Rigorous low-temperature results for the mean field p-spins interaction model

We prove that, just below the critical temperature, the mean field p-spins interaction model, for p suitably large, spontaneously decomposes into different states. The asymptotic overlaps between any two different states are zero. Under a mild (unproven) hypothesis on the weight distribution of these states, we prove that they are pure states. This situation is called in physics “one level of symmetry breaking”. Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000     

The efficient computation of periodic states of cyclically operated chemical processes

In this paper we present a shooting method in combination witha hybrid Newton–Picard method to compute efficiently theperiodic states of cyclically operated chemical processes. Themerits of the method are investigated by considering the computationof the periodic states of a rapid pressure swing adsorptionsystem and of a cooled reverse-flow reactor.We show that theseperiodically forced chemical processes exhibit low-dimensionaldynamics. The Newton–Picard method is designed to makeefficient use of this low-dimensional dynamics of the chemicalprocesses. In addition the Newton–Picard method is ableto determine the stability of the computed periodic states.As an illustration of the efficiency of the method, we computea branch of periodic states for the reverse flow reactor.     

What Mary’s Aboutness Is About

The aim of this paper is to reinforce anti-physicalism by extending the “hard problem” to a specific kind of intentional states. For reaching this target, I investigate the mental content of the new intentional states of Jackson’s Mary. I proceed in the following way: I start analyzing the knowledge argument, which highlights the “hard problem” tied to phenomenal consciousness. In a second step, I investigate a powerful physicalist reply to this argument: the phenomenal concept strategy. In a third step, I propose a constitutional account of phenomenal concepts that captures the Mary scenario adequately, but implies anti-physicalist referents. In a last step, I point at the ramifications constitutional phenomenal concepts have on the constitution of Mary’s new intentional states. Therefore, by focusing the attention on phenomenal concepts, the so-called “hard problem” of consciousness will be carried over to the alleged “easy problem” of intentional states as well.     

Expressing One’s Mind

Remarks such as ‘I am in pain’ and ‘I think that it’s raining’ are puzzling, since they seem to literally describe oneself as being in pain or having a particular thought, but their conditions of use tend to coincide with unequivocal expressions of pain or of that thought. This led Wittgenstein, among others, to treat such remarks as expressing, rather than as reporting, one’s mental states. Though such expressivism is widely recognized as untenable, Bar-On has recently advanced a neo-expressivist view, on which such remarks exhibit characteristics of both expressions of mental states and reports of those states. I argue against any attempt to see such remarks as both reporting and expressing the same mental states, and that a correct account rests on distinguishing the truth conditions of such remarks from their conditions of use.     

Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice

The Ising model on a Bethe lattice of orderk≥2 is considered. For maximum or minimum translation-invariant Gibbs states of this model, the relations between the von Neumann algebras generated by these states for the Gelfand-Neimark-Segal representation are found. These algebras can be of types III_λ, λ∈(0, 1), and III₁. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 88–93, April, 2000.     

String world surfaces in spaces with compact factor-manifolds

The closed string with point-like masses as the string hadron model is considered in the D-dimensional space M = R^1,3 ×T^{D - 4} \mathcal{M} = {R^{1,3}} \times {T^{D - 4}} , which is the direct product of the Minkowski space and the compact manifold T ^D−4 = S ¹ × ⋯ × S ¹ ((D − 4)-dimensional torus). Exact solutions of dynamical equations are obtained; in a particular case of rotational states, they describe a uniform rotation of the system. These rotational states are classified, their physical properties are studied, and Regge trajectories are determined. Central and linear rotational states are tested for stability with respect to small disturbances. It is shown that the central rotational states are not stable if the central mass is less than some threshold value.     

Reasons and passions

Jonathan Dancy has argued that agents’ reasons for their actions are facts or features of the situations rather than their psychological states. The purpose of the paper is to show that even if we grant that this is so in most of the cases, there is a class of mental states that can be reasons. Although beliefs and desires are not reasons for actions, some emotional states—like loving, liking or disliking someone—can generate reasons. The distinctive feature of these states is that their content is a particular, and not a proposition. Hence in certain situations their love or admiration can provide agents with reasons to do one particular thing rather than another.     

