Mathematics doi: 10.3390/math7030276

Authors: Ahmed A. H. Alkhalidi Ghasem A. Afrouzi Somayeh Khademloo

In this paper, we study the multiple solutions for Lagrangian systems of discrete second-order boundary value systems involving the discrete p-Laplacian operator. The technical approaches are based on a local minimum theorem for differentiable functionals in a finite dimensional space and variational methods due to Bonanno. The existence of at least one solution, as well as three solutions for the given system are discussed and some examples and remarks have also been given to illustrate the main results.

]]>Mathematics doi: 10.3390/math7030275

Authors: Luigi Brugnano Gianluca Frasca-Caccia Felice Iavernaro

In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we consider the semilinear wave equation, the nonlinear Schr&ouml;dinger equation, and the Korteweg&ndash;de Vries equation, to illustrate the main features of this novel approach.

]]>Mathematics doi: 10.3390/math7030274

Authors: Quanrui Song Jianxu Liu Songsak Sriboonchitta

Multivariate copulas have been widely used to handle risk in the financial market. This paper aimed to adopt two novel multivariate copulas, Vine copulas and Factor copulas, to measure and compare the financial risks of the emerging economy, developed economy, and global economy. In this paper, we used data from three groups (BRICS, which stands for emerging markets, specifically, those of Brazil, Russia, India, China, and South Africa; G7, which refers to developed countries; and G20, which represents the global market), separated into three periods (pre-crisis, crisis, and post-crisis) and weighed Value at Risk (VaR) and Expected Shortfall (ES) (based on their market capitalization) to compare among three copulas, C-Vine, D-Vine, and Factor copulas. Also, real financial data demonstrated that Factor copulas have stronger stability and perform better than the other two copulas in high-dimensional data. Moreover, we showed that BRICS has the highest risk and G20 has the lowest risk of the three groups.

]]>Mathematics doi: 10.3390/math7030273

Authors: Yeqing Ren Youqiang Sun Xuechun Jing Zhihua Cui Zhentao Shi

With the advent of the artificial intelligence (AI) era, the beauty camera is widely used, and makeup transfer has attracted increasing attention. In this paper, we propose an adaptive makeup transfer based on the bat algorithm to solve the problem that only a single makeup effect can be transferred. According to the characteristics of makeup style, the algorithm optimizes the weight value to get the appropriate makeup lightness by using the adaptive method. The improved algorithm can not only help to get the optimal weight values in the process of transferring the same makeup style to different targets, but also to transfer different makeup styles to the same target. Moreover, this algorithm can choose the most suitable makeup style and also the most appropriate lightness for a certain person. Experimental results show that the algorithm proposed in the paper has a better effect than the existing algorithm of makeup transfer, and the algorithm can provide users with a suitable makeup style and appropriate lightness.

]]>Mathematics doi: 10.3390/math7030272

Authors: Łyczkowska-Hanćkowiak

The analysis presented in this paper regards the security of a present value given as an ordered fuzzy number. The present value was estimated in an imprecise manner and supplemented by the forecast of its coming changes. A discount factor of such security is an ordered fuzzy number of the orientation identical to the oriented present value that determines it. All classical methods of portfolio analysis are based on the definition of the return rate. In the case of securities with a fuzzy present value, a discount factor is a better tool for portfolio analysis than the return rate, which implies the chosen methods of management of securities should be revised and transformed to equivalent methods based on a discount factor. This would enable the use of those methods in the case of a financial instrument of the oriented fuzzy present value. This paper presents example results of the realization of such a postulate. The main aim of the paper is to generalize Sharpe&rsquo;s ratio to a case of investment recommendations management formulated for a security characterized by an oriented discount factor. A five-degree rating scale was used. The whole deliberation is illustrated by broad numerical examples.

]]>Mathematics doi: 10.3390/math7030271

Authors: Wei Gao Muhammad Aamir Zahid Iqbal Muhammad Ishaq Adnan Aslam

A graph is said to be a regular graph if all its vertices have the same degree, otherwise, it is irregular. Irregularity indices are usually used for quantitative characterization of the topological structure of non-regular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? Furthermore, evaluations of the irregularity of underline molecular graphs could be valuable for QSAR/QSPR studies, and for the expressive determines of chemical and physical properties, such as enthalpy of vaporization, toxicity, resistance, Entropy, melting and boiling points. In this paper, we think over the following four irregularity measures: the irregularity index by Albertson, &sigma; irregularity index, the total irregularity index and the variance of vertex degrees. By way of graph structural estimation and derivations, we determine these irregularity measures of the molecular graphs of different classes of dendrimers.

]]>Mathematics doi: 10.3390/math7030270

Authors: Lu-Chuan Ceng Mihai Postolache Ching-Feng Wen Yonghong Yao

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduced schemes are given under suitable control conditions.

]]>Mathematics doi: 10.3390/math7030269

Authors: Xue-Shi Li Shuxia Pan

This paper deals with the dynamics of a delayed cooperative system without quasimonotonicity. Using the contracting rectangles, we obtain a sufficient condition on the stability of the unique positive steady state of the functional differential system. When the spatial domain is whole R , the existence and nonexistence of traveling wave solutions are investigated, during which the asymptotic behavior is investigated by the contracting rectangles.

]]>Mathematics doi: 10.3390/math7030268

Authors: Wu Zhang

In this paper, some new properties of Abel Grassmann&lsquo;s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied. The following important results were proved: (1) an AG-NET-Loop is weakly commutative if, and only if, it is a commutative neutrosophic extended triplet (NETG); (2) every AG-NET-Loop is the disjoint union of its maximal subgroups. At the same time, the new notion of Abel Grassmann&rsquo;s (l, l)-Loop (AG-(l, l)-Loop), which is the Abel-Grassmann&rsquo;s groupoid with the local left identity and local left inverse, were introduced. The strong AG-(l, l)-Loops were systematically analyzed, and the following decomposition theorem was proved: every strong AG-(l, l)-Loop is the disjoint union of its maximal sub-AG-groups.

]]>Mathematics doi: 10.3390/math7030267

Authors: Yilun Shang

The super connectivity &kappa; &prime; ( G ) of a graph G is the minimum cardinality of vertices, if any, whose deletion results in a disconnected graph that contains no isolated vertex. G is said to be r-super connected if &kappa; &prime; ( G ) &ge; r . In this note, we establish some asymptotic almost sure results on r-super connectedness for classical Erdős&ndash;R&eacute;nyi random graphs as the number of nodes tends to infinity. The known results for r-connectedness are extended to r-super connectedness by pairing off vertices and estimating the probability of disconnecting the graph that one gets by identifying the two vertices of each pair.

]]>Mathematics doi: 10.3390/math7030266

Authors: Piyachat Borisut Poom Kumam Vishal Gupta Naveen Mani

A class of generalized ( &psi; , &alpha; , &beta; ) &mdash;weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution.

]]>Mathematics doi: 10.3390/math7030265

Authors: Veeresha Prakasha Baleanu

The q-homotopy analysis transform method (q-HATM) is employed to find the solution for the fractional Kolmogorov&ndash;Petrovskii&ndash;Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology.

]]>Mathematics doi: 10.3390/math7030264

Authors: H. M. Younas Muhammad Mustahsan Tareq Manzoor Nadeem Salamat S. Iqbal

In this article, Optimal Homotopy Asymptotic Method (OHAM) is used to approximate results of time-fractional order Fokker-Planck equations. In this work, 3rd order results obtained through OHAM are compared with the exact solutions. It was observed that results from OHAM have better convergence rate for time-fractional order Fokker-Planck equations. The solutions are plotted and the relative errors are tabulated.

