Long vectors for quasi-Newton updates

This work concerns the derivation of formulae for updating quasi-Newton matrices used in algorithms for computing approximate minima of smooth unconstrained functions. The paper concentrates strictly on the techniques used to derive update formulae. It demonstrates a technique in which problems of finding matrices in ℝ ^{n ×n} of minimum Frobenius norm are converted to equivalent problems, using vector representations in ℝ ⁿ² and ℝ ^n(n+1)/2 of these matrices, and then solvingl ₂-minimization problems. These problems are more directly dealt with, and indeed, the paper demonstrates how this technique may be used to handle weighted sparse updates.     

Resonance expansions in quantum mechanics

The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Wing characteristics and flapping behavior of flying insects

This paper is concerned with the flapping characteristics and the structure dynamics of insect wings. The flapping behavior of some insects is studied using a threedimensional motion analysis system. The experimental system is composed of two high-speed video cameras, a motion grabber, and a personal computer. The three-dimensional representation of insect flapping can be gained by the system. The extrinsic skeleton vibration produced by insect flapping is examined with the optical displacement detector system. The structural properties of some insect wings are also studied by a three-dimensional, optical shape measurement system. Some functional principles underlying insect wing design are revealed by the measurements of surface roughness and flapping analysis.     

半径位置微扰对形状不同的空气孔结构二维光子晶体波导透射的影响

分析了不同空气孔形状的光子晶体受位置和半径微扰对于透射的影响,包括圆形,方形与椭圆形.仿真结果发现及形状相同微扰程度下,通过比较透射平坦带宽部分的分析得到透射率对位置微扰更加敏感.慢光区域正方形空气孔对于位置微扰表现较好,圆形空气孔对于半径微扰更稳健.由于不同形状的空气孔光子晶体波导结构有各自的优势,因此研究微扰对透射...     

Morphological and ultrastructural characterization of the alimentary canal in Japanese wax scale (Ceroplastes japonicus Green)

The morphology and ultrastructure of the alimentary canal in the adult female of the Japanese wax scale, Ceroplastes japonicus Green (Hemiptera: Coccoidea: Coccidae), was investigated using light microscopy, scanning electron microscopy and transmission electron microscopy. The results showed that the foregut was subdivided into a sclerotized pharynx and an oesophagus. A pair of salivary glands attached in the middle of the foregut. The loop-shaped midgut was narrow and longer than the foregut and its inner wall lined with a thick layer of epithelia. The hindgut was divided into a narrower ileum and a broader rectum, with the well-developed filter chamber enclosed in the anterior rectum. Malpighian tubules consisted of two brownish-yellow moniliform tubules with pores, approximately 1 μm in diameter, scattered on the outer surface and many spherical crystals inside the tubules.     

On the completeness of root vectors generated by systems of coupled hyperbolic equations

The paper is the second in a set of two papers, which are devoted to a unified approach to the problem of completeness of the generalized eigenvectors (the root vectors) for a specific class of linear non‐selfadjoint unbounded matrix differential operators. The list of the problems for which such operators are the dynamics generators includes the following: (a) initial boundary‐value problem (IBVP) for a non‐homogeneous string with both distributed and boundary damping; (b) IBVP for small vibrations of an ideal filament with a one‐parameter family of dissipative boundary conditions at one end and with a heavy load at the other end; this filament problem is treated for two cases of the boundary parameter: non‐singular and singular; (c) IBVP for a three‐dimensional damped wave equation with spherically symmetric coefficients and both distributed and boundary damping; (d) IBVP for a system of two coupled hyperbolic equations constituting a Timoshenko beam model with variable coefficients and boundary damping; (e) IBVP for a coupled Euler‐Bernoulli and Timoshenko beam model with boundary energy dissipation (the model known in engineering literature as bending‐torsion vibration model); (f) IBVP for two coupled Timoshenko beams model, which is currently accepted as an appropriate model describing vibrational behavior of a longer double‐walled carbon nanotube. Problems have been discussed in the first paper of the aforementioned set. Problems are discussed in the present paper.     

A combinatorial proof of the Kronecker–Weber Theorem in positive characteristic

In this paper we present a combinatorial proof of the Kronecker–Weber Theorem for global fields of positive characteristic. The main tools are the use of Witt vectors and their arithmetic developed by H.L. Schmid. The key result is to obtain, using counting arguments, how many p-cyclic extensions exist of fixed degree and bounded conductor where only one prime ramifies. We then compare this number with the number of subextensions of cyclotomic function fields of the same type and verify that these two numbers are the same.     

MATHEMATICAL STUDY OF A PEST CONTROL MODEL INCORPORATING STERILE INSECT TECHNIQUE

The menace of insect pests is a topic of major concern throughout the world. Chemical pesticides are conventionally used to control these insect pests. However, the adverse effects of these synthetic pesticides, such as high toxicity from residues in food, contamination of water and the environment resulting in human health hazard and resistance of the pest to the pesticides have necessitated development of some nonconventional approaches of biological pest control. In this research, we have focused on a mathematical model of biological pest control using the sterile insect release technique. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the crop population as a distinct dynamical equation together with the fertile and sterile insect pests. Local stability analysis is performed around the crop and fertile insect free axial equilibrium, the fertile‐insect‐free boundary equilibrium, the crop‐free boundary equilibrium and the equilibrium point of coexistence. From the study we have derived a number of thresholds for the SIRR (the main parameter for our study) that cause existence and or extinction of the crop population as well as the fertile insect pests. A global study of the model system using comparison arguments revealed existence of a global attractor for the system. Numerical simulations are done to support and augment analytical results.     

钯催化脱羰反应研究及若干昆虫性信息素的合成

综述了基于钯催化脱羰端烯化反应的若干昆虫性信息素的合成