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1.
A computable expression is derived for the raw moments of the random variableZ=N/D whereN= 1 n m iXi+ n +1s m iXi,D= n +1s l iXi+ s +1r n iXi, and theX i's are independently distributed central chi-square variables. The first four moments are required for approximating the distribution ofZ by means of Pearson curves. The exact density function ofZ is obtained in terms of sums of generalized hypergeometric functions by taking the inverse Mellin transform of theh-th moment of the ratioN/D whereh is a complex number. The casen=1,s=2 andr=3 is discussed in detail and a general technique which applies to any ratio having the structure ofZ is also described. A theoretical example shows that the inverse Mellin transform technique yields the exact density function of a ratio whose density can be obtained by means of the transformation of variables technique. In the second example, the exact density function of a ratio of dependent quardratic forms is evaluated at various points and then compared with simulated values.  相似文献   

2.
Let G be a finitely presented group given by its pre-abelian presentation <X1,…,Xm; Xe11ζ1,…,Xemmζ,ζm+1,…>, where ei≥0 for i = 1,…, m and ζj?G′ for j≥1. Let N be the subgroup of G generated by the normal subgroups [xeii, G] for i = 1,…, m. Then Dn+2(G)≡γn+2(G) (modNG′) for all n≥0, where G” is the second commutator subgroup of Gn+2(G) is the (n+2)th term of the lower central series of G and Dn+2(G) = G∩(1+△n+2(G)) is the (n+2)th dimension subgroup of G.  相似文献   

3.
《Journal of Complexity》1994,10(2):216-229
In this paper we present a minimal set of conditions sufficient to assure the existence of a solution to a system of nonnegative linear diophantine equations. More specifically, suppose we are given a finite item set U = {u1, u2, . . . , uk} together with a "size" viv(ui) ∈ Z+, such that vivj for ij, a "frequency" aia(ui) ∈ Z+, and a positive integer (shelf length) LZ+ with the following conditions: (i) L = ∏nj=1pj(pjZ+j, pjpl for jl) and vi = ∏ jAipj, Ai ⊆ {l, 2, . . . , n} for i = 1, . . . , n; (ii) (Ai\{⋂kj=1Aj}) ∩ (Al\{⋂kj=1Aj}) = ⊘∀il. Note that vi|L (divides L) for each i. If for a given mZ+, ∑ni=1aivi = mL (i.e., the total size of all the items equals the total length of the shelf space), we prove that conditions (i) and (ii) are sufficient conditions for the existence of a set of integers {b11, b12, . . . , b1m, b21, . . . , bn1, . . . , bnm}⊆ N such that ∑mj=1bij = ai, i = 1, . . . , k, and ∑ki=1bijvi = L, j =1, . . . , m (i.e., m shelves of length L can be fully utilized). We indicate a number of special cases of well known NP-complete problems which are subsequently decided in polynomial time.  相似文献   

4.
A successivity in a linear order is a pair of elements with no other elements between them. A recursive linear order with recursive successivities U is recursively categorical if every recursive linear order with recursive successivities isomorphic to U is in fact recursively isomorphic to U. We characterize those recursive linear orders with recursive successivities that are recursively categorical as precisely those with order type k1+g1+k2+g2+…+gn-1+kn where each kn is a finite order type, non-empty for i?{2,…,n-1} and each gi is an order type from among {ω,ω*,ω+ω*}∪{k·η:k<ω}.  相似文献   

5.
We consider a harmonic oscillator with delays. Linear stability is investigated by analyzing the associated characteristic transcendental equation. The bifurcation analysis of the equation shows that Hopf bifurcation can occur as the delay τ (taken as a parameter) crosses some critical values. The direction and stability of the Hopf bifurcation are considered by using the normal form theory due to Faria and Magalhães. An example is given to explain the results. Numerical simulations support our results.  相似文献   

