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1.
Congruences for finite triple harmonic sums 总被引：1，自引：0，他引：1
FU Xu-dan ZHOU Xia CAI Tian-xin 《浙江大学学报(A卷英文版)》2007,8(6):946-948
Zhao (2003a) first established a congruence for any odd prime p>3, S(1,1,1;p)≡-2Bp-3 (mod p), which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S(α,β,γ;p) (mod p) is considered for all positive integers α,β,γ. We refer to w=α β γ as the weight of the sum, and show that if w is even, S(α,β,γ;p)≡0 (mod p) for p≥w 3; if w is odd, S(α,β,γ;p)≡rBp≥w (mod p) for p≥w, here r is an explicit rational number independent of p. A congruence of Catalan number is obtained as a special case. 相似文献
2.
Using the complete genome of Plasmodiumfalciparum 3D7 which has 14 chromosomes as an example, we have examined the distribution functions for the amount of C or G and A or T consecutively and non-overlapping blocks of m bases in this system. The function P(S) about the number of the consecutive C-G or A-T content cluster conforms to the relation P(S)oce-as;values of the scaling exponent αCG are much larger than αAT; and αAT of 14 chromosomes are hardly changed, whereas αCG of 14chromosomes have a number of fluctuations. We found maximum value of A-T cluster size is much larger than C-G, which implies the existence of large A-T cluster. Our study of the width function ξ(m) of cluster C-G content showed that follows good power law ξ(m)ocm-γ. The average γ for 14 chromosomes is 0.931. These investigations provide some insight into the nucleotide clusters of DNA sequences, and help us understand other properties of DNA sequences. 相似文献
3.
YANG Cheng-lei QI Meng MENG Xiang-xu LI Xue-qing WANG Jia-ye 《浙江大学学报(A卷英文版)》2006,7(9):1522-1529
INTRODUCTION To compute the minimum distance between two convex polygons or polyhedrons is often a main step of many applications, such as collision detection (Choi et al., 2006; Li et al., 2003), path planning. In order to reduce the time complexity of the algorithm as much as possible, the convex property must be applied fully. Edelsbrunner (1985) proposed an algorithm for computing the minimum distance between two dis- joint convex polygons. The algorithm takes O(logm logn) time, and … 相似文献
4.
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
5.
LU Li-gang YAN Li-tan XIANG Li-chi 《浙江大学学报(A卷英文版)》2007,8(1):158-163
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
6.
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
7.
SO4^2- / TiO2-La2O3, a novel solid superacid, was prepared and its catalytic activities at different synthetic conditions are discussed with esterification of n-butanoic acid and n-butyl alcohol as probing reaction. The optimum conditions have also been found, mole ratio of n（La^3＋）：n（Ti^4＋） is 1：34, the soaked consistency of H2SO4 is 0.8 tool/L, the soaked time of HESO4 is 24 h, the calcining temperature is 480 ℃, the calcining time is 3 h. Then it was applied in the catalytic synthesis often important ketals and acetals as catalyst and revealed high catalytic activity. Under these conditions on which the molar ratio of aldehyde/ketone to glycol is l： 1.5, the mass ratio of the catalyst used in the reactants is 0.5%, and the reaction time is 1.0 h, the yields of ketals and acetals can reach 41.4%-95.8%. 相似文献
8.
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
9.
The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number Wh (3,3) = 9, Wh (3,3,3)≥25 on a circle was calculated by computer. 相似文献
10.
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
11.
SHAMSI Imran Haider 《Journal of Zhejiang University. Science. B》2007,8(4):266-271
The effects of salinity(50 mmol/L NaCl) and Cd(1 μmol/L CdCl2) as sole and combined on growth and photosyn-thetic parameters were studied using two soybean genotypes,Huachun 18 and NGB.The concentrations of Cd2 ,Zn2 ,Ca2 ,Mg2 ,K and Na were also determined in seeds and pods.Huachun 18 suffered a more serious decrease than NGB in net photosynthetic rate(Pn) in the treatments of salinity stress alone and combined stress(NaCl Cd),showing that it is relatively sensitive to salinity.The decrease in Pn caused by salt stress in Huachun 18 was mainly due to the reduced total chlorophyll content and photosynthetic efficiency(the ratio of variable fluorescence to maximal fluorescence,Fv/Fm),whereas the decease in NGB was mainly related to reduced stomatal conductance(Gs).The combined stress of both Na and Cd did not induce further decrease in photosynthesis and fluorescence in the two genotypes relative to salt or Cd stress alone.Greater change in the pod concentrations of Zn2 ,Ca2 ,Mg2 ,K and Na was detected under salt stress for Huachun 18 than for NGB.The results suggested that the interactive effect of NaCl-Cd on growth and nutrient uptake differs between the two soybean genotypes. 相似文献
12.
