首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 93 毫秒
1.
The main object of this presentation is to show how some simple combinatorial identities can lead to several general families of combinatorial and other series identities as well as summation formulas associated with the Fox-Wright function pΨq and various related generalized hypergeometric functions. At least one of the hypergeometric summation formulas, which is derived here in this manner, has already found a remarkable application in producing several interesting generalizations of the Karlsson-Minton summation formula. We also consider a number of other combinatorial series identities and rational sums which were proven, in recent works, by using different methods and techniques. We show that much more general results can be derived by means of certain summation theorems for hypergeometric series. Relevant connections of the results presented here with those in the aforementioned investigations are also considered.  相似文献   

2.
Earlier papers by Murty [16] and Fathi [7] have exhibited classes of linear complementarity problems for which the computational effort (number of pivot steps) required to solve them by Lemke's algorithm [13] or Murty's algorithm [15] grows exponentially with the pronlem size (number of variables). In this paper we consider the sequences of complementary bases that arise as these problems are solved by the aforementioned algorithms. There is a natural correspondence between these bases and binary n-vectors through which the basis sequences can be identified with particular hamiltonian paths on the unit n-cube and with the binary Gray code representations of the integers from 0 to 2n-1.  相似文献   

3.
We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this paper, we present rather large class of such p-adic functional series with integer coefficients which contain factorials. By recurrence relations, we constructed sequence of polynomials A k (n; x) which are a generator for a few other sequences also relevant to some problems in number theory and combinatorics.  相似文献   

4.
A new method of summation of slowly convergent series is proposed. It may be successfully applied to the summation of generalized and basic hypergeometric series, as well as some classical orthogonal polynomial series expansions. In some special cases, our algorithm is equivalent to Wynn’s epsilon algorithm, Weniger transformation [E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Computer Physics Reports 10 (1989) 189-371] or the technique recently introduced by ?í?ek et al. [J. ?í?ek, J. Zamastil, L. Skála, New summation technique for rapidly divergent perturbation series. Hydrogen atom in magnetic field, Journal of Mathematical Physics 44 (3) (2003) 962-968]. In the case of trigonometric series, our method is very similar to the Homeier’s H transformation, while in the case of orthogonal series — to the K transformation. Two iterated methods related to the proposed method are considered. Some theoretical results and several illustrative numerical examples are given.  相似文献   

5.
For a discrete time second-order stationary process, the Levinson-Durbin recursion is used to determine the coefficients of the best linear predictor of the observation at time k+1, given k previous observations, best in the sense of minimizing the mean square error. The coefficients determined by the recursion define a Levinson-Durbin sequence. We also define a generalized Levinson-Durbin sequence and note that binomial coefficients form a special case of a generalized Levinson-Durbin sequence. All generalized Levinson-Durbin sequences are shown to obey summation formulas which generalize formulas satisfied by binomial coefficients. Levinson-Durbin sequences arise in the construction of several autoregressive model coefficient estimators. The least squares autoregressive estimator does not give rise to a Levinson-Durbin sequence, but least squares fixed point processes, which yield least squares estimates of the coefficients unbiased to order 1/T, where T is the sample length, can be combined to construct a Levinson-Durbin sequence. By contrast, analogous fixed point processes arising from the Yule-Walker estimator do not combine to construct a Levinson-Durbin sequence, although the Yule-Walker estimator itself does determine a Levinson-Durbin sequence. The least squares and Yule-Walker fixed point processes are further studied when the mean of the process is a polynomial time trend that is estimated by least squares.  相似文献   

6.
In recent years, more and more algorithms and software for reconstruction of partial or entire amino acid sequences by the mass spectra of peptides appear. However, with rare exception, such sequences always contain errors due to many reasons like a chemical noise in the spectrum, incomplete fragmentation, etc. Posttranslational modifications of proteins cause additional difficulties. In this paper, we suggest a PepTiger algorithm, which can correctly identify peptides in a database by de novo sequences containing errors. The algorithm is based on the method of approximate string matching and a specially developed system of scoring, which takes into account the string distance between the de novo sequence and the sequence of the peptide candidate in the database, the difference between their masses, and the similarity between the experimental mass spectrum and the theoretical spectrum of the peptide candidate. The algorithm suggested here correctly identifies a larger number of de novo sequences than other algorithms for identification of peptides by their de novo sequences.  相似文献   

7.
We present several simple algorithms for accurately computing the sum of n floating point numbers using a wider accumulator. Let f and F be the number of significant bits in the summands and the accumulator, respectively. Then assuming gradual underflow, no overflow, and round-to-nearest arithmetic, up to ?2 F?f /(1?2?f )?+1 numbers can be accurately added by just summing the terms in decreasing order of exponents, yielding a sum correct to within about 1.5 units in the last place. In particular, if the sum is zero, it is computed exactly. We apply this result to the floating point formats in the IEEE floating point standard, and investigate its performance. Our results show that in the absence of massive cancellation (the most common case) the cost of guaranteed accuracy is about 30–40% more than the straightforward summation. If massive cancellation does occur, the cost of computing the accurate sum is about a factor of ten. Finally, we apply our algorithm in computing a robust geometric predicate (used in computational geometry), where our accurate summation algorithm improves the existing algorithm by a factor of two on a nearly coplanar set of points.  相似文献   

8.
A skew-feedback shift-register is a generalization of a linear-feedback shift-register and can be applied in decoding (interleaved) Reed–Solomon codes or Gabidulin codes beyond half their code distance. A fast algorithm is proposed which synthesizes all shortest skew-feedback shift-registers generating L sequences of varying length over a field. For fixed L, the time complexity of the algorithm is ${{\mathcal O}(M(N) \log N)}$ operations, where N is the length of a longest sequence and M(N) is the complexity of the multiplication of two skew polynomials of maximum degree N.  相似文献   

9.
In this paper, we study a countable family of uniformly distributed sequences of partitions, called LS-sequences of partitions, and we give a precise estimate of their discrepancy. Among these sequences, we identify a countable class having low discrepancy (which means of order ${{\frac{1}{N}}}$ ). We describe an explicit algorithm that associates to each of these sequences a uniformly distributed sequence of points (we call LS-sequences of points). The main result of this paper says that the discrepancy of the sequences of points associated by our algorithm to the LS-sequences of partitions is of order α N log N, if α N is the discrepancy of the corresponding sequence of partitions. We obtain therefore, in particular, a countable family of low-discrepancy sequences of points.  相似文献   

10.
We consider the problem of identifying motifs that abstracts the task of finding short conserved sites in genomic DNA. The planted (l, d)-motif problem, PMP, is the mathematical abstraction of this problem, which consists of finding a substring of length l that occurs in each s i in a set of input sequences S = {s 1, s 2, . . . ,s t } with at most d substitutions. Our propose algorithm combines the voting algorithm and pattern matching algorithm to find exact motifs. The combined algorithm is achieved by running the voting algorithm on t′ sequences, t′ < t. After that we use the pattern matching on the output of the voting algorithm and the reminder sequences, t ? t′. Two values of t′ are calculated. The first value of t′ makes the running time of our proposed algorithm less than the running time of voting algorithm. The second value of t′ makes the running time of our proposed algorithm is minimal. We show that our proposed algorithm is faster than the voting algorithm by testing both algorithms on simulated data from (9, d ≤ 2) to (19, d ≤ 7). Finally, we test the performance of the combined algorithm on realistic biological data.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号