Search

The primary objective of this work is to investigate the existence of mild solutions for some neutral stochastic integrodifferential systems in Hilbert spaces. These systems have a state-dependent delay and noninstantaneous impulses. In order to achieve this objective, the neutral stochastic integrodifferential system that has been proposed with state-dependent delay and noninstantaneous impulses is converted into an equivalent fixed point problem by means of an appropriate integral operator.Together with the theory of stochastic analysis, we develop several existence results that are founded on the theory of resolvent operators in the sense of Grimmer, Hausdorff's measures of noncompactness, and fixed point theorems.In the last part of this paper, specific examples are used to show how the general conclusions reached in this paper are made. [ABSTRACT FROM AUTHOR]

In this paper, we give a geometric construction for different allowable properties for sign pattern matrices. In Section 2, we give a construction for detecting a sign pattern matrix to be potentially nilpotent and also compute the nilpotent matrix realization for a given sign pattern matrix if it exists. In Section 3, we develop a geometric construction for potential stability. In Section 4, we establish a necessary and sufficient condition for a sign pattern matrix S to be spectrally arbitrary. For a given sign pattern matrix of order n , we prove that there exists a surface of dimension at most m for m ≤ n such that for every vector a 1 , a 2 , ⋯ , a n on the same surface, there exists a matrix A ∈ Q (S) , a qualitative class of S whose characteristic polynomial is x n − a 1 x n − 1 + ⋯ + (− 1) n a n . [ABSTRACT FROM AUTHOR]

Unwanted dispersive wiggles that arise from the leapfrog numerical scheme have been of interest in weather research and other fluid flow studies. A number of differing approaches have been developed over the last few decades to suppress such wiggles. For example, there are methods that use either smoothing filters or adaptive time-stepping. But, in addition to suppressing the wiggles, smoothing filters suppress the solution profile as well. In order to overcome this problem, in this paper, we construct a computationally efficient numerical scheme that simply eliminates the dispersive wiggles while keeping the solution profile intact. [ABSTRACT FROM AUTHOR]

We present in this paper further mathematical properties of the Odd Kappa-G family of distributions. These structural properties of this family hold for any baseline model including characterizations results based on two truncated moments and hazard and reversed hazard functions. In addition, k th lower record values and extreme values of this Odd Kappa-G family are introduced. Lastly, the bivariate probability distributions of the Odd Kapp-G (BFGMOKG) family based on FGM copula are obtained. [ABSTRACT FROM AUTHOR]

This paper examines a new class of Möbius invariant function spaces, denoted by N K (p , q) -type spaces in the unit ball of C n , which are a common basis for several known spaces of holomorphic functions. We establish several basic properties of N K (p , q) -type spaces and its closed subspaces N K , 0 (p , q) , which are Banach spaces of holomorphic functions with norms determined by a weighted nondecreasing function K : [ 0 , ∞) → [ 0 , ∞) , together with a Möbius transformation. With Green's function, we give an equivalent description of N K (p , q) -type spaces. Finally, we study the Hadamard gap series in N K (p , q) -type spaces. [ABSTRACT FROM AUTHOR]

The evidential approach uses likelihood ratios, typically the natural logarithm of the likelihood ratio representing the amount of evidence for one hypothesis versus another. One of the barriers to using the approach is the unavailability of sample size calculations for commonly used statistical tests. The t test is the most common statistical test used in scientific publications. This paper derives the equations necessary to calculate evidential probabilities and hence the required sample size for different types of t tests. Compared with the conventional Neyman-Pearson approach, the evidential approach requires larger sample sizes. This drawback is countered by the fact that users know the probability for obtaining misleading evidence (strong evidence that points to the wrong hypothesis). Even with small sample sizes, this is quite small (around 0.05) and decreases further with increasing sample sizes. The main challenge faced by the evidential researcher is of obtaining sufficiently strong evidence for or against one of the two specified hypotheses. Like the probability of a Type II error, this probability is large with a small sample size and decreases as the sample size increases. Sample size is estimated by achieving a low probability (e.g. <.1) for the combined probability of misleading and weak evidence. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a detailed mathematical model describing the dynamics of a prey-predator model under the influence of an SIS infectious disease by using nonlinear differential equations. We use the functional response of ratio-dependent Michaelis-Menten type to describe the predation strategy. In the presence of the disease, prey and predator population are divided into two disjointed classes, namely infected and susceptible. The first one is governed through due predation interaction, and the second one is governed through the propagation of disease in the prey and predator population via predation. Our aim is to analyze the effect of predation on the dynamic of the disease transmission. Important mathematical results resulting from the transmission of the disease under influence of predation are offered. First, results concerning boundedness, uniform persistence, existence and uniqueness of solutions have been developed. In addition, many thresholds have been computed and used to investigate local and global stability analysis by using Routh-Hurwitz criterion and Lyapunov principle. We also establish the Hopf bifurcation to highlight periodic fluctuation with persistence of the disease or without disease in the prey and predator population. Finally, numerical simulations are carried out to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an extended SIRB deterministic epidemiological model for Cholera was developed and strictly analysed to ascertain the impact of immigration in cholera transmission and to assess the suitability of the various control measures. The model was found to have two equilibria, namely, disease-free equilibrium (DFE) and a unique endemic equilibrium (EE). The local stability of the DFE and EE were found to be dependent on a certain epidemiological threshold known as the basic reproductive number, R 0 (number of secondary infections resulting from the introduction of a single infected individual into a population), in that DFE is stable when R 0 < 1 , whereas the EE is stable when R 0 > 1. Furthermore, we used the Lyapunov function and geometric approach respectively to show that the DFE and EE are globally asymptotically stable and that Cholera will persist in the population when R 0 > 1. Our model was fitted to Uganda Cholera cases (1999–2015). The best fit parameters were then used to carry out numerical simulation of the model. Specifically, the impact of the control over the long and short cycle transmission routes were found to be more effective than vaccination in combating the menace of Cholera in Uganda. Finally, the effects of immigration in the transmission of cholera were validated via numerical simulation using estimated and base line parameter values. [ABSTRACT FROM AUTHOR]