ANGULAR DISTRIBUTION AND MULTIPLE.VALUES BETWEEN ENTIRE FUNCTIONS AND THEIR DERIVATIVES

In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.

Firms can acquire sustainable competitive advantages by managing brand relationships and consumption values. However, previous studies do not compare consumption value with consumer satisfaction and brand commitment. Consumption value theory postulates that functional, emotional, social, and epistemic values enhance brand relationships. However, the most effective element of consumption values on consumer satisfaction or brand commitment is different. Specifically regarding running shoes, this article empirically compares functional, emotional, social, and epistemic values with consumer satisfaction and brand commitment. Using a mediated–moderation regression model, this article collected 844 Japanese samples from a marathon in Kobe, Japan, and tested how multiple consumption values affected consumer satisfaction and brand commitment, moderated by age. The results show that consumption values except epistemic value have positive effects on consumer satisfaction and brand commitment. In particular, this article uncovers the moderating effect of age in social values and consumer satisfaction. Specifically, social values affect consumer satisfaction when consumers are under 39 years old. This paper also found that functional value and social value have the strongest effect on consumer satisfaction and brand commitment, respectively, compared with other values. Contravening consumption value theory, our data suggests that epistemic value impedes brand commitment. Keywords: Consumption Values Theory, Consumer Satisfaction, Brand Commitment, Running Shoes JEL Classifications: M10, M21, M31 DOI: https://doi.org/10.32479/irmm.8713

In the present paper, a fuzzy programming model with quadratic membership functions has been developed for the solution of a Multi-Objective Transportation problem. In literature, several fuzzy programming approaches exist with various types of membership functions such as linear, exponential, hyperbolic etc. These membership functions are defined, by taking the lower and upper values of the objective functions into account. In some cases, these methods fail to obtain an integer compromise optimal solution. In the present method, two coefficients of the quadratic membership functions are determined by the lower and upper values of the objective functions. The other coefficient is taken as a variable in the fuzzy programming approach. This means that the membership curve is fixed at the two end points and set free in between. Application of the method on numerical examples proved that the approach could generate integer compromise optimal solutions.

In the present paper, optimization of functions with uncertainty by means of Genetic Algorithms (GA) is discussed. For such problems, there have been proposed methods of sampling fitness function several times and taking average of them for evaluation of each individual. However, important applications having uncertain fitness functions are online adaptation of real systems and complicated computer simulation using random variables. In such applications, possible number of fitness evaluation is quite limited. Hence, methods achieving optimization with less number of fitness evaluation is needed. In the present paper, the authors propose a GA for optimization of continuous fitness functions with observation noise utilizing history of search so as to reduce number of fitness evaluation. In the proposed method, value of fitness function at a novel search point is estimated not only by the sampled fitness value at that point but also by utilizing the fitness values of individuals stored in the history of search. Computer experiments using quadric fitness functions show that the proposed method outperforms the conventional GA of sampling fitness values several times at each search point in noisy environment.

For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of the domain of the approximated function is substantial. For instance, it was only in the mid-1950s that it was possible to constructively describe Holder classes on the segment [–1; 1] in terms of the approximation by algebraic polynomials. For that particular case, the constructive description requires the approximation at neighborhoods of the segment endpoints to be essentially better than the one in a neighborhood of its midpoint. A possible approximation quality test is to find out whether the approximation rate provides a possibility to reconstruct the smoothness of the approximated function. Earlier, we investigated the approximation of classes of smooth functions on a countable union of segments on the real axis. In the present paper, we prove that the rate of the approximation by the entire exponential-type functions provides the possibility to reconstruct the smoothness of the approximated function, i.e., a constructive description of classes of smooth functions is possible in terms of the specified approximation method. In an earlier paper, that result is announced for Holder classes, but the construction of a certain function needed for the proof is omitted. In the present paper, we use another proof; it does not apply the specified function.

Most of the existing multi-response optimization approaches focus on subjective and practical know how of the process. As a result some confusions and uncertainties are introduced in overall decision making process. In this investigation, an approach based on a Utility theory and Taguchi quality loss function has been applied to low-pressure cold spray process to deposit copper coatings, for simultaneous optimization of more than one response characteristics. In the present paper, three potential response parameters i.e. coating density, surface roughness and Micro hardness have been selected. Utility values based upon these response parameters have been analyzed for optimization by using Taguchi approach. The selected input parameters of powder feeding arrangement, substrate material, air stagnation pressure, air stagnation temperature and stand-off distance significantly improves the Utility function (raw data) comprising of quality characteristics (coating density, surface roughness and micro hardness). The percentage contribution of the parameters to achieve a higher value of utility function is: substrate material (64.59%), air stagnation pressure (16.35%), powder feeding arrangement (6.92%), air stagnation temperature (6.49%) and stand-off distance (1.84%) respectively.

In the present paper, a numerical algorithm using fifth degree quintic B-spline for fourth order singular per- turbation problem has been developed. The most of the numerical methods used for higher order singularly perturbed boundary value problems transform the problems into equivalent system of first and/or second order differential equations. However, in the present method, fifth degree B-spline is applied directly to the problem without transforming the problem into an equivalent system. The method uses values of fifth degree B-spline function and its derivatives up to the order four at nodal points. Resulting system of equations is solved to get the required quintic B-spline solution. Since perturbed problems contain boundary layers, the strategy of fitted mesh is used which assigns more mesh points in the boundary layer regions. The algorithm is tested on two problems to demonstrate the practical usefulness and superiority of the approach.

