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This paper describes the information systems as a family of equivalence relations or functions. It brings forward the notion of separation polynomial, which is an expression found by the separators (complement of the equivalence relations) via finite union operations and intersection operations. This paper adopts the minimal element method, simplified the conversion from separation disjunctive normal...
Term rewriting is a branch of theoretical computer science which combines elements of logic, universal algebra, automated theorem proving and functional programming, it has lots of application in math and computer field. Termination is a very important property of term rewriting system, and the standard detected measure is constructing a reduction order, but a right order is difficult to construct...
A new method for the parameterization of quadric surfaces is presented. To parameterize a general quadric implicit surface, the new method first translates the implicit surface to make it pass through the origin point, and then the parametric surface is obtained by substituting the coefficients of the implicit equation into the parameterization formula. As to the parameterization of a quadric implicit...
ElGamal digital signature scheme was analyzed. To overcome the shortage of ElGamal signature without message recovery, it was improved. Moreover, a kind of digital signature scheme with the function of message recovery was proposed. The security of the new scheme is based on the difficult solution of discrete logarithm on limited domain, which is as same as that of ElGamal signature scheme. Then,...
In this paper, we design a ternary even symmetric 2n-point approximating subdivision scheme which generates smooth curves of high order. We illustrate the technique with a new 4-point ternary approximating subdivision scheme which is C4 and a new 6-point ternary approximating subdivision scheme which can achieve C7-continuity. The smoothness of the new schemes is proved using Laurent polynomials.
The notion of sos-convexity has recently been proposed as a tractable sufficient condition for convexity of polynomials based on a sum of squares decomposition of the Hessian matrix. A multivariate polynomial p(x) = p(x1,...,xn)is said to be sos-convex if its Hessian H(x) can be factored as H(x) = MT(x)M(x) with a possibly nonsquare polynomial matrix M(x). The problem of deciding sos-convexity of...
Based on the p-ary subdivision rules for B-splines, we show how to design more general subdivision schemes that preserve the B-spline smoothness exactly or almost. We illustrate the technique with new 4-point C5 binary, 4-point C3 ternary and C4 ternary subdivision schemes.
The problem of approximating rational curves by polynomial curves is studied in this paper. A simple method of approximation, which uses the control points of the degree-elevated curve to approximate the original rational curve, is introduced at first. Meanwhile as to achieve better efficiency, the idea of re-parameterization of rational Bezier curves is presented. The re-parameterization makes uniform...
A novel method is proposed for the digital redesign of analogue controllers with account for the closed-loop system performance in continuous time. The method, which is based on a two-level optimization algorithm, makes it possible to place the closed-loop poles inside a specified region of the complex plane and provides for reduced-order controllers. The effectiveness of the proposed technique is...
Gaussian Periods, the basis of the theory of compass and straightedge construction, introduced by Gauss, play an important role in the history of mathematics. An efficient way of computing minimal polynomials of Gaussian Periods is proposed. Compared with other methods, the method which is much simpler and much easier to be implemented can avoid approximate computation because its progress is completed...
Based on Lagrange polynomials and variation of constants, we devise a novel 2n-1-point interpolatory ternary subdivision scheme that reproduces polynomials of degree 2n-2. We illustrate the technique with a 3-point ternary interpolatory subdivision scheme which can rebuild Hassan and Dodgson's interpolating 3-point ternary subdivision scheme and a new 5-point ternary interpolatory subdivision scheme...
In this paper we present general Julia sets of non-analytic families z??n+ c (n 3 2), we also propose some properties of these general Julia sets. Moreover, by iterated function systems theory, we give out two estimations of Hausdorff dimension of these general Julia sets when |c| is sufficient large or sufficient small.
We observe that the termination of linear programs relies only on the initial value of program variables and the iteration count. Based on such observation, we present a constructive approach to determine the termination of linear programs. Through our approach, we can also synthesis the termination condition of linear programs if they do not terminate on all inputs, and correct termination defect.
The main purpose of this paper is to study the mean value of square for sum analogous to the generalized Dedekind sum by using the mean value Theorem of Dirichlet L-functions. Based these asymptotic propertis, an interesting asymptotic formula is obtained about the mean value of square for sum analogous to the generalized Dedekind sum. These results improve and generalize some recent known results...
The goal of this paper is to present novel metrics for system usability assessment and quality assessment (SQA). Proposed metrics should provide means of capturing overall system interference with regular daily routines and habits of system users, referred to as "attentive interference". We argue that assuring the system is attentive proves essential when trying to mitigate risks related...
A new model of triangular Ball surface is proposed with its quadratic complexity. It can be constructed from the idea of Wang-Ball univaritate functions and Wang algorithm. The new bivariate basis functions look analogous to the Wang-Ball polynomials. Evaluating points on a curve can be calculated from the new recursive algorithm that is proved to be quadratic, O(n2). Thus, the calculation time is...
A recent proposed model for triangular DP surfaces provided in has been found that there is an inappropriate property in its recurrence formulae. It is lack of convexity, i.e., the summation of blending functions is not equal to one. This paper presents a new triangular DP surfaces that possesses the convexity property and quadratic evaluation complexity. These two characteristics are realized to...
We exhibit a deterministic concurrent reachability game PURGATORYn with n non-terminal positions and a binary choice for both players in every position so that any positional strategy for Player 1 achieving the value of the game within given isin < 1/2 must use non-zero behavior probabilities that are less than (isin2/(1 - isin))2n-2 . Also, even to achieve the value within say 1 - 2-n/2, doubly...
We present a method for the synthesis of non-linear ranking function of a program loop. Based on the region-based search, it reduces the non-linear ranking function discovering to the inequality checking. The inequality prover BOTTEMA then can be utilized to check validity for inequalities. In contrast to other approaches, the new approach can also discover the ranking function with the radicals due...
Quadratic Bezier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bezier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G1 quadratic Bezier curves satisfying given endpoint (positions and arbitrary...
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