共查询到20条相似文献,搜索用时 781 毫秒
1.
Tengyao Wang Joshua M. Weiss 《Journal of Computational and Applied Mathematics》2011,236(6):1497-1501
We devise an efficient algorithm that, given points z1,…,zk in the open unit disk D and a set of complex numbers {fi,0,fi,1,…,fi,ni−1} assigned to each zi, produces a rational function f with a single (multiple) pole in D, such that f is bounded on the unit circle by a predetermined positive number, and its Taylor expansion at zi has fi,0,fi,1,…,fi,ni−1 as its first ni coefficients. 相似文献
2.
Matthias Reitzner 《Advances in Mathematics》2005,191(1):178-208
Choose n random points in , let Pn be their convex hull, and denote by fi(Pn) the number of i-dimensional faces of Pn. A general method for computing the expectation of fi(Pn), i=0,…,d−1, is presented. This generalizes classical results of Efron (in the case i=0) and Rényi and Sulanke (in the case i=d−1) to arbitrary i. For random points chosen in a smooth convex body a limit law for fi(Pn) is proved as n→∞. For random points chosen in a polytope the expectation of fi(Pn) is determined as n→∞. This implies an extremal property for random points chosen in a simplex. 相似文献
3.
We assume T1,...,Tn are i.i.d.data sampled from distribution function F with density function f and C1,...,Cn are i.i.d.data sampled from distribution function G.Observed data consists of pairs(Xi,δi),i=1,...,n,where Xi=min{Ti,Ci},δi=I(Ti Ci),I(A)denotes the indicator function of the set A.Based on the right censored data{Xi,δi},i=1,...,n,we consider the problem of estimating the level set{f c}of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators.Under some regularity conditions,we establish the asymptotic normality and the exact convergence rate of theλg-measure of the symmetric difference between the level set{f c}and its plug-in estimator{fn c},where f is the density function of F,and fn is a kernel-type density estimator of f.Simulation studies demonstrate that the proposed method is feasible.Illustration with a real data example is also provided. 相似文献
4.
Xiaoling Wang Chung-Chun Yang 《Journal of Mathematical Analysis and Applications》2006,324(1):373-380
We investigate the factorization of entire solutions of the following algebraic differential equations:
bn(z)finjn(f′)+bn−1(z)fin−1jn−1(f′)+?+b0(z)fi0j0(f′)=b(z), 相似文献
5.
Peter C. Fishburn 《Discrete Applied Mathematics》1984,7(2):131-140
Suppose each of an odd number n of voters has a strict preference order on the three ‘candidates’ in {1,2,3} and votes for his most preferred candidate on a plurality ballot. Assume that a voter who votes for i is equally likely to have ijk and ikj as his preference order when {i,j,k} = {1,2,3}.Fix an integer m between (n + 1) and n inclusive. Then, given that ni of the n voters vote for i, let fm(n1,n2,n3) be the probability that one of the three candidates is preferred by m or more voters to each of the other two.This paper examines the behavior of fm over the lattice points in Ln, the set of triples of non-negative integers that sum to n. It identifies the regions in Ln where fm is 1 and where fm is 0, then shows that fm(a,b + 1, c)>fm(a + 1,b,c) whenever a + b + c + 1 = n, a≤c≤b, a<c<m and c≤n ? m. These results are used to partially identify the points in Ln where fm is minimized subject to fm>0. It is shown that at least two of the ni are equal at minimizing points. 相似文献
6.
R.P Anstee 《Journal of Algorithms in Cognition, Informatics and Logic》1985,6(1):112-131
Let G be a multigraph on n vertices, possibly with loops. An f-factor is a subgraph of G with degree fi at the ith vertex for i = 1, 2,…, n. Tutte's f-factor theorem is proved by providing an algorithm that either finds an f-factor or shows that it does not exist and does this in O(n3) operations. Note that the complexity bound is independent of the number of edges of G and the degrees fi. The algorithm is easily altered to handle the problem of looking for a symmetric integral matrix with given row and column sums by assigning loops degree one. A (g,f)-factor is a subgraph of G with degree di at the ith vertex, where gi ? di ? fi, for i = 1,2,…, n. Lovasz's (g,f)-factor theorem is proved by providing an O(n3) algorithm to either find a (g,f)-factor or show one does not exist. 相似文献
7.
Marc Prevost 《Journal of Computational and Applied Mathematics》1983,9(4):333-346
The interpolation of the function x → 1/(1 ? xt) generating the series f(t) = ∑∞i = 0citi at the zeros of an orthogonal polynomial with respect to a distribution d α satisfying some conditions will give us a process for accelerating the convergence of fn(t) = ∑ni = 0citi. Then, we shall see that the polynomial of best approximation of x → 1/(1 ? xt) over some interval or its development in Chebyshev polynomials Tn or Un are only particular cases of the main theorem.At last, we shall show that all these processes accelerate linear combinations with positive coefficients of totally monotonic and oscillating sequences. 相似文献
8.
