Bounds for the logarithm of the Euler gamma function and its derivatives

We consider differences between $\log \Gamma(x)$ and truncations of certain classical asymptotic expansions in inverse powers of $x-\lambda$ whose coefficients are expressed in terms of Bernoulli polynomials $B_n(\lambda)$, and we obtain conditions under which these differences are strictly completely monotonic. In the symmetric cases $\lambda=0$ and $\lambda=1/2$, we recover results of Sonin, N\"orlund and Alzer. Also we show how to derive these asymptotic expansions using the functional equation of the logarithmic derivative of the Euler gamma function, the representation of $1/x$ as a difference $F(x+1)-F(x)$, and a backward induction.Comment: 15 page

Non-destructive evaluation of concrete using a capacitive imaging technique : preliminary modelling and experiments

This paper describes the application of capacitive imaging to the inspection of concrete. A two-dimensional finite-element method was employed to model the electric field distribution from capacitive imaging probe, and how it interacts with concrete samples. Physical experiments with prototype capacitive imaging probes were also carried out. The proof-of-concept results indicated that the capacitive imaging technique could be used to detect cracks on the surface of concrete samples, as well as sub-surface air voids and steel reinforcement bars

Liquidity Shortages and Banking Crises

We show in this paper that bank failures can be contagious. Unlike earlier work where contagion stems from depositor panics or ex ante contractual links between banks, we argue bank failures can shrink the common pool of liquidity, creating or exacerbating aggregate liquidity shortages. This could lead to a contagion of failures and a possible total meltdown of the system. Given the costs of a meltdown, there is a possible role for government intervention. Unfortunately, liquidity problems and solvency problems interact and can cause each other, making it hard to determine the root cause of a crisis from observable factors. We propose a robust sequence of intervention.

Money in a Theory of Banking

We explore the connection between money, banks, and aggregate credit. We start with a simple real' model without money, where banks make loans repayable in goods and depositors hold claims on the bank payable on demand in goods. Aggregate production may be delayed in the economy. If so, we show that the level of ongoing bank lending, and hence of aggregate future output, can decrease with increases in the real repayment due on deposits: ceteris paribus, the higher the amount due, the more likely there will be insufficient goods, given the delay, to pay depositors, and the more new lending has to be curtailed to make up the shortfall. Thus a temporary delay in production can be exacerbated by banks into a more permanent reduction of total output. A number of inefficiencies including bank failures can result if deposits turn out to be too high. We then introduce money in this model. We show that if demand deposits are repayable in money rather than in goods, banks can be hedged against production delays: under certain circumstances, the price level will rise with delays in production, reducing the real value of the deposits banks have to pay out. But demand deposits payable in money can expose the banks to new risks: the value of money can fluctuate for reasons other than delays in aggregate production. Because deposits are convertible into money on demand, a temporary rise in money demand immediately boosts the interest rate banks have to pay depositors, which in turn boosts the real amounts banks have to repay them. This increase in the real deposit burden can again lead to the curtailment of bank lending and even bank failures. The way to combat these contractionary effects is to infuse more money into the banking system. Our analysis thus makes transparent how changes in the supply of money can work through banks to affect real economic activity, without invoking sticky prices, reserve requirements, or deposit insurance. It also suggests how bank failures could lead to a fall in prices and a contagion of bank failures, as described by Friedman and Schwartz (1963).

Banks, Short Term Debt and Financial Crises: Theory, Policy Implications and Applications

Short-term borrowing has often been blamed for precipitating financial crises. We argue that while the empirical association between a financial institution's, or country's, short-term borrowing and susceptibility to crises may, in fact, exist, the direction of causality is often precisely the opposite to the one traditionally suggested by commentators. Institutions like banks that want to enhance their ability to provide liquidity and credit to difficult borrowers have to borrow short-term. Similarly countries that have poor disclosure rules and inadequate investor protections, have limited long-term debt capacity, and will find their borrowing becoming increasingly short-term as they finance illiquid investment. Thus it is the increasing illiquidity of the investment being financed (or the deteriorating credit quality of borrowers) that necessitates short-term financing, and causes the susceptibility to crises. In fact, once illiquid investments have been financed, rather than making the system more stable, a ban on short-term financing may precipitate a more severe crisis. Even a priori, a ban is not without adverse consequences policy makers have to trade off the costs of decreased credit creation and investment against the benefits of greater stability. A ban on short-term debt often deals with symptoms rather than underlying causes.

