Irreducibility and the distribution of some exponential sums

We relate the distribution of the absolute value of some generalized Gauss sums to the absolute irreducibility of some polynomials in two variables in characteristic 0 and p.     

关于广义三项指数和的四次幂均值

The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.     

Theoretical Studies on S-Phenyl-thiabenzene,S-Phenyl-thianaphthalene,and S-Phenyl-thiaanthracene

The molecular structures of S-phenyl-thiabenzene 1, S-phenyl-1-thianaphthalene 2, S-phenyl-2-thianaphthalene 3, and S-phenyl-9-thiaanthracene 4 are studied by ab initio calculations using HF as well as DFT methods at the 6–311+G? level of theory. The non-planar boat conformers of 1–4 with 6π electrons in the heterocyclic ring appear to be more stable than the corresponding planar conformers with 8π electrons in the ring. The activation energy for the inversion at the sulfur atom is compared for 1–4. Conformational flexibility of 1–4 is studied.     

A characterization of almost simple K 3-groups

It is a well-known fact that characters of a finite group can give important information about the group's structure. Also it was proved by the third author of this article that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost simple group by using less information of its character table, and successfully characterize the almost simple K₃-groups by their orders and at most three irreducible character degrees of their character tables.     

Weight distributions of a class of cyclic codes with arbitrary number of nonzeros in quadratic case

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three nonzeros. Recently, the authors of [37] constructed a class of cyclic codes with arbitrary number of nonzeros, and computed the weight distribution for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by introducing certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.     

Two Aromatic Ester Organoimido Derivatives of Hexa­molybdate: Syntheses,Crystal Structures,and Spectroscopic Studies

Two alkylimido derivatives of hexamolybdate, (Bu₄N)₂[Mo₆O₁₈(≡N‐o‐COOCH₃C₆H₄)] ( 1 ) and (Bu₄N)₂[Mo₆O₁₈(≡N‐o‐COOCH₂CH₃C₆H₄)] ( 2 ), were synthesized in high purity and good yields by the reaction of [(C₄H₉)₄N]₄[α‐Mo₈O₂₆] and methyl anthranilate or ethyl‐o‐aminobenzoate hydrochloride with N,N′‐dicyclohexylcarbodiimide (DCC) as a dehydrating agent in dry acetonitrile solution, which were characterized by elemental analyses, IR, UV/Vis, and ¹H NMR spectroscopy as well as ESI‐MS, and single‐crystal X‐ray diffraction study. Compound 1 crystallizes in the monoclinic space group P2₁/n with one‐dimensional chain structure via intramolecular hydrogen bond. Compound 2 also crystallizes in the monoclinic space group P2₁/n with dimer structure by intramolecular hydrogen bonds and π–π interactions between the pairs of cluster anions.     

CM newforms with rational coefficients

We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce tables for weights 3 and 4, where finiteness holds unconditionally. I am indepted to K. Hulek for his continuous interest and encouragement. Partial support by the DFG Schwerpunkt 1094 “Globale Methoden in der komplexen Geometrie” is gratefully acknowledged. My thanks go also to the referee for helpful comments. Part of the revising took place while I enjoyed the hospitality of the Dipartimento di Matematica “Frederico Enriques” of Milano University. Funding from the network Arithmetic Algebraic Geometry, a Marie Curie Research Training Network, is gratefully acknowledged. I particularly thank M. Bertolini and B. van Geemen. The final version was prepared while I was funded by DFG under grant Schu 2266/2-2.     

Local electronic and electrical properties of functionalized graphene nano flakes

Based on experimental findings models of amorphous graphene related carbon materials were generated using graphene nano flakes. On the optimized structures detailed local electronic properties were investigated using density functional theory. The electrical conductivities of all these models were also estimated using an in-house program based on tight-binding method. The calculated electrical conductivity values of all the models agreed well with the trend of calculated energy gap and graphitic character.     

Families of multisums as mock theta functions

In view of the Bailey lemma and the relations between Hecke-type sums and Appell–Lerch sums given by Hickerson and Mortenson, we find that many Bailey pairs given by Slater can be used to deduce mock theta functions. Therefore, by constructing generalized Bailey pairs with more parameters, we derive some new families of mock theta functions. Meanwhile, some identities between new mock theta functions and classical ones are established. Furthermore, based on the proofs of the main theorems, many q-hypergeometric transformations are obtained.