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In this paper our aim is to give refinements of Jensen?s type inequalities for the convex function defined on the co-ordinates of the bidimensional interval in the plane.

The paper is mainly devoted to deriving the relationship between an entire function and its derivative when they share one small function except possibly a set, which is related to the famous Br?ck conjecture. In addition, two propositions of infinite products are obtained. The first one is the growth property of a certain infinite product. The second one is the property of entire solutions of the differential equation which concerns infinite products.

In this paper, we investigate applications of characteristic function of the uniform density function. Using this characteristic function, some identities and formulas associated with Bernoulli polynomials of negative order, Stirling numbers and probability distribution functions were derived.

In this paper we shall prove a theorem on a representation of ?-regularly varying sequences in the sense of Karamata [1].

The aim of this paper is to find the transformation for the coefficients of an N-linear connection on E = Osc2M, by a transformation of nonlinear connections, to define in the bundle of accelerations the general conformal almost symplectic N-linear connection notion and to determine the set of all general conformal almost symplectic N-linear connections on E. We treat also some special classes of general conformal almost symplectic N-linear connections on E.

The second order Cesaro sequence spaces of non-absolute type Xp(?2) for 1 ? p ? ? were defined and studied in [1]. It seems, however, that the characterizations of their ?-duals given there do not hold for 1 < p ? ?. In this paper, we determine the ?-duals (Xp(?2))? for 1 ? p ? ?.

The comparison of differential operators is a problem of the theory of partial differential operators with constant coefficients. This problem up to now doesn't have a complete solution. It was formulated in the sixties by Lars Hormander in his monograph "The Analysis of Linear Partial Differential Operators". Many facts of the theory of partial differential equations can be formulated by using the concept of pre-order relation over the set of differential operators, however it is too complicated to check the comparability condition of two differential operators. In this paper we get some sufficient conditions for the comparability of two differential operators.

In this paper we introduce some new difference sequence spaces combining lacunary sequences and Orlicz functions. We establish some inclusion relations between these spaces.

In this paper we give two different ways of proving the compactness of some linear operators between certain sequence spaces. One of them is based only on the theory of matrix transformations and the other uses the Hausdorf measure of noncompactness.

The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Colak [6]. In this paper we introduce the sequence spaces [V, ?, f, p]0 (?r, E), [V, ?, f, p]1 (?r, E), [V, ?, f, p]? (?r, E) S? (?r, E) and S?0 (?r, E) where E is any Banach space, examine them and give various properties and inclusion relations on these spaces. We also show that the space S? (?r, E) may be represented as a [V, ?, f, p]1 (?r, E)space.

Compact representations of switching functions provide for simplified realizations of logic networks. Recent advent of digital technology and VLSI raised a considerable interest in polynomial expressions for switching functions. Complexity of these expressions is estimated through the number of product terms. For a given function and the selected class of polynomial expressions, the number of products can be reduced by a suitable selection of polarities for switching variables, which results in Fixed Polarity Polynomial Expressions (FPPEs). This paper proposes a method for optimization of polynomial representation of switching functions. The method exploits the notion of dual polarity of switching variables and takes advantages of a simple relationship between two FPPEs for dual polarities. Calculation of FPPEs is performed along the extended dual polarity route so that each FPPE is calculated from its extended dual polarity FPPE. Conversion from one FPPE to another is carried out by using one-bit check, which ensures the efficiency of the method. The proposed method can be applied to arbitrary polynomial expressions providing that the corresponding transform matrix has the Kronecker product structure.

Many important sequence spaces arise in a natural way from various concepts of summability, namely ordinary, absolute and strong summability. In the first two cases they may be considered as the domains of the matrices that define the respective methods of summability; the situation, however, is different and more complicated in the case of strong summability. Given sequence spaces X and Y, we find necessary and sufficient conditions for the entries of a matrix to map X into Y, and characterize the subclass of those matrices that are compact operators. This paper gives a survey of recent research in the field of matrix transformations at the University of Nis Serbia and Montenegro, in the past four years.

