Asian-European Journal of Mathematics

We determine all V-proper hypersubstitutions for the variety of pseudo-complemented semilattices. Moreover, for any monoid of hypersubstitutions we will give the greatest M-solid variety of pseudo-complemented semilattices.

We perform a parameter-dependent pseudo-differential calculus of operators on a corner manifold and construct specific order reducing elements in the corresponding operator algebras.

This paper is concerned with Cauchy problem, Lyapunov transformations, Floquet and Lyapunov theorems for linear implicit dynamic equation A_tx^Δ = B_tx with index-1 on time scales. The stability of this equation under the act of these Lyapunov transformations is also considered. The results are a unification and generalization of previous results for differential-algebraic equations and implicit difference systems.

We construct suitable Boehmian spaces which are properly larger than and we extend the Fourier sine transform and the Fourier cosine transform more than one way. We prove that the extended Fourier sine and cosine transforms have expected properties like linear, continuous, one-to-one and onto from one Boehmian space onto another Boehmian space. We also establish that the well known connection among the Fourier transform, Fourier sine transform and Fourier cosine transform in the context of Boehmians. Finally, we compare the relations among the different Boehmian spaces discussed in this paper.

If X and Y are sets, we let P(X, Y) denote the set of all partial transformations from X into Y (that is, all mappings whose domain and range are subsets of X and Y, respectively). If θ ∈ P(Y, X), then P(X, Y) is a so-called "generalized semigroup" of transformations under the "sandwich operation": α * β = α ◦ θ ◦ β, for each α, β ∈ P(X, Y). We denote this semigroup by P(X, Y, θ) and, in this paper, we characterize Green's relations on it: that is, we study equivalence relations which determine when principal left (or right, or 2-sided) ideals in P(X, Y, θ) are equal. This solves a problem raised by Magill and Subbiah in 1975. We also discuss the same idea for important subsemigroups of P(X, Y, θ) and characterize when these semigroups satisfy certain regularity conditions.

Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal.158 (1998) 209–241] introduced the Nonuniform multiresolution analysis (NUMRA) whose translation set is not a group. Farkov [Orthogonal p-wavelets on ℝ₊, in Proc. Int. Conf. Wavelets and Splines (St. Petersburg State University, St. Petersburg, 2005), pp. 4–26] studied multiresolution analysis (MRA) on positive half line and constructed associated wavelets. Meenakshi et al. [Wavelets associated with Nonuniform multiresolution analysis on positive half line, Int. J. Wavelets, Multiresolut. Inf. Process.10(2) (2011) 1250018, 27pp.] studied NUMRA on positive half line and proved the analogue of Cohen's condition for the NUMRA on positive half line. We construct the associated wavelet packets for such an MRA and study its properties.

We prove the theorem: Let R be a CN-semiring. If R is right divisible two sided uniform semiring, then R is a right local semiring.

The concept of annihilator ideals is introduced in C-algebras. Some properties of these annihilator ideals are studied and then proved that the class of all annihilator ideals forms a complete Boolean algebra. A set of equivalent conditions are obtained for every ideal of a C-algebra to become an annihilator ideal. Some properties of homomorphic images and inverse images of annihilators ideals of a C-algebra are studied.

We show that the special semigroup amalgam with core as a quasi-unitary subsemigroup is embedded in a semigroup. We also show that the special semigroup amalgam within the class of left [right] quasinormal bands is embeddable in a left [right] quasinormal band.

Let g be any real-valued, bounded and compactly supported function, whose integer-translates {T_kg}_k∈ℤ form a partition of unity. Based on a new construction of dual windows associated with Gabor frames generated by g, we present a method to explicitly construct dual pairs of Gabor frames. This new method of construction is based on a family of polynomials which is closely related to the Daubechies polynomials, used in the construction of compactly supported wavelets. For any k ∈ ℕ ∪ {∞} we consider the Meyer scaling functions and use these to construct compactly supported windows g ∈ C^k(ℝ) associated with a family of smooth compactly supported dual windows . For any n ∈ ℕ the pair of dual windows g, h_n ∈ C^k(ℝ) have compact support in the interval [-2/3, 2/3] and share the property of being constant on half the length of their support. We therefore obtain arbitrary smoothness of the dual pair of windows g, h_n without increasing their support.

We study the notion of Radford biproduct Hopf algebras in the Zunino category. As an application, we describe coquasitriangular structures on the Radford biproduct Hopf group algebras.

A subgroup H of a group G is called almost ascendant if H is ascendant in a subgroup K having finite index in G. We describe the structure of periodic groups whose subgroups are almost ascendant. The main result of this paper is following theorem. Let G be a periodic group whose subgroups are almost ascendant. Then G contains a normal finite subgroup K such that every subgroup of G/K is ascendant in G/K. In particular, G/K satisfies the normalizer condition.

The extendability of a continuous semi-metric on a Tychonoff space to a compactification of the space is discussed. The extended semi-metrics are continuous on compactifications, constructed through an axiomatic approach.