System Of Inequalities Research Articles

A Splitting Method for Band Control of Brownian Motion: With Application to Mutual Reserve Optimization

As well studied in the operations research literature, optimization of a mutual reserve system (e.g., federal reserves) and a nonmutual one such as regular inventory systems requires solving simultaneous systems of quasi-variational inequalities, of which analytical solutions in closed form remain unattainable and computational solutions are still intractable. Thus far, the studies of reserve optimization are of intra-nations (e.g., central bank reserves) as opposed to inter-nations (e.g., COVID vaccine reserves of the United Nations). In this paper, we advance a method of computational analytics for mutual reserve optimization, with an international perspective in response to the intensifying challenge on global medical reserves during the COVID pandemic. A solution algorithm is developed in the context of maritime mutual insurances (a long existent international mutual reserve system) and then tested through comprehensive numerical experiments.

A Splitting Method for Band Control of Brownian Motion: With Application to Mutual Reserve Optimization

As well studied in the operations research literature, optimization of a mutual reserve system (e.g., federal reserves) and a nonmutual one such as regular inventory systems requires solving simultaneous systems of quasi-variational inequalities, of which analytical solutions in closed form remain unattainable and computational solutions are still intractable. Thus far, the studies of reserve optimization are of intra-nations (e.g., central bank reserves) as opposed to inter-nations (e.g., COVID vaccine reserves of the United Nations). In this paper, we advance a method of computational analytics for mutual reserve optimization, with an international perspective in response to the intensifying challenge on global medical reserves during the COVID pandemic. A solution algorithm is developed in the context of maritime mutual insurances (a long existent international mutual reserve system) and then tested through comprehensive numerical experiments.

Activity propagation in systems of linear inequalities and its relation to block-coordinate descent in linear programs

Activity propagation in systems of linear inequalities and its relation to block-coordinate descent in linear programs

Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications

In the paper, we start by establishing first and second-ordered analysis for a convex inequality system that contains uncertainty data, including calculating normal and tangent cones, second-ordered tangent sets for the solution set to this system, and first and second-ordered epi-subderivatives for the indicator function of its solution set. Then, we provide second-ordered necessary and sufficient optimality conditions for strict solutions of convex robust optimization problems. Moreover, an associated algorithm converging quickly to a solution for the class of quadratic robust optimization problems is proposed. The theoretical results are newly obtained under weak qualification conditions, and numerical examples show the advantage of the given method.

Development and Validation of Learning Activity Sheets in Rational Expressions and Linear Equations and Inequalities

The purpose of this research study is to develop Learning Activity Sheets (LAS) in Rational Expressions and Linear Equations and Inequalities for the students. Data were collected via survey questionnaire from three sets of evaluators. The LAS was also administered from 100 students of New Society National High School to further scrutinize its validity. The results were interpreted and analysed using the rating scale and statistical tools including on-way ANOVA and mean.
 Based from the results of the study, the researcher concluded that: there were fourteen competencies included in the developed LAS which are the not mastered and least mastered competencies of the students. The competency that received the highest mean percentage on the competency test was LAS 17 (graphs and illustrates a linear function and its (a) domain; (b) range; (c) table of values; (d) intercepts; and (e) slope). On the other hand, the competency that received the lowest mean percentage on the competency test was LAS 12 (solves problems involving systems of linear inequalities in two variables). The evaluators found the developed LAS to be effective and useful in terms of objectives, concepts, skills, usability, appropriateness, and adequacy with an interpreted mean rating of very high extent. The researcher also concluded that there is no significant difference in the standard response of the evaluators which is composed of Grade 8 math teachers, master teachers, and LRMDS-trained teachers. Based on the mean percentage results of the administered LAS, there was also a considerable improvement in the students' learning.

Design of continuous-time recurrent neural networks with piecewise-linear activation function for generation of prescribed sequences of bipolar vectors

A recurrent neural network (RNN) can generate a sequence of patterns as the temporal evolution of the output vector. This paper focuses on a continuous-time RNN model with a piecewise-linear activation function that has neither external inputs nor hidden neurons, and studies the problem of finding the parameters of the model so that it generates a given sequence of bipolar vectors. First, a sufficient condition for the model to generate the desired sequence is derived, which is expressed as a system of linear inequalities in the parameters. Next, three approaches to finding solutions of the system of linear inequalities are proposed: One is formulated as a convex quadratic programming problem and others are linear programming problems. Then, two types of sequences of bipolar vectors that can be generated by the model are presented. Finally, the case where the model generates a periodic sequence of bipolar vectors is considered, and a sufficient condition for the trajectory of the state vector to converge to a limit cycle is provided.