In this paper we deal with matrix transformations mapping in either of the sets s?(Nq), s?o(Nq) or s?(c)(Nq). Then we study some properties of the sets s?(Np Nq) and s?o(Np Nq) and give a characterization of matrix transformations in these spaces. These results generalize those given in [11, 14, 16].

This paper addresses the problem of rectangular matrix multiplication on bidirectional linear systolic arrays (SAs). We analyze all bidirectional linear SAs in terms of efficiency. We conclude that the efficiency depends on the relation between the loop boundaries in the systolic algorithm (i.e. matrix dimensions). We point out which SA is the best choice depending on the relation between matrix dimensions. We have designed bidirectional linear systolic arrays suitable for rectangular matrix multiplication.

In this paper we present iterative methods of Weierstrass's type for the simultaneous inclusion of all multiple zeros of a polynomial. The order of convergence of the proposed interval method is 1 + ?2 ? 2.414 or 3, depending on the type of the applied disk inversion. The criterion for the choice of a proper circular root-set is given. This criterion uses the already calculated entries which increases the computational efficiency of the presented algorithms. Numerical results are given to demonstrate the convergence behavior.

In this paper, we study singular integrals on product domains with kernels in L(logL)2(Sn?1?Sm?1) supported by surfaces of revolutions. We prove that our operators are bounded on Lp under certain convexity assumption on the surfaces. Also, in this paper we prove that the convexity assumption is not necessary for the L boundedness to hold. Moreover, additional related results are presented. Our condition on the kernel is known to be optimal.

In this paper, using a combination of methods used in [1],[20] and [22] the results from [3, Theorem 1], [14,Theorem 1] and [15, Theorem 1] are improved by removing the assumption of continuity, relaxing compatibility to weak compatibility property and replacing the completeness of the space with a set of four alternative conditions for functions satisfying an implicit relation.

In this paper new results concerning the measure of non-compactness in convex metric spaces are presented.

In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

In this paper, using a combination of methods used in [5], [14], [15] and [17] the results of [1, Theorems 2.2 and 2.3] and [15, Theorem 3] are improved by removing the assumptions of continuity and reciprocally continuity, relaxing compatibility and compatibility of type (A) to weakly compatibility and replacing the completeness of the space with a set of four alternative conditions for four mappings satisfying an implicit relation.

Measure partition problems are classical problems of geometric combinatorics ([1], [2], [3], [4]) whose solutions often use tools from the equivariant algebraic topology. The potential of the computational obstruction theory approach is partially demonstrated here. In this paper we reprove a result of V.V. Makeev [9] about a 6-equipartition of a measure on S2 by three planes. The advantage of our approach is that it can be applied on other more complicated questions of the similar nature.

The comparison of differential operators is a problem that was formulated in sixties by Lars Hormander, it is a part of the theory of partial differential operators with constant coefficients, this problem up to now does not have a complete solution. The urgency of this problem is stipulated by the applications of the solvability theory of differential equations in special spaces of generalized functions. In this paper we prove some results in the manifold linearity of a polynomial, these results play an important role in the comparison of two linear partial differential operators problem.

The aim of this paper is to introduce and study upper and lower almost ∞-continuous multifunctions as a generalization of some types of continuous multifunctions including almost continuity, al- most fi-continuity, almost precontinuity, almost quasi-continuity and ∞- continuity. Furthermore, basic characterizations, preservation theorems and several properties concerning upper and lower almost ∞-continuous multifunctions are investigated. The relationships between almost ∞- continuous multifunctions and the other types of continuity are also discussed.

In this paper we use the CS / TM scheme stated in [1] for the V.V. Makeev equipartition problem [7] to prove the existence of new weighted partitions. For the first time computations of the as- sociated equivariant problem are done by codes written in the package Mathematica 5.0 [2].

This paper presents the following definition which is a nat- ural combination of the definition for asymptotically equivalent, ‚- sta- tistical convergence and ae- convergence. Two nonnegative sequences (x) and (y) are said to be Sae;‚- asymptotically equivalent of multiple L provided that for every † > 0 lim n 1 ‚n k 2 In : xaek(m) yaek(m) i L ‚ † = 0

The aim of this paper is to study further characterizations and the relationships of -p-normal spaces, almost -p-normal spaces and mildly -p-normal spaces. We introduce the notion of g-pr-closed sets. Also, we obtain properties of g-pr-closed sets and the relationships be- tween g-pr-closed sets and the related generalized closed sets. By using g-pr-closed sets, we introduce new forms of generalized --precontinuity. Moreover, we obtain new characterizations of -p-normal spaces, almost -p-normal spaces and mildly -p-normal spaces and preservation theo- rems.

