An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established a...

Based on Information Theory, Feldman and Singh (2005) developed a mathematical formulation of turning angle. We used this as a basis for object recognition. Based on Shannon theory of information (1948), information content is dependent to the negative logarithm of the probability. The quantity u(M) is also called the surprisal of M. The information content is the expected value of the surprisal.

Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many noninteracting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the leading corrections to Thomas-Fermi theory, involve neither sums nor derivatives, are spatially uniform approximations, and are exceedingly accurate.

Initial estimates of aggregate output and its components are based on very incomplete source data, so they may not fully capture shifts in economic conditions. In particular, if those estimates are based partly on trends in preceding quarters, one would expect to see provisional estimates overstating activity when actual output is decelerating and understating it when actual output is accelerat...

We apply sequential Monte Carlo (SMC) to the detection of turning points in the business cycle and to the evaluation of useful statistics employed in business cycle analysis. The proposed nonlinear filtering method is very useful for sequentially estimating the latent variables and the parameters of nonlinear and non-Gaussian time-series models, such as the Markov-switching (MS) models studied ...

The American Community Survey (ACS) provides one-year (1y), three-year (3y), and fiveyear (5y) multi-year estimates (MYEs) of various demographic and economic variables for each “community,” although for small communities the 1y and 3y may not be available. These survey estimates are not truly measuring the same quantities, since they each cover different time spans. We present a metric to meas...

Recent evidence indicates that spirituality and religion are associated with both physical and psychological health. Because a belief that rewards are largely determined by external forces tends to be detrimental to mental health, the idea that God can be equated with such an external force seems contradictory to the proven benefits of religion and spirituality. The purpose of this article is t...

In this paper, we show that the asymptotic estimate for the expected number of K-level crossings of a random hyperbolic polynomial a1 sinhx+a2 sinh2x+···+ an sinhnx, where aj(j = 1,2, . . . ,n) are independent normally distributed random variables with mean zero and variance one, is (1/π) logn. This result is true for all K independent of x, provided K ≡Kn =O(√n). It is also shown that the asym...

Understanding why and how perpetrators of intimate partner violence (IPV) change their behavior is an important goal for both policy development and clinical practice. In this study, the authors investigated the concept of "turning points" for perpetrators of IPV by conducting a systematic review of qualitative studies that investigated the factors, situations, and attitudes that facilitated pe...

We study the interplay between effects of disease burden on the host population and the effects of population growth on the disease incidence, in an epidemic model of SIR type with demography and disease-caused death. We revisit the classical problem of periodicity in incidences of certain autonomous diseases. Under the assumption that the host population has a small intrinsic growth rate, usin...