共查询到20条相似文献,搜索用时 282 毫秒
1.
Suppose ( N,+,·) is a finite (left) planar nearring. Define the (line) segment in N with endpoints a and b by We prove that under many circumstances we have which is the same phenomenon as in the Euclidean plane. 相似文献
2.
In this paper, we consider the second-order nonlinear differential equation [a(t)|y′(t)|σ−1y′(t)|′+q(t)f(y(t))=r(t) where σ > 0 is a constant, a C( R, (0, ∞)), q C( R, R), f C( R, R), xf( x) > 0, f′( x) ≥ 0 for x ≠ 0. Some new sufficient conditions for the oscillation of all solutions of (*) are obtained. Several examples which dwell upon the importance of our results are also included. 相似文献
3.
In the present note we study the threshold first-order bilinear model X(t)=aX(t−1)+(b11{X(t−1)<c}+b21{X(t−1)c})X(t−1)e(t−1)+e(t), tεN where { e( t), tε N} is a sequence of i.i.d. absolutely continuous random variables, X(0) is a given random variable and a, b1, b2 and c are real numbers. Under suitable conditions on the coefficients and lower semicontinuity of the densities of the noise sequence, we provide sufficient conditions for the existence of a stationary solution process to the present model and of its finite moments of order p. 相似文献
4.
In this article, we investigate the interrelation between the discrepancies of a given hypergraph in different numbers of colors. Being an extreme example we determine the multi-color discrepancies of the k-balanced hypergraph
on partition classes of (equal) size n. Let
. Set k0 k mod c and bnkc ( n− n/ c/ k) k/ c. For the discrepancy in c colors we show if k0≠0, and
, if c divides k. This shows that, in general, there is little correlation between the discrepancies of
in different numbers of colors. If c divides k though,
holds for any hypergraph
. 相似文献
5.
Oscillation criteria for the second-order half-linear differential equation [r(t)|ξ′(t)|−1 ξ′(t)]′ + p(t)|ξ(t)|−1ξ(t)=0, t t0 are established, where > 0 is a constant and
exists for t [ t0, ∞). We apply these results to the following equation: where
, D = ( D1,…, DN), Ω a = x
N : |x| ≥ a} is an exterior domain, and c C([a, ∞),
), n > 1 and N ≥ 2 are integers. Here, a > 0 is a given constant. 相似文献
6.
Oscillation criteria are obtained by using the so called H-method for the second order neutral type delay differential equations of the form (r(t)ψ(x(t))z′(t))′+q(t)f(x(σ(t)))=0, tt0, where z( t)= x( t)+ p( t) x(τ( t)), r, p, q, τ, σ, C([ t0,∞), R) and f,ψ C( R, R). The results of the paper contains several results obtained previously as special cases. Furthermore, we are also able to fix an error in a recent paper related to the oscillation of second order nonneutral delay differential equations. 相似文献
7.
We prove that for λ ≥ 0, p ≥ 3, there exists an open ball B L2(0,1) such that the problem − (|u′|p−2 u′)′ − λ|u|p−2u = f, in (0,1) , subject to certain separated boundary conditions on (0,1), has a solution for f B. 相似文献
8.
Sufficient conditions for the uniqueness of positive solutions of boundary value problems for quasilinear differential equations of the type (|u′|m−2u′)′ + f(t,u,u′)=0, m 2 are established. These problems arise, for example, in the study of the m-Laplace equation in annular regions. 相似文献
9.
We present a characterization of those Euclidean distance matrices (EDMs) D which can be expressed as D=λ( E− C) for some nonnegative scalar λ and some correlation matrix C, where E is the matrix of all ones. This shows that the cones where
is the elliptope (set of correlation matrices) and
is the (closed convex) cone of EDMs. The characterization is given using the Gale transform of the points generating D. We also show that given points
, for any scalars λ1,λ2,…,λn such that we have ∑j=1nλjpi−pj2= forall i=1,…,n, for some scalar independent of i. 相似文献
10.
For a 1-dependent stationary sequence { Xn} we first show that if u satisfies p1= p1( u)= P( X1> u)0.025 and n>3 is such that 88 np131, then P{max(X1,…,Xn)u}=ν·μn+O{p13(88n(1+124np13)+561)}, n>3, where ν=1−p2+2p3−3p4+p12+6p22−6p1p2,μ=(1+p1−p2+p3−p4+2p12+3p22−5p1p2)−1 with pk=pk(u)=P{min(X1,…,Xk)>u}, k1 and From this result we deduce, for a stationary T-dependent process with a.s. continuous path { Ys}, a similar, in terms of P{max 0skTYs< u}, k=1,2 formula for P{max 0stYsu}, t>3 T and apply this formula to the process Ys= W( s+1)− W( s), s0, where { W( s)} is the Wiener process. We then obtain numerical estimations of the above probabilities. 相似文献
11.
