On diagonally-preconditioning the 2-step BFGS method with accumulated steps for linearly constrained nonlinear programming

We present an algorithm for very large-scale linearly constrained nonlinear programming (LCNP) based on a Limited-Storage Quasi-newton method. In large-scale programming solving the reduced Newton equation at each iteration can be expensive and may not be justified when far from a local solution; besides, the amount of storage required by the reduced Hessian matrix, and even the computing time for its Quasi-Newton approximation, may be prohibitive. An alternative based on the reduced Truncated-Newton methodology, that has proved to be satisfactory for large-scale problems, is not recommended for very large-scale problems since it requires an additional gradient evaluation and the solving of two systems of linear equations per each minor iteration. We recommend a 2-step BFGS approximation of the inverse of the reduced Hessian matrix that does not require to store any matrix since the product matrix-vector is the vector to be approximated; it uses the reduced gradient and information from two previous iterations and the so-termed restart iteration. A diagonal direct BFGS preconditioning is used.     

Change of optimum conditions of second harmonic generation of spatial limited laser beams in nonlinear crystals

Frequency doubling of spatially limited laser beams in nonlinear crystals is investigated theoretically. It was shown that the major factor, which reduces the second harmonic generation (SHG) efficiency in this case, is a diaphragm aperture effect, caused by influence of extraordinary polarized laser beams. In that case a spatial shift of mutually orthogonally polarized beams of the incident waves relative to each other in perpendicular direction of wave transmission at the entry to crystals lead to increase the efficiency of SHG of limited beams.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.     

Mass optimization of a compressed cylindrical shell with limited life

A new optimization model is proposed to design corrosion-affected structures with limited life. The optimization problem is stated as a nonlinear-programming problem. The mass of the structure is minimized. The design is considered optimal when physical wear and obsolescence arrive simultaneously. A smooth cylindrical shell compressed in the longitudinal direction is used to illustrate the model __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 97–101, March 2006.     

Reaction Rate of Small Diffusing Molecules on a Cylindrical Membrane

Biomembranes consist of a lipid bi-layer into which proteins are embedded to fulfill numerous tasks in localized regions of the membrane. Often, the proteins have to reach these regions by simple diffusion. Motivated by the observation that IP₃ receptor channels (IP₃R) form clusters on the surface of the endoplasmic reticulum (ER) during ATP-induced calcium release, the reaction rate of small diffusing molecules on a cylindrical membrane is calculated based on the Smoluchowski approach. In this way, the cylindrical topology of the tubular ER is explicitly taken into account. The problem can be reduced to the solution of the diffusion equation on a finite cylindrical surface containing a small absorbing hole. The solution is constructed by matching appropriate ‘inner’ and ‘outer’ asymptotic expansions. The asymptotic results are compared with those from numerical simulations and excellent agreement is obtained. For realistic parameter sets, we find reaction rates in the range of experimentally measured clustering rates of IP₃R. This supports the idea that clusters are formed by a purely diffusion limited process.     

Edge-pumped passively Q-switched thin Nd: YAG slab lasers

We report a high-power thin Nd: YAG slab laser with slab dimension of 1×10×60(mm) partially edgepumped by diode laser arrays.Passive Q-switching is achieved with a Cr4 : YAG microchip adopted as the saturable absorber mirror.The pulse duration is around 10ns while the pulse repetition rate is higher than 10kHz.The average output power of 70W is obtained with a slope efficiency of 36%.The diffraction limited beam quality in the thickness direction is obtained by controlling the pump beam diameter inside the slab.The laser head is very compact with size of only 60×74×150(mm).     

Mesoporous silica nanoreactors for highly efficient proteolysis

Protein digestion inside the nanoreactor channels of mesoporous silica (SBA-15) is reported, and evaluated by using peptide-mass mapping. Both proteases and substrates were efficiently captured within these biocompatible nanoreactors. After 10 minutes, the mass spectrum of the protein digests released from the mesoporous-silica-based nanoreactors revealed the presence of eight peptides covering 58% of the protein sequence with an intense signal (signal/noise ratio > 70). In comparison, the conventional overnight in-solution digestion of proteins under otherwise identical conditions generated only three peptides (27% sequence coverage). We propose that this order-of-magnitude increase in the proteolytic reaction rate is mainly attributed to two factors: substrate enrichment within mesoporous silica channels and enzyme immobilization. The surface properties and macrostructure of the mesoporous silica were studied to reveal their significant influence on proteolytic reactions.     

Band limited functions on quantum graphs

The notion of band limited functions is introduced on a quantum graph. The main results of the paper are a uniqueness theorem and a reconstruction algorithm of such functions from discrete sets of values. It turns out that some of our band limited functions can have compact supports and their frequencies can be localized on the ``time" side. It opens an opportunity to consider signals of a variable band width and to develop a sampling theory with variable rate of sampling.

     

PSA高速常规单模光纤通信系统的传输性能及其与EDFA系统的比较

本文采用计算机系统仿真的方法研究了应用相敏光放大器(PSA)并附加DCF色散补偿的高速常规单模光纤通信系统的传输性能,并和相同速率的掺铒光纤放大器(EDFA)系统进行了比较.研究着重于传输速率、放大器间距对系统码间干扰限制距离的影响.结果表明PSA系统比EDFA系统更适合于高速率传输并具有更长的传输距离.而且,对PSA系统,在放大器增益正好补偿光纤损耗的条件下,存在一相应于最大码间干扰限制距离的最佳放大器间距.     

Improved Computer Program for Magnetron Injection Gun Design

Gyrotron has received extensive attention owing to its high-power capability, especially when the wavelength shrinks below the millimeter-wave range. The electron beam of a gyrotron is typically generated by a magnetron injection gun (MIG). For high cathode current density, the MIG may operate in a region that combines temperature limited and space-charge limited emissions. An improved computer program for electron gun design is appropriate for MIGs that operate between space-charge limited and temperature limited emission. Moreover, the initial input formation of the program resembles that of the EGUN code. Analysis of a Pierce electron gun and MIGs reveals that the stimulated beam current appears consistent with the measured results. However, EGUN simulation results in which the cathode emitters of MIGs are chosen for the temperature limited emission differ from those of our simulation results. This difference is most likely owing to that the initial emitting energy can not be completely described in the EGUN simulation. Finally, the improved computer program is used to design a MIG for a Ka-band, TE₀₁ mode gyro-TWT.