On a mild generalization of the Schönemann - Eisenstein - Dumas irreducibility criterion

We state a mild generalization of the classical Schönemann and Eisenstein- Dumas irreducibility criterion in ?[x] and provide an elementary proof. In the end of the paper, we also provide a concrete example of a polynomial which is irreducible by the main result of the paper but whose irreducibility does not follow from existing criteria.     

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??In this paper we consider a class of fractional stochastic partial differential equation driven by fractional noise. We prove that the solution admits a smooth density at any fixed point (t,x)\in[0,T]\times\mathbb{R} with T>0 by using the techniques of Malliavin calculus.     

Numerical prediction of the influence of uncertain inflow conditions in pipes by polynomial chaos

Nearly all types of flow measurement devices installed in pipes are affected by the flow conditions at their inlet section, which can lead to measurement errors of several per cent. To evaluate the influence of uncertain inflow profiles on the flow field at different positions of the flow meter, a non-intrusive polynomial chaos approach is applied to simulations of turbulent pipe flow. This allows us to estimate the expected variations of the flow profiles as a function of the distance to the inlet of the pipe in an efficient way. The polynomial chaos approach shows reasonable convergence already for a small number of function evaluations. The results are validated by comparison with a quasi-Monte Carlo method and an exact solution, where available. The approximation error of the polynomial chaos method with 10 function evaluations is smaller than the one for the quasi-Monte Carlo method with 100 runs.     

Approximate inversion method for time‐fractional subdiffusion equations

The finite‐difference method applied to the time‐fractional subdiffusion equation usually leads to a large‐scale linear system with a block lower triangular Toeplitz coefficient matrix. The approximate inversion method is employed to solve this system. A sufficient condition is proved to guarantee the high accuracy of the approximate inversion method for solving the block lower triangular Toeplitz systems, which are easy to verify in practice and have a wide range of applications. The applications of this sufficient condition to several existing finite‐difference schemes are investigated. Numerical experiments are presented to verify the validity of theoretical results.     

Comprehensive study of the correlations that exist among the members of the [n]cyclacene series and the Möbius[n]cyclacene series

Cyclacenes are the smallest substructures of carbon nanotubes used in modelling studies. The systematics that exists between Hückel molecular orbital eigenvalues and eigenvectors of cyclacenes are delineated. This study of cyclacenes combines the interconnection of concepts of complementarity theorem, characteristic and matching polynomial recursion equations, embedding, greater than twofold symmetry and doubly degenerate eigenvalues, open-shell singlet character, and pairing theorem. Proof that cyclacenes have more open-shell (diradical) character than do polyacenes is also provided by the sum total of this work. Mirror-plane scission of even-ring cyclacenes gives linear polyacene fragments. This shows that the properties of the successor linear polyacene must be contained in the precursor cyclacene. Corresponding Möbius[n]cyclacene isomers display contrasting and unusual comparative properties. A partial list of contrasting properties include alternant (cyclacenes) versus nonalternant (Möbius[n]cyclacene) polyenes, presence of Hamiltonian circuits in Möbius[n]cyclacene and presence of oscillatory electronic properties in cyclacenes.     

Matching polynomial coefficients and the Hosoya indices of poly(p-phenylene) graphs

A general approach to determine the matching polynomial (MP) of a graph with two parts connected by an edge is presented in matrix product that is ultimately used in deducing recursion formulas for obtaining the MP coefficients of linear and cylindrical poly(p-phenylene) (PPP) graphs. The Hosoya indices of linear and cylindrical PPPs are derived in terms of that of the two immediately preceding graphs as well as in analytical forms with the use of transfer matrices. Ambient condition density and bulk modulus of linear PPPs with 2–6 phenyl rings have been found to correlate well with the logarithm of their Hosoya indices. Excellent correlations of diameters with the logarithm of Hosoya indices and strain energies with the inverse of the logarithm of Hosoya indices for cylindrical PPPr with r (= 6–16, 18, 20) phenyl rings are obtained. The linear relation between the logarithm of Hosoya indices and diameter and the inverse relation between diameter and strain energy corroborate the fact.     

硫杂蒽酮类光产碱剂的合成及其光化学性能研究

以硫代水杨酸和苯硫乙酸为原料,通过两步法成功合成了一种新型的单组分硫杂蒽酮类光产碱剂。利用核磁氢谱、核磁碳谱和高分辨率质谱对光产碱的结构进行了表征,通过稳态光解及电子自旋共振波谱等对光解产物进行了系统研究。该光产碱剂在400nm附近有较强的吸收,可有效引发巯基-环氧光聚合,其引发活性优于文献报道的高效光产碱体系。     

Verlinde模性范畴上的Casimir数及其应用

本文计算了秩为n+1的一类特殊的Verlinde模性范畴L的Casimir数,计算结果表明该Casimir数为2n+4.作为应用,由Higman定理知域K上的Grothendieck代数Gr(L)_Z K是半单代数当且仅当2n+4在域K中不为零.这也给出了第二类型n+1次Dickson多项式E_(n+1)(X)在K[X]中无重因式的一个等价刻画.如果2n+4在域K中为零,借助于Dickson多项式的有关因式分解定理,本文完全给出了Grothendieck代数Gr(L)_Z K的Jacobson根.     

Photoinduced depolymerization in poly(olefin sulfone) films comprised of volatile monomers doped with a photobase generator

Photoinduced depolymerization of poly(olefin sulfone)s mixed with a photobase generating compound was investigated. Irradiation of 254 nm UV light to films comprising of a mixture of a photobase generating compound and poly(olefin sulfone)s with volatile monomers caused photoinduced depolymerization and the irradiated part of the film vaporized. The effect of the poly(olefin sulfone) structure on the photoinduced depolymerization process was investigated. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Graphite dust resuspension in an HTR-10 steam generator

Graphite dust has an important effect on the safety of high-temperature gas-cooled reactors(HTR).The flow field in the steam generator was studied by the computational fluid dynamics(CFD) method,with the results indicating that the friction velocity in the windward and the leeward of the heat transfer tubes is relatively low and is higher at the sides.Further analysis of the resuspension of graphite dust indicates that the resuspension fraction reaches nearly zero for particles with a diameter less than 1 μm,whereas it will increases as the helium velocity in the steam generator increases for particle size larger than 1 μm.Moreover,the resuspension fraction increases as the particle size increases.The results also indicate that resuspension of the particles with sizes larger than 1 μm exhibited obvious differences in different parts of the steam generator.