共查询到20条相似文献,搜索用时 93 毫秒
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John Jones 《Mathematics and computers in simulation》1983,25(6):489-492
The main purpose of this work is to establish necessary conditions and sufficient conditions for the existence of a solution of matrix equations whose coefficient matrices have elements belonging to the ring of polynomials in n variables with complex coefficients and the ring of rational functions a(z1,z2,…zn)b(z1,z2,…,zn)?1 with real coefficients and b(z1,z2,…,zn)≠0 for all (z1,z2,…,zn) in Rn. Results obtained are useful in multidimensional systems theory and elsewhere. 相似文献
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M. Delfour 《Computer Methods in Applied Mechanics and Engineering》1985,50(3):231-261
Let Ω be a polygonal domain in , τh an associated triangulation and uh the finite element solution of a well-posed second-order elliptic problem on (Ω, τh). Let M = {Mi}p + qi = 1 be the set of nodes which defines the vertices of the triangulation τh: for each i, in Rn. The object of this paper is to provide a computational tool to approximate the best set of positions M? of the nodes and hence the best triangulation which minimizes the solution error in the natural norm associated with the problem.The main result of this paper are theorems which provide explicit expressions for the partial derivatives of the associated energy functional with respect to the coordinates xil, 1 ? l ? n, of each of the variable nodes Mi, i = 1,…, p. 相似文献
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Bezier's method is one of the most famous in computational geometry. In his book Numerical control Bezier gives excellent expositions of the mathematical foundations of this method. In this paper a new expression of the functions {fn,i(u)} is obtained.Using this formula, we have not only derived some properties of the functions {fn,i(u)} (for instance and functions {fn,i(u)} increase strictly at [0, 1] etc) but also simplified systematically all the mathematical discussions about Bezier's method.Finally we have proved the plotting theorem completely by matrix calculation. 相似文献
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《Computers & Mathematics with Applications》2003,45(6-9):1059-1073
We extend Henry Poincaré's normal form theory for autonomous difference equations χk + 1 = f(χk) to nonautonomous difference equations χk + 1 = fk(χk). Poincaré's nonresonance condition for eigenvalues is generalized to the new nonresonance condition λj∪ for spectral intervals. 相似文献
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J.L. Brown 《Information Sciences》1977,12(2):93-103
A given deterministic signal x(.) is distorted by passing it through a linear time-invariant filter and also by subjecting it to the action of an instantaneous nonlinearity. The resulting time crosscorrelation of the two distorted versions of the original signal is expressed by the function , where x(.) is the given signal, k(.) is the nonnegative definite impulse response of the linear filter, and g(.) is the output-input characteristic of the zero-memory nonlinear device. The problem considered is that of determining conditions on the pair (x,g) such that R2(s) ? R2(0) for all s and any choice of nonnegative definite filter function k; the principal result is the formulation of a necessary and sufficient condition for R2 to have a global maximum at the origin. In particular, the peak value occurs at the origin if and only if is real and nonnegative for all ω ? 0, where Gx(.) and X(.) are the Fourier transforms of g[x(.)] and x(.), respectively. An equivalent condition is that the correlation function , previously studied by Richardson, be nonnegative definite.Several examples are given, and it is shown that, unlike the case for R1(.), monotonicity of g(.) is not a sufficient condition for R2(.) to have a global maximum at s = 0 independently of the choice of filter characteristic k. Certain extensions of these results are given for the case when x(.) is a Gaussian random input. 相似文献
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Minoru Ito Motoaki Iwasaki Kenichi Taniguchi Tadao Kasami 《Theoretical computer science》1984,34(3):315-335
In relational databases, a query can be formulated in terms of a relational algebra expression using projection, selection, restriction, cross product and union. In this paper, we consider a problem, called the membership problem, of determining whether a given dependency d is valid in a given relational expression E over a given database scheme R that is, whether every instance of the view scheme defined by E satisfies d (assuming that the underlying constraints in R are always satisfied).Consider the case where each relation scheme in R is associated with functional dependencies (FDs) as constraints, and d is an FD. Then the complement of the membership problem is NP-complete. However, if E contains no union, then the membership problem can be solved in polynomial time. Furthermore, if E contains neither a union nor a projection, then we can construct in polynomial time a cover for valid FDs in E, that is, a set of FDs which implies every valid FD in E.Consider the case where each relation scheme in R is associated with multivalued dependencies (MVDs) as well as FDs, and d is an FD or an MVD. Even if E consists of selections and cross products only, the membership problem is NP-hard. However, if E contains no union, and each relation scheme name in R occurs in E at most once, then the membership problem can be solved in polynomial time. As a corollary of this result, it can be determined in polynomial time whether a given FD or MVD is valid in , where R1,…,Rs are relation schemes with FDs and MVDs, and is the natural join of Ri and Rj. 相似文献
