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1.
For non-negative integers k, n, let P k (n) denote the sum {fx27-1}. We show by two different means that if k ≥ 3 and odd, then n 2(n+1)2 iss a factor of the polynomial P k (n); and if k ≥ 2 and even, then n (n+1) (2n+1) is a factor of the polynomial P k (n). We also derive a relatively unknown result first obtained by Johann Faulhaber in the 17th century. Shailesh Shirali has been at Rishi Valley School, Andhra Pradesh (Krishnamurti Foundation India) since the 1980’s. He has a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis on problem solving and on historical aspects of the subject. He has been involved in the Mathematics Olympiad movement at the national and international level for the past two decades. He is the author of several expository books and articles aimed at interested high school students.  相似文献   

2.
Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β= 0 and there exist p , q ∈ Qr ( RC) such that D ( x )= px and G ( x )= qx for all x ∈ R;(ii) If both a and b are contained in C , then either a = b= 0 or D and G are C-linearly dependent;(iii) If neither a nor b is contained in C , then there exist p , q ∈ Qr ( RC) and w ∈ Qr ( R) such that α ( x ) = [ q ,x] and β ( x ) = [ x ,p] for all x ∈ R, whence D ( x )= wx-xq and G ( x )= xp + avx with v ∈ C and aw-pb= 0.  相似文献   

3.
INTRODUCTION Throughout this paper, we shall work with a filtered complete probability space (?,F,(Ft),P) sat-isfying the usual conditions. Let B=(Bt)t≥0 be a stan-dard Brownian motion with B0=0. Denote by ú the set of all non-negative real numbers. Recall that a diffusion process X starting at x≥0 is called the square of a Bessel process of dimension δ>0 if d X t = δd t 2 | X t |d Bt , X 0= x, (1) Clearly, this equation has a unique non-negative strong solution X, i.e., …  相似文献   

4.
In this paper we study the scaling behavior of nucleotide cluster in 11 chromosomes of Encephalitozoon cuniculi Genome. The statistical distribution of nucleotide clusters for 11 chromosomes is characterized by the scaling behavior of P（S） ∝ e^-αs＇ where S represents nucleotide cluster size. The cluster-size distribution P（S1＋S2） with the total size of sequential C-G cluster and A-T cluster S1＋S2 were also studied. P（S1＋S2） follows exponential decay. There does not exist the case of large C-G cluster following large A-T cluster or large A-T cluster following large C-G cluster. We also discuss the relatively random walk length function L（n） and the local compositional complexity of nucleotide sequences based on a new model. These investigations may provide some insight into nucleotide cluster of DNA sequence.  相似文献   

5.
In this work, we study the Asanov Finsler metric F=α(β2/α2 gβ/α 1)1/2exp{(G/2)arctan[β/(hα) G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.  相似文献   

6.
Consider the mixed-effect coefficient semiparametric regression modelZ=X'α+Y'β+g(T)+e, whereX, Y andT are random vectors onR p×R q×[0, 1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=Σ),g(.) is an unknown function on [0, 1], e is a random error with mean zero and variance σ2, and (X, Y, T) and (β,e), β ande are mutually independent. We estimate α,b andg(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α,b have asymptotic normality and obtain the best convergence raten −1/3 for the estimation ofg(.). Project supported by the NSFC and the Natural Science Foundation of Zhejiang Province.  相似文献   

7.
In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.  相似文献   

8.
Let k,m,n be positive integers,and k≥2,α∈(0,1],0＜r＜min {m,n} an integer,d=r (m-r)/(k α),and iff∈ Ck,α(Rm,R″),A =Cr(f)= {x ∈ Rm ,rank(Df(x))≤r},thenf(A)is d-null.Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.  相似文献   

9.
1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎｔｈｅｐａｓｔｄｅｃａｄｅｏｒｓｏ ,ｔｈｅｅｘｉｓｔｅｎｃｅｏｆｇｌｏｂａｌａｔ ｔｒａｃｔｏｒｓａｎｄｔｈｅｅｓｔｉｍａｔｅｓｏｆｔｈｅｉｒＨａｕｓｄｏｒｆｆａｎｄｆｒａｃｔａｌｄｉｍｅｎｓｉｏｎｓｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｆｏｒｎｕｍｅｒｏｕｓｄｉｓｓｉｐａ ｔｉｖｅｎｏｎｌｉｎｅａｒｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｈｉｃｈａｒｅａｕ ｔｏｎｏｍｏｕｓ[1～ 4 ].Ｔｈｅｎｏｎ ａｕｔｏｎｏｍｏｕｓｉｎｆｉｎｉｔｅ ｄｙｎａｍｉ…  相似文献   

10.
In this paper, a semi on-line version on m identical machines M1 , M2, …, Mm ( m ≥ 3 ) was considered, where the processing time of the largest job is known in advance. Our goal is to maximize the minimum machine load, an NPLS algorithm was presented and its worst-case ratio was proved to be equal to m - 1 which is the best possible value. It is concluded that if the total processing time of jobs is also known to be greater than (2 m - 1 )Pmax where pmax is the largest job‘s processing time, then the worstcase ratio is 2 - 1/m.  相似文献   

11.
Consider the positive d-dimensional lattice d (d≥2) with partial ordering ≤, let {XK; K ∈ d } be i.i.d. random vari- ables taking values in a real separable Hilbert space (H, ||·||) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K , N ∈ d . Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε 0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).  相似文献   

