Weakly infinite-dimensional spaces
International Nuclear Information System (INIS)
Fedorchuk, Vitalii V
2007-01-01
In this survey article two new classes of spaces are considered: m-C-spaces and w-m-C-spaces, m=2,3,...,∞. They are intermediate between the class of weakly infinite-dimensional spaces in the Alexandroff sense and the class of C-spaces. The classes of 2-C-spaces and w-2-C-spaces coincide with the class of weakly infinite-dimensional spaces, while the compact ∞-C-spaces are exactly the C-compact spaces of Haver. The main results of the theory of weakly infinite-dimensional spaces, including classification via transfinite Lebesgue dimensions and Luzin-Sierpinsky indices, extend to these new classes of spaces. Weak m-C-spaces are characterised by means of essential maps to Henderson's m-compacta. The existence of hereditarily m-strongly infinite-dimensional spaces is proved.
Teleportation schemes in infinite dimensional Hilbert spaces
International Nuclear Information System (INIS)
Fichtner, Karl-Heinz; Freudenberg, Wolfgang; Ohya, Masanori
2005-01-01
The success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples
On infinite-dimensional state spaces
International Nuclear Information System (INIS)
Fritz, Tobias
2013-01-01
It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V −1 U 2 V=U 3 , then finite-dimensionality entails the relation UV −1 UV=V −1 UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V −1 U 2 V=U 3 holds only up to ε and then yields a lower bound on the dimension.
On infinite-dimensional state spaces
Fritz, Tobias
2013-05-01
It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.
Geometry of quantum dynamics in infinite-dimensional Hilbert space
Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana
2018-04-01
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.
To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space
International Nuclear Information System (INIS)
Khrennikov, Andrei
2007-01-01
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'
Smooth controllability of infinite-dimensional quantum-mechanical systems
International Nuclear Information System (INIS)
Wu, Re-Bing; Tarn, Tzyh-Jong; Li, Chun-Wen
2006-01-01
Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies
International Nuclear Information System (INIS)
Arsen'ev, A.A.
1979-01-01
Example of a classical dynamical system with the infinite-dimensional phase space, satisfying the analogue of the Kubo-Martin-Schwinger conditions for classical dynamics, is constructed explicitly. Connection between the system constructed and the Fock space dynamics is pointed out
Analysis of infinite dimensional diffusions
Maas, J.
2009-01-01
Stochastic processes in infinite dimensional state spaces provide a mathematical description of various phenomena in physics, population biology, finance, and other fields of science. Several aspects of these processes have been studied in this thesis by means of new analytic methods. Firstly,
Analysis of competitive equilibrium in an infinite dimensional ...
African Journals Online (AJOL)
This paper considered the cost of allocated goods and attaining maximal utility with such price in the finite dimensional commodity space and observed that there exist an equilibrium price. It goes further to establish that in an infinite dimensional commodity space with subsets as consumption and production set there exist a ...
Dynamics of infinite-dimensional groups the Ramsey-Dvoretzky-Milman phenomenon
Pestov, Vladimir
2006-01-01
The "infinite-dimensional groups" in the title refer to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, groups of transformations of measure spaces, etc. The book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups, combinatorial Ramsey-type theorems, and the phenomenon of concentration of measure. The dynamics of infinite-dimensional groups is very much unlike that of locally compact groups. For instance, every locally compact group acts freely on a suitable compact space (Veech). By contrast, a 1983 result by Gromov and Milman states that whenever the unitary group of a separable Hilbert space continuously acts on a compact space, it has a common fixed point. In the book, this new fast-growing theory is built strictly from well-understood examples up. The book has no close counterpart and is based on recent research articles. At t...
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
International Nuclear Information System (INIS)
Guatteri, Giuseppina; Tessitore, Gianmario
2008-01-01
We study the Riccati equation arising in a class of quadratic optimal control problems with infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random.In such a context backward stochastic Riccati equations are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed
International Nuclear Information System (INIS)
Xu Hao; Shi Tianjun
2011-01-01
In this article,the qualities of Wigner function and the corresponding stationary perturbation theory are introduced and applied to one-dimensional infinite potential well and one-dimensional harmonic oscillator, and then the particular Wigner function of one-dimensional infinite potential well is specified and a special constriction effect in its pure state Wigner function is discovered, to which,simultaneously, a detailed and reasonable explanation is elaborated from the perspective of uncertainty principle. Ultimately, the amendment of Wigner function and energy of one-dimensional infinite potential well and one-dimensional harmonic oscillator under perturbation are calculated according to stationary phase space perturbation theory. (authors)
An infinite-dimensional calculus for gauge theories
Mendes, Rui Vilela
2010-01-01
A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior ...
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
Infinite dimensional groups and algebras in quantum physics
International Nuclear Information System (INIS)
Ottesen, J.T.
1995-01-01
This book is an introduction to the application of infite-dimensional groups and algebras in quantum physics. Especially considered are the spin representation of the infinite-dimensional orthogonal group, the metaplectic representation of the infinite-dimensional symplectic groups, and Loop and Virasoro algebras. (HSI)
Fractional supersymmetry and infinite dimensional lie algebras
International Nuclear Information System (INIS)
Rausch de Traubenberg, M.
2001-01-01
In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed
International Nuclear Information System (INIS)
Liu Guan-Ting; Yang Li-Ying
2017-01-01
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal. (paper)
Stochastic and infinite dimensional analysis
Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José
2016-01-01
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Rare event simulation in finite-infinite dimensional space
International Nuclear Information System (INIS)
Au, Siu-Kui; Patelli, Edoardo
2016-01-01
Modern engineering systems are becoming increasingly complex. Assessing their risk by simulation is intimately related to the efficient generation of rare failure events. Subset Simulation is an advanced Monte Carlo method for risk assessment and it has been applied in different disciplines. Pivotal to its success is the efficient generation of conditional failure samples, which is generally non-trivial. Conventionally an independent-component Markov Chain Monte Carlo (MCMC) algorithm is used, which is applicable to high dimensional problems (i.e., a large number of random variables) without suffering from ‘curse of dimension’. Experience suggests that the algorithm may perform even better for high dimensional problems. Motivated by this, for any given problem we construct an equivalent problem where each random variable is represented by an arbitrary (hence possibly infinite) number of ‘hidden’ variables. We study analytically the limiting behavior of the algorithm as the number of hidden variables increases indefinitely. This leads to a new algorithm that is more generic and offers greater flexibility and control. It coincides with an algorithm recently suggested by independent researchers, where a joint Gaussian distribution is imposed between the current sample and the candidate. The present work provides theoretical reasoning and insights into the algorithm.
Infinite Dimensional Differential Games with Hybrid Controls
Indian Academy of Sciences (India)
... zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the ...
An infinite-dimensional weak KAM theory via random variables
Gomes, Diogo A.
2016-08-31
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables\\' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
An infinite-dimensional weak KAM theory via random variables
Gomes, Diogo A.; Nurbekyan, Levon
2016-01-01
We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
Infinite-dimensional Z2sup(k)-supermanifolds
International Nuclear Information System (INIS)
Molotkov, V.
1984-10-01
In this paper the theory of finite-dimensional supermanifolds of Berezin, Leites and Kostant is generalized in two directions. First, we introduce infinite-dimensional supermanifolds ''locally isomorphic'' to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped with some additional structure) from the category of finite-dimensional Grassman superalgebras into the category of the corresponding smooth manifolds (Banach or locally convex). As examples, flag supermanifolds of Banach superspaces as well as unitary supergroups of Hilbert superspaces are constructed. Second, we define ''generalized'' supermanifolds, graded by Abelian groups Z 2 sup(k), instead of the group Z 2 (Z 2 sup(k)-supermanifolds). The corresponding superfields, describing, potentially, particles with more general statistics than Bose + Fermi, generally speaking, turn out to have an infinite number of components. (author)
International Nuclear Information System (INIS)
Ton-That, Tuong
2005-01-01
In a previous paper we gave a generalization of the notion of Casimir invariant differential operators for the infinite-dimensional Lie groups GL ∞ (C) (or equivalently, for its Lie algebra gj ∞ (C)). In this paper we give a generalization of the Casimir invariant differential operators for a class of infinite-dimensional Lie groups (or equivalently, for their Lie algebras) which contains the infinite-dimensional complex classical groups. These infinite-dimensional Lie groups, and their Lie algebras, are inductive limits of finite-dimensional Lie groups, and their Lie algebras, with some additional properties. These groups or their Lie algebras act via the generalized adjoint representations on projective limits of certain chains of vector spaces of universal enveloping algebras. Then the generalized Casimir operators are the invariants of the generalized adjoint representations. In order to be able to explicitly compute the Casimir operators one needs a basis for the universal enveloping algebra of a Lie algebra. The Poincare-Birkhoff-Witt (PBW) theorem gives an explicit construction of such a basis. Thus in the first part of this paper we give a generalization of the PBW theorem for inductive limits of Lie algebras. In the last part of this paper a generalization of the very important theorem in representation theory, namely the Chevalley-Racah theorem, is also discussed
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.
2018-04-01
This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.
Infinite Dimensional Stochastic Analysis : in Honor of Hui-Hsiung Kuo
Sundar, Pushpa
2008-01-01
This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate
Infinite-parametric extension of the conformal algebra in D>2 space-time dimension
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-09-01
On the basis of the analytic continuations of semisimple Lie algebras discovered recently by us we construct manifestly quasiconformal infinite-dimensional algebras AC(so(4,1)) and PAC(so(3,2)) extending the conformal algebras in three-dimensional Euclidean and Minkowski space-time like the Virasoro algebra extends so(2,1). Their higher spin generalizations are also constructed. A counterpart of the central extension for D>2 and possible applications in exactly solvable conformal quantum field models in D>2 are discussed. (author). 31 refs, 2 figs
International Nuclear Information System (INIS)
Li, P.D.; Li, X.Y.; Zheng, R.F.
2013-01-01
This Letter is concerned with thermo-elastic fundamental solutions of an infinite space, which is composed of two half-infinite bodies of different one-dimensional hexagonal quasi-crystals. A point thermal source is embedded in a half-space. The interface can be either perfectly bonded or smoothly contacted. On the basis of the newly developed general solution, the temperature-induced elastic field in full space is explicitly presented in terms of elementary functions. The interactions among the temperature, phonon and phason fields are revealed. The present work can play an important role in constructing farther analytical solutions for crack, inclusion and dislocation problems. -- Highlights: ► Green's functions are constructed in terms of 10 quasi-harmonic functions. ► Thermo-elastic field of a 1D hexagonal QC bi-material body is expressed explicitly. ► Both perfectly bonded and smoothly contacted interfaces are considered
Recursive tridiagonalization of infinite dimensional Hamiltonians
International Nuclear Information System (INIS)
Haydock, R.; Oregon Univ., Eugene, OR
1989-01-01
Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Energy Technology Data Exchange (ETDEWEB)
Thapliyal, Kishore, E-mail: tkishore36@yahoo.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India)
2016-03-15
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
International Nuclear Information System (INIS)
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
2016-01-01
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
Eisenstein series for infinite-dimensional U-duality groups
Fleig, Philipp; Kleinschmidt, Axel
2012-06-01
We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.
Infinite dimensional gauge structure of Kaluza-Klein theories II: D>5
International Nuclear Information System (INIS)
Aulakh, C.S.; Sahdev, D.
1985-12-01
We carry out the dimensional reduction of the pure gravity sector of Kaluza Klein theories without making truncations of any sort. This generalizes our previous result for the 5-dimensional case to 4+d(>1) dimensions. The effective 4-dimensional action has the structure of an infinite dimensional gauge theory
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
The space-time model according to dimensional continuous space-time theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2014-01-01
This article results from the Dimensional Continuous Space-Time Theory for which the introductory theoretician was presented in [1]. A theoretical model of the Continuous Space-Time is presented. The wave equation of time into absolutely stationary empty space referential will be described in detail. The complex time, that is the time fixed on the infinite phase time speed referential, is deduced from the New View of Relativity Theory that is being submitted simultaneously with this article in this congress. Finally considering the inseparable Space-Time is presented the duality equation wave-particle.
Hilbert schemes of points and infinite dimensional Lie algebras
Qin, Zhenbo
2018-01-01
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes X^{[n]} of collections of n points (zero-dimensional subschemes) in a smooth algebraic surface X. Schemes X^{[n]} turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of X^{[n]}, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of X^{[n]} a...
Lyapunov equation for infinite-dimensional discrete bilinear systems
International Nuclear Information System (INIS)
Costa, O.L.V.; Kubrusly, C.S.
1991-03-01
Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)
The Lagrangian and Hamiltonian Analysis of Integrable Infinite-Dimensional Dynamical Systems
International Nuclear Information System (INIS)
Bogolubov, Nikolai N. Jr.; Prykarpatsky, Yarema A.; Blackmorte, Denis; Prykarpatsky, Anatoliy K.
2010-12-01
The analytical description of Lagrangian and Hamiltonian formalisms naturally arising from the invariance structure of given nonlinear dynamical systems on the infinite- dimensional functional manifold is presented. The basic ideas used to formulate the canonical symplectic structure are borrowed from the Cartan's theory of differential systems on associated jet-manifolds. The symmetry structure reduced on the invariant submanifolds of critical points of some nonlocal Euler-Lagrange functional is described thoroughly for both differential and differential-discrete dynamical systems. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integral-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Backlund transformation. The connection of this hierarchy with integrable by Lax spatially two-dimensional systems is studied. (author)
Infinite families of superintegrable systems separable in subgroup coordinates
International Nuclear Information System (INIS)
Lévesque, Daniel; Post, Sarah; Winternitz, Pavel
2012-01-01
A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials. (paper)
Group theoretical construction of two-dimensional models with infinite sets of conservation laws
International Nuclear Information System (INIS)
D'Auria, R.; Regge, T.; Sciuto, S.
1980-01-01
We explicitly construct some classes of field theoretical 2-dimensional models associated with symmetric spaces G/H according to a general scheme proposed in an earlier paper. We treat the SO(n + 1)/SO(n) and SU(n + 1)/U(n) case, giving their relationship with the O(n) sigma-models and the CP(n) models. Moreover, we present a new class of models associated to the SU(n)/SO(n) case. All these models are shown to possess an infinite set of local conservation laws. (orig.)
Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems
International Nuclear Information System (INIS)
Helin, T; Burger, M
2015-01-01
A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic and difficult to analyse. Current inverse problem literature often approaches the problem by considering suitable point estimators for the task. Typically the choice is made between the maximum a posteriori (MAP) or the conditional mean (CM) estimate. The benefits of either choice are not well-understood from the perspective of infinite-dimensional theory. Most importantly, there exists no general scheme regarding how to connect the topological description of a MAP estimate to a variational problem. The recent results by Dashti and others (Dashti et al 2013 Inverse Problems 29 095017) resolve this issue for nonlinear inverse problems in Gaussian framework. In this work we improve the current understanding by introducing a novel concept called the weak MAP (wMAP) estimate. We show that any MAP estimate in the sense of Dashti et al (2013 Inverse Problems 29 095017) is a wMAP estimate and, moreover, how the wMAP estimate connects to a variational formulation in general infinite-dimensional non-Gaussian problems. The variational formulation enables to study many properties of the infinite-dimensional MAP estimate that were earlier impossible to study. In a recent work by the authors (Burger and Lucka 2014 Maximum a posteriori estimates in linear inverse problems with logconcave priors are proper bayes estimators preprint) the MAP estimator was studied in the context of the Bayes cost method. Using Bregman distances, proper convex Bayes cost functions were introduced for which the MAP estimator is the Bayes estimator. Here, we generalize these results to the infinite-dimensional setting. Moreover, we discuss the implications of our results for some examples of prior models such as the Besov prior and hierarchical prior. (paper)
Topology as fluid geometry two-dimensional spaces, volume 2
Cannon, James W
2017-01-01
This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two...
About the Infinite Repetition of Histories in Space
Directory of Open Access Journals (Sweden)
Manuel Alfonseca
2014-08-01
Full Text Available This paper analyzes two different proposals, one by Ellis and Brundrit, based on classical relativistic cosmology, the other by Garriga and Vilenkin, based on the DH interpretation of quantum mechanics, both concluding that, in an infinite universe, planets and beings must be repeated an infinite number of times. We point to possible shortcomings in these arguments. We conclude that the idea of an infinite repetition of histories in space cannot be considered strictly speaking a consequence of current physics and cosmology. Such ideas should be seen rather as examples of «ironic science» in the terminology of John Horgan.
One-dimensional gravity in infinite point distributions
Gabrielli, A.; Joyce, M.; Sicard, F.
2009-10-01
The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by “Jeans swindle” for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N -body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from “shuffled lattice” initial conditions. These show qualitative properties of the evolution (notably its “self-similarity”) like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.
The w-categories associated with products of infinite-dimensional globes
International Nuclear Information System (INIS)
Cui, H.
2000-11-01
The results in this thesis are organised in four chapters. Chapter 1 is preliminary. We state the necessary definitions and results in w- complexes, atomic complexes and products of w-complexes. Some definitions are restated to meet the requirement for the following chapters. There is a new proof for the existence of 'natural homomorphism' (Theorem 1.3.6) and a new result for the decomposition of molecules in loop-free w-complexes (Theorem 1.4.13). In Chapter 2, we study the product of three infinite dimensional globes. The main result in this chapter is that a subcomplex in the product of three infinite dimensional globes is a molecule if and only if it is pairwise molecular (Theorem 2.1.6). The definition for pairwise molecular subcomplexes is given in section 1. One direction of the main theorem, molecules are necessarily pairwise molecular, is proved in section 2. Some properties of pairwise molecular subcomplexes are studied in section 3. These properties are the preparation for a more explicit description of pairwise molecular subcomplexes, which is given in section 4. The properties for the sources and targets of pairwise molecular subcomplexes are studied in section 5, where we prove that the class of pairwise molecular subcomplexes is closed under source and target operation; there are also algorithms to calculate the sources and targets of a pairwise molecular subcomplex. Section 6 deals with the composition of pairwise molecular subcomplexes. The proof of the main theorem is completed in section 7, where an algorithm for decomposing molecules into atoms is implied in the proof. The construction of molecules in the product of three infinite dimensional globes is studied in Chapter 3. The main result is that any molecule can be constructed inductively by a systematic approach. Section 1 gives another description for molecules in the product of three infinite dimensional globes which is the theoretical basis for the construction. Section 2 states the
Evolutionary dynamics on infinite strategy spaces
Oechssler, Jörg; Riedel, Frank
1998-01-01
The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinite strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications ...
Logemann, H; Curtain, RF
2000-01-01
We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator
An infinite-dimensional model of free convection
Energy Technology Data Exchange (ETDEWEB)
Iudovich, V.I. (Rostovskii Gosudarstvennyi Universitet, Rostov-on-Don (USSR))
1990-12-01
An infinite-dimensional model is derived from the equations of free convection in the Boussinesq-Oberbeck approximation. The velocity field is approximated by a single mode, while the heat-conduction equation is conserved fully. It is shown that, for all supercritical Rayleigh numbers, there exist exactly two secondary convective regimes. The case of ideal convection with zero viscosity and thermal conductivity is examined. The averaging method is used to study convection regimes at high Reynolds numbers. 10 refs.
An infinite number of stationary soliton solutions to the five-dimensional vacuum Einstein equation
International Nuclear Information System (INIS)
Azuma, Takahiro; Koikawa, Takao
2006-01-01
We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2, 0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2, 2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical. (author)
An Integrated Approach to Parameter Learning in Infinite-Dimensional Space
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Wendelberger, Joanne Roth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-09-14
The availability of sophisticated modern physics codes has greatly extended the ability of domain scientists to understand the processes underlying their observations of complicated processes, but it has also introduced the curse of dimensionality via the many user-set parameters available to tune. Many of these parameters are naturally expressed as functional data, such as initial temperature distributions, equations of state, and controls. Thus, when attempting to find parameters that match observed data, being able to navigate parameter-space becomes highly non-trivial, especially considering that accurate simulations can be expensive both in terms of time and money. Existing solutions include batch-parallel simulations, high-dimensional, derivative-free optimization, and expert guessing, all of which make some contribution to solving the problem but do not completely resolve the issue. In this work, we explore the possibility of coupling together all three of the techniques just described by designing user-guided, batch-parallel optimization schemes. Our motivating example is a neutron diffusion partial differential equation where the time-varying multiplication factor serves as the unknown control parameter to be learned. We find that a simple, batch-parallelizable, random-walk scheme is able to make some progress on the problem but does not by itself produce satisfactory results. After reducing the dimensionality of the problem using functional principal component analysis (fPCA), we are able to track the progress of the solver in a visually simple way as well as viewing the associated principle components. This allows a human to make reasonable guesses about which points in the state space the random walker should try next. Thus, by combining the random walker's ability to find descent directions with the human's understanding of the underlying physics, it is possible to use expensive simulations more efficiently and more quickly arrive at the
Naked singularities in higher dimensional Vaidya space-times
International Nuclear Information System (INIS)
Ghosh, S. G.; Dadhich, Naresh
2001-01-01
We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension
Absolute continuity of autophage measures on finite-dimensional vector spaces
Energy Technology Data Exchange (ETDEWEB)
Raja, C R.E. [Stat-Math Unit, Indian Statistical Institute, Bangalore (India); [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]. E-mail: creraja@isibang.ac.in
2002-06-01
We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or Q{sub p} are infinitely divisible without idempotent factors and are absolutely continuous with bounded continuous density. We also show that certain semistable measures on such vector spaces are absolutely continuous. (author)
On an infinite-dimensional Lie algebra of Virasoro-type
International Nuclear Information System (INIS)
Pei Yufeng; Bai Chengming
2012-01-01
In this paper, we study an infinite-dimensional Lie algebra of Virasoro-type which is realized as an affinization of a two-dimensional Novikov algebra. It is a special deformation of the Lie algebra of differential operators on a circle of order at most 1. There is an explicit construction of a vertex algebra associated with the Lie algebra. We determine all derivations of this Lie algebra in terms of some derivations and centroids of the corresponding Novikov algebra. The universal central extension of this Lie algebra is also determined. (paper)
Criterion for the nuclearity of spaces of functions of infinite number of variables
International Nuclear Information System (INIS)
Gali, I.M.
1977-08-01
The paper formulates a new necessary and sufficient condition for the nuclearity of spaces of infinite number of variables, and defines new nuclear spaces which play an important role in the field of functional analysis and quantum field theory. Also the condition for nuclearity of the infinite weighted tensor product of nuclear spaces is given
Infinite matrices and sequence spaces
Cooke, Richard G
2014-01-01
This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi
Stochastic optimal control in infinite dimension dynamic programming and HJB equations
Fabbri, Giorgio; Święch, Andrzej
2017-01-01
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...
International Nuclear Information System (INIS)
Pal, Karoly F.; Vertesi, Tamas
2010-01-01
The I 3322 inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I 3322 inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I 3322 inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.
Estimation Methods for Infinite-Dimensional Systems Applied to the Hemodynamic Response in the Brain
Belkhatir, Zehor
2018-05-01
Infinite-Dimensional Systems (IDSs) which have been made possible by recent advances in mathematical and computational tools can be used to model complex real phenomena. However, due to physical, economic, or stringent non-invasive constraints on real systems, the underlying characteristics for mathematical models in general (and IDSs in particular) are often missing or subject to uncertainty. Therefore, developing efficient estimation techniques to extract missing pieces of information from available measurements is essential. The human brain is an example of IDSs with severe constraints on information collection from controlled experiments and invasive sensors. Investigating the intriguing modeling potential of the brain is, in fact, the main motivation for this work. Here, we will characterize the hemodynamic behavior of the brain using functional magnetic resonance imaging data. In this regard, we propose efficient estimation methods for two classes of IDSs, namely Partial Differential Equations (PDEs) and Fractional Differential Equations (FDEs). This work is divided into two parts. The first part addresses the joint estimation problem of the state, parameters, and input for a coupled second-order hyperbolic PDE and an infinite-dimensional ordinary differential equation using sampled-in-space measurements. Two estimation techniques are proposed: a Kalman-based algorithm that relies on a reduced finite-dimensional model of the IDS, and an infinite-dimensional adaptive estimator whose convergence proof is based on the Lyapunov approach. We study and discuss the identifiability of the unknown variables for both cases. The second part contributes to the development of estimation methods for FDEs where major challenges arise in estimating fractional differentiation orders and non-smooth pointwise inputs. First, we propose a fractional high-order sliding mode observer to jointly estimate the pseudo-state and input of commensurate FDEs. Second, we propose a
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations
International Nuclear Information System (INIS)
Yuen, Manwai
2011-01-01
In this Letter, we construct a new class of blowup or global solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. And the corresponding blowup or global solutions for the incompressible Euler and Naiver-Stokes equations are also given. Our constructed solutions are similar to the famous Arnold-Beltrami-Childress (ABC) flow. The obtained solutions with infinite energy can exhibit the interesting behaviors locally. Furthermore, due to divu → =0 for the solutions, the solutions also work for the 3-dimensional incompressible Euler and Navier-Stokes equations. -- Highlights: → We construct a new class of solutions to the 3D compressible or incompressible Euler and Navier-Stokes equations. → The constructed solutions are similar to the famous Arnold-Beltrami-Childress flow. → The solutions with infinite energy can exhibit the interesting behaviors locally.
New infinite-dimensional hidden symmetries for heterotic string theory
International Nuclear Information System (INIS)
Gao Yajun
2007-01-01
The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected
Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
Belitser, E.; Ghosal, S.
2003-01-01
We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a "smoothness condition," we first derive the convergence rate of the posterior distribution for a prior that
Semigroups on Frechet Spaces and Equations with Infinite Delays
Indian Academy of Sciences (India)
In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.
Classification of all solutions of the algebraic Riccati equations for infinite-dimensional systems
Iftime, O; Curtain, R; Zwart, H
2003-01-01
We obtain a complete classification of all self-adjoint solution of the control algebraic Riccati equation for infinite-dimensional systems under the following assumptions: the system is output stabilizable, strongly detectable and the filter Riccati equation has an invertible self-adjoint
On the infinite-dimensional spin-2 symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Hohm, O.; Hamburg Univ.
2005-11-01
We consider the couplings of an infinite number of spin-2 fields to gravity appearing in Kaluza-Klein theories. They are constructed as the broken phase of a massless theory possessing an infinite-dimensional spin-2 symmetry. Focusing on a circle compactification of four-dimensional gravity we show that the resulting gravity/spin-2 system in D=3 has in its unbroken phase an interpretation as a Chern-Simons theory of the Kac-Moody algebra iso(1,2) associated to the Poincare group and also fits into the geometrical framework of algebra-valued differential geometry developed by Wald. Assigning all degrees of freedom to scalar fields, the matter couplings in the unbroken phase are determined, and it is shown that their global symmetry algebra contains the Virasoro algebra together with an enhancement of the Ehlers group SL(2,R) to its affine extension. The broken phase is then constructed by gauging a subgroup of the global symmetries. It is shown that metric, spin-2 fields and Kaluza-Klein vectors combine into a Chern-Simons theory for an extended algebra, in which the affine Poincare subalgebra acquires a central extension. (orig.)
Two dimensional infinite conformal symmetry
International Nuclear Information System (INIS)
Mohanta, N.N.; Tripathy, K.C.
1993-01-01
The invariant discontinuous (discrete) conformal transformation groups, namely the Kleinian and Fuchsian groups Gamma (with an arbitrary signature) of H (the Poincare upper half-plane l) and the unit disc Delta are explicitly constructed from the fundamental domain D. The Riemann surface with signatures of Gamma and conformally invariant automorphic forms (functions) with Peterson scalar product are discussed. The functor, where the category of complex Hilbert spaces spanned by the space of cusp forms constitutes the two dimensional conformal field theory. (Author) 7 refs
Infinite-Dimensional Observer for Process Monitoring in Managed Pressure Drilling
Hasan, Agus Ismail
2015-01-01
Utilizing flow rate and pressure data in and out of the mud circulation loop provides a driller with real-time trends for the early detection of well-control problems that impact the drilling efficiency. This paper presents state estimation for infinite-dimensional systems used in the process monitoring of oil well drilling. The objective is to monitor the key process variables associated with process safety by designing a model-based nonlinear observer that directly utilizes the available in...
Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process
International Nuclear Information System (INIS)
Maslowski, Bohdan; Pospisil, Jan
2008-01-01
Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise
Solution of the Dirichlet Problem for the Poisson's Equation in a Multidimensional Infinite Layer
Directory of Open Access Journals (Sweden)
O. D. Algazin
2015-01-01
Full Text Available The paper considers the multidimensional Poisson equation in the domain bounded by two parallel hyperplanes (in the multidimensional infinite layer. For an n-dimensional half-space method of solving boundary value problems for linear partial differential equations with constant coefficients is a Fourier transform to the variables in the boundary hyperplane. The same method can be used for an infinite layer, as is done in this paper in the case of the Dirichlet problem for the Poisson equation. For strip and infinite layer in three-dimensional space the solutions of this problem are known. And in the three-dimensional case Green's function is written as an infinite series. In this paper, the solution is obtained in the integral form and kernels of integrals are expressed in a finite form in terms of elementary functions and Bessel functions. A recurrence relation between the kernels of integrals for n-dimensional and (n + 2 -dimensional layers was obtained. In particular, is built the Green's function of the Laplace operator for the Dirichlet problem, through which the solution of the problem is recorded. Even in three-dimensional case we obtained new formula compared to the known. It is shown that the kernel of the integral representation of the solution of the Dirichlet problem for a homogeneous Poisson equation (Laplace equation is an approximate identity (δ-shaped system of functions. Therefore, if the boundary values are generalized functions of slow growth, the solution of the Dirichlet problem for the homogeneous equation (Laplace is written as a convolution of kernels with these functions.
Cylindrical continuous martingales and stochastic integration in infinite dimensions
Veraar, M.C.; Yaroslavtsev, I.S.
2016-01-01
In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local
Topological vector spaces and their applications
Bogachev, V I
2017-01-01
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Non-Euclidean geometry and curvature two-dimensional spaces, volume 3
Cannon, James W
2017-01-01
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...
On the BRST charge over infinite-dimensional algebras
International Nuclear Information System (INIS)
Hlousek, Zvonimir.
