Multi-step nonlinear conjugate gradient methods for unconstrained minimization

Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of matrices. Recently, seeking fast convergence of these methods, Dai and Liao (Appl. Math. Optim. 43:87–101, 2001) proposed a conjugate gradient method based on the secant condition of quasi-Newton methods, and later Yabe and Takano (Comput. Optim. Appl. 28:203–225, 2004) proposed another conjugate gradient method based on the modified secant condition. In this paper, we make use of a multi-step secant condition given by Ford and Moghrabi (Optim. Methods Softw. 2:357–370, 1993; J. Comput. Appl. Math. 50:305–323, 1994) and propose two new conjugate gradient methods based on this condition. The methods are shown to be globally convergent under certain assumptions. Numerical results are reported.     

Contractible subgraphs, Thomassen’s conjecture and the dominating cycle conjecture for snarks

We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Hamiltonian), by Thomassen (every 4-connected line graph is Hamiltonian) and by Fleischner (every cyclically 4-edge-connected cubic graph has either a 3-edge-coloring or a dominating cycle), which are known to be equivalent, are equivalent to the statement that every snark (i.e. a cyclically 4-edge-connected cubic graph of girth at least five that is not 3-edge-colorable) has a dominating cycle.We use a refinement of the contractibility technique which was introduced by Ryjá?ek and Schelp in 2003 as a common generalization and strengthening of the reduction techniques by Catlin and Veldman and of the closure concept introduced by Ryjá?ek in 1997.     

关于线图第二大根的极限点

设Gn为线图，λ2（Gn)为Gn的第二大根，给出λ2（Gn)的最小极限点：√5-1/2.这时，Gn≌Kr 1^1(Kr 1^1是由完全图Kr 1在其一顶点处与P2的连接图。     

Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

We prove Helly-type theorems for line transversals to disjoint unit balls in ℝ ^d . In particular, we show that a family of n≥2d disjoint unit balls in ℝ ^d has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n≥4d−1 disjoint unit balls in ℝ ^d admits a line transversal if any subfamily of size 4d−1 admits a transversal. Andreas Holmsen was supported by the Research Council of Norway, prosjektnummer 166618/V30. Otfried Cheong and Xavier Goaoc acknowledge support from the French-Korean Science and Technology Amicable Relationships program (STAR).     

Embedded design based virtual instrument program for positron beam automation

Automation of positron beam experiment with a single chip embedded design using a programmable system on chip (PSoC) which provides easy interfacing of the high-voltage DC power supply is reported. Virtual Instrument (VI) control program written in Visual Basic 6.0 ensures the following functions (i) adjusting of sample high voltage by interacting with the programmed PSoC hardware, (ii) control of personal computer (PC) based multi channel analyzer (MCA) card for energy spectroscopy, (iii) analysis of the obtained spectrum to extract the relevant line shape parameters, (iv) plotting of relevant parameters and (v) saving the file in the appropriate format. The present study highlights the hardware features of the PSoC hardware module as well as the control of MCA and other units through programming in Visual Basic.     

精馏塔控制实质的探讨

本文从精馏操作原理出发,得出精馏塔控制的实质是在塔板结构与塔板数不变的条件下,改变操作条件,以使精馏塔在受到干扰后仍能维持原来的塔顶或塔底产品组成。应用这些基本关系,推导出操作变量的近似计算公式。这些关系式经过计算验证,误差在允许范围内,在控制中是可以应用的。     

行AFC电路的波形分析

分析了行ＡＦＣ电路的工作原理，建立了行ＡＦＣ鉴相电路的数学模型，分析了鉴相波形。     

Wetting, adsorption and surface critical phenomena

Our understanding of interfacial phenomena at the surfaces of critical systems, and in particular at the surfaces of critical binary liquid mixtures, has improved significantly in the past decade. There is now substantial agreement between theory and experiment. In this paper we review recent experimental progress, provide a conceptual framework within which the majority of these experiments can now be understood, and discuss critically any remaining unresolved discrepancies between experiments or with theory.     

n维向量组的极大无关组的求法

介绍两种求ｎ维向量组的极大无关组的方法。     

Tutte uniqueness of line graphs

We prove that if a graph H has the same Tutte polynomial as the line graph of a d-regular, d-edge-connected graph, then H is the line graph of a d-regular graph. Using this result, we prove that the line graph of a regular complete t-partite graph is uniquely determined by its Tutte polynomial. We prove the same result for the line graph of any complete bipartite graph.