Complete Caps in with Both N and q Odd

In this work, an inductive method to construct complete caps in affine spaces is provided. Using this tool, for odd and q odd, complete caps smaller than all already known ones are obtained.     

Binding Characteristics Study of DNA based Aptamers for E. coli O157:H7

E. coli O157:H7 is a pathogenic bacterium producing verotoxins that could lead to serious complications such as hemolytic uremia syndrome. Fast detection of such pathogens is important. For rapid detection, aptamers are quickly gaining traction as alternative biorecognition molecules besides conventional antibodies. Several DNA aptamers have been selected for E. coli O157:H7. Nonetheless, there has not been a comparative study of the binding characteristics of these aptamers. In this work, we present a comprehensive analysis of binding characteristics including binding affinity (K_d) and binding capacity (B_max) of DNA-based aptamers for E. coli O157:H7 using qPCR. Our results show that aptamer E18R has the highest binding capacity to E. coli 157:H7 and the highest specificity over non-pathogenic E. coli strains K12 and DH5α. Our study also finds that the common biotin-tag modification at 5′ end typically changes the binding capacity significantly. For most of the selected aptamers, the binding capacity after a biotin-tag modification decreases. There exists a discrepancy in the binding capability between the selected aptamer and the aptamer used for detection. Our study also shows that a lower concentration of Mg²⁺ ions in the binding buffer leads to a decrease in the binding capacity of E17F and E18R, while it does not affect the binding capacity of S1 and EcoR1.     

Higher-Order $(F,\alpha, \beta, \rho, d, E) $-Convexity in Fractional Programming

In this paper we define higher order $(F,\alpha, \beta, \rho,d, E)$-convex function with respect to $E$-differentiable function $K$ and obtain optimality conditions for nonlinear programming problem (NP) from the concept of higher order $(F,\alpha, \beta, \rho,d)$-convexity. Here, we establish Mond-Weir and Wolfe duality for (NP) and utilize these duality in nonlinear fractional programming problem.     

On Estimates of the Boltzmann Collision Operator with Cut-off

We present new estimates of the Boltzmann collision operator in weighted Lebesgue and Bessel potential spaces. The main focus is put on hard potentials under the assumption that the angular part of the collision kernel fulfills some weighted integrability condition. In addition, the proofs for some previously known -estimates have been considerably shortened and carried out by elementary methods. For a class of metric spaces, the collision integral is seen to be a continuous operator into the same space. Furthermore, we give a new pointwise lower bound as well as asymptotic estimates for the loss term without requiring that the entropy is finite.     

A Generalized Fourier Approximation in Anti-plane Cosserat Elasticity

In the present paper we use the modification of Kupradze’s method of generalized Fourier series for the treatment of interior and exterior Dirichlet and Neumann boundary-value problems arising in a linear theory of anti-plane elasticity which includes the effects of material microstructure.     

On Dual Configurational Forces

The dual conservation laws of elasticity are systematically re-examined by using both Noether's variational approach and Coleman–Noll–Gurtin's thermodynamics approach. These dual conservation laws can be interpreted as the dual configurational force, and therefore they provide the dual energy–momentum tensor. Some previously unknown and yet interesting results in elasticity theory have been discovered. As an example, we note the following duality condition between the configuration force (energy–momentum tensor) and the dual configuration force (dual energy–momentum tensor) ,

Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.      

Stopping a Viscous Fluid by a Feedback Dissipative Field: I. The Stationary Stokes Problem

We consider a planar stationary flow of an incompressible viscous fluid in a semiinfinite strip governed by the Stokes system with a body forces field. We show how this fluid can be stopped at a finite distance of the entrance of the semi-infinite strip by means of a feedback field depending in a sub-linear way on the velocity field. This localization effect is proved reducing the problem to a non-linear bi-harmonic type one for which the localization of solutions is obtained by means of the application of a suitable energy method. Since the presence of the non-linear terms defined through the body forces field is not standard in the fluid mechanics literature, we establish also some results about the existence and uniqueness of weak solutions for this problem.     

Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder

The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite cylinder is proved. We assume that the initial data and the external forces do not depend on x₃ and find the solution (u, p) having the following form

正交各向异性厚板的边界元解法

本文利用 Hormander 算子法和平面波分解法导出了计入剪切变形的正交各向异性厚板的基本解。建立了计入剪切变形的正交各向异性厚板的边界积分方程。文中详细地讨论了基本解的数值计算,并用边界元法分析了一些算例。