Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by exp...
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Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic f...
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The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.
The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the i...
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The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the initialproblem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initialproblems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.
The complicated characteristics of the powder were studied by fractal theory. It is illustrated that powder shape, binder structure, feedstock and mold filling flow in powder injection molding process possess obvious ...
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The complicated characteristics of the powder were studied by fractal theory. It is illustrated that powder shape, binder structure, feedstock and mold filling flow in powder injection molding process possess obvious fractal characteristics. Based on the result of SEM, the fractal dimensions of the projected boundary of carbonylic iron and carbonylic nickel particles were determined to be 1.074±0.006 and 1.230±0.005 respectively by box counting measurement. The results show that the fractal dimension of the projected boundary of carbonylic iron particles is close to smooth curve of one dimension, while the fractal dimension of the projected boundary of carbonylic nickel particle is close to that of trisection Koch curve, indicating that the shape characteristics of carbonylic nickel particles can be described and analyzed by the characteristics of trisection Koch curve. It is also proposed that the fractal theory can be applied in the research of powder injection molding in four aspects.
Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference...
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Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference approximations for Hamilton-Jacobi equation and hyperbolic conservation laws. In this paper we present the relaxing system for HamiltonJacobiequations in arbitrary space dimensions, and high resolution relaxing schemes for Hamilton-Jacobi equation, based on using the local relaxation approximation. The schemes are numerically tested on a variety of 1D and 2D problems, including a problem related to optimal control problem. High-order accuracy in smooth regions, good resolution of discontinuities, and convergence to viscosity solutions are observed.
This paper aims at a comprehensive understanding of the novel elastic property of double-stranded DNA (dsDNA) discovered very recently through single-molecule manipulation techniques. A general elastic model for doubl...
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This paper aims at a comprehensive understanding of the novel elastic property of double-stranded DNA (dsDNA) discovered very recently through single-molecule manipulation techniques. A general elastic model for double-stranded biopolymers is proposed, and a structural parameter called the folding angle φ is introduced to characterize their deformations. The mechanical property of long dsDNA molecules is then studied based on this model, where the base-stacking interactions between DNA adjacent nucleotide base pairs, the steric effects of base pairs, and the electrostatic interactions along DNA backbones are taken into account. Quantitative results are obtained by using a path integral method, and excellent agreement between theory and the observations reported by five major experimental groups are attained. The strong intensity of the base stacking interactions ensures the structural stability of DNA, while the short-ranged nature of such interactions makes externally stimulated large structural fluctuations possible. The entropic elasticity, highly extensibility, and supercoiling property of DNA are all closely related to this account. The present work also suggests the possibility that negative torque can induce structural transitions in highly extended DNA from the right-handed B form to left-handed configurations similar to the Z-form configuration. Some formulas concerned with the application of path integral methods to polymeric systems are listed in the Appendixes.
An elastic model for double-stranded polymers is constructed to study the recently observed DNA entropic elasticity, cooperative extensibility, and supercoiling property. With the introduction of a new structural para...
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An elastic model for double-stranded polymers is constructed to study the recently observed DNA entropic elasticity, cooperative extensibility, and supercoiling property. With the introduction of a new structural parameter (the folding angle ϕ), bending deformations of sugar-phosphate backbones, steric effects of nucleotide base pairs, and base-stacking interactions are considered. The comprehensive agreements between theory and experiments both on torsionally relaxed DNA and on negatively supercoiled DNA strongly indicate that base-stacking interactions, although short-ranged in nature, dominate the elasticity of DNA and, hence, are of vital biological significance.
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