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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 investigate a non-linear Langevin equation with periodic, multi-point and non-local fractional integral boundary conditions. The contraction mapping theorem is employed to determine sufficient conditions for the uniqueness of the solution. Also, different results in the existence of solution are demonstrated by using Krasnoselskii and Leray-Schauder theorems. Finally, some examples are provided as applications of the theorems in order to support the main outcomes of this paper. [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]

Ever since the founding work by Finney (1945), it has been widely known and accepted that aliased effects in two-level regular designs cannot be "de-aliased" without adding more runs. A result by Wu in his 2011 Fisher Lecture showed that aliased effects can sometimes be "de-aliased" using a new framework based on the concept of conditional main effects (CMEs). This idea is further developed in this paper into a methodology that can be readily used. Some key properties are derived that govern the relationships among CMEs or between them and related effects. As a consequence, some rules for data analysis are developed. Based on these rules, a new CME-based methodology is proposed. Three real examples are used to illustrate the methodology. The CME analysis can often lead to models with fewer effect terms and smaller p values for the selected effects. Moreover, the selected CME effects are often more interpretable. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a closed formula for the Kostant's partition function for the Lie algebras sl4(C) and sp6(C): Using this function, one can compute the weight multiplicity of irreducible representations of the Lie algebras sl4(C) and sp6(C). [ABSTRACT FROM AUTHOR]

In this paper, we study an excision theorem of the dihedral and reflexive (co)homology theory of associative algebras. That is, for such an extension, we obtain a six-term exact sequence in the dihedral cohomology. Also, we present and prove the relation between cyclic and dihedral cohomology of algebras and some examples. [ABSTRACT FROM AUTHOR]

In this paper, by applying the behavior of measure of noncompactness in L∞( R n), we study the existence of solutions of an infinite system of integral equations in the space L∞( R n). Finally, an example is included to show the usefulness of the outcome. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of singularly perturbed parabolic convection-diffusion problems with two small positive parameters multiplying the convection and diffusion terms. A parameter-uniform computational method is developed to solve these problems. The stability and consistency of the method are well established. Numerical experimentation is done and it is observed that the formulated method is stable, consistent and gives more accurate results than some methods exist in the literature. [ABSTRACT FROM AUTHOR]

In this paper, it has been proved that if a 3-dimensional cosymplectic manifold M 3 admits a Yamabe soliton, then either M 3 is locally flat or the potential field is a contact vector field. Some special potential vector fields of Yamabe solitons on 3-dimensional cosymplectic manifolds have been considered and some other results have been obtained. Also, for general (2 n + 1) -dimensional case, it will be shown that if an f − cosymplectic manifold M 2 n + 1 admits a contact Yamabe soliton structure, then M 2 n + 1 is a cosymplectic manifold. Finally, an example of Yamabe soliton on a 3-dimensional cosymplectic manifold is provided. [ABSTRACT FROM AUTHOR]

Insecticide spraying of housing units is an important control measure for vector-borne infections such as Chagas disease. However, some vectors may survive treatment, due to imperfect spraying by the operator or because they hide deep in the cracks or other places, and re-emerge in the same unit when the effect of the insecticide wears off. While several mathematical models of this phenomenon have been previously described and studied in the literature, the model presented here is more basic than existing ones. Thus it is more amenable to mathematical analysis, which is carried out here. In particular, we demonstrate that an initially very high spraying rate may push the system into a region of the state space with low endemic levels of infestation that can be maintained in the long run at relatively moderate cost, while in the absence of an aggressive initial intervention the same average cost would only allow a much less significant reduction in long-term infestation levels. [ABSTRACT FROM AUTHOR]

To illustrate and document the tenuous connection between the Wilcoxon-Mann-Whitney (WMW) procedure and medians, its relationship to mean ranks is first contrasted with the relationship of a t-test to means. The quantity actually tested: is then described and recommended as the basis for an alternative summary statistic that can be employed instead of medians. In order to graphically represent an estimate of the quantity: Pr(X1 < X2) + Pr(X1 = X2)/2, use of a bubble plot, an ROC curve and a dominance diagram are illustrated. Several counter-examples (real and constructed) are presented, all demonstrating that the WMW procedure fails to be a test of medians. The discussion also addresses another, less common and perhaps less clear cut, but potentially even more important misconception: that the WMW procedure requires continuous data in order to be valid. Discussion of other issues surrounding the question of the WMW procedure and medians is presented, along with the authors' teaching experience with the topic. SAS code used for the examples is included as supplementary material. [ABSTRACT FROM AUTHOR]