Inequality Principle Research Articles

Averaging principle for stochastic variational inequalities with application to PDEs with nonlinear Neumann conditions

Stochastic variational inequalities have been widely used in various areas. In this paper we establish averaging principles for a separated time-scale system of fully coupled stochastic system characterized by stochastic variational inequalities. Under non-Lipschitz continuous conditions, we show that the classical weak convergence result holds for this type of stochastic systems. Strong convergence is also studied for the cases when the diffusion coefficients of the slow motions do not depend on the fast motion components. As an application, we study the homogenization of generalized backward SDEs and semilinear parabolic variational inequalities with nonlinear Neumann boundary conditions.

Heterogeneous Multi-Agent-Based Fault Diagnosis Scheme for Actuation System

In this paper, a fault diagnosis method of a heterogeneous multi-agent is proposed that realizes the rapid and accurate fault diagnosis of a redundant multi-type actuation system of large aircraft. Firstly, the multi-agent model of a large aircraft actuation system is established, the composition of the actuation system and the relationship between each multi-agent are clarified and three different types of actuator mathematical models are established. Secondly, a fault detection and isolation (FDI) model is established and transformed into an optimization problem according to different performance index requirements. Aiming at the optimization problem, combined with the principle of linear matrix inequality (LMI), the fault diagnosis algorithm of a heterogeneous multi-agent system is designed. Moreover, the threshold judgment method based on the error signal is presented. Finally, the three actuator models of the aileron actuation system of large aircraft are combined to complete the fault diagnosis of a heterogeneous multi-agent system under the given model interference and model fault. The obtained results demonstrate and validate that the proposed method can accurately and effectively diagnose the faults of the actuator and its associated actuators.

Stochastic Energy Management of Active Distribution Network Based on Improved Approximate Dynamic Programming

The energy management (EM) of active distribution network (ADN) under uncertainties is a stochastic, nonconvex and nonlinear problem, which cannot be solved by traditional algorithms in acceptable time. In this paper, we decouple this computationally intractable problem into a series of subproblems which are easier to handle, and then solve them successively according to an improved approximate dynamic programming (IADP) algorithm. Different from the existing approximate dynamic programming (ADP) algorithms, which need to update value functions iteratively, IADP obtains approximate value functions directly using Galerkin method. Such that the time of updating approximate value functions can be omitted. Furthermore, the influence of each basis function on the approximate value function is evaluated according to the absolute value inequality principle. Then the unimportant basis functions are removed from the basis function set to speed up the algorithm. The historical data can also be embedded into IADP to facilitate the online decision-making and reduce the dependency of real-time forecast information. Numerical simulations on two modified IEEE test systems and a real 682-bus ADN are given to illustrate the effectiveness of the proposed approach.

Defending the honor of religious minorities in the Islamic and western law

The honor of religious minorities is among the challenging subjects that have today created some challenges between the governments as well as the governments and the religious minorities. In general, governments consider defending religious minorities to be a good strategy for unity, peace, and reconciliation. Regarding the challenging nature of the subject and its importance, the author has aimed to investigate the “defending of the honor of religious minorities in the Islamic and Western law” with a descriptive-analytical approach using the library method. The results indicate that honor of religious minorities is the same as protecting the inherent dignity of religious minorities. The theory of dignity and the principle of inequality and indiscrimination in Islamic and western laws emphasize the necessity of protecting the honor of religious minorities. In this regard, defending the honor of religious minorities is a necessity in the current era and the justice-based legal theory is one of its most important foundations. Regarding the necessities and foundations of defending the honor of religious minorities, Islamic and Western laws have adopted some strategies such as the right to protection and recognition of the existence and identity of religious minorities.

Post Triangular Rewiring Method for Shorter RRT Robot Path Planning

This paper proposed the 'Post Triangular Rewiring' method that minimizes the sacrifice of planning time and overcomes the limit of Optimality of sampling-based algorithm such as Rapidly-exploring Random Tree (RRT) algorithm. The proposed 'Post Triangular Rewiring' method creates a closer to the optimal path than RRT algorithm before application through the triangular inequality principle. The experiments were conducted to verify a performance of the proposed method. When the method proposed in this paper are applied to the RRT algorithm, the Optimality efficiency increase compared to the planning time.