Liquidity Shortages and Banking Crises

Banks can fail either because they are insolvent or because an aggregate shortage of liquidity can render them insolvent. We show that bank failures can themselves cause liquidity shortages. The failure of some banks can then lead to a cascade of failures and a possible total meltdown of the system. Contagion here is not caused by contractual or informational links between banks but because bank failure could lead to a contraction in the common pool of liquidity. There is a possible role for government intervention. Unfortunately, liquidity problems and solvency problems interact, and can each cause the other. It is therefore hard to determine the root cause of a crisis from observable factors. The practical difficulty of determining the most appropriate intervention, as well as the costs of the wrong kind of intervention (such as infusing capital when the need is for liquidity) have to be traded off against the costs of a meltdown, which can be substantial. We propose a robust sequence of intervention.

A Theory of Bank Capital

Banks can create liquidity because their deposits are fragile and prone to runs. Increased uncertainty can make deposits excessively fragile in which case there is a role for outside bank capital. Greater bank capital reduces liquidity creation by the bank but enables the bank to survive more often and avoid distress. A more subtle effect is that banks with different amounts of capital extract different amounts of repayment from borrowers. The optimal bank capital structure trades off the effects of bank capital on liquidity creation, the expected costs of bank distress, and the ease of forcing borrower repayment. The model can account for phenomena such as the decline in average bank capital in the United States over the last two centuries. It points to overlooked side-effects of policies such as regulatory capital requirements and deposit insurance.

Liquidity Risk, Liquidity Creation and Financial Fragility: A Theory of Banking

Both investors and borrowers are concerned about liquidity. Investors desire liquidity because they are uncertain about when they will want to eliminate their holding of a financial asset. Borrowers are concerned about liquidity because they are uncertain about their ability to continue to attract or retain funding. Because borrowers typically cannot repay investors on demand, investors will require a premium or significant control rights when they lend to borrowers directly, as compensation for the illiquidity investors will be subject to. We argue that banks can resolve these liquidity problems that arise in direct lending. Banks enable depositors to withdraw at low cost, as well as buffer firms from the liquidity needs of their investors. We show the bank has to have a fragile capital structure, subject to bank runs, in order to perform these functions. Far from being an aberration to be regulated away, the funding of illiquid loans by a bank with volatile demand deposits is rationalized in the context of the functions it performs. This model can be used to investigate important issues such as narrow banking and bank capital requirements.

Breaking Kelvin: Circulation conservation and vortex breakup in MHD at low Magnetic Prandtl Number

In this paper we examine the role of weak magnetic fields in breaking Kelvin's circulation theorem and in vortex breakup in two-dimensional magnetohydrodynamics for the physically important case of a low magnetic Prandtl number (low $Pm$) fluid. We consider three canonical inviscid solutions for the purely hydrodynamical problem, namely a Gaussian vortex, a circular vortex patch and an elliptical vortex patch. We examine how magnetic fields lead to an initial loss of circulation $\Gamma$ and attempt to derive scaling laws for the loss of circulation as a function of field strength and diffusion as measured by two non-dimensional parameters. We show that for all cases the loss of circulation depends on the integrated effects of the Lorentz force, with the patch cases leading to significantly greater circulation loss. For the case of the elliptical vortex the loss of circulation depends on the total area swept out by the rotating vortex and so this leads to more efficient circulation loss than for a circular vortex.Comment: 21 pages, 12 figure