Separability and the Twisted Frobenius Bimodule

This paper begins with an introduction to <img src="/content/l867jll9gwm78431/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Frobenius structure on a finite-dimensional Hopf subalgebra pair. In Section 2 a study is made of a generalization of Frobenius bimodules and <img src="/content/l867jll9gwm78431/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Frobenius extensions. Also a special type of twisted Frobenius bimodule which gives an endomorphism ring theorem and converse is studied. Section 3 brings together material on separable bimodules, the dual definitions of split and separable extension, and a theorem of Sugano on endomorphism rings of separable bimodules. In Section 4, separable twisted Frobenius bimodules are characterized in terms of data that generalizes a Frobenius homomorphism and a dual base. In the style of duality, two corollaries characterizing split <img src="/content/l867jll9gwm78431/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Frobenius and separable <img src="/content/l867jll9gwm78431/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Frobenius extensions are proven. Sugano"s theorem is extended to <img src="/content/l867jll9gwm78431/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Frobenius extensions and their endomorphism rings. In Section 5, the problem of when separable extensions are Frobenius extensions is discussed. A Hopf algebra example and a matrix example are given of finite rank free separable <img src="/content/l867jll9gwm78431/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Frobenius extensions which are not Frobenius in the ordinary sense.     

Transferability of some properties of localized molecular orbitals

The localized molecular orbitals of some related ten- and eighteen-electron systems have been studied. The transferability of the kinetic, self-interaction, Coulomb and exchange interaction energies on localized orbitals have been shown. The standard deviation of the kinetic and of the interaction energies (including exchange) are less than 2.5% except for lone pair orbitals of the oxygen atoms where the standard deviation is close to 4%.     

MBAMT,a new locating and chelating agen in TLC and ring colorimetric determination of Cu(II), Co(II), Ni(II), Pd(II), Pt(IV), and Rh(III)

Summary Synthesis of MBAMT (3-methyl-4-benzylideneamino-5-mercapto-1,2,4-triazole) and its IR and NMR spectral data are reported. The high stability of the characteristically coloured chelates with Cu(II), Co(II), Ni(II), Pd(II), Pt(IV) and Rh(III) has been made the basis for their efficient ascending TLC separations on silica gel <img src="/content/y77368t9l7425723/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">G<img src="/content/y77368t9l7425723/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> layers, when present together. Results of four different solvent systems are included to assess efficient resolution of the chelates along with their limits of identification and separation. TLC separations, followed by the ring colorimetric determination of the six metal ions (as ternary mixtures) are tabulated.MBAMT=3-methyl-4-benzylideneamino-5-mercapto-1,2,4-triazole.     

Intercalates of α-Sn(HP04)2·H2O with aromatic and heterocyclic bases and some comments on their orientation in the interlayer region

The intercalation of amines into <img src="/content/l71r7h76h65h0763/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-tin(IV) hydrogen phosphate, <img src="/content/l71r7h76h65h0763/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-Sn(HP0<sub>4</sub>)<sub>2</sub>·H<sub>2</sub>0, (<img src="/content/l71r7h76h65h0763/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-SnP) can occur to give mono- or bilayers of the guest molecule. The distribution and orientation of the amines is influenced by geometrical factors, acidity of the guest molecule and moreover, the degree of charge localisation of the guest organic cations. Regarding the monolayer formation, there are two possibilities. The first is that aromatic amines form monolayers with parallel orientation of the amine with respect to the phosphate layer, when the charge is delocalised over the aromatic ring. Monolayer formation with perpendicular orientation occurs when the positive charge is localised in opposite parts of the aromatic ring molecule. Bilayer formation occurs when the positive charge is localised in one part of the molecule and simultaneous interaction with two adjacent layers is not possible.     

A new approach to variational CI calculations on systems containing non-interacting molecules

A new method to perform variational CI calculations on systems containing non-interacting molecules is presented.     

A structurally diverse heterocyclic library: A benzothiazepine-fused β -lactam library derived from reaction of 2,3-dihydro-1,5-benzothiazepines and acyl chlorides: Synthesis and stereochemistry

A 1<i>H</i>-azeto[2,1-<i>d</i>][1,5]benzothiazepin-1-one, <img src="/content/v1uu3717l703652n/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-lactam derivatives of dihydrobenzothiazepines library derived from reactions of 2,4-disubstituted 2,3-dihydro-1,5-benzothiazepines and acyl chlorides, including phthalimidoacetyl chloride, chloroacetyl chloride, dichloroacetyl chloride and phenoxyacetyl chloride, was built up through parallel solution-phase synthesis. Stereochemistry of 1<i>H</i>-azeto[2,1-<i>d</i>][1,5]benzothiazepin-1-ones in the reaction process is discussed.     

Effects of phonon-phonon coupling on low-lying states in neutron-rich Sn isotopes

Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.     

A Novel Stereoselective Synthesis of <Emphasis Type="Italic">cis</Emphasis>-Configured Erythrinane and Erythrinane Type Analogues

Summary. &lt;i>N&lt;/i>-Alkylation of certain angularly substituted heterocycles by C&lt;sub>2&lt;/sub>- and C&lt;sub>3&lt;/sub>-units provided appropriate precursors to construct stereoselectively the erythrinanone and several erythrinanone type analogues by intramolecular &lt;i>Friedel-Crafts&lt;/i> acylation. The resulting aromatic ketones were catalytically reduced affording the corresponding parent frameworks including the hitherto unknown tetracyclus A-norschelhammerane. On the other hand, the stereoselective reduction of the carbonyl moiety offered a convenient approach to 11-hydroxylated erythrinanes with the natural occurring &lt;img src="/content/385kde7l8hpbnhup/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-configuration. The structures and the stereochemistry of the target compounds were proved by NMR spectroscopy.Part of PhD thesis, LMU M&uuml;nchen, D     

On the Existence of Solutions of Quasivariational Inclusion Problems

Quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of general vector ideal, proper, Pareto, weak quasioptimization problems, quasivariational inequalities, and vector quasiequilibrium problems. Further, we prove theorems on the existence for solutions of systems of these inclusions. As a corollary, we obtain an ideal minimax theorem concerning vector functions.