Ｉｎ 1935 ,Ｐ .Ｅｒｄ¨ｏｓａｎｄＧＳｚｅｋｅｒｅｓｏｂｔａｉｎｅｄｔｈｅｃｌａｓｓｉｃａｌｉｎｅｑｕａｌｉｔｙＲ (ｍ ,ｎ)≤Ｒ (ｍ - 1,ｎ) Ｒ(ｍ ,ｎ - 1) . Ｉｎ 196 8,Ｋ .ＷａｌｋｅｒｐｒｏｖｅｄｔｈａｔＲ(ｎ ,ｎ)≤ 4Ｒ(ｎ- 2 ,ｎ) 2 . Ｉｎ 1998,ＨｕａｎｇＹ .Ｒ .ａｎｄＺｈａｎｇＫ .Ｍ .[1,2 ] ｐｒｏｖｅｄｔｈａｔＲ(ｍ ,ｎ)≤ 12 (β 3γ 5 ) 12 γ(4α 2 β - 3γ 6 ) (β 1) 2 Ｉｎｔｈｉｓｐａｐｅｒ ,ｗｅｏｂｔａｉｎｓｏｍｅｎｅｗｕｐｐｅｒｂｏｕｎｄｓｆｏｒＲ(ｍ ,ｎ ,ｌ)ａｎｄＲ(ｍ … 相似文献
13.
Shailesh A. Shirali 《Resonance》2007,12(7):27-43
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
14.
Effect of lead exposure on the immune function of lymphocytes and erythrocytes in preschool children
Objective: To investigate the influence of lead exposure on the immune function of lymphocytes and erythrocytes in preschool children. Materials and methods: A group of 217 children three to six years of age from a rural area were given a thorough physical examination and the concentration of lead in blood samples taken from each subject was determined. The indices of lymphocyte immunity (CD 3CD 4, CD 3CD 8, CD 4CD 8, CD-3CD 19) and erythrocyte immunity (RBC-C3b, RBC-IC, RFER, RFIR, CD35 and its average fluorescence intensity) of 40 children with blood lead levels above 0.483 μmol/L were measured and compared with a control group. Results: The blood lead levels of the 217 children ranged from 0.11 μmol/L to 2.11 μmol/L. The CD 3CD 4and CD 4CD 8 cells were lower (P＜0.01) and the CD 3CD 8 cells were higher in the lead-poisoned subjects than those in the control group (P＜0.05). CD 3 and CD-3CD 19 did not show significant differences. Although the RBC-C3b rosette forming rate was lower and the RBC-IC rosette forming rate was higher in the lead-poisoned group, this difference could not be shown to be statistically significant (P＞0.05). RFIR was found to be lower in the lead-poisoned group (P＜0.01). Compared with the control group, the positive rate of CD35 was not found to be significantly different in a group of 25 lead-poisoned children (P＞0.05), while the average fluorescence intensity was lower in the lead-poisoned group (P＜0.05). Conclusion: Lead exposure can result in impaired immune function of T lymphocytes and erythrocytes in preschool children. 相似文献
15.
姜海益 《浙江大学学报(A卷英文版)》2004,5(7):754-758
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
16.
In this note, we prove that the convergence rate of the modified Gauss-Seidel (MGS) method with preconditional I Sa isa monotonic function of preconditioning parameter a. Based on this result, to achieve better convergence rate we suggest proformingtwice preconditoning when applying the MGS method to solve a linear system whose coefficient matrix is an irreducible non-singularM-matrix. 相似文献
17.
In an effort to find the effect of mass transfer ,surface tesion and drag forces on the velocity distribution,the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method).The effect of mass transfer on velocity distribution based on the complicated function(G(Ch^s))was presented and the dffects of a complicated function were studied in two cases:in the first case,G(Ch^s) was constant;in the second,G(Ch^s) was variable.The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region.One empirical equation was used to describe this change and the predected values had a better agreement with the experimental values.To verify the moedl hypotheses,hollow fiber membranes were spun from 20:80 polybenzimidazole/polyetherimide dopes with 25.6 wt％ solid in N,N-dimethylacetamide (DMAc) using water as the external and internal coagulants.Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes,it is found that the model calculated values were in a good agreement with the experimental values. 相似文献
18.
In the light of Ф-mapping method and the relationship between entropy and the Euler characteristic, the intrinsic topological structure of entropy of Kerr black holes is studied. From the Ganss-Bonnet-Chem theorem, it is shown that the entropy of Kerr black hole is determined by singularities of the Killing vector field of spacetime. These singularities naturally carry topological numbers, Hopf indices and Brouwer degrees, which can also be viewed as topological quantization of entropy of Kerr black holes. Specific results S = A/4 for non-extreme Kerr black holes and S = 0 for extreme ones are calculated independently by using the above-mentioned methods. 相似文献
19.
1 Ｉｎｔｒｏｄｕｃｔｉｏｎ Ｉｎｔｈｅｐａｓｔｄｅｃａｄｅｏｒｓｏ ,ｔｈｅｅｘｉｓｔｅｎｃｅｏｆｇｌｏｂａｌａｔ ｔｒａｃｔｏｒｓａｎｄｔｈｅｅｓｔｉｍａｔｅｓｏｆｔｈｅｉｒＨａｕｓｄｏｒｆｆａｎｄｆｒａｃｔａｌｄｉｍｅｎｓｉｏｎｓｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｆｏｒｎｕｍｅｒｏｕｓｄｉｓｓｉｐａ ｔｉｖｅｎｏｎｌｉｎｅａｒｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｈｉｃｈａｒｅａｕ ｔｏｎｏｍｏｕｓ[1～ 4 ].Ｔｈｅｎｏｎ ａｕｔｏｎｏｍｏｕｓｉｎｆｉｎｉｔｅ ｄｙｎａｍｉ… 相似文献
20.
In this paper, the Tφ-convex functions were introduced as a generalizations of convex functions. Then the characteristics of the Tφ-convex functions were discussed. Furthermore, some new inequalities for the Tφ-convex functions were derived. 相似文献