1988-01-01
The author studies the BRST charge defined over an infinite algebra of gauged local symmetries. This is of great importance to string theories. The BRST charge of the gauge symmetry must be nilpotent. In string theories this implies the cancellation of conformal anomalies in critical dimension; 26 for bosonic string, 10 for superstring, and 2 for O(2) string. Furthermore, the O(2) symmetry of the O(2) string (a string theory with two, two-dimensional supersymmetries) is realized as a Kac-Moody symmetry. In general, the BRST quantization of the local, gauged KAC-Moody symmetry requires special care due to chiral anomaly. The chiral anomaly breaks the chiral gauge invariance, and the corresponding BRST charge is not nilpotent. To arrive at the nilpotent BRST charge for the gauged Kac-Moody symmetry, one has to modify the theory by adding a one-cocycle over the gauge group. A similar problem and its solution exist in the case of supersymmetric Kac-Moody algebras. The BRST charge of the first quantized string theory is a building block of the covariant string field theory. The BRST invariance of the first quantized theory generalizes to gauge invariance of string field theory. In Witten's open string field theory the BRST charge plays a role of exterior derivation on the space of string field functionals. The Fock space realization of the theory was given by Gross and Jevicki. For the consistency of the theory it is crucial that all the vertex operators are BRST invariant. The ghost part of the vertex comes in few varieties. The author has shown that all the versions of the ghost vertex are equivalent, as long as the total vertex is BRST invariant
International Nuclear Information System (INIS)
Honeck, H.C.
1984-01-01
1 - Description of problem or function: HAMMER performs infinite lattice, one-dimensional cell multigroup calculations, followed (optionally) by one-dimensional, few-group, multi-region reactor calculations with neutron balance edits. 2 - Method of solution: Infinite lattice parameters are calculated by means of multigroup transport theory, composite reactor parameters by few-group diffusion theory. 3 - Restrictions on the complexity of the problem: - Cell calculations - maxima of: 30 thermal groups; 54 epithermal groups; 20 space points; 20 regions; 18 isotopes; 10 mixtures; 3 thermal up-scattering mixtures; 200 resonances per group; no overlap or interference; single level only. - Reactor calculations - maxima of : 40 regions; 40 mixtures; 250 space points; 4 groups
Selfadjoint operators in spaces of functions of infinitely many variables
Berezanskiĭ, Yu M
1986-01-01
Questions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses.
Institute of Scientific and Technical Information of China (English)
Hua WANG; ALATANCANG; Junjie HUANG
2011-01-01
The authors investigate the completeness of the system of eigen or root vectors of the 2 x 2 upper triangular infinite-dimensional Hamiltonian operator H0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained. Finally,the obtained results are tested in several examples.
Infinite-Dimensional Boundary Observer for Lithium-Ion Battery State Estimation
DEFF Research Database (Denmark)
Hasan, Agus; Jouffroy, Jerome
2017-01-01
This paper presents boundary observer design for state-of-charge (SOC) estimation of lithium-ion batteries. The lithium-ion battery dynamics are governed by thermal-electrochemical principles, which mathematically modeled by partial differential equations (PDEs). In general, the model is a reaction......-diffusion equation with time-dependent coefficients. A Luenberger observer is developed using infinite-dimensional backstepping method and uses only a single measurement at the boundary of the battery. The observer gains are computed by solving the observer kernel equation. A numerical example is performed to show...
Is the Free Vacuum Energy Infinite?
International Nuclear Information System (INIS)
Shirazi, S. M.; Razmi, H.
2015-01-01
Considering the fundamental cutoff applied by the uncertainty relations’ limit on virtual particles’ frequency in the quantum vacuum, it is shown that the vacuum energy density is proportional to the inverse of the fourth power of the dimensional distance of the space under consideration and thus the corresponding vacuum energy automatically regularized to zero value for an infinitely large free space. This can be used in regularizing a number of unwanted infinities that happen in the Casimir effect, the cosmological constant problem, and so on without using already known mathematical (not so reasonable) techniques and tricks
The Analysis of Corporate Bond Valuation under an Infinite Dimensional Compound Poisson Framework
Directory of Open Access Journals (Sweden)
Sheng Fan
2014-01-01
Full Text Available This paper analyzes the firm bond valuation and credit spread with an endogenous model for the pure default and callable default corporate bond. Regarding the stochastic instantaneous forward rates and the firm value as an infinite dimensional Poisson process, we provide some analytical results for the embedded American options and firm bond valuations.
Renner, R; Cirac, J I
2009-03-20
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.
Infinite-dimensional Lie algebras in 4D conformal quantum field theory
International Nuclear Information System (INIS)
Bakalov, Bojko; Nikolov, Nikolay M; Rehren, Karl-Henning; Todorov, Ivan
2008-01-01
The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of two-dimensional chiral conformal field theory, to a higher (even) dimensional spacetime. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V M (x, y), where the M span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite-dimensional Lie algebra: a central extension of sp(∞,R) corresponding to the field R of reals, of u(∞, ∞) associated with the field C of complex numbers, and of so*(4∞) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N) and U(N,H)=Sp(2N), respectively
The new Big Bang Theory according to dimensional continuous space-time theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2014-01-01
This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.
The New Big Bang Theory according to Dimensional Continuous Space-Time Theory
Martini, Luiz Cesar
2014-04-01
This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.
Interpolation in Spaces of Functions
Directory of Open Access Journals (Sweden)
K. Mosaleheh
2006-03-01
Full Text Available In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces
On renormalisation of the quantum stress tensor in curved space-time by dimensional regularisation
International Nuclear Information System (INIS)
Bunch, T.S.
1979-01-01
Using dimensional regularisation, a prescription is given for obtaining a finite renormalised stress tensor in curved space-time. Renormalisation is carried out by renormalising coupling constants in the n-dimensional Einstein equation generalised to include tensors which are fourth order in derivatives of the metric. Except for the special case of a massless conformal field in a conformally flat space-time, this procedure is not unique. There exists an infinite one-parameter family of renormalisation ansatze differing from each other in the finite renormalisation that takes place. Nevertheless, the renormalised stress tensor for a conformally invariant field theory acquires a nonzero trace which is independent of the renormalisation ansatz used and which has a value in agreement with that obtained by other methods. A comparison is made with some earlier work using dimensional regularisation which is shown to be in error. (author)
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-10-01
The irreducible Racah basis for SU(N + 1|N) is introduced. An analytic continuation with respect to N leads to infinite-dimensional superalgebras su(υ + 1|υ). Large υ limit su(∞ + 1|∞) is calculated. The higher spin Sugawara construction leading to generalizations of the Virasoro algebra with infinite tower of higher spin currents is proposed and related WZNW and Toda models as well as possible applications in string theory are discussed. (author). 32 refs
Riemann surfaces, Clifford algebras and infinite dimensional groups
International Nuclear Information System (INIS)
Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.
1990-01-01
We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)
International Nuclear Information System (INIS)
Agarwal, Ravi P.; Baghli, Selma; Benchohra, Mouffak
2009-01-01
The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Frechet spaces, combined with the semigroup theory
Classical r-matrices and Poisson bracket structures on infinite-dimensional groups
International Nuclear Information System (INIS)
Aratyn, H.; Nissimov, E.; Pacheva, S.
1992-01-01
Starting with a canonical symplectic structure defined on the contangent bundle T * G we derive, via Dirac hamiltonian reduction, Poisson brackets (PBs) on an arbitrary infinite-dimensional group G (admitting central extension). The PB structures are given in terms of an r-operator kernel related to the two-cocycle of the underlying Lie algebra and satisfying a differential classical Yang-Baxter equation. The explicit expressions of the PBs among the group variables for the (N, 0) for N=0, 1, ..., 4 (super-) Virasoro groups and the group of area-preserving diffeomorphisms on the torus are presented. (orig.)
International Nuclear Information System (INIS)
Chang, Y.-K.; Anguraj, A.; Mallika Arjunan, M.
2009-01-01
In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage's fixed point theorem.
Energy Technology Data Exchange (ETDEWEB)
Chang, Y.-K. [Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070 (China)], E-mail: lzchangyk@163.com; Anguraj, A. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: angurajpsg@yahoo.com; Mallika Arjunan, M. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: arjunphd07@yahoo.co.in
2009-02-28
In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage's fixed point theorem.
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2013-01-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)
On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations
International Nuclear Information System (INIS)
Westerberg, A.
1997-01-01
We discuss a previously discovered extension of the infinite-dimensional Lie algebra map(M,g) which generalizes the Kac-Moody algebras in 1+1 dimensions and the Mickelsson-Faddeev algebras in 3+1 dimensions to manifolds M of general dimensions. Furthermore, we review the method of regularizing current algebras in higher dimensions using pseudodifferential operator (PSDO) symbol calculus. In particular, we discuss the issue of Lie algebra cohomology of PSDOs and its relation to the Schwinger terms arising in the quantization process. Finally, we apply this regularization method to the algebra with partial success, and discuss the remaining obstacles to the construction of a Fock space representation. (orig.)
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-06-01
With any semisimple Lie algebra g we associate an infinite-dimensional Lie algebra AC(g) which is an analytic continuation of g from its root system to its root lattice. The manifest expressions for the structure constants of analytic continuations of the symplectic Lie algebras sp2 n are obtained by Poisson-bracket realizations method and AC(g) for g=sl n and so n are discussed. The representations, central extension, supersymmetric and higher spin generalizations are considered. The Virasoro theory is a particular case when g=sp 2 . (author). 9 refs
Hadronic currents in the infinite momentum frame
International Nuclear Information System (INIS)
Toth, K.
1975-01-01
The problem of the transformation properties of hadronic currents in the infinite momentum frame (IMF) is investigated. A general method is proposed to deal with the problem which is based upon the concept of group contraction. The two-dimensional aspects of the IMF description are studied in detail, and the current matrix elements of a three-dimensional Poincare covariant theory are reduced to those of a two-dimensional one. It is explicitlyshown that the covariance group of the two-dimensional theory may either be a 'non-relativistic' (Galilei) group, or a 'relativistic' (Poincare) one depending on the value of a parameter reminiscent of the light velocity in the three-dimensional theory. The value of this parameter cannot be determined by kinematical argument. These results offer a natural generalization of models which assume Galilean symmetry in the infinite momentum frame
Extended supersymmetry in four-dimensional Euclidean space
International Nuclear Information System (INIS)
McKeon, D.G.C.; Sherry, T.N.
2000-01-01
Since the generators of the two SU(2) groups which comprise SO(4) are not Hermitian conjugates of each other, the simplest supersymmetry algebra in four-dimensional Euclidean space more closely resembles the N=2 than the N=1 supersymmetry algebra in four-dimensional Minkowski space. An extended supersymmetry algebra in four-dimensional Euclidean space is considered in this paper; its structure resembles that of N=4 supersymmetry in four-dimensional Minkowski space. The relationship of this algebra to the algebra found by dimensionally reducing the N=1 supersymmetry algebra in ten-dimensional Euclidean space to four-dimensional Euclidean space is examined. The dimensional reduction of N=1 super Yang-Mills theory in ten-dimensional Minkowski space to four-dimensional Euclidean space is also considered
International Nuclear Information System (INIS)
Yeh, L.
1992-01-01
The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite- mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena
International Nuclear Information System (INIS)
Gonchar, N.S.
1986-01-01
This paper presents a mathematical method developed for investigating a class of systems of infinite-dimensional integral equations which have application in statistical mechanics. Necessary and sufficient conditions are obtained for the uniqueness and bifurcation of the solution of this class of systems of equations. Problems of equilibrium statistical mechanics are considered on the basis of this method
Belkhatir, Zehor; Mechhoud, Sarra; Laleg-Kirati, Taous-Meriem
2016-01-01
This paper deals with joint parameters and input estimation for coupled PDE-ODE system. The system consists of a damped wave equation and an infinite dimensional ODE. This model describes the spatiotemporal hemodynamic response in the brain
NUSSE, HE; TEDESCHINILALLI, L
The phenomenon of the coexistence of infinitely many sinks for two dimensional dissipative diffeomorphisms is a result due to Newhouse [Ne1, Ne2]. In fact, for each parameter value at which a homoclinic tangency is formed nondegenerately, there exist intervals in the parameter space containing dense
Euclidean scalar Green function in a higher dimensional global monopole space-time
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
2002-01-01
We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole space-time, i.e., a (1+d)-space-time with d≥3 which presents a solid angle deficit. Our result is expressed in terms of an infinite sum of products of Legendre functions with Gegenbauer polynomials. Although this Green function cannot be expressed in a closed form, for the specific case where the solid angle deficit is very small, it is possible to develop the sum and obtain the Green function in a more workable expression. Having this expression it is possible to calculate the vacuum expectation value of some relevant operators. As an application of this formalism, we calculate the renormalized vacuum expectation value of the square of the scalar field, 2 (x)> Ren , and the energy-momentum tensor, μν (x)> Ren , for the global monopole space-time with spatial dimensions d=4 and d=5
Morozov, Oleg I.
2018-06-01
The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.
Harmonic analysis on local fields and adelic spaces. I
International Nuclear Information System (INIS)
Osipov, D V; Parshin, A N
2008-01-01
We develop harmonic analysis on the objects of a category C 2 of infinite-dimensional filtered vector spaces over a finite field. This category includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. As the main result, we construct the theory of the Fourier transform on these objects and obtain two-dimensional Poisson formulae
Numerical and spectral investigations of novel infinite elements
International Nuclear Information System (INIS)
Barai, P.; Harari, I.; Barbonet, P.E.
1998-01-01
Exterior problems of time-harmonic acoustics are addressed by a novel infinite element formulation, defined on a bounded computational domain. For two-dimensional configurations with circular interfaces, the infinite element results match Quell both analytical values and those obtained from. other methods like DtN. Along 1uith the numerical performance of this formulation, of considerable interest are its complex-valued eigenvalues. Hence, a spectral analysis of the present scheme is also performed here, using various infinite elements
Limitations of discrete-time quantum walk on a one-dimensional infinite chain
Lin, Jia-Yi; Zhu, Xuanmin; Wu, Shengjun
2018-04-01
How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form eiξ A ⊗1p, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form eiξ A ⊗1p. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator 1 or the Pauli operator σx.
Quantum diffusion in semi-infinite periodic and quasiperiodic systems
International Nuclear Information System (INIS)
Zhang Kaiwang
2008-01-01
This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C(t) ∼ t −δ and d(t) ∼ t β . However, it finds that 0 < δ < 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed
Wigner-Kirkwood expansion of the phase-space density for half infinite nuclear matter
International Nuclear Information System (INIS)
Durand, M.; Schuck, P.
1987-01-01
The phase space distribution of half infinite nuclear matter is expanded in a ℎ-series analogous to the low temperature expansion of the Fermi function. Besides the usual Wigner-Kirkwood expansion, oscillatory terms are derived. In the case of a Woods-Saxon potential, a smallness parameter is defined, which determines the convergence of the series and explains the very rapid convergence of the Wigner-Kirkwood expansion for average (nuclear) binding energies
Quantum control in infinite dimensions
International Nuclear Information System (INIS)
Karwowski, Witold; Vilela Mendes, R.
2004-01-01
Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite-dimensional control Lie algebra. Here we show that by adding a discrete operation to a Lie algebra it is possible to obtain full control in infinite dimensions with a small number of control operators
Squashed entanglement in infinite dimensions
International Nuclear Information System (INIS)
Shirokov, M. E.
2016-01-01
We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. It is also shown that the second definition gives an adequate lower semicontinuous extension of this measure to all states of the infinite-dimensional bipartite system. A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information is proved and its corollaries are considered. Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for quantum conditional mutual information (proved in the Appendix by using Winter’s technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.
Coherent states in the fermionic Fock space
International Nuclear Information System (INIS)
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions. (paper)
Semi-infinite Weil complex and the Virasoro algebra
International Nuclear Information System (INIS)
Feigin, B.; Frenkel, E.
1991-01-01
We define a semi-infinite analogue of the Weil algebra associated with an infinite-dimensional Lie algebra. It can be used for the definition of semi-infinite characteristic classes by analogy with the Chern-Weil construction. The second term of a spectral sequence of this Weil complex consists of the semi-infinite cohomology of the Lie algebra with coefficients in its 'adjoint semi-infinite symmetric powers'. We compute this cohomology for the Virasoro algebra. This is just the BRST cohomology of the bosonic βγ-system with the central charge 26. We give a complete description of the Fock representations of this bosonic system as modules over the Virasoro algebra, using Friedan-Martinec-Shenker bosonization. We derive a combinatorial identity from this result. (orig.)
Scattering by multiple parallel radially stratified infinite cylinders buried in a lossy half space.
Lee, Siu-Chun
2013-07-01
The theoretical solution for scattering by an arbitrary configuration of closely spaced parallel infinite cylinders buried in a lossy half space is presented in this paper. The refractive index and permeability of the half space and cylinders are complex in general. Each cylinder is radially stratified with a distinct complex refractive index and permeability. The incident radiation is an arbitrarily polarized plane wave propagating in the plane normal to the axes of the cylinders. Analytic solutions are derived for the electric and magnetic fields and the Poynting vector of backscattered radiation emerging from the half space. Numerical examples are presented to illustrate the application of the scattering solution to calculate backscattering from a lossy half space containing multiple homogeneous and radially stratified cylinders at various depths and different angles of incidence.
DEFF Research Database (Denmark)
Domadiya, Parthkumar Gandalal; Manconi, Elisabetta; Vanali, Marcello
2016-01-01
Adding periodicity to structures leads to wavemode interaction, which generates pass- and stop-bands. The frequencies at which stop-bands occur are related to the periodic nature of the structure. Thus structural periodicity can be shaped in order to design vibro-acoustic filters for reducing...... method deals with the evaluation of a vibration level difference (VLD) in a finite periodic structure embedded within an infinite one-dimensional waveguide. This VLD is defined to predict the performance in terms of noise and vibration insulation of periodic cells embedded in an otherwise uniform...
Plymen, Roger; Robinson, Paul
1995-01-01
Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.
Unitary representations of some infinite-dimensional Lie algebras motivated by string theory on AdS3
International Nuclear Information System (INIS)
Andreev, Oleg
1999-01-01
We consider some unitary representations of infinite-dimensional Lie algebras motivated by string theory on AdS 3 . These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for string theory on AdS 3 exists
International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
Tutschke, W; Yang, C
2004-01-01
There is almost no field in Mathematics which does not use Mathe matical Analysis. Computer methods in Applied Mathematics, too, are often based on statements and procedures of Mathematical Analysis. An important part of Mathematical Analysis is Complex Analysis because it has many applications in various branches of Mathematics. Since the field of Complex Analysis and its applications is a focal point in the Vietnamese research programme, the Hanoi University of Technology organized an International Conference on Finite or Infinite Dimensional Complex Analysis and Applications which took place in Hanoi from August 8 - 12, 2001. This conference th was the 9 one in a series of conferences which take place alternately in China, Japan, Korea and Vietnam each year. The first one took place th at Pusan University in Korea in 1993. The preceding 8 conference was th held in Shandong in China in August 2000. The 9 conference of the was the first one which took place above mentioned series of conferences in Vietnam....
Alternative structures and bi-Hamiltonian systems on a Hilbert space
International Nuclear Information System (INIS)
Marmo, G; Scolarici, G; Simoni, A; Ventriglia, F
2005-01-01
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide a few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and the non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems
On the space dimensionality based on metrics
International Nuclear Information System (INIS)
Gorelik, G.E.
1978-01-01
A new approach to space time dimensionality is suggested, which permits to take into account the possibility of altering dimensionality depending on the phenomenon scale. An attempt is made to give the definition of dimensionality, equivalent to a conventional definition for the Euclidean space and variety. The conventional definition of variety dimensionality is connected with the possibility of homeomorphic reflection of the Euclidean space on some region of each variety point
Finiteness properties of congruence classes of infinite matrices
Eggermont, R.H.
2014-01-01
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
Quantization of a Hamiltonian system with an infinite number of degrees of freedom
International Nuclear Information System (INIS)
Zhidkov, P.E.
1994-01-01
We propose a method of quantization of a discrete Hamiltonian system with an infinite number of degrees of freedom. Our approach is analogous to the usual finite-dimensional quantum mechanics. We construct an infinite-dimensional Schroedinger equation. We show that it is possible to pass from the finite-dimensional quantum mechanics to our construction in the limit when the number of particles tends to infinity. In the paper rigorous mathematical methods are used. 9 refs. (author)
Towers and ladders: Infinite parameter symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aulakh, C.S.
1984-05-01
We introduce a class of infinite dimensional algebras with a 'generalized loop structure' by considering the global symmetries of the four dimensional Lagrangian obtained by compactifying general relativity coupled to Yang-Mills in six dimensions down to M 4 xS 2 . The generalization to arbitrary dimensions is then obvious. We show by explicit construction that such algebras possess an infinite number of finite sub-algebras. Among which, for the six dimensional case, is so(1,3) realized on S 2 with vanishing Casimir invariants. This so(1,3) may be interpreted, in accord with a previous conjecture of Salam and Strathdee [Ann. Phys. 141, 316(1982)], as the 'ladder' symmetry for the Kaluza-Klein towers. (author)
Quark ensembles with infinite correlation length
Molodtsov, S. V.; Zinovjev, G. M.
2014-01-01
By studying quark ensembles with infinite correlation length we formulate the quantum field theory model that, as we show, is exactly integrable and develops an instability of its standard vacuum ensemble (the Dirac sea). We argue such an instability is rooted in high ground state degeneracy (for 'realistic' space-time dimensions) featuring a fairly specific form of energy distribution, and with the cutoff parameter going to infinity this inherent energy distribution becomes infinitely narrow...
Positive operator semigroups from finite to infinite dimensions
Bátkai, András; Rhandi, Abdelaziz
2017-01-01
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate t...
Of towers and ladders: Infinite parameter symmetries in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aulakh, C.S.
1984-01-01
We introduce a class of infinite dimensional algebras with a 'generalized loop structure' by considering the global symmetries of the four-dimensional lagrangian obtained by compactifying general relativity coupled to Yang-Mills in six-dimensions down to M 4 x S 2 . The generalization to arbitrary dimensions is then obvious. We show by explicit construction that such algebras possess an infinite number of finite sub-algebras among which, for the six-dimensional case, is so (1, 3), realized on S 2 with vanishing Casimir invariants. This so (1, 3) may be interpreted, in accordance with a previous conjecture of Salam and Strathdee, as the 'ladder' symmetry for the Kaluza-Klein towers. (orig.)
Asymptotic symmetries of Rindler space at the horizon and null infinity
International Nuclear Information System (INIS)
Chung, Hyeyoun
2010-01-01
We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.
Classification of locally 2-connected compact metric spaces
DEFF Research Database (Denmark)
Thomassen, Carsten
2005-01-01
The aim of this paper is to prove that, for compact metric spaces which do not contain infinite complete graphs, the (strong) property of being "locally 2-dimensional" is guaranteed just by a (weak) local connectivity condition. Specifically, we prove that a locally 2-connected, compact metric sp...... space M either contains an infinite complete graph or is surface like in the following sense: There exists a unique surface S such that S and M. contain the same finite graphs. Moreover, M is embeddable in S, that is, M is homeomorphic to a subset of S....
Discrete symmetries and coset space dimensional reduction
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1989-01-01
We consider the discrete symmetries of all the six-dimensional coset spaces and we apply them in gauge theories defined in ten dimensions which are dimensionally reduced over these homogeneous spaces. Particular emphasis is given in the consequences of the discrete symmetries on the particle content as well as on the symmetry breaking a la Hosotani of the resulting four-dimensional theory. (orig.)
Three-dimensional spin-3 theories based on general kinematical algebras
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, Eric [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Grumiller, Daniel; Prohazka, Stefan [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria); Rosseel, Jan [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland); Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria)
2017-01-25
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible Inönü-Wigner contraction procedures of the kinematical algebra of spin-3 theory in three dimensional (anti-) de Sitter space-time. We demonstrate how to construct associated actions of Chern-Simons type, directly in the ultra-relativistic case and by suitable algebraic extensions in the non-relativistic case. We show how to give these kinematical algebras an infinite-dimensional lift by imposing suitable boundary conditions in a theory we call “Carroll Gravity”, whose asymptotic symmetry algebra turns out to be an infinite-dimensional extension of the Carroll algebra.
Coset space dimensional reduction of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D. (Physik Dept., Technische Univ. Muenchen, Garching (Germany)); Zoupanos, G. (CERN, Geneva (Switzerland))
1992-10-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.).
Coset space dimensional reduction of gauge theories
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1992-01-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.)
The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting
International Nuclear Information System (INIS)
Schuster, T; Schöpfer, F; Rieder, A
2012-01-01
This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)
Infinite Random Graphs as Statistical Mechanical Models
DEFF Research Database (Denmark)
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...
A note on tensor fields in Hilbert spaces
Directory of Open Access Journals (Sweden)
LEONARDO BILIOTTI
2002-06-01
Full Text Available We discuss and extend to infinite dimensional Hilbert spaces a well-known tensoriality criterion for linear endomorphisms of the space of smooth vector fields in n.Discutimos e estendemos para espaços de Hilbert um critério de tensorialidade para endomorfismos do espaço dos campos vetoriais em Rpot(n.
Big bang in a universe with infinite extension
Energy Technology Data Exchange (ETDEWEB)
Groen, Oeyvind [Oslo College, Department of Engineering, PO Box 4, St Olavs Pl, 0130 Oslo (Norway); Institute of Physics, University of Oslo, PO Box 1048 Blindern, 0316 Oslo (Norway)
2006-05-01
How can a universe coming from a point-like big bang event have infinite spatial extension? It is shown that the relativity of simultaneity is essential in answering this question. Space is finite as defined by the simultaneity of one observer, but it may be infinite as defined by the simultaneity of all the clocks participating in the Hubble flow.
Big bang in a universe with infinite extension
International Nuclear Information System (INIS)
Groen, Oeyvind
2006-01-01
How can a universe coming from a point-like big bang event have infinite spatial extension? It is shown that the relativity of simultaneity is essential in answering this question. Space is finite as defined by the simultaneity of one observer, but it may be infinite as defined by the simultaneity of all the clocks participating in the Hubble flow
Infinite Spin Fields in d = 3 and Beyond
Directory of Open Access Journals (Sweden)
Yurii M. Zinoviev
2017-08-01
Full Text Available In this paper, we consider the frame-like formulation for the so-called infinite (continuous spin representations of the Poincare algebra. In the three-dimensional case, we give explicit Lagrangian formulation for bosonic and fermionic infinite spin fields (including the complete sets of the gauge-invariant objects and all the necessary extra fields. Moreover, we find the supertransformations for the supermultiplet containing one bosonic and one fermionic field, leaving the sum of their Lagrangians invariant. Properties of such fields and supermultiplets in four and higher dimensions are also briefly discussed.
Sakuraba, Takao
The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A
Fractal electrodynamics via non-integer dimensional space approach
Tarasov, Vasily E.
2015-09-01
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.
Inequality for the infinite-cluster density in Bernoulli percolation
International Nuclear Information System (INIS)
Chayes, J.T.; Chayes, L.
1986-01-01
Under a certain assumption (which is satisfied whenever there is a dense infinite cluster in the half-space), we prove a differential inequality for the infinite-cluster density, P/sub infinity/(p), in Bernoulli percolation. The principal implication of this result is that if P/sub infinity/(p) vanishes with critical exponent β, then β obeys the mean-field bound β< or =1. As a corollary, we also derive an inequality relating the backbone density, the truncated susceptibility, and the infinite-cluster density
Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2
International Nuclear Information System (INIS)
Babbitt, D.; Thomas, L.
1977-01-01
In its ground state representation, the infinite, spin 1/2 Heisenberg chain provides a model for spin wave scattering, which entails many features of the quantum mechanical N-body problem. Here, we give a complete eigenfunction expansion for the Hamiltonian of the chain in this representation, for all numbers of spin waves. Our results resolve the questions of completeness and orthogonality of the eigenfunctions given by Bethe for finite chains, in the infinite volume limit. (orig.) [de
The coadjoint orbit spaces of Diff(S1) and Teichmueller spaces
International Nuclear Information System (INIS)
Nag, S.; Verjovsky, A.
1989-09-01
Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations (Diff (S 1 )) carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kaehler manifolds. These are N = Diff (S 1 )/Rot (S 1 ) and M = Diff (S 1 )/Moeb (S 1 ). Note that N is a holomorphic disc fiber space over M. Now, M can be naturally considered as embedded in the classical universal Teichmueller space T(1), simply by noting that a diffeomorphism of S 1 is a quasisymmetric homeomorphism. T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion of M in T(1) is complex analytic. In the latter portion of this paper it is shown that the unique homogeneous Kaehler metric carried by M = Diff (S 1 )/SL(2, R) induces precisely the Weil-Petersson metric on the Teichmueller space. This is via our identification of M as a holomorphic submanifold of universal Teichmueller space. Now recall that every Teichmueller space T(G) of finite or infinite dimension is contained canonically and holomorphically within T(1). Our computations allow us also to prove that every T(G), G any infinite Fuchsian group, projects out of M transversely. This last assertion is related to the ''fractal'' nature of G-invariant quasicircles, and to Mostow rigidity on the line. Our results thus connect the loop space approach to bosonic string theory with the sumover moduli (Polyakov path integral) approach. (author). 21 refs
International Nuclear Information System (INIS)
Kornreich, D.E.; Ganapol, B.D.
1997-01-01
The linear Boltzmann equation for the transport of neutral particles is investigated with the objective of generating benchmark-quality evaluations of solutions for homogeneous infinite media. In all cases, the problems are stationary, of one energy group, and the scattering is isotropic. The solutions are generally obtained through the use of Fourier transform methods with the numerical inversions constructed from standard numerical techniques such as Gauss-Legendre quadrature, summation of infinite series, and convergence acceleration. Consideration of the suite of benchmarks in infinite homogeneous media begins with the standard one-dimensional problems: an isotropic point source, an isotropic planar source, and an isotropic infinite line source. The physical and mathematical relationships between these source configurations are investigated. The progression of complexity then leads to multidimensional problems with source configurations that also emit particles isotropically: the finite line source, the disk source, and the rectangular source. The scalar flux from the finite isotropic line and disk sources will have a two-dimensional spatial variation, whereas a finite rectangular source will have a three-dimensional variation in the scalar flux. Next, sources emitting particles anisotropically are considered. The most basic such source is the point beam giving rise to the Green's function, which is physically the most fundamental transport problem, yet may be constructed from the isotropic point source solution. Finally, the anisotropic plane and anisotropically emitting infinite line sources are considered. Thus, a firm theoretical and numerical base is established for the most fundamental neutral particle benchmarks in infinite homogeneous media
Infinite additional symmetries in two-dimensional conformal quantum field theory
International Nuclear Information System (INIS)
Zamolodchikov, A.B.
1986-01-01
This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form associative algebras with quadratic determining relations. ''Minimal models'' of conforma field theory with such additional symmetries are considered. The space of local fields occurring in a conformal field theory with additional symmetry corresponds to a certain (in general, reducible) representation of the corresponding algebra of the symmetry
Infinite-Order Symmetries for Quantum Separable Systems
International Nuclear Information System (INIS)
Miller, W.; Kalnins, E.G.; Kress, J.M.; Pogosyan, G.S.
2005-01-01
We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, we can develop a calculus for conformal symmetries of the time-dependent Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries
Infinite-order symmetries for quantum separable systems
International Nuclear Information System (INIS)
Miller, W.; Kalnins, E.G.; Kress, J.M.; Pogosyan, G.S.