]]>Mathematics doi: 10.3390/math7030263

Authors: Claudia Fassino Giovanni Pistone Maria Piera Rogantin

Given a multivariate complex centered Gaussian vector Z = ( Z 1 , ⋯ , Z p ) with non-singular covariance matrix &Sigma; , we derive sufficient conditions on the nullity of the complex moments and we give a closed-form expression for the non-null complex moments. We present conditions for the factorisation of the complex moments. Computational consequences of these results are discussed.

]]>Mathematics doi: 10.3390/math7030262

Authors: Beong In Yun

It is well known that feed-forward neural networks can be used for approximation to functions based on an appropriate activation function. In this paper, employing a new sigmoidal function with a parameter for an activation function, we consider a constructive feed-forward neural network approximation on a closed interval. The developed approximation method takes a simple form of a superposition of the parametric sigmoidal function. It is shown that the proposed method is very effective in approximation of discontinuous functions as well as continuous ones. For some examples, the availability of the presented method is demonstrated by comparing its numerical results with those of an existing neural network approximation method. Furthermore, the efficiency of the method in extended application to the multivariate function is also illustrated.

]]>Mathematics doi: 10.3390/math7030261

Authors: Debajit Sensarma Samar Sen Sarma

Networks have an important role in our daily lives. The effectiveness of the network decreases with the breaking down of some vertices or links. Therefore, a less vulnerable communication network is required for greater stability. Vulnerability is the measure of resistance of the network after failure of communication links. In this article, a graph has been taken for modeling a network and integrity as a measure of vulnerability. The approach is to estimate the integrity or upper bound of integrity of at least one connected graph or network constructed from the given graphic integer sequence. Experiments have been done with random graphs, complex networks and also a comparison between two parameters, namely the vertex connectivity and graph integrity as a measure of the network vulnerability have been carried out by removing vertices randomly from various complex networks. A comparison with the existing method shows that the algorithm proposed in this article provides a much better integrity measurement.

]]>Mathematics doi: 10.3390/math7030260

Authors: Anam Luqman Muhammad Akram Ahmad N. Al-Kenani

The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the q th power of the truth-membership and the q th power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter q, q &ge; 1 . In this research study, we design a new framework for handling uncertain data by means of the combinative theory of q-rung orthopair fuzzy sets and hypergraphs. We define q-rung orthopair fuzzy hypergraphs to achieve the advantages of both theories. Further, we propose certain novel concepts, including adjacent levels of q-rung orthopair fuzzy hypergraphs, ( &alpha; , &beta; ) -level hypergraphs, transversals, and minimal transversals of q-rung orthopair fuzzy hypergraphs. We present a brief comparison of our proposed model with other existing theories. Moreover, we implement some interesting concepts of q-rung orthopair fuzzy hypergraphs for decision-making to prove the effectiveness of our proposed model.

]]>Mathematics doi: 10.3390/math7030259

Authors: Chang-Jian Zhao Wing-Sum Cheung

In the paper, we give some new improvements of the Kantorovich type inequalities by using Popoviciu&rsquo;s, H&ouml;lder&rsquo;s, Bellman&rsquo;s and Minkowski&rsquo;s inequalities. These results in special case yield Hao&rsquo;s, reverse Cauchy&rsquo;s and Minkowski&rsquo;s inequalities.

]]>Mathematics doi: 10.3390/math7030258

Authors: Shimeng Shen Wenpeng Zhang

In this article, our main purpose is to introduce a new and generalized quadratic Gauss sum. By using analytic methods, the properties of classical Gauss sums, and character sums, we consider the calculating problem of its fourth power mean and give two interesting computational formulae for it.

]]>Mathematics doi: 10.3390/math7030257

Authors: Yanran Hong Dongsheng Xu Kaili Xiang Han Qiao Xiangxiang Cui Huaxiang Xian

Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method.

]]>Mathematics doi: 10.3390/math7030256

Authors: Jarunee Soontharanon Saowaluck Chasreechai Thanin Sitthiwirattham

In this article, we propose a coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line and study its existence result by using Schauder&rsquo;s fixed point theorem. An example is provided to illustrate the results.

]]>Mathematics doi: 10.3390/math7030255

Authors: Yan Tang Yeol Je Cho

In this paper, the split variational inclusion problem (SVIP) and the system of equilibrium problems (EP) are considered in Hilbert spaces. Inspired by the works of Byrne et al., L&oacute;pez et al., Moudafi and Thukur, Sobumt and Plubtieng, Sitthithakerngkiet et al. and Eslamian and Fakhri, a new self-adaptive step size algorithm is proposed to find a common element of the solution set of the problems SVIP and EP. Convergence theorems are established under suitable conditions for the algorithm and application to the common solution of the fixed point problem, and the split convex optimization problem is considered. Finally, the performances and computational experiments are presented and a comparison with the related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.

]]>Mathematics doi: 10.3390/math7030254

Authors: Yuri Luchko

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

]]>Mathematics doi: 10.3390/math7030253

Authors: Lotfi Zeghadnia Bachir Achour Jean Loup Robert

The Colebrook-White equation is often used for calculation of the friction factor in turbulent regimes; it has succeeded in attracting a great deal of attention from researchers. The Colebrook&ndash;White equation is a complex equation where the computation of the friction factor is not direct, and there is a need for trial-error methods or graphical solutions; on the other hand, several researchers have attempted to alter the Colebrook-White equation by explicit formulas with the hope of achieving zero-percent (0%) maximum deviation, among them Dejan Brkić and Pavel Praks. The goal of this paper is to discuss the results proposed by the authors in their paper:&rdquo; Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright &omega;-Function&rdquo; and to propose more accurate formulas.

]]>Mathematics doi: 10.3390/math7030252

Authors: Chiranjibe Jana Madhumangal Pal

Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft set and the union operations on sets, then applying it to B C K / B C I -algebras. Firstly, we introduce the notion of the ( &alpha; , &beta; ) -Union-Soft ( ( &alpha; , &beta; ) -US) set, with some supporting examples. Then, we discuss the soft B C K / B C I -algebras, which are called ( &alpha; , &beta; ) -US algebras, ( &alpha; , &beta; ) -US ideals, ( &alpha; , &beta; ) -US closed ideals, and ( &alpha; , &beta; ) -US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an ( &alpha; , &beta; ) -US ideal to be an ( &alpha; , &beta; ) -US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of ( &alpha; , &beta; ) -unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of ( &alpha; , &beta; ) -unions. Finally, the extension property for an ( &alpha; , &beta; ) -US commutative ideal is established.

]]>Mathematics doi: 10.3390/math7030251

Authors: Şeyda Gür Tamer Eren Hacı Mehmet Alakaş

The achievement of health organizations&rsquo; goals is critically important for profitability. For this purpose, their resources, materials, and equipment should be efficiently used in the services they provide. A hospital has sensitive and expensive equipment, and the use of its equipment and resources needs to be balanced. The utilization of these resources should be considered in its operating rooms, as it shares both expense expenditure and revenue generation. This study&rsquo;s primary aim is the effective and balanced use of equipment and resources in hospital operating rooms. In this context, datasets from a state hospital were used via the goal programming and constraint programming methods. According to the wishes of hospital managers, three scenarios were separately modeled in both methods. According to the obtained results, schedules were compared and analyzed according to the current situation. The hospital-planning approach was positively affected, and goals such as minimization cost, staff and patient satisfaction, prevention over time, and less use were achieved.

