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In this paper, first we show that every n-inner product space can be reduced to (n-1) inner product space. Then we construct a new concept of fuzzy n-inner product space. Furthermore, we show that every fuzzy n-inner product space can be reduced to fuzzy (n-1) inner product space. [ABSTRACT FROM AUTHOR]

In this paper, Almost Distributive Fuzzy Lattice (ADFL) is characterized by ADL's in terms of level set Aα of a Fuzzy Relation A. The concepts of ideals, filters, the smallest ideal and the smallest filter containing a non empty subset of R of an ADFL are introduced, and some results are proved. In addition, the meet "∧" and join "∨" of two ideals(filters) of an ADFL are defined, and finally it is proved that for any two ideals I and J of an ADFL L, I ∧ J and I V J are also ideals of L, and for any two filter F and G of an ADFL L, F ∧ G and F V G are also filters of L. [ABSTRACT FROM AUTHOR]

This paper implements Rakhimov-Bekbaev approach to present a complete list of isomorphism classes of a subclass of complex filiform Leibniz algebras obtained from naturally graded non-Lie filiform Leibniz algebra. This class is split into two subclasses. In this paper we shall consider the second class which is denoted by SLbn in dimension n. The isomorphism criteria in terms of invariant functions for SLb10 are presented. We represent SLb10as a union of subsets and show that some of these subsets are represented as union of infinitely many orbits (a set of isomorphic to each other algebras) while others are represented as just a single orbit. In former case we give invariant functions to distinguish the orbits, while for the latter case the representatives of the single orbits are provided. As a result, we give the list of isomorphism classes with the table of multiplications. [ABSTRACT FROM AUTHOR]

Let A be a class of functions of the form f(z) = z + Σ∞n-2 anZn which are analytic in the open unit disc D = {z∊ C : |z| 1

The first goal of the present paper is to provide an introduction to the concept of semi bounded set and it is variations in bornological sets (BS). We study semi boundedness properties and keep track behaviour of semi boundedness under some set operations. Then, the concept of bornological ideal (BI) is given. It is provoked by intention to give the definition of semi boundedness with respect to (BI). It extends the notion of semi bounded sets in (BS). Finally, we study some properties of semi bounded sets with respect to a bornological ideal. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a new class of open sets, called generalized semi-open sets with respect to an ideal, which is an extension of generalized semi open sets. Then, by using these sets, we study properties of compact spaces and continuous maps via ideals. [ABSTRACT FROM AUTHOR]

Series defined by means of the Mittag-Leffer functions are considered in this paper and the behaviour of these series on the boundaries of their convergence domains is investigated. Necessary and sufficient conditions for their overconvergence are proposed. [ABSTRACT FROM AUTHOR]

In this paper, we study a certain class of generalized Hurwitz- Lerch zeta functions. A new and useful property of the generalized Hurwitz- Lerch zeta functions such that their partial differential equations are derived. [ABSTRACT FROM AUTHOR]

In this paper, a general concept of complex twistulant matrices is introduced, namely, left and right twistulant matrices. Group structures of some subsets of such matrices are studied. First, it is shown that every right twistulant matrix is diagonalizable. Using this diagonalizability, group structures of complex twistulant matrices are determined. Sufficient conditions for some subsets of these matrices to be a group under the usual matrix multiplication are given. In some cases, the necessary conditions are determined as well. The commutativity of such groups is also investigated. The well-known group structures of circulant matrices can be viewed as corollaries. [ABSTRACT FROM AUTHOR]

In this paper, we study 1-types over sets of countable theory which has /0-definable binary relation of linear order. [ABSTRACT FROM AUTHOR]

The paper aims to investigate the classification problem of 5th dimensional complex filiform Leibniz algebras. There are two sources to get classification of filiform Leibniz algebras. The first of them is the naturally graded non-Lie filiform Leibniz algebras and another one is the naturally graded filiform Lie algebras. Here we consider Leibniz algebras appearing both sources. It is known that this class in its turn can be split into three subclasses, first and second classes are non-Lie filiform Leibniz algebras while the third class include the filiform Lie algebra. However, isomorphisms within each class were not investigated there. In this paper we propose an approach to the isomorphism problem in terms of invariants. Using this approach we give the complete classification of one of the above mentioned of complex filiform Leibniz algebras in 5th dimension. [ABSTRACT FROM AUTHOR]

