Let T (n, p) denote the class of functions of the form f (z) = z p − ∑ ∞ k=n ak+pz k+p (ak+p ≥ 0; p, n ∈ N ) which are analytic and p-valent in the open unit disc U = {z : |z| < 1}. For functions f j (z) ( j = 1, 2) belonging to T (n, p), generalizations of the modified-Hadamard product of f1(z) and f2(z) represented by ( f1∆ f2) (r, s; z) (r, s ∈ R) are introduced. In this paper, we obtain sev...

For a random variable Y, denote its survival function by ( ) ( ) = SY t P Y t > , its density function by ( ) fY t , and its hazard function by ( ) ( ( ) ) Y fY t h t SY t = − . Given a covariate (vector) Z which does not depend on time Y,(Z,Y) follows a time-independent covariate PH (TIPH) model or Cox’s regression model if the conditional hazard function of | Y Z is ( ) ( ) | ( ) | | , Z Y z ...

P(X = z t) = w t > 0. How to learn parameters {(w t , z t)} k t=1 ? Relatively straightforward given iid sample.

A sequence {an} in a group G is a T -sequence if there is a Hausdorff group topology τ on G such that an τ −→ 0. In this paper, we provide several sufficient conditions for a sequence in an abelian group to be a T -sequence, and investigate special sequences in the Prüfer groups Z(p∞). We show that for p 6= 2, there is a Hausdorff group topology τ on Z(p∞) that is determined by a T -sequence, w...

The Furstenberg–Sárközy theorem asserts that the difference set E?E of a subset E?N with positive upper density intersects image any polynomial P?Z[n] for which P(0)=0. Furstenberg's approach relies on correspondence principle and version Poincaré recurrence theorem, is derived from ergodic-theoretic result measure-preserving system (X,B,?,T) A?B ?(A)>0, one has c(A):=limN???1N?n=1N?(A?T?P(n)A)...

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Let P (z) be a polynomial of degree n and M(P, t) = Max|z|=t |P (z)|. In this paper we shall estimate M(P ′ , ρ) in terms of M(P, r) where P (z) does not vanish in the disk |z| ≤ K, K ≥ 1, 0 ≤ r < ρ < K and obtain an interesting refinement of some result of Dewan and Malik. We shall also obtain an interesting generalization as well as a refinement of well-known result of P. Turan for polynomial...

Gramhrar-heeocl p u r h e r s whi c h par form a uord-byword , p a r t so f-s p c o ~ t l p s y c h i a t r i c i n t e r v i e w s. The a l g o r i t h m uoeo p a t t e r n-m a t c h i n g r u l e s u h i c h a t t e m p t t o c h a r a c t e r i z e ths i n p u t e x p r e s s i o n s by p r o g r e s e i v e t y t r a n s f o r n ~ l n g them i n t o p a t t e r n s u h l c h match, c o n l ...

The spherical-harmonics method, also called the PN method, is used to develop solutions to a class of multi-group or non-gray radiation transport problems. The multigroup model considered allows an anisotropic scattering law and transfer from any group to any group. In addition to a spherical-harmonics solution for the case of a homogeneous radiative-transfer equation, a particular solution for...