Approximation-solvability of population biology systems based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators

The aim of this paper is to investigate existence, uniqueness and convergence of approximants of nonzero positive weak solutions for a class of population biology systems, which are models of one species based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators and involved logistic growth and harvesting rates. Toward this end, we foremost develop a kind of new general variational inequality principles with generalized duality mappings in reflexive Banach spaces. Then, we employ the new principle to obtain our main results for a general p-Laplacian elliptic inequality and the population biology systems. We note that the results are different from those relevant work of p-Laplacian elliptic inequalities in the literature, it is because a pseudo-contractive operator may not be an S-contractive operator and vice versa.

Symmetrization with respect to mixed volumes

In this paper we introduce a new symmetrization with respect to mixed volume or anisotropic curvature integral, which generalizes the one with respect to quermassintegral due to Talenti [26] and Tso [28]. We show a Pólya-Szegő type principle for such symmetrization — it diminishes the anisotropic Hessian integral for quasi-convex functions. We achieve this by a systematic study of invariants on non-symmetric matrices with real eigenvalues and the higher order anisotropic mean curvatures of level sets, which may be of independent interest. As applications, we establish a comparison principle for anisotropic Hessian equations and sharp anisotropic Sobolev inequalities.

Crakenstein’s Brave New Pandemic World: The Place of Art, Science, and Storytelling

The present article aims at examining the place of art, science, and storytelling in Margaret Atwood’s Oryx and Crake (2003), comparing the novel to Mary Shelley’s Frankenstein (1818) and Aldous Huxley’s Brave New World (1932) , mainly in what concerns some characters who are on the margins. In this context, scientific knowledge set against humanistic knowledge is the generating principle of social inequalities, and people concerned with arts are relegated to an inferior place. In the three novels, those who value words amid the techno-scientific developments of society are condemned to live alone for not fitting in. However, Oryx and Crake presents a possible rereading of Shelley’s and Huxley’s works, leading the central character to a less tragic closure, even though still in a devastated landscape. Ironically, in the aftermath of a pandemic, when the rules of science do no longer apply, it is a “words person” who survives, embracing his existence all through the act of storytelling. Atwood’s novel, therefore, celebrates and updates the classics in some way, transposing them to a brand-new universe, where – through her apocalyptic visions – it is also possible to make a parallel with the new coronavirus pandemic that we have faced in the real scenario.

A variety of uncertainty principles for the Hankel-Stockwell transform

In this work, we establish \(L^p\) local uncertainty principle for the Hankel-Stockwell transform and we deduce \(L^p\) version of Heisenberg-Pauli-Weyl uncertainty principle. Next, By combining these principles and the techniques of Donoho-Stark we present uncertainty principles of concentration type in the \(L^p\) theory, when \(1< p\leqslant2\). Finally, Pitt's inequality and Beckner's uncertainty principle are proved for this transform.

FQ‐MEC: Fuzzy‐Based Q‐Learning Approach for Mobility‐Aware Energy‐Efficient Clustering in MANET

Different schemes have been proposed for increasing network lifetime in mobile ad hoc networks (MANETs) where nodes move uncertainly in any direction. Mobility awareness and energy efficiency are two inescapable optimization problems in such networks. Clustering is an important technique to improve scalability and network lifetime, as it relies on grouping mobile nodes into logical subgroups, called clusters, to facilitate network management. One of the challenging issues in this domain is to design a real‐time routing protocol that efficiently prolongs the network lifetime in MANET. In this paper, a novel fuzzy‐based Q‐learning approach for mobility‐aware energy‐efficient clustering (FQMEC) is proposed that relies on deciding the behavioral pattern of the nodes based on their stability and residual energy. Also, Chebyshev’s inequality principle is applied to get node connectivity for load balancing by taking history from the monitoring phase to increase the learning accuracy. Extensive simulations are performed using the NS‐2 network simulator, and the proposed scheme is compared with reinforcement learning (RL). The obtained results show the effectiveness of the proposed protocol regarding network lifetime, packet delivery ratio, average end‐to‐end delay, and energy consumption.

Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form $$\begin{aligned} (r(t)((y(t)+p(t)y(\tau (t)))')^\alpha )'+q(t)y^\alpha (\sigma (t))=0,\ t\geqslant t_0, \end{aligned}$$ when $$\int _{}^\infty r^{-\frac{1}{\alpha }}(s){\text{d}}s<\infty $$ . We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation. An example is provided to illustrate the results.