]]>Mathematics doi: 10.3390/math7030250

Authors: Umesh Balande Deepti Shrimankar

Firefly-Algorithm (FA) is an eminent nature-inspired swarm-based technique for solving numerous real world global optimization problems. This paper presents an overview of the constraint handling techniques. It also includes a hybrid algorithm, namely the Stochastic Ranking with Improved Firefly Algorithm (SRIFA) for solving constrained real-world engineering optimization problems. The stochastic ranking approach is broadly used to maintain balance between penalty and fitness functions. FA is extensively used due to its faster convergence than other metaheuristic algorithms. The basic FA is modified by incorporating opposite-based learning and random-scale factor to improve the diversity and performance. Furthermore, SRIFA uses feasibility based rules to maintain balance between penalty and objective functions. SRIFA is experimented to optimize 24 CEC 2006 standard functions and five well-known engineering constrained-optimization design problems from the literature to evaluate and analyze the effectiveness of SRIFA. It can be seen that the overall computational results of SRIFA are better than those of the basic FA. Statistical outcomes of the SRIFA are significantly superior compared to the other evolutionary algorithms and engineering design problems in its performance, quality and efficiency.

]]>Mathematics doi: 10.3390/math7030249

Authors: Bashir Ahmad Ymnah Alruwaily Ahmed Alsaedi Sotiris K. Ntouyas

We discuss the existence and uniqueness of solutions for a Caputo-type fractional order boundary value problem equipped with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions on an arbitrary domain. Modern tools of functional analysis are applied to obtain the main results. Examples are constructed for the illustration of the derived results. We also investigate different kinds of Ulam stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, and Ulam-Hyers-Rassias stability for the problem at hand.

]]>Mathematics doi: 10.3390/math7030248

Authors: Serkan Araci Gauhar Rahman Abdul Ghaffar Azeema Kottakkaran Sooppy Nisar

Several fractional calculus operators have been introduced and investigated. In this sequence, we aim to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators and Caputo-type MSM fractional differential operators of extended Mittag-Leffler function (EMLF). We also investigate the statistical distribution associated with the EMLF. Finally, we derive some of the particular cases of the main results.

]]>Mathematics doi: 10.3390/math7030247

Authors: Lara Orcos Cristina Jordán Alberto Magreñán

This study aims to implement and evaluate a methodological proposal using the hologram as a teaching medium for the learning of concepts related to areas and volumes of geometrical bodies. The study has been carried out with a sample of 78 students in the third year of secondary education from a privately-owned but state-funded school in Madrid. Thirty-five students who have been taught traditionally formed the control group, and 43 formed the experimental group in which the methodology was implemented. To evaluate its goodness, we have used the Student&rsquo;s t-test to assess the existence of significant differences between both groups. The results reported by the test show that there is a difference of 3.9 points between the scores of both groups which is significant at the level of 0.05. In addition, the user experience in the experimental group has also been evaluated to assess the students&rsquo; opinions of the hologram in the learning process. The overall results have assisted us in corroborating the efficacy of the hologram as a teaching medium.

]]>Mathematics doi: 10.3390/math7030246

Authors: Yue Liu Shuangfu Suo Guoying Meng Deyong Shang Long Bai Jianwen Shi

Springs are critical components in mining vibrating screen elastic supports. However, long-term alternating loads are likely to lead to spring failures, likely resulting in structural damages to the vibrating screen and resulting in a lower separation efficiency. Proper dynamic models provide a basis for spring failure diagnosis. In this paper, a six-degree-of-freedom theoretical rigid body model of a mining vibrating screen is proposed, and a dynamic equation is established in order to explore the dynamic characteristics. Numerical simulations, based on the Newmark-&beta; algorithm, are carried out, and the results indicate that the model proposed is suitable for revealing the dynamic characteristics of the mining vibrating screen. Meanwhile, the mining vibrating screen amplitudes change with the spring failures. Therefore, six types of spring failure are selected for simulations, and the results indicate that the spring failures lead to an amplitude change for the four elastic support points in the x, y, and z directions, where the changes depend on certain spring failures. Hence, the key to spring failure diagnosis lies in obtaining the amplitude change rules, which can reveal particular spring failures. The conclusions provide a theoretical basis for further study and experiments in spring failure diagnosis for a mining vibrating screen.

]]>Mathematics doi: 10.3390/math7030245

Authors: Enrico Feoli Paola Ganis

The use of the evenness (E(&lambda;)) of the eigenvalues of similarity matrices corresponding to different hierarchical levels of ecosystem classifications, is suggested to test correlation (or predictivity) between biological communities and environmental factors as one alternative of analysis of variance (parametric or non-parametric). The advantage over traditional methods is the fact that similarity matrices can be obtained from any kind of data (mixed and missing data) by indices such as those of Goodall and Gower. The significance of E(&lambda;) is calculated by permutation techniques. One example of application of E(&lambda;) is given by a data set describing plant community types (beech forests of the Italian peninsula).

]]>Mathematics doi: 10.3390/math7030244

Authors: Vildan Yazıcı Zahir Muradoğlu

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

]]>Mathematics doi: 10.3390/math7030243

Authors: Siqi Zhang Hui Gao Guiwu Wei Yu Wei Cun Wei

In this paper, we design the EDAS (evaluation based on distance from average solution) model with picture 2-tuple linguistic numbers (P2TLNs). First, we briefly reviewed the definition of P2TLSs and introduced the score function, accuracy function, and operational laws of P2TLNs. Then, we combined the traditional EDAS model for multiple criteria group decision making (MCGDM) with P2TLNs. Our presented model was more accurate and effective for considering the conflicting attributes. Finally, a numerical case for green supplier selection was given to illustrate this new model, and some comparisons were also conducted between the picture 2-tuple linguistic weighted averaging (P2TLWA), picture 2-tuple linguistic weighted geometric (P2TLWG) aggregation operators and EDAS model with P2TLNs, to further illustrate the advantages of the new method.

]]>Mathematics doi: 10.3390/math7030242

Authors: Juan Aguarón María Teresa Escobar José María Moreno-Jiménez Alberto Turón

The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.

]]>Mathematics doi: 10.3390/math7030241

Authors: Ebrahim Analouei Adegani Teodor Bulboacă Ahmad Motamednezhad

Using several applications of the theory of differential subordination we obtain sufficient conditions for usually normalized analytic functions to belong to certain subclasses of close-to-convex functions and close-to-convex functions of order &alpha; .

]]>Mathematics doi: 10.3390/math7030240

Authors: Saima Mushtaq Mohsan Raza Muhey U Din

In this article, we are mainly interested in finding the sufficient conditions under which Lommel functions and hyper-Bessel functions are close-to-convex with respect to the certain starlike functions. Strongly starlikeness and convexity of Lommel functions and hyper-Bessel functions are also discussed. Some applications are also the part of our investigation.

]]>Mathematics doi: 10.3390/math7030239

Authors: Zhongwei Feng Chunqiao Tan

The consumer environmental awareness promotes green manufacturing and the behavioral preferences of members become prevailing in supply chain management. To promote further development of green supply chains, a two-echelon green supply chain with a manufacturer and a retailer is considered, where the manufacturer is loss-averse and the retailer is risk-neutral. We use a Stackelberg game to investigate the impacts of loss aversion and green efficiency coefficient on retail price, wholesale price, green degree, profits of members, and profit of the green supply chain under the assumption that manufacturer&rsquo;s reference point of loss aversion is equal to the subgame perfect equilibrium partition. It is shown that, in the centralized decision-making setting (CDS), green degree and profit of the green supply chain are higher than those in the decentralized decision-making setting (DDS), while in the decentralized decision-making setting with a loss-averse manufacturer (DDS-LAM) loss aversion of manufacturer further decreases green degree and profit of green supply chain. It is also found that profits of the manufacturer and the retailer decrease with levels of loss aversion of manufacturer. Furthermore, it is also shown that wholesale price and retail price in the three decision-making settings depend on the green efficiency coefficient. Wholesale price and retail price in DDS-LAM are always the lowest (highest) if the green efficiency coefficient is sufficiently high (low). Finally, executing a greening cost-sharing contract can improve chain members&rsquo; profits if the retailer shares an appropriate proportion with the loss-averse manufacturer.

