Gorenstein projective bimodules via monomorphism categories and filtration categories

We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras A and B, we use the special monomorphism category $\mathsf{Mon}(B,A\text{-}\mathsf{Gproj})$ to describe some Gorenstein projective bimodules over the tensor product of A and B. If one of the two algebras is Gorenstein, we give a sufficient and necessary condition for $\mathsf{Mon}(B,A\text{-}\mathsf{Gproj})$ being the category of all Gorenstein projective bimodules. In addition, if both A and B are Gorenstein, we can describe the category of all Gorenstein projective bimodules via filtration categories. Similarly, in this case, we get the same result for infinitely generated Gorenstein projective bimodules.     

A variational approach for a generalized emden-fowler equation

Existence of positive solutions of singular boundary value problems related to Emden-Fowler equation is proved. A general minimization theorem in Sobolev spaces is applied.     

Results from solvophobic theory applied to methylene selectivity in reversed-phase HPLC

A significant amount of work has been previously dedicated to the understanding of methylene selectivity parameter. The conventional theory applied for this understanding was mostly based on the assumption that the difference in the Gibbs free energy of transfer from the mobile phase to the stationary phase is a constant for any two compounds in a homologous series that differ by a CH₂ group. In the present study, it is shown based on solvophobic theory that this assumption is indeed correct, but it provides a theoretical justification for it. Exemplification of the results of theory was obtained using the values for methylene selectivity (α(CH₂)) measured experimentally for seven different C18 chromatographic columns including two core–shell columns and using water and either methanol or acetonitrile as an organic component. Four different homologous series of compounds were used for evaluation. The study proved the theoretical prediction that the values for α(CH₂) obtained using different homologous series of compounds are only slightly different from those obtained using the toluene–butylbenzene series. Even using different homologous series, the same type of information regarding the columns comparison, and the changes in log α(CH₂) with the solvent composition was obtained.     

Chemical aspects of the radiation stability of macrocyclic extractants designed for 90Sr separation

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ESSENTIALLY ALGEBRAIC CATEGORIES

Abstract

Various familiar concepts of algebraic categories (such as primitive and quasiprimitive categories of algebras as well as varietal, monadic, regular monadic, and regular categories) are contrasted with each other and with the new notion of essentially algebraic categories.

The new notion has pleasant features and covers several cases of an apparently algebraic nature, which are not covered by any of the older concepts.     

Syntheses of dibenzo-18-crown-6 lariat isomers and their complexation with lanthanoid nitrates

Two constitutional isomers of dibenzo-18-crown-6 derivatives (6 and 7) were synthesised and their binding behaviours towards trivalent lanthanoid cations (La^3 + , Ce^3 + , Pr^3 + , Nd^3 + , Sm^3 + , Eu^3 + , Gd^3 +  and Tb^3 + ) were investigated. Both isomers expressed better binding affinities towards Sm^3 +  and Tb^3 +  than a group of other lanthanoids, as measured by the ligand-to-metal charge-transfer (LMCT) band intensity at ca. 425 nm using UV–vis spectroscopic method. Additionally, the trans isomer 7 was shown to have a higher binding ability than the cis isomer 6 towards Tb^3 + .

     

H_6P_2W_（18）O_（62）á18H_2O： A green and reusable catalyst for one-pot synthesis of pyrano[4,3-b]pyrans in water

A convenient,effcient and environmentally benign procedure has been developed for the synthesis of pyrano[4,3-b]pyran derivatives via a one-pot,three-component reaction of 4-hydroxy-6-methylpyran-2-one,aldehydes and malononitrile in water using H6P2W18O62á18H2O as catalyst.Reusability of the catalyst and reaction media,short reaction times and easy isolation of products are some added advantages of the present methodology.