共查询到20条相似文献,搜索用时 15 毫秒
1.
Wolfgang M Schmidt 《Advances in Mathematics》1980,38(2):128-151
If is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then there are integers x1,… xs not all zero, with |(x1,… xs)| < 1. 相似文献
2.
G.F Clements 《Journal of Combinatorial Theory, Series A》1984,37(1):91-97
Let kn ? kn?1 ? … ? k1 be positive integers and let () denote the coefficient of xi in . For given integers l, m, where 1 ? l ? kn + kn?1 + … + k1 and , it is shown that there exist unique integers m(l), m(l ? 1),…, m(t), satisfying certain conditions, for which . Moreover, any m l-subsets of a multiset with ki elements of type i, i = 1, 2,…, n, will contain at least different (l ? 1)-subsets. This result has been anticipated by Greene and Kleitman, but the formulation there is not completely correct. If k1 = 1, the numbers () are binomial coefficients and the result is the Kruskal-Katona theorem. 相似文献
3.
Chungming An 《Journal of Number Theory》1974,6(1):1-6
A Dirichlet series associated with a positive definite form of degree δ in n variables is defined by where ? ∈ , α ∈ n, 〈x, y〉 = x1y1 + ? + xnyn, e(a) = exp (2πia) for a ∈ , and s = σ + ti is a complex number. The author proves that: (1) DF(s, ?, α) has analytic continuation into the whole s-plane, (2) DF(s, ?, α), ? ≠ 0, is a meromorphic function with at most a simple pole at . The residue at is given explicitly. (3) ? = 0, α ? n, DF(s, 0, α) is analytic for . 相似文献
4.
Michio Ozeki 《Journal of Number Theory》1977,9(1):112-120
Let F1(x, y),…, F2h+1(x, y) be the representatives of equivalent classes of positive definite binary quadratic forms of discriminant ?q (q is a prime such that q ≡ 3 mod 4) with integer coefficients, then the number of integer solutions of Fi(x, y) = n (i = 1,…, 2h + 1) can be calculated for each natural number n using L-functions of imaginary quadratic field ((?q)1/2). 相似文献
5.
Let n be a positive integer, L a subset of {0, 1,…,n}. We discuss the existence of partitions (or tilings) of the n-dimensional binary vector space Fn into L-spheres. By a L-sphere around an x in Fn we mean {y ? Fn, d(x, y) ? L}, d(x, y) being the Hamming distance betwe en x and y. These tilings are generalizations of perfect error correcting codes. We show that very few such tilings exist (Theorem 2) and characterize them all for any L ? {0, 1,…,[n]}. 相似文献
6.
R.J Cook 《Journal of Number Theory》1983,17(1):80-92
Let k be an odd positive integer. Davenport and Lewis have shown that the equations with integer coefficients, have a nontrivial solution in integers x1,…, xN provided that Here it is shown that for any ? > 0 and k > k0(?) the equations have a nontrivial solution provided that 相似文献
7.
T.H Jackson 《Journal of Number Theory》1983,16(3):333-342
For an indefinite quadratic form f(x1, …, xn) let P(f) denote the greatest lower bound of the positive values assumed by f for integers x1, …, xn. This paper investigates the values of for nonzero ternary forms of signature ?1 and finds two new classes of forms with . 相似文献
8.
For a stationary autoregressive model of order s, the partial autocorrelation coefficients of order , =0,1,2,…,s?1, are defined; the partial autocorrelation coefficient of order zero being the same as the autocorrelation coefficient of order one. Denoting these s parameters by ?1,π1,…,πs?1, it is shown that their sample images, namely r1,1,…,s?1, are asymptotically independently normally distributed with means equal to the corresponding population values and asymptotic variances given by , where n is the size of the sample from the autoregressive process of order s. The partial correlogram of the model and application of the result are discussed. 相似文献
9.
If p is a polynomial with all roots inside the unit disc and C its companion matrix, then the Lyapunov equation has a unique solution for every positive semidefinite matrix P. We characterize sets of vectors x0,…,xn?1 and y0,…,yn?1 such that X = G(x0,…,xn?1)= G(y0,…, yn?1)-1. Geometrical connections between such bases and contractions with one- dimensional defect spaces are established. 相似文献
10.
A technique for the numerical approximation of matrix-valued Riemann product integrals is developed. For a ? x < y ? b, Im(x, y) denotes , and Am(x, y) denotes an approximation of Im(x, y) of the form , where ak and yik are fixed numbers for i = 1, 2,…, m and k = 1, 2,…, N and xik = x + (y ? x)yik. The following result is established. If p is a positive integer, F is a function from the real numbers to the set of w × w matrices with real elements and F(1) exists and is continuous on [a, b], then there exists a bounded interval function H such that, if n, r, and s are positive integers, , then Further, if F(j) exists and is continuous on [a, b] for j = 1, 2,…, p + 1 and A is exact for polynomials of degree less than p + 1 ? j for j = 1, 2,…, p, then the preceding result remains valid when Aj is substituted for Ij. 相似文献
11.
David Terman 《Journal of Differential Equations》1983,47(3):406-443
We consider the pure initial value problem for the system of equations , the initial data being (ν(x, 0), w(x, 0)) = (?(x), 0). Here , where H is the Heaviside step function and . This system is of the FitzHugh-Nagumo type and has several applications including nerve conduction and distributed chemical/ biochemical systems. It is demonstrated that this system exhibits a threshold phenomenon. This is done by considering the curve s(t) defined by s(t) = sup{x: v(x, t) = a}. The initial datum, ?(x), is said to be superthreshold if limt→∞ s(t) = ∞. It is proven that the initial datum is superthreshold if ?(x) > a on a sufficiently long interval, ?(x) is sufficiently smooth, and ?(x) decays sufficiently fast to zero as . 相似文献
12.
