Sequence Space

Given three Banach spaces X, Y and Z and a bounded bilinear map , a sequence x=n(xn)⊆X is called B-absolutely summable if is finite for any y∈Y. Connections of this space with are presented. A sequence x=n(xn)⊆X is called B-unconditionally summable if is finite for any y∈Y and z∗∈Z∗ and for any M⊆N there exists xM∈X for which ∑n∈M〈B(xn,y),z∗〉=〈B(xM,y),z∗〉 for all y∈Y and z∗∈Z∗. A bilinear version of Orlicz–Pettis theorem is given in this setting and some applications are presented.

Evolution is a highly complex multilevel process and mathematical modeling of evolutionary phenomenon requires proper abstraction and radical reduction to essential features. Examples are natural selection, Mendel’s laws of inheritance, optimization by mutation and selection, and neutral evolution. An attempt is made to describe the roots of evolutionary theory in mathematical terms. Evolution can be studied in vitro outside cells

In this study, we used in vitro protein evolution with ribosome and phage display to optimize the affinity of a human IL-13-neutralizing antibody, a therapeutic candidate for the treatment of asthma, >150-fold to 81 pM by using affinity-driven stringency selections. Simultaneously, the antibody potency to inhibit IL-13-dependent proliferation in a cell-based functional assay increased 345-fold to an IC50 of 229 pM. The panoply of different optimized sequences resulting from complementarity-determining region-targeted mutagenesis and error-prone PCR using ribosome display was contrasted with that of complementarity-determining region-targeted mutagenesis alone using phage display. The data highlight the advantage of the ribosome-display approach in identifying beneficial mutations across the entire sequence space. A comparison of mutation hotspots from in vitro protein evolution to knockout mutations from alanine scanning demonstrated that in vitro evolution selects the most appro...

This paper is concerned with the estimation and evaluation of wavelet coefficients of the composition F◦ u of two functions F and u from the wavelet coefficients of u. Our main objective is to show that certain sequence spaces that can be used to measure the sparsity of the arrays of wavelet coefficients are stable under a class of nonlinear

Binod CHANDRA TRIPATHY1 and AYHAN ESI2 1Mathematical Sciences Division; Institute of Advanced Study in Science and Technology; Paschim Boragaon; GARCHUK; GUWAHATI-781 035, INDIA 2Inonu University, Science and Art Faculty in Adiyaman, 02040, Adıyaman, ...

The idea of difierence sequence spaces were intro- duced by Kizmaz (6) and generalized by Et. and Colak (4). Later Tripathy, Esi and Tripathy (15) introduced the notion of the new difierence operator ¢n m for n;m 2 N. In this paper we intro- duced some new type of generalized difierence sequence spaces deflned by a modulus function and the

Consider an n by n matrix x_ij, and consider the quantity || x_{i,pi(i)} ||_X where X is a symmetric sequence space as a random variable where the permutation pi is chosen randomly. This was considered by Kwapien and Schutt, and we extend their results to rearrangement invariant spaces. We also consider the property of D and D^* convexity for rearrangement invariant spaces.

In this work, we define new sequence spaces by combining generalized weighted mean and difference operator. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the alpha, beta and gamma duals, and obtain bases for these sequence spaces. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes (c(u,v,):ℓ_∞) and (c(u,v,):c) are established.