2005-01-01
A calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space is developed. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, it can develop a calculus for conformal symmetries of the time-dependent Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries [ru
International Nuclear Information System (INIS)
Nag, S.; Verjovsky, A.
1988-08-01
Precisely two coadjoint orbit spaces of the group of string reparametrizations carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex manifolds. These are M 1 =Diff(S 1 )/Rot(S 1 ) and M 2 =Diff(S 1 )/Mo-barb(S 1 ). M 2 can be naturally considered as (embedded in) the classical univeral Teichmueller space T(Δ), simply by noting that a diffeomorphism of S 1 is a quasi-symmetric homeomorphism. T(Δ) is itself a homomorphically homogeneous complex Banach manifold. We prove that the inclusion of M 2 in T(Δ) is complex analytic. Every Teichmueller space of finite or infinite dimension is contained canonically and holomorphically in T(Δ). Our result thus appears to connect the loop space approach to bosonic string theory with the sum-over moduli (Polyakov path integral) approach. (author). 12 refs
International Nuclear Information System (INIS)
Kumar, Raghwendra; Puri, R.R.; Biswas, D.
2004-01-01
The relationship between the injected current density j 0 and the dominant fundamental oscillation frequency f of a virtual cathode in a one-dimensional grounded infinite planar drift space of length L is determined numerically. If the electrons, each of mass m e and charge e, are injected with velocity v 0 , it is found that for vertical bar j 0 vertical bar >>m e v 0 3 /18π vertical bar e vertical bar L 2 , f∼√(vertical bar j 0 vertical bar) which is in contrast to the relation f∼vertical bar j 0 vertical bar reported by earlier workers
Zero Divisors in Associative Algebras over Infinite Fields
Schweitzer, Michael; Finch, Steven
1999-01-01
Let F be an infinite field. We prove that the right zero divisors of a three-dimensional associative F-algebra A must form the union of at most finitely many linear subspaces of A. The proof is elementary and written with students as the intended audience.
International Nuclear Information System (INIS)
Sasaki, Ryu; Yamanaka, Itaru
1987-01-01
The quantum version of an infinite set of polynomial conserved quantities of a class of soliton equations is discussed from the point of view of naive continuum field theory. By using techniques of two dimensional field theories, we show that an infinite set of quantum commuting operators can be constructed explicitly from the knowledge of its classical counterparts. The quantum operators are so constructed as to coincide with the classical ones in the ℎ → 0 limit (ℎ; Planck's constant divided by 2π). It is expected that the explicit forms of these operators would shed some light on the structure of the infinite dimensional Lie algebras which underlie a certain class of quantum integrable systems. (orig.)
International Nuclear Information System (INIS)
Sasaki, Ryu; Yamanaka, Itaru.
1986-08-01
The quantum version of an infinite set of polynomial conserved quantities of a class of soliton equations is discussed from the point of view of naive continuum field theory. By using techniques of two dimensional field theories, we show that an infinite set of quantum commuting operators can be constructed explicitly from the knowledge of its classical counterparts. The quantum operators are so constructed as to coincide with the classical ones in the ℎ → 0 limit (ℎ; Planck's constant divided by 2π). It is expected that the explicit forms of these operators would shed some light on the structure of the infinite dimensional Lie algebras which underlie certain class of quantum integrable systems. (author)
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
Piccirillo, Bruno; Slussarenko, Sergei; Marrucci, Lorenzo; Santamato, Enrico
2015-10-19
The standard method for experimentally determining the probability distribution of an observable in quantum mechanics is the measurement of the observable spectrum. However, for infinite-dimensional degrees of freedom, this approach would require ideally infinite or, more realistically, a very large number of measurements. Here we consider an alternative method which can yield the mean and variance of an observable of an infinite-dimensional system by measuring only a two-dimensional pointer weakly coupled with the system. In our demonstrative implementation, we determine both the mean and the variance of the orbital angular momentum of a light beam without acquiring the entire spectrum, but measuring the Stokes parameters of the optical polarization (acting as pointer), after the beam has suffered a suitable spin-orbit weak interaction. This example can provide a paradigm for a new class of useful weak quantum measurements.
Algebra of orthofermions and equivalence of their thermodynamics to the infinite U Hubbard model
International Nuclear Information System (INIS)
Kishore, R.; Mishra, A.K.
2006-01-01
The equivalence of thermodynamics of independent orthofermions to the infinite U Hubbard model, shown earlier for the one-dimensional infinite lattice, has been extended to a finite system of two lattice sites. Regarding the algebra of orthofermions, the algebraic expressions for the number operator for a given spin and the spin raising (lowering) operators in the form of infinite series are rearranged in such a way that the ith term, having the form of an infinite series, of the number (spin raising (lowering)) operator represents the number (spin raising (lowering)) operator at the ith lattice site
Three-dimensional oscillator and Coulomb systems reduced from Kaehler spaces
International Nuclear Information System (INIS)
Nersessian, Armen; Yeranyan, Armen
2004-01-01
We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kaehler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kaehler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid originate. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to a monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is a non-Kaehler one. Finally, we extend these results to the family of Kaehler spaces with conic singularities
Wang, Lihua; Zeng, Yi; Shen, Aiguo; Zhou, Xiaodong; Hu, Jiming
2015-02-07
Novel three-dimensional (3D) nano-assemblies of noble metal nanoparticle (NP)-infinite coordination polymers (ICPs) are conveniently fabricated through the infiltration of HAuCl4 into hollow Au@Ag@ICPs core-shell nanostructures and its replacement reaction with Au@Ag NPs. The present 3D nano-assemblies exhibit highly efficient and specific intrinsic oxidase-like activity even without adding any cosubstrate.
Infinite permutations vs. infinite words
Directory of Open Access Journals (Sweden)
Anna E. Frid
2011-08-01
Full Text Available I am going to compare well-known properties of infinite words with those of infinite permutations, a new object studied since middle 2000s. Basically, it was Sergey Avgustinovich who invented this notion, although in an early study by Davis et al. permutations appear in a very similar framework as early as in 1977. I am going to tell about periodicity of permutations, their complexity according to several definitions and their automatic properties, that is, about usual parameters of words, now extended to permutations and behaving sometimes similarly to those for words, sometimes not. Another series of results concerns permutations generated by infinite words and their properties. Although this direction of research is young, many people, including two other speakers of this meeting, have participated in it, and I believe that several more topics for further study are really promising.
On dimensional reduction over coset spaces
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1990-01-01
Gauge theories defined in higher dimensions can be dimensionally reduced over coset spaces giving definite predictions for the resulting four-dimensional theory. We present the most interesting features of these theories as well as an attempt to construct a model with realistic low energy behaviour within this framework. (author)
Wigner's infinite spin representations and inert matter
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [CBPF, Rio de Janeiro (Brazil); Institut fuer Theoretische Physik FU-Berlin, Berlin (Germany)
2017-06-15
Positive energy ray representations of the Poincare group are naturally subdivided into three classes according to their mass and spin content: m > 0, m = 0 finite helicity and m = 0 infinite spin. For a long time the localization properties of the massless infinite spin class remained unknown, until it became clear that such matter does not permit compact spacetime localization and its generating covariant fields are localized on semi-infinite space-like strings. Using a new perturbation theory for higher spin fields we present arguments which support the idea that infinite spin matter cannot interact with normal matter and we formulate conditions under which this also could happen for finite spin s > 1 fields. This raises the question of a possible connection between inert matter and dark matter. (orig.)
Spinors and supersymmetry in four-dimensional Euclidean space
International Nuclear Information System (INIS)
McKeon, D.G.C.; Sherry, T.N.
2001-01-01
Spinors in four-dimensional Euclidean space are treated using the decomposition of the Euclidean space SO(4) symmetry group into SU(2)xSU(2). Both 2- and 4-spinor representations of this SO(4) symmetry group are shown to differ significantly from the corresponding spinor representations of the SO(3, 1) symmetry group in Minkowski space. The simplest self conjugate supersymmetry algebra allowed in four-dimensional Euclidean space is demonstrated to be an N=2 supersymmetry algebra which resembles the N=2 supersymmetry algebra in four-dimensional Minkowski space. The differences between the two supersymmetry algebras gives rise to different representations; in particular an analysis of the Clifford algebra structure shows that the momentum invariant is bounded above by the central charges in 4dE, while in 4dM the central charges bound the momentum invariant from below. Dimensional reduction of the N=1 SUSY algebra in six-dimensional Minkowski space (6dM) to 4dE reproduces our SUSY algebra in 4dE. This dimensional reduction can be used to introduce additional generators into the SUSY algebra in 4dE. Well known interpolating maps are used to relate the N=2 SUSY algebra in 4dE derived in this paper to the N=2 SUSY algebra in 4dM. The nature of the spinors in 4dE allows us to write an axially gauge invariant model which is shown to be both Hermitian and anomaly-free. No equivalent model exists in 4dM. Useful formulae in 4dE are collected together in two appendixes
Exact solution for the Poisson field in a semi-infinite strip.
Cohen, Yossi; Rothman, Daniel H
2017-04-01
The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.
Probabilistic Infinite Secret Sharing
Csirmaz, László
2013-01-01
The study of probabilistic secret sharing schemes using arbitrary probability spaces and possibly infinite number of participants lets us investigate abstract properties of such schemes. It highlights important properties, explains why certain definitions work better than others, connects this topic to other branches of mathematics, and might yield new design paradigms. A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a colle...
Two-particle correlations in the one-dimensional Hubbard model: a ground-state analytical solution
Vallejo, E; Espinosa, J E
2003-01-01
A solution to the extended Hubbard Hamiltonian for the case of two-particles in an infinite one-dimensional lattice is presented, using a real-space mapping method and the Green function technique. This Hamiltonian considers the on-site (U) and the nearest-neighbor (V) interactions. The method is based on mapping the correlated many-body problem onto an equivalent site-impurity tight-binding one in a higher dimensional space. In this new space we obtained the analytical solution for the ground state binding energy. Results are in agreement with the numerical solution obtained previously [1], and with those obtained in the reciprocal space [2]. (Author)
Quantum Mechanics and Black Holes in Four-Dimensional String Theory
Ellis, Jonathan Richard; Nanopoulos, Dimitri V
1992-01-01
In previous papers we have shown how strings in a two-dimensional target space reconcile quantum mechanics with general relativity, thanks to an infinite set of conserved quantum numbers, ``W-hair'', associated with topological soliton-like states. In this paper we extend these arguments to four dimensions, by considering explicitly the case of string black holes with radial symmetry. The key infinite-dimensional W-symmetry is associated with the $\\frac{SU(1,1)}{U(1)}$ coset structure of the dilaton-graviton sector that is a model-independent feature of spherically symmetric four-dimensional strings. Arguments are also given that the enormous number of string {\\it discrete (topological)} states account for the maintenance of quantum coherence during the (non-thermal) stringy evaporation process, as well as quenching the large Hawking-Bekenstein entropy associated with the black hole. Defining the latter as the measure of the loss of information for an observer at infinity, who - ignoring the higher string qua...
Selfadjointness of the Liouville operator for infinite classical systems
Energy Technology Data Exchange (ETDEWEB)
Marchioro, C [Camerino Univ. (Italy). Istituto di Matematica; Pellegrinotti, A [Rome Univ. (Italy). Istituto di Matematica; Pulvirenti, M [Ancona Univ. (Italy). Istituto di Matematica
1978-02-01
We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed.
Nambu, Y.
1967-01-01
The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.
On asphericity of convex bodies in linear normed spaces.
Faried, Nashat; Morsy, Ahmed; Hussein, Aya M
2018-01-01
In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ -iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asphericity for each set that has a nonempty boundary set with respect to the flat space generated by it. We also give a formula to determine the center and the radius of the smallest ball containing a nonempty nonsingleton set K in a linear normed space, and the center and the radius of the largest ball contained in it provided that K has a nonempty boundary set with respect to the flat space generated by it. As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.
TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.
Selfadjointness of the Liouville operator for infinite classical systems
International Nuclear Information System (INIS)
Marchioro, C.; Pellegrinotti, A.; Pulvirenti, M.
1978-01-01
We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed. (orig.) [de
International Nuclear Information System (INIS)
Fradkin, E.S.; Palchik, M.Ya.
1996-02-01
We study a family of exactly solvable models of conformally-invariant quantum field theory in D-dimensional space. We demonstrate the existence of D-dimensional analogs of primary and secondary fields. Under the action of energy-momentum tensor and conserved currents, the primary fields creates an infinite set of (tensor) secondary fields of different generations. The commutators of secondary fields with zero components of current and energy-momentum tensor include anomalous operator terms. We show that the Hilbert space of conformal theory has a special sector which structure is solely defined by the Ward identities independently on the choice of dynamical model. The states of this sector are constructed from secondary fields. Definite self-consistent conditions on the states of the latter sector fix the choice of the field model uniquely. In particular, Lagrangian models do belong to this class of models. The above self-consistent conditions are formulated as follows. Special superpositions Q s , s = 1,2,... of secondary fields are constructed. Each superposition is determined by the requirement that the form of its commutators with energy-momentum tensor and current (i.e. transformation properties) should be identical to that of a primary field. Each equation Q s (x) = 0 is consistent, and defines an exactly solvable model for D ≥ 3. The structure of these models are analogous to that of well-known two dimensional conformal models. The states Q s (x) modul 0> are analogous to the null-vectors of two dimensional theory. In each of these models one can obtain a closed set of differential equations for all the higher Green functions, as well as algebraic equations relating the scale dimension of fundamental field to the D-dimensional analog of a central charge. As an example, we present a detailed discussion of a pair of exactly solvable models in even-dimensional space D ≥ 4. (author). 28 refs
Two-dimensional black holes and non-commutative spaces
International Nuclear Information System (INIS)
Sadeghi, J.
2008-01-01
We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon
Anisotropic fractal media by vector calculus in non-integer dimensional space
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2014-08-15
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
Tarasov, Vasily E.
2014-08-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2014-01-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media
Dimensional regularization in configuration space
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1995-09-01
Dimensional regularization is introduced in configuration space by Fourier transforming in D-dimensions the perturbative momentum space Green functions. For this transformation, Bochner theorem is used, no extra parameters, such as those of Feynman or Bogoliubov-Shirkov are needed for convolutions. The regularized causal functions in x-space have ν-dependent moderated singularities at the origin. They can be multiplied together and Fourier transformed (Bochner) without divergence problems. The usual ultraviolet divergences appear as poles of the resultant functions of ν. Several example are discussed. (author). 9 refs
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Energy Technology Data Exchange (ETDEWEB)
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
The use of virtual reality to reimagine two-dimensional representations of three-dimensional spaces
Fath, Elaine
2015-03-01
A familiar realm in the world of two-dimensional art is the craft of taking a flat canvas and creating, through color, size, and perspective, the illusion of a three-dimensional space. Using well-explored tricks of logic and sight, impossible landscapes such as those by surrealists de Chirico or Salvador Dalí seem to be windows into new and incredible spaces which appear to be simultaneously feasible and utterly nonsensical. As real-time 3D imaging becomes increasingly prevalent as an artistic medium, this process takes on an additional layer of depth: no longer is two-dimensional space restricted to strategies of light, color, line and geometry to create the impression of a three-dimensional space. A digital interactive environment is a space laid out in three dimensions, allowing the user to explore impossible environments in a way that feels very real. In this project, surrealist two-dimensional art was researched and reimagined: what would stepping into a de Chirico or a Magritte look and feel like, if the depth and distance created by light and geometry were not simply single-perspective illusions, but fully formed and explorable spaces? 3D environment-building software is allowing us to step into these impossible spaces in ways that 2D representations leave us yearning for. This art project explores what we gain--and what gets left behind--when these impossible spaces become doors, rather than windows. Using sketching, Maya 3D rendering software, and the Unity Engine, surrealist art was reimagined as a fully navigable real-time digital environment. The surrealist movement and its key artists were researched for their use of color, geometry, texture, and space and how these elements contributed to their work as a whole, which often conveys feelings of unexpectedness or uneasiness. The end goal was to preserve these feelings while allowing the viewer to actively engage with the space.
Belkhatir, Zehor
2016-08-05
This paper deals with joint parameters and input estimation for coupled PDE-ODE system. The system consists of a damped wave equation and an infinite dimensional ODE. This model describes the spatiotemporal hemodynamic response in the brain and the objective is to characterize brain regions using functional Magnetic Resonance Imaging (fMRI) data. For this reason, we propose an adaptive estimator and prove the asymptotic convergence of the state, the unknown input and the unknown parameters. The proof is based on a Lyapunov approach combined with a priori identifiability assumptions. The performance of the proposed observer is illustrated through some simulation results.
Boundary crossover in semi-infinite non-equilibrium growth processes
International Nuclear Information System (INIS)
Allegra, Nicolas; Fortin, Jean-Yves; Henkel, Malte
2014-01-01
The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk are analysed. The causal interactions of the interface with the boundary lead to a roughness larger near to the boundary than deep in the bulk. This is exemplified in the semi-infinite Edwards–Wilkinson model in one dimension, from both its exact solution and numerical simulations, as well as from simulations on the semi-infinite one-dimensional Kardar–Parisi–Zhang model. The non-stationary scaling of interface heights and widths is analysed and a universal scaling form for the local height profile is proposed. (paper)
We live in the quantum 4-dimensional Minkowski space-time
Hwang, W-Y. Pauchy
2015-01-01
We try to define "our world" by stating that "we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge group $SU_c(3) \\times SU_L(2) \\times U(1) \\times SU_f(3)$ built-in from the outset". We begin by explaining what "space" and "time" are meaning for us - the 4-dimensional Minkowski space-time, then proceeding to the quantum 4-dimensional Minkowski space-time. In our world, there are fields, or, point-like particles. Particle physics is described by the so-called ...
Dimensional reduction from entanglement in Minkowski space
International Nuclear Information System (INIS)
Brustein, Ram; Yarom, Amos
2005-01-01
Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature. (author)
DEFF Research Database (Denmark)
Brander, David; Rossman, Wayne; Schmitt, Nicholas
2010-01-01
We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\\R^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group $SU_2$ with...
Directory of Open Access Journals (Sweden)
Bipan Hazarika
2016-10-01
Full Text Available In this paper we introduce the spaces V^λ[A,M,Δ,p]o,V^λ[A,M,Δ,p] and V^λ[A,M,Δ,p]∞ generated by infinite matrices defined by Orlicz functions. Also we introduce the concept of S^λ[A,Δ]−convergence and derive some results between the spaces S^λ[A,Δ] and V^λ[A,Δ]. Further, we study some geometrical properties such as order continuity, the Fatou property and the Banach–Saks property of the new space V^λα[A,Δ,p]∞. Finally, we introduce the notion of almost λ-statistically-[A, Δ]-convergence of order α or S^λα[A,Δ]−convergence and obtain some inclusion relations between the set S^λα[A,Δ] and the space V^λα[A,Δ,p]∞.
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions
International Nuclear Information System (INIS)
Goreac, D.
2009-01-01
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability. Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253-260, Chapman and Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153-164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case
Bing, Xue; Yicai, Ji
2018-06-01
In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.
Quantum phase space points for Wigner functions in finite-dimensional spaces
Luis Aina, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.
Quantum phase space points for Wigner functions in finite-dimensional spaces
International Nuclear Information System (INIS)
Luis, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas
Electromagnetic-field equations in the six-dimensional space-time R6
International Nuclear Information System (INIS)
Teli, M.T.; Palaskar, D.
1984-01-01
Maxwell's equations (without monopoles) for electromagnetic fields are obtained in six-dimensional space-time. The equations possess structural symmetry in space and time, field and source densities. Space-time-symmetric conservation laws and field solutions are obtained. The results are successfully correlated with their four-dimensional space-time counterparts
International Nuclear Information System (INIS)
Naumis, Gerardo G.; Bazan, A.; Torres, M.; Aragon, J.L.; Quintero-Torres, R.
2008-01-01
One of the few examples in which the physical properties of an incommensurable system reflect an underlying higher dimensionality is presented. Specifically, we show that the reflectivity distribution of an incommensurable one-dimensional cavity is given by the density of states of a tight-binding Hamiltonian in a two-dimensional triangular lattice. Such effect is due to an independent phase decoupling of the scattered waves, produced by the incommensurable nature of the system, which mimics a random noise generator. This principle can be applied to design a cavity that avoids resonant reflections for almost any incident wave. An optical analogy, by using three mirrors with incommensurable distances between them, is also presented. Such array produces a countable infinite fractal set of reflections, a phenomena which is opposite to the effect of optical invisibility
Bond-diluted interface between semi-infinite Potts bulks: criticality
International Nuclear Information System (INIS)
Cavalcanti, S.B.; Tsallis, C.
1986-01-01
Within a real space renormalisation group framework, we discuss the criticality of a system constituted by two (not necessarily equal) semi-infinite ferromagnetic q-state Potts bulks separated by an interface. This interface is a bond-diluted Potts ferromagnet with a coupling constant which is in general different from those of both bulks. The phase diagram presents four physically different phases, namely the paramagnetic one, and the surface, single bulk and double bulk ferromagnetic ones. These various phases determine a multicritical surface which contains a higher order multicritical line. The critical concentration P c that is the concentration of the interface bonds which surface magnetic ordering is possible even if the bulks are disordered. An interesting feature comes out which is that P c varies continuously with J 1 /J s and J 2 /J s . The standard two-dimensional percolation concentration is recovered for J 1 =J 2 =0. (author) [pt
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Impulsive evolution inclusions with infinite delay and multivalued jumps
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2012-08-01
Full Text Available In this paper we prove the existence of a mild solution for a class of impulsive semilinear evolution differential inclusions with infinite delay and multivalued jumps in a Banach space.
Classical symmetries of some two-dimensional models
International Nuclear Information System (INIS)
Schwarz, J.H.
1995-01-01
It is well-known that principal chiral models and symmetric space models in two-dimensional Minkowski space have an infinite-dimensional algebra of hidden symmetries. Because of the relevance of symmetric space models to duality symmetries in string theory, the hidden symmetries of these models are explored in some detail. The string theory application requires including coupling to gravity, supersymmetrization, and quantum effects. However, as a first step, this paper only considers classical bosonic theories in flat space-time. Even though the algebra of hidden symmetries of principal chiral models is confirmed to include a Kac-Moody algebra (or a current algebra on a circle), it is argued that a better interpretation is provided by a doubled current algebra on a semi-circle (or line segment). Neither the circle nor the semi-circle bears any apparent relationship to the physical space. For symmetric space models the line segment viewpoint is shown to be essential, and special boundary conditions need to be imposed at the ends. The algebra of hidden symmetries also includes Virasoro-like generators. For both principal chiral models and symmetric space models, the hidden symmetry stress tensor is singular at the ends of the line segment. (orig.)
Infinite time interval backward stochastic differential equations with continuous coefficients.
Zong, Zhaojun; Hu, Feng
2016-01-01
In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).
Multi-dimensional cosmology and GUP
International Nuclear Information System (INIS)
Zeynali, K.; Motavalli, H.; Darabi, F.
2012-01-01
We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and d-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions
Multi-dimensional cosmology and GUP
Energy Technology Data Exchange (ETDEWEB)
Zeynali, K.; Motavalli, H. [Department of Theoretical Physics and Astrophysics, University of Tabriz, 51666-16471, Tabriz (Iran, Islamic Republic of); Darabi, F., E-mail: k.zeinali@arums.ac.ir, E-mail: f.darabi@azaruniv.edu, E-mail: motavalli@tabrizu.ac.ir [Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz (Iran, Islamic Republic of)
2012-12-01
We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and d-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions.
Green functions and scattering amplitudes in many-dimensional space
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1993-01-01
Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation. (author)
Identification of Architectural Functions in A Four-Dimensional Space
Directory of Open Access Journals (Sweden)
Firza Utama
2012-06-01
Full Text Available This research has explored the possibilities and concept of architectural space in a virtual environment. The virtual environment exists as a different concept, and challenges the constraints of the physical world. One of the possibilities in a virtual environment is that it is able to extend the spatial dimension higher than the physical three-dimension. To take the advantage of this possibility, this research has applied some geometrical four-dimensional (4D methods to define virtual architectural space. The spatial characteristics of 4D space is established by analyzing the four-dimensional structure that can be comprehended by human participant for its spatial quality, and by developing a system to control the fourth axis of movement. Multiple three-dimensional spaces that fluidly change their volume have been defined as one of the possibilities of virtual architecturalspace concept in order to enrich our understanding of virtual spatial experience.
International Nuclear Information System (INIS)
Yang, Zhanfeng; Liu, Guozhi; Shao, Hao; Chen, Changhua; Sun, Jun
2013-01-01
This paper reports the space-charge limited current (SLC) and virtual cathode behaviors in one-dimensional grounded drift space. A simple general analytical solution and an approximate solution for the planar diode are given. Through a semi-analytical method, a general solution for SLC in one-dimensional drift space is obtained. The behaviors of virtual cathode in the drift space, including dominant frequency, electron transit time, position, and transmitted current, are yielded analytically. The relationship between the frequency of the virtual cathode oscillation and the injected current presented may explain previously reported numerical works. Results are significant in facilitating estimations and further analytical studies
On infinitely divisible semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas; Rosiński, Jan
2015-01-01
to non Gaussian infinitely divisible processes. First we show that the class of infinitely divisible semimartingales is so large that the natural analog of Stricker's theorem fails to hold. Then, as the main result, we prove that an infinitely divisible semimartingale relative to the filtration generated...... by a random measure admits a unique decomposition into an independent increment process and an infinitely divisible process of finite variation. Consequently, the natural analog of Stricker's theorem holds for all strictly representable processes (as defined in this paper). Since Gaussian processes...... are strictly representable due to Hida's multiplicity theorem, the classical Stricker's theorem follows from our result. Another consequence is that the question when an infinitely divisible process is a semimartingale can often be reduced to a path property, when a certain associated infinitely divisible...
The Long Time Behavior of a Stochastic Logistic Model with Infinite Delay and Impulsive Perturbation
Lu, Chun; Wu, Kaining
2016-01-01
This paper considers a stochastic logistic model with infinite delay and impulsive perturbation. Firstly, with the space $C_{g}$ as phase space, the definition of solution to a stochastic functional differential equation with infinite delay and impulsive perturbation is established. According to this definition, we show that our model has an unique global positive solution. Then we establish the sufficient and necessary conditions for extinction and stochastic permanence of the...
On quantization of free fields in stationary space-times
International Nuclear Information System (INIS)
Moreno, C.
1977-01-01
In Section 1 the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections, is analysed, an existence and uniqueness theorem is given for the Lichnerowicz distribution kernel G 1 together with its proper Fourier expansion, and the Hilbert spaces of frequency-part solutions defined by means of G 1 are constructed. In Section 2 an analysis, a theorem and a construction similar to the above are formulated for the free real field spin 1, mass m>0, in one kind of static space-times. (Auth.)
Green function and scattering amplitudes in many dimensional space
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1991-06-01
Methods for solving scattering are studied in many dimensional space. Green function and scattering amplitudes are given in terms of the requested asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many dimensional space. Phase-shift analysis are developed for hypercentral potentials and for non-hypercentral potentials with the hyperspherical adiabatic approximation. (author) 16 refs., 3 figs
Diagonalization of Bounded Linear Operators on Separable Quaternionic Hilbert Space
International Nuclear Information System (INIS)
Feng Youling; Cao, Yang; Wang Haijun
2012-01-01
By using the representation of its complex-conjugate pairs, we have investigated the diagonalization of a bounded linear operator on separable infinite-dimensional right quaternionic Hilbert space. The sufficient condition for diagonalizability of quaternionic operators is derived. The result is applied to anti-Hermitian operators, which is essential for solving Schroedinger equation in quaternionic quantum mechanics.
Few helium atoms in quasi two-dimensional space
International Nuclear Information System (INIS)
Kilic, Srecko; Vranjes, Leandra
2003-01-01
Two, three and four 3 He and 4 He atoms in quasi two-dimensional space above graphite and cesium surfaces and in 'harmonic' potential perpendicular to the surface have been studied. Using some previously examined variational wave functions and the Diffusion Monte Carlo procedure, it has been shown that all molecules: dimers, trimers and tetramers, are bound more strongly than in pure two- and three-dimensional space. The enhancement of binding with respect to unrestricted space is more pronounced on cesium than on graphite. Furthermore, for 3 He 3 ( 3 He 4 ) on all studied surfaces, there is an indication that the configuration of a dimer and a 'free' particle (two dimers) may be equivalently established
Quark ensembles with the infinite correlation length
Zinov'ev, G. M.; Molodtsov, S. V.
2015-01-01
A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble.
Quark ensembles with the infinite correlation length
International Nuclear Information System (INIS)
Zinov’ev, G. M.; Molodtsov, S. V.
2015-01-01
A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble
Quark ensembles with the infinite correlation length
Energy Technology Data Exchange (ETDEWEB)
Zinov’ev, G. M. [National Academy of Sciences of Ukraine, Bogoliubov Institute for Theoretical Physics (Ukraine); Molodtsov, S. V., E-mail: molodtsov@itep.ru [Joint Institute for Nuclear Research (Russian Federation)
2015-01-15
A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble.
Lorentz covariant tempered distributions in two-dimensional space-time
International Nuclear Information System (INIS)
Zinov'ev, Yu.M.
1989-01-01
The problem of describing Lorentz covariant distributions without any spectral condition has hitherto remained unsolved even for two-dimensional space-time. Attempts to solve this problem have already been made. Zharinov obtained an integral representation for the Laplace transform of Lorentz invariant distributions with support in the product of two-dimensional future light cones. However, this integral representation does not make it possible to obtain a complete description of the corresponding Lorentz invariant distributions. In this paper the author gives a complete description of Lorentz covariant distributions for two-dimensional space-time. No spectral conditions is assumed
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
A method is proposed for classification of exactly and completely integrable embeddings of two dimensional manifoilds into Riemann or non-Riemann enveloping space, which are based on the algebraic approach to the integration of nonlinear dynamical systems.Here the grading conditions and spectral structure of the Lax-pair operators taking the values in a graded Lie algebra that pick out the integrable class of nonlinear systems are formulated 1n terms of a structure of the 3-d fundamental form tensors. Corresponding to every embedding of three-dimensional subalgebra sb(2) into a simple finite-dimensional (infinite-dimensional of finite growth) Lie algebra L is a definite class of exactly (completely) integrable embeddings of two dimensional manifold into the corresponding enveloping space supplied with the structure of L
On the space of connections having non-trivial twisted harmonic spinors
International Nuclear Information System (INIS)
Bei, Francesco; Waterstraat, Nils
2015-01-01
We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yields an invertible operator has infinitely many connected components if the untwisted Dirac operator is invertible and the dimension of the twisting bundle is sufficiently large
On the space of connections having non-trivial twisted harmonic spinors
Energy Technology Data Exchange (ETDEWEB)
Bei, Francesco, E-mail: bei@math.hu-berlin.de [Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin (Germany); Waterstraat, Nils, E-mail: n.waterstraat@kent.ac.uk [School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF (United Kingdom)
2015-09-15
We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yields an invertible operator has infinitely many connected components if the untwisted Dirac operator is invertible and the dimension of the twisting bundle is sufficiently large.
