A model of the liquid-crystal phase transition and the quasicrystal model of liquid

We compare properties of the crystal structure and of the quasicrystal model of liquid. We show that if the Lennard-Jones potential is used to model the properties of argon, then the temperature of the phase transition between the densely packed face-centered and the body-centered cubic structure is very close to the liquid-crystal transition temperature. Based on this, we propose a model of the phase transition consisting in a change of just the short-range order, which then leads to a change of the long-range order. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 155–171, April, 2007.     

A model of the neocortex

We try to explain the function of the cerebral cortex by representing it as a large array of small computers, each of which applies a certain algorithm for learning to predict the inputs from the senses or other parts of the brain. This view ignores the role of the brain as a classifying device, but it puts forward its role as a learner of the laws of evolution of sequences of patterns. Memory is not seen here as a list of facts but as an operator predicting certain parameters of the future states of reality from its present and past states. The problem of connecting the classifying or listing capacity of the brain with the structures described here is still open.     

Stability of the LCD model

The growing network model with loops and multiple edges proposed by Bollobás et al. (Random Structures and Algorithms 18(2001)) is restudied from another perspective. Based on the first-passage probability of Markov chains, we prove that the degree distribution of the LCD model is power-law with degree exponent 3 as the network size grows to infinity.     

Quantum-field model of the deuteron

A quantum-field model of the deuteron is investigated for the case of a scalar field with point interaction. In the strong-coupling limit, exact solutions of the nonlinear field equations for the deuteron are found. The results are compared with the experimental values for the energy, radius, and mass of the deuteron. A scheme for eliminating the ultraviolet divergences in strong-coupling theory is proposed.Institute of Mathematical Problems in Biology, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 2, pp. 219–229, August, 1994.     

Large deviation principles for the Hopfield model and the Kac-Hopfield model

Summary We study the Kac version of the Hopfield model and prove a Lebowitz-Penrose theorem for the distribution of the overlap parameters. At the same time, we prove a large deviation principle for the standard Hopfield model with infinitely many patterns.Work partially supported by the Commission of the European Communities under contract No. SC1-CT91-0695     

一类相依索赔离散风险模型研究

研究了一类相依索赔的离散风险模型,得到了利率为0时模型的最终破产概率所满足的积分方程,以及破产持续n期的概率所满足的表达式.进而,得到了利率不为0时该模型的最终破产概率所满足的积分方程,并利用鞅论技巧导出了最终破产概率的一个Lundberg型上界,最后运用Matlab软件随机模拟破产概率并与Lundberg型上界作比较.     

A new model of conflict analysis - the three dimensional graph model

The purpose of this paper is to put forward a new model of conflict analysis - the 3-D graph model and its stability analysis, including the three most important factors of conflict analysis. The rules concerning the movement of multiple players are still considered based on practical restrictions. Therefore the 3-D graph model may be used to solve real problems effectivity.     

Covariant quantization of the Volovich-Katanaev model

The Volovich-Katanaev model of two-dimensional gravity with dynamic torsion is considered in terms of the Batalin-Vilkovysky quantization and in the framework of the background field method. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 114, No. 3, pp. 399–409, March. 1998.     

Hamiltonian interpretation of the Volterra model

We consider a differential-difference Volterra system in the new Hamiltonian formulation of L. A. Takhtadzhyan and L. D. Faddeev. The connection with the quantum method of the inverse problem and conformally invariant two-dimensional field theory is discussed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 150, pp. 17–25, 1986.     

A three-chamber model of the cochlea

We construct a three-chamber hydrodynamic model of the cochlea, based on the two-chamber model with Reissner's membrane added. The anisotropic stiffness values of both membranes are obtained from Bekesy's hair probe experiments. The membrane response in the two- and three-chamber models is examined as a function of some of the cochlea parameters.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 133–143, 1985.I would like to acknowledge the help of Prof. V. M. Babich in the course of this research.     

Solution of the model Lagerstrom problem

Translated from Matematicheskie Zametki, Vol. 56, No. 4, pp. 3–8, October, 1994.     

The maximality of the core model

Our main results are: 1) every countably certified extender that coheres with the core model is on the extender sequence of , 2) computes successors of weakly compact cardinals correctly, 3) every model on the maximal 1-small construction is an iterate of , 4) (joint with W. J. Mitchell) is universal for mice of height whenever , 5) if there is a such that is either a singular countably closed cardinal or a weakly compact cardinal, and fails, then there are inner models with Woodin cardinals, and 6) an -Erdös cardinal suffices to develop the basic theory of .

     

Sensitivity analysis of the newsvendor model

Quality of decisions in inventory management models depends on the accuracy of parameter estimates used for decision making. In many situations, error in decision making is unavoidable. In such cases, sensitivity analysis is necessary for better implementation of the model. Though the newsvendor model is one of the most researched inventory models, little is known about its robustness. In this paper, we perform sensitivity analysis of the classical newsvendor model. Conditions for symmetry/skewness of cost deviation (i.e., deviation of expected demand–supply mismatch cost from its minimum) have been identified. These conditions are closely linked with symmetry/skewness of the demand density function. A lower bound of cost deviation is established for symmetric unimodal demand distributions. Based on demonstrations of the lower bound, we found the newsvendor model to be sensitive to sub-optimal ordering decisions, more sensitive than the economic order quantity model. Order quantity deviation (i.e., deviation of order quantity from its optimum) is explored briefly. We found the magnitude of order quantity deviation to be comparable with that of parameter estimation error. Mean demand is identified as the most influential parameter in deciding order quantity deviation.     

Markov degree of the Birkhoff model

We prove the conjecture by Diaconis and Eriksson (J. Symbolic Comput. 41(2):182–195, 2006) that the Markov degree of the Birkhoff model is three. In fact, we prove the conjecture in a generalization of the Birkhoff model, where each voter is asked to rank a fixed number, say r, of candidates among all candidates.     

Turing pattern of the Oregonator model

The Oregonator model is the mathematical dynamics which describes the Field-Körös-Noyes mechanics of the famous Belousov-Zhabotinskii? reaction. In this work, we establish some fundamental analytic properties of this dynamics and its corresponding steady state. Under various conditions on the parameters and the size of the reactor, we examine the existence and non-existence of non-constant steady states. In particular, for some properly chosen parameter ranges, we prove the occurrence of the Turing pattern generated by this Oregonator model. Our results exhibit interesting and very different roles of the diffusion rates and the reactor in the formation of the Turing pattern. Our mathematical analysis mainly relies on a priori estimates and the topological degree argument.     

Parameter estimation of the WMTD model

The MTD （mixture transition distribution） model based on Weibull distribution （WMTD model） is proposed in this paper, which is aimed at its parameter estimation. An EM algorithm for estimation is given and shown to work well by some simulations. And bootstrap method is used to obtain confidence regions for the parameters. Finally, the results of a real example--predicting stock prices--show that the WMTD model proposed is able to capture the features of the data from thick-tailed distribution better than GMTD （mixture transition distribution） model.     

Thermodynamic properties of the Peierls model

Theoretical and Mathematical Physics -