rss_2.0Mathematics FeedSciendo RSS Feed for Mathematics Feed Reasoning and Information Intelligent Mining<abstract> <title style='display:none'>Abstract</title> <p>P-sets (P stand for Packet) and P-matrix are novel and effective mathematical tools for studying dynamic information systems. In this paper, the concept of P-information mining is given by using the dynamic characteristics of P-sets and P-matrix structure. In addition, the reasoning theorem of P-matrix and the reasoning structure are given. Moreover, the information intelligent mining method under the condition of P-matrix reasoning is obtained. As the application, intelligent recognition of information image was shown.</p> </abstract>ARTICLE2022-06-15T00:00:00.000+00:00Set-valued minimax fractional programming problems under -cone arcwise connectedness<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of <italic>ρ-</italic>cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under <italic>ρ</italic>-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under <italic>ρ</italic>-cone arcwise connectedness assumption.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions<abstract> <title style='display:none'>Abstract</title> <p>The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic differential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic– Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Stability kernel in finite games with perturbed payoffs<abstract> <title style='display:none'>Abstract</title> <p>The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., i.e. a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (, )--(, )-invexity<abstract> <title style='display:none'>Abstract</title> <p>There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (<italic>p, r</italic>)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invex functions but not in the class of (1, −1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Some examples of solutions to an inverse problem for the first-passage place of a jump-diffusion process<abstract> <title style='display:none'>Abstract</title> <p>We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If <italic>X</italic>(<italic>t</italic>) is a one-dimensional diffusion with jumps, starting from a random position <italic>η</italic> ∈ [<italic>a, b</italic>], let be <italic>τ</italic><sub>a,b</sub> the time at which <italic>X</italic>(<italic>t</italic>) first exits the interval (<italic>a, b</italic>), and <italic>π</italic><sub>a</sub> = <italic>P</italic> (<italic>X</italic>(<italic>τ</italic><sub>a,b</sub>) ≤ <italic>a</italic>) the probability of exit from the left of (<italic>a, b</italic>). Given a probability <italic>q</italic> ∈ (0, 1), the problem consists in finding the density <italic>g</italic> of <italic>η</italic> (if it exists) such that <italic>π</italic><sub>a</sub> = <italic>q</italic>; it can be seen as a problem of optimization.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00A new approach to maximize the overall return on investment with price and stock dependent demand under the nonlinear holding cost<abstract> <title style='display:none'>Abstract</title> <p>This study investigates an inventory model for deteriorating products with a price and stock-dependent demand pattern where the holding cost is a non-linear function of both time and stock level. Moreover, a decreased price and a higher stock level lead to a higher rate of demand. Consequently, in this article, we present a new approach, aiming at maximization of the return on investment by maximizing the profit/cost ratio. If an inventory manager has the potential to invest in a variety of projects, but disposes of only limited resources, it is logical to strategically plan towards a better return on investment. As a result, the manager’s objective will be to develop an inventory policy with a possibly high return on investment. Therefore, a new strategy is considered in this article to optimize the profitability ratio in terms of replenishment time and selling price, which is determined as the proportion between the profit and the overall cost of the inventory scheme. This research demonstrates that optimizing the profitability ratio is equivalent to decreasing the average inventory cost of a product per unit. Also, the optimality is graphically checked and one numerical illustration is discussed to explain the result of the proposed model. Finally, sensitivity analysis of key parameters is performed to show the applicability of the proposed model. The profit/cost ratio is more sensitive to price elasticity markup or purchasing cost compared to the other parameters used. Also, for decision-makers, several helpful management insights are derived.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control<abstract> <title style='display:none'>Abstract</title> <p>The Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint<abstract> <title style='display:none'>Abstract</title> <p>This paper is devoted to a sufficient second-order condition for a weak local minimum in a simple optimal control problem with one control constraint <italic>G</italic>(<italic>u</italic>) ≤ 0, given by a <italic>C</italic><sup>2</sup>-function. A similar second-order condition was obtained earlier by the author for a strong minimum in a much more general problem. In the present paper, we would like to take a narrower perspective than before and thus provide shorter and simpler proofs. In addition, the paper uses the first and second order tangents to the set <italic>U</italic>, defined by the inequality <italic>G</italic>(<italic>u</italic>) ≤ 0. The main difficulty of the proof, clearly shown in the paper, refers to the set, where the gradient <italic>H</italic><italic><sub>u</sub></italic> of the Hamiltonian is small, but the condition of quadratic growth of the Hamiltonian is satisfied. The paper can be valuable for self-explanation and provides a basis for extensions.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Throwback<abstract> <title style='display:none'>Abstract</title> <p>With this short composition, I’d like to share with you a few events of my scientific life</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00On the robustness of the topological derivative for Helmholtz problems and applications<abstract> <title style='display:none'>Abstract</title> <p>We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function <italic>J</italic>(<italic>u</italic><sub>∈</sub>) with respect to a small hole <italic>B</italic><sub>∈</sub> around a given point <italic>x</italic><sub>0</sub> ∈ <italic>B</italic><sub>∈</sub> ⊂ Ω depends on various parameters, like the frequency <italic>k</italic> chosen or certain material parameters or even the shape parameters of the hole <italic>B</italic><sub>∈</sub>. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Distributed optimal control problems driven by space-time fractional parabolic equations<abstract> <title style='display:none'>Abstract</title> <p>We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial fractional derivatives of Sturm-Liouville type. We first prove existence and uniqueness of solutions of STFPEs on an open bounded interval and study their regularity. Then we show existence and uniqueness of solutions to a quadratic distributed optimal control problem. We derive an adjoint problem using the right-Caputo derivative in time and provide optimality conditions for the control problem. Moreover, we propose a finite difference scheme to find the approximate solution of the considered optimal control problem. In the proposed scheme, the well-known L1 method has been used to approximate the time-fractional Caputo derivative, while the spatial derivative is approximated using the Grünwald-Letnikov formula. Finally, we demonstrate the accuracy and the performance of the proposed difference scheme via examples.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00“Cum grano salis”<abstract> <title style='display:none'>Abstract</title> <p>This short note is devoted to presentation of the essential points in the history of collaboration between the present-day Department of Computer Science and Artificial Intelligence of the University of Granada and the Systems Research Institute, Polish Academy of Science, with special emphasis on the place, taken in this collaboration by <italic>Control and Cybernetics</italic>. Thus, I mention encounters, conference meetings, jointly undertaken projects, as well as certain selected publications. In doing this, I also try to delineate the substance matter of the collaboration, which formed the backbone of it.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00A novel approach to hierarchical contextual bipolar queries: A winnow operator approach<abstract> <title style='display:none'>Abstract</title> <p>We propose a new approach to the bipolar database queries, which involve a necessary (required) and optional (desired) conditions, connected with a non-conventional aggregation operator “and possibly”, combined with a context, exemplified by “find houses which are cheap and – with respect to other houses in town – possibly close to a railroad station”. We use our winnow operator based interpretation of the bipolar queries. We assume that the query, posed by the human user, involves terms, which do not directly relate to attributes, and which are then to be <italic>decoded</italic> using a concept of a query hierarchy, leading to the queries, which involve terms directly related to attribute values. The original query is considered to be of level 0, at the bottom of the precisiation hierarchy, then its required and optional parts are assumed to be bipolar queries themselves, both accounting for context. The precisiation proceeds further, to level 1 queries, level 2, etc. A real estate related example is provided as illustration.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Preface measures for Atanassov’s intuitionistic fuzzy sets: some dilemmas and challenges<abstract> <title style='display:none'>Abstract</title> <p>We discuss some aspects of similarity measures in the context of Atanassov’s intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a relatively new tool for the modeling and simulation and, because of their construction, present us with new challenges as far the similarity measures are concerned. Specifically, we claim that the distances alone are not a proper measure of similarity for the IFSs. We stress the role of a lack of knowledge concerning elements (options, decisions, etc.) and point out the role of the opposing (complementing) elements. We also pay attention to the fact that it is not justified to talk about similarity when one has not enough knowledge about the compared objects/elements. Some novel measures of similarity are presented.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:00Social choice, stable outcomes and deliberative democracy<abstract> <title style='display:none'>Abstract</title> <p>It has turned out that all voting rules fail on some intuitively plausible desiderata. This has led some political scientists to argue that the notion of the will of the people is profoundly ambiguous and the absence of voting equilibria a generic state of a airs. As a constructive remedy to this some authors have introduced the idea of <italic>deliberative democracy</italic>. This view of democracy has much to recommend itself, most importantly the emphasis on individuals in devising the decision alternatives. Some empirical evidence also suggests that the deliberative institutions provide an escape from some of the most notorious incompatibility results in social choice theory. We shall critically examine this suggestion. The view emerging from this examination is that social choice theory and deliberative democracy are complementary, not competing approaches to democratic decision making.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:0050 years of history, the present and the future<abstract> <title style='display:none'>Abstract</title> <p>In this short note, we outline the history of the Journal, present its recent developments, as well as changes that we are going through, with some attempt at sketching the plans for the future. Some illustrations are provided, concerning the publication statistics, especially with respect to the last 15 years.</p> </abstract>ARTICLE2022-08-12T00:00:00.000+00:003D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm<abstract> <title style='display:none'>Abstract</title> <p>This article studies the generation of 3D animation simulation based on gray value algorithm and fractal interpolation algorithm. The article uses fractal technology combined with the Diamond-Square algorithm to generate height data and then color it. This algorithm optimizes the 3D animation process. The results show that the algorithm is fast in generating speed and only needs to input a few simple animation parameters to generate different 3D animations.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method<abstract> <title style='display:none'>Abstract</title> <p>The paper calculates the nonlinear dynamic differential equation model based on the stiffness of the gear teeth and gives the calculation method of the spring stiffness of the transmission system. Choose the Lyapunov energy function and derive the adaptive law that can make the system asymptotically stable globally. At the same time, we discussed the influence of the phase combination of the coupling shaft's torsional stiffness and the gears' meshing stiffness in the multi-stage gear transmission system on the system dynamics. The example calculation shows that the asymptotic method has higher solution accuracy and higher calculation efficiency. This algorithm is a highly versatile analytical solution method.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00en-us-1