]]>Mathematics doi: 10.3390/math7030238

Authors: Kwang-Wu Chen

A preferential arrangement on [ [ n ] ] = { 1 , 2 , &hellip; , n } is a ranking of the elements of [ [ n ] ] where ties are allowed. The number of preferential arrangements on [ [ n ] ] is denoted by r n . The Delannoy number D ( m , n ) is the number of lattice paths from ( 0 , 0 ) to ( m , n ) in which only east ( 1 , 0 ) , north ( 0 , 1 ) , and northeast ( 1 , 1 ) steps are allowed. We establish a symmetric identity among the numbers r n and D ( p , q ) by means of algebraic and combinatorial methods.

]]>Mathematics doi: 10.3390/math7030237

Authors: Hongwei Tao Hengyang Wu Yixiang Chen

Measurement of software trustworthiness is an important research field in the software engineering, which is very useful for analyzing the software quality. In this paper, we propose a mathematical programming approach to allocate the trustworthy degree to each sub-attribute of some software attribute appropriately and then to make the trustworthy degree of this attribute maximize under some constraint conditions. Some sufficient or necessary conditions for analyzing this mathematical programming problem are investigated. Moreover, a polynomial allocation algorithm is given for computing the optimal solution of this mathematical programming. Finally, an example is given in order to show the significance of this work. The results obtained here are useful for improving the software quality by adjusting the trustworthy degree of each sub-attribute under the same cost.

]]>Mathematics doi: 10.3390/math7030236

Authors: Huarong Zhang Minxia Luo

In this paper, we give the &ldquo;generator&rdquo; of int-soft filters and propose the notion of t-int-soft filters on residuated lattices. We study the properties of t-int-soft filters and obtain some commonalities (e.g., the extension property, quotient characteristics, and a triple of equivalent characteristics). We also use involution-int-soft filters as an example and show some basic properties of involution-int-soft filters. Finally, we investigate the relations among t-int-soft filters and give a simple method for judging their relations.

]]>Mathematics doi: 10.3390/math7030235

Authors: Onur Alp İlhan Shakirbay G. Kasimov Shonazar Q. Otaev Haci Mehmet Baskonus

In this paper, we study the solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, and with Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes.

]]>Mathematics doi: 10.3390/math7030234

Authors: Yosef Daryanto Hui Ming Wee Gede Agus Widyadana

Nowadays, many countries have implemented carbon pricing policies. Hence, the industry adapts to this policy while striving for its main goal of maximizing financial benefits. Here, we study a single manufacturer&ndash;retailer inventory decision considering carbon emission cost and item deterioration for an imperfect production system. This study examines two models considering two cases of quality inspection. The first is when the buyer performs the quality inspection, and the second is when the quality inspection becomes the vendor&rsquo;s responsibility so that no defective products are passed to the buyer. Carbon emission costs are incorporated under a carbon tax policy, and we consider the carbon footprint from transporting and warehousing the items. The objective is to jointly optimize the delivery quantity and number of deliveries per production cycle that minimize the total cost and reduce the total carbon emissions. This study provides solution procedures to solve the models, as well as two numerical examples.

]]>Mathematics doi: 10.3390/math7030233

Authors: Shahida Bashir Medhit Fatima Muhammad Shabir

Our main objective is to introduce the innovative concept of ( &alpha; , &beta; ) -bipolar fuzzy ideals and ( &alpha; , &beta; ) -bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set h = ( S ; h n , h p ) in an ordered ternary semigroup S is the ( &isin; , &isin; &or; q ) -bipolar fuzzy generalized bi-ideal of S , it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the ( &isin; , &isin; &or; q ) -bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the ( &isin; , &isin; &or; q ) -bipolar fuzzy generalized bi-ideals.

]]>Mathematics doi: 10.3390/math7030232

Authors: Roberto Ugolotti Laura Sani Stefano Cagnoni

Properly configuring Evolutionary Algorithms (EAs) is a challenging task made difficult by many different details that affect EAs&rsquo; performance, such as the properties of the fitness function, time and computational constraints, and many others. EAs&rsquo; meta-optimization methods, in which a metaheuristic is used to tune the parameters of another (lower-level) metaheuristic which optimizes a given target function, most often rely on the optimization of a single property of the lower-level method. In this paper, we show that by using a multi-objective genetic algorithm to tune an EA, it is possible not only to find good parameter sets considering more objectives at the same time but also to derive generalizable results which can provide guidelines for designing EA-based applications. In particular, we present a general framework for multi-objective meta-optimization, to show that &ldquo;going multi-objective&rdquo; allows one to generate configurations that, besides optimally fitting an EA to a given problem, also perform well on previously unseen ones.

]]>Mathematics doi: 10.3390/math7030231

Authors: Nadeem Salamat Muhammad Mustahsan Malik M. Saad Missen

The first-order fuzzy differential equation has two possible solutions depending on the definition of differentiability. The definition of differentiability changes as the product of the function and its first derivative changes its sign. This switching of the derivative&rsquo;s definition is handled with the application of min, max operators. In this paper, a numerical technique for solving fuzzy initial value problems is extended to solving higher-order fuzzy differential equations. Fuzzy Taylor series is used to develop the fuzzy differential transformation method for solving this problem. This leads to a single solution for higher-order differential equations.

]]>Mathematics doi: 10.3390/math7030230

Authors: Michael Gr. Voskoglou

The assessment of a system&rsquo;s performance is a very important task, enabling its designer/user to correct its weaknesses and make it more effective. Frequently, in practice, a system&rsquo;s assessment is performed under fuzzy conditions, e.g., using qualitative instead of numerical grades, incomplete information about its function, etc. The present review summarizes the author&rsquo;s research on building assessment models for use in a fuzzy environment. Those models include the measurement of a fuzzy system&rsquo;s uncertainty, the application of the center of gravity defuzzification technique, the use of triangular fuzzy or grey numbers as assessment tools, and the application of the fuzzy relation equations. Examples are provided of assessing human (students and athletes) and machine (case-based reasoning systems in computers) capacities, illustrating our results. The outcomes of those examples are compared to the outcomes of the traditional methods of calculating the mean value of scores assigned to the system&rsquo;s components (system&rsquo;s mean performance) and of the grade point average index (quality performance) and useful conclusions are obtained concerning their advantages and disadvantages. The present review forms a new basis for further research on systems&rsquo; assessment in a fuzzy environment.

