The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...

The homeobox gene superfamily is highly conserved during evolution. These genes act as transcription factors during several important developmental processes through their 60 amino acid homeodomains that recognize and bind to the regulatory region of their target genes. We isolated a novel homeobox gene designated Tex1 from a mouse testis cDNA library by degenerate oligonucleotide polymerase ch...

Abstract Since the emergence of Triple Helix, expansions to Quadruple, Quintuple, N-tuple helices, and models decomposing higher-order helices into multiple interrelated triple or two-layer have been proposed. Albeit presenting alternative conceptual frameworks these different Helix seem unsuited address internal boundaries institutional spheres university, industry, government. Addressing this...

Jing Yang, 2 Charles W. Wolgemuth, 3, 4 and Greg Huber 3, 5, ∗ Richard Berlin Center for Cell Analysis & Modeling, University of Connecticut Health Center, Farmington, Connecticut 06030, USA Department of Physics, Haverford College, Haverford, Pennsylvania 19041, USA Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut 06030, USA Departments of Physics an...

This study compared the different effects of pectin (PE) and ?-carrageenan (CG) on multilevel structures (i.e. granule, crystallites, helices, fractals, short-range order) in vitro digestibility extruded rice starch (MERS). The addition either PE or CG altered multiscale structures, increased resistant component (RC) content, reduced predicted glycemic index (pGI), with being more effective esp...