The mass gap for Higgs models on a unit lattice

An isomorphism is established between eertain compact and noncompact formulations of Abelian gauge theory on a lattice. For weak coupling, the mass gap predicted by the Higgs mechanism is then established.     

Studies on the Selectivity of Porous Polymers Containing Different Functional Groups

Three types of porous polymers containing different functional groups were synthesized as stationary phases for gas chromatography. The influence of functional groups in the copolymer skeletons on their selectivities was studied. To determine the selectivities of these copolymers, two procedures were applied: the selectivity triangle and the general selectivity. As a reference phase Porapak Q which does not contain any functional groups was used.     

(Higgs)2, 3 quantum fields in a finite volume

This is the third paper of a series, and contains a proof of the bounds on the effective actions needed in the two previous papers. The proof is based on perturbative analysis of renormalization.     

Empirical parameters of lewis acidity and basicity for aqueous binary solvent mixtures

Empirical parameters of Lewis acidity, E^N_T, introduced by Reichardt et al., and Lewis basicity, B_KT , introduced by Kamlet and Taft, have been determined for mixtures of water with ten organic solvents. In the case of water/alcohol mixtures a distinct dependence between these acidity and basicity parameters have been found. For the other solvent mixtures the E^N_T on B_KT dependence is more complex even if these parameters are purified from non-specific solute/solvent interactions.     

Meso-[2.2]paracyclophanyltriphenylporphyrin: A simple representative of cyclophanylporphyrins

(R + S)Meso-[2.2]Paracyclophanyltriphenylporphyrin 3 , a member of a novel class of cyclophanylporphyrins, was obtained and characterized by spectroscopic and electrochemical methods. Compared to meso-tetra[2.2]paracyclophanylporphyrin 1, it represents a simplified structure designed for the investigation of electronic interactions between the [2.2]paracyclophane moiety and porphyrin core and for use in metallation reactions.     

Solid-state molecular organization and solution behavior of methane-1,1-diphosphonic acid derivatives of heterocyclic amines: the role of the topochemical ring modification and the intramolecular hydrogen bonds in monosubstituted piperid-1-ylmethane-1,1-diphosphonic acids

The crystal structures of 3-methylpiperid-1-ylmethane-1,1-diphosphonic (2), 4-methylpiperid-1-ylmethane-1,1-diphosphonic (3), 2-ethylpiperid-1-ylmethane-1,1-diphosphonic (4), and 2-methylpiperid-1-ylmethane-1,1-diphosphonic (5) acids have been determined and are discussed with respect to their molecular organization and crystal-packing preferences. The chair conformation, predominant also in solution, favors equatorial positioning of the bulky substituents of the heterocyclic N and C atoms. The molecular geometry also provides access to intramolecular hydrogen-bond formation between the axial protons located on the nitrogen atoms, as well as the carbon atoms closest to it, and phosphonic/phosphonate oxygen atoms. The molecules preferably arrange in monolayers, observed in all crystals with an exception of 3. The layers are held in place in the third direction through van der Waals interactions. The analysis of two-dimensional hydrogen-bonded networks is concentrated on revealing how the substituent's topology of the molecule affects the solid-state organization in well-defined structures and is aimed at unraveling the consequences and the possible conformational changes by stepwise network disruption upon crystal dissolution in water. The solution NMR studies are focused on revealing the role that the topochemistry of the substituent plays for the stereodynamics in 2-5. It is demonstrated that in contrast to piperid-1-ylmethane-1,1-diphosphonic acid (1), in which the ring inversion/rotation around the C-N bond concerted with the N-H...O hydrogen-bond breaking/formation process leads to a mixture of two interconverting conformers, the concerted N-H...O breaking/rotation/N-H...O formation process in 2 and 3 allows for a predominance of one conformer in solution. However, placement of a substituent at 2-position in the ring hampers the rotation around the C-N bond; this makes 4 and 5 significantly less flexible relative to compounds 1-3. In addition, both compounds 4 and 5 are proved to exist as a mixture of two conformers, the equilibrium of which in acidic solution is shifted towards the conformer found in solid state. In alkaline solutions of 4 and 5, the equilibrium is shifted towards the conformer that is forced by the flipping of the heterocyclic ring. These results correlate well with recently documented differences in the biological potency of this group of compounds.     

(Higgs)2,3 quantum fields in a finite volume

This is the second part of the paper entitled, “(Higgs)_2,3 Quantum Fields in a Finite Volume.” The proof of an upper bound for vacuum energy is completed with the exception of some technical estimates.     

Natural bond orbital (NBO) analysis of the angular group induced bond alternation (AGIBA) substituent effect

The geometries, natural charges, and resonance structures of 11 monosubstituted benzene derivatives were analyzed at the B3LYP/6‐311++G(d,p) and HF/6‐311++G(d, p) levels of theory. The following angular substituents were chosen: OCH₃, CH₂CH₃, OH, SH, NHCH₃, NHNH₂, N?O, CH?CH₂, N?CH₂, N?NH, and CHO. The analysis of resonance structures was performed by using two different methodologies: harmonic oscillator stabilization energies (HOSE) and natural resonance theory (NRT). Also, the natural bond orbital (NBO) donor–acceptor stabilization energies for different resonance structures were calculated. We found that for all the substituents, the purely geometric resonance stabilization parameter (HOSE) is linearly correlated with quantum chemically derived resonance structure weight (NRT) of a given structure. Also, the calculations provide qualitative support for the earlier assumption of a through space angular group induced bond alternation (AGIBA) effect. Copyright © 2010 John Wiley & Sons, Ltd.