]]>Mathematics doi: 10.3390/math7030229

Authors: Nitu Kumari Nishith Mohan

Diffusion has long been known to induce pattern formation in predator prey systems. For certain prey-predator interaction systems, self diffusion conditions ceases to induce patterns, i.e., a non-constant positive solution does not exist, as seen from the literature. We investigate the effect of cross diffusion on the pattern formation in a tritrophic food chain model. In the formulated model, the prey interacts with the mid level predator in accordance with Holling Type II functional response and the mid and top level predator interact via Crowley-Martin functional response. We prove that the stationary uniform solution of the system is stable in the presence of diffusion when cross diffusion is absent. However, this solution is unstable in the presence of both self diffusion and cross diffusion. Using a priori analysis, we show the existence of a inhomogeneous steady state. We prove that no non-constant positive solution exists in the presence of diffusion under certain conditions, i.e., no pattern formation occurs. However, pattern formation is induced by cross diffusion because of the existence of non-constant positive solution, which is proven analytically as well as numerically. We performed extensive numerical simulations to understand Turing pattern formation for different values of self and cross diffusivity coefficients of the top level predator to validate our results. We obtained a wide range of Turing patterns induced by cross diffusion in the top population, including floral, labyrinth, hot spots, pentagonal and hexagonal Turing patterns.

]]>Mathematics doi: 10.3390/math7030228

Authors: Lingqiang Li

In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer&rsquo;s diagonal condition, the other approach extends the G&auml;hler&rsquo;s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures.

]]>Mathematics doi: 10.3390/math7030227

Authors: Srikanth Raghavendran Veena Narayanan

This paper presents a review of the Prouhet Tarry Escott problem. The solutions of the Prouhet Tarry Escott problem are significant because of its numerous applications. Available literature about the present topic has been critically examined. The ideal and non-ideal symmetric solutions of the problem are pointed out. The present work also aims to familiarize one with the different existing methods of obtaining the solutions of the Tarry Escott problem. Difficulties and possible future research directions are addressed. This review contributes a clear picture of the Prouhet Tarry Escott problem.

]]>Mathematics doi: 10.3390/math7030226

Authors: Wachirapong Jirakitpuwapat Poom Kumam Yeol Je Cho Kanokwan Sitthithakerngkiet

In 2014, Cui and Wang constructed an algorithm for demicontractive operators and proved some weak convergence theorems of their proposed algorithm to show the existence of solutions for the split common fixed point problem without using the operator norm. By Cui and Wang&rsquo;s motivation, in 2015, Boikanyo constructed also a new algorithm for demicontractive operators and obtained some strong convergence theorems for this problem without using the operator norm. In this paper, we consider a viscosity iterative algorithm in Boikanyo&rsquo;s algorithm to approximate to a solution of this problem and prove some strong convergence theorems of our proposed algorithm to a solution of this problem. Finally, we apply our main results to some applications, signal processing and others and compare our algorithm with five algorithms such as Cui and Wang&rsquo;s algorithm, Boikanyo&rsquo;s algorithm, forward-backward splitting algorithm and the fast iterative shrinkage-thresholding algorithm (FISTA).

]]>Mathematics doi: 10.3390/math7030225

Authors: Cristina Amorós Ioannis K. Argyros Ruben González Á. Alberto Magreñán Lara Orcos Íñigo Sarría

The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a center-Lipschitz condition where the ball radii are greater than previous studies. We investigate the dynamics of the method. To validate the theoretical results obtained, a real-world application related to chemistry is provided.

]]>Mathematics doi: 10.3390/math7030224

Authors: Harendra Singh Rajesh K. Pandey Hari Mohan Srivastava

The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method. The Ritz method has allowed many researchers to solve different forms of fractional variational problems in recent years. The NLFVP is solved by applying the Ritz method using different orthogonal polynomials. Further, the approximate solution is obtained by solving a system of nonlinear algebraic equations. Error and convergence analysis of the discussed method is also provided. Numerical simulations are performed on illustrative examples to test the accuracy and applicability of the method. For comparison purposes, different polynomials such as 1) Shifted Legendre polynomials, 2) Shifted Chebyshev polynomials of the first kind, 3) Shifted Chebyshev polynomials of the third kind, 4) Shifted Chebyshev polynomials of the fourth kind, and 5) Gegenbauer polynomials are considered to perform the numerical investigations in the test examples. Further, the obtained results are presented in the form of tables and figures. The numerical results are also compared with some known methods from the literature.

]]>Mathematics doi: 10.3390/math7030223

Authors: Kamal Shah Poom Kumam Inam Ullah

This manuscript is devoted to establishing existence theory of solutions to a nonlinear coupled system of fractional order differential equations (FODEs) under integral boundary conditions (IBCs). For uniqueness and existence we use the Perov-type fixed point theorem. Further, to investigate multiplicity results of the concerned problem, we utilize Krasnoselskii&rsquo;s fixed-point theorems of cone type and its various forms. Stability analysis is an important aspect of existence theory as well as required during numerical simulations and optimization of FODEs. Therefore by using techniques of functional analysis, we establish conditions for Hyers-Ulam (HU) stability results for the solution of the proposed problem. The whole analysis is justified by providing suitable examples to illustrate our established results.

]]>Mathematics doi: 10.3390/math7030222

Authors: Fuyu Yuan Chenxi Li Xin Gao Minghao Yin Yiyuan Wang

The minimum total dominating set (MTDS) problem is a variant of the classical dominating set problem. In this paper, we propose a hybrid evolutionary algorithm, which combines local search and genetic algorithm to solve MTDS. Firstly, a novel scoring heuristic is implemented to increase the searching effectiveness and thus get better solutions. Specially, a population including several initial solutions is created first to make the algorithm search more regions and then the local search phase further improves the initial solutions by swapping vertices effectively. Secondly, the repair-based crossover operation creates new solutions to make the algorithm search more feasible regions. Experiments on the classical benchmark DIMACS are carried out to test the performance of the proposed algorithm, and the experimental results show that our algorithm performs much better than its competitor on all instances.

]]>Mathematics doi: 10.3390/math7030221

Authors: Lei Gao Zhen-yun Jiang Fan Min

First-arrival picking is a critical step in seismic data processing. This paper proposes the first-arrival picking through sliding windows and fuzzy c-means (FPSF) algorithm with two stages. The first stage detects a range using sliding windows on vertical and horizontal directions. The second stage obtains the first-arrival travel times from the range using fuzzy c-means coupled with particle swarm optimization. Results on both noisy and preprocessed field data show that the FPSF algorithm is more accurate than classical methods.

]]>Mathematics doi: 10.3390/math7030220

Authors: Fahd Almutairi S.M. Khaled Abdelhalim Ebaid

The influence of second-order velocity slip on the MHD flow of nanofluid in a porous medium under the effects of homogeneous-heterogeneous reactions has been analyzed. The governing flow equation is exactly solved and compared with those in the literature for the skin friction coefficient in the absence of the second slip, where great differences have been observed. In addition, the effects of the permanent parameters on the skin friction coefficient, the velocity, and the concentration have been discussed in the presence of the second slip. As an important result, the behavior of the skin friction coefficient at various values of the porosity and volume fraction is changed from increasing (in the absence of the second slip) to decreasing (in the presence of the second slip), which confirms the importance of the second slip in modeling the boundary layer flow of nanofluids. In addition, five kinds of nanofluids have been investigated for the velocity profiles and it is found that the Ag-water nanofluid is the lowest. For only the heterogeneous reaction, the concentration equation has been exactly solved, while the numerical solution is applied in the general case. Accordingly, a reduction in the concentration occurs with the strengthening of the heterogenous reaction and also with the increase in the Schmidt parameter. Moreover, the Ag-water nanofluid is of lower concentration than the Cu-water nanofluid. This is also true for the general case, when both of the homogenous and heterogenous reactions take place.

