Exoplanets could have lots of oxygen but no life - Big Think

Apr 20, 2021·Under these conditions, the molten surface of a young exoplanet can freeze while the limited water supply is still found only as steam (vapor) in the atmosphere. This prevents oxygen …

### Exoplanets could have lots of oxygen but no life - Big Think

Apr 19, 2021·If an exoplanet houses life, it almost certainly will have gaseous oxygen. But a new study modeling the development of rocky planets identifies three scenarios in which oxygen can …

### It's Elemental - The Element Oxygen

Oxygen is the third most abundant element in the universe and makes up nearly 21% of the earth's atmosphere. Oxygen accounts for nearly half of the mass of the earth's crust, two thirds of the mass of the human body and nine tenths of the mass of water. Large amounts of oxygen can be extracted from liquefied air through a process known as ...


text:
# LECTURER IN PURE MATHEMATICS (TWO POSITIONS AVAILABLE)

Job no: 0039336
Work type: Continuing
Location: Parkville

School of Mathematics and Statistics
Faculty of Science

Salary: $92,654 –$110,022 p.a. plus 17% superannuation

The School of Mathematics and Statistics is seeking to expand its expertise in Pure Mathematics. Applications from researchers working in some area of Analysis are strongly encouraged.

The successful applicant is expected to lead a vigorous research program in pure mathematics, and should also have a strong commitment to teaching and the supervision of research students. Teaching will occur within the School of Mathematics and Statistics undergraduate and MSc programs. He/she is also required to supervise research students at undergraduate, MSc and PhD levels.

The University of Melbourne provides a wide range of opportunities for exciting research collaborations within the School, wider University, as well as externally. The successful applicant will be expected to undertake administrative tasks for the School.

Close date: 16 Aug 2015

Organisation:
Job location:
The University of Melbourne
Grattan Street
Parkville VIC 3010
Australia
Contact and application information
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text:
Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

## Many-Argument Relations

Edmund Woronowicz
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

### Summary.

Definitions of relations based on finite sequences. The arity of relation, the set of logical values {\it Boolean} consisting of {\it false} and {\it true} and the operations of negation and conjunction on them are defined.

#### MML Identifier: MARGREL1

The terminology and notation used in this paper have been introduced in the following articles [4] [2] [6] [1] [7] [3] [5]

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[3] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[4] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[5] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[6] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[7] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.


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# Just simplify everything, right?

Geometry Level 4

In the domain $[ 0^ \circ, 360 ^ \circ ],$ how many solutions are there to $\frac {\tan 2x- \tan x}{1+\tan 2x\tan x}=1?$

×


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# Which of the following is correct? A) The partial pressure of oxygen in systemic venous blood is...

## Question:

Which of the following is correct?

A) The partial pressure of oxygen in systemic venous blood is normally 40 mmHg.

B) The partial pressure of carbon dioxide in systemic venous blood is normally 40 mmHg.

C) The partial pressure of oxygen is normally lower in the alveoli than in systemic arterial blood.

D) The partial pressure of carbon dioxide is normally higher in the alveoli than in systemic arterial blood.

E) The partial pressures of carbon dioxide in the alveoli and pulmonary arterial blood are the same.

## Arteries:

An essential blood vessel that plays a major role in supplying blood is known as the arteries. Four layers of arteries, such as tunica externa, tunica media, tunica interna and basal membrane. Arteries carry oxygen-rich blood.

The partial pressure of carbon dioxide is always higher in pulmonary arteries because the partial pressure of oxygen is low in the pulmonary capillaries. Oxygen diffuses out of the membrane, so the partial pressure of carbon dioxide is normally higher in alveoli.

Therefore the correct option is D)

According to Bohr, effect gases moves from the low-pressure area to the high-pressure area.

• Option A) is incorrect because the partial pressure of oxygen in venous blood is about 70 to 80 mmHg.
• Option B) is incorrect because the partial pressure of carbon dioxide in venous blood is about 104 mmHg.
• Option C) is incorrect because the partial pressure of oxygen is high in system arterial blood.
• Option E) is incorrect because pulmonary arterial blood pressure differs from alveoli.

