A polyhedron with alls—t cuts as vertices,and adjacency of cuts

Consider the polyhedron represented by the dual of the LP formulation of the maximums–t flow problem. It is well known that the vertices of this polyhedron are integral, and can be viewed ass–t cuts in the given graph. In this paper we show that not alls–t cuts appear as vertices, and we give a characterization. We also characterize pairs of cuts that form edges of this polyhedron. Finally, we show a set of inequalities such that the corresponding polyhedron has as its vertices alls–t cuts.Work done at the Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, India.     

On Bounded Variation Functions by General MKZD Operators

In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.     

[8+2] Cycloadditions involving 8-aryl-8-azaheptafulvenes and activated styrenes: efficient synthesis of dihydro-1-azaazulenes

Efficient [8+2] cycloaddition reactions of 8-aryl-8-azaheptafulvenes with doubly activated styrenes, leading to a facile synthesis of 1-aza-2-aryl-dihydroazulene derivatives are described.     

Simultaneous approximation for Bézier variant of Szász-Mirakyan-Durrmeyer operators

We study the rate of convergence in simultaneous approximation for the Bézier variant of Szász-Mirakyan-Durrmeyer operators by using the decomposition technique of functions of bounded variation.     

The processes of ordering and formation of two-dimensional glasses at metal surfaces

Using the experimental results obtained for the Dy-Mo(1 1 2) system, we discuss the possibilities and mechanisms of formation of two-dimensional (2D) glasses on metal surfaces. It has been found that in the coverage range 0.07 < θ < 0.58, ordered Dy superstructures formed and observed at T < 400 K are irreversibly destroyed by annealing to higher temperatures and turn into an amorphous (glass) structure on cooling. It is supposed that this conversion is caused by the formation, at T > 400 K, of a Dy-Mo surface alloy in which the rate of Dy surface diffusion is strongly reduced in comparison with its value in the absence of alloying. As a result, the mobility of Dy adatoms becomes too low at the temperatures corresponding to the ordered equilibrium state of the surface, and this state cannot be achieved in reasonable relaxation time. This interpretation is corroborated by the experimental data on substantial suppression of surface diffusion in some coadsorbed layers. Since surface glasses contact with ordered (crystalline) substrates, their structure may have a peculiar character different from that of “conventional” metal glasses. Surface glasses can find a number of applications as rather stable systems that combine low dimensionality, specific electronic structure of their constituents and extremely high density of defects.     

Synthesis of Novel Benzofuran‐Gathered C‐2,4,6‐substituted Pyrimidine Derivatives Conjugated by Sulfonyl Chlorides: Orally Bioavailable,Selective, Effective Antioxidants and Antimicrobials Drug Candidates

In the present study, we have made an effort to develop the novel synthetic antioxidants and antimicrobials with improved potency. The novel benzofuran‐gathered C‐2,4,6‐substituted pyrimidine derivatives 5a , 5b , 5c , 5d , 5e , 5f , 6a , 6b , 6c , 6d , 6e , 6f , 7a , 7b , 7c , 7d , 7e , 7f , 8a , 8b , 8c , 8d , 8e , 8f , 9a , 9b , 9c , 9d , 9e , 9f were synthesized by simple and efficient four‐step reaction pathway. Initially, o‐alkyl derivative of salicylaldehyde readily furnish corresponding 2‐acetyl benzofuran 2 in good yield, upon the treatment with potassium tertiary butoxide in the presence of molecular sieves. Further, Claisen–Schmidt condensation with aromatic aldehydes via treatment with thiourea followed by coupling reaction with different sulfonyl chlorides afforded target compounds. The structures of newly synthesized compounds were confirmed by IR, ¹H NMR, ¹³C NMR, mass, and elemental analysis and further screened for their antioxidant and antimicrobial activities. The results showed that the synthesized compounds 8b , 8e , 9b , and 9e produced significant antioxidant activity with 50% inhibitory concentration higher than that of reference, whereas compounds 7d and 7c produced dominant antimicrobial activity at concentrations 1.0 and 0.5 mg/mL compared with standard Gentamicin and Nystatin, respectively.     

An Efficient Synthesis of 3‐(3‐benzyl‐2‐(phenylimino)‐2,3‐dihydrothiazol‐4‐yl)‐6‐methyl‐4‐(2‐oxo‐2‐phenylethoxy)‐3,4‐dihydro‐2H‐pyran‐2‐one Derivatives via Multi‐Component Approach

An easy, highly efficient and a new convenient one‐pot, two‐step approach to the synthesis of 3‐(3‐benzyl‐2‐(phenylimino)‐2,3‐dihydrothiazol‐4‐yl)‐6‐methyl‐4‐(2‐oxo‐2‐phenylethoxy)‐3,4‐dihydro‐2H‐pyran‐2‐one is described. These compounds were synthesized from 3‐(3‐benzyl‐2‐(phenylimino)‐2,3‐dihydrothiazol‐4‐yl)‐4‐hydroxy‐6‐methyl‐3,4‐dihydro‐2H‐pyran‐2‐one and α‐bromoketones in good yields. The compounds 4 were synthesized by a multi‐component reaction between 1 , 2 , and 3 and the prominent features of this protocol are mild reaction conditions, operation simplicity, and good to high yields of products.