Spherical particle Brownian motion in viscous medium as non-Markovian random process

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered.     

AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

The author proves that if f : C→Cn is a transcendental vector valued meromorphic function of finite order and assume Σa∈Cn ∪{∞}δ(a) = 2, then,where .This result extends the related results for meromorphic function by Singh and Kulkarni.     

Utilization of characteristic polynomials in vibration analysis of non-uniform beams under a moving mass excitation

Vibration of non-uniform beams with different boundary conditions subjected to a moving mass is investigated. The beam is modeled using Euler–Bernoulli beam theory. Applying the method of eigenfunction expansion, equation of motion has been transformed into a number of coupled linear time-varying ordinary differential equations. In non-uniform beams, the exact vibration functions do not exist and in order to solve these equations using eigenfunction expansion method, an adequate set of functions must be selected as the assumed vibration modes. A set of polynomial functions called as beam characteristic polynomials, which is constructed by considering beam boundary conditions, have been used along with the vibration functions of the equivalent uniform beam with similar boundary conditions, as the assumed vibration functions. Orthogonal polynomials which are generated by utilizing a Gram–Schmidt process are also used, and results of their application show no advantage over the set of simple non-orthogonal polynomials. In the numerical examples, both natural frequencies and forced vibration of three different non-uniform beams with different shapes and boundary conditions are scrutinized.     

Spectral analysis of eigenparameter dependent boundary value transmission problems

In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with the boundary value transmission problems on the suitable Hilbert spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which are established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces.     

Schrödinger operators on periodic discrete graphs

We consider Schrödinger operators with periodic potentials on periodic discrete graphs. The spectrum of the Schrödinger operator consists of an absolutely continuous part (a union of a finite number of non-degenerated bands) plus a finite number of flat bands, i.e., eigenvalues of infinite multiplicity. We obtain estimates of the Lebesgue measure of the spectrum in terms of geometric parameters of the graph and show that they become identities for some class of graphs. Moreover, we obtain stability estimates and show the existence and positions of large number of flat bands for specific graphs. The proof is based on the Floquet theory and the precise representation of fiber Schrödinger operators, constructed in the paper.     

α，α‘—二氧代烯酮环二硫代缩酮类化合物的特征红外光谱（Ⅲ）

研究了5种α，α‘-二氧代烯酮环二硫代缩酮类化合物的碳基、碳碳双键、碳硫等一些特征红外光谱，尤其着重研究了共轭体系下的各种特征谱带随化学结构而变化的规律。     

Convergence on layer-adapted meshes and anisotropic interpolation error estimates of non-standard higher order finite elements

For a general class of finite element spaces based on local polynomial spaces E with Pp⊂E⊂Qp we construct a vertex-edge-cell and point-value oriented interpolation operators that fulfil anisotropic interpolation error estimates.Using these estimates we prove ε-uniform convergence of order p for the Galerkin FEM and the LPSFEM for a singularly perturbed convection-diffusion problem with characteristic boundary layers.     

Uncertainty functions, a compact way of summarising or specifying the behaviour of analytical systems

Analytical chemists can advantageously use an uncertainty function to describe the performance of an analytical system in terms of the standard uncertainty or standard deviation as a function of the concentration of the analyte. This “characteristic function” is useful for estimating uncertainty at a new concentration. A similar function can be used to prescribe the uncertainty that is regarded as fit for purpose for a particular application. This “fitness function” is useful in setting standards of accuracy in proficiency tests and similar exercises without revealing the concentration of the analyte. In combination, these two functions provide a rational basis for method selection.     

Simultaneous confidence and prediction bands in the certification of pressure-volume curves for the pore size analysis of solids by means of mercury porosimetry

The pore size analysis of solids is widely applied in chemical industries, materials engineering, ceramic production, environmental engineering, catalysis, chromatography, nanotechnology, and many other fields. In spite of several new methods used for determining the pore size distribution of meso- and macropores [see IUPAC Recommendations of 1994], mercury porosimetry has remained one of the most popular methods employed for the characterisation of porous materials. In this paper, a new way is described for the estimation of certified pressure-volume curves from experimental curves measured by different laboratories in connection with the certification of new reference materials for a comparatively low-pressure range of mercury intrusion (<2 MPa). Simultaneous confidence and prediction bands for the certified pressure-volume curves are constructed by bootstrapping.