From the Bethe Ansatz to the Gessel-Viennot theorem

We state and prove several theorems that demonstrate how the coordinate Bethe Ansatz for the eigenvectors of suitable transfer matrices of a generalized inhomogeneous, five-vertex model on the square lattice, given certain conditions hold, is equivalent to the Gessel-Viennot determinant for the number of configurations ofN non-intersecting directed lattice paths, or vicious walkers, with various boundary conditions. Our theorems are sufficiently general to allow generalisation to any regular planar lattice.     

Synthesis and Screening of Phosphodiesterase 5 Inhibitory Activity of Fused and Isolated Triazoles Based on Thieno[2,3‐d]pyrimidines

Novel fused and isolated triazoles based on thieno[2,3‐d]pyrimidines were synthesized starting from 2‐aminothiophene ester and structurally confirmed by spectral and analytical data. The synthesized triazolo compounds were screened for their phosphodiesterase 5 inhibitory activity and showed encouraging activity than did sildenafil as a reference drug.     

Single Peptide Backbone Surrogate Mutations to Regulate Angiotensin GPCR Subtype Selectivity

Mutating the side-chains of amino acids in a peptide ligand, with unnatural amino acids, aiming to mitigate its short half-life is an established approach. However, it is hypothesized that mutating specific backbone peptide bonds with bioisosters can be exploited not only to enhance the proteolytic stability of parent peptides, but also to tune its receptor subtype selectivity. Towards this end, four [Y]⁶-Angiotensin II analogues are synthesized where amide bonds have been replaced by 1,4-disubstituted 1,2,3-triazole isosteres in four different backbone locations. All the analogues possessed enhanced stability in human plasma in comparison with the parent peptide, whereas only two of them achieved enhanced AT₂R/AT₁R subtype selectivity. This diversification has been studied through 2D NMR spectroscopy and unveiled a putative more structured microenvironment for the two selective ligands accompanied with increased number of NOE cross-peaks. The most potent analogue, compound 2 , has been explored regarding its neurotrophic potential and resulted in an enhanced neurite growth with respect to the established agent C21.     

An analytical technique for solving a class of strongly nonlinear conservative systems

Recently, an analytical technique has been developed to determine approximate solutions of strongly nonlinear differential equations containing higher order harmonic terms. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. Previously such algebraic equations for the Duffing equation were solved in powers of a small parameter; but the solutions measure desired results when the amplitude is an order of 1. In this article different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. Moreover, two or three terms of this power series solution measure a good result when the amplitude is an order of 1. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the Duffing oscillator but it is also useful for many other nonlinear problems.     

Mean Length of Finite Clusters in Directed Compact Percolation Near a Damp Wall

The mean length of finite clusters is derived exactly for the case of directed compact percolation near a damp wall. We find that the result involves elliptic integrals and exhibits similar critical behaviour to the dry wall case.     

Antihyperglycaemic and hypolipidaemic effects of the methanolic extract of Caralluma tuberculata in streptozotocin-induced diabetic rats

The antihyperglycaemic and hypolipidaemic effects of the methanolic extract of Caralluma tuberculata were investigated in streptozotocin (STZ)-induced diabetic rats. The antihyperglycaemic activity was assessed by the reduction in fasting blood glucose (54% at 4th week) and the peak of blood glucose at 120?min of an oral glucose tolerance test in diabetic rats. Further, the tested extract also increased plasma insulin by 206.8%. The hypolipidaemic action of the extract was evident by the significant decrease in the levels of total cholesterol, triglycerides and LDL-cholesterol by 41.5%, 36.7% and 49.1%, respectively, compared to diabetic rat values. Interestingly, the extract increased the cardio-protective lipid HDL-cholesterol by 147.97% as compared to diabetic rat value. The present data suggests that the methanolic extract of C. tuberculata has both antihyperglycaemic and hypolipidaemic effects in STZ-induced diabetic rats that may need further studies to be used in the management of diabetes and associated hyperlipedaemia.     

Androgen receptor antagonists and anti-prostate cancer activities of some synthesized steroidal candidates

In continuation of our previous work, a novel series of steroid derivatives were synthesized and their androgen receptor (AR) antagonist activities and in vivo antiandrogenic properties were evaluated. Twenty-one heterocyclic derivatives containing a cyanopyrane ring fused to a steroidal moiety were conveniently synthesized and screened for their antagonistic, antiandrogen and prostate anticancer activities comparable to that of bicalutamide as the reference control. Some of the compounds exhibited better antagonistic, antiandrogen and prostate anticancer activities than the reference controls. Initially the acute toxicity of the compounds was assayed via the determination of their LD(50). Synthetic steroidal structures fused to a substituted cyanopyrane ring seem to be a promising approach in the search for novel leads for potent antagonistic, antiandrogen and prostate anticancer agents.     

Synthesis and in vitro antimicrobial activity of some pyrazolyl-1-carboxamide derivatives

A series of 3,5-disubstituted pyrazole-1-carboxamides were obtained by treatment of chalcones with semicarbazide hydrochloride in dioxane containing sodium acetate/acetic acid as a buffer solution. N-acetyl derivatives of pyrazole-1-carboxamides were isolated in good yields either by treatment of the carboxamide derivatives with acetic anhydride or refluxing chalcones with semicarbazide in ethanol containing few drops of acetic acid to give the corresponding hydrazones. Subsequent treatment of hydrazones with acetic anhydride gave the desired N-acetyl pyrazole-1-carboxamides derivatives. When chalcones were refluxed with dioxane containing few drops of acetic acid, 4,5-dihydropyrazole-1-carboxamides were isolated, which were subsequently oxidized using 5% sodium hypochlorite in dioxane to afford pyrazole-1-carboxamides. The structures of isolated compounds were confirmed by elemental analyses and spectral methods. The isolated compounds were tested for their antimicrobial activities.     

Synthesis of N 1 -Substituted,N 3 -[ P -(3-Ethoxy-Carbonyl-4,5-Dihydronaphtho[1,2- c ]Pyrazol-2-YL)Benzenesulfonyl]Urea and Thiourea Derivatives. Class of Cyclooxygenase-2 Inhibitors

Several urea and thiourea derivatives ( 2a-f ) were prepared by the reaction of dihydronaphthopyrazolylbenzenesulfonamide ( 1 ) with the corresponding isocyanates and isothiocyanates, respectively. The benzenesulfonylthioureas ( 2d , e ) were cyclized with ethyl bromoacetate, ethyl g -bromopropionate and f -bromoacetophenones to give the corresponding 4-oxothiazolidine ( 3a , b ), 4-oxo-5,6-dihydrothiazine ( 4a , b ) and thiazoline derivatives ( 5a-d ) respectively.     

A Convenient Synthesis for Some New Pyrido[4′,3′:4,5]thieno[2,3-d]pyrimidines and Related Fused 1,2,4-Triazolo and 1,3,4-Thiadiazolo-derivatives

Diethyl 2-isothiocyanato-4,5,6,7-tetrahydrothieno[2,3-c]pyridine-3,6 dicarboxylate 1 is a convenient and useful starting matrial for the constructions of heterocyclic systems. It was utilized to synthesize derivatives of the novel heterocyclic systems pyrido[4',3':4,5]thieno[2,3-d]pyrimidine 4 , 10 , pyrido[4',3':4,5]thieno[2,3-d]-[1,2,4]triazolo[1,5-a]pyrimidine 7 , 11a-e and pyrido[4',3':4,5]thieno[2,3-d][1,3,4]thiadiazolo[3,2-a]pyrimidine 12-14 .