]]>Mathematics doi: 10.3390/math7030219

Authors: Nabiullah Khan Talha Usman Kottakkaran Sooppy Nisar

A variety of polynomials, their extensions, and variants, have been extensively investigated, mainly due to their potential applications in diverse research areas. Motivated by their importance and potential for applications in a variety of research fields, numerous polynomials and their extensions have recently been introduced and investigated. In this paper, we introduce generalized Laguerre poly-Genocchi polynomials and investigate some of their properties and identities, which were found to extend some known results. Among them, an implicit summation formula and addition-symmetry identities for generalized Laguerre poly-Genocchi polynomials are derived. The results presented here, being very general, are pointed out to reduce to yield formulas and identities for relatively simple polynomials and numbers.

]]>Mathematics doi: 10.3390/math7030218

Authors: Lu-Chuan Ceng Xiaoye Yang

This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.

]]>Mathematics doi: 10.3390/math7030217

Authors: Yuhong Huo Jia-Bao Liu

The present paper attempts to investigate the problem of robust H &infin; control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H &infin; norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H &infin; problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.

]]>Mathematics doi: 10.3390/math7030216

Authors: Imtiaz Ahmad Muhammad Ahsan Zaheer-ud Din Ahmad Masood Poom Kumam

In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation on regular and irregular domains.

]]>Mathematics doi: 10.3390/math7030215

Authors: Ming Tian Meng-Ying Tong

In this paper, based on the Yamada iteration, we propose an iteration algorithm to find a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping. We obtain a weak convergence theorem in Hilbert space. In particular, the set of zero points of an inverse strongly-monotone mapping can be transformed into the solution set of the variational inequality problem. Further, based on this result, we also obtain some new weak convergence theorems which are used to solve the equilibrium problem and the split feasibility problem.

]]>Mathematics doi: 10.3390/math7030214

Authors: Anupam Das Bipan Hazarika Poom Kumam

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example.

]]>Mathematics doi: 10.3390/math7020213

Authors: Herbert Dueñas Ruiz Francisco Marcellán Alejandro Molano

In this paper, we study a classification of symmetric ( 1 , 1 ) -coherent pairs by using a symmetrization process. In particular, the positive-definite case is carefully described.

]]>Mathematics doi: 10.3390/math7020212

Authors: Chunji Li Cheon Seoung Ryoo

Let 1 &lt; a &lt; b &lt; c &lt; d and &alpha; ^ 5 : = 1 , a , b , c , d &and; be a weighted sequence that is recursively generated by five weights 1 , a , b , c , d . In this paper, we give sufficient conditions for the positive quadratic hyponormalities of W &alpha; x and W &alpha; y , x , with &alpha; x : x , &alpha; ^ 5 and &alpha; y , x : y , x , &alpha; ^ 5 .

]]>Mathematics doi: 10.3390/math7020211

Authors: Saufianim Jana Aksah Zarina Bibi Ibrahim Iskandar Shah Mohd Zawawi

In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal diagonal elements which will results in only one evaluation of the Jacobian and one LU decomposition for each time step. For the SDIBBDF method to have practical significance in solving stiff problems, its stability region must at least cover almost the whole of the negative half plane. Step size restriction of the proposed method have to be considered in order to ensure stability of the method in computing numerical results. Efficiency of the SDIBBDF method in solving stiff ODEs is justified when it managed to outperform the existing methods for both accuracy and computational time.

]]>Mathematics doi: 10.3390/math7020210

Authors: Ansheng Ye Fang Miao Zehui Shao Jia-Bao Liu Janez Žerovnik Polona Repolusk

Let &gamma; ( D ) denote the domination number of a digraph D and let C m □ C n denote the Cartesian product of C m and C n , the directed cycles of length n &ge; m &ge; 3 . Liu et al. obtained the exact values of &gamma; ( C m □ C n ) for m up to 6 [Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36&ndash;39]. Shao et al. determined the exact values of &gamma; ( C m □ C n ) for m = 6 , 7 [On the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 619695]. Mollard obtained the exact values of &gamma; ( C m □ C n ) for m = 3 k + 2 [M. Mollard, On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths, Discuss. Math. Graph Theory 33(2) (2013) 387&ndash;394.]. In this paper, we extend the current known results on C m □ C n with m up to 21. Moreover, the exact values of &gamma; ( C n □ C n ) with n up to 31 are determined.

]]>Mathematics doi: 10.3390/math7020209

Authors: Jia Wei He Yong Liang Bashir Ahmad Yong Zhou

This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order &alpha; &isin; ( 1 , 2 ) . The main tools of our study include the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed-point theorem. As an application, we apply the obtained results to a control problem.

]]>Mathematics doi: 10.3390/math7020208

Authors: Dariusz Banaś Jerzy Michnik

When analyzing the possibility of supporting the decision-making process, one should take into account the essential properties of economic entities (the system and its objects). As a result, the development of an effective business model ought to be based on rationality and the characteristics of the system being modeled. Such an approach implies the use of an appropriate analysis and modeling method. Since the majority of relationships in the model are described using the experts&rsquo; tacit knowledge, methods known as &ldquo;soft&rdquo; are more suitable than &ldquo;hard&rdquo; in those situations. Fuzzy cognitive mappings (FCM) are therefore commonly used as a technique for participatory modeling of the system, where stakeholders can convey their knowledge to the model of the system in question. In this study, we introduce a novel approach: the extended weighted influence nonlinear gauge system (WINGS), which may equally well be applied to the decision problems of this type. Appraisal of high-value and long-term offers in the sector of the telecommunication supplier industry serves as a real-world case study for testing the new method. A comparison with FCM provides a deeper understanding of the similarities and differences of the two approaches.

]]>Mathematics doi: 10.3390/math7020207

Authors: Ioannis K. Argyros Stepan Shakhno

We present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipschitz-type condition and the notion of the restricted convergence region. These modifications of earlier conditions result in a tighter convergence analysis and more precise information on the location of the solution. These advantages are obtained under the same computational effort. Using illuminating examples, we further justify the superiority of our new results over earlier ones.

]]>Mathematics doi: 10.3390/math7020206

Authors: K.S. Nisar D.L. Suthar M. Bohra S.D. Purohit

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo&rsquo;s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava&rsquo;s polynomials and the generalized Mathieu series, containing the factor x &lambda; ( x k + c k ) &minus; &rho; in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann&ndash;Liouville and Erd&eacute;lyi&ndash;Kober fractional integral operators are also considered.

]]>Mathematics doi: 10.3390/math7020205

Authors: Erhan Güler Ömer Kişi

We consider Ulisse Dini-type helicoidal hypersurfaces with timelike axis in Minkowski 4-space E 1 4 . Calculating the Gaussian and the mean curvatures of the hypersurfaces, we demonstrate some special symmetries for the curvatures when they are flat and minimal.

]]>Mathematics doi: 10.3390/math7020204

Authors: Fevzi Yaşar Kuddusi Kayaduman

Matrix F^ derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces lp(F) and l&infin;(F); (1 &le; p &lt; &infin;) were examined. Then, Başarır et al. (2015) defined the spaces c0(F) and c(F) and Candan (2015) examined the spaces c(F(r,s)) and c0(F(r,s)). Later, Yaşar and Kayaduman (2018) defined and studied the spaces cs(F(s,r)) and bs(F(s,r)). In this study, we built the spaces cs(F) and bs(F). They are the domain of the matrix F on cs and bs, where F is a triangular matrix defined by Fibonacci Numbers. Some topological and algebraic properties, isomorphism, inclusion relations and norms, which are defined over them are examined. It is proven that cs(F) and bs(F) are Banach spaces. It is determined that they have the &gamma;, &beta;, &alpha; -duals. In addition, the Schauder base of the space cs(F) are calculated. Finally, a number of matrix transformations of these spaces are found.

