Search results for: analytic functions

Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Hadia Rafi

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To make any decision in any work/task/project it involves many factors that needed to be looked. The analytic Hierarchy process (AHP) is based on the judgments of experts to derive the required results this technique measures the intangibles and then by the help of judgment and software analysis the comparisons are made which shows how much a certain element/unit leads another. AHP includes how an inconsistent judgment should be made consistent and how the judgment should be improved when possible. The Priority scales are obtained by multiplying them with the priority of their parent node and after that they are added.

Keywords: AHP, priority scales, parent node, software analysis

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Hyeondal Jeong, Yoonjung Baek

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This study was carried out a meta-analysis on team workforce diversity and team outcomes. Using data from 3,534 teams in 13 studies conducted in team-level settings, we examined whether contextual factors at research local and team-size, influenced team outcomes of team workforce diversity. This meta-analytic examines the team workforce diversity and team outcomes. 13 studies included in the analysis are studies published from 2009 to 2014. We first examined the correlations between all types of diversity and team performance, significant result (Fisher`s Z = .112, k = 32, 95% CI = 0.039 to 0.183). After the analysis was conducted to moderating effect of research local (Republic of Korea=1, other area=0) and team-size. As a result, research local moderating effect had a significant but team-size was not supported. Based on the above findings suggest implications and future research directions.

Keywords: team workforce diversity, team outcomes, meta- analytic, cross-cultural research

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Authors: Priestly Malambo, Sonja Van Putten, Hanlie Botha, Gerrit Stols

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The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully.

Keywords: secondary school, mathematical reasoning, student-teachers, functions

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Narissara Nuthammachot, Dimitris Stratoulias

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Fire is one of the main causes of environmental and ecosystem change. Therefore, it is a challenging task for fire risk assessment fire potential mapping. The study area is Hua Sai district, Nakorn Sri Thammarat province, which covers in a part of peat swamp forest areas. 55 fire points in peat swamp areas were reported from 2012 to 2016. Analytic Hierarchy Process (AHP) and Geographic Information System (GIS) methods were selected for this study. The risk fire area map was arranged on these factors; elevation, slope, aspect, precipitation, distance from the river, distance from town, and land use. The results showed that the predicted fire risk areas are found to be in appreciable reliability with past fire events. The fire risk map can be used for the planning and management of fire areas in the future.

Keywords: analytic hierarchy process, fire risk assessment, geographic information system, peat swamp forest

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Authors: H. Erbiyik, A. Bal, M. Sirakaya, Ö. Yesildal, E. Yolcu

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The emergence of many environmental issues began with the Industrial Revolution. The depletion of natural resources and emerging environmental challenges over time requires enterprises and managers to take into consideration environmental factors while managing business. If we take notice of these causes; the design and implementation of environmentally friendly green purchasing, production and waste management systems become very important at green logistics systems. Companies can adopt green supply chain with the awareness of these facts. The concept of green supply chain constitutes from green purchasing, green production, green logistics, waste management and reverse logistics. In this study, we wanted to identify the concept of green supply chain and why green supply chain should be applied. In the practice part of the study an analytic hierarchy process (AHP) study is conducted on an aluminum production company to evaluate suppliers.

Keywords: aluminum sector, analytic hierarchy process, decision making, green logistics

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Haoshu Li, Shaolong Wan

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The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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Authors: Kassim A. Jassim

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In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α).

Keywords: meromorphic multivalent function, Ruscheweyh derivative, hadamard product

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Authors: Baghdasaryan Marinka

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The particular significance of comprehensive estimation of the increase in the operation efficiency of the mill motor electromechanical system, providing the main technological process for obtaining a metallic concentrate, as well as the technical state of the system are substantiated. The works carried out in the sphere of investigating, creating, and improving the operation modes of electric drive motors and ore-grinding mills have been studied. Analytic dependences for estimating the operation modes of the ore-grinding mills aimed at improving the ore-crashing process maintenance and technical service efficiencies have been obtained. The obtained analytic dependencies establish a link between the technological and power parameters of the electromechanical system, and allow to estimate the state of the system and reveal the controlled parameters required for the efficient management in case of changing the technological parameters. It has been substantiated that the changes in the technological factors affecting the consumption power of the drive motor do not cause an instability in the electromechanical system.

