Erosion of efficiency in non-uniform linear chromatography

In linear chromatography (i.e. chromatography performed in the absence of sample overloading), when the plate height of a column is roughly uniform along its length, variations in the velocities of solutes are the only possible causes of erosion of efficiency. The sources of these variations (variations in capacity ratio and in the density of the mobile phase, etc.) play no direct role in the erosion of efficiency except through their effect on solute velocities. In other words, what eventually causes the erosion of efficiency is merely variation in the time required for solutes to traverse equally small segments of a column. Significant erosion can only arise from abrupt and deep deceleration of solutes in one or several relatively small segments of a column. If erosion of efficiency caused by pressure gradients in linear SFC is to be large, the depth and the sharpness of the deceleration of a solute must go beyond that hitherto confirmed experimentally. Many relevant examples are analyzed graphically.     

Forces at the nuclei of a molecule in the presence of non-uniform electric field

The interaction Hamiltonian within the Bloch gauge for the potentials of the electric field has been used to define electric multipole moment operators. Perturbation theory has been applied to evaluate the induced electronic moments and electric field at the nuclei in the presence of spatially non-uniform electric fields of high intensity. Multipole nuclear electric shielding tensors have been defined to describe the contributions arising from a non-homogeneous electric field. These quantities are useful to rationalize linear and non-linear responses of a molecule in the presence of intense external electric perturbations.     

Hall effects and entropy generation applications for peristaltic flow of modified hybrid nanofluid with electroosmosis phenomenon

The electroosmotic peristaltic flow of modified hybrid nanofluid in presence of entropy generation has been presented in this thermal model. The Hall impact and thermal radiation with help of nonlinear relations has also been used to modify the analysis. The assumed flow is considered due to a non-uniform trapped channel. The properties of modified hybrid nanofluid model are focused with interaction of three distinct types of nanoparticles namely copper ($Cu)$, silver ($Ag$) and aluminum oxide ($A{l}_2{O}_3).$ The mathematical modeling and significances of entropy generation and Bejan number are identified. With certain flow assumptions, the governing equations are attained for optimized peristaltic electroosmotic problem. Widely used assumptions of long wave length and low Reynolds number reduced the governing equations in ordinary differential equations. The ND solver is flowed for the solution process. The physical significant of results is observed by assigning the numerical values to parameters.     

Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure

Elastic analysis of a functionally graded thick-walled cylindrical pressure vessel is analytically studied in the present research. Gradation is considered for all mechanical properties along the thickness direction based on a power function. The constitutive relations are developed in the general cylindrical coordinate system for an axisymmetric pressurized cylinder. For simulation of these two deformation components, first order shear deformation theory is considered. The FG cylinder is subjected to longitudinally non-uniform pressure along the length of the cylinder. The present problem is applicable for simulation of non-uniform pressurized cylinder by fluids or gases.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).     

光突发交换网络中最长队列优先调度组装机制

提出了光突发交换网络中的最长队列优先调度（LQF-SA）机制,将边缘节点的突发组装和突发调度两种技术紧密结合在一起.在现实网络中,业务通常是非均匀分布的,即在某些源宿对之间存在更大的业务流量.仿真结果表明,LQF-SA机制可以很好地完成非均匀分布业务流的组装.即使在均匀分布业务流输入下,LQF-SA机制在突发大小分布、组装效率和突发丢失率等方面也优于已提出的轮询调度组装（RR-SA）机制.     

Improving the sharpness of a non-uniformly illuminated image by an integral mask-filtering approach

We demonstrate an extended mask-filtering approach to improve the sharpness of an image with non-uniform illumination. The proposed method comprises two different masks which cope with higher and lower spatial frequencies respectively. By using this integral algorithm, the enhanced image has much better performance than that derived from the conventional technique.     

The distribution of the domination number of class cover catch digraphs for non-uniform one-dimensional data

For two or more classes of points in R^d with d≥1, the class cover catch digraphs (CCCDs) can be constructed using the relative positions of the points from one class with respect to the points from one or all of the other classes. The CCCDs were introduced by Priebe et al. [C.E. Priebe, J.G. DeVinney, D.J. Marchette, On the distribution of the domination number of random class catch cover digraphs. Statistics and Probability Letters 55 (2001) 239-246] who investigated the case of two classes, X and Y. They calculated the exact (i.e., finite sample) distribution of the domination number of the CCCDs based on X points relative to Y points both of which were uniformly distributed on a bounded interval. We investigate the distribution of the domination number of the CCCDs based on data from non-uniform X points on an interval with end points from Y. Then we extend these calculations for multiple Y points on bounded intervals.