Georgia College & State University

About: Georgia College & State University is a education organization based out in Milledgeville, Georgia, United States. It is known for research contribution in the topics: Population & Higher education. The organization has 950 authors who have published 1591 publications receiving 37027 citations.

Large deviations for trajectories of sums of independent random variables

Abstract: Given a sequence of independent, but not necessarily identically distributed random variables,Yi, letSk denote thekth partial sum. Define a function\(\tilde S:[0,\infty ) \to \mathbb{R}\) by taking\(\tilde S(t)\) to be the piecewise linear interpolant of the points (k, Sk), evaluated att, whereS0=0, andk=0, 1, 2,... Fort∈[0, 1], let\(\tilde S_n (t)\mathop = \limits^{def} \tilde S(nt)\). The\(\tilde S_n \) are called trajectories. With regularity and moment conditions on theYi, a large deviation principle is proved for the\(\tilde S_n \).

Hypoglycemia Spiking Mortality Syndrome in Broilers with Rickets and a Subsequent Investigation of Feed Restriction as a Contributing Factor

Abstract: Several cases of elevated mortality with neurologic signs in 14-to-16-day-old broilers were presented to the Poultry Diagnostic and Research Center from one local integrated company. Suspected of "spiking mortality" associated with hypoglycemia, blood glucose levels were <150 mg/dl overall, with several birds with blood glucose levels as low as 30 mg/dl. Tissues, submitted for histopathology, revealed rickets in 50% of the birds. Virus isolation and serology for reovirus and infectious bursal disease virus were negative. After evaluation of these cases, a brief investigation was conducted to determine the effects of feed restriction on the induction of rickets and resulting hypoglycemia. One-hundred 1-day-old broilers were randomly assigned to three treatment groups of: 1) ad libitum feed, 2) 25% restriction, and 3) 50% restriction. Restriction began on the fifth day of age and continued to 21 days of age. Samples collected during the course of the study included whole blood for blood glucose measurements and proximal tibiotarsus for histopathologic examination for rickets. We were unable to reproduce the clinical signs of spiking mortality, neurologic changes, or hypoglycemia experimentally. Histopathology of the growth plates of the proximal tibiotarsus did indicate mild changes consistent with rickets, but the changes were not significant between treatment groups.

Critical parameters for reaction–diffusion equations involving space–time fractional derivatives

Abstract: We will look at reaction–diffusion type equations of the following type, $$\begin{aligned} \partial ^\beta _tV(t,x)=-(-\Delta )^{\alpha /2} V(t,x)+I^{1-\beta }_t[V(t,x)^{1+\eta }]. \end{aligned}$$ We first study the equation on the whole space by making sense of it via an integral equation. Roughly speaking, we will show that when $$0<\eta \leqslant \eta _c$$ , there is no global solution other than the trivial one while for $$\eta >\eta _c$$ , non-trivial global solutions do exist. The critical parameter $$\eta _c$$ is shown to be $$\frac{1}{\eta ^*}$$ where $$\begin{aligned} \eta ^*:=\sup _{a>0}\left\{ \sup _{t\in (0,\,\infty ),x\in \mathbb {R}^d}t^a\int _{\mathbb {R}^d}G(t,\,x-y)V_0(y)\,\mathrm{d}y<\infty \right\} \end{aligned}$$ and $$G(t,\,x)$$ is the heat kernel of the corresponding unforced operator. $$V_0$$ is a non-negative initial function. We also study the equation on a bounded domain with Dirichlet boundary condition and show that the presence of the fractional time derivative induces a significant change in the behavior of the solution.