Mannheim Curves in Nonflat 3-Dimensional Space Forms
Directory of Open Access Journals (Sweden)
Wenjing Zhao
2015-01-01
Full Text Available We consider the Mannheim curves in nonflat 3-dimensional space forms (Riemannian or Lorentzian and we give the concept of Mannheim curves. In addition, we investigate the properties of nonnull Mannheim curves and their partner curves. We come to the conclusion that a necessary and sufficient condition is that a linear relationship with constant coefficients will exist between the curvature and the torsion of the given original curves. In the case of null curve, we reveal that there are no null Mannheim curves in the 3-dimensional de Sitter space.
Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model
International Nuclear Information System (INIS)
Hao Sanru; Li Wei
1989-01-01
This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed
New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity
Energy Technology Data Exchange (ETDEWEB)
Sundell, Per; Yin, Yihao [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago de Chile (Chile)
2017-01-11
We present new infinite-dimensional spaces of bi-axially symmetric asymptotically anti-de Sitter solutions to four-dimensional Vasiliev higher spin gravity, obtained by modifications of the Ansatz used in https://arxiv.org/abs/1107.1217, which gave rise to a Type-D solution space. The current Ansatz is based on internal semigroup algebras (without identity) generated by exponentials formed out of the bi-axial symmetry generators. After having switched on the vacuum gauge function, the resulting generalized Weyl tensor is given by a sum of generalized Petrov type-D tensors that are Kerr-like or 2-brane-like in the asymptotic AdS{sub 4} region, and the twistor space connection is smooth in twistor space over finite regions of spacetime. We provide evidence for that the linearized twistor space connection can be brought to Vasiliev gauge.
Stiffness and Mass Matrices of FEM-Applicable Dynamic Infinite Element with Unified Shape Basis
International Nuclear Information System (INIS)
Kazakov, Konstantin
2009-01-01
This paper is devoted to the construction and evaluation of mass and stiffness matrices of elastodynamic four and five node infinite elements with unified shape functions (EIEUSF), recently proposed by the author. Such elements can be treated as a family of elastodynamic infinite elements appropriate for multi-wave soil-structure interaction problems. The common characteristic of the proposed infinite elements is the so-called unified shape function, based on finite number of wave shape functions. The idea and the construction of the unified shape basis are described in brief. This element belongs to the decay class of infinite elements. It is shown that by appropriate mapping functions the formulation of such an element can be easily transformed to a mapped form. The results obtained using the proposed infinite elements are in a good agreement with the superposed results obtained by a series of standard computational models. The continuity along the finite/infinite element line (artificial boundary) in two-dimensional substructure models is also discussed in brief. In this type of computational models such a line marks the artificial boundary between the near and the far field of the model.
Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
International Nuclear Information System (INIS)
Avrutin, V; Granados, A; Schanz, M
2011-01-01
Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs
Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
Avrutin, V.; Granados, A.; Schanz, M.
2011-09-01
Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs.
Monoenergetic particle transport in a semi-infinite medium with reflection
International Nuclear Information System (INIS)
Ganapol, B.D.
1993-01-01
Next to neutron or photon transport in infinite geometry, particle transport in semi-infinite geometry is probably the most investigated transport problem. When the mean free path for particle interaction is small compared to the physical dimension of the scattering medium, the infinite or semi-infinite geometry assumption is reasonable for a variety of applications. These include nondestructive testing, photon transport in plant canopies, and inverse problems associated with well logging. Another important application of the transport solution in a semi-infinite medium is as a benchmark to which other more approximate methods can be compared. In this paper, the transport solution in a semi-infinite medium with both diffuse and specular reflection at the free surface is solved analytically and numerically evaluated. The approach is based on a little-known solution obtained by Sobelev for the problem with specular reflection, which itself originates from the classical albedo problem solution without reflection. Using Sobelev's solution as a partial Green's function, the exiting flux for diffuse reflection can be obtained. In this way, the exiting flux for a half-space with both constant diffuse and specular reflection coefficients is obtained for the first time. This expression can then be extended to the complex plane to obtain the interior flux as an inverse Laplace transform, which is numerically evaluated
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces
International Nuclear Information System (INIS)
Robinson, James C
2009-01-01
This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X − X is finite, d H (X − X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hölder continuous inverse when the box-counting dimension of X is finite and k > 2d B (X). A related argument shows that if the Assouad dimension of X − X is finite and k > d A (X − X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L ∞ (X)
Newton law in DGP brane-world with semi-infinite extra dimension
International Nuclear Information System (INIS)
Park, D.K.; Tamaryan, S.; Miao Yangang
2004-01-01
Newton potential for DGP brane-world scenario is examined when the extra dimension is semi-infinite. The final form of the potential involves a self-adjoint extension parameter α, which plays a role of an additional mass (or distance) scale. The striking feature of Newton potential in this setup is that the potential behaves as seven-dimensional in long range when α is non-zero. For small α there is an intermediate range where the potential is five-dimensional. Five-dimensional Newton constant decreases with increase of α from zero. In the short range the four-dimensional behavior is recovered. The physical implication of this result is discussed in the context of the accelerating behavior of universe
Symmetry Reduction in Infinite Games with Finite Branching
DEFF Research Database (Denmark)
Markey, Nicolas; Vester, Steen
2014-01-01
infinite-state games on graphs with finite branching where the objectives of the players can be very general. As particular applications, it is shown that the technique can be applied to reduce the state space in parity games as well as when doing modelchecking of the Alternating-time temporal logic ATL....
Recipes for stable linear embeddings from Hilbert spaces to R^m
Puy, Gilles; Davies, Michael; Gribonval, Remi
2017-01-01
We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to Rm that satisfies a restricted isometry property (RIP) on an arbitrary signal model, i.e., a subset of H. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP with high probability. We also describe a generic technique ...
Recipes for stable linear embeddings from Hilbert spaces to R^m
Puy, Gilles; Davies, Mike; Gribonval, Rémi
2015-01-01
We consider the problem of constructing a linear map from a Hilbert space $\\mathcal{H}$ (possibly infinite dimensional) to $\\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\\mathcal{S} \\subset \\mathcal{H}$. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP on $\\mathcal{S}$ with h...
Superconductivity and the existence of Nambu's three-dimensional phase space mechanics
International Nuclear Information System (INIS)
Angulo, R.; Gonzalez-Bernardo, C.A.; Rodriguez-Gomez, J.; Kalnay, A.J.; Perez-M, F.; Tello-Llanos, R.A.
1984-01-01
Nambu proposed a generalization of hamiltonian mechanics such that three-dimensional phase space is allowed. Thanks to a recent paper by Holm and Kupershmidt we are able to show the existence of such three-dimensional phase space systems in superconductivity. (orig.)
Directory of Open Access Journals (Sweden)
Zhou Yinying
2014-01-01
Full Text Available We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009, Min and Chang (2012, Plubtieng and Punpaeng (2007, S. Takahashi and W. Takahashi (2007, Tada and Takahashi (2007, Gang and Changsong (2009, Ying (2013, Y. Yao and J. C. Yao (2007, and Yong-Cho and Kang (2012.
Wave function of an electron infinitely moving in the field of a one-dimensional layered structure
International Nuclear Information System (INIS)
Khachatrian, A.Zh.; Andreasyan, A.G.; Mgerian, G.G.; Badalyan, V.D.
2003-01-01
A method for finding the wave function of an electron infinitely moving in the field of an arbitrary layered structure bordered on both sides with two different semi infinite media is proposed. It is shown that this problem in the general form can be reduced to the solution of some system of linear finite-difference equations. The proposed approach is discussed in detail for the case of a periodic structure
Supersymmetric quantum mechanics in three-dimensional space, 1
International Nuclear Information System (INIS)
Ui, Haruo
1984-01-01
As a direct generalization of the model of supersymmetric quantum mechanics by Witten, which describes the motion of a spin one-half particle in the one-dimensional space, we construct a model of the supersymmetric quantum mechanics in the three-dimensional space, which describes the motion of a spin one-half particle in central and spin-orbit potentials in the context of the nonrelativistic quantum mechanics. With the simplest choice of the (super) potential, this model is shown to reduce to the model of the harmonic oscillator plus constant spin-orbit potential of unit strength of both positive and negative signs, which was studied in detail in our recent paper in connection with ''accidental degeneracy'' as well as the ''graded groups''. This simplest model is discussed in some detail as an example of the three-dimensional supersymmetric quantum mechanical system, where the supersymmetry is an exact symmetry of the system. More general choice of a polynomial superpotential is also discussed. It is shown that the supersymmetry cannot be spontaneously broken for any polynomial superpotential in our three-dimensional model; this result is contrasted to the corresponding one in the one-dimensional model. (author)
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available In a wireless ad hoc network, messages are transmitted, received, and forwarded in a finite geometrical region and the transmission of messages is highly dependent on the locations of the nodes. Therefore the study of geometrical relationship between nodes in wireless ad hoc networks is of fundamental importance in the network architecture design and performance evaluation. However, most previous works concentrated on the networks deployed in the two-dimensional region or in the infinite three-dimensional space, while in many cases wireless ad hoc networks are deployed in the finite three-dimensional space. In this paper, we analyze the geometrical characteristics of the three-dimensional wireless ad hoc network in a finite space in the framework of random graph and deduce an expression to calculate the distance probability distribution between network nodes that are independently and uniformly distributed in a finite cuboid space. Based on the theoretical result, we present some meaningful results on the finite three-dimensional network performance, including the node degree and the max-flow capacity. Furthermore, we investigate some approximation properties of the distance probability distribution function derived in the paper.
Visualising very large phylogenetic trees in three dimensional hyperbolic space
Directory of Open Access Journals (Sweden)
Liberles David A
2004-04-01
Full Text Available Abstract Background Common existing phylogenetic tree visualisation tools are not able to display readable trees with more than a few thousand nodes. These existing methodologies are based in two dimensional space. Results We introduce the idea of visualising phylogenetic trees in three dimensional hyperbolic space with the Walrus graph visualisation tool and have developed a conversion tool that enables the conversion of standard phylogenetic tree formats to Walrus' format. With Walrus, it becomes possible to visualise and navigate phylogenetic trees with more than 100,000 nodes. Conclusion Walrus enables desktop visualisation of very large phylogenetic trees in 3 dimensional hyperbolic space. This application is potentially useful for visualisation of the tree of life and for functional genomics derivatives, like The Adaptive Evolution Database (TAED.
Anomalous current in periodic Lorentz gases with infinite horizon
Energy Technology Data Exchange (ETDEWEB)
Dolgopyat, Dmitrii I [University of Maryland, College Park (United States); Chernov, Nikolai I [University of Alabama at Birmingham, Birmingham, Alabama (United States)
2009-08-31
Electric current is studied in a two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, that is, free flights between collisions are bounded, the resulting current J is proportional to the voltage difference E, that is, J=1/2 D*E+o(||E||), where D* is the diffusion matrix of a Lorentz particle moving freely without an electric field (see a mathematical proof). This formula agrees with Ohm's classical law and the Einstein relation. Here the more difficult model with an infinite horizon is investigated. It is found that infinite corridors between scatterers allow the particles (electrons) to move faster, resulting in an abnormal current (causing 'superconductivity'). More precisely, the current is now given by J=1/2 DE| log||E|| | + O(||E||), where D is the 'superdiffusion' matrix of a Lorentz particle moving freely without an electric field. This means that Ohm's law fails in this regime, but the Einstein relation (suitably interpreted) still holds. New results are also obtained for the infinite-horizon Lorentz gas without external fields, complementing recent studies by Szasz and Varju. Bibliography: 31 titles.
Anomalous current in periodic Lorentz gases with infinite horizon
International Nuclear Information System (INIS)
Dolgopyat, Dmitrii I; Chernov, Nikolai I
2009-01-01
Electric current is studied in a two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, that is, free flights between collisions are bounded, the resulting current J is proportional to the voltage difference E, that is, J=1/2 D*E+o(||E||), where D* is the diffusion matrix of a Lorentz particle moving freely without an electric field (see a mathematical proof). This formula agrees with Ohm's classical law and the Einstein relation. Here the more difficult model with an infinite horizon is investigated. It is found that infinite corridors between scatterers allow the particles (electrons) to move faster, resulting in an abnormal current (causing 'superconductivity'). More precisely, the current is now given by J=1/2 DE| log||E|| | + O(||E||), where D is the 'superdiffusion' matrix of a Lorentz particle moving freely without an electric field. This means that Ohm's law fails in this regime, but the Einstein relation (suitably interpreted) still holds. New results are also obtained for the infinite-horizon Lorentz gas without external fields, complementing recent studies by Szasz and Varju. Bibliography: 31 titles.
Guiding modes of semi-infinite nanowire and their dispersion character
International Nuclear Information System (INIS)
Sun, Yuming; Su, Yuehua; Dai, Zhenhong; Wang, Weitian
2014-01-01
Conventionally, the optical properties of finite semiconductor nanowires have been understood and explained in terms of an infinite nanowire. This work describes completely different photonic modes for a semi-finite nanowire based on a rigorous theoretical method, and the implications for the finite one. First, the special eigenvalue problem charactered by the end results in a distinctive mode spectrum for the semi-infinite dielectric nanowire. Meanwhile, the results show hybrid degenerate modes away from cutoff frequency, and transverse electric–transverse magnetic (TE–TM) degeneracy. Second, accompanying a different mode spectrum, a semi-finite nanowire also shows a distinctive dispersion relation compared to an infinite nanowire. Taking a semi-infinite, ZnO nanowire as an example, we find that the ℏω−k z space is not continuous in the interested photon energy window, implying that there is no uniform polariton dispersion relation for semi-infinite nanowire. Our method is shown correct through a field-reconstruction for a thin ZnO nanowire (55 nm in radius) and position determination of FP modes for a ZnO nanowire (200 nm in diameter). The results are of great significance to correctly understand the guiding and lasing mechanisms of semiconductor nanowires. (paper)
Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models
Martin Burda; Artem Prokhorov
2012-01-01
Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling scenarios. In economics, they have been particularly useful in estimating nonparametric distributions of latent variables. However, these models have been rarely applied in more than one dimension. Indeed, the multivariate case suffers from the curse of dimensionality, with a rapidly increas...
Infinite sets of conservation laws for linear and non-linear field equations
International Nuclear Information System (INIS)
Niederle, J.
1984-01-01
The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation
Mappings with closed range and finite dimensional linear spaces
International Nuclear Information System (INIS)
Iyahen, S.O.
1984-09-01
This paper looks at two settings, each of continuous linear mappings of linear topological spaces. In one setting, the domain space is fixed while the range space varies over a class of linear topological spaces. In the second setting, the range space is fixed while the domain space similarly varies. The interest is in when the requirement that the mappings have a closed range implies that the domain or range space is finite dimensional. Positive results are obtained for metrizable spaces. (author)
The Schrödinger–Robinson inequality from stochastic analysis on a complex Hilbert space
International Nuclear Information System (INIS)
Khrennikov, Andrei
2013-01-01
We explored the stochastic analysis on a complex Hilbert space to show that one of the cornerstones of quantum mechanics (QM), namely Heisenberg's uncertainty relation, can be derived in the classical probabilistic framework. We created a new mathematical representation of quantum averages: as averages with respect to classical random fields. The existence of a classical stochastic model matching with Heisenberg's uncertainty relation makes the connection between classical and quantum probabilistic models essentially closer. In real physical situations, random fields are valued in the L 2 -space. Hence, although we model QM and not QFT, the classical systems under consideration have an infinite number of degrees of freedom. And in our modeling, infinite-dimensional stochastic analysis is the basic mathematical tool. (comment)
Guide for the 2 infinities - the infinitely big and the infinitely small
International Nuclear Information System (INIS)
Armengaud, E.; Arnaud, N.; Aubourg, E.; Bassler, U.; Binetruy, P.; Bouquet, A.; Boutigny, D.; Brun, P.; Chassande-Mottin, E.; Chardin, G.; Coustenis, A.; Descotes-Genon, S.; Dole, H.; Drouart, A.; Elbaz, D.; Ferrando, Ph.; Glicenstein, J.F.; Giraud-Heraud, Y.; Halloin, H.; Kerhoas-Cavata, S.; De Kerret, H.; Klein, E.; Lachieze-Rey, M.; Lagage, P.O.; Langer, M.; Lebrun, F.; Lequeux, J.; Meheut, H.; Moniez, M.; Palanque-Delabrouille, N.; Paul, J.; Piquemal, F.; Polci, F.; Proust, D.; Richard, F.; Robert, J.L.; Rosnet, Ph.; Roudeau, P.; Royole-Degieux, P.; Sacquin, Y.; Serreau, J.; Shifrin, G.; Sida, J.L.; Smith, D.; Sordini, V.; Spiro, M.; Stolarczyk, Th.; Suomijdrvi, T.; Tagger, M.; Vangioni, E.; Vauclair, S.; Vial, J.C.; Viaud, B.; Vignaud, D.
2010-01-01
This book is to be read from both ends: one is dedicated to the path towards the infinitely big and the other to the infinitely small. Each path is made of a series of various subject entries illustrating important concepts or achievements in the quest for the understanding of the concerned infinity. For instance the part concerning the infinitely small includes entries like: quarks, Higgs bosons, radiation detection, Chooz neutrinos... while the part for the infinitely big includes: the universe, cosmic radiations, black matter, antimatter... and a series of experiments such as HESS, INTEGRAL, ANTARES, JWST, LOFAR, Planck, LSST, SOHO, Virgo, VLT, or XMM-Newton. This popularization work includes also an important glossary that explains scientific terms used in the entries. (A.C.)
Embedding of attitude determination in n-dimensional spaces
Bar-Itzhack, Itzhack Y.; Markley, F. Landis
1988-01-01
The problem of attitude determination in n-dimensional spaces is addressed. The proper parameters are found, and it is shown that not all three-dimensional methods have useful extensions to higher dimensions. It is demonstrated that Rodriguez parameters are conveniently extendable to other dimensions. An algorithm for using these parameters in the general n-dimensional case is developed and tested with a four-dimensional example. The correct mathematical description of angular velocities is addressed, showing that angular velocity in n dimensions cannot be represented by a vector but rather by a tensor of the second rank. Only in three dimensions can the angular velocity be described by a vector.
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
Selfdual strings and loop space Nahm equations
International Nuclear Information System (INIS)
Gustavsson, Andreas
2008-01-01
We give two independent arguments why the classical membrane fields should be take values in a loop algebra. The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations. The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as su(N) for any N) that satisfies the algebraic structure of the membrane theory
Space charge-limited emission studies using Coulomb's Law
Carr, Christopher G.
2004-01-01
Approved for Public Release; Distribution is Unlimited Child and Langmuir introduced a solution to space charge limited emission in an infinite area planar diode. The solution follows from starting with Poisson's equation, and requires solving a non-linear differential equation. This approach can also be applied to cylindrical and spherical geometries, but only for one-dimensional cases. By approaching the problem from Coulomb's law and applying the effect of an assumed charge distribution...
Dimensional expansion for the Ising limit of quantum field theory
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.
1993-01-01
A recently proposed technique, called dimensional expansion, uses the space-time dimension D as an expansion parameter to extract nonperturbative results in quantum field theory. Here we apply dimensional-expansion methods to examine the Ising limit of a self-interacting scalar field theory. We compute the first few coefficients in the dimensional expansion of γ 2n , the renormalized 2n-point Green's function at zero momentum, for n=2, 3, 4, and 5. Because the exact results for γ 2n are known at D=1 we can compare the predictions of the dimensional expansion at this value of D. We find typical accuracies of less than 5%. The radius of convergence of the dimensional expansion for γ 2n appears to be 2n/(n-1). As a function of the space-time dimension D, γ 2n appears to rise monotonically with increasing D and we conjecture that it becomes infinite at D=2n/(n-1). We presume that for values of D greater than this critical value γ 2n vanishes identically because the corresponding φ 2n scalar quantum field theory is free for D>2n/(n-1)
On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay
Directory of Open Access Journals (Sweden)
Fang Li
2012-01-01
Full Text Available Of concern is a class of nonlinear neutral fractional integrodifferential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. An example is given to illustrate the existence result.
Electromagnetic interactions in relativistic infinite component wave equations
International Nuclear Information System (INIS)
Gerry, C.C.
1979-01-01
The electromagnetic interactions of a composite system described by relativistic infinite-component wave equations are considered. The noncompact group SO(4,2) is taken as the dynamical group of the systems, and its unitary irreducible representations, which are infinite dimensional, are used to find the energy spectra and to specify the states of the systems. First the interaction mechanism is examined in the nonrelativistic SO(4,2) formulation of the hydrogen atom as a heuristic guide. A way of making a minimal relativistic generalization of the minimal ineractions in the nonrelativistic equation for the hydrogen atom is proposed. In order to calculate the effects of the relativistic minimal interactions, a covariant perturbation theory suitable for infinite-component wave equations, which is an algebraic and relativistic version of the Rayleigh-Schroedinger perturbation theory, is developed. The electric and magnetic polarizabilities for the ground state of the hydrogen atom are calculated. The results have the correct nonrelativistic limits. Next, the relativistic cross section of photon absorption by the atom is evaluated. A relativistic expression for the cross section of light scattering corresponding to the seagull diagram is derived. The Born amplitude is combusted and the role of spacelike solutions is discussed. Finally, internal electromagnetic interactions that give rise to the fine structure splittings, the Lamb shifts and the hyperfine splittings are considered. The spin effects are introduced by extending the dynamical group
A conceptual approach to approximate tree root architecture in infinite slope models
Schmaltz, Elmar; Glade, Thomas
2016-04-01
Vegetation-related properties - particularly tree root distribution and coherent hydrologic and mechanical effects on the underlying soil mantle - are commonly not considered in infinite slope models. Indeed, from a geotechnical point of view, these effects appear to be difficult to be reproduced reliably in a physically-based modelling approach. The growth of a tree and the expansion of its root architecture are directly connected with both intrinsic properties such as species and age, and extrinsic factors like topography, availability of nutrients, climate and soil type. These parameters control four main issues of the tree root architecture: 1) Type of rooting; 2) maximum growing distance to the tree stem (radius r); 3) maximum growing depth (height h); and 4) potential deformation of the root system. Geometric solids are able to approximate the distribution of a tree root system. The objective of this paper is to investigate whether it is possible to implement root systems and the connected hydrological and mechanical attributes sufficiently in a 3-dimensional slope stability model. Hereby, a spatio-dynamic vegetation module should cope with the demands of performance, computation time and significance. However, in this presentation, we focus only on the distribution of roots. The assumption is that the horizontal root distribution around a tree stem on a 2-dimensional plane can be described by a circle with the stem located at the centroid and a distinct radius r that is dependent on age and species. We classified three main types of tree root systems and reproduced the species-age-related root distribution with three respective mathematical solids in a synthetic 3-dimensional hillslope ambience. Thus, two solids in an Euclidian space were distinguished to represent the three root systems: i) cylinders with radius r and height h, whilst the dimension of latter defines the shape of a taproot-system or a shallow-root-system respectively; ii) elliptic
State-space dimensionality in short-memory hidden-variable theories
International Nuclear Information System (INIS)
Montina, Alberto
2011-01-01
Recently we have presented a hidden-variable model of measurements for a qubit where the hidden-variable state-space dimension is one-half the quantum-state manifold dimension. The absence of a short memory (Markov) dynamics is the price paid for this dimensional reduction. The conflict between having the Markov property and achieving the dimensional reduction was proved by Montina [A. Montina, Phys. Rev. A 77, 022104 (2008)] using an additional hypothesis of trajectory relaxation. Here we analyze in more detail this hypothesis introducing the concept of invertible process and report a proof that makes clearer the role played by the topology of the hidden-variable space. This is accomplished by requiring suitable properties of regularity of the conditional probability governing the dynamics. In the case of minimal dimension the set of continuous hidden variables is identified with an object living an N-dimensional Hilbert space whose dynamics is described by the Schroedinger equation. A method for generating the economical non-Markovian model for the qubit is also presented.
Linear measure functional differential equations with infinite delay
Monteiro, G. (Giselle Antunes); Slavík, A.
2014-01-01
We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.
Structure of Hilbert space operators
Jiang, Chunlan
2006-01-01
This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen-Douglas operators by using K -theory, complex geometry and operator algebra tools. Sample Chapter(s). Chapter 1: Background (153 KB). Contents: Jordan Standard Theorem and K 0 -Group; Approximate Jordan Theorem of Opera
Crystal manyfold universes in /AdS space
Kaloper, N.
2000-02-01
We derive crystal braneworld solutions, comprising of intersecting families of parallel /n+2-branes in a /4+n-dimensional /AdS space. Each family consists of alternating positive and negative tension branes. In the simplest case of exactly orthogonal families, there arise different crystals with unbroken /4D Poincaré invariance on the intersections, where our world can reside. A crystal can be finite along some direction, either because that direction is compact, or because it ends on a segment of /AdS bulk, or infinite, where the branes continue forever. If the crystal is interlaced by connected /3-branes directed both along the intersections and orthogonal to them, it can be viewed as an example of a Manyfold universe proposed recently by Arkani-Hamed, Dimopoulos, Dvali and the author. There are new ways for generating hierarchies, since the bulk volume of the crystal and the lattice spacing affect the /4D Planck mass. The low energy physics is sensitive to the boundary conditions in the bulk, and has to satisfy the same constraints discussed in the Manyfold universe. Phenomenological considerations favor either finite crystals, or crystals which are infinite but have broken translational invariance in the bulk. The most distinctive signature of the bulk structure is that the bulk gravitons are Bloch waves, with a band spectrum, which we explicitly construct in the case of a /5-dimensional theory.
Newton's law in braneworlds with an infinite extra dimension
Ito, Masato
2001-01-01
We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the wave function of gravity is described in terms of the Bessel functions of $(2+n/2)$-order and that estimate the correction to Newton's law. In particular, the Newton's law for $n=1$ can be exactly obtained.
Analysing Infinite-State Systems by Combining Equivalence Reduction and the Sweep-Line Method
DEFF Research Database (Denmark)
Mailund, Thomas
2002-01-01
The sweep-line method is a state space exploration method for on-the-fly verification aimed at systems exhibiting progress. Presence of progress in the system makes it possible to delete certain states during state space generation, which reduces the memory used for storing the states. Unfortunat......The sweep-line method is a state space exploration method for on-the-fly verification aimed at systems exhibiting progress. Presence of progress in the system makes it possible to delete certain states during state space generation, which reduces the memory used for storing the states....... Unfortunately, the same progress that is used to improve memory performance in state space exploration often leads to an infinite state space: The progress in the system is carried over to the states resulting in infinitely many states only distinguished through the progress. A finite state space can...... property essential for the sweep-line method. We evaluate the new method on two case studies, showing significant improvements in performance, and we briefly discuss the new method in the context of Timed Coloured Petri Nets, where the “increasing global time” semantics can be exploited for more efficient...
The algebraic size of the family of injective operators
Directory of Open Access Journals (Sweden)
Bernal-González Luis
2017-01-01
Full Text Available In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.
Heyl, Markus; Vojta, Matthias
2015-09-01
In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational-invariant and disordered systems. As a concrete application, we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems, we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.
CSL Model Checking Algorithms for Infinite-state Structured Markov chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Raskin, J.-F.; Thiagarajan, P.S.
2007-01-01
Jackson queueing networks (JQNs) are a very general class of queueing networks that find their application in a variety of settings. The state space of the continuous-time Markov chain (CTMC) that underlies such a JQN, is highly structured, however, of infinite size in as many dimensions as there
Heat transfer in a Couette flow with part of the space between the plates filled with porous medium
International Nuclear Information System (INIS)
Carrocci, L.R.; Liu, C.Y.; Ismail, K.A.R.
1982-01-01
The effect of various parameters in the temperature profile is shown under boundary conditions for the Couette flow between infinite plates with part of the space filled with porous medium. The parameters observed are: pressure gradient, permeability, the non-dimensional product PE (Prandtl number x Eckert number), the relation between the thermal conductibility coefficient between porous region and pure fluid, and finally the non-dimensional product PR (Prandtl number x Reynolds number). (E.G.) [pt
Modeling and control of flexible space structures
Wie, B.; Bryson, A. E., Jr.
1981-01-01
The effects of actuator and sensor locations on transfer function zeros are investigated, using uniform bars and beams as generic models of flexible space structures. It is shown how finite element codes may be used directly to calculate transfer function zeros. The impulse response predicted by finite-dimensional models is compared with the exact impulse response predicted by the infinite dimensional models. It is shown that some flexible structures behave as if there were a direct transmission between actuator and sensor (equal numbers of zeros and poles in the transfer function). Finally, natural damping models for a vibrating beam are investigated since natural damping has a strong influence on the appropriate active control logic for a flexible structure.
Vector calculus in non-integer dimensional space and its applications to fractal media
Tarasov, Vasily E.
2015-02-01
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.
Four Dimensional Trace Space Measurement
Energy Technology Data Exchange (ETDEWEB)
Hernandez, M.
2005-02-10
Future high energy colliders and FELs (Free Electron Lasers) such as the proposed LCLS (Linac Coherent Light Source) at SLAC require high brightness electron beams. In general a high brightness electron beam will contain a large number of electrons that occupy a short longitudinal duration, can be focused to a small transverse area while having small transverse divergences. Therefore the beam must have a high peak current and occupy small areas in transverse phase space and so have small transverse emittances. Additionally the beam should propagate at high energy and have a low energy spread to reduce chromatic effects. The requirements of the LCLS for example are pulses which contain 10{sup 10} electrons in a temporal duration of 10 ps FWHM with projected normalized transverse emittances of 1{pi} mm mrad[1]. Currently the most promising method of producing such a beam is the RF photoinjector. The GTF (Gun Test Facility) at SLAC was constructed to produce and characterize laser and electron beams which fulfill the LCLS requirements. Emittance measurements of the electron beam at the GTF contain evidence of strong coupling between the transverse dimensions of the beam. This thesis explores the effects of this coupling on the determination of the projected emittances of the electron beam. In the presence of such a coupling the projected normalized emittance is no longer a conserved quantity. The conserved quantity is the normalized full four dimensional phase space occupied by the beam. A method to determine the presence and evaluate the strength of the coupling in emittance measurements made in the laboratory is developed. A method to calculate the four dimensional volume the beam occupies in phase space using quantities available in the laboratory environment is also developed. Results of measurements made of the electron beam at the GTF that demonstrate these concepts are presented and discussed.
Stability of plane wave solutions of the two-space-dimensional nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Martin, D.U.; Yuen, H.C.; Saffman, P.G.
