关于代数多项式的一个积分表示式

研究了代数多项式导数的Bernstein不等式和Markov不等式．通过代数多项式导数的一个积分表示式,给出这两个著名不等式以及它们的离散形式的证明．     

Foundation of credibilistic logic

In this paper, credibilistic logic is introduced as a new branch of uncertain logic system by explaining the truth value of fuzzy formula as credibility value. First, credibilistic truth value is introduced on the basis of fuzzy proposition and fuzzy formula, and the consistency between credibilistic logic and classical logic is proved on the basis of some important properties about truth values. Furthermore, a credibilistic modus ponens and a credibilistic modus tollens are presented. Finally, a comparison between credibilistic logic and possibilistic logic is given.     

高阶Bernoulli数的递推公式及其应用

给出了高阶Bernoulli数的一个递推公式和Nrlund数的一个计算公式,推广了Namias[4],Deeba和Rodriguez[5],Tuenter[6]的结果.     

Off-line coupling of pressurized liquid extraction and LC/ED for the determination of retinyl acetate and tocopherols in infant formulas

An analytical methodology including pressurized liquid extraction (PLE) as sample treatment to isolate retinyl acetate and tocopherols from infant formulas has been developed. The milk extracts were kept at −18 °C for 30 min and after filtration could be injected directly into the chromatographic system. Thus, a rapid and simple routine control method of these products is possible.

The parameters affecting both the extraction process and the liquid chromatography (LC) system were optimized. PLE was performed using one cycle of extraction during a static time of 5 min. Methanol was chosen as the extraction solvent for a temperature of 50 °C. Chromatographic separation was accomplished using a RP-18 column; the mobile phase used was methanol–water (94:6, v/v) containing 2.5 mM acetic acid/sodium acetate buffer. Electrochemical detection in amperometric mode with a glassy carbon electrode at +1100 mV was applied. The proposed methodology was successfully used for the determination of retinyl acetate, δ-tocopherol, (β + γ)-tocopherol and -tocopherol in different infant formulas. The analytes were evaluated in the same chemical form present in the samples. Recoveries were between 92 and 106%. A certified reference material of milk powder was also analyzed.     

Two-parameter p, q-variation Paths and Integrations of Local Times

In this paper, we prove two main results. The first one is to give a new condition for the existence of two-parameter -variation path integrals. Our condition of locally bounded -variation is more natural and easy to verify than those of Young. This result can be easily generalized to multi-parameter case. The second result is to define the integral of local time pathwise and then give generalized It’s formula when is only of bounded -variation in . In the case that is of locally bounded variation in , the integral is the Lebesgue–Stieltjes integral and was used by Elworthy, Truman and Zhao. When is of only locally -variation, where , , and , the integral is a two-parameter Young integral of -variation rather than a Lebesgue–Stieltjes integral. In the special case that is independent of , we give a new condition for Meyer's formula and is defined pathwise as a Young integral. For this we prove the local time is of -variation in for each , for each almost surely (-variation in the sense of Lyons and Young, i.e. ).     

An Itô formula for a fractional Brownian sheet with arbitrary Hurst parameters

By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the fractional Brownian sheet with arbitrary Hurst parameters .

     

Algebraic properties of some new vector-valued rational interpolants

In a recent paper of the author [A. Sidi, A new approach to vector-valued rational interpolation, J. Approx. Theory, 130 (2004) 177–187], three new interpolation procedures for vector-valued functions F(z), where , were proposed, and some of their properties were studied. In this work, after modifying their definition slightly, we continue the study of these interpolation procedures. We show that the interpolants produced via these procedures are unique in some sense and that they are symmetric functions of the points of interpolation. We also show that, under the conditions that guarantee uniqueness, they also reproduce F(z) in case F(z) is a rational function.     

An estimate for multivariate interpolation II

Suppose u is a function on a domain Ω in all of whose mth order distributional derivatives are in L^p(Ω) and m is sufficiently large to imply that u is continuous. If the values of u on a sufficiently dense, but not necessarily regular, grid of points are in l^p we obtain an estimate of the L^p(Ω) norm of u in terms of the l^p norm of these values and the L^p norms of its mth order derivatives. This result is useful in obtaining error estimates for certain interpolation schemes.     

Optimal quadrature problem on classes defined by kernels satisfying certain oscillation properties

We consider some classes of 2π-periodic functions defined by a class of operators having certain oscillation properties, which include the classical Sobolev class and a class of analytic functions which can not be represented as a convolution class as its special cases. Let be the largest integer not bigger than x. We prove that on these classes of functions the rectangular formula

On best localized bandlimited functions

Let, for σ > 0, be the set of complex functions f ∈ L ¹ (ℝ) with the Fourier transforms vanishing outside the interval [−σ; σ]. In this paper, we study the problem of the best approximation of the Dirac function δ (which has the Fourier transform with widest support supp ) by functions . More precisely, we consider the quantity inf and its extremal functions . __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 548–564, October–December, 2006.