Baer Criterion for Injectivity of Projection Algebras

Projection algebras are M-sets for the monoid M = (ℕ^∞, min) which are used by computer scientists for algebraic specification of process algebras. In contrast to the case of modules it is well known that the Baer Criterion does not generally hold for injectivity of M-sets for an arbitrary monoid M. Here, introducing a closure operator, we prove that the Baer Criterion does hold for injectivity of projection algebras.     

Algebra in a Grothendieck topos: Injectivity in quasi-equational classes

This paper gives a study of injectivity and some related notions in quasi-equational classes of algebras in an arbitrary Grothendieck topos E. The main purpose is to describe the relationship between the class mod Σ of models of a set Σ of quasi-equations in the category of sets Ens and the corresponding class mod(Σ, E) of models of Σ in E with respect to residual smallness, boundedness of essential extensions and injectivity. The basic nature of our results is that, for any given Σ, whatever holds in Ens, concerning these notions, also holds in E. In particular, this substantially improves the earlier results of Howlett [5] regarding the existence of enough injectives in mod(Σ, E).     

A simple graphical approach to predict local residue conformation using NMR chemical shifts and density functional theory

The dependency of amino acid chemical shifts on φ and ψ torsion angle is, independently, studied using a five‐residue fragment of ubiquitin and ONIOM(DFT:HF) approach. The variation of absolute deviation of ¹³C^α chemical shifts relative to φ dihedral angle is specifically dependent on secondary structure of protein not on amino acid type and fragment sequence. This dependency is observed neither on any of ¹³C^β, and ¹H^α chemical shifts nor on the variation of absolute deviation of ¹³C^α chemical shifts relative to ψ dihedral angle. The ¹³C^α absolute deviation chemical shifts (ADCC) plots are found as a suitable and simple tool to predict secondary structure of protein with no requirement of highly accurate calculations, priori knowledge of protein structure and structural refinement. Comparison of Full‐DFT and ONIOM(DFT:HF) approaches illustrates that the trend of ¹³C^α ADCC plots are independent of computational method but not of basis set valence shell type. © 2016 Wiley Periodicals, Inc.     

Module Arens regularity for semigroup algebras

We extend the concept of Arens regularity of a Banach algebra to the case that there is an -module structure on , and show that when S is an inverse semigroup with totally ordered subsemigroup E of idempotents, then A=ℓ ¹(S) is module Arens regular if and only if an appropriate group homomorphic image of S is finite. When S is a discrete group, this is just Young’s theorem which asserts that ℓ ¹(S) is Arens regular if and only if S is finite. An erratum to this article can be found at     

An in silico approach to design peptide mimetics based on docking and molecular dynamics simulation of EGFR–matuzumab complex

Epidermal growth factor receptor (EGFR) plays an essential role in anticancer therapy. Matuzumab is an antibody for the treatment of colorectal, lung and stomach cancer. Matuzumab binds efficiently to EGFR and blocks its phosphorylation. The recent clinical successes have established application of peptides for cancer treatment. The present contribution introduces an in silico approach to design peptides based on molecular dynamics simulation (MDs) of the matuzumab-EGFR complex in water environment. Moreover, principal component analysis has been used to select multiple conformations of the complex in MDs for designing the peptides. The paratope and epitope in each conformation of the complex were determined, and the alanine scanning was used to identify the hot spots of EGFR conformers. The conformations of the peptides were optimized using PEP-FOLD server and MDs. The selected conformations were analyzed in a docking study to realize the binding site of the EGFR. Finally, pharmokinetics properties of the peptides were calculated. The designed oligopeptides were EWRSYYYWH, YYYWHNEWN, YYYWHNEWS and HNHSRNYGS with a higher affinity to the EGFR relative to the previously reported peptides. The newly designed peptides were investigated for their in vivo toxicities on rats, and all of them were non-toxic.     

Fe3O4–SiO2–Bi2O3-catalyzed One-Pot Synthesis of Tetrahydrobenzo[b]pyran Derivatives Under Solvent-Free Conditions

Russian Journal of Organic Chemistry - A Fe3O4–SiO2–Bi2O3 magnetic nanocatalyst was used to synthesize tetrahydrobenzo[b]pyran derivatives from malononitrile, cyclohexane-1,3-dione, and...     

Coloring of character graphs

In this paper, we study the character graph Δ(G) of a finite solvable group G. We prove that sum of the chromatic number of Δ(G) and the matching number of complement graph of Δ(G) is equal to the order of Δ(G). Also, we prove that when Δ(G) is not a block, the chromatic number of Δ(G) is equal to the clique number of Δ(G).     

Tautomerism of the antiepileptic drug Felbamate: A DFT study

The Felbamate is a novel anticonvulsant and neuropathic pain drug that can exist as three possible tautomers. Herein, employing density functional theory (DFT) and handling the solvent effects with the PCM model, the structural parameters, energy behavior, natural bond orbital analysis (NBO), as well as the tautomerism of Felbamate are investigated. F1 is the kinetically and thermodynamically most stable tautomer of Felbamate, which contains the amide group in each of the carbamate moieties. The calculated NMR chemical shifts and IR vibrational frequencies are in good agreement with the experimental values, confirming the suitability of the optimized geometry for Felbamate. The tautomerization reaction of F1 to each of the other tautomers occurs via an intramolecular proton transfer. This reaction affects considerably the structural parameters and atomic charges of the Felbamate molecule. A large HOMO-LUMO energy gap implies a high stability of the F1 tautomer.     

Some relations between rank of a graph and its complement

Let G be a graph of order n and rank(G) denotes the rank of its adjacency matrix. Clearly, . In this paper we characterize all graphs G such that or n + 2. Also for every integer n ? 5 and any k, 0 ? k ? n, we construct a graph G of order n, such that .