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Andrew Chi-Chih Yao 《Theoretical computer science》1982,19(2):203-218
Extending a result of Borodin et al. [1], we show that any branching program using linear queries “∑iλixi:c” to sort n numbers x1, x2,…,xn must satisfy the time-space tradeoff relation . The same relation is also shown to be true for branching programs that uses queries “min R = ?” where R is any subset of {x1, x2,…,xn}. 相似文献
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Using the result of Heintz and Sieveking [1], we show that the polynomials with b positive real different from one, and Σ1?j?djrXj with r rational not integer, are hard to compute. 相似文献
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《Theoretical computer science》2002,284(2):199-206
We discuss the uniform computational complexity of the derivatives of C∞-functions in the model of Ko and Friedman (Ko, Complexity Theory of Real Functions, Birkhäuser, Basel, 1991; Ko, Friedman, Theor. Comput. Sci. 20 (1982) 323–352). We construct a polynomial time computable real function g∈C∞[−1,1] such that the sequence is not bounded by any recursive function. On the other hand, we show that if f∈C∞[−1,1] is polynomial time computable and the sequence of the derivatives of f is uniformly polynomially bounded, i.e., |f(n)(x)| is bounded by 2p(n) for all x∈[−1,1] for some polynomial p, then the sequence is uniformly polynomial time computable. 相似文献
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William P. Wardlaw 《Computers & Education》1978,2(3):247-257
Two examples are given in which the computer was used to supplement intuition in abstract algebra. In the first example, the computer was used to search Cayley tables of 4 element groupoids to find those which are 5-associative but not 4-associative. (n-associative means that the product of any n elements is independent of the way the factors are grouped by parentheses.) The computer generated examples suggested the existence of n element groupoids which are (2n?2+1)-associative but not (2n-2)-associative, for each integer n≧4.In the second example, the computer counted the numbers g2(m) of invertible 2×2 matrices with entries chosen from the ring Zmof integers, for m = 2, 3, 4,…, 18. The insight gained from these results led to a proof that there are invertible n×n matrices over Zm.Some applications to graduate and undergraduate instruction are indicated. 相似文献
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Gilbert G. Walter 《Information Sciences》1983,30(1):67-77
In the classification problem the value of the discrete random variable I must be estimated from that of a random variable X given a random sample (I1, X1),(I2, X2),…,(In, Xn). A classification rule giving such an estimate can be based on most nonparametric density estimators which are based on delta sequences. The rate at which the nonerror rate for this rule converges to the optimal is calculated. It is found to be , where d is the dimension of the variable X under mild assumptions on the densities. A procedure for choosing an associated parameter for small samples is given. 相似文献
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《Computers & Mathematics with Applications》2003,45(6-9):1445-1460
We consider the boundary value problem where m ≥ 1 and (−1)m f Rm → [0, ∞) is continuous. By using Amann and Leggett-Williams' fixed-point theorems, we develop growth conditions on f so that the boundary value problem has triple positive symmetric solutions. The results obtained are then applied in the investigation of radial solutions for certain partial difference equation subject to Lidstone type conditions. 相似文献
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Roger D. Nussbaum 《Systems & Control Letters》1983,3(5):243-246
A.S. Morse has raised the following question: Do there exist differentiable functions with the property that for every nonzero real number λ and every (x0, y0) ∈ 2 the solution (x(t),y(t)) of , , , is defined for all t ? 0 and satisfies and y(t) is bounded on [0,∞)? We prove that the answer is yes, and we give explicit real analytic functions f and g which work. However, we prove that if f and g are restricted to be rational functions, the answer is no. 相似文献
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An upperbound to the probability of error per class in a multivariate pattern classification is derived. The bound, given by is derived with minimal assumptions; specifically the mean vectors exist and are distinct and the covariance matrices exist and are non-singular. No other assumptions are made about the nature of the distributions of the classes. In equation (i) N is the number of features in the feature (vector) space and Ri is a measure of the “radial neighbourhood” of a class. An expression for Ri is developed. A comparison to the multivariate Gaussian hypothesis is presented. 相似文献