In this paper we Studied the polynomial coefficients and approximation errors for functions of the form f(z) = ∑∞ k=1 qk(z)[γ(z)] k−1 belong to L(B), the class of all functions holomorphic on Caratheödory domain B. The lower (p, q)-order and generalized lower (p, q)-type with respect to proximate order have been characterized in terms of these polynomial coefficients and approximation errors.

data types. An abstract data type is a collection of objects together with a set of operations defined on those objects. Examples include sets, dictionaries (also known as key-value stores or associative arrays) and graphs. The operations associated with a data type fall into one of two categories: query operations, which return information about the objects; and update operations, which modify...

We analyze charge order in hole-doped cuprates within the the spin-fermion model. We show that a magnetically mediated interaction, which is known to give rise to d-wave superconductivity and charge order with momentum along zone diagonal, also gives rise to charge order with momenta Qx = (2Q,0) and Qy = (0,2Q) consistent with the experiments. We show that an instability towards Qk = 〈c k+Qck−Q...

We present a program to measure the parton densities in the pomeron using diffractive deep inelastic scattering and diffractive photoproduction, and to test the resulting parton densities by applying them to other processes such as the diffractive production of jets in hadron-hadron collisions. Since QCD factorization has been predicted not to apply to hard diffractive scattering, this program ...

In this paper, we introduce the notion of q-quasiadditivity of arithmetic functions, as well as the related concept of q-quasimultiplicativity, which generalise strong q-additivity and -multiplicativity, respectively. We show that there are many natural examples for these concepts, which are characterised by functional equations of the form f(qk+ra+b) = f(a)+f(b) or f(qk+ra+b) = f(a)f(b) for al...

Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy le...

In various frameworks, to assess the joint distribution of a kdimensional random vector X = (X1, . . . , Xk), one selects some putative conditional distributions Q1, . . . , Qk. Each Qi is regarded as a possible (or putative) conditional distribution for Xi given (X1, . . . , Xi−1, Xi+1, . . . , Xk). The Qi are compatible if there is a joint distribution P for X with conditionals Q1, . . . , Qk...

In the topology of coordinatewise convergence ∇∞ is a compact, metrizable and separable space. Denote by C(∇∞) the algebra of real continuous functions on ∇∞ with pointwise operations and the supremum norm. In C(∇∞) there is a distinguished dense subspace F := R [q1, q2, . . . ] generated (as a commutative unital algebra) by algebraically independent continuous functions qk(x) := ∑∞ i=1 x k+1 i...

We present new constructions for (n, w, λ) optical orthogonal codes (OOC) using techniques from finite projective geometry. In one case codewords correspond to (q − 1)-arcs contained in Baer subspaces (and, in general, kth-root subspaces) of a projective space. In the other construction, we use sublines isomorphic to PG(1, q) lying in a projective plane isomorphic to PG(1, qk), k > 1. Our const...