The goal of this paper is to present two theorems that char- acterize asymptotically statistical equivalent of multiple L and the reg- ularity of asymptotically statistical convergence by using a sequence of infinite matrices.

In this paper, we introduce a new class of multivalent functions defined by convolution and Dziok-Srivastava operator and study some properties of this class e.g. coefficient estimates, integral representation, distortion and closure theorems, convolution and integral operator.

The eventually positive inverse eigenvalue problem(EPIEP) asks when a list ? = (???2,???n) of n complex numbers is the spectrum of a real n ? n eventually positive matrix. In this paper, a constructive method is presented to solve the EPIEP. Using this method, it is easy to find the realizing matrix, i.e. a real eventually positive matrix with the spectrum ?. And a complete answer to the EPIEP prescribed the left and the right Perron eigenvectors of the realizing matrix is also given.

In this paper we define some subclass of meromorphic functions and we obtain some properties of these classes. .

In this paper an algorithm for minimization of C 1,1 functions, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish for this algorithm general hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence.

In this paper we study some concepts involving distance in inserted graphs with an emphasize on centers in inserted graphs. More precisely we prove that for every non-trivial connected graph H there exists a graph G such that H is the center of G and the inserted graph of H is the center of the inserted graph of G. Graphs which are the periphery of some inserted graph are characterized. .

In this paper further characterizations of Hermitian, normal and EP operators on Hilbert spaces are established. Thus the recent results of O. M. Baksalary and G. Trenkler (Linear Multilin. Algebra, to appear) are extended to the infinite dimensional setting with proofs based on operator matrices.

B.Y. Chen [4] showed that there exists no proper warped CR-submanifolds N_ x ? NT of a Kaehler manifold and obtained many results on CR-warped products NT x ? N_. Contact CR-warped product submanifolds in Sasakian manifold were studied by I. Hasegawa and I. Mihai [6]. In this paper we have investigated the existence of contact CR-warped product submanifolds in more general setting of trans-Sasakian manifolds. .

The aim of this paper is to find a generalization of topological groups. The concept arises out of the investigation to obtain a group structure on the set [X,Y], of homotopy classes of maps from a space X to a given space Y for all X which is natural with respect to X. We also study the generalized topological groups. Finally, associated with each generalized topological group we construct a contra variant functor from the homotopy category of pointed topological spaces and base point preserving continuous maps to the category of groups and homomorphism.

The aim of this paper is to introduce and characterize the vividly (1, 2)-?-irresolute mapping and blurry (1, 2)-?-irresolute mapping. We also define (1, 2)-?-T2 spaces and (1, 2)-semi-preregular spaces. These spaces are characterized by a new class of open sets, called (1,2)-semipre-?-open sets. .

In this paper, we define and study fuzzy generalized ?-closed sets and r-open sets of a given L-fuzzy topological space and prime element r ? P(L) and coprime element a ? M(L). The concept of L-fuzzy r-open sets was introduced in [10], and it was proved that all r-open sets for L-fuzzy topological space form a new L-fuzzy topology, which is called stratiform L-fuzzy topology. Making use of the fuzzy generalized ?-closed sets, fuzzy generalized ?-continuous map is presented. .

One of the main tasks of the deformation theory is to point out to the rigid and flexible surfaces. In this paper we signify a torus like class of surfaces generated by parallelogram in ?3. It is proved that this class is rigid due to infinitesimal bending. Infinitesimal bending of generated surfaces is considered using Cohn-Vossen's method. .

In the paper herein we treat some problems concerning the metric structure on the 2-tangent bundle: T2M. We determine the set of all metric semi-symmetric N-linear connections, in the case when the nonlinear connection N is fixed. We prove that the sets: TN of the transformations of N-linear connection having the same nonlinear connections N and msT N of the transformations of metric semi-symmetric N-linear connections, having the same nonlinear connection N, together with the composition of mappings are groups. We obtain some important invariants of the group msT N and we give their properties. We also study the transformation laws of the torsion and curvature d-tensor fields, with respect to the transformations of the groups TN and msT N.