Exploring Complex Dynamics of Spatial Predator–Prey System: Role of Predator Interference and Additional Food

In this paper, an attempt has been made to understand the role of predator’s interference and additional food on the dynamics of a diffusive population model. We have studied a predator–prey interaction system with mutually interfering predator by considering additional food and Crowley–Martin functional response (CMFR) for both the reaction–diffusion model and associated spatially homogeneous system. The local stability analysis ensures that as the quantity of alternative food decreases, predator-free equilibrium stabilizes. Moreover, we have also obtained a condition providing a threshold value of additional food for the global asymptotic stability of coexisting steady state. The nonspatial model system changes stability via transcritical bifurcation and switches its stability through Hopf-bifurcation with respect to certain ranges of parameter determining the quantity of additional food. Conditions obtained for local asymptotic stability of interior equilibrium solution of temporal system determines the local asymptotic stability of associated diffusive model. The global stability of positive equilibrium solution of diffusive model system has been established by constructing a suitable Lyapunov function and using Green’s first identity. Using Harnack inequality and maximum modulus principle, we have established the nonexistence of nonconstant positive equilibrium solution of the diffusive model system. A chain of patterns on increasing the strength of additional food as spots[Formula: see text][Formula: see text][Formula: see text]stripes[Formula: see text][Formula: see text][Formula: see text]spots has been obtained. Various kind of spatial-patterns have also been demonstrated via numerical simulations and the roles of predator interference and additional food are established.

Paulo Freire, las pedagogías post-críticas y el dilema pedagógico

El Manifiesto para una Pedagogía Post-crítica de Hodgson, Vlieghe y Zamojski comparte varios elementos con las propuestas que, con el mismo nombre, circulan desde finales de la década de 1980. Dos de los elementos con los que estos autores pretenden distanciarse de la pedagogía crítica, y que me interesan aquí en particular, son la propuesta de asumir la igualdad entre educadores y educandos como un punto de partida —en lugar de la superioridad de los primeros sobre los segundos— y la de abstenerse de proponer compromisos sustantivos sobre un futuro utópico hacia el cual se debe avanzar y que sirve para juzgar el presente. Al analizar la obra del autor posiblemente más importante de la pedagogía crítica, Paulo Freire, señalo que un afán de igualdad ya se encontraba en su obra de manera explícita y contundente. A la vez, sin embargo, también existen en ella varios elementos relacionados con un afán de justicia y dignidad más allá de la relación pedagógica —las ideas de conciencia crítica y concienciación— que, de modo contradictorio, materializan un principio de desigualdad. Los proponentes del Manifiesto para una Pedagogía Post-crítica definen de antemano un principio de igualdad entre educadores y educandos, con lo cual terminan evadiendo una de las dimensiones de la responsabilidad de cuidado que corresponde a la práctica educativa de la pedagogía crítica. Propongo que, al tomar la educación crítica como una práctica de cuidado, ninguno de estos afanes podrá evadirse. Concluyo que una pedagogía crítica se constituye en la atención siempre presente y profunda hacia las necesidades de los educandos, en la tensión entre un afán de igualdad y un afán de justicia y dignidad.

The Existence and Stability of Periodic Solutions with a Boundary Layer in a Two-Dimensional Reaction-Diffusion Problem in the Case of Singularly Perturbed Boundary Conditions of the Second Kind

The existence of time-periodic solutions of the boundary-layer type to a two-dimensional reaction–diffusion problem with a small-parameter coefficient of a parabolic operator is proved in the case of singularly perturbed boundary conditions of the second kind. An asymptotic approximation with respect to the small parameter is constructed for these solutions. The set of boundary conditions for which these solutions exist is studied and the local uniqueness and asymptotic Lyapunov stability are established for them. It is shown that, unlike the analogous Dirichlet problem, for which such a solution is unique, there can be several solutions of this kind for the problem under consideration, each of which has its domains of stability and local uniqueness. To prove these facts, results based on the asymptotic principle of differential inequalities are used. Keywords: , , , , , , .

