we have applied the method of integration of the heisenberg equation of motion proposed by bender and dunne, and m. kamella and m. razavy to the potential v(q) = v q - µ q with linear and nonlinear dissipation. we concentrate our calculations on the evolution of basis set of weyl ordered operators and calculate the mean position , velocity , the commutation relation [q, p], and the energy of pa...

Ordered sheaves on a small quantaloid Q have been defined in terms of Q-enriched categorical structures; they form a locally ordered category Ord(Q). It has previously been shown by the second author that the " free-cocompletion " KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as category of Eilenberg-Moore algebras. In the first part of this paper we apply Q-enriched category t...

Let B be a complex unital Banach algebra. We consider the Banach algebra A = B × C ordered by the algebra cone K = {(a, ξ) ∈ A : ‖a‖ ≤ ξ}, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in B. 1. Ordered Banach algebras The aim of this paper is to stress the aspect of the applicability of the ordered Banach algebra...

Ordered sheaves on a small quantaloid Q have been defined in terms of Qenriched categorical structures; they form a locally ordered category Ord(Q). The free-cocompletion KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as category of Eilenberg-Moore algebras. In this paper we give an intrinsic description of the Kleisli algebras: we call them the locally principally generated Q-m...

The ideal extensions of semigroups—without order—have been first considered by Clifford (1950). In this paper, we give the main theorem of the ideal extensions for ordered sets. If P , Q are disjoint ordered sets, we construct (all) the ordered sets V which have an ideal P ′ which is isomorphic to P , and the complement of P ′ in V is isomorphic toQ. Conversely, we prove that every extension of...

In this paper,The concept of a (∈,∈ ∨q)-fuzzy ideal in an ordered Abel-Grassmann groupoid is introduced. In partcicular, left regular ordered Abel-Grassmann groupoids are characterized by using the (∈ ,∈ ∨q)-fuzzy ideals.

For a coequality q we say that it is regular coequality on set X ordered under the antiorder ̨ if there exists an anti-order on X=q such that the natural mapping W X ! X=q is a reverse isotone surjection of anti-ordered sets. The lattice of regular coequalities is described. 2000 Mathematics Subject Classification: 03F65, 06F05

Approximate string matching with k differences is considered. Filtration of the text is a widely adopted technique to reduce the text area processed by dynamic programming. We present sublinear filtration algorithms based on the locations of q-grams in the pattern. Samples of q-grams are drawn from the text at fixed periods, and only if consecutive samples appear in the pattern approximately in...

An algorithm is described for finding the maximal weight chain between two points in a locally finite partial order under the restriction that all but • (or fewer) successive pairs in the chain belong to a given subset of the partial order relation. Applications of the method in molecular genetics, critical path scheduling, and other fields are discussed. Let P be a set with two locally finite ...