In this paper we propose for study a class of close to convex functions with negative coefficients defined by using a modified Salagean operator. .

Robin HarteWe have known Trevor West since before he was Trevor West, and that’s notyesterday. Our first encounter would have been over fifty years ago, when we bothpresented for the Entrance Scholarship Examination for Trinity College. And heknew all about us: the Midleton Mafia and Bennet’s Brewery Boys [17] had ussussed. But they didn’t know about The Plough: “Twixt finger and thumb, thesquat pen sits: I’ll dig with it.” Seamus Heaney [10] knew all about The Plough -it got him a Nobel Prize. And dig with it we did - all through the physics paper- while the young Tim Starr sat and chewed the end of his pencil (they were verypoor in Midleton in those days). This must have disconcerted him, because shortlyafterwards Tim Starr changed his name to Trevor West. Then of course he ralliedhimself, soon scaling the heights of college society. By the time we came out the otherend of Trinity College he had appointed himself our political commissar, vigilant lestwe should reveal to the waiting Brits the depths of our collective ignorance of mattersTripos Three. He fumbled the ball a little on his first outing when he had to bebrought back to the Smythies seminar with a proper proof of Lemma 5 [11]:Hans Freudenthal single handedly kept West and ourself away from partiallyordered vector spaces for nearly twenty years. But then he was handed the verycold hot potato that was the Olangunju thesis, which together with two research

Famous models of conditional heteroscedasticity describe various effects of behavior of the financial markets. In this paper, we investigate the related model, called Split-ARCH, in some of its stochastic aspects, as the necessary and sufficient conditions of the strong stationarity and the estimation procedure. The basic asymptotic properties of those estimates are described, too. The most important segment of our work is dedicated to the practical issue of Split-ARCH model in analysis of the dynamics of the real data. We compared the Split-ARCH with standard models of ARCH type and showed that it was better stochastic model for the explanation of the world market prices of some precious metals. .

We prove that, for certain indices of 6, there are functions whose Cesaro means of order 5 of the Fourier expansion with respect to the polynomials associated with the measure (1 - ?)?(l + ?)? + MAr, where At is the delta function at a point t, are divergent almost everywhere on [-1,1]. We follow Meaney's paper (2003), where divergent Cesaro and Riesz means of Jacobi expansions were proved. .

In this paper are considered some sufficient conditions under which, for given sequence (Ti)i?1 of operators on an infinite-dimensional complex Hilbert space, there is a dense set of points whose orbits under each Ti tend strongly to infinity. .

In this paper we have introduced a subclass AR(n, ?, ?, ?, ?) of univalent functions with negative coefficients defined by Salagean operator D?. We have obtained sharp results for coefficient estimates, distortion and closure bounds, Hadamard product and other results. .

In this paper we prove existence of weak extremal solutions for third order nonlinear discontinuous two-point boundary value problems. Further, we obtain two weak differential inequalities for proving boundedness and uniqueness of solutions of related boundary value problems. .

The purpose of this paper is to give two new types of irresolute functions called, completely g-irresolute functions and weakly g-irresolute functions. We obtain theirs characterizations and theirs basic properties. .

In this paper, we prove a common fixed point theorem for a quadruple of mappings by using an implicit relation [6] and property (E.A) [1] under weak compatibility. Our theorem improves and generalizes the main Theorems of Popa [6] and Aamri and Moutawakil [1] .Various examples verify the importance of weak compatibility and property (E.A) in the existence of common fixed point and examples are also given to the implicit relation and to validate our main Theorem. We also show that property (E.A) and Meir-Keeler type contractive condition are independent to each other. .

In this paper we characterize the matrix classes (l(p, u),??) and (l(p, u), ?) which generalize the matrix classes given by Mursaleen [6]. .

In this paper a general fixed point theorem for converse commuting multivalued mappings, which generalize Theorems 2.1 and 2.2 from [3], is proved. .