1980-01-01
The stability of plane, periodic solutions of the two-dimensional nonlinear Schroedinger equation to infinitesimal, two-dimensional perturbation has been calculated and verified numerically. For standing wave disturbances, instability is found for both odd and even modes; as the period of the unperturbed solution increases, the instability associated with the odd modes remains but that associated with the even mode disappears, which is consistent with the results of Zakharov and Rubenchik, Saffman and Yuen and Ablowitz and Segur on the stability of solitons. In addition, we have identified travelling wave instabilities for the even mode perturbations which are absent in the long-wave limit. Extrapolation to the case of an unperturbed solution with infinite period suggests that these instabilities may also be present for the soliton. In other words, the soliton is unstable to odd, standing-wave perturbations, and very likely also to even, travelling-wave perturbations. (orig.)
Six-dimensional real and reciprocal space small-angle X-ray scattering tomography.
Schaff, Florian; Bech, Martin; Zaslansky, Paul; Jud, Christoph; Liebi, Marianne; Guizar-Sicairos, Manuel; Pfeiffer, Franz
2015-11-19
When used in combination with raster scanning, small-angle X-ray scattering (SAXS) has proven to be a valuable imaging technique of the nanoscale, for example of bone, teeth and brain matter. Although two-dimensional projection imaging has been used to characterize various materials successfully, its three-dimensional extension, SAXS computed tomography, poses substantial challenges, which have yet to be overcome. Previous work using SAXS computed tomography was unable to preserve oriented SAXS signals during reconstruction. Here we present a solution to this problem and obtain a complete SAXS computed tomography, which preserves oriented scattering information. By introducing virtual tomography axes, we take advantage of the two-dimensional SAXS information recorded on an area detector and use it to reconstruct the full three-dimensional scattering distribution in reciprocal space for each voxel of the three-dimensional object in real space. The presented method could be of interest for a combined six-dimensional real and reciprocal space characterization of mesoscopic materials with hierarchically structured features with length scales ranging from a few nanometres to a few millimetres--for example, biomaterials such as bone or teeth, or functional materials such as fuel-cell or battery components.
Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices
Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah
2018-03-01
The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.
Infinite-genus surfaces and the universal Grassmannian
Davis, Simon
1995-01-01
Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying the inclusion of these surfaces in the Grassmannian. In particular, a subset of the class of $O_{HD}$ surfaces can be identified with a subset of the Grassmannian. The concept of flux through the ideal boundary is used to study the connection bet...
International Nuclear Information System (INIS)
Nishiyama, Seiya; Providencia, Joao da; Komatsu, Takao
2007-01-01
To go beyond perturbative method in terms of variables of collective motion, using infinite-dimensional fermions, we have aimed to construct the self-consistent-field (SCF) theory, i.e., time dependent Hartree-Fock theory on associative affine Kac-Moody algebras along the soliton theory. In this paper, toward such an ultimate goal we will reconstruct a theoretical frame for a υ (external parameter)-dependent SCF method to describe more precisely the dynamics on the infinite-dimensional fermion Fock space. An infinite-dimensional fermion operator is introduced through Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent and a Υ-periodic potential. As an illustration, we derive explicit expressions for the Laurent coefficients of soliton solutions for sl n and for su n on infinite-dimensional Grassmannian. The associative affine Kac-Moody algebras play a crucial role to determine the dynamics on the infinite-dimensional fermion Fock space
Socolovsky, Eduardo A.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The cosine or correlation measures of similarity used to cluster high dimensional data are interpreted as projections, and the orthogonal components are used to define a complementary dissimilarity measure to form a similarity-dissimilarity measure pair. Using a geometrical approach, a number of properties of this pair is established. This approach is also extended to general inner-product spaces of any dimension. These properties include the triangle inequality for the defined dissimilarity measure, error estimates for the triangle inequality and bounds on both measures that can be obtained with a few floating-point operations from previously computed values of the measures. The bounds and error estimates for the similarity and dissimilarity measures can be used to reduce the computational complexity of clustering algorithms and enhance their scalability, and the triangle inequality allows the design of clustering algorithms for high dimensional distributed data.
Semi-infinite assignment and transportation games
Timmer, Judith B.; Sánchez-Soriano, Joaqu´ın; Llorca, Navidad; Tijs, Stef; Goberna, Miguel A.; López, Marco A.
2001-01-01
Games corresponding to semi-infinite transportation and related assignment situations are studied. In a semi-infinite transportation situation, one aims at maximizing the profit from the transportation of a certain good from a finite number of suppliers to an infinite number of demanders. An
An existence theorem for a type of functional differential equation with infinite delay
Izsak, F.
We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.
Topological properties of function spaces $C_k(X,2)$ over zero-dimensional metric spaces $X$
Gabriyelyan, S.
2015-01-01
Let $X$ be a zero-dimensional metric space and $X'$ its derived set. We prove the following assertions: (1) the space $C_k(X,2)$ is an Ascoli space iff $C_k(X,2)$ is $k_\\mathbb{R}$-space iff either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (2) $C_k(X,2)$ is a $k$-space iff either $X$ is a topological sum of a Polish locally compact space and a discrete space or $X$ is not locally compact but $X'$ is compact, (3) $C_k(X,2)$ is a sequential space iff $X$ is a Pol...
International Nuclear Information System (INIS)
Terauchi, Masami; Takahashi, Mariko; Tanaka, Michiyoshi
1994-01-01
The convergent-beam electron diffraction (CBED) method for determining three-dimensional space groups is extended to the determination of the (3 + 1)-dimensional space groups for one-dimensional incommensurately modulated crystals. It is clarified than an approximate dynamical extinction line appears in the CBED discs of the reflections caused by an incommensurate modulation. The extinction enables the space-group determination of the (3 + 1)-dimensional crystals or the one-dimensional incommensurately modulated crystals. An example of the dynamical extinction line is shown using an incommensurately modulated crystal of Sr 2 Nb 2 O 7 . Tables of the dynamical extinction lines appearing in CBED patterns are given for all the (3 + 1)-dimensional space groups of the incommensurately modulated crystal. (orig.)
Three-dimensional space: locomotory style explains memory differences in rats and hummingbirds.
Flores-Abreu, I Nuri; Hurly, T Andrew; Ainge, James A; Healy, Susan D
2014-06-07
While most animals live in a three-dimensional world, they move through it to different extents depending on their mode of locomotion: terrestrial animals move vertically less than do swimming and flying animals. As nearly everything we know about how animals learn and remember locations in space comes from two-dimensional experiments in the horizontal plane, here we determined whether the use of three-dimensional space by a terrestrial and a flying animal was correlated with memory for a rewarded location. In the cubic mazes in which we trained and tested rats and hummingbirds, rats moved more vertically than horizontally, whereas hummingbirds moved equally in the three dimensions. Consistent with their movement preferences, rats were more accurate in relocating the horizontal component of a rewarded location than they were in the vertical component. Hummingbirds, however, were more accurate in the vertical dimension than they were in the horizontal, a result that cannot be explained by their use of space. Either as a result of evolution or ontogeny, it appears that birds and rats prioritize horizontal versus vertical components differently when they remember three-dimensional space.
Dirac equation in 5- and 6-dimensional curved space-time manifolds
International Nuclear Information System (INIS)
Vladimirov, Yu.S.; Popov, A.D.
1984-01-01
The program of plotting unified multidimensional theory of gravitation, electromagnetism and electrically charged matter with transition from 5-dimensional variants to 6-dimensional theory possessing signature (+----+) is developed. For recording the Dirac equation in 5- and 6-dimensional curved space-time manifolds the tetrad formalism and γ-matrix formulation of the General Relativity Theory are used. It is shown that the 6-dimensional theory case unifies the two private cases of 5-dimensional theory and corresponds to two possibilities of the theory developed by Kadyshevski
Quantum walks with infinite hitting times
International Nuclear Information System (INIS)
Krovi, Hari; Brun, Todd A.
2006-01-01
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition, which for discrete time quantum walks is that the degeneracy of the evolution operator be greater than the degree of the graph. The set of initial states which give an infinite hitting time form a subspace. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. In the case of the discrete walk, if this condition is satisfied the walk will have infinite hitting times for any choice of a coin operator, and we give a class of graphs with infinite hitting times for any choice of coin. Hitting times are not very well defined for continuous time quantum walks, but we show that the idea of infinite hitting-time walks naturally extends to the continuous time case as well
Use of one-dimensional Cosserat theory to study instability in a viscous liquid jet
International Nuclear Information System (INIS)
Bogy, D.B.
1978-01-01
The problem of the instability of an incompressible viscous liquid jet is considered within the context of one-dimensional Cosserat equations. Linear stability analyses are performed for both the infinite and semi-infinite jets. The results obtained for the inviscid case are compared with the corresponding results derived from ideal fluid equations. They are also compared with recent results by other authors obtained from a different set of one-dimensional jet equations. Solutions are also obtained, within the framework of the linearized theory, to the jet break-up problems formulated as an initial-value problem for the infinite jet and as a boundary-value problem for the semi-infinite jet
On infinite regular and chiral maps
Arredondo, John A.; Valdez, Camilo Ramírez y Ferrán
2015-01-01
We prove that infinite regular and chiral maps take place on surfaces with at most one end. Moreover, we prove that an infinite regular or chiral map on an orientable surface with genus can only be realized on the Loch Ness monster, that is, the topological surface of infinite genus with one end.
International Nuclear Information System (INIS)
Sprung, D.W.L.
1975-01-01
This paper is a brief review of those aspects of the effective interaction problem that can be grouped under the heading of infinite partial summations of the perturbation series. After a brief mention of the classic examples of infinite summations, the author turns to the effective interaction problem for two extra core particles. Their direct interaction is summed to produce the G matrix, while their indirect interaction through the core is summed in a variety of ways under the heading of core polarization. (orig./WL) [de
Extremal rotating black holes in the near-horizon limit: Phase space and symmetry algebra
Directory of Open Access Journals (Sweden)
G. Compère
2015-10-01
Full Text Available We construct the NHEG phase space, the classical phase space of Near-Horizon Extremal Geometries with fixed angular momenta and entropy, and with the largest symmetry algebra. We focus on vacuum solutions to d dimensional Einstein gravity. Each element in the phase space is a geometry with SL(2,R×U(1d−3 isometries which has vanishing SL(2,R and constant U(1 charges. We construct an on-shell vanishing symplectic structure, which leads to an infinite set of symplectic symmetries. In four spacetime dimensions, the phase space is unique and the symmetry algebra consists of the familiar Virasoro algebra, while in d>4 dimensions the symmetry algebra, the NHEG algebra, contains infinitely many Virasoro subalgebras. The nontrivial central term of the algebra is proportional to the black hole entropy. The conserved charges are given by the Fourier decomposition of a Liouville-type stress-tensor which depends upon a single periodic function of d−3 angular variables associated with the U(1 isometries. This phase space and in particular its symmetries can serve as a basis for a semiclassical description of extremal rotating black hole microstates.
Manifold learning to interpret JET high-dimensional operational space
International Nuclear Information System (INIS)
Cannas, B; Fanni, A; Pau, A; Sias, G; Murari, A
2013-01-01
In this paper, the problem of visualization and exploration of JET high-dimensional operational space is considered. The data come from plasma discharges selected from JET campaigns from C15 (year 2005) up to C27 (year 2009). The aim is to learn the possible manifold structure embedded in the data and to create some representations of the plasma parameters on low-dimensional maps, which are understandable and which preserve the essential properties owned by the original data. A crucial issue for the design of such mappings is the quality of the dataset. This paper reports the details of the criteria used to properly select suitable signals downloaded from JET databases in order to obtain a dataset of reliable observations. Moreover, a statistical analysis is performed to recognize the presence of outliers. Finally data reduction, based on clustering methods, is performed to select a limited and representative number of samples for the operational space mapping. The high-dimensional operational space of JET is mapped using a widely used manifold learning method, the self-organizing maps. The results are compared with other data visualization methods. The obtained maps can be used to identify characteristic regions of the plasma scenario, allowing to discriminate between regions with high risk of disruption and those with low risk of disruption. (paper)
Rare events in finite and infinite dimensions
Reznikoff, Maria G.
Thermal noise introduces stochasticity into deterministic equations and makes possible events which are never seen in the zero temperature setting. The driving force behind the thesis work is a desire to bring analysis and probability to bear on a class of relevant and intriguing physical problems, and in so doing, to allow applications to drive the development of new mathematical theory. The unifying theme is the study of rare events under the influence of small, random perturbations, and the manifold mathematical problems which ensue. In the first part, we apply large deviation theory and prefactor estimates to a coherent rotation micromagnetic model in order to analyze thermally activated magnetic switching. We consider recent physical experiments and the mathematical questions "asked" by them. A stochastic resonance type phenomenon is discovered, leading to the definition of finite temperature astroids. Non-Arrhenius behavior is discussed. The analysis is extended to ramped astroids. In addition, we discover that for low damping and ultrashort pulses, deterministic effects can override thermal effects, in accord with very recent ultrashort pulse experiments. Even more interesting, perhaps, is the study of large deviations in the infinite dimensional context, i.e. in spatially extended systems. Inspired by recent numerical investigations, we study the stochastically perturbed Allen Cahn and Cahn Hilliard equations. For the Allen Cahn equation, we study the action minimization problem (a deterministic variational problem) and prove the action scaling in four parameter regimes, via upper and lower bounds. The sharp interface limit is studied. We formally derive a reduced action functional which lends insight into the connection between action minimization and curvature flow. For the Cahn Hilliard equation, we prove upper and lower bounds for the scaling of the energy barrier in the nucleation and growth regime. Finally, we consider rare events in large or infinite
Karve, Pranav M.
2016-12-28
We discuss a methodology for computing the optimal spatio-temporal characteristics of surface wave sources necessary for delivering wave energy to a targeted subsurface formation. The wave stimulation is applied to the target formation to enhance the mobility of particles trapped in its pore space. We formulate the associated wave propagation problem for three-dimensional, heterogeneous, semi-infinite, elastic media. We use hybrid perfectly matched layers at the truncation boundaries of the computational domain to mimic the semi-infiniteness of the physical domain of interest. To recover the source parameters, we define an inverse source problem using the mathematical framework of constrained optimization and resolve it by employing a reduced-space approach. We report the results of our numerical experiments attesting to the methodology\\'s ability to specify the spatio-temporal description of sources that maximize wave energy delivery. Copyright © 2016 John Wiley & Sons, Ltd.
Quantum vacuum energy in two dimensional space-times
International Nuclear Information System (INIS)
Davies, P.C.W.; Fulling, S.A.
1977-01-01
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed. (author)
Quantum vacuum energy in two dimensional space-times
Energy Technology Data Exchange (ETDEWEB)
Davies, P C.W.; Fulling, S A [King' s Coll., London (UK). Dept. of Mathematics
1977-04-21
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed.
How the flip target behaves in four-dimensional space
International Nuclear Information System (INIS)
Antillon, A.; Kats, J.
1985-01-01
We use available coupling theory for understanding how a flip target in a 4-dimensional phase space reduces a gaussian beam of particles. Experimental evidence at the AGS can be qualitatively explained by this theory
Quantum infinite square well with an oscillating wall
International Nuclear Information System (INIS)
Glasser, M.L.; Mateo, J.; Negro, J.; Nieto, L.M.
2009-01-01
A linear matrix equation is considered for determining the time dependent wave function for a particle in a one-dimensional infinite square well having one moving wall. By a truncation approximation, whose validity is checked in the exactly solvable case of a linearly contracting wall, we examine the cases of a simple harmonically oscillating wall and a non-harmonically oscillating wall for which the defining parameters can be varied. For the latter case, we examine in closer detail the dependence on the frequency changes, and we find three regimes: an adiabatic behabiour for low frequencies, a periodic one for high frequencies, and a chaotic behaviour for an intermediate range of frequencies.
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Directory of Open Access Journals (Sweden)
George Isac
2004-01-01
Full Text Available In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.
Quantum interest in (3+1)-dimensional Minkowski space
International Nuclear Information System (INIS)
Abreu, Gabriel; Visser, Matt
2009-01-01
The so-called 'quantum inequalities', and the 'quantum interest conjecture', use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a timelike observer, potentially preventing the existence of exotic phenomena such as 'Alcubierre warp drives' or 'traversable wormholes'. Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or nonexistence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple variational proof of one version of the quantum interest conjecture in (3+1)-dimensional Minkowski space.
Method of solving conformal models in D-dimensional space I
International Nuclear Information System (INIS)
Fradkin, E.S.; Palchik, M.Y.
1996-01-01
We study the Hilbert space of conformal field theory in D-dimensional space. The latter is shown to have model-independent structure. The states of matter fields and gauge fields form orthogonal subspaces. The dynamical principle fixing the choice of model may be formulated either in each of these subspaces or in their direct sum. In the latter case, gauge interactions are necessarily present in the model. We formulate the conditions specifying the class of models where gauge interactions are being neglected. The anomalous Ward identities are derived. Different values of anomalous parameters (D-dimensional analogs of a central charge, including operator ones) correspond to different models. The structure of these models is analogous to that of 2-dimensional conformal theories. Each model is specified by D-dimensional analog of null vector. The exact solutions of the simplest models of this type are examined. It is shown that these models are equivalent to Lagrangian models of scalar fields with a triple interaction. The values of dimensions of such fields are calculated, and the closed sets of differential equations for higher Green functions are derived. Copyright copyright 1996 Academic Press, Inc
Hyper dimensional phase-space solver and its application to laser-matter
Energy Technology Data Exchange (ETDEWEB)
Kondoh, Yoshiaki; Nakamura, Takashi; Yabe, Takashi [Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, Kanagawa (Japan)
2000-03-01
A new numerical scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space is described. At each time step, the distribution function and its first derivatives are advected in phase space by the Cubic Interpolated Propagation (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are not required. The scheme guarantees the exact conservation of the mass. The numerical results show good agreement with the theory. Even if we reduce the number of grid points in the v-direction, the scheme still gives stable, accurate and reasonable results with memory storage comparable to particle simulations. Owing to this fact, the scheme has succeeded to be generalized in a straightforward way to deal with the six-dimensional, or full-dimensional problems. (author)
Hyper dimensional phase-space solver and its application to laser-matter
International Nuclear Information System (INIS)
Kondoh, Yoshiaki; Nakamura, Takashi; Yabe, Takashi
2000-01-01
A new numerical scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space is described. At each time step, the distribution function and its first derivatives are advected in phase space by the Cubic Interpolated Propagation (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are not required. The scheme guarantees the exact conservation of the mass. The numerical results show good agreement with the theory. Even if we reduce the number of grid points in the v-direction, the scheme still gives stable, accurate and reasonable results with memory storage comparable to particle simulations. Owing to this fact, the scheme has succeeded to be generalized in a straightforward way to deal with the six-dimensional, or full-dimensional problems. (author)
Elasticity of fractal materials using the continuum model with non-integer dimensional space
Tarasov, Vasily E.
2015-01-01
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.
''Free-space'' boundary conditions for the time-dependent wave equation
International Nuclear Information System (INIS)
Lindman, E.L.
1975-01-01
Boundary conditions for the discrete wave equation which act like an infinite region of free space in contact with the computational region can be constructed using projection operators. Propagating and evanescent waves coming from within the computational region generate no reflected waves as they cross the boundary. At the same time arbitrary waves may be launched into the computational region. Well known projection operators for one-dimensional waves may be used for this purpose in one dimension. Extensions of these operators to higher dimensions along with numerically efficient approximations to them are described for higher-dimensional problems. The separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics
The nominalized infinitive in French : structure and change
Directory of Open Access Journals (Sweden)
Petra Sleeman
2010-01-01
Full Text Available Many European languages have both nominal and verbal nominalized infinitives. They differ, however, in the degree to which the nominalized infinitives possess nominal and verbal properties. In this paper, nominalized infinitives in French are analyzed. It is shown that, whereas Old French was like other Romance languages in possessing both nominal and verbal nominalized infinitives, Modern French differs parametrically from other Romance languages in not having verbal infinitives and in allowing nominal infinitives only in a scientific style of speech. An analysis is proposed, within a syntactic approach to morphology. that tries to account for the loss of the verbal properties of the nominalized infinitive in French. It is proposed that the loss results from a change in word order (the loss of the OV word order in favor of the VO word order and a change in the morphological analysis of the nominalized infinitive: instead of a zero suffix analysis, a derivational analysis was adopted by the speakers of French. It is argued that the derivational analysis restricted nominalization to Vo, which made nominalization of infinitives less ìverbalî than in other Romance languages
Semi-infinite fractional programming
Verma, Ram U
2017-01-01
This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research envi...
A covariant form of the Maxwell's equations in four-dimensional spaces with an arbitrary signature
International Nuclear Information System (INIS)
Lukac, I.
1991-01-01
The concept of duality in the four-dimensional spaces with the arbitrary constant metric is strictly mathematically formulated. A covariant model for covariant and contravariant bivectors in this space based on three four-dimensional vectors is proposed. 14 refs
Jia, Chen
2017-09-01
Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.
Ambiguities about infinite nuclear matter
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1978-01-01
Exact solutions of the harmonic-oscillator and infinite hyperspherical well are given for the ground state of a infinitely heavy (N=Z) nucleus. The density of matter is a steadily decreasing function. The kinetic energy per particle is 12% smaller than the one predicted by the Fermi sea
Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms
Lawn , Marie-Amélie; Roth , Julien
2011-01-01
9 pages; We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well ...
International Nuclear Information System (INIS)
Guenther, Uwe; Zhuk, Alexander; Bezerra, Valdir B; Romero, Carlos
2005-01-01
We study multi-dimensional gravitational models with scalar curvature nonlinearities of types R -1 and R 4 . It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with a warped product structure. Special attention has been paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the R -1 model that configurations with stabilized extra dimensions do not provide a late-time acceleration (they are AdS), whereas the solution branch which allows for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R 4 model, we obtain that the stability region in parameter space depends on the total dimension D = dim(M) of the higher dimensional spacetime M. For D > 8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D 4 model
International Nuclear Information System (INIS)
Corti, D.S.; Debenedetti, P.G.
1998-01-01
The rigorous statistical mechanics of metastability requires the imposition of internal constraints that prevent access to regions of phase space corresponding to inhomogeneous states. We derive exactly the Helmholtz energy and equation of state of the one-dimensional hard rod fluid under the influence of an internal constraint that places an upper bound on the distance between nearest-neighbor rods. This type of constraint is relevant to the suppression of boiling in a superheated liquid. We determine the effects of this constraint upon the thermophysical properties and internal structure of the hard rod fluid. By adding an infinitely weak and infinitely long-ranged attractive potential to the hard core, the fluid exhibits a first-order vapor-liquid transition. We determine exactly the equation of state of the one-dimensional superheated liquid and show that it exhibits metastable phase equilibrium. We also derive statistical mechanical relations for the equation of state of a fluid under the action of arbitrary constraints, and show the connection between the statistical mechanics of constrained and unconstrained ensembles. copyright 1998 The American Physical Society
Statistical mechanical analysis of (1 + ∞) dimensional disordered systems
International Nuclear Information System (INIS)
Skantzos, Nikolaos Stavrou
2001-01-01
Valuable insight into the theory of disordered systems and spin-glasses has been offered by two classes of exactly solvable models: one-dimensional models and mean-field (infinite-range) ones, which, each carry their own specific techniques and restrictions. Both classes of models are now considered as 'exactly solvable' in the sense that in the thermodynamic limit the partition sum can been carried out analytically and the average over the disorder can be performed using methods which are well understood. In this thesis I study equilibrium properties of spin systems with a combination of one-dimensional short- and infinite-range interactions. I find that such systems, under either synchronous or asynchronous spin dynamics, and even in the absence of disorder, lead to phase diagrams with first-order transitions and regions with a multiple number of locally stable states. I then proceed to the study of recurrent neural network models with (1+∞)-dimensional interactions, and find that the competing short- and long-range forces lead to highly complex phase diagrams and that unlike infinite-range (Hopfield-type) models these phase diagrams depend crucially on the number of patterns stored, even away from saturation. To solve the statics of such models for the case of synchronous dynamics I first make a detour to solve the synchronous counterpart of the one-dimensional random-field Ising model, where I prove rigorously that the physics of the two random-field models (synchronous vs. sequential) becomes asymptotically the same, leading to an extensive ground state entropy and an infinite hierarchy of discontinuous transitions close to zero temperature. Finally, I propose and solve the statics of a spin model for the prediction of secondary structure in random hetero-polymers (which are considered as the natural first step to the study of real proteins). The model lies in the class of (1+∞)-dimensional disordered systems as a consequence of having steric- and hydrogen
Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces
International Nuclear Information System (INIS)
Arai, A.
1985-01-01
We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)
The Infinitive Marker across Scandinavian
DEFF Research Database (Denmark)
Christensen, Ken Ramshøj
2007-01-01
In this paper I argue that the base-position of the infinitive marker in the Scandinavian languages and English share a common origin site. It is inserted as the top-most head in the VP-domain. The cross-linguistic variation in the syntactic distribution of the infinitive marker can be accounted...
Order and chaos in the one-dimensional ϕ4 model: N-dependence and the Second Law of Thermodynamics
Hoover, William Graham; Aoki, Kenichiro
2017-08-01
We revisit the equilibrium one-dimensional ϕ4 model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit positive Lyapunov exponents! The periodic orbits confine every particle in a periodic chain to trace out either the same or a mirror-image trajectory in its two-dimensional phase space. These ;computationally stable; sets of pairs of single-particle orbits are either symmetric or antisymmetric to the very last computational bit. In such a periodic chain the odd-numbered and even-numbered particles' coordinates and momenta are either identical or differ only in sign. ;Positive Lyapunov exponents; can and do result if an infinitesimal perturbation breaking a perfect two-dimensional antisymmetry is introduced so that the motion expands into a four-dimensional phase space. In that extended space a positive exponent results. We formulate a standard initial condition for the investigation of the microcanonical chaotic number dependence of the model. We speculate on the uniqueness of the model's chaotic sea and on the connection of such collections of deterministic and time-reversible states to the Second Law of Thermodynamics.
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
Hărăguş-Courcelle, M.; Schneider, G.
We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.
Three-dimensional space charge distribution measurement in electron beam irradiated PMMA
International Nuclear Information System (INIS)
Imaizumi, Yoichi; Suzuki, Ken; Tanaka, Yasuhiro; Takada, Tatsuo
1996-01-01
The localized space charge distribution in electron beam irradiated PMMA was investigated using pulsed electroacoustic method. Using a conventional space charge measurement system, the distribution only in the depth direction (Z) can be measured assuming the charges distributed uniformly in the horizontal (X-Y) plane. However, it is difficult to measure the distribution of space charge accumulated in small area. Therefore, we have developed the new system to measure the three-dimensional space charge distribution using pulsed electroacoustic method. The system has a small electrode with a diameter of 1mm and a motor-drive X-Y stage to move the sample. Using the data measured at many points, the three-dimensional distribution were obtained. To estimate the system performance, the electron beam irradiated PMMA was used. The electron beam was irradiated from transmission electron microscope (TEM). The depth of injected electron was controlled using the various metal masks. The measurement results were compared with theoretically calculated values of electron range. (author)
Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory
Riello, Aldo
2018-01-01
I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.
Properties of semi-infinite nuclei
International Nuclear Information System (INIS)
El-Jaick, L.J.; Kodama, T.
1976-04-01
Several relations among density distributions and energies of semi-infinite and infinite nuclei are iventigated in the framework of Wilets's statistical model. The model is shown to be consistent with the theorem of surface tension given by Myers and Swiatecki. Some numerical results are shown by using an appropriate nuclear matter equation of state
Directory of Open Access Journals (Sweden)
Meili Li
2015-01-01
Full Text Available The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.
Geodesics on a hot plate: an example of a two-dimensional curved space
International Nuclear Information System (INIS)
Erkal, Cahit
2006-01-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion
Geodesics on a hot plate: an example of a two-dimensional curved space
Energy Technology Data Exchange (ETDEWEB)
Erkal, Cahit [Department of Geology, Geography, and Physics, University of Tennessee, Martin, TN 38238 (United States)
2006-07-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion.
Directory of Open Access Journals (Sweden)
L. Z. Wu
2017-01-01
Full Text Available Rainfall infiltration into an unsaturated region of the earth’s surface is a pervasive natural phenomenon. During the rainfall-induced seepage process, the soil skeleton can deform and the permeability can change with the water content in the unsaturated porous medium. A coupled water infiltration and deformation formulation is used to examine a problem related to the mechanics of a two-dimensional region of semi-infinite extent. The van Genuchten model is used to represent the soil-water characteristic curve. The model, incorporating coupled infiltration and deformation, was developed to resolve the coupled problem in a semi-infinite domain based on numerical methods. The numerical solution is verified by the analytical solution when the coupled effects in an unsaturated medium of semi-infinite extent are considered. The computational results show that a numerical procedure can be employed to examine the semi-infinite unsaturated seepage incorporating coupled water infiltration and deformation. The analysis indicates that the coupling effect is significantly influenced by the boundary conditions of the problem and varies with the duration of water infiltration.
On obtaining classical mechanics from quantum mechanics
International Nuclear Information System (INIS)
Date, Ghanashyam
2007-01-01
Constructing a classical mechanical system associated with a given quantum-mechanical one entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations. The Hilbert space of any quantum-mechanical system naturally has the structure of an infinite-dimensional symplectic manifold ('quantum phase space'). There is also a systematic, quotienting procedure which imparts a bundle structure to the quantum phase space and extracts a classical phase space as the base space. This works straightforwardly when the Hilbert space carries weakly continuous representation of the Heisenberg group and one recovers the linear classical phase space R 2N . We report on how the procedure also allows extraction of nonlinear classical phase spaces and illustrate it for Hilbert spaces being finite dimensional (spin-j systems), infinite dimensional but separable (particle on a circle) and infinite dimensional but non-separable (polymer quantization). To construct a corresponding classical dynamics, one needs to choose a suitable section and identify an effective Hamiltonian. The effective dynamics mirrors the quantum dynamics provided the section satisfies conditions of semiclassicality and tangentiality
Exotic distributions of rigid unit modes in the reciprocal spaces of framework aluminosilicates
International Nuclear Information System (INIS)
Dove, Martin T; Pryde, Alexandra K A; Heine, Volker; Hammonds, Kenton D
2007-01-01
Until recently it was assumed that rigid unit modes, defined as the zero-frequency solutions to the dynamical equations for an infinite framework of rigid corner-linked tetrahedra, were confined to a small set of normal modes with wavevectors on lines or planes of special symmetry in reciprocal space. Using a search method that explores the full three-dimensional reciprocal space, we have located rigid unit modes with wavevectors on exotic curved surfaces in reciprocal space for a range of silicate minerals. This has led to the realization that the crystal structures of these minerals contain rather more topological floppiness than had previously been realized. The origin of the exotic RUM surfaces remains to be understood
Intertwined Hamiltonians in two-dimensional curved spaces
International Nuclear Information System (INIS)
Aghababaei Samani, Keivan; Zarei, Mina
2005-01-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle
Infinite Grassmannian and moduli space of G-bundles
International Nuclear Information System (INIS)
Kumar, S.; Ramanathan, A.
