ALBERT

Description: Mathematics, Vol. 6, Pages 172: Optimizing Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Bounded Variables Mathematics doi: 10.3390/math6090172 Authors: Hui-Chin Tang Shen-Tai Yang A single constrained ordered weighted averaging aggregation (COWA) problem is of considerable importance in many disciplines. Two models are considered: the maximization COWA problem with lower bounded variables and the minimization COWA problem with upper bounded variables. For a three-dimensional case of these models, we present the explicitly optimal solutions theoretically and empirically. The bounds and weights can affect the optimal solution(x1',x2',x3') of the three-dimensional COWA problem with bounded variables.

Description: Mathematics, Vol. 6, Pages 170: Convergence in Fuzzy Semi-Metric Spaces Mathematics doi: 10.3390/math6090170 Authors: Hsien-Chung Wu The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy semi-metrics, the different types of triangle inequalities can be obtained. We also study the convergence of these two types of dual fuzzy semi-metrics.

Description: Mathematics, Vol. 6, Pages 171: Almost Periodic Solutions of First-Order Ordinary Differential Equations Mathematics doi: 10.3390/math6090171 Authors: Seifedine Kadry Gennady Alferov Gennady Ivanov Artem Sharlay Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In the works of Lebedeva [1], regarding the number of periodic solutions of equations first order, they required a high degree of smoothness. Franco et al. required the smoothness of the second derivative of the Schwartz equation [2]. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty.

Description: Mathematics, Vol. 6, Pages 169: A Nonlinear Systems Framework for Cyberattack Prevention for Chemical Process Control Systems † Mathematics doi: 10.3390/math6090169 Authors: Helen Durand Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an analysis of three control designs how control laws can be inspected for this property. A chemical process example illustrates that control approaches intended for cyberattack prevention which seem intuitive are not cyberattack-resilient unless they meet the requirements of a nonlinear systems description of this property.

Description: Mathematics, Vol. 6, Pages 168: Equivalences of Riemann Integral Based on p-Norm Mathematics doi: 10.3390/math6090168 Authors: Ray-Ming Chen In the usual Riemann integral setting, the Riemann norm or a mesh is adopted for Riemann sums. In this article, we use the p-norm to define the p-integral and show the equivalences between the Riemann integral and the p-integral. The p-norm provides an alternative approach to define the Riemann integral. Based on this norm, we also derive some other equivalences of the Riemann integral and the p-integral.

Description: Mathematics, Vol. 6, Pages 167: Progress in Mathematical Ecology Mathematics doi: 10.3390/math6090167 Authors: Sergei Petrovskii n/a

Description: Mathematics, Vol. 6, Pages 166: A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems Mathematics doi: 10.3390/math6090166 Authors: Xiaojie Dou  Jin-San Cheng  In this paper, by transforming the given over-determined system into a square system, we prove a necessary and sufficient condition to certify the simple real zeros of the over-determined system by certifying the simple real zeros of the square system. After certifying a simple real zero of the related square system with the interval methods, we assert that the certified zero is a local minimum of sum of squares of the input polynomials. If the value of sum of squares of the input polynomials at the certified zero is equal to zero, it is a zero of the input system. As an application, we also consider the heuristic verification of isolated zeros of polynomial systems and their multiplicity structures.

Description: Mathematics, Vol. 6, Pages 165: Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration Mathematics doi: 10.3390/math6090165 Authors: Ekaterina Gromova Anastasiya Malakhova Arsen Palestini A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the cumulative distribution function (c.d.f.) of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively.

Description: Mathematics, Vol. 6, Pages 163: Higher Order Hamiltonian Systems with Generalized Legendre Transformation Mathematics doi: 10.3390/math6090163 Authors: Dana Smetanová The aim of this paper is to report some recent results regarding second order Lagrangians corresponding to 2nd and 3rd order Euler–Lagrange forms. The associated 3rd order Hamiltonian systems are found. The generalized Legendre transformation and geometrical correspondence between solutions of the Hamilton equations and the Euler–Lagrange equations are studied. The theory is illustrated on examples of Hamiltonian systems satisfying the following conditions: (a) the Hamiltonian system is strongly regular and the Legendre transformation exists; (b) the Hamiltonian system is strongly regular and the Legendre transformation does not exist; (c) the Legendre transformation exists and the Hamiltonian system is not regular but satisfies a weaker condition.

Description: Mathematics, Vol. 6, Pages 164: Introducing Weights Restrictions in Data Envelopment Analysis Models for Mutual Funds Mathematics doi: 10.3390/math6090164 Authors: Antonella Basso Stefania Funari Data envelopment analysis has been applied in a number of papers to measure the performance of mutual funds, besides a great many applications on the more diverse fields of performance evaluation. The data envelopment analysis models proposed in the mutual funds literature do not generally set restrictions on the weights assigned to the input and output variables. In this paper, we study the effects of the introduction of different weight restrictions on the results of the performance evaluation of mutual funds. In addition, we provide a unified matrix representation for three widely used approaches on weight restrictions: virtual weight restrictions with constraints on all decision-making units (DMUs) (on all funds); virtual weight restrictions with constraints only on the target unit; assurance regions. Using the unified matrix representation of the weights constraints, we formulate the data envelopment analysis (DEA ) efficiency model and express the efficient frontier in a unified way for the different weight restrictions considered. We investigate the effects of the different weight restrictions on the performance evaluation by means of an empirical application on a set of European mutual funds. Moreover, we study the behaviour of the fund performance scores as the restrictions on the weights become increasingly strict.