Eichler Cohomology of Generalized Modular Forms of Real Weights

In this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the isomorphism for large weights by constructing the map from the space of cusp forms to the cohomology group.Comment: Accepted in Proceedings of the American Mathematical Societ

Precise Molecular Structures of Cysteine, Cystine, Hydrogen-Bonded Dicysteine, Cysteine Dipeptide, Glutathione and Acetyl Cysteine Based on Additivity of Atomic Radii

Structures of molecules are usually represented by arbitrary line drawings, ball and stick or space filling models. In recent years, the author found that using the appropriate radii of atoms and ions, bond lengths in inorganic, organic and biomolecules and of hydrogen bonds are exact sums of the radii of the adjacent atoms and or ions. This additivity of atomic radii was shown to hold also for the bond lengths in the twenty essential amino acids. On this basis, the atomic structures of the very important molecules mentioned in the title, have been presented here for the first time. It is hoped that these precise structures and their dimensions will shed new light into their role in biochemistry, pharmaceutical chemistry, environmental chemistry, biomedicine and in the mechanism of protein folding

Atomic and molecular structures of positronium, dipositronium and positronium hydride

The three positron based chemical entities, analogous to hydrogen atom, hydrogen molecule and hydride, are drawing increasing attention in the literature. While a lot is known about the binding energies, not much is known about the radii of the atoms and ions and bond lengths and structures of these exotic entities. This article brings for the first time exact values of these structural properties which are comparable with known data. It is hoped that the results will be of help for a better understanding and further development of the chemistry and physics of these exotic compounds and of their possible role as intermediates in chemical and interfacial processes

Absolute Aqueous Redox Potentials ( via a new link between aqueous and gaseous properties)

The new finding here, that the conventional standard potentials (based on S.H.E.) are linearly dependent on ionization potentials, has yielded the absolute values of aqueous standard potentials

Golden sections of inter-atomic distances as exact ionic radii of atoms

The Golden ratio which appears in the geometry of a variety of creations in Nature is found to arise right in the Bohr radius of the hydrogen atom due to the opposite charges of the electron and proton. The bond length of the hydrogen molecule is the diagonal of a square on the Bohr radius and hence also has two Golden sections, which form the cationic and anionic radii of hydrogen. It is shown here that these radii account quantitatively for the bond lengths of many hydrides when added to the atomic and Golden ratio based ionic radii of many other atoms