1993-03-01
Let C be a smooth irreducible projective curve and G a simply connected simple affine algebraic group of C. We study in this paper the relationship between the space of vacua defined in Conformal Field Theory and the space of sections of a line bundle on the moduli space of G-bundles over C. (author). 33 refs
One-dimensional super Calabi-Yau manifolds and their mirrors
Energy Technology Data Exchange (ETDEWEB)
Noja, S. [Dipartimento di Matematica, Università degli Studi di Milano,Via Saldini 50, I-20133 Milano (Italy); Cacciatori, S.L. [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy); Piazza, F. Dalla [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); Marrani, A. [Centro Studi e Ricerche ‘Enrico Fermi’,Via Panisperna 89A, I-00184 Roma (Italy); Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova,and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy); Re, R. [Dipartimento di Matematica e Informatica, Università degli Studi di Catania,Viale Andrea Doria 6, 95125 Catania (Italy)
2017-04-18
We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY’s having reduced manifold equal to ℙ{sup 1}, namely the projective super space ℙ{sup 1|2} and the weighted projective super space Wℙ{sub (2)}{sup 1|1}. Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces ℙ{sup n|m}. We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of ℙ{sup 1|2}, whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of ℙ{sup 1|m}, discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that ℙ{sup 1|2} is self-mirror, whereas Wℙ{sub (2)}{sup 1|1} has a zero dimensional mirror. Also, the mirror map for ℙ{sup 1|2} naturally endows it with a structure of N=2 super Riemann surface.
Large deviations for noninteracting infinite-particle systems
International Nuclear Information System (INIS)
Donsker, M.D.; Varadhan, S.R.S.
1987-01-01
A large deviation property is established for noninteracting infinite particle systems. Previous large deviation results obtained by the authors involved a single I-function because the cases treated always involved a unique invariant measure for the process. In the context of this paper there is an infinite family of invariant measures and a corresponding infinite family of I-functions governing the large deviations
Introducing the Dimensional Continuous Space-Time Theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2013-01-01
This article is an introduction to a new theory. The name of the theory is justified by the dimensional description of the continuous space-time of the matter, energy and empty space, that gathers all the real things that exists in the universe. The theory presents itself as the consolidation of the classical, quantum and relativity theories. A basic equation that describes the formation of the Universe, relating time, space, matter, energy and movement, is deduced. The four fundamentals physics constants, light speed in empty space, gravitational constant, Boltzmann's constant and Planck's constant and also the fundamentals particles mass, the electrical charges, the energies, the empty space and time are also obtained from this basic equation. This theory provides a new vision of the Big-Bang and how the galaxies, stars, black holes and planets were formed. Based on it, is possible to have a perfect comprehension of the duality between wave-particle, which is an intrinsic characteristic of the matter and energy. It will be possible to comprehend the formation of orbitals and get the equationing of atomics orbits. It presents a singular comprehension of the mass relativity, length and time. It is demonstrated that the continuous space-time is tridimensional, inelastic and temporally instantaneous, eliminating the possibility of spatial fold, slot space, worm hole, time travels and parallel universes. It is shown that many concepts, like dark matter and strong forces, that hypothetically keep the cohesion of the atomics nucleons, are without sense.
Differential calculus in normed linear spaces
Mukherjea, Kalyan
2007-01-01
This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab ini...
Energy Technology Data Exchange (ETDEWEB)
Vubangsi, M.; Tchoffo, M.; Fai, L. C. [Mesoscopic and Multilayer Structures Laboratory, Physics Department, University of Dschang, P.O. Box 417 Dschang (Cameroon); Pisma’k, Yu. M. [Department of Theoretical Physics, Saint Petersburg State University, Saint Petersburg (Russian Federation)
2015-12-15
The problem of a particle with position and time-dependent effective mass in a one-dimensional infinite square well is treated by means of a quantum canonical formalism. The dynamics of a launched wave packet of the system reveals a peculiar revival pattern that is discussed. .
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
International Nuclear Information System (INIS)
Zilhao, Miguel; Herdeiro, Carlos; Witek, Helvi; Nerozzi, Andrea; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo
2010-01-01
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
Nonrenormalizable quantum field models in four-dimensional space-time
International Nuclear Information System (INIS)
Raczka, R.
1978-01-01
The construction of no-cutoff Euclidean Green's functions for nonrenormalizable interactions L/sub I/(phi) = lambda∫ddelta (epsilon): expepsilonphi: in four-dimensional space-time is carried out. It is shown that all axioms for the generating functional of the Euclidean Green's function are satisfied except perhaps SO(4) invariance
Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay
Directory of Open Access Journals (Sweden)
Hassane Bouzahir
2007-02-01
Full Text Available We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.
Influence of cusps and intersections on the Wilson loop in ν-dimensional space
International Nuclear Information System (INIS)
Bezerra, V.B.
1984-01-01
A discussion is given about the influence of cusps and intersections on the calculation of the Wilson loop in ν-dimensional space. In particular, for the two-dimensional case, it is shown that there are no divergences. (Author) [pt
Dimensional Analysis with space discrimination applied to Fickian difussion phenomena
International Nuclear Information System (INIS)
Diaz Sanchidrian, C.; Castans, M.
1989-01-01
Dimensional Analysis with space discrimination is applied to Fickian difussion phenomena in order to transform its partial differen-tial equations into ordinary ones, and also to obtain in a dimensionl-ess fom the Ficks second law. (Author)
Proving productivity in infinite data structures
Zantema, H.; Raffelsieper, M.; Lynch, C.
2010-01-01
For a general class of infinite data structures including streams, binary trees, and the combination of finite and infinite lists, we investigate the notion of productivity. This generalizes stream productivity. We develop a general technique to prove productivity based on proving context-sensitive
Variational Infinite Hidden Conditional Random Fields
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja; Ghahramani, Zoubin
2015-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An Infinite hidden conditional random field is a hidden conditional random field with a countably infinite number of
The metric on field space, functional renormalization, and metric–torsion quantum gravity
International Nuclear Information System (INIS)
Reuter, Martin; Schollmeyer, Gregor M.
2016-01-01
Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
The searchlight problem for neutrons in a semi-infinite medium
International Nuclear Information System (INIS)
Ganapol, B.D.
1993-01-01
The solution of the Search Light Problem for monoenergetic neutrons in a semi-infinite medium with isotropic scattering illuminated at the free surface is obtained by several methods at various planes within the medium. The sources considered are a normally-incident pencil beam and an isotropic point source. The analytic solution is effected by a recently developed numerical inversion technique applied to the Fourier-Bessel transform. This transform inversion results from the solution method of Rybicki, where the two-dimensional problem is solved by casting it as a variant of a one-dimensional problem. The numerical inversion process results in a highly accurate solution. Comparisons of the analytic solution with results from Monte Carlo (MCNP) and discrete ordinates transport (DORT) codes show excellent agreement. These comparisons, which are free of any associated data or cross section set dependencies, provide significant evidence of the proper operation of both the transport codes tested
Rayleigh scattering of a cylindrical sound wave by an infinite cylinder.
Baynes, Alexander B; Godin, Oleg A
2017-12-01
Rayleigh scattering, in which the wavelength is large compared to the scattering object, is usually studied assuming plane incident waves. However, full Green's functions are required in a number of problems, e.g., when a scatterer is located close to the ocean surface or the seafloor. This paper considers the Green's function of the two-dimensional problem that corresponds to scattering of a cylindrical wave by an infinite cylinder embedded in a homogeneous fluid. Soft, hard, and impedance cylinders are considered. Exact solutions of the problem involve infinite series of products of Bessel functions. Here, simple, closed-form asymptotic solutions are derived, which are valid for arbitrary source and receiver locations outside the cylinder as long as its diameter is small relative to the wavelength. The scattered wave is given by the sum of fields of three linear image sources. The viability of the image source method was anticipated from known solutions of classical electrostatic problems involving a conducting cylinder. The asymptotic acoustic Green's functions are employed to investigate reception of low-frequency sound by sensors mounted on cylindrical bodies.
An Alternative to Wave Mechanics on Curved Spaces
Tomaschitz, R
1992-01-01
Geodesic motion in infinite spaces of constant negative curvature provides for the first time an example where a basically quantum mechanical quantity, a ground-state energy, is derived from Newtonian mechanics in a rigorous, non-semiclassical way. The ground state energy emerges as the Hausdorff dimension of a quasi-self-similar curve at infinity of three-dimensional hyperbolic space H in which our manifolds are embedded and where their universal covers are realized. This curve is just the locus of the limit set L(G) of the Kleinian group G of covering transformations, which determines the bounded trajectories in the manifold; all of them lie in the quotient C(L)/G, C(L) being the hyperbolic convex hull of L(G). The three-dimensional hyperbolic manifolds we construct can be visualized as thickened surfaces, topological products I x S, I a finite open interval, the fibers S compact Riemann surfaces. We give a short derivation of the Patterson formula connecting the ground-state energy with the Hausdorff dimen...
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)
On the problem of quantum control in infinite dimensions
Mendes, R. Vilela; Man'ko, Vladimir I.
2010-01-01
In the framework of bilinear control of the Schr\\"odinger equation with bounded control operators, it has been proved that the reachable set has a dense complemement in ${\\cal S}\\cap {\\cal H}^{2}$. Hence, in this setting, exact quantum control in infinite dimensions is not possible. On the other hand it is known that there is a simple choice of operators which, when applied to an arbitrary state, generate dense orbits in Hilbert space. Compatibility of these two results is established in this...
Stationary strings near a higher-dimensional rotating black hole
International Nuclear Information System (INIS)
Frolov, Valeri P.; Stevens, Kory A.
2004-01-01
We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D (five-dimensional) Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration that crosses the infinite redshift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole, there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a space-time with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string
Time-dependent gravitating solitons in five dimensional warped space-times
Giovannini, Massimo
2007-01-01
Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.
Infinite periodic minimal surfaces and their crystallography in the hyperbolic plane
International Nuclear Information System (INIS)
Sadoc, J.F.; Charvolin, J.
1989-01-01
Infinite periodic minimal surfaces are now being introduced to describe some complex structures with large cells, formed by inorganic and organic materials, which can be considered as crystals of surfaces or films. Among them are the spectacular cubic crystalline structures built by amphiphilic molecules in the presence of water. The crystallographic properties of these surfaces are studied from an intrinsic point of view, using operations of groups of symmetry defined by displacements on their surface. This approach takes advantage of the relation existing between these groups and those characterizing the tilings of the hyperbolic plane. First, the general bases of the particular crystallography of the hyperbolic plane are presented. Then the translation subgroups of the hyperbolic plane are determined in one particular case, that of the tiling involved in the problem of cubic structures of liquid crystals. Finally, it is shown that the infinite periodic minimal surfaces used to describe these structures can be obtained from the hyperbolic plane when some translations are forced to identity. This is indeed formally analogous to the simple process of transformation of a Euclidean plane into a cylinder, when a translation of the plane is forced to identity by rolling the plane onto itself. Thus, this approach transforms the 3D problem of infinite periodic minimal surfaces into a 2D problem and, although the latter is to be treated in a non-Euclidean space, provides a relatively simple formalism for the investigation of infinite periodic surfaces in general and the study of the geometrical transformations relating them. (orig.)
Negating the Infinitive in Biblical Hebrew
DEFF Research Database (Denmark)
Ehrensvärd, Martin Gustaf
1999-01-01
The article examines the negating of the infinitive in biblical and post-biblical Hebrew. The combination of the negation ayin with infinitive is widely claimed to belong to the linguistic layer commonly referred to as late biblical Hebrew and scholars use it to late-date texts. The article showa...
Improving the Instruction of Infinite Series
Lindaman, Brian; Gay, A. Susan
2012-01-01
Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…
Supersolids: Solids Having Finite Volume and Infinite Surfaces.
Love, William P.
1989-01-01
Supersolids furnish an ideal introduction to the calculus topic of infinite series, and are useful for combining that topic with integration. Five examples of supersolids are presented, four requiring only a few basic properties of infinite series and one requiring a number of integration principles as well as infinite series. (MNS)
Persistence and extinction for a stochastic logistic model with infinite delay
Chun Lu; Xiaohua Ding
2013-01-01
This article, studies a stochastic logistic model with infinite delay. Using a phase space, we establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and stochastic permanence. A threshold between weak persistence and extinction is obtained. Our results state that different types of environmental noises have different effects on the persistence and extinction, and that the delay has no impact on the persistence and ext...
Development of the three dimensional flow model in the SPACE code
International Nuclear Information System (INIS)
Oh, Myung Taek; Park, Chan Eok; Kim, Shin Whan
2014-01-01
SPACE (Safety and Performance Analysis CodE) is a nuclear plant safety analysis code, which has been developed in the Republic of Korea through a joint research between the Korean nuclear industry and research institutes. The SPACE code has been developed with multi-dimensional capabilities as a requirement of the next generation safety code. It allows users to more accurately model the multi-dimensional flow behavior that can be exhibited in components such as the core, lower plenum, upper plenum and downcomer region. Based on generalized models, the code can model any configuration or type of fluid system. All the geometric quantities of mesh are described in terms of cell volume, centroid, face area, and face center, so that it can naturally represent not only the one dimensional (1D) or three dimensional (3D) Cartesian system, but also the cylindrical mesh system. It is possible to simulate large and complex domains by modelling the complex parts with a 3D approach and the rest of the system with a 1D approach. By 1D/3D co-simulation, more realistic conditions and component models can be obtained, providing a deeper understanding of complex systems, and it is expected to overcome the shortcomings of 1D system codes. (author)
Diffusion and sorption in particles and two-dimensional dispersion in a porous media
International Nuclear Information System (INIS)
Rasmuson, A.
1980-01-01
A solution of the two-dimensional differential equation of dispersion from a disk source, coupled with a differential equation of diffusion and sorption in particles, is developed. The solution is obtained by the successive use of the Laplace and the Hankel transforms and is given in the form of an infinite double-integral. If the lateral dispersion is negligible, the solution is shown to simplify to a solution presented earlier. Dimensionless quantities are introduced. A steady-state condition is obtained after long time. This is investigated in some detail. An expression is derived for the highest concentration which may be expected at a point in space. An important relation is obtained when longitudinal dispersion is neglected. The solution for any value of the lateral dispersion coefficient and radial distance from the source is then obtained by simple multiplication of a solution for no lateral dispersion with the steady-state value. A method for integrating the infinite double integral is given. Some typical examples are shown. (Auth.)
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group
International Nuclear Information System (INIS)
Wang, S.J.
1993-04-01
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)
Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms
International Nuclear Information System (INIS)
Lawn, Marie-Amélie; Roth, Julien
2011-01-01
We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. This generalizes a recent work of the first author for spacelike immersed Lorentzian surfaces in ℝ 2,1 to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0, 2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.
Friedrichs systems in a Hilbert space framework: Solvability and multiplicity
Antonić, N.; Erceg, M.; Michelangeli, A.
2017-12-01
The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.
Efficient and accurate nearest neighbor and closest pair search in high-dimensional space
Tao, Yufei
2010-07-01
Nearest Neighbor (NN) search in high-dimensional space is an important problem in many applications. From the database perspective, a good solution needs to have two properties: (i) it can be easily incorporated in a relational database, and (ii) its query cost should increase sublinearly with the dataset size, regardless of the data and query distributions. Locality-Sensitive Hashing (LSH) is a well-known methodology fulfilling both requirements, but its current implementations either incur expensive space and query cost, or abandon its theoretical guarantee on the quality of query results. Motivated by this, we improve LSH by proposing an access method called the Locality-Sensitive B-tree (LSB-tree) to enable fast, accurate, high-dimensional NN search in relational databases. The combination of several LSB-trees forms a LSB-forest that has strong quality guarantees, but improves dramatically the efficiency of the previous LSH implementation having the same guarantees. In practice, the LSB-tree itself is also an effective index which consumes linear space, supports efficient updates, and provides accurate query results. In our experiments, the LSB-tree was faster than: (i) iDistance (a famous technique for exact NN search) by two orders ofmagnitude, and (ii) MedRank (a recent approximate method with nontrivial quality guarantees) by one order of magnitude, and meanwhile returned much better results. As a second step, we extend our LSB technique to solve another classic problem, called Closest Pair (CP) search, in high-dimensional space. The long-term challenge for this problem has been to achieve subquadratic running time at very high dimensionalities, which fails most of the existing solutions. We show that, using a LSB-forest, CP search can be accomplished in (worst-case) time significantly lower than the quadratic complexity, yet still ensuring very good quality. In practice, accurate answers can be found using just two LSB-trees, thus giving a substantial
Marginal Stability Boundaries for Infinite-n Ballooning Modes in a Quasi-axisymmetric Stellarator
International Nuclear Information System (INIS)
Hudson, S.R.; Hegna, C.C.
2003-01-01
A method for computing the ideal-MHD stability boundaries in three-dimensional equilibria is employed. Following Hegna and Nakajima [Phys. Plasmas 5 (May 1998) 1336], a two-dimensional family of equilibria are constructed by perturbing the pressure and rotational-transform profiles in the vicinity of a flux surface for a given stellarator equilibrium. The perturbations are constrained to preserve the magnetohydrodynamic equilibrium condition. For each perturbed equilibrium, the infinite-n ballooning stability is calculated. Marginal stability diagrams are thus constructed that are analogous to (s; a) diagrams for axisymmetric configurations. A quasi-axisymmetric stellarator is considered. Calculations of stability boundaries generally show regions of instability can occur for either sign of the average magnetic shear. Additionally, regions of second-stability are present
Revivals in an infinite square well in the presence of a δ well
International Nuclear Information System (INIS)
Vugalter, G.A.; Sorokin, V.A.; Das, A.K.
2002-01-01
We have investigated quantum revivals of wave packets in a one-dimensional infinite square well potential containing a δ well in the middle. The time-dependent Schroedinger equation for this composite potential admits formally exact solutions. We present analytical results for revival properties in three physically motivated approximations: wave packets containing eigenstates with large numbers in the presence of an arbitrary δ well, 'shallow' and 'deep' δ wells. Analytical results in the case of a 'shallow' δ well have been tested numerically
International Nuclear Information System (INIS)
Vrankar, L.; Turk, G.; Runovc, F.; Kansa, E.J.
2006-01-01
Many heat-transfer problems involve a change of phase of material due to solidification or melting. Applications include: the safety studies of nuclear reactors (molten core concrete interaction), the drilling of high ice-content soil, the storage of thermal energy, etc. These problems are often called Stefan's or moving boundary value problems. Mathematically, the interface motion is expressed implicitly in an equation for the conservation of thermal energy at the interface (Stefan's conditions). This introduces a non-linear character to the system which treats each problem somewhat uniquely. The exact solution of phase change problems is limited exclusively to the cases in which e.g. the heat transfer regions are infinite or semi-infinite one dimensional-space. Therefore, solution is obtained either by approximate analytical solution or by numerical methods. Finite-difference methods and finite-element techniques have been used extensively for numerical solution of moving boundary problems. Recently, the numerical methods have focused on the idea of using a mesh-free methodology for the numerical solution of partial differential equations based on radial basis functions. In our case we will study solid-solid transformation. The numerical solutions will be compared with analytical solutions. Actually, in our work we will examine usefulness of radial basis functions (especially multiquadric-MQ) for one-dimensional Stefan's problems. The position of the moving boundary will be simulated by moving grid method. The resultant system of RBF-PDE will be solved by affine space decomposition. (author)
Infinitely connected subgraphs in graphs of uncountable chromatic number
DEFF Research Database (Denmark)
Thomassen, Carsten
2016-01-01
Erdős and Hajnal conjectured in 1966 that every graph of uncountable chromatic number contains a subgraph of infinite connectivity. We prove that every graph of uncountable chromatic number has a subgraph which has uncountable chromatic number and infinite edge-connectivity. We also prove that......, if each orientation of a graph G has a vertex of infinite outdegree, then G contains an uncountable subgraph of infinite edge-connectivity....
Physical properties of the half-filled Hubbard model in infinite dimensions
International Nuclear Information System (INIS)
Georges, A.; Krauth, W.
1993-01-01
A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented. The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition. This coupled problem is solved numerically. Results for thermodynamic quantities (specific heat, entropy, . . .), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed. The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated. A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported
Quantum theory of spinor field in four-dimensional Riemannian space-time
International Nuclear Information System (INIS)
Shavokhina, N.S.
1996-01-01
The review deals with the spinor field in the four-dimensional Riemannian space-time. The field beys the Dirac-Fock-Ivanenko equation. Principles of quantization of the spinor field in the Riemannian space-time are formulated which in a particular case of the plane space-time are equivalent to the canonical rules of quantization. The formulated principles are exemplified by the De Sitter space-time. The study of quantum field theory in the De Sitter space-time is interesting because it itself leads to a method of an invariant well for plane space-time. However, the study of the quantum spinor field theory in an arbitrary Riemannian space-time allows one to take into account the influence of the external gravitational field on the quantized spinor field. 60 refs
Quantization of coset space σ-models coupled to two-dimensional gravity
International Nuclear Information System (INIS)
Korotkin, D.; Samtleben, H.
1996-07-01
The mathematical framework for an exact quantization of the two-dimensional coset space σ-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. The two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the whole isomonodromic sector. The Dirac brackets arising from the coset constraints are calculated. Their quantization allows to relate exact solutions of the corresponding Wheeler-DeWitt equations to solutions of a modified (Coset) Knizhnik-Zamolodchikov system. On the classical level, a set of observables is identified, that is complete for essential sectors of the theory. Quantum counterparts of these observables and their algebraic structure are investigated. Their status in alternative quantization procedures is discussed, employing the link with Hamiltonian Chern-Simons theory. (orig.)
On the Infinite Loch Ness monster
Arredondo, John A.; Maluendas, Camilo Ramírez
2017-01-01
In this paper we present in a topological way the construction of the orientable surface with only one end and infinite genus, called \\emph{The Infinite Loch Ness Monster}. In fact, we introduce a flat and hyperbolic construction of this surface. We discuss how the name of this surface has evolved and how it has been historically understood.
Biçer, M.; Kaşkaş, A.
2018-03-01
The infinite medium Green's function is used to solve the half-space albedo, slab albedo and Milne problems for the unpolarized Rayleigh scattering case; these problems are the most classical problems of radiative transfer theory. The numerical results are obtained and are compared with previous ones.
Kamihigashi, Takashi
2017-01-01
Given a sequence [Formula: see text] of measurable functions on a σ -finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text], we provide a sufficient condition for the following inequality to hold: [Formula: see text] Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time.
Three-dimensional theory for interaction between atomic ensembles and free-space light
International Nuclear Information System (INIS)
Duan, L.-M.; Cirac, J.I.; Zoller, P.
2002-01-01
Atomic ensembles have shown to be a promising candidate for implementations of quantum information processing by many recently discovered schemes. All these schemes are based on the interaction between optical beams and atomic ensembles. For description of these interactions, one assumed either a cavity-QED model or a one-dimensional light propagation model, which is still inadequate for a full prediction and understanding of most of the current experimental efforts that are actually taken in the three-dimensional free space. Here, we propose a perturbative theory to describe the three-dimensional effects in interaction between atomic ensembles and free-space light with a level configuration important for several applications. The calculations reveal some significant effects that were not known before from the other approaches, such as the inherent mode-mismatching noise and the optimal mode-matching conditions. The three-dimensional theory confirms the collective enhancement of the signal-to-noise ratio which is believed to be one of the main advantages of the ensemble-based quantum information processing schemes, however, it also shows that this enhancement needs to be understood in a more subtle way with an appropriate mode-matching method
Barroso, JA
2000-01-01
This book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.Infinite d
Gauge fields in nonlinear group realizations involving two-dimensional space-time symmetry
International Nuclear Information System (INIS)
Machacek, M.E.; McCliment, E.R.
1975-01-01
It is shown that gauge fields may be consistently introduced into a model Lagrangian previously considered by the authors. The model is suggested by the spontaneous breaking of a Lorentz-type group into a quasiphysical two-dimensional space-time and one internal degree of freedom, loosely associated with charge. The introduction of zero-mass gauge fields makes possible the absorption via the Higgs mechanism of the Goldstone fields that appear in the model despite the fact that the Goldstone fields do not transform as scalars. Specifically, gauge invariance of the Yang-Mills type requires the introduction of two sets of massless gauge fields. The transformation properties in two-dimensional space-time suggest that one set is analogous to a charge doublet that behaves like a second-rank tensor in real four-dimensional space time. The other set suggests a spin-one-like charge triplet. Via the Higgs mechanism, the first set absorbs the Goldstone fields and acquires mass. The second set remains massless. If massive gauge fields are introduced, the associated currents are not conserved and the Higgs mechanism is no longer fully operative. The Goldstone fields are not eliminated, but coupling between the Goldstone fields and the gauge fields does shift the mass of the antisymmetric second-rank-tensor gauge field components
Directory of Open Access Journals (Sweden)
Li Wang
2016-12-01
Full Text Available In this article, we show the existence of infinitely many solutions for the fractional p-Laplacian equations of Schrodinger-Kirchhoff type equation $$ M([u]_{s, p}^p (-\\Delta _p^s u+V(x|u|^{p-2}u= \\alpha |u|^{ p_s^{*}-2 }u+\\beta k(x|u|^{q-2}u \\quad x\\in \\mathbb{R}^N, $$ where $(-\\Delta ^s_p$ is the fractional p-Laplacian operator, $[u]_{s,p}$ is the Gagliardo p-seminorm, $0 sp$, $1space. By means of the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters $\\alpha$ and $\\beta$.
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
Hudetz, T.
1990-01-01
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
International Nuclear Information System (INIS)
Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.
1990-01-01
Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
Three dimensional monocular human motion analysis in end-effector space
DEFF Research Database (Denmark)
Hauberg, Søren; Lapuyade, Jerome; Engell-Nørregård, Morten Pol
2009-01-01
In this paper, we present a novel approach to three dimensional human motion estimation from monocular video data. We employ a particle filter to perform the motion estimation. The novelty of the method lies in the choice of state space for the particle filter. Using a non-linear inverse kinemati...
Model space dimensionalities for multiparticle fermion systems
International Nuclear Information System (INIS)
Draayer, J.P.; Valdes, H.T.
1985-01-01
A menu driven program for determining the dimensionalities of fixed-(J) [or (J,T)] model spaces built by distributing identical fermions (electrons, neutrons, protons) or two distinguihable fermion types (neutron-proton and isospin formalisms) among any mixture of positive and negative parity spherical orbitals is presented. The algorithm, built around the elementary difference formula d(J)=d(M=J)-d(M=J+1), takes full advantage of M->-M and particle-hole symmetries. A 96 K version of the program suffices for as compilated a case as d[(+1/2, +3/2, + 5/2, + 7/2-11/2)sup(n-26)J=2 + ,T=7]=210,442,716,722 found in the 0hω valence space of 56 126 Ba 70 . The program calculates the total fixed-(Jsup(π)) or fixed-(Jsup(π),T) dimensionality of a model space generated by distributing a specified number of fermions among a set of input positive and negative parity (π) spherical (j) orbitals. The user is queried at each step to select among various options: 1. formalism - identical particle, neutron-proton, isospin; 2. orbits -bumber, +/-2*J of all orbits; 3. limits -minimum/maximum number of particles of each parity; 4. specifics - number of particles, +/-2*J (total), 2*T; 5. continue - same orbit structure, new case quit. Though designed for nuclear applications (jj-coupling), the program can be used in the atomic case (LS-coupling) so long as half integer spin values (j=l+-1/2) are input for the valnce orbitals. Mutiple occurrences of a given j value are properly taken into account. A minor extension provides labelling information for a generalized seniority classification scheme. The program logic is an adaption of methods used in statistical spectroscopy to evaluate configuration averages. Indeed, the need for fixed symmetry leve densities in spectral distribution theory motivated this work. The methods extend to other group structures where there are M-like additive quantum labels. (orig.)
Topics in Two-Dimensional Quantum Gravity and Chern-Simons Gauge Theories
Zemba, Guillermo Raul
A series of studies in two and three dimensional theories is presented. The two dimensional problems are considered in the framework of String Theory. The first one determines the region of integration in the space of inequivalent tori of a tadpole diagram in Closed String Field Theory, using the naive Witten three-string vertex. It is shown that every surface is counted an infinite number of times and the source of this behavior is identified. The second study analyzes the behavior of the discrete matrix model of two dimensional gravity without matter using a mathematically well-defined construction, confirming several conjectures and partial results from the literature. The studies in three dimensions are based on Chern Simons pure gauge theory. The first one deals with the projection of the theory onto a two-dimensional surface of constant time, whereas the second analyzes the large N behavior of the SU(N) theory and makes evident a duality symmetry between the only two parameters of the theory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).
High-dimensional free-space optical communications based on orbital angular momentum coding
Zou, Li; Gu, Xiaofan; Wang, Le
2018-03-01
In this paper, we propose a high-dimensional free-space optical communication scheme using orbital angular momentum (OAM) coding. In the scheme, the transmitter encodes N-bits information by using a spatial light modulator to convert a Gaussian beam to a superposition mode of N OAM modes and a Gaussian mode; The receiver decodes the information through an OAM mode analyser which consists of a MZ interferometer with a rotating Dove prism, a photoelectric detector and a computer carrying out the fast Fourier transform. The scheme could realize a high-dimensional free-space optical communication, and decodes the information much fast and accurately. We have verified the feasibility of the scheme by exploiting 8 (4) OAM modes and a Gaussian mode to implement a 256-ary (16-ary) coding free-space optical communication to transmit a 256-gray-scale (16-gray-scale) picture. The results show that a zero bit error rate performance has been achieved.
Degrees of infinite words, polynomials and atoms
J. Endrullis; J. Karhumaki; J.W. Klop (Jan Willem); A. Saarela
2016-01-01
textabstractOur objects of study are finite state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite automata for recognising and
Degrees of infinite words, polynomials and atoms
Endrullis, Jörg; Karhumäki, Juhani; Klop, Jan Willem; Saarela, Aleksi
2016-01-01
Our objects of study are finite state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite automata for recognising and transforming
International Nuclear Information System (INIS)
Davidson, R.; Kozak, J.J.
1978-01-01
In this paper we study the emission of a two-level atom in a radiation field in the case where one mode of the field is assumed to be excited initially, and where the system is assumed to be of infinite extent. (The restriction to a one-dimensional field, which has been made throughout this series, is not essential: It is made chiefly for ease of presentation of the mathematical methods.) An exact expression is obtained for the probability rho (t) that the two-level quantum system is in the excited state at time t. This problem, previously unsolved in radiation theory, is tackled by reformulating the expression found in VII [J. Math. Phys. 16, 1013 (1975)] of this series for the time evolution of rho (t) in a finite system in the presence of an extra photon, and then constructing the infinite-system limit. A quantitative assessment of the role of the extra photon and of the coupling constant in influencing the dynamics is obtained by studying numerically the expression derived for rho (t) for a particular choice of initial condition. The study presented here casts light on the problem of time-reversal invariance and clarifies the sense in which exponential decay is universal; in particular, we find that: (1) It is the infinite-system limit which converts the time-reversible solutions of VII into the irreversible solution obtained here, and (2) it is the weak-coupling limit that imposes exponential form on the time dependence of the evolution of the system. The anticipated generalization of our methods to more complicated radiation-matter problems is discussed, and finally, several problems in radiation chemistry and physics, already accessible to exact analysis given the approach introduced here, are cited
Remarks for one-dimensional fractional equations
Directory of Open Access Journals (Sweden)
Massimiliano Ferrara
2014-01-01
Full Text Available In this paper we study a class of one-dimensional Dirichlet boundary value problems involving the Caputo fractional derivatives. The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result. Concrete examples of applications are presented.
