
The ATSP polytope can be expressed by an asymmetric polynomial-size linear program.
A model that represents the rate of changes of the population with limited environmental resources can be described by,
where
For a set
This paper investigates the existence of monadic balanced ternary designs (BTDs). A monadic BTD is a BTD where each size
are sufficient for the existence of monadic BTDs
We consider the placement of detection devices at the vertices of a graph
Recently, four new vertex colorings of graphs (in which adjacent vertices may be colored the same) were introduced for the purpose of distinguishing every pair of adjacent vertices. For each graph and for each of these four colorings, the minimum number of required colors never exceeds the chromatic number of the graph. In this paper, we summarize some of the results obtained on these colorings and introduce some relationships among them.
We address the problem: for which values of
Let
In this article we answer the question in the affirmative.
This paper considers the Lehmer matrix and its recursive analogue. The determinant of the Lehmer matrix is derived explicitly by both its LU and Cholesky factorizations. We further define a generalized Lehmer matrix with
Random number generators are a small part of any computer simulation project. Yet they are the heart and the engine that drives the project. Often times software houses fail to understand the complexity involved in building a random number generator that will satisfy the project requirements and will be able to produce realistic results. Building a random number generator with a desirable periodicity, that is uniform, that produces all the random permutations with equal probability, and at random, is not an easy task. In this paper we provide tests and metrics for testing random number generators for uniformity and randomness. These tests are in addition to the already existing tests for uniformity and randomness, which we modify by running each test a large number of times on sub-sequences of random numbers, each of length
For a connected graph
for every two distinct vertices
A graph
In this study, we analyze the structure of the full collineation group of certain Veblen-Wedderburn (VW) planes of orders
A Sarvate-Beam Quad System
In this paper, we present (by using Cauchy-Schwarz inequalities) some new results amongst the parameters of balanced arrays (B-arrays) with two symbols and having strength four, which are necessary for the existence of such balanced arrays. We then discuss and illustrate their use and applications.
The Oberwolfach problem (OP) asks whether
Let
We consider the problem of relocating a sensor node in its neighborhood so that the connectivity of the network is not altered. In this context, we introduce the notion of \in-free and out-free regions to capture the set of points where the node can be relocated by conserving connectivity. We present a characterization of maximal free-regions that can be used for identifying the position where the node can be moved to increase the reliability of the network connectivity. In addition, we prove that the free-region computation problem has a lower bound
Chain integrator backstepping is a recursive design tool that has been used in nonlinear control systems. The complexity of the computation of the chain integrator backstepping control law makes inevitable the use of a computer algebra system. A recursive algorithm is designed to compute the integrator backstepping control process. A computer algebra program (Maple procedure) is developed for symbolic computation of the control function using a newly developed recursive algorithm. We will present some demonstrative examples to show the stability of the control systems using Lyapunov functions.
Chain integrator backstepping is a recursive design tool that has been used in nonlinear control systems. The complexity of the computation of the chain integrator backstepping control law makes inevitable the use of a computer algebra system. A recursive algorithm is designed to compute the integrator backstepping control process. A computer algebra program (Maple procedure) is developed for symbolic computation of the control function using a newly developed recursive algorithm. We will present some demonstrative examples to show the stability of the control systems using Lyapunov functions.
Let
The intractability of the traditional discrete logarithm problem (DLP) forms the basis for the design of numerous cryptographic primitives. In
Beautifully Ordered Balanced Incomplete Block Designs,
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