Keywords: electromechanical system, estimation, operation mode, productivity, technological process, the mill filling degree

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Artion Kashuri, Rozana Liko

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In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences.

Keywords: convex functions, Hermite-Hadamard inequality, special means, time scale

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Fariha Asif

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The main purpose of this study was to investigate the effectiveness of eclectic approach in teaching of communicative functions. The objectives of the study were to get the information about the use of communicative functions through eclectic approach and to point out the most effective way of teaching functional communication and social interaction with the help of communicative activities through eclectic approach. The next step was to select sample from the selected population. As the research was descriptive so a questionnaire was developed on the basis of hypothesis and distributed to different selected schools of Lahore, Pakistan. Then data was tabulated, analyzed and interpreted through computer by finding percentages of different responses given by teachers to see the results. It was concluded that eclectic approach is effective in teaching communicative functions and communicative functions are better when taught through eclectic approach and communicative activities are more appropriate way of teaching communicative functions. It was found those teachers who were qualified in ELT gave better opinions as compare to those who did not have this degree. Techniques like presentations, dialogues and roleplay proved to be effective for teaching functional communication through communicative activities and also motivate the students not only in learning rules but also in using them to communicate with others.

Keywords: methodology, functions, teaching, ESP

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Jugal K. Prajapat, Manivannan M.

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In this article we have studied a class of sense preserving harmonic mappings in the unit disk D. Let B⁰H (α, β) denote the class of sense-preserving harmonic mappings f=h+g ̅ in the open unit disk D and satisfying the condition |z h״(z)+α (h׳(z)-1) | ≤ β - |z g″(z)+α g′(z)| (α > -1, β > 0). We have proved that B⁰H (α, β) is close-to-convex in D. We also prove that the functions in B⁰H (α, β) are stable harmonic univalent, stable harmonic starlike and stable harmonic convex in D for different values of its parameters. Further, the coefficient estimates, growth results, area theorem, boundary behavior, convolution and convex combination properties of the class B⁰H (α, β) of harmonic mapping are obtained.

Keywords: analytic, univalent, starlike, convex and close-to-convex

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

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In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.

Keywords: NFV, resource allocation, virtual routing function, minimum power consumption

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Authors: Yamin Sayyari

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In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Jensen's inequality, m-convex function, Convex function, Inequality

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Authors: Halimi Mohamed Taher, Kordoghli Bassem, Ben Hassen Mohamed, Sakli Faouzi

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Textile and clothing manufacturing industry is based largely on subcontracting system. Choosing the right subcontractor became a strategic decision that can affect the financial position of the company and even his market position. Subcontracting firms in Tunisia are lead to define an appropriate selection process which takes into account several quantitative and qualitative criteria. In this study, a methodology is proposed that includes a Fuzzy Analytic Hierarchy Process (AHP) in order to incorporate the ambiguities and uncertainties in qualitative decision. Best subcontractors for two Tunisian firms are determined based on model results.

Keywords: AHP, subcontractor, multicriteria, selection

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Authors: Shams Alyusof

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This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

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Authors: Latif Yanar, Muharrem Kaçan

