AFM, SEM and GIXRD studies of thin films of red polycarbazolyldiacetylenes

In this paper we report the results of a morphological and structural investigation on film properties of a soluble polydiacetylene, the poly[1,6-bis(3,6-dihexadecyl-N-carbazolyl)-2,4-hexadiyne] (polyDCHD-HS). The red films of this polymer, prepared by standard spin-coating techniques, revealed absence of linear dichroism and birefringence in contrast with the ordered mesophases detected by powder X-ray studies. In order to interpret the optical behavior of this polymer, we performed AFM and SEM studies of polyDCHD-HS films spun on hydrophylic and hydrophobic glass substrates. We found the presence of surfaces organized in rod-like particles, more regularly oriented on the hydrophylic substrate. GIXRD studies, carried out on films sufficiently thick to allow the observation of the diffraction pattern, reveled the presence of a lamellar structure with a spacing of 3.22 nm. The low intensity of the diffraction peaks and the isotropic linear optical properties of the films show that the lamellar mesophases are not extended over large areas. These findings were compared with the data obtained from AFM and SEM studies on films of two other polydiacetylenes, the poly[1-(3,6-dihexadexyl-N-carbazolyl)-6-(N-carbazolyl)-2,4-hexadyine] (polya-DCHD) and the poly[1,6-bis(3,6-dipalmitoyl-N-carbazolyl)-2,4-hexadyine] (polyDPCHD), spun on hydrophylic glass substrate. The results confirmed the presence of nodular morphologies which seem to be a general characteristic of this class of materials. The particles organization appears instead related to the chemical nature of the substituents on the carbazolyl rings.     

The Tate-Voloch conjecture for Drinfeld modules

We study the v-adic distance from the torsion of a Drinfeld module to an affine variety.     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

Effective-field theory and the nuclear many-body problem

We review many-body calculations of the equation of state of dilute neutron matter in the context of effective-field theories of the nucleon-nucleon interaction.     

逆序数的应用

本文通过“1 4-1 5”智力玩具和最优戴断切割问题两个实例 ,讨论了逆序数在解决实际问题中的应用     

Thermal and chemical nanofractal relaxation

We studied shape relaxation of nano-fractal islands, during annealing, after their growth from antimony cluster deposition on graphite surface. Annealing at 180^°C shows evidence of an increase of the fractal branch width with time followed by branch fragmentation, without changing the fractal dimension. The time evolution of the width of the arm suggests the surface self-diffusion mechanism as the main relaxation process. With Monte Carlo simulations, we confirmed the observed behavior. Comparison is done with our previous results on fragmentation of nano-fractal silver islands when impurity added to the incident cluster promotes rapid fragmentation by surface self-diffusion enhancement [1].     

Front roughening in three-dimensional imbibition

We investigate the structure and dynamics of the interface between two immiscible liquids in a three-dimensional disordered porous medium. We apply a phase-field model that includes explicitly disorder and discuss both spontaneous and forced imbibition. The structure of the interface is dominated by a length scale ξ_× which arises from liquid conservation. We further show that disorder in the capillary and permeability act on different length scales and give rise to different scalings and structures of the interface properties. We conclude with a range of applications.     

Differential operators on Hilbert modular forms

We investigate differential operators and their compatibility with subgroups of SL₂n(R). In particular, we construct Rankin-Cohen brackets for Hilbert modular forms, and more generally, multilinear differential operators on the space of Hilbert modular forms. As an application, we explicitly determine the Rankin-Cohen bracket of a Hilbert-Eisenstein series and an arbitrary Hilbert modular form. We use this result to compute the Petersson inner product of such a bracket and a Hilbert modular cusp form.     

Ordered OLPS and CF Nth numerators

Definitions, theorems and examples are established for a general model of Laurent polynomial spaces and ordered orthogonal Laurent polynomial sequences, ordered with respect to ordered bases and orthogonal with respect to inner products ·=L°⊙ decomposed into transition functional ⊙ and strong moment functional, or, more generally, sample functional L couplings. Under this formulation that is shown to subsume those in the existing literature, new fundamental results are produced, including necessary and sufficient conditions for ordered OLPS to be sequences of nth numerators of continued fractions, in contrast to the classical result concerning nth denominators which is shown to hold only in special cases.     

Scalar and axial-vector mesons

Almost thirty years ago, Penny G. Estabrooks asked “Where and what are the scalar mesons?” (P. Estabrooks, Phys. Rev. D 19, 2678 (1979)). The first part of her question can now be confidently responded (E. van Beveren et al., Z. Phys. C 30, 615 (1986)). However, with respect to the “What” many puzzles remain unanswered. Scalar and axial-vector mesons form part of a large family of mesons. Consequently, though it is useful to pay them some extra attention, there is no point in discussing them as isolated phenomena. The particularity of structures in the scattering of --basically-- pions and kaons with zero angular momentum is the absence of the centrifugal barrier, which allows us to “see” strong interactions at short distances. Experimentally observed differences and similarities between scalar and axial-vector mesons on the one hand, and other mesons on the other hand, are very instructive for further studies. Nowadays, there exists an abundance of theoretical approaches towards the mesonic spectrum, ranging from confinement models of all kinds, i.e., glueballs, and quark-antiquark, multiquark and hybrid configurations, to models in which only mesonic degrees of freedom are taken into account. Nature seems to come out somewhere in the middle, neither preferring pure bound states, nor effective meson-meson physics with only coupling constants and possibly form factors. As a matter of fact, apart from a few exceptions, like pions and kaons, Nature does not allow us to study mesonic bound states of any kind, which is equivalent to saying that such states do not really exist. Hence, instead of extrapolating from pions and kaons to the remainder of the meson family, it is more democratic to consider pions and kaons mesonic resonances that happen to come out below the lowest threshold for strong decay. Nevertheless, confinement is an important ingredient for understanding the many regularities observed in mesonic spectra. Therefore, excluding quark degrees of freedom is also not the most obvious way of describing mesons in general, and scalars and axial-vectors in particular.