E. Helly’s theorem asserts that any bounded sequence of monotone real functions contains a pointwise convergent subsequence. We reprove this theorem in a generalized version in terms of monotone functions on linearly ordered sets. We show that the cardinal number responsible for this generalization is exactly the splitting number. We also show that a positive answer to a problem of S. Saks is o...

optix is a new member of the Six/so gene family from Drosophila that contains both a six domain and a homeodomain. Because of its high amino acid sequence similarity with the mouse Six3 gene, optix is considered to be the orthologous gene from Drosophila rather than sine oculis, as previously believed. optix expression was detected in the eye, wing and haltere imaginal discs. Ectopic expression...

This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar functi...

This paper considers the classical Shannon sampling theorem in multiresolution spaceswith scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal. They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which...

abstract accurate prediction of hourly minimum temperature is required for various crop models which simulate photosynthesis and transpiration. such data can be used for crop protection and reducing the crops injuries due to freezing as well. our objective of this study is employing trigonometric and pattern recognition (k-nn) approaches to evaluate their potential in prediction of hourly tempe...

The main objective of this paper is to establish several new lower and upper bounds for the functions $\sinh x/x$ $\cosh x$. Following simple approach, our results give refinements generalizations some known inequalities involving these functions.