Convex Functions, Partial Orderings, and Statistical by Josip E. Pečarić, Frank Proschan and Y.L. Tong (Eds.)

By Josip E. Pečarić, Frank Proschan and Y.L. Tong (Eds.)

Show description

Read Online or Download Convex Functions, Partial Orderings, and Statistical Applications PDF

Best technique books

Triumph Bonneville, T100, Speedmaster, America, Thruxton and Scrambler Service and Repair Manual - 2001 to 2007 (Haynes Service and Repair Manuals)

Triumph Bonneville, T100, Speedmaster, the United States, Thruxton and Scrambler provider and service handbook - 2001 to 2007 (Haynes provider and service Manuals) КНИГИ,ТЕХНИКА Author(s): Matthew Coombs, Phil Mather writer: Haynes Date : 2008 Pages: 272 structure : PDF OCR: N Language : English ISBN-10: 1844257363 measurement : 21.

Испытания и измерения в электросетях 0,4-20 кВ

Книга посвящена вопросам испытания электрооборудования воздушных распределительных сетей 0,4-20 кВ. Освещены вопросы измерения электрических параметров сети, рассмотрены методы испытания электрооборудования на стационарных стендах и с помощью передвижных лабораторий, описаны виды и объем испытаний, даны сведения об испытательной аппаратуре и электролабораториях.

Fiber Optic Sensors, Second Edition (Optical Science and Engineering Series)

The necessity for either intrinsic and extrinsic fiber optic sensor applied sciences maintains to develop. to satisfy the calls for of this quick increasing applications-driven industry, Fiber Optic Sensors, moment version provides either the newest advances in fiber optic sensor expertise, comparable to the applying of photonic crystal fibers to fiber optic gyroscopes, and up to date software possibilities, together with using fiber optic sensors as a minimally invasive clinical remedy.

Additional info for Convex Functions, Partial Orderings, and Statistical Applications

Example text

Many other inequalities can be obtained from it. Thus this inequality and many of its useful consequences are discussed here. 1. Theorem (Jensen's Inequality). If I is an interval in ~ and f: I -- ~ is convex, x = (Xl' . . , Xn) E I" (n 2: 2), P = (PI' ... , Pi> 0), and Pk = r . ~ ~ lPi (k = 1 , ... 1) = ... = Xn. Proof. 1) is by induction. The case n = 2 follows from the definition of convex functions. Suppose that the result is valid for all 43 44 2. Jensen's and Jensen-Stelfensen's Inequalities k, 2:5 k :5 n - 1.

B) Let ui(t) = ti, i = 0, 1, . . , n. Then C ( l , t, t2, . . , t") is the set of all n-convex functions on (a, b). , l,l, [ X o , . . , 3 * * . 9 1, t, . . , t" Xn-I 9 Xn XO,X I , ... xn and 1, t, . . , tn (xi-xj)>o i>j is the well-known van der Monde's determinant. 4. Functions Convex with Respect to an ECT System of Functions 25 (c) If Uo(t) = 1 and u1(t) satisfies u{(t) > 0 for all t E (a, b), then C(1, UI(t» comprises the set of all functions which are convex with respect to Ul(t) on (a, b) (Karlin and Studden, 1966, p.

Assume that f, g g(b):::Sf(b), E W::'[a, b]. (a) If g(k)(a)2:f(k)(a) (k=0, ... 99) and [Xo, ... ,xn]g:::s[xo, ... 100) then g(k)(b) :::Sf(k)(b) (k = 1, ... , n -1). (b) If g(m)(b) = f(m)(b) for some 1 :::s m :::s n - 1, then g == f. Proof. 99) we have - g, Sn-l = b and So = ... = k (b - a) [a, ... ,j ~ O a. Then from . (b - a Y2: 0 ] • for k = 0, ... 66 yields (a). Now assume that h(m)(b) = 0 for some 1:::s m :::s n -1. 66, h e Ilm-l on [a, b] and thus m O=(b-a) [a, ... ,a,b]h=h(b)(m times) m-l h(j)(a) 2: j=O .

Download PDF sample

Rated 4.34 of 5 – based on 40 votes