Mean field methods for atomic and nuclear reactions: The link between time–dependent and time–independent approaches

Abstact: Three variants of mean field methods for atomic and nuclear reactions are compared with respect to both conception and applicability: The time–dependent Hartree–Fock method solves the equation of motion for a Hermitian density operator as initial value problem, with the colliding fragments in a continuum state of relative motion. With no specification of the final state, the method is restricted to inclusive reactions. The time–dependent mean field method, as developed by Kerman, Levit and Negele as well as by Reinhardt, calculates the density for specific transitions and thus applies to exclusive reactions. It uses the Hubbard–Stratonovich transformation to express the full time-development operator with two–body interactions as functional integral over one–body densities. In stationary phase approximation and with Slater determinants as initial and final states, it defines non–Hermitian, time–dependent mean field equations to be solved self–consistently as boundary value problem in time. The time–independent mean field method of Giraud and Nagarajan is based on a Schwinger–type variational principle for the resolvent. It leads to a set of inhomogeneous, non-Hermitian equations of Hartree–Fock type to be solved for given total energy. All information about initial and final channels is contained in the inhomogeneities, hence the method is designed for exclusive reactions. A direct link is established between the time–dependent and time–independent versions. Their relation is non–trivial due to the non–linear nature of mean field methods. Received: 7 January 1998 / Revised version: 20 April 1998     

以广义相对论为例谈实验检验的总体方案设计

以广义相对论为例，论述了如何根据物理理论的逻辑体系设计实验，以检验理论的正确性，对于广义相对论，检验实验应包括对等效原理的检验实验，对牛顿极限的检验实验，以及对广义相对论推论的检验实验。     

L-shaped decomposition of two-stage stochastic programs with integer recourse

We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of the method is established when Gomory’s fractional cutting plane algorithm or a branch-and-bound algorithm is applied.     

Parity violation effects of weak interactions on the origin of biomolecular chirality

Summary The process through which the extremely weak parity violation interaction can become the selector of biomolecular chirality via beta-radiolysis over a timet=1500 y is proposed. The mechanism is discussed by using realistic values of the rate constants.

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Riassunto Si dimostra che l'interazione debole avrebbe indotto l'attuale chiralità delle molecole biologiche. Il meccanismo proposto è quello della radiolisi. Usando opportuni valori dei parametri cinetici, l'arco temperale del fenomeno è stimato in 1500 anni.

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Резюме Предлагается процесс, с помощью которого чрезвычайно слабое взаимодействие с нарушением четности может стать селектором биомолекулярной киральности через бета-радиолиз в течениеt=1500 лет. Обсуждается предложенный механизм, используя реалистические значения для постоянных взаимодействия.

     

A unified approach to one-parametric general quadratic programming

A method is proposed for finding local minima to the parametric general quadratic programming problem where all the coefficients are linear or polynomial functions of a scalar parameter. The local minimum vector and the local minimum value are determined explicitly as rational functions of the parameter. A numerical example is given.     

Sensitivity improvement of a two-mode gravitational-radiation detector through the use of a transducer not perfectly tuned to the antenna

Summary The detailed analysis of the behaviour of a gravitational-wave antenna coupled to a passive resonant transducer has been performed for short bursts of gravitational radiation. An expression for the noise temperature of the system is given for the general case of a transducer with resonant frequency and mechanical quality factor different from those of the antenna. The analysis of the optimum noise temperature obtainable for a given system shows that the optimum performance is obtained when the frequency of the transducer is slightly different from that of the antenna. The main point of this paper has been presented byC. Cosmelli at theSecond Workshop on Precision Measurements on Relativistic Effects in Astrophysical Systems, held in Rome, 11–13 July 1983.     

General energy decay in a Timoshenko-type system of thermoelasticity of type III with a viscoelastic damping

In this paper we consider a one-dimensional linear thermoelastic system of Timoshenko type, where the heat conduction is given by Green and Naghdi theories. We prove a general decay result, from which the exponential and polynomial decays are only special cases.     

Assessing the MALDI-TOF MS sample preparation procedure to analyze the influence of thermo-oxidative ageing and thermo-mechanical degradation on poly (Lactide)

Multiple processing by means of successive injection cycles was used to simulate the thermo-mechanical degradation effects on the oligomeric distribution of PLA under mechanical recycling. Likewise, an accelerated thermal ageing over PLA glass transition was performed in order to simulate its service life. MALDI-TOF MS was used for the analysis and the sample preparation procedure was assessed by means of a statistical Design of Experiments (DoE). The quality effects in use for the analysis were signal-to-noise ratio and Resolution. Different matrixes, analyte/matrix proportions and the use of NaTFA as cationization agent were considered. A deep inspection of the statistical results provided a better understanding of the influence of the different factors, individually or in combination, to the signal. The application of DoE for the improvement of the MALDI measurement of PLA stated that the best combination of factors (levels) was the following: matrix (s-DHB), proportion analyte/matrix (1/5 V/V), and no use of cationization agent. Degradation primarily affected the initially predominant cyclic [LA_C]_n and linear H[LA_L]_nOH species, where LA stands for a PLA repeating unit. Intramolecular and intermolecular transesterifications as well as hydrolytic and homolytic reactions took place during the formation and disappearance of oligomeric species. In both degradation mechanisms induced by thermal ageing and thermo-mechanical degradation, the formation of H[LA_L]_nOCH₃ by intermolecular transesterifications was highlighted.     

Fast block diagonalization of k-tridiagonal matrices

In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e.g., another derivation of a very recent result on generalized k-Fibonacci numbers in [M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456-4461]; efficient (symbolic) algorithm for computing the matrix determinant.     

On a new class of Finsler metrics

In this paper, the geometric meaning of (α,β)-norms is made clear. On this basis, a new class of Finsler metrics called general (α,β)-metrics are introduced, which are defined by a Riemannian metric and a 1-form. These metrics not only generalize (α,β)-metrics naturally, but also include some metrics structured by R. Bryant. The spray coefficients formula of some kinds of general (α,β)-metrics is given and the projective flatness is also discussed.