Synthesis,Antibacterial, and Antioxidant Evaluation of Novel Series of Condensed Thiazoloquinazoline with Pyrido,Pyrano, and Benzol Moieties as Five- and Six-Membered Heterocycle Derivatives

A novel synthesis of thiazolo[2,3-b]quinazolines 4(a–e), pyrido[2′,3′:4,5]thiazolo[2,3-b]quinazolines {5(a–e), 6(a–e), and 7(a–e)}, pyrano[2′,3′:4,5]thiazolo[2,3-b]quinazolines 8(a–e), and benzo[4,5]thiazolo[2,3-b]quinazoloine9(a–e) derivatives starting from 2-(Bis-methylsulfanyl-methylene)-5,5-dimethyl-cyclohexane-1,3-dione 2 as efficient α,α dioxoketen dithioacetal is reported and the synthetic approaches of these types of compounds will provide an innovative molecular framework to the designing of new active heterocyclic compounds. In our study, we also present optimization of the synthetic method along with a biological evaluation of these newly synthesized compounds as antioxidants and antibacterial agents against the bacterial strains, like S. aureus, E. coli, and P. aeruginosa. Among all the evaluated compounds, it was found that some showed significant antioxidant activity at 10 μg/mL while the others exhibited better antibacterial activity at 100 μg/mL. The results of this study showed that compound 6(c) possessed remarkable antibacterial activity, whereas compound 9(c) exhibited the highest efficacy as an antioxidant. The structures of the new synthetic compounds were elucidated by elemental analysis, IR, ¹H-NMR, and ¹³C-NMR.     

Review paper: Design of a mass and ion kinetic energy spectrometer for organic chemical work

The design of a mass spectrometer for the determination of the structural formulae of organic compounds is discussed. The ion-optical characteristics of electric and magnetic sectors and also of quadrupole mass analysers are considered and the additional information that can be gleaned when such components are combined in various ways is listed. The advantages of using collision cells for inducing fragmentation of selected ion species are listed including those that result when the collision cell is floated at an electrical potential different from that of the incident ion beam. Important performance characteristics are the resolution with which a particular ion may be selected and the resolution with which daughter ions formed from it can be separated. It is concluded, that for instruments comprising three analysing units together with the appropriate collision cells, the most versatile combinations and those with the highest performance are an arrangement consisting of a magnetic sector followed by an electric sector, this being followed either by a further magnetic sector or a quadrupole. The properties of these two systems are compared in detail.     

A proof of Markov's theorem for polynomials on Banach spaces

Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The statement of this theorem differs little from the classical case for the real line except that absolute values are replaced by norms. Our proof depends only on elementary computations and explicit formulas and gives a new proof of the classical theorem as a special case. Our approach makes no use of the classical polynomial inequalities usually associated with Markov's theorem. Instead, the essential ingredients are a Lagrange interpolation formula for the Chebyshev nodes and a Christoffel-Darboux identity for the corresponding bivariate Lagrange polynomials. We use these tools to extend a single variable inequality of Rogosinski to the case of two real variables. The general Markov theorem is an easy consequence of this.     

An Identification Problem for First-Order Degenerate Differential Equations

We study a first-order identification problem in a Banach space. We discuss the nondegenerate and mainly the degenerate case. As a first step, suitable hypotheses on the involved closed linear operators are made in order to obtain unique solvability after reduction to a nondegenerate case; the general case is then handled with the help of new results on convolutions. Some applications to partial differential equations motivate this abstract approach.Communicated by I. GalliganiWork partially supported by MIUR (Ministero dell’ Istruzione, dell’ Università e dalla Ricerca), Project PRIN 2004011204 “Analisi Matematica nei Problemi Inversi,” and by the University of Bologna Funds for Selected Research Topics.     

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress. This instability is called the Rayleigh-Plateau instabilty. We consider the model developed by Spencer et ...     

On product-cordial index sets and friendly index sets of 2-regular graphs and generalized wheels

A vertex labeling f : V → Z2 of a simple graph G = (V, E) induces two edge labelings f+ , f*: E → Z2 defined by f+ (uv) = f(u)+f(v) and f*(uv) = f(u)f(v). For each i∈Z2 , let vf(i) = |{v ∈ V : f(v) = i}|, e+f(i) = |{e ∈ E : f+(e) = i}| and e*f(i)=|{e∈E:f*(e)=i}|. We call f friendly if |vf(0)-vf(1)|≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets{|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)| : f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.     

Automorphisms of η‐like computable linear orderings and Kierstead's conjecture

We develop an approach to the longstanding conjecture of Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η‐like computable linear ordering , such that has no interval of order type η, and such that the order type of is determined by a ‐limitwise monotonic maximal block function, there exists computable such that has no nontrivial automorphism.     

The Approximation Numbers of Hardy-Type Operators on Trees

The Hardy operator T_a on a tree is defined by Properties of T_a as a map from L^p() into itselfare established for 1 p . The main result is that, with appropriateassumptions on u and v, the approximation numbers a_n(T_a) ofT_a satisfy for a specified constant _p and 1 p < . This extends results of Naimark, Newmanand Solomyak for p = 2. Hitherto, for p 2, (*) was unknowneven when is an interval. Also, upper and lower estimates forthe l^q and weak-l^q norms of a_n(T_a) are determined. 2000 MathematicalSubject Classification: 47G10, 47B10.