Neutral Inclusions Research Articles

Hilfer Fractional Neutral Stochastic Volterra Integro-Differential Inclusions via Almost Sectorial Operators

In our paper, we mainly concentrate on the existence of Hilfer fractional neutral stochastic Volterra integro-differential inclusions with almost sectorial operators. The facts related to fractional calculus, stochastic analysis theory, and the fixed point theorem for multivalued maps are used to prove the result. In addition, an illustration of the principle is provided.

Experimental investigation of thermal architected metamaterials for regulating transient heat transfer

Metamaterials have innovative functionalities as a result of artificial design. By arbitrarily designing thermal conductivity, thermal metamaterials have achieved thermal invisible cloaks, camouflages, and deceptions in steady-state. However, density and specific heat capacity have sometimes been overlooked, despite the fact that they are critical for managing transient heat flow and that density are an indicator of creating lightweight materials. The traditional materials are incapable of synchronously controlling thermal conductivity, density, and specific heat capacity. In this research, we experimentally investigate a novel thermal architected metamaterial that can modulate (accelerate or decelerate) transient heat transfer velocity without disrupting the steady-state. The novel type of thermal architected metamaterial achieves efficiency using a topology based on neutral inclusion theory. The transient heat transfer velocity is regulated by altering the effective density and specific heat capacity on the one hand, while the steady-state heat transfer is maintained by keeping the effective thermal conductivity on the other. The density of the architected metamaterial could be adjusted by selecting an appropriate specific heat capacity. The method we provide can be utilized to create lightweight energy-efficient materials (by accelerating transient heat transfer) as well as lightweight engineered thermal protection materials (by decelerating transient heat transfer). Moreover, the proposed thermal architected metamaterial could control heat flow velocity continuously, and this characteristic covers the gaps left by natural materials.

Solutions of Neutral Differential Inclusions

Motivated by the study of neutral differential inclusions, we establish a new fixed point theorem for multivalued countably Meir-Keeler condensing mappings via an arbitrary measure of weak noncompactness which in turn include the fixed point theorems of Krasnoselskii and Dhage as special cases in non separable spaces.

Topological Structure of the Solution Sets for Impulsive Fractional Neutral Differential Inclusions with Delay and Generated by a Non-Compact Demi Group

In this paper, we give an affirmative answer to a question about the sufficient conditions which ensure that the set of mild solutions for a fractional impulsive neutral differential inclusion with state-dependent delay, generated by a non-compact semi-group, are not empty compact and an Rδ-set. This means that the solution set may not be a singleton, but it has the same homology group as a one-point space from the point of view of algebraic topology. In fact, we demonstrate that the solution set is an intersection of a decreasing sequence of non-empty compact and contractible sets. Up to now, proving that the solution set for fractional impulsive neutral semilinear differential inclusions in the presence of impulses and delay and generated by a non-compact semigroup is an Rδ-set has not been considered in the literature. Since fractional differential equations have many applications in various fields such as physics and engineering, the aim of our work is important. Two illustrative examples are given to clarify the wide applicability of our results.

An investigation on the approximate controllability of impulsive neutral delay differential inclusions of second order

This paper mainly focuses on the approximate controllability for second‐order impulsive neutral differential inclusions with infinite delay. By using the results related to cosine and sine function of operators, Dhage's fixed point theorem, and their outcome when combined with the properties of differential inclusions, our primary discussions are proved. Finally, we provided an example for the illustration of the theory obtained.

An analysis on the approximate controllability of Hilfer fractional neutral differential systems in Hilbert spaces

This manuscript concerns the approximate controllability results in Hilbert space of Hilfer fractional differential inclusions. We show that the Hilfer fractional neutral differential inclusions are approximately controllable using Bohnenblust-Karlin’s fixed point theorem. Further, nonlocal conditions are extended to the existence results. Furthermore, an application is shown to demonstrate the theoretical conclusions utility.

Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses

<p style='text-indent:20px;'>This paper aims to establish the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay. Sufficient conditions for approximate controllability have been established for the proposed control problem. The tools for study include the fixed point theorem for discontinuous multi-valued operators with the <inline-formula><tex-math id="M3">\begin{document}$ \alpha- $\end{document}</tex-math></inline-formula>resolvent operator. Finally, the proposed results are illustrated with the help of an example.</p>

ISIEA: An image database of social inclusion and exclusion in young Asian adults

Human beings have a fundamental need to belong. Evaluating and dealing with social exclusion and social inclusion events, which represent negative and positive social interactions, respectively, are closely linked to our physical and mental health. In addition to traditional paradigms that simulate scenarios of social interaction, images are utilized as effective visual stimuli for research on socio-emotional processing and regulation. Since the current mainstream emotional image database lacks social stimuli based on a specific social context, we introduced an open-access image database of social inclusion/exclusion in young Asian adults (ISIEA). This database contains a set of 164 images depicting social interaction scenarios under three categories of social contexts (social exclusion, social neutral, and social inclusion). All images were normatively rated on valence, arousal, inclusion score, and vicarious feeling by 150 participants in Study 1. We additionally examined the relationships between image ratings and the potential factors influencing ratings. The importance of facial expression and social context in the image rating of ISIEA was examined in Study 2. We believe that this database allows researchers to select appropriate materials for socially related studies and to flexibly conduct experimental control.

A discussion on approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions

AbstractIn this paper, the approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions in Hilbert spaces is considered. By using the stochastic analysis theory, fractional calculus, multivalued maps, and Karlin's fixed point technique, a new set of necessary and sufficient conditions, are formulated which guarantees the approximate controllability of the nonlinear Hilfer fractional stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, two examples are presented to illustrate the theory of the obtained results.

A generalized neutral-type inclusion problem in the frame of the generalized Caputo fractional derivatives

In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of ( vartheta (t)-vartheta (s)) along with differential operator frac{1}{vartheta '(t)},frac{mathrm{d}}{mathrm{d}t}. We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results.

Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type

The basic motivation of this research paper is the approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type which generalized the Riemann-Liouville fractional derivative. Combining with the techniques of fractional calculus, fixed point theorem for multi-value dmaps and Sobolev-type and Clarke subdifferential to the approximate controllability system we obtain new existence result of mild solutions. Next, we demonstrate linear and semilinear systems for approximate controllability. Finally, to verify our theoretical results, an illustration is also included.

Interferometric experiments on the transmission matrix of diffusive neutral inclusions

By using tailored disorder in the regime of diffusive light propagation, core-shell cloaking structures have previously been presented. These structures make the cloak and an arbitrary interior nearly indistinguishable from the diffusive surrounding. This statement holds true for all incident polarizations of light, a broad range of incident directions of light in three dimensions, and a broad range of visible wavelengths. Here, by performing interferometric transmission-matrix experiments, we investigate the statistical wave properties of miniaturized versions of such structures. By using singular-value decomposition, we derive the eigenchannels and eigenvalues to assess the degree of wave correlation among multiply scattered waves. We find small but significant differences in the eigenvalue distributions, suggesting that the degree of wave correlation is lower for the neutral inclusion than for a homogeneously disordered reference sample, which corresponds to the surrounding of the neutral inclusion. Likewise, we find similar differences between optically inspecting the core-shell neutral inclusion and its spatial neighborhood. These differences allow us to reveal the neutral inclusion due to different statistics of the underlying random walks of light.

Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

A class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.

A note on approximate controllability of the Hilfer fractional neutral differential inclusions with infinite delay

In this study, we establish the approximate controllability of the Hilfer fractional neutral differential inclusions with infinite delay. The main result of this article is proven by applying some ideas of semigroup theory with fractional order and Dhage's fixed point theorem. Firstly, we prove the approximate controllability of the Hilfer fractional system. Next, we extend our study to the system with nonlocal conditions. Finally, theoretical and practical applications are presented to assist in the effectiveness of our discussion.

Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay

AbstractIn this article, we determine a set of appropriate conditions for approximate controllability of second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay. We verify the main results by applying ideas about the cosine function, sine functions, and fixed point approach. Next, we continue the discussion to the nonlocal second‐order Sobolev‐type differential system. In the end, we provide a theoretical application to assist in the effectiveness of our discussion.

Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions.

New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core–shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, weak and strong with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the strong NI is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed ‘unphysical’ materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit.

On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay

In our manuscript, we organize a group of sufficient conditions of neutral integro-differential inclusions of Sobolev-type with infinite delay via resolvent operators. By applying Bohnenblust-Karlin's fixed point theorem for multivalued maps, we proved our results. Lastly, we present an application to support the validity of the study.

Immunological Activities of Crude Polysaccharides Extracts of Climacodon pulcherrimus (Phanerochaetaceae) in Lipopolysaccharide-Induced Rat Macrophages and Neutrophils' Responses.

Mushroom contains a wide variety of components with high immune-modulating properties. Mushroom polysaccharides are known as immunocorrectors with wide areas of usage, which balance the immune system without resulting in the entire immune suppression or overreaction. To explore the potentially immunomodulatory role of Climacodon pulcherrimus, the present study was intended to evaluate the in vitro immunomodulatory activity of C. pulcherrimus polysaccharides (CPP) on rat neutrophils and macrophages. CPP was studied on lipopolysaccharide-induced neutrophils and macrophages' responses. The effect on phagocytosis, release of reactive oxygen intermediates (ROI), nitric oxide (NO), lysosomal enzyme release and neutrophil myeloperoxidase, and neutrophil adherence was assessed. The cytotoxicity of CPP against macrophages using 3-(4,5-dimethylthiazole-2-yl)-2, 5-diphenyltetrazolium bromide assay and neutral red inclusion assay was also assessed. ENPC (endopolysaccharides) markedly enhanced phagocytosis of macrophages and neutrophils, whereas the EXPC (exopolysaccharides) increased only that of neutrophils at 0.34 and 0.68 mg/mL. The production of NO evidently increased in ENPC- and EXPC-treated neutrophil and macrophage cultures. The production of ROI in a concentration-dependent manner increased in ENPC-treated (0.08-5.55 mg/mL) and EXPC-treated (0.17 and 0.34 mg/mL) macrophage cultures and ENPC-treated neutrophils, whereas it decreased in EXPC-treated neutrophils. The secretion of acid phosphatase increased in ENPC- and EXPC-treated macrophage and neutrophil cultures. Neutrophil myeloperoxidase release increased in EXPC-treated (5.55 mg/mL) cultures, whereas it decreased in ENPC-treated cultures. ENPC and EXPC increased the adhesion of neutrophils to microplate. These findings demonstrated that CPP displayed a dual mode of action, inhibiting or enhancing numerous phagocytic activities of macrophages and neutrophils.

Approximate controllability of second order nonlocal neutral differential evolution inclusions

Abstract In our manuscript, we organize a group of sufficient conditions of approximate controllability for second order nonlocal neutral differential evolution inclusions. Next, we develop the result to analyze approximate controllability of impulsive systems. Lastly, a model is presented for illustration of theory.

Inclusions of General Shapes Having Constant Field Inside the Core and NonElliptical Neutral Coated Inclusions With Anisotropic Conductivity

For certain shapes of inclusions embedded in a body, the field inside the inclusion is uniform for some boundary condition. We provide a construction scheme for inclusions of general shapes having such a uniformity property in two dimensions based on the conformal mapping technique for the potential problem. Using this complex analysis method, we also design nonelliptical neutral coated inclusions with anisotropic conductivity. Neutral coated inclusions do not perturb a background uniform field when they are inserted into a homogeneous matrix. Although coated inclusions of various shapes are neutral to a single field, only concentric ellipses or confocal ellipsoids can be neutral to all uniform fields. This paper presents our work relating to the construction of nonelliptical coated inclusions with anisotropic conductivity in two dimensions that are neutral to all uniform fields, where the assignment of the flux condition on the boundary of the core depends on the applied background field. Using these neutral inclusions, we obtain cylindrical neutral inclusions in three dimensions, with no flux applied to the boundary of the core and with the anisotropic conductivity function of the shell given in accordance with the background uniform field.