]]>Mathematics doi: 10.3390/math7020203

Authors: Ying Wang Xinling Wu Nasrin Dehgardi Jafar Amjadi Rana Khoeilar Jia-Bao Liu

Let k be a positive integer, and set [ k ] : = { 1 , 2 , &hellip; , k } . For a graph G, a k-rainbow dominating function (or kRDF) of G is a mapping f : V ( G ) &rarr; 2 [ k ] in such a way that, for any vertex v &isin; V ( G ) with the empty set under f, the condition ⋃ u &isin; N G ( v ) f ( u ) = [ k ] always holds, where N G ( v ) is the open neighborhood of v. The weight of kRDF f of G is the summation of values of all vertices under f. The k-rainbow domination number of G, denoted by &gamma; r k ( G ) , is the minimum weight of a kRDF of G. In this paper, we obtain the k-rainbow domination number of grid P 3 □ P n for k &isin; { 2 , 3 , 4 } .

]]>Mathematics doi: 10.3390/math7020202

Authors: Jia-Bao Liu Mobeen Munir Raheel Farooki Muhammad Imran Qureshi Quratulien Muneer

Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In particular, we establish general closed formulas for Stanley depth of quotient of edge ideals associated with the m t h -power of a wheel graph, for m &ge; 3 , gear graphs and anti-web gear graphs.

]]>Mathematics doi: 10.3390/math7020201

Authors: Jian Lu Shu-Bo Chen Jia-Bao Liu Xiang-Feng Pan Ying-Jie Ji

The Resistance-Harary index of a connected graph G is defined as R H ( G ) = &sum; { u , v } &sube; V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G. A graph G is called a unicyclic graph if it contains exactly one cycle and a fully loaded unicyclic graph is a unicyclic graph that no vertex with degree less than three in its unique cycle. Let U ( n ) and U ( n ) be the set of unicyclic graphs and fully loaded unicyclic graphs of order n, respectively. In this paper, we determine the graphs of U ( n ) with second-largest Resistance-Harary index and determine the graphs of U ( n ) with largest Resistance-Harary index.

]]>Mathematics doi: 10.3390/math7020200

Authors: Hong Li Jun Cheng Hou-Biao Li Shou-Ming Zhong

In this paper, stability analysis of a fractional-order linear system described by the Caputo&ndash;Fabrizio (CF) derivative is studied. In order to solve the problem, character equation of the system is defined at first by using the Laplace transform. Then, some simple necessary and sufficient stability conditions and sufficient stability conditions are given which will be the basis of doing research of a fractional-order system with a CF derivative. In addition, the difference of stability domain between two linear systems described by two different fractional derivatives is also studied. Our results permit researchers to check the stability by judging the locations in the complex plane of the dynamic matrix eigenvalues of the state space.

]]>Mathematics doi: 10.3390/math7020199

Authors: Ilwoo Cho Palle Jorgensen

In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , &tau; 0 ) induced by measurable functions on p-adic number fields Q p over primes p . In particular, we are interested in the cases where such free-probabilistic information is affected by primes in given closed intervals of the set R of real numbers by defining suitable &ldquo;truncated&rdquo; linear functionals on LS .

]]>Mathematics doi: 10.3390/math7020198

Authors: Janak Raj Sharma Ioannis K. Argyros Sunil Kumar

We generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study their local convergence. In a previous study, the Taylor expansion of higher order derivatives is employed which may not exist or may be very expensive to compute. However, the hypotheses of the present study are based on the first Fr&eacute;chet-derivative only, thereby the application of methods is expanded. New analysis also provides the radius of convergence, error bounds and estimates on the uniqueness of the solution. Such estimates are not provided in the approaches that use Taylor expansions of derivatives of higher order. Moreover, the order of convergence for the methods is verified by using computational order of convergence or approximate computational order of convergence without using higher order derivatives. Numerical examples are provided to verify the theoretical results and to show the good convergence behavior.

]]>Mathematics doi: 10.3390/math7020197

Authors: Stephen Luecking

The sculptor adapts the geometry of spline surfaces commonly used in 3D modeling programs in order to translate some of the topological nature of these virtual surfaces into his sculpture. He realizes the patchwise geometry of such surfaces by gluing square modules of neoprene rubber edge to edge to define the surface which he then torques and bends into sculptures. While limited by the nature of actual materials, the finished sculptures successfully incorporate the expressive tension and flow of forms sought by the sculptor. He presents images of finished works and provides an analysis of the emotive values of a select sculpture.

]]>Mathematics doi: 10.3390/math7020196

Authors: Songting Yin

We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfying the mean value formula must be a harmonic function, then the Minkowski space is Euclidean.

]]>Mathematics doi: 10.3390/math7020195

Authors: Selçuk BAŞ Talat KÖRPINAR

In this paper, a new modified roller coaster surface according to a modified orthogonal frame is investigated in Euclidean 3-space. In this method, a new modified roller coaster surface is modeled. Both the Gaussian curvature and mean curvature of roller coaster surfaces are investigated. Subsequently, we obtain several characterizations in Euclidean 3-space.

]]>Mathematics doi: 10.3390/math7020194

Authors: Eskandar Ameer Muhammad Arshad Dong Yun Shin Sungsik Yun

The purpose of this paper is to introduce the notion of generalized multivalued &psi; , ϕ-type contractions and generalized multivalued &psi; , ϕ-type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. Our results are extension and improvement of the Suzuki and Nadler contraction theorems, Jleli and Samet, Piri and Kumam, Mizoguchi and Takahashi, and Liu et al. fixed point theorems. We provide an example for supporting our new results. Moreover, an application of our main result to the existence of solution of system of functional equations is also presented.

]]>Mathematics doi: 10.3390/math7020193

Authors: Pooja Dhawan Jatinderdeep Kaur

In the present work, the concept of F -generalized contractive type mappings by using C -class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results improve and generalize various results existing in the literature. The effectiveness of the obtained results is verified with the help of some comparative examples.

]]>Mathematics doi: 10.3390/math7020192

Authors: Emir Hüseyin Özder Evrencan Özcan Tamer Eren

Shift scheduling problems (SSPs) are advanced NP-hard problems which are generally evaluated with integer programming. This study presents an applicable shift schedule of workers in a large-scale natural gas combined cycle power plant (NGCCPP), which realize 35.17% of the total electricity generation in Turkey alone, as at of the end of 2018. This study included 80 workers who worked three shifts in the selected NGCCPP for 30 days. The proposed scheduling model was solved according to the skills of the workers, and there were nine criteria by which the workers were evaluated for their abilities. Analytic network process (ANP) is a method used for obtaining the weights of workers&rsquo; abilities in a particular skill. These weights are used in the proposed scheduling model as concepts in goal programming (GP). The SSP&ndash;ANP&ndash;GP model sees employees&rsquo; everyday preferences as their main feature, bringing high-performance to the highest level, and bringing an objective functionality, and lowering the lowest success of daily choice. At the same time, the model introduced large-scale and soft constraints that reflect the nature of the shift requirements of this program by specifying the most appropriate program. The required data were obtained from the selected NGCCPP and the model solutions were approved by the plant experts. The SSP&ndash;ANP&ndash;GP model was resolved at a reasonable time. Monthly acquisition time was significantly reduced, and the satisfaction of the employees was significantly increased by using the obtained program. When past studies were examined, it was determined that a shift scheduling problem of this size in the energy sector had not previously been studied.

