828 research outputs found
Generalized Frobenius Number of Three Variables
For , we let be a -tuple
of positive integers with and, for a
non-negative integer , the generalized Frobenius number of , , the largest integer that has at most
representations in terms of with non-negative integer
coefficients. In this article, we give a formula for the generalized Frobenius
number of three positive integers with certain conditions.Comment: 13 pages, comments welcom
The girth, odd girth, distance function, and diameter of generalized Johnson graphs
For any non-negative integers , the {\em generalized Johnson
graph}, , is the undirected simple graph whose vertices are the
-subsets of a -set, and where any two vertices and are adjacent
whenever . In this article, we derive formulas for the girth,
odd girth, distance function, and diameter of
Means of iterates
We determine continuous bijections f, acting on a real interval into itself, whose
k-fold iterate is the quasi-arithmetic mean of all its subsequent iterates from f0 up to fn
(where 0 k n). Namely, we prove that if at most one of the numbers k, n is odd, then
such functions consist of at most three affine pieces
Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions
2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15By making use of the fractional differential operator Ω^λz (0 ≤ λ < 1) due
to Owa and Srivastava, a new subclass of univalent functions denoted by
k−SPλ (0 ≤ k < ∞) is introduced. The class k−SPλ unifies the concepts of
k-uniformly convex functions and k-starlike functions. Certain basic
properties of k − SPλ such as inclusion theorem, subordination theorem, growth
theorem and class preserving transforms are studied.* The present investigation is partially supported by National Board
for Higher Mathematics, Department of Atomic Energy, Government of
India under Grant No. 48/2/2003-R&D-I
Iso-array rewriting P systems with context-free iso-array rules
A new computing model called P system is a highly distributed and
parallel theoretical model, which is proposed in the area of membrane computing. Ceterchi et al. initially proposed array rewriting P systems by extending the notion of string rewriting P systems to arrays (2003). A theoretical model for picture generation using context-free iso-array grammar rules and puzzle iso-array grammar rules are introduced by Kalyani et al. (2004, 2006). Also iso-array rewriting P systems for iso-picture languages have been studied by Annadurai et al. (2008). In this paper we consider the context-free iso-array rules and context-free puzzle iso-array rules in iso-array rewriting P systems and examine the generative powers
of these P systems
Arithmetic functions and fixed points of powers of permutations
Let be a permutation of a nonempty finite or countably infinite set
and let count the number of fixed points of the
th power of . This paper explains how the arithmetic function determines the
conjugacy class of the permutation , constructs an algorithm to compute
the conjugacy class from the fixed point counting function , and describes the arithmetic functions that are fixed point
counting functions of permutations.Comment: Revised and corrected; 10 page
Byg og hold bøtte!
Sven-Olov Wallenstein: The Silences of Mies, Stockholm 2008 (Axl Books
A geometrical approach to the motion planning problem for a submerged rigid body
The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique
- …