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In this study, an Analytic Hierarchy Process and Analytic Network Process Decision Support System (DSS) model for determination of a navy base place in another country is proposed together with a decision support software (DESTEC 1.0) developed using C Sharp programming language. The proposed software also has the ability of performing the fuzzy models (Fuzzy AHP and Fuzzy ANP) of the proposed DSS to cope with the ambiguous and linguistic nature of the model. The AHP and ANP model, for a decision support for selecting the best place among the alternatives, including the criteria and alternatives, is developed and solved by the experts from Turkish Navy and Turkish academicians related to international relations branches of the universities in Turkey. Also, the questionnaires used for weighting of the criteria and the alternatives are filled by these experts.Some of our alternatives are: economic and political stability of the third country, the effect of another super power in that country, historical relations, security in that country, social facilities in the city in which the base will be built, the transportation security and difficulty from a main city that have an airport to the city will have the base etc. Over 20 criteria like these are determined which are categorized in social, political, economic and military aspects. As a result all the criteria and three alternatives are evaluated by different people who have background and experience to weight the criteria and alternatives as it must be in AHP and ANP evaluation system. The alternatives got their degrees all between 0 – 1 and the total is 1. At the end the DSS advices one of the alternatives as the best one to the decision maker according to the developed model and the evaluations of the experts.

Keywords: analytic hierarchical process, analytic network process, fuzzy logic, naval base place selection, multiple criteria decision making

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Authors: Mojtaba Hakimi-Moghaddam

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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: Jose Juan Peña, J. Morales, J. García-Ravelo

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In the search of potential models applied in the theoretical treatment of diatomic molecules, some of them have been constructed by using standard hyperbolic functions as well as from the so-called q-deformed hyperbolic functions (sc q-dhf) for displacing and modifying the shape of the potential under study. In order to transcend the scope of hyperbolic functions, in this work, a kind of generalized q-deformed hyperbolic functions (g q-dhf) is presented. By a suitable transformation, through the q deformation parameter, it is shown that these g q-dhf can be expressed in terms of their corresponding standard ones besides they can be reduced to the sc q-dhf. As a useful application of the proposed approach, and considering a class of exactly solvable multi-parameter exponential-type potentials, some new q-deformed quantum interactions models that can be used as interesting alternative in quantum physics and quantum states are presented. Furthermore, due that quantum potential models are conditioned on the q-dependence of the parameters that characterize to the exponential-type potentials, it is shown that many specific cases of q-deformed potentials are obtained as particular cases from the proposal.

Keywords: diatomic molecules, exponential-type potentials, hyperbolic functions, q-deformed potentials

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Authors: Wann-Ming Wey

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In today's popularity and progress of information technology, the big data set and its analysis are no longer a major conundrum. Now, we could not only use the relevant big data to analysis and emulate the possible status of urban development in the near future, but also provide more comprehensive and reasonable policy implementation basis for government units or decision-makers via the analysis and emulation results as mentioned above. In this research, we set Taipei City as the research scope, and use the relevant big data variables (e.g., population, facility utilization and related social policy ratings) and Analytic Network Process (ANP) approach to implement in-depth research and discussion for the possible reduction of land use in primary and secondary schools of Taipei City. In addition to enhance the prosperous urban activities for the urban public facility utilization, the final results of this research could help improve the efficiency of urban land use in the future. Furthermore, the assessment model and research framework established in this research also provide a good reference for schools or other public facilities land use and adaptive reuse strategies in the future.

Keywords: adaptive reuse, analytic network process, big data, land use strategy

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Authors: Smita Sonker

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Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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Authors: Juliza Hidayati, Yesie M. Sinuhaji, Sawarni Hasibuan

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A company producing drinking water through many incompatibility issues that affect supply chain performance. The study was conducted to determine the factors that affect the performance of the supply chain and improve it. To obtain the dominant factors affecting the performance of the supply chain used Analytic Network Process, while to improve performance is done by using Kaizen. Factors affecting the performance of the supply chain to be a reference to identify the cause of the non-conformance. Results weighting using ANP indicates that the dominant factor affecting the level of performance is the precision of the number of shipments (15%), the ability of the fulfillment of the booking amount (12%), and the number of rejected products when signing (12%). Incompatibility of the factors that affect the performance of the supply chain are identified, so that found the root cause of the problem is most dominant. Based on the weight of Risk Priority Number (RPN) gained the most dominant root cause of the problem, namely the poorly maintained engine, the engine worked for three shifts, machine parts that are not contained in the plant. Improvements then performed using the Kaizen method of systematic and sustainable.

Keywords: analytic network process, booking amount, risk priority number, supply chain performance

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