Abstract. If f(t) = ∑∞ k=0 akt k converges for all t ∈ IR with all coefficients ak ≥ 0, then the function f(< x,y >) is positive definite on H ×H for any inner product space H. Set K = {k : ak > 0}. We show that f(< x,y >) is strictly positive definite if and only if K contains the index 0 plus an infinite number of even integers and an infinite number of odd integers.

potato image segmentation is an important part of image-based potato defect detection. this paper presents a robust potato color image segmentation through a combination of a fuzzy rule based system, an image thresholding based on genetic algorithm (ga) optimization and morphological operators. the proposed potato color image segmentation is robust against variation of background, distance and ...

The partial sums f3(z) of some extermal functions for various classes S∗, K and R of starlike functions, convex functions and functions with positive real part in the open unit disk U, respectively, are discussed. In general, the partial sums can not preserve the same character as the initial functions. The object of the present paper is to discuss the radius problems for partial sums of some e...

The class of univalent harmonic functions on the unit disc satisfying the condition ∑∞ k=2 (k m − αk)(|ak|+ |bk|) ≤ (1−α)(1−|b1|) is given. Sharp coefficient relations and distortion theorems are given for these functions. In this paper we find that many results of Özturk and Yalcin [5] are incorrect. Some of the results of this paper correct the theorems and examples of [5]. Further, sharp coe...

for some α (0≤α< 1). We say that f(z) is in the class ∑C(α) of such functions. The class ∑∗(α) and various other subclasses of ∑ have been studied rather extensively by Nehari and Netanyahu [9], Clunie [4], Pommerenke [11, 12], Miller [7], Royster [13], and others (cf., e.g., Bajpai [2], Goel and Sohi [6], Mogra et al. [8], Uralegaddi and Ganigi [15], Cho et al. [3], Aouf [1], and Uralegaddi an...

I t i s well-known t h a t k r i g i n g and i n t e r p o l a t i o n by s p l i n e s a r e e q u i v a l e n t . Kr ig ing i s based on a s t o c h a s t i c f o r m u l a t i o n whereas s p l i n e s a r e f o r m u l a t e d I n a d e t e r m i n i s t i c way. A t h i r d p r e s e n t a t i o n i s g i v e n i n terms of Rad ia l P a s i s F u n c t i o n s . The c n n n e c t l o n s b...