Novel Strategies for Heterocyclic Constructions via 1, 4-Dipolar Intermediates

In the thesis entitled " Novel Strategies for Heterocyclic Constructions via 1 ,4-Dipolar Intermediates"Synthesis of a complex organic molecules essentially involves the formation of carbon-carbon and carbon-heteroatom bonds. Various synthetic methods are available for these processes involving ionic, pericyclic and radical reactions. Among the pericyclic reactions, dipolar cycloaddition reactions, introduced by Huisgen, have emerged as a very powerful tool for heterocyclic construction. Heterocyclic compounds remain an important class of organic molecules due to their natural abundance and remarkable biological activity, thus constituting an intergral part of pharmaceutical industry. In this respect, developing newer synthetic methodology for heterocyclic construction has been an area of immense interest. In recent years, 1,3-dipolar cycloaddition reactions proved to be efficient routes to a wide variety of five membered heterocycles, as attested by their application in the total synthesis of various complex organic molecules. However, the potential application of similar 1,4- dipolar cycloaddition reactions for the construction of six memebered heterocycles remained underexploited. In this context, a systematic investigation of the reactivity of 1,4-dipoles generated from nitrogen heterocycles (pyridine and its analogues) and dimethyl acetylenedicarboxy!ate (DMAD) towards various dipolarophiles has been carried out and the results are embodied.

Novel1, 3-Dipolar Cycloaddition Reactions of Acyclic Carbonyl Ylides and Related Chemistry

The thesis entitled novel 1,3-dipolar cycloaddition reactions of acyclic carbonyl ylides and related chemistry embodies the results of the investigations carried out to explore the reactivity of acyclic carbonyl ylides,generated by the reaction of dicarbomethoxy carbine and aldehydes towards dipolarophiles such as activated styrenes,1,2-and 1,4-quinones. In conclusion ,we have explored the reactivity pattern of acyclic carbonyl ylides derived from dicarbomethoxycarbene and aldehyde towards activated styrenes with a view to develop a stereoselective synthesis of highly substituted tetrahydrofuran derivatives. It was also found that the ylide could be trapped by various 1,2-and 1,4-diones to form dioxolane derivatives. It is noteworthy that the cycloaddition is highly region- and stereoselective. With isatins the ylide preferentially adds to the more electrone deficient carbonyl group making it regiospecific. Hetrocyclic compounds are of pivotal importance in organic chemistry, and enormous efforts have been devoted to develop new methodologies for their synthesis. It is noteworthy in this context that, 1,3-dipolar cycloaddition reaction,otherwise called Huisgen reaction, constitutes one of the most efficient methods for the synthesis of five membered heterocycles. Among the various dipoles, carbonyl ylides have received substiancial attention in recent years largely due to their utility in the synthesis of a wide range of oxygen hetrocycles, which are often found as structural subunits of many bioactive natural products.

Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

Influence of residual cations (Na+, K+ and Mg2+) in the alkylation activity of benzene with 1-octene over rare earth metal ion exchanged FAU–Y zeolite

The effect of residual cations in rare earth metal modified faujasite–Y zeolite has been monitored using magic angle spinning NMR spectral analysis and catalytic activity studies. The second metal ions being used are Na+, K+ and Mg+. From a comparison of the spectra of different samples, it is concluded that potassium and magnesium exchange causes a greater downfield shift in the 29Si NMR peaks. Also, lanthanum exchanged samples show migration behavior from large cages to small cages, which causes the redistribution of second counter cations. It is also observed that Mg2+ causes the most effective migration of lanthanum ions due to its greater charge. The prepared systems were effectively employed for the alkylation of benzene with 1-octene in the vapor phase. From the deactivation studies it is observed that the as-exchanged zeolites possess better stability towards reaction condition over the pure HFAU zeolite.

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto 11 and beta distributions. Further, we generalize the identities for fire Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in file context of lengthbiased models are also explored

Dynamic cumulative residual Renyi’s entropy

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon’s entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi’s entropy, and study its properties.We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models

Rényi’s residual entropy: A quantile approach

In the present paper, we introduce a quantile based Rényi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Rényi’s entropy function, the quantile version uniquely determines the distribution