Regularized iterative method for ill-posed linear systems based on matrix splitting

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov?s regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The convergence of such a well-posed system is discussed by using different types of matrix splittings. Comparison analysis of both systems are studied by operating certain types of weak splittings. Further, we have extended the double splitting of [Song J. and Song Y, Calcolo 48(3), 245-260, 2011] to double weak splitting of type II for nonsingular symmetric matrices. In addition to that, some more comparison results are presented with the help of such weak double splittings of type I and type II.

The LPM effect in sequential bremsstrahlung: nearly complete results for QCD

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. Previous work has computed overlap effects for double splitting g → gg → ggg. To make use of those results, one also needs calculations of related virtual loop corrections to single splitting g → gg in order to cancel severe (power-law) infrared (IR) divergences. This paper provides calculations of nearly all such processes involving gluons and discusses how to organize the results to demonstrate the cancellation. In the soft emission limit, our results reproduce the known double-log behavior of earlier authors who worked in leading-log approximation. We also present a first (albeit numerical and not yet analytic) investigation of sub-leading, single IR logarithms. Ultraviolet divergences appearing in our calculations correctly renormalize the coupling αs in the usual LPM result for leading-order g → gg.

Comparison Theorems of Spectral Radius for Splittings of Matrices

A class of the iteration method from the double splitting of coefficient matrix for solving the linear system is further investigated. By structuring a new matrix, the iteration matrix of the corresponding double splitting iteration method is presented. On the basis of convergence and comparison theorems for single splittings, we present some new convergence and comparison theorems on spectral radius for splittings of matrices.

Experimental Analysis for the Low-Temperature Growth of Poly-Si Films by Using Double Excimer Laser

This paper is to investigate a double splitting excimer laser technique for making poly Si films. In this research, a KrF excimer laser of 248 nm in wavelength is used to irradiate a-Si films of 0.1 m in thickness on glass substrate to produce poly-Si ones. The control parameters are laser intensity (200~500 mJ/cm2), laser pulse number (1~2 shots) and delay time between two shots (one nanosecond). Average grain sizes from SEM photos are used to analyze the effects of these parameters. Firstly, in the excimer laser experiment, different laser fluences are utilized to study the effect on the microstructure of the silicon film. Purely from the viewpoint of heat transfer, the Si film obtains more energy has the slower cooling or solidification rate, which results in the larger grain. From the experimental results, it can be found that the grain size increases until the laser fluence increases up to the critical value of complete melting, which limits the grain growth method of energy increase. In this work, a double-splitting-laser method is proposed. In the method, a laser pulse from an excimer laser is divided into two pulses by a beam splitter. The cyclic optical path is used to control the delay time of the second pulse. Optical mirrors and optical attenuators are utilized to adjust the energy density of these two laser pulses. The delay time between these two pulses is changeable and controlled in the order of nanosecond. The second pulse is applied when the Si film is solidifying after the irradiation of the first one. This could enhance the solidification time and enlarge the grain size of the poly-Si film.

Factors influencing the rooting of Gisela 5 (Prunus cerasus × Prunus canescens) cherry rootstock hardwood cuttings

In this study, the effect of double splitting, cooling in pre-storage, collection date, indole-3-butyric acid (IBA) dipping of shoot tip and base, gibberellic acid (GA3), Agrobacterium radiobacter and A. rhizogenes on the callusing and rooting of Gisela 5 cherry rootstock hardwood cuttings was investigated. Double splitting and bacteria did not affect the callusing and rooting of cuttings. The callusing and rooting of cuttings kept at 0–3°C for 15 days or more were significantly reduced. The callusing and rooting percentages were highest when only the base of cuttings was treated with 1000 mg/L IBA solution. The rooting percentage of cuttings increased when 10–20 mg/L GA3 was applied the same day cuttings were placed on a bottom heat bench. The results showed that the best periods to collect Gisela 5 hardwood cuttings were the later half of November and early March. No correlation between the collection date and starch content, and the starch content and the callusing and rooting of Gisela 5 hardwood cuttings was found.