R.S. Singh 《Journal of multivariate analysis》1976,6(2):338-342
Let Xj = (X1j ,…, Xpj), j = 1,…, n be n independent random vectors. For x = (x1 ,…, xp) in Rp and for α in [0, 1], let Fj(x) = αI(X1j < x1 ,…, Xpj < xp) + (1 ? α) I(X1j ≤ x1 ,…, Xpj ≤ xp), where I(A) is the indicator random variable of the event A. Let Fj(x) = E(Fj(x)) and Dn = supx, α max1 ≤ N ≤ n |Σ0n(Fj(x) ? Fj(x))|. It is shown that P[Dn ≥ L] < 4pL exp{?2(L2n?1 ? 1)} for each positive integer n and for all L2 ≥ n; and, as n → ∞, with probability one. 相似文献
13.
Jorge L.C Sanz Thomas S Huang 《Journal of Mathematical Analysis and Applications》1984,104(1):302-308
In this paper, the problem of phase reconstruction from magnitude of multidimensional band-limited functions is considered. It is shown that any irreducible band-limited function f(z1…,zn), zi ? , i=1, …, n, is uniquely determined from the magnitude of f(x1…,xn): | f(x1…,xn)|, xi ? , i=1,…, n, except for (1) linear shifts: i(α1z1+…+αn2n+β), β, αi?, i=1,…, n; and (2) conjugation: . 相似文献
14.
A set {b1,b2,…,bi} ? {1,2,…,N} is said to be a difference intersector set if {a1,a2,…,as} ? {1,2,…,N}, j > ?N imply the solvability of the equation ax ? ay = b′; the notion of sum intersector set is defined similarly. The authors prove two general theorems saying that if a set {b1,b2,…,bi} is well distributed simultaneously among and within all residue classes of small moduli then it must be both difference and sum intersector set. They apply these theorems to investigate the solvability of the equations (, , , (where () denotes the Legendre symbol) and to show that “almost all” sets form both difference and sum intersector sets. 相似文献
15.
The system is investigated, where x and y are scalar functions of time (t ? 0), and n space variables , and F and G are nonlinear functions. Under certain hypotheses on F and G it is proved that there exists a unique spherically symmetric solution , which is bounded for r ? 0 and satisfies x(0) >x0, y(0) > y0, x′(0) = 0, y′(0) = 0, and x′ < 0, y′ > 0, ?r > 0. Thus, (x(r), y(r)) represents a time independent equilibrium solution of the system. Further, the linearization of the system restricted to spherically symmetric solutions, around (x(r), y(r)), has a unique positive eigenvalue. This is in contrast to the case n = 1 (i.e., one space dimension) in which zero is an eigenvalue. The uniqueness of the positive eigenvalue is used in the proof that the spherically symmetric solution described is unique. 相似文献
16.
Stanley J Benkoski 《Journal of Number Theory》1976,8(2):218-223
If r, k are positive integers, then denotes the number of k-tuples of positive integers (x1, x2, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r = 1. An explicit formula for is derived and it is shown that .If S = {p1, p2, …, pa} is a finite set of primes, then 〈S〉 = {p1a1p2a2…psas; pi ∈ S and ai ≥ 0 for all i} and denotes the number of k-tuples (x1, x3, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r ∈ 〈S〉. Asymptotic formulas for are derived and it is shown that . 相似文献
17.
The initial and boundary value problem for the degenerate parabolic equation vt = Δ(?(v)) + F(v) in the cylinder bounded, for a certain class of point functions ? satisfying ?′(v) ? 0 (e.g., ) is considered. In the case that F(v) sign , the equation has a global time solution. The same is true for α = 1 provided the measure of Ω is sufficiently small. In the case that is nondecreasing a condition is given on the initial state v(x, 0) which implies that the solution must blow up in finite time. The existence of such initial states is discussed. 相似文献
18.
John Michael S Rassias 《Journal of Mathematical Analysis and Applications》1982,85(1):106-113
In this paper we establish maximum principles of the Cauchy problem for hyperbolic equations in 3 and n + 1(n ? 2). Our maximum principles generalize the results of Weinberger [5], and Sather [3, 4] for a class of equations such that the coefficients can be allowed to depend upon t, as well, in {x1, x2, t}-space and {x1, x2,…, xn, t}-space. Throughout this paper, the influence of the work of Douglis [1] is apparent. See [2]. 相似文献
19.
Let R = (r1,…, rm) and S = (s1,…, sn) be nonnegative integral vectors, and let (R, S) denote the class of all m × n matrices of 0's and 1's having row sum vector R and column sum vector S. An invariant position of (R, S) is a position whose entry is the same for all matrices in (R, S). The interchange graph G(R, S) is the graph where the vertices are the matrices in (R, S) and where two matrices are joined by an edge provided they differ by an interchange. We prove that when 1 ≤ ri ≤ n ? 1 (i = 1,…, m) and 1 ≤ sj ≤ m ? 1 (j = 1,…, n), G(R, S) is prime if and only if (R, S) has no invariant positions. 相似文献
20.
A new normal form of Boolean functions based on the sum (mod 2), product and negation is presented. Let n = {1, 2,…, n}, let As be the family of s-element subsets of a set A and let πa?φxa = 1. Then every Boolean function ?(x1,x2,…,xn) has a normal form with unique coefficients dA? {0, 1}. A transformation of Galois normal form into the present normal form is also shown. 相似文献