International Journal of Mathematics and Mathematical Sciences

List of Papers (Total 881)

The effect of random scale changes on limits of infinitesimal systems

Suppose S={{Xnj,   j=1,2,…,kn}} is an infinitesimal system of random variables whose centered sums converge in law to a (necessarily infinitely divisible) distribution with Levy representation determined by the triple (γ,σ2,M). If {Yj,   j=1,2,…} are independent indentically distributed random variables independent of S, then the system S′={{YjXnj,j=1,2,…,kn}} is obtained by...

Existence theorem for the difference equation Yn

For the difference equation (Yn

On the Hankel determinants of close-to-convex univalent functions

The rate of growth of Hankel determinant for close-to-convex functions is determined. The results in this paper are best possible.

Yet another characterization of the sine function

In this expository paper, it is shown that if an entire function of exponential type vanishes at least once in the complex plane and if it has exactly the same number of zeros (counting multiplicities) as its second derivative, then this function must take the form Asin(Bz

Classification of injective factors: The wok of Alain Connes

The fundamental results of A. Connes which determine a complete set of isomorphism classes for most injective factors are discussed in detail. After some introductory remarks which lay the foundation for the subsequent discussion, an historical survey of some of the principal lines of the investigation in the classification of factors is presented, culminating in the Connes...

Effectiveness of transposed inverse sets in faber regions

The effectiveness properties, in Faber regions, of the transposed inverse of a given basic set of polynominals, are investigated in the present paper. A certain inevitable normalizing substitution, is first formulated, to be undergone by the given set to ensure the existence of the transposed inverse in the Faber region. The first main result of the present work (Theorem 2.1), on...

On mixed finite element techniques for elliptic problems

The main aim of this paper is to consider the numerical approximation of mildly nonlinear elliptic problems by means of finite element methods of mixed type. The technique is based on an extended variational principle, in which the constraint of interelement continuity has been removed at the expense of introducing a Lagrange multiplier.

Closed spectral measures in Fréchet spaces

Closed spectral measures, which are often used in the theory of operators, have the desirable property that their L1-space is complete. In this note criteria are given which assure the closedness of spectral measures acting in Fréchet spaces.

A note on generalized harmonic-Cesàro summability

This note shows that conjectures proposed by G. Das and P.C. Mohapatra [1] on inclusion relations between two generalized Harmonic-Cesàro methods of summability, are true.

Reducible functional differential equations

This is the first part of a survey on analytic solutions of functional differential equations (FDE). Some classes of FDE that can be reduced to ordinary differential equations are considered since they often provide an insight into the structure of analytic solutions to equations with more general argument deviations. Reducible FDE also find important applications in the study of...

On some extensions of Hardy’s inequality

We present in this paper some new integral inequalities which are related to Hardy's inequality, thus bringing into sharp focus some of the earlier results of the author.

Comparison theorems for fourth order differential equations

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equations yiv−p(x)y=0 and yiv

Finite p′-nilpotent groups. I

In this paper we consider finite p′-nilpotent groups which is a generalization of finite p-nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in this generalized setting. The paper also considers the conditions under which product of p′-nilpotent groups will be a p...

An energy concerving modification of numerical methods for the integration of equations of motion

In the integration of the equations of motion of a system of particles, conventional numerical methods generate an error in the total energy of the same order as the truncation error. A simple modification of these methods is described, which results in exact conservation of the energy.

Mixed foliate CR-submanifolds in a complex hyperbolic space are non-proper

It was conjectured in [1 II] (also in [2]) that mixed foliate CR-submanifolds in a complex hyperbolic space are either complex submanifolds or totally real submanifolds. In this paper we give an affirmative solution to this conjecture.

An application of stress energy tensor to the vanishing theorem of differential forms

The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclidean n-space, the complex n-space, and the complex hyperbolic space form, if any vector bundle valued p-form with conservative stress energy tensor is of finite norm or slowly divergent norm...

Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations

The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques. We consider first a nonlinear dissipative wave equation; second, a nonlinear equation modeling convectlon-diffusion processes; and finally, an elliptic partial differential equation.

An inequality of W. L. Wang and P. F. Wang

In this note we present a proof of the inequality Hn/H′n≤Gn/G′n where Hn and Gn (resp. H′n and G′n) denote the weighted harmonic and geometric means of x1,…,xn (resp. 1−x1,…,1−xn) with xi∈(0,1/2], i=1,…,n.

A note on neighborhoods of analytic functions having positive real part

Let P denote the set of all functions analytic in the unit disk D={z||z|<1} having the form p(z)=1

Convexity preserving summability matrices

The main result of this paper gives the necessary and sufficient conditions for the Abel matrices to preserve the convexity of sequences. Also, the higher orders of the Cesáro method are shown to be convexity-preserving matrices.

Measuring static complexity

The concept of “pattern” is introduced, formally defined, and used to analyze various measures of the complexity of finite binary sequences and other objects. The standard Kolmogoroff-Chaitin-Solomonoff complexity measure is considered, along with Bennett's ‘logical depth’, Koppel's ‘sophistication'’, and Chaitin's analysis of the complexity of geometric objects. The pattern...

Note on pointwise contractive projections

Let C(X) be the space of real-valued continuous functions on a Hausdorff completely regular topological space X. endowed with the compact-open topology. In this paper necessary and sufficient conditions are given for a subspace of C(X) to be the range of a pointwise contractive projection in C(X).

Solutions to Lyapunov stability problems of sets: nonlinear systems with differentiable motions

Time-invariant nonlinear systems with differentiable motions are considered. The algorithmic necessary and sufficient conditions are established in various forms for one-shot construction of a Lyapunov function, for asymptotic stability of a compact invariant set and for the exact determination of the asymptotic stability domain of the invariant set.

Radical classes of l-groups

The main results of this paper concern radical classes of l-groups. In the sections 2-3 the relationship between several radical classes of l-groups are discussed and the characteristic properties for several radical mappings are given. In the sections 5-6 we give nice concrete descriptions of some important radical classes of l-groups using the structure theorems of a complete l...