Báo cáo hóa học: "ON SOME TURÁN-TYPE INEQUALITIES" potx

... article Abstract In the present paper we establish some new Opial-type inequalities involving higher- order partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality ... paper is to establish some new Opial-type inequalities involving higher-order part ial derivatives by an exten- sion of Das’s idea [28]. Our results in special cases yield...

Ngày tải lên: 21/06/2014, 03:20

... t t  e t − 1  dt. (2.6) ON SOME TURÁN-TYPE INEQUALITIES A. LAFORGIA AND P. NATALINI Received 14 September 2005; Accepted 20 September 2005 We prove Tur ´ an-type inequalities for some special functions ... Mathematicae 44 (1982), no. 3, 295–301. [7] A. Laforgia and P. Natalini, Tur ´ an-type inequalities for some special functions, to appear in Journal of Inequalities in Pure and Appl...

Ngày tải lên: 22/06/2014, 21:20

... boundary. It is possible to estimate the difference |K ε - K 0 | more precisely in some partial cases. For some particular cases, it is in fact possible to construct an asymptotic expansion for ... equation in a domain perforated along the boundary. Russ Math Surv. 45(4), 123 (1990) 8. Sobolev, SL: Some applications of functional analysis in mathematical physics. Translations of Mathema...

Ngày tải lên: 20/06/2014, 23:20

... P k  x   ≤ C(φ)φ(A)(A ⊂ X bounded) (4.16) for some C(φ) > 0. Some estimates, or even explicit formulas, for the minimal constant C(φ) in some important Banach spaces may be found in [2,Chapter2]. 318 ... com- pact. Suppose that g(x) = λx for some λ>0andx ∈ S( 2 ). Writing this out in components means that −µ k ξ k =−µ k ξ k +(1−x)µ k = λξ k for all k,henceλ =−µ k for some...

Ngày tải lên: 23/06/2014, 00:20

... MULTIPLE HARDY-HILBERT INTEGRAL INEQUALITIES WITH SOME PARAMETERS HONG YONG Received 19 April 2006; Revised 30 May 2006; Accepted 5 June 2006 By introducing some parameters and norm x α (x ∈ R n ), ... K<K 1 .Hencetheconstantfactorin(3.20)isthebest possible. Since (3.21)and(3.20) are equivalent, the constant factor in (3.21)isalsothebest possible.  4. Some corollaries Corollary 4....

Ngày tải lên: 22/06/2014, 22:20

... Advances in Signal Processing see [9, 23–27] and so forth. We now briefly review its definition and some basic properties. For given function f (t) ∈ L 1 (R)∩L 2 (R)andf (t) 2 = 1 (in this article ... 359–367, 2007. [21] A. Stern, “Uncertainty principles in linear canonical transform domains and some of their implications in optics,” Journal of the Optical Society of America A, vol. 25, n...

Ngày tải lên: 21/06/2014, 20:20

... (0,∞), (b) Γ is strictly increasing, Γ(2t) ≥ ηΓ(t)forsomefixedη>1andΓ(2t) ≤ cΓ(t)for some constant c ≥ η>1. (c) Γ  (t) ≥ αΓ(t)/t on (0,∞)forsomefixedα ∈ (0,log 2 c]andΓ  (t) is monotone on (0, ∞). Definit ... (0,∞), (b  ) Γ is strictly decreasing, Γ(t) ≥ ηΓ(2t)forsomefixedη>1andΓ(t) ≤ cΓ(2t)for some constant c ≥ η>1. (c  ) |Γ  (t)|≥αΓ(t)/t on (0,∞)forsomefixedα ∈ (0, log 2 c]a...

Ngày tải lên: 22/06/2014, 22:20

... the fractal dimensions Dim and  δ can be derived from M ∗s and M s ∗ , respectively. Moreover, some inequalities about the dimension of product sets and product measures are obtained. Copyright ... ≤  δ(μ × ν) ≤  δ(μ)+Dim(ν) ≤ Dim(μ × ν) ≤ Dim(μ)+Dim(ν). (1.6) 2. Background Let us first recall some basic properties of Hausdorff measure, Hausdorff dimension, packing measure, packing dimens...

Ngày tải lên: 22/06/2014, 22:20

... problem (1.3), we prove several new results guaranteeing the existence of solutions (see Section 3). Some location information on the solution set of problem (1.3) is also available through our results, ... problem (1.3) and hypothesis (H2). The rest of the paper is organized as follows. Section 2 contains some preliminary results to set up our topological degree framework. Section 3 is d...

Ngày tải lên: 23/06/2014, 00:20

... = (1−x) c−a−b F (c−a, c−b; c; x), c < a+b. Some basic properties of this series may be found in standard handbooks, see for ex- ample [1]. For some rational triples (a, b, c), the functions ... complete answer to an open question posed in [2]. 2. Preliminary results In this section, we recall some well-known properties of the Gaussian hypergeometric function F(a, b; c; x) and certain...

Ngày tải lên: 18/06/2014, 15:20