The q-deformed harmonic oscillator, coherent states, and the uncertainty relation

For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We calculate the product of the “coordinate-momentum” uncertainties in q-oscillator eigenstates and in coherent states. For the oscillator, this product is minimum in the ground state and equals 1/2, as in the standard quantum mechanics. For coherent states, the q-deformation results in a violation of the standard uncertainty relation; the product of the coordinate-and momentum-operator uncertainties is always less than 1/2. States with the minimum uncertainty, which tends to zero, correspond to the values of λ near the convergence radius of the q-exponential. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 315–322, May, 2006.     

Bound States of a Particle in the Field of Receding Point Potentials

We study bound states in a nonstationary system of receding δ-centers. We consider the states characterized by different depths of point spectrum levels in one-dimensional and three-dimensional problems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 385–392, December, 2005.     

Recurrence and ergodicity of interacting particle systems

Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of their ergodic invariant measures. The question arises whether a.s.the process eventually stays close to one of these ergodic states, or if it changes between the attainable ergodic states infinitely often (“recurrence”). Under the assumption that there exists a convergence–determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer a question raised by Ed Perkins concerning the change of the locally predominant type in a model of mutually catalytic branching. Received: 22 January 1999 / Revised version: 24 May 1999     

Bar-On on Self-Knowledge and Expression

I critically discuss the account of self-knowledge presented in Dorit Bar-On’s Speaking My Mind (OUP 2004), focusing on Bar-On’s understanding of what makes our capacity for self-knowledge puzzling and on her ‘neo-expressivist’ solution to the puzzle. I argue that there is an important aspect of the problem of self-knowledge that Bar-On’s account does not sufficiently address. A satisfying account of self-knowledge must explain not merely how we are able to make accurate avowals about our own present mental states, but how we can reasonably regard ourselves as entitled to claim self-knowledge. Addressing this aspect of the problem of self-knowledge requires confronting questions about the metaphysical nature of mental states, questions that Bar-On’s approach seeks to avoid.     

Bifurcation analysis of the mathematical model of the NO+CO/Pt(100) reaction

The article presents a detailed bifurcation analysis of steady and periodic states for a new mathematical model of the NO+CO/Pt(100) reaction. Various bifurcation diagrams are constructed in the planes of partial reagent pressures and surface temperature. Regions with oscillations and multiple steady solutions are investigated. Isolated branches of steady and periodic states are identified. An “explosive” bifurcation of the periodic solution leading to chaotic alternation of small-and large-amplitude oscillations is detected and analyzed for the first time. A good quantitative fit is demonstrated between modeling results and experimental data. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 52–78.     

Continuous Selections and Locally Pseudocompact Groups

We characterize locally pseudocompact groups by means of the selection theory. Our result is the selection version of the well-known Comfort—Ross theorem on pseudocompactness which states that a topological group is pseudocompact if and only its Stone—Čech compactification is a topological group.     

Re-extending Chebyshev’s theorem about Bertrand’s conjecture

In this paper, Chebyshev’s theorem (1850) about Bertrand’s conjecture is re-extended using a theorem about Sierpinski’s conjecture (1958). The theorem had been extended before several times, but this extension is a major extension far beyond the previous ones. At the beginning of the proof, maximal gaps table is used to verify initial states. The extended theorem contains a constant r, which can be reduced if more initial states can be checked. Therefore, the theorem can be even more extended when maximal gaps table is extended. The main extension idea is not based on r, though. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1701–1706, December, 2007.     

Decomposition of variables and duality in non-Abelian models

We consider inhomogeneous current states in low-dimensional systems characterized by spatial separation of phase states with ordered spin and charge degrees of freedom. We show that near the self-duality point in the Ginzburg-Landau spinor model, the inhomogeneity degree of non-Abelian states is higher than that of states with an Abelian distribution of degrees of freedom. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 510–517, June, 2007.     