The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows

PurposeThis paper aims to develop a bi-objective mixed integer non-linear programing model to optimize the supply chain networks consisting of raw material providers, final product manufacturers and distribution centers. Raw material substitution caused by varying raw material supply amounts, prices and carbon emissions and final product substitution due to different product prices and carbon emissions are considered.Design/methodology/approachThe proposed model aims to achieve total profit maximization and total carbon emission minimization. The objective function of carbon emissions is converted into a maximization problem by changing minimum to maximum. The composite objective function is the weighted sum of the bias value of each objective function. The model is then solved using software Lingo12.FindingsNumerical analysis results show that an increase in the number of alternate raw materials for original raw material helps improve supply chain network performance, and variation in that number causes detectable but not significant changes in downstream final product substitution results.Originality/valueThe major differences between this work and existing research are as follows: first, although previous research considered carbon emissions in supply chain network optimization, it has not considered the substitution effects of products or raw materials. This paper considers the substitution of both raw material and productions. Second, the item substitution considered by previous research is derived from inventory shortage or price difference of original items. However, the substitution considered in the present paper is a response to differences in purchase price, production cost and carbon emissions for items.

A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media

We know that the elliptic modular function j(z) gives the birational invariant of the elliptic curve with the analytic modulus z, and that the elliptic modular functions belonging to the congruence-subgroups are obtained from the values of elliptic functions at the points of finite order on elliptic curves. This is not only the origin of those functions, but one of the most essential points to which we may ascribe the significance of elliptic modular functions in number-theory. It is important to generalize these facts, namely, to investigate in a more general case the relation between automorphic functions with one or more variables and systems of algebraic varieties, especially, systems of abelian varieties. The object of this paper is to give some results on this subject. We shall deal with certain systems of polarized abelian varieties parametrized by holomorphic functions and show that there exist meromorphic functions whose values are considered as of the members of the systems (Theorem 1). The theory developed here will be chiefly concerned with systems of abelian varieties with non-trivial endomorphisms, since I have already given elsewhere a theory for Siegel's modular functions [11]. I am particularly interested, in the present paper, in the determination of the fields of definition for fields of automorphic functions. This is the first problem which confronts us when we proceed beyond a formal treatment in the arithmetic theory of automorphic functions. We obtain a criterion (Theorem 2) applicable even in the case of compact fundamental domain where one can not employ Fourier expansions. The last part of the paper is devoted to the theory of a certain type of automorphic functions of one variable known in the literature as functions belonging to indefinite ternary quadratic forms [8], [5]; they occur as moduli of abelian varieties of dimension 2 whose endomorphismrings are isomorphic to an order of an indefinite quaternion algebra. We get in this case the field of rational numbers as a field of definition for the function-field. We can also prove the congruence formulae for the modular correspondences, which give a generalization of what is obtained in [3], [10]. We shall treat these formulae in a subsequent paper together with the theory of the functions belonging to congruence-subgroups. Our method can be applied to other types of automorphic functions, for example, to Hilbert's modular functions, by considering a system of

Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection

In the present paper we show that every distribution T in D′Lp (D′Lp(E) in the vector-valued case) has a representation as boundary value of a holomorphic function T (with values in E). This problem was considered in [1], [5], [12]. The representing functions are characterized by growth conditions. It is shown that the conditions in [1] and [5] don't extend to the vector-valued case while the conditions in [12] do.

In the present paper we demonstrate the application of single-objective and multi-objective optimization methods for solving the problem of ship design characteristics optimization. The impact analysis of local criteria on the values of design characteristics and elements of a ship has been carried out. The most frequently used methods of multicriteria optimization and their application to solving the problem of ship design characteristics substantiation, with taking into account the requirements to seakeeping and economic efficiency are considered. The multicriteria optimization results obtained by different methods are compared with the results of single-criteria optimization. Finally, numerical examples are implemented to demonstrate that an attempt to find a compromise solution often decrease the values of local criteria of optimality. It is established that the application of multi-criteria optimization methods for solving the ship design problems makes clear the role of each local optimality criteria and assess it influence on functional efficiency and design characteristics values.

Let $$\begin{aligned} A_{q}^{(\alpha )}(a;z)=\sum _{k=0}^{\infty }\frac{(a;q)_{k}q^{\alpha k^2} z^k}{(q;q)_{k}}, \end{aligned}$$ where $$\alpha >0,~0<q<1.$$ In a paper of Ruiming Zhang, he asked under what conditions the zeros of the entire function $$A_{q}^{(\alpha )}(a;z)$$ are all real and established some results on the zeros of $$A_{q}^{(\alpha )}(a;z)$$ which present a partial answer to that question. In the present paper, we will set up some results on certain entire functions which includes that $$A_{q}^{(\alpha )}(q^l;z),~l\ge 2$$ has only infinitely many negative zeros that gives a partial answer to Zhang’s question. In addition, we establish some results on zeros of certain entire functions involving the Rogers–Szegő polynomials and the Stieltjes–Wigert polynomials.