Finding the Least Element of a Nonnegative Solution Set of a Class of Polynomial Inequalities

In this paper, we consider the least element problem of a nonnegative solution set of a system of inequalities defined by a homogeneous polynomial mapping and a vector. In the set under consideration, the homogeneous polynomial mapping is defined by a tensor. When the tensor involved is square, the set under consideration is just the feasible region of the tensor complementarity problem (TCP). We first introduce the concept of the generalized -tensor, which is a natural generalization of the -tensor. Then, under the assumption that the considered set is nonempty and the tensor involved is a generalized -tensor, we propose an iterative method for finding the least element of the considered set. Specifically, by recognizing the position indices of positive components in the least element continuously, we solve a series of lower-dimensional system of tensor equations corresponding to these indices and prove that the least element of the set can be obtained within finite step iterations. When the tensor involved is square, the least element obtained is also a solution of the TCP. Compared with the existing methods for finding the least-element solution of the TCP with a -tensor, our method does not require any additional assumptions and has lower computational cost. Preliminary numerical experiments show that the proposed method is effective.

A Family of Multi-Step Subgradient Minimization Methods

For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with a built-in algorithm for finding the descent direction that forms an acute angle with all subgradients in the neighborhood of the current minimum. Minimizing the function along the opposite direction (with a minus sign) enables the algorithm to go beyond the neighborhood of the current minimum. The family of algorithms for finding the descent direction is based on solving systems of inequalities. The finite convergence of the algorithms on separable bounded sets is proved. Algorithms for solving systems of inequalities are used to organize the RSM family. On quadratic functions, the methods of the RSM family are equivalent to the conjugate gradient method (CGM). The methods are intended for solving high-dimensional problems and are studied theoretically and numerically. Examples of solving convex and non-convex smooth and non-smooth problems of large dimensions are given.

A system of wave inequalities with inverse-square potentials in an exterior domain

ABSTRACT We study the existence and nonexistence of solutions to a system of wave inequalities with inverse-square potentials in an exterior domain of R N , under inhomogeneous Dirichlet-type boundary conditions. Our study yields naturally existence and nonexistence results for the corresponding stationary wave system.

The Social Construction of Age: Concepts and Measurement

Age as an individual characteristic is ubiquitous in social science research because it has important associations with numerous outcomes of interest. Yet age is rarely treated as a phenomenon that requires explanation or theoretical attention. To advance research in sociology and beyond, we bring together previously siloed literatures on the conceptualization and measurement of age. Our framework presents age as a system of inequality that can be understood through concepts and processes that operate at multiple levels of analysis. At the individual level, we argue age is best conceptualized and operationalized as multidimensional. We review a range of measures, from birth cohort to physical appearance, that can be fruitfully combined in empirical research to account for this complexity. The multidimensionality of age also highlights how it is “done” in interactions, connecting the social construction of age to the intersectional production of inequality.

Remembering Herbert Gutman's Work, Culture, and Society Fifty Years On

Remembering Herbert Gutman's <i>Work, Culture, and Society</i> Fifty Years On

Optimal Pricing With Weighted Factors in a Product Transportation System Based on the Min-Plus Fuzzy Relation Inequality

In this work, we introduce the fuzzy relation inequalities with min-plus composition for describing the pricing problem in a product transportation system. Some basic properties of the min-plus inequalities system are investigated. We define the concept of feasible index chain and further investigate the corresponding quasi-maximal solution. Moreover, it is found that the solution set of a min-plus system could be generated by a unique minimum solution and a finite number of quasi-maximal solutions. As a consequence, one is able to find the complete solution set of a min-plus system. Besides, motivated by the optimal managerial objective, we establish an optimization model with the min-plus inequalities constraints. A so-called FIS-based algorithm is developed for searching an optimal solution of our studied optimization model. We have provided a simple numerical example for checking the effectiveness of our proposed FIS-based algorithm. The obtained optimal solution would be helpful for the system manager, as an optimal pricing scheme.

Development of a two-variable linear inequality system mathematics learning design with a problem-based learning model

Teachers are designers, implementers, and evaluators of learning. The teacher's ability to design learning that favors students will greatly affect the quality of the learning process and the learning outcomes that will then be obtained by students. This study aims to develop a problem-based learning design for the more interesting topic of systems of two-variable linear inequalities. This development research uses the Dick Carey development model. The Dick Carey model can be an alternative for teachers in designing pro-student learning because, by design, this model starts with student and context analysis as well as instructional analysis, which will provide sufficient information and evidence about the characteristics and needs of students as well as instructional objectives that are appropriate to the level of their education and stage of development.