In 1994, van Trung (Discrete Math. 128 (1994) 337–348) [9] proved that if, for some positive integers d and h, there exists an Sλ( t, k, v) such that then there exists an Sλ(v−t+1)( t, k, v+1) having v+1 pairwise disjoint subdesigns Sλ( t, k, v). Moreover, if Bi and Bj are any two blocks belonging to two distinct such subdesigns, then d| Bi∩ Bj|< k− h. In 1999, Baudelet and Sebille (J. Combin. Des. 7 (1999) 107–112) proved that if, for some positive integers, there exists an Sλ( t, k, v) such that where m=min{ s, v− k} and n=min{ i, t}, then there exists an having
pairwise disjoint subdesigns Sλ( t, k, v). The purpose of this paper is to generalize these two constructions in order to produce a new recursive construction of t-designs and a new extension theorem of t-designs. 相似文献
12.
We shall establish some new criteria for the oscillation of all solutions of higher-order difference equations of the form δm(xn-xn-r)+qnf(xn-g=0, m1 相似文献
13.
Let
denote a field, and let V denote a vector space over
with finite positive dimension. We consider a pair of linear transformations A: V→ V and A*: V→ V satisfying both conditions below: 1. [(i)] There exists a basis for V with respect to which the matrix representing A is diagonal and the matrix representing A* is irreducible tridiagonal. 2. [(ii)] There exists a basis for V with respect to which the matrix representing A* is diagonal and the matrix representing A is irreducible tridiagonal.
We call such a pair a Leonard pair on V. Refining this notion a bit, we introduce the concept of a Leonard system. We give a complete classification of Leonard systems. Integral to our proof is the following result. We show that for any Leonard pair A,A* on V, there exists a sequence of scalars β,γ,γ*,,* taken from
such that both where [r,s] means rs−sr. The sequence is uniquely determined by the Leonard pair if the dimension of V is at least 4. We conclude by showing how Leonard systems correspond to q-Racah and related polynomials from the Askey scheme. 相似文献
14.
Let {ζ k} be the normalized sums corresponding to a sequence of i.i.d. variables with zero mean and unit variance. Define random measures and let G be the normal distribution. We show that for each continuous function h satisfying ∫ hd G<∞ and a mild regularity assumption, one has a.s. 相似文献
15.
Let q be a nonnegative real number, and λ and σ be positive constants. This article studies the following impulsive problem: for n = 1, 2, 3,…, . The number λ * is called the critical value if the problem has a unique global solution u for λ < λ *, and the solution blows up in a finite time for λ > λ *. For σ < 1, existence of a unique λ * is established, and a criterion for the solution to decay to zero is studied. For σ > 1, existence of a unique λ * and three criteria for the blow-up of the solution in a finite time are given respectively. It is also shown that there exists a unique T* such that u exists globally for T> T*, and u blows up in a finite time for T < T*. 相似文献
16.
In this paper, we shall show that under suitable conditions on f and K, the inequalities imply that the integro-differential inequalities have no positive solutions, respectively. 相似文献
17.
Integrity, a measure of network reliability, is defined as where G is a graph with vertex set V and m( G− S) denotes the order of the largest component of G− S. We prove an upper bound of the following form on the integrity of any cubic graph with n vertices: Moreover, there exist an infinite family of connected cubic graphs whose integrity satisfies a linear lower bound I( G)>β n for some constant β. We provide a value for β, but it is likely not best possible. To prove the upper bound we first solve the following extremal problem. What is the least number of vertices in a cubic graph whose removal results in an acyclic graph? The solution (with a few minor exceptions) is that n/3 vertices suffice and this is best possible. 相似文献
18.
Consider the first-order neutral nonlinear difference equation of the form , where τ > 0, σ i ≥ 0 ( i = 1, 2,…, m) are integers, { pn} and { qn} are nonnegative sequences. We obtain new criteria for the oscillation of the above equation without the restrictions Σ n=0∞ qn = ∞ or Σ n=0∞ nqn Σ j=n∞ qj = ∞ commonly used in the literature. 相似文献
19.
We give a characterization for the geometric mean inequality to hold for the case 0 < q < p ≤ ∞, p > 1, where f is positive a.e. on (0, ∞), and C > 0 independent of f. 相似文献
20.
This paper considers a class of nonlinear difference equations Δ3yn + ƒ(n, yn, yn−r) = 0, n N (n0) . A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given. 相似文献
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