Shiv Nadar University

About: Shiv Nadar University is a education organization based out in Dadri, Uttar Pradesh, India. It is known for research contribution in the topics: Population & Graphene. The organization has 1015 authors who have published 1924 publications receiving 18420 citations.

Generalized Envelope Theorems: Applications to Dynamic Programming

Abstract: We show in this paper that the class of Lipschitz functions provides a suitable framework for the generalization of classical envelope theorems for a broad class of constrained programs relevant to economic models, in which nonconvexities play a key role, and where the primitives may not be continuously differentiable. We give sufficient conditions for the value function of a Lipschitz program to inherit the Lipschitz property and obtain bounds for its upper and lower directional Dini derivatives. With strengthened assumptions we derive sufficient conditions for the directional differentiability, Clarke regularity, and differentiability of the value function, thus obtaining a collection of generalized envelope theorems encompassing many existing results in the literature. Some of our findings are then applied to decision models with discrete choices, to dynamic programming with and without concavity, to the problem of existence and characterization of Markov equilibrium in dynamic economies with nonconvexities, and to show the existence of monotone controls in constrained lattice programming problems.

In silico study of peptide inhibitors against BACE 1

Abstract: Peptides are increasingly used as inhibitors of various disease specific targets. Several naturally occurring and synthetically developed peptides are undergoing clinical trials. Our work explores the possibility of reusing the non-expressing DNA sequences to predict potential drug-target specific peptides. Recently, we experimentally demonstrated the artificial synthesis of novel proteins from non-coding regions of Escherichia coli genome. In this study, a library of synthetic peptides (Synpeps) was constructed from 2500 intergenic E. coli sequences and screened against Beta-secretase 1 protein, a known drug target for Alzheimer’s disease (AD). Secondary and tertiary protein structure predictions followed by protein–protein docking studies were performed to identify the most promising enzyme inhibitors. Interacting residues and favorable binding poses of lead peptide inhibitors were studied. Though initial results are encouraging, experimental validation is required in future to develop efficient target specific inhibitors against AD.

Chapter 24 – Cardanol-Based Benzoxazines and Their Applications

Abstract: This chapter explores the utility of cardanol as a potential feedstock for the synthesis of benzoxazine monomers and polymers. Cardanol is a renewable phenolic compound obtained from the plant Anacardium occidentale L. Commercially it is produced as cashew nut shell liquid (CNSL) as a byproduct of cashew nut processing. It is currently under exploration as a valuable phenolic reagent in benzoxazine monomers and polymers. Cardanol-based benzoxazines are attractive monomers due to their sustainable aspect, opportunities for solventless synthesis, and processing. To date, Cardanol monomers have primarily been utilized for adhesive and composite applications, but they are ideal candidates for a variety of other applications, which need further exploration.

Derivatives of tensor powers and their norms

Abstract: The norm of the mth derivative of the map that takes an operator to its kth antisymmetric tensor power is evaluated. The case m = 1 has been studied earlier by Bhatia and Friedland (R. Bhatia and S. Friedland. Variation of Grassman powers and spectra. Linear Algebra and its Applications, 40:1-18, 1981). For this purpose a multilinear version of a theorem of Russo and Dye is proved: it is shown that a positive m-linear map between C � -algebras attains its norm at the m-tuple (I, I,...,I). Expressions for derivatives of the maps that take an operator to its kth tensor power and kth symmetric tensor power are also obtained. The norms of these derivatives are computed. Derivatives of the map taking a matrix to its permanent are also evaluated.