“Fuzzy hypotheses are more realistic than the crisp (classic) hypotheses”. This is one of the statements that we may see in the papers about fuzzy hypothesis testing. In this paper we show that the best test function for the fuzzy hypotheses is equal to the best test function for the random hypotheses in the Bayesian framework. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

In the present paper, we consider Fekete-Szegö inequalities for certain subclasses of analytic and bi-univalent functions defined by subordination. [ABSTRACT FROM AUTHOR]

In this paper, we define soft pair-wise b-open set on soft bitopological spaces. We also give properties of these soft sets and compared each other soft pair-wise open sets. [ABSTRACT FROM AUTHOR]

Mahalanobis distance Δ² values are commonly in the range of 0 to where higher values represent greater distance between class means or points. The increase in Mahalanobis distance is unbounded as the distance multiply. To certain extend, the unbounded distance values pose difficulties in the evaluation and decision for instance in the sensors closeness test. This paper proposes an approach to [0, 1] bounded Mahalanobis distance Δ² that enable researcher to easily perform sensors closeness test. The experimental data of four different types of rice based on three different electronic nose sensors namely InSniff, PEN3, and Cyranose320 were analyzed and sensor closeness test seems successfully performed within the [0, 1] bound. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalised differential operator. Some properties of certain class containing this operator are investigated. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate some properties of functions of new class, radii of closeto-convexity, starlikeness, and convexity. [ABSTRACT FROM AUTHOR]

Let G = (V,E) be a simple connected graph. A vertex labeling of f:V ⌢ {0,1} of G induces two edge labelings f+, f*:E⌢ {0,1} defined by f+(xy) = f(x)+f(y)(mod2) and f*(xy) = f(x)f(y) for each edge xy ∈ E. For i∈ {0,1}, let vf(i) = |{v∈V:f(v)=i}|, e+f(i) = |{e∈E:f+ (e) = i}| and e*f(i) = |e ∈ E:f* (e) = i}| . A labeling f is called friendly if |vf (1)-vf(0)|≤1 . The friendly index set and the product-cordial index set of G are defined as the sets {|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)|:f is friendly}. In this paper, we completely determine the friendly index sets and product-cordial index sets of gear graphs. We also show that the product-cordial indices of a graph can be obtained from its adjacency matrix. [ABSTRACT FROM AUTHOR]

This paper aims to propose a new method in decomposing ???? into circuits. Our method introduces two new strategies: Wing Strategy (WinS) and Endpoint Strategy (Endp-S). WinS contains first wing and second wing, while Endp-S contains first endpoint and second endpoint. The crucial task for generating circuits in WinS is two vertices of K4 are fixed to be the first wing, meanwhile in Endp-S, the vertices of the first wing are then put into the first endpoint, consecutively. Once the set of circuits are produced from these strategies, the drawing of that circuits can be obtained. [ABSTRACT FROM AUTHOR]

The aim of this paper is to use the notion of Ψ-operations in double fuzzy topological spaces to study the concept of (r,s)-fuzzy generalized ΨΡ-closed sets and (r,s)-fuzzy generalized ΨΡ-open sets, some characterizations and properties of these concepts are given. Moreover, we discussed the relationship between these sets in double fuzzy topological spaces. [ABSTRACT FROM AUTHOR]

This paper focuses on the functional |a2a4-a32| for subclasses of analytic functions denoted by R(β), 0 ≤ β < 1 and H(β), 0 ≤ β < 0.2287. The upper bound |a2a4-a32| for R(β) and H(β) are obtained. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce new classes of functions called totally-continuous functions and its variants totally semi-continuous functions and semi totally-continuous functions in double fuzzy topological spaces. Their characterizations, examples and relationship with other notions of continuous functions in this space are provided. [ABSTRACT FROM AUTHOR]

In this paper, we deal with variety of 3-dimensional Leibniz algebras. We collect the set of necessary criteria of contractions. Calculating the invariant quantities, we use the criteria to find possible one-parametric contractions. Using the contractions, we find the rigid algebras which would form the irreducible components of the variety of 3-dimensional complex Leibniz algebras. [ABSTRACT FROM AUTHOR]

Anomalous diffusion can be roughly characterized by the property that the diffusive particles do not follow the Gaussian statistics. When the mean squared displacement of the particles behaves in time like a power function, time- and/or space-fractional derivatives were shown to be useful in modeling of such diffusion processes. In this paper, a special class of anomalous diffusion processes, the so called neutral-fractional diffusion, is considered. The starting point is a stochastic formulation of the model in terms of the continuous time random walk processes. The neutralfractional diffusion equation in form of a partial differential equation with the fractional derivatives of the same order both in time and in space is then derived from the master equation for a special choice of the probability density functions. An explicit form of the fundamental solution of the Cauchy problem for the neutral-fractional diffusion equation is presented. Its properties are studied and illustrated by plots. [ABSTRACT FROM AUTHOR]