Fabio Zanolin 《Results in Mathematics》1992,21(1-2):224-250
We prove the existence of periodic solutions in a compact attractor of (R+)n for the Kolmogorov system x′i = xifi(t, x1, …, xn), i = l, …, n in the competitive case. Extension to differential delay equations are con- sidered too. Applications are given to Lotka-Volterra systems with periodic coefficients. 相似文献
9.
We investigate the convergence of simultaneous Hermite-Padé approximants to then-tuple of power series $$f_i (z) = \sum\limits_{k = 0}^\infty {C_k^{(i)} z^k ,} i = 1,2,...,n,$$ where $$C_0^{(i)} = 1;C_k^{(i)} = \prod\limits_{p = 0}^{k - 1} {\frac{1}{{(C - q^{\gamma i + p} )}},} k \ge 1.$$ HereC, q∈?, γ i ∈?,i=1, 2,...,n. For |C|≠1, ifq=eiθ, θ∈(0, 2π) and θ/2π is irrational, eachf i (z),i=1,...,n, has a natural boundary on its circle of convergence. We show that “close-to-diagonal” and other sequences of Hermite-Padé approximants converge in capacity to (f 1(z),..., fn (z)) inside the common circle of convergence of eachf i (z),i=1,...,n. 相似文献
10.
A continuous function f from a continuum X onto a continuum Y is quasi-monotone if, for every subcontinuum M of Y with nonvoid interior, f-1(M) has a finite number of components each of which is mapped onto M by f. A θn-continuum is one that no subcontinuum separates into more than n components. It is known that if f is quasi-monotone and X is a θ1-continuum, then Y is a θ1-continuum or a θ2-continuum that is irreducible between two points. Examples are given to show that this cannot be generalized to a θn-continuum and n + 1 points for any n >1, but it is proved that if f is quasi-monotone and X is a θn-continuum, then Y is a θn-continuum or a θn+1-continuum that is the union of n + 2 continua H,S1,S2,…,Sn+1, whe for each i, Si is the closure of a component of Y H, Si is irreducible from some point Pi to H, and H is irreducible about its boundary. Some theorems and examples are given concerning the preservation of decomposition elements by a quasi-monotone map defined on a θn-continuum that admits a monotone, upper-semicontinuous decomposition onto a finite graph. 相似文献
11.
Gil Kalai 《Israel Journal of Mathematics》1984,48(2-3):161-174
LetK 1,…Kn be convex sets inR d. For 0≦i denote byf ithe number of subsetsS of {1,2,…,n} of cardinalityi+1 that satisfy ∩{K i∶i∈S}≠Ø. We prove:Theorem.If f d+r=0 for somer r>=0, then {fx161-1} This inequality was conjectured by Katchalski and Perles. Equality holds, e.g., ifK 1=…=Kr=Rd andK r+1,…,Kn aren?r hyperplanes in general position inR d. The proof uses multilinear techniques (exterior algebra). Applications to convexity and to extremal set theory are given. 相似文献
12.
M.S. Stawski 《Journal of Number Theory》1983,16(1):75-86
Let U = U0 × U1 × … × Un be an open polyring in a non-Archimedean valued, locally non-compact field. Let the function f be defined in the polyring U and satisfy the following conditions: (1) f is holomorphic for every x ∈ U0 separately in each of the rest variables yi ∈ Ui, i = 1, 2,…,n; (2) f is holomorphic in x ∈ U0 for every (y1,…,yn) ∈ V1 × … × Vn, where Vi is a certain disk from the ring Ui. Then, if the valuation is dense, the function f is holomorphic in the polyring U. If the valuation is discrete, then the function f is holomorphic in a domain close to the polyring U. 相似文献
13.
ChaoHua Jia 《中国科学 数学(英文版)》2012,55(3):465-474
If n is a positive integer,let f (n) denote the number of positive integer solutions (n 1,n 2,n 3) of the Diophantine equation 4/n=1/n1 + 1/n2 + 1/n3.For the prime number p,f (p) can be split into f 1 (p) + f 2 (p),where f i (p) (i=1,2) counts those solutions with exactly i of denominators n 1,n 2,n 3 divisible by p.In this paper,we shall study the estimate for mean values ∑ p相似文献
14.