Carbon Dioxide Transport in the Blood

from

Chapter 13 / Lesson 4
118K

Carbon dioxide is transported in the blood in two different forms, bicarbonate and carbaminohemoglobin. In this lesson, dive into carbon dioxide transportation in the blood, in the lungs, and in metabolizing tissues.


text:
# aliquote

## < a quantity that can be divided into another a whole number of time />

Typing Haskell in Haskell (PDF, 38 pp.). #haskell


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# Is the reaction thermodynamically favored or not?

$\ce{CO(g) + 2H2(g) +O2(g) <=> 2CH3OH(g)}$,

$\Delta H=-128\ \mathrm{kJ/mol}$
$\Delta S=-409.2\ \mathrm{J/(mol \cdot K)}$

Determine if the reaction if thermodynamically favored.

I just wanted someone to see if my logic is right. Since there are 4 moles on the reactants side and and 2 on the products side the reaction would not be thermodynamically favored because the reaction decreases the amount of entities, which decreases the entropy.

Your reasoning is correct but there is more to it.

Look at it from the point of view of Gibbs Free Energy,

$\Delta G = \Delta H - T \Delta S$

For a given reaction if:

$\Delta G >0$, the reaction is nonspontaneous in the forward direction, not thermodynamically favourable

$\Delta G < 0$, the reaction is spontaneous in the forward direction, thermodynamically favourable

If we substitute the values for $\Delta H$ and $\Delta S$:

$\Delta G=(-128\ \mathrm{kJ/mol}) - T\left(-0.409\ \mathrm{kJ/(mol \cdot K)}\right)$

Mathematically, $\Delta G$ will become positive only when $T$ is greater than 313K. Because of this, the reaction is thermodynamically favorable at any temperature less than 313K (since $\Delta G$ will be negative), but is not thermodynamically favorable at any temperature greater than 313K (since $\Delta G$ will be positive).

• thank you! I did not think about the reasoning using delta G or H to figure out that delta G was negative. This helped a lot! – sloth1111 Jan 5 '14 at 22:02
• Just one more thing, in your last sentence you mention about "when $T$ becomes very negative", but that doesn't make sense, as absolute temperatures are always positive except in certain systems while using a certain definition of absolute temperature. – Nicolau Saker Neto Jan 5 '14 at 22:13
• I meant from a mathematical perspective, but I should make that more clear – pingOfDoom Jan 5 '14 at 22:23
• What @pingOfDoom is saying is that only way that delta G can become positive is if T is negative. Because this is physically impossible, delta G can never be positive. – Georgeos Hardo Jan 1 '17 at 3:53


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Using Fourier Analysis to determine Green's Function of Laplace's equation

I have previously seen the Green's function for Laplace's equation in two spatial dimensions determined using the method of images. Since then, I have learned some more Fourier analysis and have attempted this problem using Fourier machinery. I'm still in the process of learning, and would therefore appreciate if someone can point out if there's anything wrong with my work.

Let $\mathcal{L} = \Delta = \partial_{x}^{2} + \partial_{y}^{2}$. Green's function must satisfy $\mathcal{L}G(x, y; x_{0}, y_{0}) = \delta((x,y) - (x_{0}, y_{0}))$.

Before taking the Fourier transform, we note that the Fourier transform of $\mathcal{L}$ can be written as the polynomial $-(\xi_{1}^{2} + \xi_{2}^{2})$, where $(\xi_{1}, \xi_{2})$ live in the range of the Fourier transform. Thus, if we let $z = (x,y)$, $z_{0} = (x_{0}, y_{0})$ and $\xi = (\xi_{1}, \xi_{2})$:

$$\mathcal{F} \left[ \mathcal{L}G(z ; z_{0})\right] = \mathcal{F}[\delta(z - z_{0})]$$

which I have reduced to:

$$\mathcal{F}(\mathcal{L})(\xi) \mathcal{F}(G)(\xi; z_{0}) = e^{-i \xi \cdot z_{0}}$$

and so we can take the inverse Fourier transform to find the Green's function:

$$G(z, z_{0}) = \frac{1}{(2 \pi)^{2}} \int_{\mathbb{R}^{2}} \frac{e^{-i \xi \cdot z_{0}}}{-(\xi_{1}^{2} + \xi_{2}^{2})} e^{i \xi \cdot z} d\xi = \frac{1}{4 \pi^{2}} \int_{\mathbb{R}^{2}} \frac{e^{-i \xi \cdot (z_{0} - z)}}{-(\xi_{1}^{2} + \xi_{2}^{2})} d\xi$$

I suppose that if I use this method, it's okay to learn the solution in integral form? Or is there a straightforward way to compute this integral?