Mahanthesh, B.; Gireesha, B. J.; Shashikumar, N. S.; Hayat, T.; Alsaedi, A.
2018-06-01
Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Kármán transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect.
Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems
International Nuclear Information System (INIS)
Barbu, Viorel; Marinelli, Carlo
2008-01-01
We study the existence theory for parabolic variational inequalities in weighted L 2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L 2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs
Coherent states on horospheric three-dimensional Lobachevsky space
Energy Technology Data Exchange (ETDEWEB)
Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by; Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by [Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus); Rybak, I., E-mail: Ivan.Rybak@astro.up.pt [Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus); Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto (Portugal); Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2016-08-15
In the paper it is shown that due to separation of variables in the Laplace-Beltrami operator (Hamiltonian of a free quantum particle) in horospheric and quasi-Cartesian coordinates of three dimensional Lobachevsky space, it is possible to introduce standard (“conventional” according to Perelomov [Generalized Coherent States and Their Applications (Springer-Verlag, 1986), p. 320]) coherent states. Some problems (oscillator on horosphere, charged particle in analogy of constant uniform magnetic field) where coherent states are suitable for treating were considered.
International Nuclear Information System (INIS)
Li Zhiyuan; Ho Kaiming
2003-01-01
The plane-wave-based transfer-matrix method (TMM) exhibits a peculiar advantage of being capable of solving eigenmodes involved in an infinite photonic crystal and electromagnetic (EM) wave propagation in finite photonic crystal slabs or even semi-infinite photonic crystal structures within the same theoretical framework. In addition, this theoretical approach can achieve much improved numerical convergency in solution of photonic band structures than the conventional plane-wave expansion method. In this paper we employ this TMM in combination with a supercell technique to handle two important kinds of three-dimensional (3D) photonic crystal waveguide structures. The first one is waveguides created in a 3D layer-by-layer photonic crystal that possesses a complete band gap, the other more popular one is waveguides built in a two-dimensional photonic crystal slab. These waveguides usually have mirror-reflection symmetries in one or two directions perpendicular to their axis. We have taken advantage of these structural symmetries to reduce the numerical burden of the TMM solution of the guided modes. The solution to the EM problems under these mirror-reflection symmetries in both the real space and the plane-wave space is discussed in a systematic way and in great detail. Both the periodic boundary condition and the absorbing boundary condition are employed to investigate structures with or without complete 3D optical confinement. The fact that the EM field components investigated in the TMM are collinear with the symmetric axes of the waveguide brings great convenience and clarity in exploring the eigenmode symmetry in both the real space and the plane-wave space. The classification of symmetry involved in the guided modes can help people to better understand the coupling of the photonic crystal waveguides with external channels such as dielectric slab or wire waveguides
The exp-normal distribution is infinitely divisible
Pinelis, Iosif
2018-01-01
Let $Z$ be a standard normal random variable (r.v.). It is shown that the distribution of the r.v. $\\ln|Z|$ is infinitely divisible; equivalently, the standard normal distribution considered as the distribution on the multiplicative group over $\\mathbb{R}\\setminus\\{0\\}$ is infinitely divisible.
On some midpoint-type algorithms
Directory of Open Access Journals (Sweden)
Giuseppe Marino
2018-04-01
Full Text Available We introduce iterative methods approximating fixed points for nonlinear operators defined on infinite-dimensional spaces. The starting points are the Implicit and Explicit Midpoint Rules, which generate polygonal functions approximating a solution for an ordinary differential equation infinite-dimensional spaces. The purpose is to determine suitable conditions on the mapping and the underlying space, in order to get strong convergence of the generated sequence to a common solution of a fixed point problem and a variational inequality. The authors contributions appear in the papers [34], [60], [61].
Kac-Moody algebra is not hidden symmetry of chiral models
International Nuclear Information System (INIS)
Devchand, C.; Schiff, J.
1997-01-01
A detailed examination of the infinite dimensional loop algebra of hidden symmetry transformations of the Principal Chiral Model reveals it to have a structure differing from a standard centreless Kac-Moody algebra. A new infinite dimensional Abelian symmetry algebra is shown to preserve a symplectic form on the space of solutions. (author). 15 refs
Directory of Open Access Journals (Sweden)
Jing Niu
2013-01-01
reproducing kernel on infinite interval is obtained concisely in polynomial form for the first time. Furthermore, as a particular effective application of this method, we give an explicit representation formula for calculation of reproducing kernel in reproducing kernel space with boundary value conditions.
Bayoumi, A
2003-01-01
All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and
Understanding the Behaviour of Infinite Ladder Circuits
Ucak, C.; Yegin, K.
2008-01-01
Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…
Application of data mining in three-dimensional space time reactor model
International Nuclear Information System (INIS)
Jiang Botao; Zhao Fuyu
2011-01-01
A high-fidelity three-dimensional space time nodal method has been developed to simulate the dynamics of the reactor core for real time simulation. This three-dimensional reactor core mathematical model can be composed of six sub-models, neutron kinetics model, cay heat model, fuel conduction model, thermal hydraulics model, lower plenum model, and core flow distribution model. During simulation of each sub-model some operation data will be produced and lots of valuable, important information reflecting the reactor core operation status could be hidden in, so how to discovery these information becomes the primary mission people concern. Under this background, data mining (DM) is just created and developed to solve this problem, no matter what engineering aspects or business fields. Generally speaking, data mining is a process of finding some useful and interested information from huge data pool. Support Vector Machine (SVM) is a new technique of data mining appeared in recent years, and SVR is a transformed method of SVM which is applied in regression cases. This paper presents only two significant sub-models of three-dimensional reactor core mathematical model, the nodal space time neutron kinetics model and the thermal hydraulics model, based on which the neutron flux and enthalpy distributions of the core are obtained by solving the three-dimensional nodal space time kinetics equations and energy equations for both single and two-phase flows respectively. Moreover, it describes that the three-dimensional reactor core model can also be used to calculate and determine the reactivity effects of the moderator temperature, boron concentration, fuel temperature, coolant void, xenon worth, samarium worth, control element positions (CEAs) and core burnup status. Besides these, the main mathematic theory of SVR is introduced briefly next, on the basis of which SVR is applied to dealing with the data generated by two sample calculation, rod ejection transient and axial
Infinite elements for soil-structure interaction analysis in multi-layered halfspaces
International Nuclear Information System (INIS)
Yun, Chung Bang; Kim, Jae Min; Yang, Shin Chu
1994-01-01
This paper presents the theoretical aspects of a computer code (KIESSI) for soil-structure interaction analysis in a multi-layered halfspace using infinite elements. The shape functions of the infinite elements are derived from approximate expressions of the analytical solutions. Three different infinite elements are developed. They are the horizontal, the vertical and the comer infinite elements (HIE, VIE and CIE). Numerical example analyses are presented for demonstrating the effectiveness of the proposed infinite elements
International Nuclear Information System (INIS)
Chen, G.S.; Christenson, J.M.
1985-01-01
In this paper, the authors present some initial results from an investigation of the application of a locally one-dimensional (LOD) finite difference method to the solution of the two-dimensional, two-group reactor kinetics equations. Although the LOD method is relatively well known, it apparently has not been previously applied to the space-time kinetics equations. In this investigation, the LOD results were benchmarked against similar computational results (using the same computing environment, the same programming structure, and the same sample problems) obtained by the TWIGL program. For all of the problems considered, the LOD method provided accurate results in one-half to one-eight of the time required by the TWIGL program
Optical asymmetric cryptography using a three-dimensional space-based model
International Nuclear Information System (INIS)
Chen, Wen; Chen, Xudong
2011-01-01
In this paper, we present optical asymmetric cryptography combined with a three-dimensional (3D) space-based model. An optical multiple-random-phase-mask encoding system is developed in the Fresnel domain, and one random phase-only mask and the plaintext are combined as a series of particles. Subsequently, the series of particles is translated along an axial direction, and is distributed in a 3D space. During image decryption, the robustness and security of the proposed method are further analyzed. Numerical simulation results are presented to show the feasibility and effectiveness of the proposed optical image encryption method
Dynamics of a neuron model in different two-dimensional parameter-spaces
Rech, Paulo C.
2011-03-01
We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades.
The curvature and the algebra of Killing vectors in five-dimensional space
International Nuclear Information System (INIS)
Rcheulishvili, G.
1990-12-01
This paper presents the Killing vectors for a five-dimensional space with the line element. The algebras which are formed by these vectors are written down. The curvature two-forms are described. (author). 10 refs
International Nuclear Information System (INIS)
Sumadi A H A; H, Zainuddin
2014-01-01
Using Isham's group-theoretic quantization scheme, we construct the canonical groups of the systems on the two-dimensional sphere and one-dimensional complex projective space, which are homeomorphic. In the first case, we take SO(3) as the natural canonical Lie group of rotations of the two-sphere and find all the possible Hamiltonian vector fields, and followed by verifying the commutator and Poisson bracket algebra correspondences with the Lie algebra of the group. In the second case, the same technique is resumed to define the Lie group, in this case SU (2), of CP'.We show that one can simply use a coordinate transformation from S 2 to CP 1 to obtain all the Hamiltonian vector fields of CP 1 . We explicitly show that the Lie algebra structures of both canonical groups are locally homomorphic. On the other hand, globally their corresponding canonical groups are acting on different geometries, the latter of which is almost complex. Thus the canonical group for CP 1 is the double-covering group of SO(3), namely SU(2). The relevance of the proposed formalism is to understand the idea of CP 1 as a space of where the qubit lives which is known as a Bloch sphere
A connection between free and classical infinite divisibility
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Thorbjørnsen, Steen
2004-01-01
In this paper we continue our studies, initiated in Refs. 2–4, of the connections between the classes of infinitely divisible probability measures in classical and in free probability. We show that the free cumulant transform of any freely infinitely divisible probability measure equals...... the classical cumulant transform of a certain classically infinitely divisible probability measure, and we give several characterizations of the latter measure, including an interpretation in terms of stochastic integration. We find, furthermore, an alternative definition of the Bercovici–Pata bijection, which...
Energy Technology Data Exchange (ETDEWEB)
Bruno, Oscar P., E-mail: obruno@caltech.edu; Lintner, Stéphane K.
2013-11-01
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.
International Nuclear Information System (INIS)
Edelen, Dominic G B
2003-01-01
Local action of the fundamental group SO(a, 4 + k - a) is used to show that any solution of an algebraically closed differential system, that is generated from matrix Lie algebra valued 1-forms on a four-dimensional parameter space, will generate families of immersions of four-dimensional spacetimes R 4 in flat (4 + k)-dimensional spaces M 4+k with compatible signature. The algorithm is shown to work with local action of SO(a, 4 + k - a) replaced by local action of GL(4 + k). Immersions generated by local action of the Poincare group on the target spacetime are also obtained. Evaluations of the line elements, immersion loci and connection and curvature forms of these immersions are algebraic. Families of immersions that depend on one or more arbitrary functions are calculated for 1 ≤ k ≤ 4. Appropriate sections of graphs of the conformal factor for two and three interacting line singularities immersed in M 6 are given in appendix A. The local immersion theorem given in appendix B shows that all local solutions of the immersion problem are obtained by use of this method and an algebraic extension in exceptional cases
Asymptotics for Two-dimensional Atoms
DEFF Research Database (Denmark)
Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip
2012-01-01
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....
Semantic coherence in English accusative-with-bare-infinitive constructions
DEFF Research Database (Denmark)
Jensen, Kim Ebensgaard
2013-01-01
Drawing on usage-based cognitively oriented construction grammar, this paper investigates the patterns of coattraction of items that appear in the two VP positions (the VP in the matrix clause, and the VP in the infinitive subordinate clause) in the English accusative-with-bare-infinitive constru......Drawing on usage-based cognitively oriented construction grammar, this paper investigates the patterns of coattraction of items that appear in the two VP positions (the VP in the matrix clause, and the VP in the infinitive subordinate clause) in the English accusative...... relations of English accusatives-with-bare-infinitives through the relations of semantic coherence between the two VPs....
LaFleur, Karl; Cassady, Kaitlin; Doud, Alexander; Shades, Kaleb; Rogin, Eitan; He, Bin
2013-01-01
Objective At the balanced intersection of human and machine adaptation is found the optimally functioning brain-computer interface (BCI). In this study, we report a novel experiment of BCI controlling a robotic quadcopter in three-dimensional physical space using noninvasive scalp EEG in human subjects. We then quantify the performance of this system using metrics suitable for asynchronous BCI. Lastly, we examine the impact that operation of a real world device has on subjects’ control with comparison to a two-dimensional virtual cursor task. Approach Five human subjects were trained to modulate their sensorimotor rhythms to control an AR Drone navigating a three-dimensional physical space. Visual feedback was provided via a forward facing camera on the hull of the drone. Individual subjects were able to accurately acquire up to 90.5% of all valid targets presented while travelling at an average straight-line speed of 0.69 m/s. Significance Freely exploring and interacting with the world around us is a crucial element of autonomy that is lost in the context of neurodegenerative disease. Brain-computer interfaces are systems that aim to restore or enhance a user’s ability to interact with the environment via a computer and through the use of only thought. We demonstrate for the first time the ability to control a flying robot in the three-dimensional physical space using noninvasive scalp recorded EEG in humans. Our work indicates the potential of noninvasive EEG based BCI systems to accomplish complex control in three-dimensional physical space. The present study may serve as a framework for the investigation of multidimensional non-invasive brain-computer interface control in a physical environment using telepresence robotics. PMID:23735712
Energy Technology Data Exchange (ETDEWEB)
Belloni, M., E-mail: mabelloni@davidson.edu [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R.W., E-mail: rick@phys.psu.edu [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States)
2014-07-01
The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems.
Persistence and extinction for a stochastic logistic model with infinite delay
Directory of Open Access Journals (Sweden)
Chun Lu
2013-11-01
Full Text Available This article, studies a stochastic logistic model with infinite delay. Using a phase space, we establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and stochastic permanence. A threshold between weak persistence and extinction is obtained. Our results state that different types of environmental noises have different effects on the persistence and extinction, and that the delay has no impact on the persistence and extinction for the stochastic model in the autonomous case. Numerical simulations illustrate the theoretical results.
Quantum theory of string in the four-dimensional space-time
International Nuclear Information System (INIS)
Pron'ko, G.P.
1986-01-01
The Lorentz invariant quantum theory of string is constructed in four-dimensional space-time. Unlike the traditional approach whose result was breaking of Lorentz invariance, our method is based on the usage of other variables for description of string configurations. The method of an auxiliary spectral problem for periodic potentials is the main tool in construction of these new variables
Finite-temperature symmetry restoration in the four-dimensional Φ4 model with four components
International Nuclear Information System (INIS)
Jansen, K.
1990-01-01
The finite-temperature symmetry restoration in the four-dimensional φ 4 theory with four components and with an infinite self-coupling is studied by means of Monte Carlo simulations on lattices with time extensions L t =4,5,6 and space extensions 12 3 -28 3 . The numerical calculations are done by means of the Wolff cluster algorithm which is very efficient for simulations near a phase transition. The numerical results are in good agreement with an improved one-loop expansion and with the 1/N-expansion, indicating that in the electroweak theory the symmetry restoration temperature T sr is about 350 GeV. (orig.)
Infinite sets of conservation laws for linear and nonlinear field equations
International Nuclear Information System (INIS)
Mickelsson, J.
1984-01-01
The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the 'coupling constant') the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant under the group of space-time symmetries. As an example, our method is applied to the Korteweg-de Vries equation and to the massless Thirring model. (orig.)
Wanko, Jeffrey J.
2009-01-01
This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…
Gradient flow for the one-dimensional Mumford-Shah functional
International Nuclear Information System (INIS)
Gobbino, M.
1998-01-01
In order to introduce a notion of gradient flow for the one-dimensional Mumford-Shah functional M S(u), the article considers a family {F hatε} of regular functionals, defined in spaces of piecewise constant functions, which converge in a variational sense to M S(u). Moreover, given an initial datum U 0 , with M S(u 0 ) 0ε } of piecewise constant approximations of u 0 , the evolution problems are considered. For large classes of initial data, the family {u ε (t)} converges, as ε→0 + , to a certain u(t), which is the solution of the heat equation with homogeneous Neumann boundary conditions in a suitable variable domain. On the other hand, for some special u 0 , the family {u ε (t)} has infinitely many limit points as ε→0 +
Directory of Open Access Journals (Sweden)
Watcharaporn Cholamjiak
2009-01-01
Full Text Available We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006 and Nakajo and Takahashi (2003.
Controllability Problem of Fractional Neutral Systems: A Survey
Directory of Open Access Journals (Sweden)
Artur Babiarz
2017-01-01
Full Text Available The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems.
Dynamics with infinitely many derivatives: variable coefficient equations
International Nuclear Information System (INIS)
Barnaby, Neil; Kamran, Niky
2008-01-01
Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also from cosmologists. Crucial to any application is a firm understanding of the mathematical structure of infinite order partial differential equations. In our previous work we developed a formalism to study the initial value problem for linear infinite order equations with constant coefficients. Our approach relied on the use of a contour integral representation for the functions under consideration. In many applications, including the study of cosmological perturbations in nonlocal inflation, one must solve linearized partial differential equations about some time-dependent background. This typically leads to variable coefficient equations, in which case the contour integral methods employed previously become inappropriate. In this paper we develop the theory of a particular class of linear infinite order partial differential equations with variable coefficients. Our formalism is particularly well suited to the types of equations that arise in nonlocal cosmological perturbation theory. As an example to illustrate our formalism we compute the leading corrections to the scalar field perturbations in p-adic inflation and show explicitly that these are small on large scales.
The Mathai-Quillen formalism and topological field theory
International Nuclear Information System (INIS)
Blau, Matthias.
1992-01-01
These lecture notes give an introductory account of an approach to cohomological field theory due to Atiyah and Jeffrey which is based on the construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics covered are: an explanation of regularized Euler numbers of infinite dimensional vector bundles; interpretation of supersymmetric quantum mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over space of connections. (author). 44 refs
Semiclassical investigation of the revival phenomena in a one-dimensional system
International Nuclear Information System (INIS)
Wang Zhexian; Heller, Eric J
2009-01-01
In a quantum revival, a localized wave packet re-forms or 'revives' into a compact reincarnation of itself long after it has spread in an unruly fashion over a region restricted only by the potential energy. This is a purely quantum phenomenon, which has no classical analog. Quantum revival and Anderson localization are members of a small class of subtle interference effects resulting in a quantum distribution radically different from the classical after long time evolution under classically nonlinear evolution. However, it is not clear that semiclassical methods, which start with the classical density and add interference effects, are in fact capable of capturing the revival phenomenon. Here we investigate two different one-dimensional systems, the infinite square well and Morse potential. In both the cases, after a long time the underlying classical manifolds are spread rather uniformly over phase space and are correspondingly spread in coordinate space, yet the semiclassical amplitudes are able to destructively interfere over most of coordinate space and constructively interfere in a small region, correctly reproducing a quantum revival. Further implications of this ability are discussed
Semiclassical investigation of the revival phenomena in a one-dimensional system
Energy Technology Data Exchange (ETDEWEB)
Wang Zhexian [Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Heller, Eric J [Department of Physics and Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 (United States)
2009-07-17
In a quantum revival, a localized wave packet re-forms or 'revives' into a compact reincarnation of itself long after it has spread in an unruly fashion over a region restricted only by the potential energy. This is a purely quantum phenomenon, which has no classical analog. Quantum revival and Anderson localization are members of a small class of subtle interference effects resulting in a quantum distribution radically different from the classical after long time evolution under classically nonlinear evolution. However, it is not clear that semiclassical methods, which start with the classical density and add interference effects, are in fact capable of capturing the revival phenomenon. Here we investigate two different one-dimensional systems, the infinite square well and Morse potential. In both the cases, after a long time the underlying classical manifolds are spread rather uniformly over phase space and are correspondingly spread in coordinate space, yet the semiclassical amplitudes are able to destructively interfere over most of coordinate space and constructively interfere in a small region, correctly reproducing a quantum revival. Further implications of this ability are discussed.
Semiclassical investigation of the revival phenomena in a one-dimensional system
Wang, Zhe-xian; Heller, Eric J.
2009-07-01
In a quantum revival, a localized wave packet re-forms or 'revives' into a compact reincarnation of itself long after it has spread in an unruly fashion over a region restricted only by the potential energy. This is a purely quantum phenomenon, which has no classical analog. Quantum revival and Anderson localization are members of a small class of subtle interference effects resulting in a quantum distribution radically different from the classical after long time evolution under classically nonlinear evolution. However, it is not clear that semiclassical methods, which start with the classical density and add interference effects, are in fact capable of capturing the revival phenomenon. Here we investigate two different one-dimensional systems, the infinite square well and Morse potential. In both the cases, after a long time the underlying classical manifolds are spread rather uniformly over phase space and are correspondingly spread in coordinate space, yet the semiclassical amplitudes are able to destructively interfere over most of coordinate space and constructively interfere in a small region, correctly reproducing a quantum revival. Further implications of this ability are discussed.
Curvature of super Diff(S1)/S1
International Nuclear Information System (INIS)
Oh, P.; Ramond, P.
1987-01-01
Motivated by the work of Bowick and Rajeev, we calculate the curvature of the infinite-dimensional flag manifolds Diff(S 1 )/S 1 and Super Diff(S 1 )/S 1 using standard finite-dimensional coset space techniques. We regularize the infinite by ζ-function regularization and recover the conformal and superconformal anomalies respectively for a specific choice of the torsion. (orig.)
International Nuclear Information System (INIS)
Feinsilver, Philip; Schott, Rene
2009-01-01
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.
Influence of cusps and intersections on the calculation of the Wilson loop in ν-dimensional space
International Nuclear Information System (INIS)
Bezerra, V.B.
1984-01-01
A discussion is given about the influence of cusps and intersections on the calculation of the Wilson Loop in ν-dimensional space. In particular, for the two-dimensional case, it is shown that there are no divergences. (Author) [pt
Compactified cosmological simulations of the infinite universe
Rácz, Gábor; Szapudi, István; Csabai, István; Dobos, László
2018-06-01
We present a novel N-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low k modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically projected cosmological simulations. It uses stereographic projection for space compactification and naive O(N^2) force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P3M) algorithm with similar spatial and mass resolution. The N2 force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 running matching initial conditions.
Compactified Cosmological Simulations of the Infinite Universe
Rácz, Gábor; Szapudi, István; Csabai, István; Dobos, László
2018-03-01
We present a novel N-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low k modes and, its fundamental geometry and topology match observations. Our approach is also capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations. Our initial implementation of the method is called StePS which stands for Stereographically Projected Cosmological Simulations. It uses stereographic projection for space compactification and naive O(N^2) force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P3M) algorithm with similar spatial and mass resolution. The N2 force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 running matching initial conditions.
Nam, Julia EunJu; Mueller, Klaus
2013-02-01
Gaining a true appreciation of high-dimensional space remains difficult since all of the existing high-dimensional space exploration techniques serialize the space travel in some way. This is not so foreign to us since we, when traveling, also experience the world in a serial fashion. But we typically have access to a map to help with positioning, orientation, navigation, and trip planning. Here, we propose a multivariate data exploration tool that compares high-dimensional space navigation with a sightseeing trip. It decomposes this activity into five major tasks: 1) Identify the sights: use a map to identify the sights of interest and their location; 2) Plan the trip: connect the sights of interest along a specifyable path; 3) Go on the trip: travel along the route; 4) Hop off the bus: experience the location, look around, zoom into detail; and 5) Orient and localize: regain bearings in the map. We describe intuitive and interactive tools for all of these tasks, both global navigation within the map and local exploration of the data distributions. For the latter, we describe a polygonal touchpad interface which enables users to smoothly tilt the projection plane in high-dimensional space to produce multivariate scatterplots that best convey the data relationships under investigation. Motion parallax and illustrative motion trails aid in the perception of these transient patterns. We describe the use of our system within two applications: 1) the exploratory discovery of data configurations that best fit a personal preference in the presence of tradeoffs and 2) interactive cluster analysis via cluster sculpting in N-D.
Born in an infinite universe: A cosmological interpretation of quantum mechanics
International Nuclear Information System (INIS)
Aguirre, Anthony; Tegmark, Max
2011-01-01
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave-function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad infinitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wave function, the remainder consists of a superposition of indistinguishable terms, so that arguably 'collapse' of the wave function is irrelevant, and the ''many worlds'' of Everett's interpretation are unified into one. Finally, the analysis suggests a 'cosmological interpretation' of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the
Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces
International Nuclear Information System (INIS)
Khrennikov, Andrei
2010-01-01
One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.
Neutrino stress tensor regularization in two-dimensional space-time
International Nuclear Information System (INIS)
Davies, P.C.W.; Unruh, W.G.
1977-01-01
The method of covariant point-splitting is used to regularize the stress tensor for a massless spin 1/2 (neutrino) quantum field in an arbitrary two-dimensional space-time. A thermodynamic argument is used as a consistency check. The result shows that the physical part of the stress tensor is identical with that of the massless scalar field (in the absence of Casimir-type terms) even though the formally divergent expression is equal to the negative of the scalar case. (author)
Coset Space Dimensional Reduction approach to the Standard Model
International Nuclear Information System (INIS)
Farakos, K.; Kapetanakis, D.; Koutsoumbas, G.; Zoupanos, G.
1988-01-01
We present a unified theory in ten dimensions based on the gauge group E 8 , which is dimensionally reduced to the Standard Mode SU 3c xSU 2 -LxU 1 , which breaks further spontaneously to SU 3L xU 1em . The model gives similar predictions for sin 2 θ w and proton decay as the minimal SU 5 G.U.T., while a natural choice of the coset space radii predicts light Higgs masses a la Coleman-Weinberg
Infinite symmetry in the quantum Hall effect
Directory of Open Access Journals (Sweden)
Lütken C.A.
2014-04-01
Full Text Available The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the location of quantum critical points predicted by the symmetry is in increasingly accurate agreement with scaling experiments. The symmetry severely constrains the structure of the effective quantum field theory that encodes the low energy limit of quantum electrodynamics of 1010 charges in two dirty dimensions. If this is a non-linear σ-model the target space is a torus, rather than the more familiar sphere. One of the simplest toroidal models gives a critical (correlation length exponent that agrees with the value obtained from numerical simulations of the quantum Hall effect.
International Nuclear Information System (INIS)
Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut
2014-01-01
To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p < 0.001). No significant difference in image quality between T2W 2D-TSE and T2W 3D-SPACE (p = 0.056) occurred. The kappa values for inter-observer agreement were 0.714 for T2W 2D-TSE and 0.899 for T2W 3D-SPACE. Three-dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.
Energy Technology Data Exchange (ETDEWEB)
Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut [School of Medicine, Gazi University, Ankara (Turkey)
2014-12-15
To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p < 0.001). No significant difference in image quality between T2W 2D-TSE and T2W 3D-SPACE (p = 0.056) occurred. The kappa values for inter-observer agreement were 0.714 for T2W 2D-TSE and 0.899 for T2W 3D-SPACE. Three-dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.
Hirschman, Isidore Isaac
2014-01-01
This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book.The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the app
Self-dual Skyrmions on the spheres S2 N +1
Amari, Y.; Ferreira, L. A.
2018-04-01
We construct self-dual sectors for scalar field theories on a (2 N +2 )-dimensional Minkowski space-time with the target space being the 2 N +1 -dimensional sphere S2 N +1. The construction of such self-dual sectors is made possible by the introduction of an extra functional in the action that renders the static energy and the self-duality equations conformally invariant on the (2 N +1 )-dimensional spatial submanifold. The conformal and target-space symmetries are used to build an ansatz that leads to an infinite number of exact self-dual solutions with arbitrary values of the topological charge. The five-dimensional case is discussed in detail, where it is shown that two types of theories admit self-dual sectors. Our work generalizes the known results in the three-dimensional case that lead to an infinite set of self-dual Skyrmion solutions.
An alternative to wave mechanics on curved spaces
International Nuclear Information System (INIS)
Tomaschitz, R.
1992-01-01
Geodesic motion in infinite spaces of constant negative curvature provides for the first time an example where a basically quantum mechanical quantity, a ground-state energy, is derived from Newtonian mechanics in a rigorous, non-semiclassical way. The ground state energy emerges as the Hausdorff dimension of a quasi-self-similar curve at infinity of three-dimensional hyperbolic space H 3 in which our manifolds are embedded and where their universal covers are realized. This curve is just the locus of the limit set Λ(Γ) of the Kleinian group Γ of covering transformations, which determines the bounded trajectories in the manifold; all of them lie in the quotient C(Λ)/Γ, C(Γ) being the hyperbolic convex hull of Λ(Γ). The three-dimensional hyperbolic manifolds we construct can be visualized as thickened surfaces, topological products IxS, I a finite open interval, the fibers S compact Riemann surfaces. We give a short derivation of the Patterson formula connecting the ground-state energy with the Hausdorff dimension δ of Λ, and give various examples for the calculation of δ from the tessellations of the boundary of H 3 , induced by the universal coverings of the manifolds. 33 refs., 13 figs., 2 tabs
3-dimensional interactive space (3DIS)
International Nuclear Information System (INIS)
Veitch, S.; Veitch, J.; West, S.J.
1991-01-01
This paper reports on the 3DIS security system which uses standard CCTV cameras to create 3-Dimensional detection zones around valuable assets within protected areas. An intrusion into a zone changes light values and triggers an alarm that is annunciated, while images from multiple cameras are recorded. 3DIS lowers nuisance alarm rates and provides superior automated surveillance capability. Performance is improved over 2-D systems because activity around, above or below the zone does to cause an alarm. Invisible 3-D zones protect assets as small as a pin or as large as a 747 jetliner. Detection zones are created by excising subspaces from the overlapping fields of view of two or more video cameras. Hundred of zones may co-exist, operating simultaneously. Intrusion into any 3-D zone will cause a coincidental change in light values, triggering an alarm specific to that space
Lekhnitskii's formalism of one-dimensional quasicrystals and its ...
Indian Academy of Sciences (India)
To illustrate its utility, the generalized Lekhnitskii's formal- ism is used to analyse the coupled phonon and phason fields in an infinite quasicrystal medium con- taining an elliptic rigid inclusion. Keywords. Generalized Lekhnitskii's formalism; one-dimensional quasicrystals; plane problems; elliptic inclusion. PACS Nos 61.44.
