A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

A contribution to the global formulation of the higher-order Poincaré-Cartan form

The global formulation of the higher-order Poincaré-Cartan form for Lagrangian field theories in the calculus of variations is re-examined in terms of the theory of lifts of tensor fields on a manifold to its higher-order prolongated jet bundles.Partially supported by CNPq, Brazil, Proc. MA 30.1115/79.     

Thermodynamic conditions for a symmetric form of superfluid's equations

Summary Going on with a research started in a previous paper, we examine carefully Putterman's system of superfluid hydrodynamic equations, assuming as viewpoint the theory of quasi-linear hyperbolic symmetric systems with constraints. We prove that such a system is always hyperbolic. It can be put in a symmetric form, provided suitable thermodynamic conditions, ensuring the convexity of the entropy function, hold.

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Riassunto Si approfondisce l'esame, iniziato in un precedente lavoro, del sistema di equazioni idrodinamiche del superfluido di Putterman dal punto di vista della teoria dei sistemi quasi lineari iperbolici simmetrici e con vincoli. Si dimostra che tale sistema è sempre iperbolico e può essere posto in forma simmetrica quando siano soddisfatte opportune condizioni termodinamiche che assicurano la convessità della funzione entropia.

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Резюме Углубляется начатое в одной из предыдущих работ исследование системы гидродинамических уравнений супержидкости Паттермана с точки зрения теории систем квазилинейных гиперболических симметрических и со связями. Доказывается, что такая система является всегда гиперболической и может быть приведена к симметрической форме, когда выполнены соответствующие термодинамические условия, обеспечивающие вьшуклость функции энергии.

     

Chaotic dynamics in biological information processing: A heuristic outline

Summary A given but otherwise random environmental time series impinging on the input of a certain biological processor passes through with overwhelming probability practically undetected. A very small percentage of environmental stimuli, though, is ?captured? by the processor's nonlinear dissipative operator asinitial conditions, that is, assolutions of the processor's dissipative dynamics. The processor, then, is in such cases instrumental in compressing or abstracting those stimuli, thereby making the external world to collapse from a previous regime of a ?pure state? of suspended animation onto a set of stable eigenfunctions or ?categories?—chaotic strange attractors. The characteristics of this cognitive set depend on the operator involved and the hierarchical level where the abstraction takes place. In this paper we model the physics of such a cognitive process and the role that the thalamo-cortical pacemaker of the (human) brain plays in both stimulating the individual attractors and permutating them on a time division multiplexing basis. A synthesis of the Markovian processes taking place within each individual attractor-memory and the Markovian or semi-Markovian process involving the intermittent jumping among the different attractor-memories are discussed.

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Riassunto Una data ma casuale serie temporale ambientale che influisce sull'immissione di un determinato processore biologico passa con schiacciante probabilità praticamente inosservata. Una piccolissima percentuale di stimoli ambientali, tuttavia, è catturata dall'operatore dissipativo non lineare del processore comecondizioni iniziali, cioè comesoluzioni della dinamica dissipativa del processore. Il processore è quindi, in tali casi, strumentale nel comprimere o estrarre quegli stimoli, facendo perciò collassare il mondo esterno da un precedente regime di ?stato puro? ad animazione sospesa ad un gruppo di autofunzioni stabili o ?categorie?—attrattori caotici strani. Le caratteristiche di questo gruppo cognitivo dipendono dall'operatore coinvolto e dal livello gerarchico in cui l'estrazione ha luogo. In questo lavoro si modella la fisica di tale processo cognitivo e il ruolo che lo stimolatore talamo-corticale del cervello (umano) ha sia nello stimolare gli attrattori individuali che nel permutarli su una base che manda segnali multiplex a divisione temporale. Si discute una sintesi dei processi markoviani che hanno luogo all'interno di ogni attrattore-memoria individuale e il processo markoviano o semimarkoviano che interessa il salto intermittente tra i diversi attrattori-memoria.

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Резюме Временная последовательность на входе некоторого биологического процессора может иметь практически недетектируемую вероятность. Очень небольшой процент стимулов окружающей среды ?захватывается? нелинейным диссипативным оператором процессора как начальные условия, т.е. представляется как решение диссипативпой динамики процессора. Затем процессор обрабатывает внешние стимулы, вынуждая внешний мир коллапсировать из предыдущего режима ?чистого состояния? приостановленного оживления в систему собственных функций или ?категорий?. Характеристики зтой познавательной системы зависят от используемого оператора и иерархического уровня, на котором происходит абстрагирование. В зтой статье мы моделируем физику такого познавательного процесса. Обсуждается синтез марковских процессов, происходящий внутри отдельного злемента ?атрактор-память?, и марковский или полумарковский процесс, включающий пережежающиеся прыжки между различными злементами ?атракторпамять?.

     

Wetting in Potts and Blume-Capel models

We discuss the wetting of the interface between two ordered phases by the disordered one in the Potts model withq large. We argue that a low-temperature expansion can be used in this situation, with logq replacing. This model is analogous to the Blume-Capel model at low temperatures, which we use as an example to review the low-temperature expansions.     

Radiative frequency shift without ultraviolet divergency in a two-level hydrogenic atom

Summary By taking into account the retardation effects a finite result for the frequency shift of the Lyman α-radiation from a two-level hydrogenic atom is obtained. This result shows a nonnegligible correction as compared to previous results obtained in the dipole approximation with a cut-off frequency.     

On the structure of split Leibniz triple systems

We study the structure of arbitrary split Leibniz triple systems with a coherent 0-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length, the simplicity of the Leibniz triple systems is characterized.     

Construction of inclusions with vanishing generalized polarization tensors by imperfect interfaces

We investigate the problem of planar conductivity inclusion with imperfect interface conditions. We assume that the inclusion is simply connected. The presence of the inclusion causes a perturbation in the incident background field. This perturbation admits a multipole expansion of which coefficients we call as the generalized polarization tensors (GPTs), extending the previous terminology for inclusions with perfect interfaces. We derive explicit matrix expressions for the GPTs in terms of the incident field, material parameters, and geometry of the inclusion. As an application, we construct GPT-vanishing structures of general shape that result in negligible perturbations for all uniform incident fields. The structure consists of a simply connected core with an imperfect interface. We provide numerical examples of GPT-vanishing structures obtained by our proposed scheme.     

C1 Rational interpolating surface under local coordinate systems

A method of constructing rational interpolating surface under local coordinate systems is presented, which can be used to solve the large torsion problem of surfaces. This kind of surface has better approximating effect and its properties can be easily discussed, so it has practical applications not only in CAD but also infinite element analysis and other fields. An example is given in the paper.Projects Supported by the Science Fund of Education Committee.