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991.
It is well known that the Stickelberger–Swan theorem is very important for determining the reducibility of polynomials over a binary field. Using this theorem the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on was determined. We discuss this problem for Type II pentanomials, namely xm+xn+2+xn+1+xn+1F2[x] for even m. Such pentanomials can be used for the efficient implementation of multiplication in finite fields of characteristic two. Based on the computation of the discriminant of these pentanomials with integer coefficients, we will characterize the parity of the number of irreducible factors over F2 and establish necessary conditions for the existence of this kind of irreducible pentanomials.Our results have been obtained in an experimental way by computing a significant number of values with Mathematica and extracting the relevant properties. 相似文献
992.
An important question in insurance is how to evaluate the probabilities of (non-) ruin of a company over any given horizon
of finite length. This paper aims to present some (not all) useful methods that have been proposed so far for computing, or
approximating, these probabilities in the case of discrete claim severities. The starting model is the classical compound
Poisson risk model with constant premium and independent and identically distributed claim severities. Two generalized versions
of the model are then examined. The former incorporates a non-constant premium function and a non-stationary claim process.
The latter takes into account a possible interdependence between the successive claim severities. Special attention will be
paid to a recursive computational method that enables us to tackle, in a simple and unified way, the different models under
consideration. The approach, still relatively little known, relies on the use of remarkable families of polynomials which
are of Appell or generalized Appell (Sheffer) types. The case with dependent claim severities will be revisited accordingly.
相似文献
993.
Hsien-Chung Wu 《Fuzzy Optimization and Decision Making》2009,8(1):1-28
The KKT optimality conditions for multiobjective programming problems with fuzzy-valued objective functions are derived in
this paper. The solution concepts are proposed by defining an ordering relation on the class of all fuzzy numbers. Owing to
this ordering relation being a partial ordering, the solution concepts proposed in this paper will follow from the similar
solution concept, called Pareto optimal solution, in the conventional multiobjective programming problems. In order to consider
the differentiation of fuzzy-valued function, we invoke the Hausdorff metric to define the distance between two fuzzy numbers
and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the KKT optimality conditions
are elicited naturally by introducing the Lagrange function multipliers. 相似文献
994.
Laiyi Zhu Zhiyong Huang School of Information People's University of China Beijing P. R. China 《分析论及其应用》2009,(1)
We study the optimal order of approximation for |x|α (0 < α < 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained. 相似文献
995.
Sotirios E. Notaris. 《Mathematics of Computation》2006,75(255):1217-1231
We evaluate explicitly the integrals , with the being any one of the four Chebyshev polynomials of degree . These integrals are subsequently used in order to obtain error bounds for interpolatory quadrature formulae with Chebyshev abscissae, when the function to be integrated is analytic in a domain containing in its interior.
996.
We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval . The monic integer transfinite diameter is defined as the infimum of all such supremums. We show that if has length , then .
We make three general conjectures relating to the value of for intervals of length less than . We also conjecture a value for where . We give some partial results, as well as computational evidence, to support these conjectures.
We define functions and , which measure properties of the lengths of intervals with on either side of . Upper and lower bounds are given for these functions.
We also consider the problem of determining when is a Farey interval. We prove that a conjecture of Borwein, Pinner and Pritsker concerning this value is true for an infinite family of Farey intervals.
997.
It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to |x| at equally spaced nodes in [-1, 1] diverges everywhere, except at zero and the end-points. In the present paper, we prove that the sequence of Lagrange interpolation polynomials corresponding to |x|α(2 <α< 4) on equidistant nodes in [-1,1] diverges everywhere, except at zero and the end-points. 相似文献
998.
We consider unitary analogs of one-dimensional Anderson models on
defined by the product U
ω=D
ω
S where S is a deterministic unitary and D
ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We
prove that the spectrum of U
ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on
together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials
characterized by Verblunsky coefficients of constant modulus and correlated random phases
Mathematics Subject Classification. 82B44, 42C05, 81Q05 相似文献
999.
Roman Witu?a 《Journal of Mathematical Analysis and Applications》2010,361(1):276-279
Taking advantage of Nadarajah's representation of modified Chebyshev polynomials by means of the random variable that has the Student's t distribution [S. Nadarajah, On modified Chebyshev polynomials, J. Math. Anal. Appl. 334 (2007) 1492-1494] the scope of this paper is the generation of the identities for the moments of linear rescaling random variables that have the Student's t distribution. 相似文献
1000.
Renukadevi S. Dyavanal 《Journal of Mathematical Analysis and Applications》2010,372(1):252-261
In this paper, we investigate uniqueness problems of meromorphic functions concerning differential polynomials sharing non-zero finite value and give some results. As particular cases of our results we deduce some significant results which improve several earlier results of Fang and Hong (2001) [2], Yang and Yi (2003) [7], Lin and Yi (2004) [5] and others. 相似文献