The paper deals with polyhedral (parallelotope-valued) estimates for reachable sets of linear differential systems and is devoted to investigation of so called tight estimates. First, we construct the new families of tight internal and external estimates. Second, we study properties of boundedness and unboundedness on the infinite time interval of external estimates for reachable sets of systems with stable matrices and present new results concerning the family of the tight external estimates. [ABSTRACT FROM AUTHOR]

This paper deals with the enumeration of the different classes of 2-element fuzzy hypergroups and with the construction of some classes of 2-element mimic fuzzy hypergroups. It also introduces the notion of the pseudo-mimic fuzzy hypergroup. [ABSTRACT FROM AUTHOR]

To improve space utilization, the method for handling spaces plays an important role in the container loading problem. This paper deals with loading a set of cuboid items into a single container to maximize the utilization of the space. Six space partitions are presented and a set of rules for merging spaces is proposed. Through experimentation, using a benchmark data set, the influence of partitioning and merging are analyzed. The experimental results show that partitioning and merging in which all loaded boxes have one hundred percent support from below can produce good space utilization. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the classes Tnp(λ,A,B) and Knp(λ,μ,m,A,B) and we apply to the (n,δ)-neighborhoods of functions in the class Knp(λ,μ,m,A,B). [ABSTRACT FROM AUTHOR]

The locating-chromatic number of a graph G can be defined as the cardinality of a minimum ordered partition Π of the vertex-set V(G) such that every two vertices in G have different coordinates with respect to Π and every two adjacent vertices in G are not in the same partition class in Π. In this case, the coordinate of a vertex v is defined as the distances from the vertex v to all partition classes in Π. In this paper, we discuss the locating-chromatic number of Halin graph, namely a planar graph H = T ⊎ C which constructed from a plane embedding of a tree T with at least four vertices, by connecting all the leaves of T (the vertices of degree 1) to form a cycle C that passes around the tree in the natural cyclic order defined by the embedding of the tree. In particular, we investigate the locating-chromatic number of the Halin graph H = T ⊎C, where T is a subdivision of a star and a double star. [ABSTRACT FROM AUTHOR]

In this paper, we construct explicitly a multi-centered metric in (n+1)-dimensional static spacetimes which belong to a class of (pseudo)-Riemannian manifolds. Our starting point is to embed an n-dimensional complete manifold into an (n+1)-dimensional manifold which admits a timelike Killing vector. Then, the scalar curvature depends on the Laplace-Beltrami operator of the n-dimensional submanifold. This operator is set to be equals to the linear combination of the Dirac-delta function on the submanifold which can be thought of as remove points on (n+1)-dimensional manifold. Using completeness of the n-dimensional submanifold it can be shown that the solution does indeed exist. As an example we give the explicit form for flat Euclidean geometries, sphere, and hyperbolic geometries. [ABSTRACT FROM AUTHOR]

Let G be a connected graph G. Let c be a k-coloring of V(G) which induces an ordered partition Π = {S1,S2, ...,Sk} of V(G), where Si is the set of vertices receiving color i. The color code cΠ(ν) of vertex ν is the ordered k-tuple (d(ν,S1), d(ν, S2), ..., d(ν, Sk)), where d(ν, Si) = min {d(ν, x)|x ∈ Si}, for 1 ≤ i ≤ k. If the color codes of all vertices are different, then c is called a locating-coloring of G. The locating-chromatic number of G, denoted by χL(G) is the smallest k such that G has a locating k-coloring. In this paper, we investigate graphs with locating-chromatic number 3. In particular, we determine all maximal graphs having cycles (in terms of the number of edges) with locating-chromatic number 3. From this result, we then characterize all graphs on n vertices containing cycles with locating-chromatic number 3. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study and introduce some properties of differential subordination for multivalent functions, also we will determine various results on admissible functions with the operator Dσf(z) and derive the sufficient conditions for subordination and superordination for subclass of multivalent functions. [ABSTRACT FROM AUTHOR]

In this paper we determine a class of of generalized diffusion equations that is nonlinear self-adjoint. [ABSTRACT FROM AUTHOR]