International Journal of Mathematics and Mathematical Sciences

List of Papers (Total 1,910)

Relative integral basis for algebraic number fields

At first conditions are given for existence of a relative integral basis for OK≅Okn−1⊕I with [K;k]=n. Then the constrtiction of the ideal I in OK≅Okn−1⊕I is given for proof of existence of a relative integral basis for OK4(m1,m2)/Ok(​m3). Finally existence and construction of the relative integral basis for OK6(n3,−3)/Ok3(n3),OK6(n3,−3)/Ok2(−3) for some values of n are given.

Semiprime SF-rings whose essential left ideals are two-sided

It is proved that if R is a semiprime ELT-ring and every simple right R-module is flat then R is regular. Is R regular if R is a semiprime ELT-ring and every simple right R-module is flat? In this note, we give a positive answer to the question.

On the Ricci tensor of real hypersurfaces of quaternionic projective space

We study some conditions on the Ricci tensor of real hypersurfaces of quaternionic projective space obtaining among other results an improvement of the main theorem in [9].

Observations on a variant of compatibility

We consider a variation of the concept of compatible maps introduced by Hicks and Saliga [1], and obtain generalizations ofresults by Hicks and Saliga and others.

On the vertical bundle of a pseudo-Finsler manifold

We define the Liouville distribution on the tangent bundle of a pseudo-Finsler manifold and prove that it is integrable. Also, we find geometric properties of both leaves of Liouville distribution and the vertical distribution.

Existance theroms for the matrix Riccati equation W′

Sufficient conditions are established for the matrix Riccati equation to have a symmetric solution on a given interval. The criteria involve integral conditions on the coefficient matrices of the Riccati equation. The present results are compared with previously known results.

On Tucker's key theorem

A new proof of a (slightly extended) geometric version of Tucker's fundamental result is given.

A note on Riesz elements in C*-algebras

It is known that every Riesz operator R on a Hilbert space can be written R=Q

A class of generalized uniform asymptotic expansions

In [1] E. L. Reiss obtained a multivariable expansion of the problem L[y]≡y″

A Stone-Weierstrass theorem for group representations

It is well known that if G is a compact group and π a faithful (unitary) representation, then each irreducible representation of G occurs in the tensor product of some number of copies of π and its contragredient. We generalize this result to a separable type I locally compact group G as follows: let π be a faithful unitary representation whose matrix coefficient functions vanish...

Fixed-point-free embeddings of graphs in their complements

The following is proved: If G is a labeled (p,p−2) graph where p≥2, then there exists an isomorphic embedding ϕ of G in its complement G¯ such that ϕ has no fixed vertices. The extension to (p,p−1) graphs is also considered.

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...

(n-2)-tightness and curvature of submanifolds with boundary

The purpose of this note is to establish a connection between the notion of (n−2)-tightness in the sense of N.H. Kuiper and T.F. Banchoff and the total absolute curvature of compact submanifolds-with-boundary of even dimension in Euclidean space. The argument used is a certain geometric inequality similar to that of S.S. Chern and R.K. Lashof where equality characterizes (n−2...

A note on the homomorphism theorem for hemirings

The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K).

Generalized Beatty sequences

A well-known result due to S. Beatty is that if α and β are positive irrational numbers satisfying α−1

Sign changes in linear combinations of derivatives and convolutions of Polya frequency functions

We obtain upper bounds on the number of sign changes of linear combinations of derivatives and convolutions of Polya frequency functions using the variation diminishing properties of totally positive functions. These constitute extensions of earlier results of Karlin and Proschan.

Rings with a finite set of nonnilpotents

Let R be a ring and let N denote the set of nilpotent elements of R. Let n be a nonnegative integer. The ring R is called a θn-ring if the number of elements in R which are not in N is at most n. The following theorem is proved: If R is a θn-ring, then R is nil or R is finite. Conversely, if R is a nil ring or a finite ring, then R is a θn-ring for some n. The proof of this...

Equivalence classes of matrices over a finite field

Let Fq=GF(q) denote the finite field of order q and F(m,q) the ring of m×m matrices over Fq. Let Ω be a group of permutations of Fq. If A,BϵF(m,q) then A is equivalent to B relative to Ω if there exists ϕϵΩ such that ϕ(A)=B where ϕ(A) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced...

Existence theorem for the difference equation Yn

For the difference equation (Yn

Mean-periodic functions

We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn)). This extends to n-variables the work of L. Schwartz on mean-periodicity and also extends L. Ehrenpreis

Closed form bound-state perturbation theory

The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner...

Generalized Köthe-Toeplitz duals

The α and β-duals spaces of generalized ℓp spaces are characterized, where 0<p≤∞. The question of when the α and β dual spaces coincide is also considered.

Operator representation of weakly Cauchy sequences in projective tensor products of Banach spaces

It is shown that the above sequences always determine linear transformations and if the sequences are bounded under the least cross norm, that the transformations are continuous. Such operators are characterized to within algebraic isomorphism with the weak-star sequential closure of the tensor product space in its second dual, and consequently certain classes of weakly...

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.