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In this article we establish the uniqueness of solutions to first-order matrix dynamic equations on time scales. These results extend the results presented in [16], to more complex systems of n x n matrices. Following the ideas in [5, Chap 5], we identify Lipschitz conditions that are suitable for generalizing n x n models on time scales. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of solutions to first order non-linear initial value problems within the field of "dynamic equations on time scales". We employ the method of upper and lower solutions and Schauder's fixed point theorem. We also provide sufficient conditions under which the upper and lower solutions converge uniformly to a solution. Some examples are given to illustrate the new results. [ABSTRACT FROM AUTHOR]

Abstract: This article investigates both basic qualitative and basic quantitative properties of solutions to first- and higher-order dynamic equations on time scales and thus provides a foundation and framework for future advanced nonlinear studies in the field. Particular focus lies in the: existence; uniqueness; dependency; approximation; and explicit representation, of solutions to nonlinear initial value problems. The main tools used are from modern areas of nonlinear analysis, including: the fixed-point theorems of Banach and Schäfer; the method of successive approximations; a novel definition of measuring distance in metric spaces and normed spaces; and a “separation” of variables technique is introduced to the general time scale setting. The new results compliment and extend those of Stefan Hilger’s seminal paper of 1990. As an application of the new results we present and analyse a simple model from economics, known as the Keynesian–Cross model with “lagged” income, in the general time scale environment. Ideas suggesting further applications and possible new directions for the novel results are also presented. [Copyright &y& Elsevier]

Snitrosoglutathione (GSNO) reductase regulates novel endogenous S-nitrosothiol signaling pathways, and mice deficient in GSNO reductase are protected from airways hyperreactivity. S-nitrosothiols are present in the airway, and patients with cystic fibrosis (CF) tend to have low S-nitrosothiol levels that may be attributed to upregulation of GSNO reductase activity. The present study demonstrates that 1) GSNO reductase activity is increased in the cystic fibrosis bronchial epithelial (CFBE41o-) cells expressing mutant F508del-cystic fibrosis transmembrane regulator (CFTR) compared with the wild-type CFBE41o- cells, 2) GSNO reductase expression level is increased in the primary human bronchial epithelial cells expressing mutant F508del-CFTR compared with the wild-type cells, 3) GSNO reductase colocalizes with cochaperone Hsp70/Hsp90 organizing protein (Hop; Stip1) in human airway epithelial cells, 4) GSNO reductase knockdown with siRNA increases the expression and maturation of CFTR and decreases Stip1 expression in human airway epithelial cells, 5) increased levels of GSNO reductase cause a decrease in maturation of CFTR, and 6) a GSNO reductase inhibitor effectively reverses the effects of GSNO reductase on CFTR maturation. These studies provide a novel approach to define the subcellular location of the interactions between Stip1 and GSNO reductase and the role of S-nitrosothiols in these interactions. [ABSTRACT FROM AUTHOR]