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# Questions

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### How to isolate $f(x)$ in $f(x+a)=f(x)+a\times g(x)$?

nov 2 11 at 2:54 Barry Cipra 3,2041818

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-1
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### How to find the sum? [closed]

nov 15 11 at 1:27 GarouDan 314

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### Matrices. $XX^t=A$. $X=?$

nov 7 11 at 7:03 Brendan McKay 9,11111333

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### Odd perfect numbers. What’s the best progess we now about them? [closed]

oct 31 11 at 14:08 GarouDan 314

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### How to prove? Prime numbers. [closed]

nov 2 11 at 15:42 GarouDan 314

0


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Meaning of regression coefficients

I am having some trouble understanding exactly what is meant by the "true" Regression coefficients. Let's say it is stated that "the true regression coefficients are given as $$y=a+bx+e$$ where the error term fulfills all the OLS assumptions. Does this mean

a) Given knowledge of the value x takes one would describe their belief about the value y takes with the probability distribution on the right hand side.

b)a one unit change of x in a certain instance would cause the expected value of y to change by b.

a) not sure what exactly you mean here by probability distribution but if you mean the distribution of potential Y given the distribution of estimated coefficient b and a it would be correct, although usually we look at expectation to get single number than on distribution in which case it would be $$E(Y|X)$$

b) is correct

• but aren't these two interpretations mutually exclusive? – Jemlin95 Jan 5 at 1:03
• @Jemlin95 why do you think they are? – 1muflon1 Jan 5 at 1:07
• Let's say the "true" model for health expenditure is given as h=a+bi+e where i is income. According to the second interpretation if I were to give a family an extra 1 unit a month I would expect their health expenditures to rise by b units. According to the first interpretation this may not be true since perhaps people who earn more spend a higher proprtion of their income on health expenditures. – Jemlin95 Jan 5 at 1:24
• @Jemlin95 I am not sure if I understood your A interpretation correctly (b is clear and it’s correct) I understood your A interpretation in a way that at any point there is a distribution of Y for example if b=2 and standard error of b=0.1 then if x increases by 1 the mean expected increase of Y will be 2 but there will be an distribution around this expected increase t(2,0.1) so for example with 95% confidence the true increase will be somewhere between approximately 1.8 and 2.2. Maybe I misunderstood your A so let me know if you mean something else by distribution – 1muflon1 Jan 5 at 1:29
• No, I mean that the expected value of y conditional on x is equal to a+bx – Jemlin95 Jan 5 at 1:32

It might be too long for a comment so I write it as an answer. Apologies if I missed any ongoing discussions. Let me say the general background first and then my thoughts about OP's question.

The model $$y=a+bx+e$$ as such tells us nothing about what the true $$b$$ is. We need more restrictions to identify $$b$$. There can be many ways of making identifying restrictions. Some are:

1. $$E(e|x)=0$$,

2. $$median(e|x)=0$$,

3. $$e|x \sim N(0, \sigma^2)$$,

4. the distribution of $$e$$ conditional on $$x$$ is independent of $$x$$,

5. $$E(e|z_1, z_2)=0$$ for some other given $$z_1$$ and $$z_2$$,

or many possible others. We have 3 => 1, 4 => 1, 3 => 2, and 4 => 2. Each identifying restriction is associated with the "true" $$b$$ parameter. The true $$b$$ identified by 1 is not necessary equal to that by 2. We know that the true $$b$$ by 1 (the probability limit of OLS) may be different from the true $$b$$ by 5 (the probability limit of 2SLS).

Identification by condition 1 gives OP's "interpretation b". OP's "interpretation a" seems related with option 3 or 4 above, but it is unclear since OP does not give enough information about the population distribution. The distribution of $$y$$ (or equivalently of $$e$$) given $$x$$ should be specified somehow to achieve the identification of the true $$b$$.

