Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations

We use Fr\"olicher-Nijenhuis theory to obtain global Helmholtz conditions, expressed in terms of a semi-basic 1-form, that characterize when a semispray is locally Lagrangian. We also discuss the relation between these Helmholtz conditions and their classic formulation written using a multiplier matrix. When the semi-basic 1-form is 1-homogeneous (0-homogeneous) we show that two (one) of the Helmholtz conditions are consequences of the other ones. These two special cases correspond to two inverse problems in the calculus of variation: Finsler metrizability for a spray, and projective metrizability for a spray

Hidden vortex lattices in a thermally paired superfluid

We study the evolution of rotational response of a hydrodynamic model of a two-component superfluid with a non-dissipative drag interaction, as the system undergoes a transition into a paired phase at finite temperature. The transition manifests itself in a change of (i) vortex lattice symmetry, and (ii) nature of vortex state. Instead of a vortex lattice, the system forms a highly disordered tangle which constantly undergoes merger and reconnecting processes involving different types of vortices, with a "hidden" breakdown of translational symmetry.Comment: 4 pages, 5 figs. Submitted to Physical Review. Online suppl. material available; Ref. 6. V2: Fig. 1 re-sent, URL in Ref. 6 correcte

Does the Community Reinvestment Act influence lending? an analysis of changes in bank low-income mortgage activity

Anecdotal evidence that the Community Reinvestment Act (CRA) influences the lending behavior of financial institutions has not been uniformly supported by empirical research. We revisit this issue by evaluating changes in low-income mortgage lending at commercial banks over the 1992-96 period. Our empirical results fail to support a hypothesis that banks respond to public and regulatory pressure exerted as a result of a downgrade in CRA rating by increasing low-income mortgage lending. The findings are consistent with the contention that during this period regulators stressed adjustments in the lending process of banks (e.g., documentation of lending program and efforts directed at targeted markets) more than lending performance. The findings underscore the importance of regulatory efforts made later in the decade to more closely link enforcement of the CRA to lending outcomes.Community Reinvestment Act of 1977 ; Mortgages ; Bank loans ; Financial institutions

Geometric properties of electromagnetic waves

This work studies geometrical properties of electromagnetic wave propagation. The work starts by studying geometrical properties of electromagnetic Gaussian beams in inhomogeneous anisotropic media. These are asymptotical solutions to Maxwell's equations that have a very characteristic feature. Namely, at each time instant the entire energy of the solution is concentrated around one point in space. When time moves forward, a Gaussian beam propagates along a curve. In recent work by A. P. Kachalov, Gaussian beams have been studied from a geometrical point of view. Under suitable conditions on the media, Gaussian beams propagate along geodesics. Furthermore, the shape of a Gaussian beam is determined by a complex tensor Riccati equation. The first paper of this dissertation provides a partial classification of media where Gaussian beams geometrize. The second paper shows that the real part of a solution to the aforementioned Riccati equation is essentially the shape operator for the phase front for the Gaussian beam. An important phenomena for electromagnetic Gaussian beams is that their propagation depend on their polarization. The last paper studies this phenomena from a very general point of view in arbitrary media. It also studies a connection between contact geometry and electromagnetism.reviewe

The Relationship of Jump Shooting Ability in Basketball to Selected Measurable Traits

The game of basketball has undergone changes over the years and today it is a fast-moving game wherein all of the players have an opportunity to score. The very nature of the game indicates that accurate shooting is essential to the final outcome. Sharmin stated the obvious, that in basketball, the team which wins scores more points than its opponent, and “Accurate shooting is the backbone of the game. This idea is supported by Benington and Newall who stated that The skill of shooting has probably developed more than any other aspect of the game of basketball. Part of the reason for more efficient shooting skill has been the development of the jump shot. Because of the versatility of the jump shot, it has become the most important offensive weapon in the game of basketball. Benington and Newall\u27s point is supported by Sharmin who said. \u27\u27The jump shot is the most effective and potent shot in basketball today. Wooden also supported this viewpoint as he stated that his teams score more points from jump shots than all of the other types of shots combined. With the jump shots established as the popular method of shooting, it would be of value to coaches to be able to predict success in scoring from the field by utilizing the jump shot. Since accurate shooting depends upon certain physical qualities, it was valuable for the investigator to study the relationship of selected anatomical measurements and motor responses to jump shooting ability in basketball. The purpose of this investigation was to study the relationship between jump shooting ability in basketball and the qualities of hand-eye coordination, hand reaction time, speed of movement time, hand size, grip strength, peripheral vision, depth perception, kinesthetic perception, leg power, wrist flexibility, wrist strength, and agility. 1. There is no relationship between jump shooting ability in basketball and selected anatomical measurements and motor responses. 2. A multiple regression equation to significantly predict jump shooting ability in basketball cannot be developed