The graphs of polytopes with involutory automorphisms

Steinitz’ theorem states that a graph is the graph of a 3-dimensional convex polytope if and only if it is planar and 3-connected. Grünbaum has shown that Steinitz’ proof can be modified to characterize the graphs of polytopes that are centrally symmetric or have a plane of symmetry. We show how to modify Steinitz’ proof to take care of the remaining involutory case—polytopes that are symmetric about a line. Research supported by NSF Grant GP-3470.     

Stability of one-phase equilibrium states of a two-phase elastic medium with zero surface tension coefficient. One-dimensional case

All the equilibrium states of a one-dimensional variational phase-transition problem are explicitly found. The temperature-dependence of the stability of one-phase equilibrium states is studied. Bibliography: 5 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 32, 2006, pp. 3–19.     

Fuzzy identification problem for continuous extremal fuzzy dynamic system

This work deals with the problems of the Continuous Extremal Fuzzy Dynamic System (CEFDS) optimization and briefly discusses the results developed by Sirbiladze (Int J Gen Syst 34(2):107–138, 2005a; 34(2):139–167, 2005b; 34(2):169–198, 2005c; 35(4):435–459, 2006a; 35(5):529–554, 2006b; 36(1): 19–58, 2007; New Math Nat Comput 4(1):41–60, 2008a; Mat Zametki, 83(3):439–460, 2008b). The basic properties of extended extremal fuzzy measures and Sugeno’s type integrals are considered and several variants of their representation are given. Values of extended extremal conditional fuzzy measures are defined as a levels of expert knowledge reflections of CEFDS states in the fuzzy time intervals. The notions of extremal fuzzy time moments and intervals are introduced and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy dynamic systems are discussed. A new approach in modeling of CEFDS is developed. Applying the results of Sirbiladze (Int J Gen Syst 34(2) 107–138, 2005a; 34(2):139–167, 2005b), fuzzy processes with possibilistic uncertainty, the source of which are expert knowledge reflections on the states on CEFDS in extremal fuzzy time intervals, are constructed (Sirbiladze in Int J Gen Syst 34(2):169–198, 2005c). The dynamics of CEFDS’s is described. Questions of the ergodicity of CEFDS are considered. A fuzzy-integral representation of a continuous extremal fuzzy process is given. Based on the fuzzy-integral model, a method and an algorithm are developed for identifying the transition operator of CEFDS. The CEFDS transition operator is restored by means of expert data with possibilistic uncertainty, the source of which is expert knowledge reflections on the states of CEFDS in the extremal fuzzy time intervals. The regularization condition for obtaining quasi-optimal estimator of the transition operator is represented by the theorems. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of CEFDS states.     

First Hitting Time Analysis of the Independence Metropolis Sampler

In this paper, we study a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), in the finite state space case. The IMS is often used in designing components of more complex Markov Chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues of the transition kernel. We derive a simple form formula for the mean first hitting time and we show tight lower and upper bounds on the mean first hitting time with the upper bound being the product of two factors: a “local” factor corresponding to the target state and a “global” factor, common to all the states, which is expressed in terms of the total variation distance between the target and the proposal probabilities. We also briefly discuss properties of the distribution of the first hitting time for the IMS and analyze its variance. We conclude by showing how some non-independence Metropolis–Hastings algorithms can perform better than the IMS and deriving general lower and upper bounds for the mean first hitting times of a Metropolis–Hastings algorithm.     

Maslov probability spaces related to the Bose—Einstein and Fermi—Dirac statistics

For systems of indistinguishable particles, we describe probability spaces factored by the equivalence relations identifying configurations which differ by permutation of particles, under the condition that identical states are forbidden (Fermi—Dirac statistics) or admissible (Bose—Einstein statistics). It is assumed that the states of particles have different probabilities; these correspond either to the presence of an external potential, or to a pair interaction potential, or to a collective interaction. The spaces constructed in the paper are related to specific queuing models. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 746–759, May, 1999.