6.
Let (M m , T) be a smooth involution on a closed smooth m-dimensional manifold and F = ∪ j=0 n F j (nm) its fixed point set, where F j denotes the union of those components of F having dimension j. The famous Five Halves Theorem of J. Boardman, announced in 1967, establishes that, if F is nonbounding, then m ≤ 5/2n. In this paper we obtain an improvement of the Five Halves Theorem when the top dimensional component of F, F n , is nonbounding. Specifically, let ω = (i 1, i 2, …, i r ) be a non-dyadic partition of n and s ω (x 1, x 2, …, x n ) the smallest symmetric polynomial over Z 2 on degree one variables x 1, x 2, …, x n containing the monomial \(x_1^{i_1 } x_2^{i_2 } \cdots x_r^{i_r }\). Write s ω (F n ) ∈ H n (F n , Z 2) for the usual cohomology class corresponding to s ω (x 1, x 2, …, x n ), and denote by ?(F n ) the minimum length of a nondyadic partition ω with s ω (F n ) ≠ 0 (here, the length of ω = (i 1, i 2, …, i r ) is r). We will prove that, if (M m , T) is an involution for which the top dimensional component of the fixed point set, F n , is nonbounding, then m ≤ 2n + ?(F n ); roughly speaking, the bound for m depends on the degree of decomposability of the top dimensional component of the fixed point set. Further, we will give examples to show that this bound is best possible.  相似文献   

7.
Given a triple (G, W, γ) of an open bounded set G in the complex plane, a weight function W(z) which is analytic and different from zero in G, and a number γ with 0 ≤ γ ≤ 1, we consider the problem of locally uniform rational approximation of any function ƒ(z), which is analytic in G, by weighted rational functions Wmi+ni(z)Rmi, ni(z)i = 0, where Rmi, ni(z) = Pmi(z)/Qni(z) with deg Pmimi and deg Qnini for all i ≥ 0 and where mi + ni → ∞ as i → ∞ such that lim mi/[mi + ni] = γ. Our main result is a necessary and sufficient condition for such an approximation to be valid. Applications of the result to various classical weights are also included.  相似文献   

8.
A proof is given for the existence and uniqueness of a correspondence between two pairs of sequences {a},{b} and {ω},{μ}, satisfying bi>0 for i=1,…,n?1 and ω11<?<μn?1n, under which the symmetric Jacobi matrices J(n,a,b) and J(n?1,a,b) have eigenvalues {ω} and {μ} respectively. Here J(m,a,b) is symmetric and tridiagonal with diagonal elements ai (i=1,…,m) and off diagonal elements bi (i=1,…,m?1). A new concise proof is given for the known uniqueness result. The existence result is new.  相似文献   

9.
Let S(m|n,r)Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξi,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module Dλ,Q over the field Q of rational numbers, under the action of S(m|n,r)Z. This Z-form is the Z-span of modified bideterminants [T?:Ti] defined in this work. We also prove that each [T?:Ti] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux Ti.  相似文献   

10.
In connection with the problem of finding the best projections of k-dimensional spaces embedded in n-dimensional spaces Hermann König asked: Given mR and nN, are there n×n matrices C=(cij), i, j=1,…,n, such that cii=m for all i, |cij|=1 for ij, and C2=(m2+n?1)In? König was especially interested in symmetric C, and we find some families of matrices satisfying this condition. We also find some families of matrices satisfying the less restrictive condition CCT=(m2+n?1)In.  相似文献   

11.
LetG be a compact group andM 1(G) be the convolution semigroup of all Borel probability measures onG with the weak topology. We consider a stationary sequence {μ n } n=?∞ +∞ of random measures μ n n (ω) inM 1(G) and the convolutions $$v_{m,n} (\omega ) = \mu _m (\omega )* \cdots *\mu _{n - 1} (\omega ), m< n$$ and $$\alpha _n^{( + k)} (\omega ) = \frac{1}{k}\sum\limits_{i = 1}^k {v_{n,n + i} (\omega ),} \alpha _n^{( - k)} (\omega ) = \frac{1}{k}\sum\limits_{i = 1}^k {v_{n - i,n} (\omega )} $$ We describe the setsA m + (ω) andA n + (ω) of all limit points ofv m,n(ω) asm→?∞ orn→+∞ and the setA (ω) of its two-sided limit points for typical realizations of {μ n (ω)} n=?∞ +∞ . Using an appropriate random ergodic theorem we study the limit random measures ρ n (±) (ω)=lim k→∞ α n k) (ω).  相似文献   

12.
Given natural numbers n≥3 and 1≤a,rn−1, the rose window graph Rn(a,r) is a quartic graph with vertex set {xiiZn}∪{yiiZn} and edge set {{xi,xi+1}∣iZn}∪{{yi,yi+r}∣iZn}∪{{xi,yi}∣iZn}∪{{xi+a,yi}∣iZn}. In this paper rotary maps on rose window graphs are considered. In particular, we answer the question posed in [S. Wilson, Rose window graphs, Ars Math. Contemp. 1 (2008), 7-19. http://amc.imfm.si/index.php/amc/issue/view/5] concerning which of these graphs underlie a rotary map.  相似文献   

