Existence of Solutions of Nonlinear Neutral Stochastic Differential Inclusions in a Hilbert Space

Abstract

In this paper, the existence of mild solutions of a class of non-linear neutral stochastic differential inclusions in Hilbert space is studied. The results are obtained by using a new fixed point theorem for a condensing map due to Martelli. For an application of the result, the neutral stochastic reaction-diffusion inclusion is also discussed.     

Phase transition at 204–250 K in the crystals of β-alanine: kinetically irreproduceable,or an artefact?

The crystals and the powder samples of β-alanine were studied in the wide temperature range by adiabatic calorimetry, differential scanning calorimetry, IR- and Raman spectroscopy and X-ray diffraction. No phase transitions could be observed. A small anomaly observed at about 256 K in the Cp(T) dependences measured for the samples re-crystallized from water was shown to be due to the presence of a small (about 0.14% of the total sample mass) amount of solvent inclusions. This anomaly was not observed in the solvent-free samples, either powders or single crystals.     

Cloaking of 2D particle geometries in a surface medium

We theoretically examine the cloaking condition for two-dimensional particles with varying geometry embedded inside a surface medium. General solutions are obtained for multi-layer particle configurations with either all positive or partially negative constitutive parameters respectively. Cloaking of particle geometries that are large relative to the incident wavelength is demonstrated. Theoretical predictions are compared to full-wave numerical simulations for arrays of particles consisting of different geometries.     

Ultrastructural analysis of midgut cells from Culex quinquefasciatus (Diptera: Culicidae) larvae resistant to Bacillus sphaericus

The larvicidal action of the entomopathogen Bacillus sphaericus towards Culex quinquefasciatus is due to the binary (Bin) toxin present in crystals, which are produced during bacterial sporulation. The Bin toxin needs to recognize and bind specifically to a single class of receptors, named Cqm1, which are 60-kDa α-glucosidases attached to the apical membrane of midgut cells by a glycosylphosphatidylinositol anchor. C. quinquefasciatus resistance to B. sphaericus has been often associated with the absence of the α-glucosidase Cqm1 in larvae midgut microvilli. In this work, we aimed to investigate, at the ultrastructural level, the midgut cells from C. quinquefasciatus larvae whose resistance relies on the lack of the Cqm1 receptor. The morphological analysis showed that midgut columnar cells from the resistant larvae are characterized by a pronounced production of lipid inclusions, throughout the 4th instar. At the end of this stage, resistant larvae had an increased size and number of these inclusions in the midgut cells, while only a small number were observed in the cells from susceptible larvae. The morphological differences in the midgut cells of resistant larvae found in this work suggested that the lack of the Cqm1 receptor, which also has a physiological role as being an α-glucosidase, can be related to changes in the cell metabolism. The ultrastructural effects of Bin toxin on midgut epithelial cells from susceptible and resistant larvae were also investigated. The cytopathological alterations observed in susceptible larvae treated with a lethal concentration of toxin included breakdown of the endoplasmic reticulum, mitochondrial swelling, microvillar disruption and vacuolization. Some effects were observed in cells from resistant larvae, although those alterations did not lead to larval death, indicating that the receptor Cqm1 is essential to mediate the larvicidal action of the toxin.This is the first ultrastructural study to show differences in the cell morphology of resistant larvae and further investigation is needed to understand the impact of the lack of expression of midgut enzymes on the physiology of resistant insects.     

Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems

We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.     

Spatial Patterns for reaction-diffusion systems with conditions described by inclusions

We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.     

Shape evolutions under state constraints: A viability theorem

The aim of this paper is to adapt the Viability Theorem from differential inclusions (governing the evolution of vectors in a finite-dimensional space) to so-called morphological inclusions (governing the evolution of nonempty compact subsets of the Euclidean space).In this morphological framework, the evolution of compact subsets of is described by means of flows along differential inclusions with bounded and Lipschitz continuous right-hand side. This approach is a generalization of using flows along bounded Lipschitz vector fields introduced in the so-called velocity method alias speed method in shape analysis.Now for each compact subset, more than just one differential inclusion is admitted for prescribing the future evolution (up to first order)—correspondingly to the step from ordinary differential equations to differential inclusions for vectors in the Euclidean space.We specify sufficient conditions on the given data such that for every initial compact set, at least one of these compact-valued evolutions satisfies fixed state constraints in addition. The proofs follow an approximative track similar to the standard approach for differential inclusions in , but they use tools about weak compactness and weak convergence of Banach-valued functions. Finally the viability condition is applied to constraints of nonempty intersection and inclusion, respectively, in regard to a fixed closed set .