]]>Mathematics doi: 10.3390/math7020191

Authors: Shouzhen Zeng Shahzaib Asharf Muhammad Arif Saleem Abdullah

A divergence measure plays a crucial part in discriminating two probability distributions and drawing inferences constructed on such discrimination. The intention of this study is to propose such a divergence measure based on Jensen inequality and exponential entropy in the settings of probability theory. Further, the idea has been generalized to fuzzy sets to familiarize a novel picture fuzzy divergence measure. Besides proposing the validity, some of its key properties are also deliberated. Finally, two illustrative examples are solved based on the proposed picture fuzzy divergence measure which shows the expediency and effectiveness of the proposed approach.

]]>Mathematics doi: 10.3390/math7020190

Authors: Lakshman Mahto Syed Abbas Mokhtar Hafayed Hari M. Srivastava

In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order &alpha; &isin; ( 0 , 1 ) . Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover, we establish the approximate controllability of the problem by applying a unique continuation property via internal control which acts on a sub-domain.

]]>Mathematics doi: 10.3390/math7020189

Authors: Mehran Ullah Biswajit Sarkar Iqra Asghar

This study develops an integrated production-inventory model for a two-echelon supply chain network with controllable probabilistic deterioration. The investment in preservation technology is considered a decision variable to control the deteriorated quantity of an integrated system. The objective of the study is to optimize preservation investment, the number of shipments and shipment quantity, so that the total cost per unit of time of the supply chain is minimized. The study proposes a solution method, and the results show that investment in preservation technology reduces the total supply chain cost by 13%. Additionally, preservation increases the lot size, thus increasing the production cycle length, which reduces the ordering cost of the system. Furthermore, this study shows that preservation leads to a reduction of solid waste from deteriorated products. Total deteriorated products reduced to 8 units from 235 units, hence, preservation generates positive environmental benefits along with economic impacts. The robustness of the proposed model is illustrated with a numerical example, sensitivity analysis, and graphical representations. Moreover, comparative study and managerial insights are given to extract significant insights from the model.

]]>Mathematics doi: 10.3390/math7020188

Authors: Sezgin Sucu Serhan Varma

In this contribution, we define a new operator sequence which contains analytic functions. Using approximation techniques found by Korovkin, some results are derived. Moreover, a generalization of this operator sequence called Kantorovich type generalization is introduced.

]]>Mathematics doi: 10.3390/math7020187

Authors: Lu-Chuan Ceng Qing Yuan

In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions.

]]>Mathematics doi: 10.3390/math7020186

Authors: Shuman Meng Yujun Cui

In this article, by using the monotone iterative technique coupled with the method of upper and lower solution, we obtain the existence of extremal iteration solutions to conformable fractional differential equations involving Riemann-Stieltjes integral boundary conditions. At the same time, the comparison principle of solving such problems is investigated. Finally, an example is given to illustrate our main results. It should be noted that the conformal fractional derivative is essentially a modified version of the first-order derivative. Our results show that such known results can be translated and stated in the setting of the so-called conformal fractional derivative.

]]>Mathematics doi: 10.3390/math7020185

Authors: Atiq-ur Rehman Mustanser Hussain Adeel Farooq Muhammad Akram

In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process.

]]>Mathematics doi: 10.3390/math7020184

Authors: Penghong Wang Fei Xue Hangjuan Li Zhihua Cui Liping Xie Jinjun Chen

Locating node technology, as the most fundamental component of wireless sensor networks (WSNs) and internet of things (IoT), is a pivotal problem. Distance vector-hop technique (DV-Hop) is frequently used for location node estimation in WSN, but it has a poor estimation precision. In this paper, a multi-objective DV-Hop localization algorithm based on NSGA-II is designed, called NSGA-II-DV-Hop. In NSGA-II-DV-Hop, a new multi-objective model is constructed, and an enhanced constraint strategy is adopted based on all beacon nodes to enhance the DV-Hop positioning estimation precision, and test four new complex network topologies. Simulation results demonstrate that the precision performance of NSGA-II-DV-Hop significantly outperforms than other algorithms, such as CS-DV-Hop, OCS-LC-DV-Hop, and MODE-DV-Hop algorithms.

]]>Mathematics doi: 10.3390/math7020183

Authors: Seth Kermausuor Eze R. Nwaeze Ana M. Tameru

In this paper, we introduced some new integral inequalities of the Hermite&ndash;Hadamard type for functions whose second derivatives in absolute values at certain powers are strongly &eta; -convex functions via the Katugampola fractional integrals.

]]>Mathematics doi: 10.3390/math7020182

Authors: Melih Yucesan Suleyman Mete Faruk Serin Erkan Celik Muhammet Gul

Supplier selection is one of the most important multi-criteria decision-making (MCDM) problems for decision-makers in the competitive market. Today&rsquo;s organizations are seeking new ways to reduce the negative effects they have on the environment and to achieve a greener system. Currently, the concept of green supplier selection has gained great importance for its ability to incorporate environmental or green criteria into classical supplier selection practices. Therefore, in this study, a multi-phase MCDM model based on the best-worst method (BWM) and the interval type-2 fuzzy technique for order preference by similarity to ideal solution (IT2F TOPSIS) is proposed. A case study in a plastic injection molding facility in Turkey was carried out to show the applicability of the proposed integrated methodology. The paper offers insights into decision-making, methodology, and managerial implications. Results of the case study are examined and suggestions for future research are provided.

]]>Mathematics doi: 10.3390/math7020181

Authors: Hari M. Srivastava Qazi Zahoor Ahmad Nasir Khan Nazar Khan Bilal Khan

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk U . In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q-starlike functions. We also highlight some known consequences of our main results.

]]>Mathematics doi: 10.3390/math7020180

Authors: Clemente Cesarano Paolo Emilio Ricci

The third and fourth pseudo-Chebyshev irrational functions of half-integer degree are defined. Their definitions are connected to those of the first- and second-kind pseudo-Chebyshev functions. Their orthogonality properties are shown, with respect to classical weights.

]]>Mathematics doi: 10.3390/math7020179

Authors: Yu-Cheng Wang Tin-Chih Toly Chen

Existing fuzzy analytic hierarchy process (FAHP) methods usually aggregate the fuzzy pairwise comparison results produced by multiple decision-makers (DMs) rather than the fuzzy weights estimations. This is problematic because fuzzy pairwise comparison results are subject to uncertainty and lack consensus. To address this problem, a partial-consensus posterior-aggregation FAHP (PCPA-FAHP) approach is proposed in this study. The PCPA-FAHP approach seeks a partial consensus among most DMs instead of an overall consensus among all DMs, thereby increasing the possibility of reaching a consensus. Subsequently, the aggregation result is defuzzified using the prevalent center-of-gravity method. The PCPA-FAHP approach was applied to a supplier selection problem to validate its effectiveness. According to the experimental results, the PCPA-FAHP approach not only successfully found out the partial consensus among the DMs, but also shrunk the widths of the estimated fuzzy weights to enhance the precision of the FAHP analysis.

]]>Mathematics doi: 10.3390/math7020178

Authors: Vasily E. Tarasov Valentina V. Tarasova

A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral and integro-differential operators with the confluent hypergeometric Kummer function in the kernel. These operators allow us to propose an economic accelerator, in which the memory and lag are taken into account. The fractional differential equation, which describes the dynamics of national income in this generalized model, is suggested. The solution of this fractional differential equation is obtained in the form of series of the confluent hypergeometric Kummer functions. The asymptotic behavior of national income, which is described by this solution, is considered.

]]>Mathematics doi: 10.3390/math7020177

Authors: Alexander Sipin

New Monte Carlo algorithms for solving the Cauchy problem for the second order parabolic equation with smooth coefficients are considered. Unbiased estimators for the solutions of this problem are constructed.

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