Uncovering the trade-induced air pollution inequality among Belt and Road Initiative (BRI) countries

Although trade does not only boost the economy but also exacerbates environmental transfers but still the evidence for air pollution's unequal exchange embodied in trade among the Belt and Road Initiative (BRI) countries is rarely discussed in the extant literature. From the perspective of an integrated evaluation framework comprising a multi-regional input-output model, system balance theory, and complex network theory, this research paper uncovers the spatial- and temporal changes of trade-induced air pollution inequality among countries along the BRI route for the time period from 2011 to 2016. The study findings point out that there exists an obvious spatial heterogeneity in the unequal relations among BRI economies. This implies that a large number of country pairs demonstrate weak inequalities, whereas a relatively small number of country pairs represent strong inequalities. In addition, the countries' positions indicate a unique characteristic of “duality and inverse”, which is majorly manifested as pure causers represented by Moldova and Belarus, net beneficiaries symbolized by China and Russia, and pure victims exemplified by Bhutan. Meanwhile, nearly half of the dual identities are represented by Singapore. Besides this, the proposal and implementation of the BRI exert a positive influence on both system stability and inequality mitigation by supporting the balance of triangles. Finally, this paper posits that the environmental inequality system of the Belt and Road is not as complex as imagined since the 3-node motif classification is relatively simple. Our findings are helpful for mitigating air pollution inequalities so as to support the sustainable development of green BRI.

A New System of Differential Quasi-Hemivariational Inequalities in Contact Mechanics

A New System of Differential Quasi-Hemivariational Inequalities in Contact Mechanics

Elliptic inequalities with nonlinear convolution and Hardy terms in cone-like domains

We study the inequality −Δu−μ|x|2u≥(|x|−α⁎up)uq in an unbounded cone CΩρ⊂RN (N≥2) generated by a subdomain Ω of the unit sphere SN−1⊂RN, p,q,ρ>0, μ∈R and 0≤α<N. In the above, |x|−α⁎up denotes the standard convolution operator in the cone CΩρ. We discuss the existence and nonexistence of positive solutions in terms of N,p,q,α,μ and Ω. Extensions to systems of inequalities are also investigated.

On the critical curve for systems of hyperbolic inequalities in an exterior domain of the half-space

We establish blow-up results for a system of semilinear hyperbolic inequalities in an exterior domain of the half-space. The considered system is investigated under an inhomogeneous Dirichlet-type boundary condition depending on both time and space variables. In certain cases, an optimal criterium of Fujita-type is derived. Our results yield naturally sharp nonexistence criteria for the corresponding stationary wave system and equation.

On Cm solutions to systems of linear inequalities

Recent work of C. Fefferman and the first author [8] has demonstrated that the linear system of equations∑j=1MAij(x)Fj(x)=fi(x)(i=1,…,N), has a Cm solution F=(F1,…,FM) if and only if f1,…,fN satisfy a certain finite collection of partial differential equations. Here, the Aij are fixed semialgebraic functions.In this paper, we consider the analogous problem for systems of linear inequalities:∑j=1MAij(x)Fj(x)≤fi(x)(i=1,…,N). Our main result is a negative one, demonstrated by counterexample: the existence of a Cm solution F may not, in general, be determined via an analogous finite set of partial differential inequalities in f1,…,fN.

The effect of GeoGebra android on increasing mathematical understanding ability based on gender

This study aims to describe the increase of students' mathematical understanding ability in learning the two-variable linear equation system (SPLDV) and the two-variable linear inequality system (SPTLDV) with Android GeoGebra media reviewed by gender. This experimental quasi research is one group pretest postest design. The sample in this study was a class XI of 32 students with Purposive Random Sampling techniques. Data collection in this study uses an instrument for a mathematical understanding ability test in the form of a description. The results of the study can be concluded in the learning of Android GeoGebra, the mathematical understanding of male students is significantly different from the mathematical understanding of female students. It means that in learning the Android GeoGebra Improvement of the Mathematical Understanding Ability of Male Students is greater than female students. Thus it can be concluded that in the learning of Android GeoGebra, an increase in the mathematical understanding of male students is better than female students.

An Oblivious Ellipsoid Algorithm for Solving a System of (In)Feasible Linear Inequalities

The ellipsoid algorithm is a fundamental algorithm for computing a solution to the system of m linear inequalities in n variables [Formula: see text] when its set of solutions has positive volume. However, when [Formula: see text] is infeasible, the ellipsoid algorithm has no mechanism for proving that (P) is infeasible. This is in contrast to the other two fundamental algorithms for tackling [Formula: see text], namely, the simplex and interior-point methods, each of which can be easily implemented in a way that either produces a solution of [Formula: see text] or proves that [Formula: see text] is infeasible by producing a solution to the alternative system [Formula: see text]. This paper develops an oblivious ellipsoid algorithm (OEA) that either produces a solution of [Formula: see text] or produces a solution of [Formula: see text]. Depending on the dimensions and other condition measures, the computational complexity of the basic OEA may be worse than, the same as, or better than that of the standard ellipsoid algorithm. We also present two modified versions of OEA, whose computational complexity is superior to that of OEA when [Formula: see text]. This is achieved in the first modified version by proving infeasibility without producing a solution of [Formula: see text], and in the second version by using more memory. Funding: J. Lamperski and R. M. Freund were supported by the Air Force Office of Scientific Research [Grant FA9550-19-1-0240].