13.
The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), uttuxxa(un)xx+b(um)xxxx=0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given.  相似文献   

14.
15.
Let p be an odd prime, let d be a positive integer such that (d,p?1)=1, let r denote the p-adic valuation of d and let m=1+3+32+…+3r. It is shown that for every p-adic integer n the equation Σi=1mXid=n has a nontrivial p-adic solution. It is also shown that for all p-adic units a1, a2, a3, a4 and all p-adic integers n the equation Σi=14aiXip=n has a nontrivial p-adic solution. A corollary to each of these results is that every p-adic integer is a sum of four pth powers of p-adic integers.  相似文献   

16.
17.
J. Conde 《Discrete Mathematics》2009,309(10):3166-1344
In the context of the degree/diameter problem, the ‘defect’ of a graph represents the difference between the corresponding Moore bound and its order. Thus, a graph with maximum degree d and diameter two has defect two if its order is n=d2−1. Only four extremal graphs of this type, referred to as (d,2,2)-graphs, are known at present: two of degree d=3 and one of degree d=4 and 5, respectively. In this paper we prove, by using algebraic and spectral techniques, that for all values of the degree d within a certain range, (d,2,2)-graphs do not exist.The enumeration of (d,2,2)-graphs is equivalent to the search of binary symmetric matrices A fulfilling that AJn=dJn and A2+A+(1−d)In=Jn+B, where Jn denotes the all-one matrix and B is the adjacency matrix of a union of graph cycles. In order to get the factorization of the characteristic polynomial of A in Q[x], we consider the polynomials Fi,d(x)=fi(x2+x+1−d), where fi(x) denotes the minimal polynomial of the Gauss period , being ζi a primitive ith root of unity. We formulate a conjecture on the irreducibility of Fi,d(x) in Q[x] and we show that its proof would imply the nonexistence of (d,2,2)-graphs for any degree d>5.  相似文献   

18.
In this paper, we are studying Dirichlet series Z(P,ξ,s) = Σn?N1rP(n)?s ξn, where PR+ [X1,…,Xr] and ξn = ξ1n1ξrnr, with ξiC, such that |ξi| = 1 and ξi ≠ 1, 1 ≦ ir. We show that Z(P, ξ,·) can be continued holomorphically to the whole complex plane, and that the values Z(P, ξ, ?k) for all non negative integers, belong to the field generated over Q by the ξi and the coefficients of P. If, there exists a number field K, containing the ξi, 1 ≦ ir, and the coefficients of P, then we study the denominators of Z(P, ξ, ?k) and we define a B-adic function ZB(P, ξ,·) which is equal, on class of negative integers, to Z(P, ξ, ?k).  相似文献   

19.
A partition of N is called “admissible” provided some cell has arbitrarily long arithmetic progressions of even integers in a fixed increment. The principal result is that the statement “Whenever {Ai}i < r is an admissible partition of N, there are some i < r and some sequence 〈xnn < ω of distinct members of N such that xn + xm?Ai whenever {m, n} ? ω″ is true when r = 2 and false when r ? 3.  相似文献   

20.
Maria Monks 《Discrete Mathematics》2009,309(16):5196-1883
All continuous endomorphisms f of the shift dynamical system S on the 2-adic integers Z2 are induced by some , where n is a positive integer, Bn is the set of n-blocks over {0, 1}, and f(x)=y0y1y2… where for all iN, yi=f(xixi+1xi+n−1). Define D:Z2Z2 to be the endomorphism of S induced by the map {(00,0),(01,1),(10,1),(11,0)} and V:Z2Z2 by V(x)=−1−x. We prove that D, V°D, S, and V°S are conjugate to S and are the only continuous endomorphisms of S whose parity vector function is solenoidal. We investigate the properties of D as a dynamical system, and use D to construct a conjugacy from the 3x+1 function T:Z2Z2 to a parity-neutral dynamical system. We also construct a conjugacy R from D to T. We apply these results to establish that, in order to prove the 3x+1 conjecture, it suffices to show that for any mZ+, there exists some nN such that R−1(m) has binary representation of the form or .  相似文献   

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