How to interpret $$b$$ is actually the same as how to define the true $$b$$, and defining $$b$$ requires restrictions. Like I said at the beginning, just writing $$y=a+bx+e$$ is uninformative about what the true $$b$$ is.

Now to the question, OP says, "the error term fulfills all the OLS assumptions", which I understand as $$E(e|x)=0$$. Then OP's interpretation "b" is correct. Note that "b" is correct because OP assumed so ("the OLS assumptions fulfilled") not because of any other fancy reasons.

The true $$b$$ associated with OP's "a" (if the probability distribution was specified) may or may not be equal to the true $$b$$ associated with $$E(e|x)=0$$. But if the distribution of $$e$$ conditional on $$x$$ is independent of the $$x$$ value, then its conditional mean should also be independent of $$x$$. So "a" is also correct if "a" is rephrased to something like: (c) "Given knowledge of the value $$x$$ takes one would describe their belief about the value $$y$$ takes with the probability distribution describe by the right hand side under the assumption that the distribution of $$e$$ conditional on $$x$$ is independent of $$x$$". That's because 4 implies 1. Here correct means the true parameter defined by "c" is the same as the true parameter defined by "b".


text:
Notice

This document is for a development version of Ceph.

# Stability¶

Cephadm is a new feature in the Octopus release and has seen limited use in production and at scale. We would like users to try cephadm, especially for new clusters, but please be aware that some functionality is still rough around the edges. We expect fairly frequent updates and improvements over the first several bug fix releases of Octopus.

Cephadm management of the following components are currently well-supported:

• Monitors

• Managers

• OSDs

• CephFS file systems

• rbd-mirror

• NFS

• iSCSI

The following components are working with cephadm, but the documentation is not as complete as we would like, and there may be some changes in the near future:

• RGW

Cephadm support for the following features is still under development:

• RGW-HA

If you run into problems, you can always pause cephadm with:

ceph orch pause

Or turn cephadm off completely with:

ceph orch set backend ''


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CAS：78-93-3

CAS：108-94-1

CAS：67-64-1

CAS：64-19-7

CAS：141-78-6

CAS：108-88-3

CAS：71-43-2

CAS：64-17-5

CAS：67-56-1

### Ethyl acetate - American Chemical Society

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### Hydrolysis of ethyl acetate in hydrochloric acid solutions …

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text:
Compact Schur-Weyl duality and the affine Type B/C Brauer algebra

Research paper by Kieran Calvert

Indexed on: 18 Dec '20Published on: 25 Sep '19Published in: arXiv - Mathematics - Representation Theory

Abstract

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups. Thus we obtain a compact analogue of Schur-Weyl duality. We study functors $F_{\mu,k}$ from the category of admissible $O(p,q)$ or $Sp_{2n}(\mathbb{R})$ modules to representations of the type B/C affine Brauer algebra $\mathfrak{B}_k^\theta$. Thus providing a Akawaka-Suzuki-esque link between $O(p,q)$ (or $Sp_{2n}(\mathbb{R})$) and $\mathfrak{B}_k^\theta$. Furthermore these functors take non spherical principal series modules to principal series modules for the graded Hecke algebra of type $D_k$, $C_{n-k}$ or $B_{n-k}$. With this we get a functorial correspondence between admissible simple $O(p,q)$ (or $Sp_{2n}(\mathbb{R})$) modules and graded Hecke algebra modules.


text:
# What happens when the frequency of A.C becomes infinite?

In an alternating current, the flow of electric charge periodically reverses direction, and the number of times it does that is called the frequency of the current. However, if the frequency of an AC is made infinite, would any current flow? I asked this question to my school teacher and he was unable to provide me with an answer unfortunately.

If I consider a horizontal wire, through which an AC is flowing, then I can say that an electron in the wire is moving 50 times left and 50 times right, if the frequency is assumed to be 50Hz. It seems to me that if I increase the frequency, the displacement of the electrons in both the directions, that is left and right, will gradually decrease, and finally become 0, when frequency is infinite, thus making I = 0.

What have I got wrong?