12.
Using SnxTi1-xO2 as carriers, CuO/Sn0.9Ti0.1O2 and CuO/Sn0.7Ti0.3O2 catalysts with different loading amounts of copper oxide (CuO) were prepared by an impregnation method. The catalytic properties of CuO/Sn0.9Ti0.1O2 and CuO/Sn0.7Ti0.3O2 were examined using a microreactor-gas chromatography (GC) NO CO reaction system and the methods of BET (Brun- auer-Emmett-Teller), TG-DTA (themogravimetric and differential thermal analysis), X-ray diffraction (XRD) and H2-temperature programmed reduction (TPR). The results showed that NO conversions of Sn0.9Ti0.1O2 and Sn0.7Ti0.3O2 were 47.2% and 43.6% respectively, which increased to 95.3% and 90.9% at 6 wt% CuO loading. However, further increase in CuO loading caused a decrease in the catalytic activity. The nitrogen adsorption-desorption isotherm and pore-size distribution curve of Sn0.9Ti0.1O2 and Sn0.7Ti0.3O2 represented type IV of the BDDT (Brunauer, Deming, Deming and Teller) system and a typical mesoporous sample. There were two CuO diffraction peaks (2θ 35.5° and 38.7°), and the diffraction peak areas increased with increasing CuO loading. TPR analysis also detected three peaks (α, β and γ) from the CuO-loaded catalysts, suggesting that the α peak was the reduction of the highly dispersed copper oxide, the β peak was the reduction of the isolated copper oxide, and the γ peak was the reduction of crystal phase copper oxide. In addition, a fourth peak (δ) of the catalysts meant that the SnxTi1-xO2 mixed oxides could be reductive.  相似文献   

13.
几乎正则图的全符号控制   总被引：1，自引：2，他引：1  
1IntroductionFor notation and graph theory terminology we ingeneral follow[1].LetG=(V,E)be a graph with thevertex setVand the edge setE,andletvbe a vertexinV.The open neighborhood ofvisN(v)={u∈V|uv∈E}and the closed neighborhood ofvisN[v]={v}∪N(v).The d…  相似文献   

14.
The construction of multirate rearrangeable network has long been an interesting problem. Of many results published, all were achieved on 3-stage Clos network. The monotone routing algorithm proposed by Huet al. (2001) was also first applied to 3-stage Clos network. In this work, we adopt this algorithm and apply it to log d (N,m,p) networks. We first analyze the properties of log d (N,m,p) networks. Then we use monotone algorithm in log d (N,0,p) network. Furthermore we extend the result to construct multirate rearrangeable networks based on log d (N,m,p) network (1≤m≤n−1). Project (No. 10371028) supported by the National Natural Science Foundation of China  相似文献   

15.
１ＩｎｔｒｏｄｕｃｔｉｏｎＤｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｉｔｈｔｕｒｎｉｎｇｐｏｉｎｔｓｅｘｉｓｔｗｉｄｅｌｙｉｎｍａｎｙｐｒｏｂｌｅｍｓｏｆｍａｔｈｅｍａｔｉｃｓｐｈｙｓｉｃｓ,ｓｏｔｈｅｓｅｐｒｏｂｌｅｍｓａｒｅｖｅｒｙｉｍｐｏｒｔａ...  相似文献   

16.
Let M‘ be a closed submanifold isometrically immersed in a unit sphere S^n p. Denote by R, H and S, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form of M‘, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for M‘ immersed in S^n p with parallel normalized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.  相似文献   

17.
LetH n be the set of real algebraic polynomials of degreen, whose zeros all lie in the interval [−1,1]. The well known Turán type inequalities tell us that forf(x)∈H n , it holds ‖f′‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities underL p norm for 0<p≤∞. Our results essentially extend the result of Wang and Zhou (2002), and the method used in this paper is simpler and more direct than that of Wang and Zhou (2002). The results and methods have their own values in approximation theory and computation.  相似文献   

18.
Hot extrusion was conducted in the α+β phase region for promoting mechanical properties of Ti42Al9V0.3Y. The microstructures and tensile properties before and after hot extrusion were studied. The results show that the microstructure of the as-cast alloy mainly consists of massive γ phase in β matrix and the as-extruded alloy mainly consists of lamellar α2/γ, lamellar β/γ, and strip γ propagating from elongated β phase. In the as-cast alloy, the predominantly observed fracture mode is transgranular cleavage failure at room temperature and intergranular fracture at 650-750 °C. After hot extrusion, it transforms into transgranular cleavage-like failure, including translamellar cleavage and delamination. The excellent tensile properties of the as-extruded material are attributed to the obvious refined microstructure with broken YAl2 particles and the micro-crack shielding action of the TiAl lamellasome.  相似文献   

19.
INTRODUCTION In recent years, significant progress has been made in the study of Finsler metris which have straight lines in local coordinates (Hamel, 1903). Finsler metrics with this property are called locally projectively flat metrics. An important fact about these metrics is that locally projectively flat Finsler metrics have scalar flag curvature, a natural extension of the sectional curvature in Riemannian geometry. In general, it also depends on the direction (flag pole) in the se…  相似文献   

20.
Hierarchical Bayesian method for estimating the failure probabilityp i under DOOF by taking the quasi-Beta distributionB(p i−1, 1, 1,b) as the prior distribution is proposed in this paper. The weighted Least Squares Estimate method was used to obtain the formula for computing reliability distribution parameters and estimating the reliability characteristic values under DOOF. Taking one type of aerospace electrical connector as an example, the correctness of the above method through statistical analysis of electrical connector accelerated life test data was verified. Project (No. 59975081) supported by the National Natural Science Foundation of China  相似文献   

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