For a number ? > 0 and a real function f on an interval [a, b], denote by N(?, f, [a, b]) the least upper bound of the set of indices n for which there is a family of disjoint intervals [a i , b i ], i = 1, …, n, on [a, b] such that |f(a i ) ? f(b i )| > ? for any i = 1, …, n (sup Ø = 0). The following theorem is proved: if {f j } is a pointwise bounded sequence of real functions on the interval [a, b] such that n(?) ≡ lim sup j→∞ N(?, f j , [a, b]) < ∞ for any ? > 0, then the sequence {f j } contains a subsequence which converges, everywhere on [a, b], to some function f such that N(?, f, [a, b]) ≤ n(?) for any ? > 0. It is proved that the main condition in this theorem related to the upper limit is necessary for any uniformly convergent sequence {f j } and is “almost” necessary for any everywhere convergent sequence of measurable functions, and many pointwise selection principles generalizing Helly’s classical theorem are consequences of our theorem. Examples are presented which illustrate the sharpness of the theorem. 相似文献
15.
Ivan Soprunov 《Journal of Pure and Applied Algebra》2007,209(2):383-392
We consider families of sparse Laurent polynomials f1,…,fn with a finite set of common zeros Zf in the torus Tn=(C−{0})n. The global residue assigns to every Laurent polynomial g the sum of its Grothendieck residues over Zf. We present a new symbolic algorithm for computing the global residue as a rational function of the coefficients of the fi when the Newton polytopes of the fi are full-dimensional. Our results have consequences in sparse polynomial interpolation and lattice point enumeration in Minkowski sums of polytopes. 相似文献
16.
Jarmila Chvátalová 《Discrete Mathematics》1975,11(3):249-253
If G is a graph with p vertices and at least one edge, we set φ (G) = m n max |f(u) ? f(v)|, where the maximum is taken over all edges uv and the minimum over all one-to-one mappings f : V(G) → {1, 2, …, p}: V(G) denotes the set of vertices of G.Pn will denote a path of length n whose vertices are integers 1, 2, …, n with i adjacent to j if and only if |i ? j| = 1. Pm × Pn will denote a graph whose vertices are elements of {1, 2, …, m} × {1, 2, …, n} and in which (i, j), (r, s) are adjacent whenever either i = r and |j ? s| = 1 or j = s and |i ? r| = 1.Theorem.If max(m, n) ? 2, thenφ(Pm × Pn) = min(m, n). 相似文献
17.
By the decomposition theorem dim X ≦ n if and only if X admits a decomposition into n+1 zero-dimensional subspaces Z i for i = 0,... n. If f: X → X is a homeomorphism, then under some dimensional restrictions on the set of periodic points, the Z i can be chosen to be images of Z 0 under iterates of f. 相似文献
18.
Yasuhiro Takeuchi Norihiko Adachi 《Journal of Mathematical Analysis and Applications》1981,79(1):141-162
This paper presents sufficient conditions for the existence of a nonnegative and stable equilibrium point of a dynamical system of Volterra type, (1) , for every q = (q1,…, qn)T?Rn. Results of a nonlinear complementarity problem are applied to obtain the conditions. System (1) has a nonnegative and stable equilibrium point if (i) f(x) = (f1(x),…,fn(x))T is a continuous and differentiable M-function and it satisfies a certain surjectivity property, or (ii), f(x) is continuous and strongly monotone on R+0n. 相似文献
19.
A. A. Agrachev 《Mathematical Notes》1974,16(4):897-900
We show that if Φ is an arbitrary countable set of continuous functions of n variables, then there exists a continuous, and even infinitely smooth, function ψ(x1,...,xn) such that ψ(x 1, ...,x n ) ?g [? (f 1(x 1, ... ,f f (x n ))] for any function ? from Φ and arbitrary continuous functions g and fi, depending on a single variable. 相似文献
20.
《Finite Fields and Their Applications》2001,7(1):197-204
Let F be a finite field with q=pf elements, where p is a prime. Let N be the number of solutions (x1,…,xn) of the equation c1xd11+···+cnxdnn=c over the finite fields, where d1∣q−1, ciϵF*(i=1, 2,…,n), and cϵF. In this paper, we prove that if b1 is the least integer such that b1≥∑ni=1 (f/ri) (Di, p−1)/(p−1), then q[b1/f]−1∣N, where ri is the least integer such that di∣pri−1, Didi=pri−1, the (Di, p−1) denotes the greatest common divisor of Di and p−1, [b1/f] denotes the integer part of b1/f. If di=d, then this result is an improvement of the theorem that pb∣N, where b is an integer less than n/d, obtained by J. Ax (1969, Amer. J. Math.86, 255–261) and D. Wan (1988, Proc. AMS103, 1049–1052), under a certain natural restriction on d and n. 相似文献