Oscillation of Second-Order Emden–Fowler Neutral Differential Equations with Advanced and Delay Arguments

In this paper, we study the oscillation of the second-order Emden–Fowler neutral differential equations with advanced and delay arguments $$\begin{aligned} (r(t)(x(t)+p(t)x(\tau (t)))')'+q(t)x^\gamma (\sigma (t))=0,\ \quad t\geqslant t_0, \end{aligned}$$where $$\tau (t)\leqslant t$$, $$\sigma (t)\geqslant t$$. Sufficient conditions for oscillation of the equation are obtained by using the inequality principle, comparison principle and Riccati transform. Two examples are given to illustrate the results.

Small Literature as a Problem. Could It Be Solved?

Th e article discusses the status and functioning of so-called small literatures, including Lithuanian literature, in the global system of world literature. Referring to Franco Moretti and Pascale Casanova’s interpretation of world literature system as based on the principle of inequality, the author discusses the conception of belonging to small literatures as a destiny and interprets the onecentric world literary system as hegemonic. Being dominated by grand literatures, small literatures have very restricted possibilities of gravitation towards the center of world literature. In that theoretical context, the article considers the following issues: is it possible and how is it possible to avoid the destiny of small literatures staying in the periphery of world literature, what role in this situation plays the writer himself, what depends on the culture and research politics, could literary scholars play the role of mediators and what could be the alternatives for onecentered world literary system.

Conceptual Framework for Finding Approximations to Minimum Weight Triangulation and Traveling Salesman Problem of Planar Point Sets

We introduce a novel Conceptual Framework for finding approximations to both Minimum Weight Triangulation (MWT) and optimal Traveling Salesman Problem (TSP) of planar point sets. MWT is a classical problem of Computational Geometry with various applications, whereas TSP is perhaps the most researched problem in Combinatorial Optimization. We provide motivation for our research and introduce the fields of triangulation and polygonization of planar point sets as theoretical bases of our approach, namely, we present the Isoperimetric Inequality principle, measured via Compactness Index, as a key link between our two stated problems. Our experiments show that the proposed framework yields tight approximations for both problems.

DIALOGUE AS AN ELEMENT OF URBAN CULTURE OF POSTCLEISTHENIC ATHENS

The research shows the way to liberate the word from the imperative hierarchical social system to the equality, to the cooperative search for truth. It’s the way from Logos to Dialogos. The article analyzes the development of the social structure of Athens from the Mycenaean Age to the end of the 6th century BC. The author highlights the main stages and principles of this development: dysnomia, eunomia, isonomia. Special attention was paid to the definitions and explication the relationship between these principles. Dysnomia is characterized as wrong order, lawlessness. It was a principle of total political inequality, where the class of urban aristocracy is endowed with full rights, and ordinary people do not have them at all. Eunomia is the conception of good order, the right social system. It was a principle of geometrical equality that left power in the hands of the aristocracy, but expanded the rights of the people. The author shows that Eunomia“s role in the development of the political equality in Athens as a transitional stage to the notion of Isonomia was fundamental. He claims that the emergence of dialogue as a social phenomenon, and partly as a genre, in Athens becomes possible after Cleisthenes“ reforms on the ground of principle of Isonomia (an equal distribution of political power or full arithmetical equality).

OSCILLATION BEHAVIOR OF SOLUTION OF IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATION

In this paper, we study the oscillation of impulsive Caputo fractional differential equation. Sufficient conditions for the asymptotic and oscillation of the equation are obtained by using the inequality principle and Bihari Lemma. An example is given to illustrate the results. This is the first time to study the oscillation of impulsive fractional differential equation with Caputo derivative.

Ground-State Phase Diagram of a Mixed Spin-3/2 and Spin-7/2 Ising Model: A Study of Complex [Cr(CN)4(μ-CN)2Gd(H2O)4-(bpy)]n.4nH2O.1.5nbpy

In this work, the phase transitions, for a molecular-based magnet, are examined using mean field method (MFM). The longitudinal magnetizations can be achieved by minimizing the free energy is an interesting function for locating and induction of spin compensation temperatures as well. By applying Blume-Capel (BC) configuration to a system consisting of two sublattices for a mixed spin-3/2 and spin-7/2on a square lattice in the anisotropies plane, the ground-state phase diagram of this system has been built. On principles of Bogoliubov inequality (BI) of the free energy, it has been investigated the spin compensation phenomena. In particular, characteristic ferrimagnetic features have been shown depending on an unequal crystal field parameters (DA, DB<-1.0) applied on the A−sites and B−sites, respectively.