International Nuclear Information System (INIS)
Ryu, Jeong-Soo; Seo, Choon-Gyo; Kim, Jae-Min; Yun, Chung-Bang
2010-01-01
This paper proposes a slightly new three-dimensional radial-shaped dynamic infinite elements fully coupled to finite elements for an analysis of soil-structure interaction system in a horizontally layered medium. We then deal with a seismic analysis technique for a three-dimensional soil-structure interactive system, based on the coupled finite-infinite method in frequency domain. The dynamic infinite elements are simulated for the unbounded domain with wave functions propagating multi-generated wave components. The accuracy of the dynamic infinite element and effectiveness of the seismic analysis technique may be demonstrated through a typical compliance analysis of square surface footing, an L-shaped mat concrete footing on layered soil medium and two kinds of practical seismic analysis tests. The practical analyses are (1) a site response analysis of the well-known Hualien site excited by all travelling wave components (primary, shear, Rayleigh waves) and (2) a generation of a floor response spectrum of a nuclear power plant. The obtained dynamic results show good agreement compared with the measured response data and numerical values of other soil-structure interaction analysis package.
Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.
Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter
2012-04-01
This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.
On infinite walls in deformation quantization
International Nuclear Information System (INIS)
Kryukov, S.; Walton, M.A.
2005-01-01
We examine the deformation quantization of a single particle moving in one dimension (i) in the presence of an infinite potential wall (ii) confined by an infinite square well, and (iii) bound by a delta function potential energy. In deformation quantization, considered as an autonomous formulation of quantum mechanics, the Wigner function of stationary states must be found by solving the so-called *-genvalue ('stargenvalue') equation for the Hamiltonian. For the cases considered here, this pseudo-differential equation is difficult to solve directly, without an ad hoc modification of the potential. Here we treat the infinite wall as the limit of a solvable exponential potential. Before the limit is taken, the corresponding *-genvalue equation involves the Wigner function at momenta translated by imaginary amounts. We show that it can be converted to a partial differential equation, however, with a well-defined limit. We demonstrate that the Wigner functions calculated from the standard Schroedinger wave functions satisfy the resulting new equation. Finally, we show how our results may be adapted to allow for the presence of another, non-singular part in the potential
Modeling Dispersion of Chemical-Biological Agents in Three Dimensional Living Space
International Nuclear Information System (INIS)
William S. Winters
2002-01-01
This report documents a series of calculations designed to demonstrate Sandia's capability in modeling the dispersal of chemical and biological agents in complex three-dimensional spaces. The transport of particles representing biological agents is modeled in a single room and in several connected rooms. The influence of particle size, particle weight and injection method are studied
Příklonky a vazaly infinitivu : Clitics and Infinitive Vassals
Directory of Open Access Journals (Sweden)
Ilona Starý Kořánová
2017-12-01
Full Text Available Word order of Czech enclitics is quite difficult to acquire for students of Czech as foreign language. While native speakers can “hear” the correct word order, the foreigner needs a set of rules to guide him. The usual rule for the word order of fixed enclitics seems to be breached quite often. The article focuses on one type of sentences in which the rule for the word order of fixed enclitics is violated, namely in sentences which except for a finite verb include an infinitive and consequently two series of enclitics. The finite verb and the infinitive each syntactically govern (are governor to their respective enclitics which in turn are their subjects (recta. If the infinitive is part of the sentence predicate, the enclitics follow the usual rule of word order unless the infinitive becomes part of the sentence rhema (comments. In that case its subjects precede it. If the infinitive is not part of the sentence predicate (in other words it is subject, object or complement, precedes it then the infinitive subjects follow it. However, if the infinitive is not part of the sentence predicate, and is placed at the sentence end, then its subjects precede it. If the infinitive functions as an attribute to a noun, it follows the noun. If the nominal phrase N + infinitive starts a sentence then the reflexive particle se/si follows the infinitive in 98% of cases. If the enclitic personal pronouns occur in the reversed order, i.e. Acc.–Dat. order, or two dative enclitics follow one immediately after another then the enclitics subjects are as close as possible to their regens/ governor. The so-called contact dative, which does not have a governor, is not bound in this way
Existence and uniqueness of Gibbs states for a statistical mechanical polyacetylene model
International Nuclear Information System (INIS)
Park, Y.M.
1987-01-01
One-dimensional polyacetylene is studied as a model of statistical mechanics. In a semiclassical approximation the system is equivalent to a quantum XY model interacting with unbounded classical spins in one-dimensional lattice space Z. By establishing uniform estimates, an infinite-volume-limit Hilbert space, a strongly continuous time evolution group of unitary operators, and an invariant vector are constructed. Moreover, it is proven that any infinite-limit state satisfies Gibbs conditions. Finally, a modification of Araki's relative entropy method is used to establish the uniqueness of Gibbs states
Eigenmodes of three-dimensional spherical spaces and their application to cosmology
International Nuclear Information System (INIS)
Lehoucq, Roland; Weeks, Jeffrey; Uzan, Jean-Philippe; Gausmann, Evelise; Luminet, Jean-Pierre
2002-01-01
This paper investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular, whereas in the Euclidean case too-small universes are excluded by present CMB data, in the spherical case, candidate topologies will always exist even if the total energy density parameter of the universe is very close to unity
Eigenmodes of three-dimensional spherical spaces and their application to cosmology
Energy Technology Data Exchange (ETDEWEB)
Lehoucq, Roland [CE-Saclay, DSM/DAPNIA/Service d' Astrophysique, F-91191 Gif sur Yvette (France); Weeks, Jeffrey [15 Farmer St, Canton, NY 13617-1120 (United States); Uzan, Jean-Philippe [Institut d' Astrophysique de Paris, GReCO, CNRS-FRE 2435, 98 bis, Bd Arago, 75014 Paris (France); Gausmann, Evelise [Instituto de Fisica Teorica, Rua Pamplona, 145 Bela Vista - Sao Paulo - SP, CEP 01405-900 (Brazil); Luminet, Jean-Pierre [Laboratoire Univers et Theories, CNRS-FRE 2462, Observatoire de Paris, F-92195 Meudon (France)
2002-09-21
This paper investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular, whereas in the Euclidean case too-small universes are excluded by present CMB data, in the spherical case, candidate topologies will always exist even if the total energy density parameter of the universe is very close to unity.
Possibilities of identifying cyber attack in noisy space of n-dimensional abstract system
Energy Technology Data Exchange (ETDEWEB)
Jašek, Roman; Dvořák, Jiří; Janková, Martina; Sedláček, Michal [Tomas Bata University in Zlin Nad Stranemi 4511, 760 05 Zlin, Czech republic jasek@fai.utb.cz, dvorakj@aconte.cz, martina.jankova@email.cz, michal.sedlacek@email.cz (Czech Republic)
2016-06-08
This article briefly mentions some selected options of current concept for identifying cyber attacks from the perspective of the new cyberspace of real system. In the cyberspace, there is defined n-dimensional abstract system containing elements of the spatial arrangement of partial system elements such as micro-environment of cyber systems surrounded by other suitably arranged corresponding noise space. This space is also gradually supplemented by a new image of dynamic processes in a discreet environment, and corresponding again to n-dimensional expression of time space defining existence and also the prediction for expected cyber attacksin the noise space. Noises are seen here as useful and necessary for modern information and communication technologies (e.g. in processes of applied cryptography in ICT) and then the so-called useless noises designed for initial (necessary) filtering of this highly aggressive environment and in future expectedly offensive background in cyber war (e.g. the destruction of unmanned means of an electromagnetic pulse, or for destruction of new safety barriers created on principles of electrostatic field or on other principles of modern physics, etc.). The key to these new options is the expression of abstract systems based on the models of microelements of cyber systems and their hierarchical concept in structure of n-dimensional system in given cyberspace. The aim of this article is to highlight the possible systemic expression of cyberspace of abstract system and possible identification in time-spatial expression of real environment (on microelements of cyber systems and their surroundings with noise characteristics and time dimension in dynamic of microelements’ own time and externaltime defined by real environment). The article was based on a partial task of faculty specific research.
Possibilities of identifying cyber attack in noisy space of n-dimensional abstract system
International Nuclear Information System (INIS)
Jašek, Roman; Dvořák, Jiří; Janková, Martina; Sedláček, Michal
2016-01-01
This article briefly mentions some selected options of current concept for identifying cyber attacks from the perspective of the new cyberspace of real system. In the cyberspace, there is defined n-dimensional abstract system containing elements of the spatial arrangement of partial system elements such as micro-environment of cyber systems surrounded by other suitably arranged corresponding noise space. This space is also gradually supplemented by a new image of dynamic processes in a discreet environment, and corresponding again to n-dimensional expression of time space defining existence and also the prediction for expected cyber attacksin the noise space. Noises are seen here as useful and necessary for modern information and communication technologies (e.g. in processes of applied cryptography in ICT) and then the so-called useless noises designed for initial (necessary) filtering of this highly aggressive environment and in future expectedly offensive background in cyber war (e.g. the destruction of unmanned means of an electromagnetic pulse, or for destruction of new safety barriers created on principles of electrostatic field or on other principles of modern physics, etc.). The key to these new options is the expression of abstract systems based on the models of microelements of cyber systems and their hierarchical concept in structure of n-dimensional system in given cyberspace. The aim of this article is to highlight the possible systemic expression of cyberspace of abstract system and possible identification in time-spatial expression of real environment (on microelements of cyber systems and their surroundings with noise characteristics and time dimension in dynamic of microelements’ own time and externaltime defined by real environment). The article was based on a partial task of faculty specific research.
Possibilities of identifying cyber attack in noisy space of n-dimensional abstract system
Jašek, Roman; Dvořák, Jiří; Janková, Martina; Sedláček, Michal
2016-06-01
This article briefly mentions some selected options of current concept for identifying cyber attacks from the perspective of the new cyberspace of real system. In the cyberspace, there is defined n-dimensional abstract system containing elements of the spatial arrangement of partial system elements such as micro-environment of cyber systems surrounded by other suitably arranged corresponding noise space. This space is also gradually supplemented by a new image of dynamic processes in a discreet environment, and corresponding again to n-dimensional expression of time space defining existence and also the prediction for expected cyber attacksin the noise space. Noises are seen here as useful and necessary for modern information and communication technologies (e.g. in processes of applied cryptography in ICT) and then the so-called useless noises designed for initial (necessary) filtering of this highly aggressive environment and in future expectedly offensive background in cyber war (e.g. the destruction of unmanned means of an electromagnetic pulse, or for destruction of new safety barriers created on principles of electrostatic field or on other principles of modern physics, etc.). The key to these new options is the expression of abstract systems based on the models of microelements of cyber systems and their hierarchical concept in structure of n-dimensional system in given cyberspace. The aim of this article is to highlight the possible systemic expression of cyberspace of abstract system and possible identification in time-spatial expression of real environment (on microelements of cyber systems and their surroundings with noise characteristics and time dimension in dynamic of microelements' own time and externaltime defined by real environment). The article was based on a partial task of faculty specific research.
Quasi-integrability and two-dimensional QCD
International Nuclear Information System (INIS)
Abdalla, E.; Mohayaee, R.
1996-10-01
The notion of integrability in two-dimensional QCD is discussed. We show that in spite of an infinite number of conserved charges, particle production is not entirely suppressed. This phenomenon, which we call quasi-integrability, is explained in terms of quantum corrections to the combined algebra of higher-conserved and spectrum-generating currents. We predict the qualitative form of particle production probabilities and verify that they are in agreement with numerical data. We also discuss four-dimensional self-dual Yang-Mills theory in the light of our results. (author). 25 refs, 4 figs, 1 tab
The infinite limit as an eliminable approximation for phase transitions
Ardourel, Vincent
2018-05-01
It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al., 2000). Based on this theory, I argue for the plausibility for eliminating the infinite limit for studying phase transitions. I offer a new account for phase transitions in finite systems, and I argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.
Room Scanner representation and measurement of three-dimensional spaces using a smartphone
International Nuclear Information System (INIS)
Bejarano Rodriguez, Mauricio
2013-01-01
An algorithm was designed to measure and represent three-dimensional spaces using the resources available on a smartphone. The implementation of the fusion sensor has enabled to use basic trigonometry to calculate the lengths of the walls and the corners of the room. The OpenGL library was used to create and visualize the three-dimensional model of the measured internal space. A library was created to export the represented model to other commercial formats. A certain level of degradation is obtained once an attempt is made to measure long distances because the algorithm depends on the degree of inclination of the smarthphone to perform the measurements. For this reason, at higher elevations are obtained more accurate measurements. The capture process was changed in order to correct the margin of error to measure soccer field. The algorithm has recorded measurements less than 3% margin of error through the process of subdividing the measurement area. (author) [es
Distribution of high-dimensional entanglement via an intra-city free-space link.
Steinlechner, Fabian; Ecker, Sebastian; Fink, Matthias; Liu, Bo; Bavaresco, Jessica; Huber, Marcus; Scheidl, Thomas; Ursin, Rupert
2017-07-24
Quantum entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Increasing the dimensionality of entanglement has been shown to improve robustness and channel capacities in secure quantum communications. Here we report on the distribution of genuine high-dimensional entanglement via a 1.2-km-long free-space link across Vienna. We exploit hyperentanglement, that is, simultaneous entanglement in polarization and energy-time bases, to encode quantum information, and observe high-visibility interference for successive correlation measurements in each degree of freedom. These visibilities impose lower bounds on entanglement in each subspace individually and certify four-dimensional entanglement for the hyperentangled system. The high-fidelity transmission of high-dimensional entanglement under real-world atmospheric link conditions represents an important step towards long-distance quantum communications with more complex quantum systems and the implementation of advanced quantum experiments with satellite links.
Semi-infinite photocarrier radiometric model for the characterization of semiconductor wafer
International Nuclear Information System (INIS)
Liu Xianming; Li Bincheng; Huang Qiuping
2010-01-01
The analytical expression is derived to describe the photocarrier radiometric (PCR) signal for a semi-infinite semiconductor wafer excited by a square-wave modulated laser. For comparative study, the PCR signals are calculated by the semi-infinite model and the finite thickness model with several thicknesses. The fitted errors of the electronic transport properties by semi-infinite model are analyzed. From these results it is evident that for thick samples or at high modulation frequency, the semiconductor can be considered as semi-infinite.
The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator
International Nuclear Information System (INIS)
Borzov, V. V.; Damaskinsky, E. V.
2014-01-01
In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators
A tetrahedrally coordinated cobalt(II) aminophosphonate containing one-dimensional channels
International Nuclear Information System (INIS)
Gemmill, William R.; Smith, Mark D.; Reisner, Barbara A.
2005-01-01
A tetrahedrally coordinated cobalt(II) phosphonate, Co(O 3 PCH 2 CH 2 NH 2 ), has been synthesized using hydrothermal techniques. X-ray diffraction indicates that this material is a three-dimensional open framework with rings aligned along a single axis forming infinite one-dimensional channels. The framework decomposes just above 400 deg. C. Magnetic susceptibility data are consistent with weak antiferromagnetic ordering at low temperatures
Twisting gravitational waves and eigenvector fields for SL(2,C on an infinite jet
Directory of Open Access Journals (Sweden)
J. D. Finley III
2000-07-01
Full Text Available A system of coupled vector-field-valued partial differential equations is presented, the solutions to which would determine two coupled, infinite-dimensional vector-field realizations of the group SL(2,C. While the general solution is (partially presented, the complicated nature of that solution is deplored, and the hope expressed that someone can replace it by something much more natural. The physical origins of the problem are briefly described. The problem arises out of searches for Backlund transforms of a system of PDE's that describe twisting, Petrov type N solutions of Einstein's vacuum field equations.
DEFF Research Database (Denmark)
Srba, Jiří
2002-01-01
This paper provides a comprehensive summary of equivalence checking results for infinite-state systems. References to the relevant papers will be updated continuously according to the development in the area. The most recent version of this document is available from the web-page http://www.brics.dk/~srba/roadmap....
Faster exact algorithms for computing Steiner trees in higher dimensional Euclidean spaces
DEFF Research Database (Denmark)
Fonseca, Rasmus; Brazil, Marcus; Winter, Pawel
The Euclidean Steiner tree problem asks for a network of minimum total length interconnecting a finite set of points in d-dimensional space. For d ≥ 3, only one practical algorithmic approach exists for this problem --- proposed by Smith in 1992. A number of refinements of Smith's algorithm have...
Surface properties of semi-infinite Fermi systems
International Nuclear Information System (INIS)
Campi, X.; Stringari, S.
1979-10-01
A functional relation between the kinetic energy density and the total density is used to analyse the surface properties of semi-infinite Fermi systems. One find an explicit expression for the surface thickness in which the role of the infinite matter compressibility, binding energy and non-locality effects is clearly shown. The method, which holds both for nuclear and electronic systems (liquid metals), yields a very simple relation between the surface thickness and the surface energy
Li, Xiaodi; Shen, Jianhua; Akca, Haydar; Rakkiyappan, R.
2018-04-01
We introduce the Razumikhin technique to comparison principle and establish some comparison results for impulsive functional differential equations (IFDEs) with infinite delays, where the infinite delays may be infinite time-varying delays or infinite distributed delays. The idea is, under the help of Razumikhin technique, to reduce the study of IFDEs with infinite delays to the study of scalar impulsive differential equations (IDEs) in which the solutions are easy to deal with. Based on the comparison principle, we study the qualitative properties of IFDEs with infinite delays , which include stability, asymptotic stability, exponential stability, practical stability, boundedness, etc. It should be mentioned that the developed results in this paper can be applied to IFDEs with not only infinite delays but also persistent impulsive perturbations. Moreover, even for the special cases of non-impulsive effects or/and finite delays, the criteria prove to be simpler and less conservative than some existing results. Finally, two examples are given to illustrate the effectiveness and advantages of the proposed results.
Dynamics of a neuron model in different two-dimensional parameter-spaces
International Nuclear Information System (INIS)
Rech, Paulo C.
2011-01-01
We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades. - Research highlights: → We report parameter-spaces obtained for the Hindmarsh-Rose neuron model. → Regardless of the combination of parameters, a typical scenario is preserved. → The scenario presents a comb-shaped chaotic region immersed in a periodic region. → Periodic regions near the chaotic region are in period-adding bifurcation cascades.
Energy Technology Data Exchange (ETDEWEB)
Breban, Romulus [Institut Pasteur, Paris Cedex 15 (France)
2016-09-15
Five-dimensional (5D) space-time symmetry greatly facilitates how a 4D observer perceives the propagation of a single spinless particle in a 5D space-time. In particular, if the 5D geometry is independent of the fifth coordinate then the 5D physics may be interpreted as 4D quantum mechanics. In this work we address the case where the symmetry is approximate, focusing on the case where the 5D geometry depends weakly on the fifth coordinate. We show that concepts developed for the case of exact symmetry approximately hold when other concepts such as decaying quantum states, resonant quantum scattering, and Stokes drag are adopted, as well. We briefly comment on the optical model of the nuclear interactions and Millikan's oil drop experiment. (orig.)
Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time
Energy Technology Data Exchange (ETDEWEB)
Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)
2014-11-15
This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)
Efficient and accurate nearest neighbor and closest pair search in high-dimensional space
Tao, Yufei; Yi, Ke; Sheng, Cheng; Kalnis, Panos
2010-01-01
Nearest Neighbor (NN) search in high-dimensional space is an important problem in many applications. From the database perspective, a good solution needs to have two properties: (i) it can be easily incorporated in a relational database, and (ii
Irreducible quantum group modules with finite dimensional weight spaces
DEFF Research Database (Denmark)
Pedersen, Dennis Hasselstrøm
a finitely generated U q -module which has finite dimensional weight spaces and is a sum of those. Our approach follows the procedures used by S. Fernando and O. Mathieu to solve the corresponding problem for semisimple complex Lie algebra modules. To achieve this we have to overcome a number of obstacles...... not present in the classical case. In the process we also construct twisting functors rigerously for quantum group modules, study twisted Verma modules and show that these admit a Jantzen filtration with corresponding Jantzen sum formula....
Nomura, A; Yamazaki, Y; Tsuji, T; Kawasaki, Y; Tanaka, S
1996-09-15
For all biological particles such as cells or cellular organelles, there are three-dimensional coordinates representing the centroid or center of gravity. These coordinates and other numerical parameters such as volume, fluorescence intensity, surface area, and shape are referred to in this paper as geometric properties, which may provide critical information for the clarification of in situ mechanisms of molecular and cellular functions in living organisms. We have established a method for the elucidation of these properties, designated the three-dimensional labeling program (3DLP). Algorithms of 3DLP are so simple that this method can be carried out through the use of software combinations in image analysis on a personal computer. To evaluate 3DLP, it was applied to a 32-cell-stage sea urchin embryo, double stained with FITC for cellular protein of blastomeres and propidium iodide for nuclear DNA. A stack of optical serial section images was obtained by confocal laser scanning microscopy. The method was found effective for determining geometric properties and should prove applicable to the study of many different kinds of biological particles in three-dimensional space.
Geometric stability and electronic structure of infinite and finite phosphorus atomic chains
International Nuclear Information System (INIS)
Qiao Jingsi; Zhou Linwei; Ji Wei
2017-01-01
One-dimensional mono- or few-atomic chains were successfully fabricated in a variety of two-dimensional materials, like graphene, BN, and transition metal dichalcogenides, which exhibit striking transport and mechanical properties. However, atomic chains of black phosphorus (BP), an emerging electronic and optoelectronic material, is yet to be investigated. Here, we comprehensively considered the geometry stability of six categories of infinite BP atomic chains, transitions among them, and their electronic structures. These categories include mono- and dual-atomic linear, armchair, and zigzag chains. Each zigzag chain was found to be the most stable in each category with the same chain width. The mono-atomic zigzag chain was predicted as a Dirac semi-metal. In addition, we proposed prototype structures of suspended and supported finite atomic chains. It was found that the zigzag chain is, again, the most stable form and could be transferred from mono-atomic armchair chains. An orientation dependence was revealed for supported armchair chains that they prefer an angle of roughly 35 ° –37 ° perpendicular to the BP edge, corresponding to the [110] direction of the substrate BP sheet. These results may promote successive research on mono- or few-atomic chains of BP and other two-dimensional materials for unveiling their unexplored physical properties. (special topic)
F4 quantum integrable, rational and trigonometric models: space-of-orbits view
International Nuclear Information System (INIS)
Turbiner, A V; Vieyra, J C Lopez
2014-01-01
Algebraic-rational nature of the four-dimensional, F 4 -invariant integrable quantum Hamiltonians, both rational and trigonometric, is revealed and reviewed. It was shown that being written in F 4 Weyl invariants, polynomial and exponential, respectively, both similarity-transformed Hamiltonians are in algebraic form, they are quite similar the second order differential operators with polynomial coefficients; the flat metric in the Laplace-Beltrami operator has polynomial (in invariants) matrix elements. Their potentials are calculated for the first time: they are meromorphic (rational) functions with singularities at the boundaries of the configuration space. Ground state eigenfunctions are algebraic functions in a form of polynomials in some degrees. Both Hamiltonians preserve the same infinite flag of polynomial spaces with characteristic vector (1, 2, 2, 3), it manifests exact solvability. A particular integral common for both models is derived. The first polynomial eigenfunctions are presented explicitly.
Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability
Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.
2018-02-01
As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi
Dimensional transitions in thermodynamic properties of ideal Maxwell–Boltzmann gases
International Nuclear Information System (INIS)
Aydin, Alhun; Sisman, Altug
2015-01-01
An ideal Maxwell–Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale. (paper)
Three-dimensional studies on resorption spaces and developing osteons.
Tappen, N C
1977-07-01
Resorption spaces and their continuations as developing osteons were traced in serial cross sections from decalcified long bones of dogs, baboons and a man, and from a human rib. Processes of formation of osteons and transverse (Volkmann's) canals can be inferred from three-dimensional studies. Deposits of new osseous tissue begin to line the walls of the spaces soon after termination of resorption. The first deposits are osteoid, usually stained very darkly by the silver nitrate procedure utilized, but a lighter osteoid zone adjacent to the canals occurs frequently. Osteoid linings continue to be produced as lamellar bone forms around them; the large canals of immature osteons usually narrow very gradually. Frequently they terminate both proximally and distally as resorption spaces, indicating that osteons often advance in opposite directions as they develop. Osteoclasts of resorption spaces tunnel preferentially into highly mineralized bone, and usually do not use previously existing canals as templates for their advance. Osteons evidently originate by localized resorption of one side of the wall of an existing vascular channel in bone, with subsequent orientation of the resorption front along the axis of the shaft. Advancing resorption spaces also apparently stimulate the formation of numerous additional transverse canal connections to neighboring longitudinal canals. Serial tracing and silver nitrate differential staining combine to reveal many of the processes of bone remodeling at work, and facilitate quantitative treatment of the data. Further uses in studies of bone tissue and associated cells are recommended.
Superintegrability in two-dimensional Euclidean space and associated polynomial solutions
International Nuclear Information System (INIS)
Kalnins, E.G.; Miller, W. Jr; Pogosyan, G.S.
1996-01-01
In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the spectral functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial base for each of the nonsubgroup base, not just the subgroup cartesian and polar coordinate case, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the N-dimensional isotropic quantum oscillator. 28 refs., 1 tab
Three-dimensional reciprocal space x-ray coherent scattering tomography of two-dimensional object.
Zhu, Zheyuan; Pang, Shuo
2018-04-01
X-ray coherent scattering tomography is a powerful tool in discriminating biological tissues and bio-compatible materials. Conventional x-ray scattering tomography framework can only resolve isotropic scattering profile under the assumption that the material is amorphous or in powder form, which is not true especially for biological samples with orientation-dependent structure. Previous tomography schemes based on x-ray coherent scattering failed to preserve the scattering pattern from samples with preferred orientations, or required elaborated data acquisition scheme, which could limit its application in practical settings. Here, we demonstrate a simple imaging modality to preserve the anisotropic scattering signal in three-dimensional reciprocal (momentum transfer) space of a two-dimensional sample layer. By incorporating detector movement along the direction of x-ray beam, combined with a tomographic data acquisition scheme, we match the five dimensions of the measurements with the five dimensions (three in momentum transfer domain, and two in spatial domain) of the object. We employed a collimated pencil beam of a table-top copper-anode x-ray tube, along with a panel detector to investigate the feasibility of our method. We have demonstrated x-ray coherent scattering tomographic imaging at a spatial resolution ~2 mm and momentum transfer resolution 0.01 Å -1 for the rotation-invariant scattering direction. For any arbitrary, non-rotation-invariant direction, the same spatial and momentum transfer resolution can be achieved based on the spatial information from the rotation-invariant direction. The reconstructed scattering profile of each pixel from the experiment is consistent with the x-ray diffraction profile of each material. The three-dimensional scattering pattern recovered from the measurement reveals the partially ordered molecular structure of Teflon wrap in our sample. We extend the applicability of conventional x-ray coherent scattering tomography to
Classical gauge theories on the coadjoint orbits of infinite dimensional groups
International Nuclear Information System (INIS)
Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung
1991-01-01
We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)
Turnpike phenomenon and infinite horizon optimal control
Zaslavski, Alexander J
2014-01-01
This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value intergrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis, and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Resea...
Conservation laws for two (2 + 1)-dimensional differential-difference systems
International Nuclear Information System (INIS)
Yu Guofu; Tam, H.-W.
2006-01-01
Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced
Free topological vector spaces
Gabriyelyan, Saak S.; Morris, Sidney A.
2016-01-01
We define and study the free topological vector space $\\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\\mathbb{V}(X)$ is a $k_\\omega$-space if and only if $X$ is a $k_\\omega$-space. If $X$ is infinite, then $\\mathbb{V}(X)$ contains a closed vector subspace which is topologically isomorphic to $\\mathbb{V}(\\mathbb{N})$. It is proved that if $X$ is a $k$-space, then $\\mathbb{V}(X)$ is locally convex if and only if $X$ is discrete and countable. If $X$ is a metrizable space it is shown ...
Finite Metric Spaces of Strictly negative Type
DEFF Research Database (Denmark)
Hjorth, Poul G.
If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...
International Nuclear Information System (INIS)
Vu Ngoc Phat; Jong Yeoul Park
1995-10-01
The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs
Robust Consumption-Investment Problem on Infinite Horizon
Energy Technology Data Exchange (ETDEWEB)
Zawisza, Dariusz, E-mail: dariusz.zawisza@im.uj.edu.pl [Jagiellonian University in Krakow, Institute of Mathematics, Faculty of Mathematics and Computer Science (Poland)
2015-12-15
In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.
Transmission properties of one-dimensional ternary plasma photonic crystals
International Nuclear Information System (INIS)
Shiveshwari, Laxmi; Awasthi, S. K.
2015-01-01
Omnidirectional photonic band gaps (PBGs) are found in one-dimensional ternary plasma photonic crystals (PPC) composed of single negative metamaterials. The band characteristics and transmission properties are investigated through the transfer matrix method. We show that the proposed structure can trap light in three-dimensional space due to the elimination of Brewster's angle transmission resonance allowing the existence of complete PBG. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material, and number of unit cells (N) for TE and TM polarizations. It is seen that PBG characteristics is apparent even in an N ≥ 2 system, which is weakly sensitive to the incident angle and completely insensitive to the polarization. Finite PPC could be used for multichannel transmission filter without introducing any defect in the geometry. We show that the locations of the multichannel transmission peaks are in the allowed band of the infinite structure. The structure can work as a single or multichannel filter by varying the number of unit cells. Binary PPC can also work as a polarization sensitive tunable filter
Transmission properties of one-dimensional ternary plasma photonic crystals
Energy Technology Data Exchange (ETDEWEB)
Shiveshwari, Laxmi [Department of Physics, K. B. Womens' s College, Hazaribagh 825 301 (India); Awasthi, S. K. [Department of Physics and Material Science and Engineering, Jaypee Institute of Information Technology, Noida 201 304 (India)
2015-09-15
Omnidirectional photonic band gaps (PBGs) are found in one-dimensional ternary plasma photonic crystals (PPC) composed of single negative metamaterials. The band characteristics and transmission properties are investigated through the transfer matrix method. We show that the proposed structure can trap light in three-dimensional space due to the elimination of Brewster's angle transmission resonance allowing the existence of complete PBG. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material, and number of unit cells (N) for TE and TM polarizations. It is seen that PBG characteristics is apparent even in an N ≥ 2 system, which is weakly sensitive to the incident angle and completely insensitive to the polarization. Finite PPC could be used for multichannel transmission filter without introducing any defect in the geometry. We show that the locations of the multichannel transmission peaks are in the allowed band of the infinite structure. The structure can work as a single or multichannel filter by varying the number of unit cells. Binary PPC can also work as a polarization sensitive tunable filter.
Compound Structure-Independent Activity Prediction in High-Dimensional Target Space.
Balfer, Jenny; Hu, Ye; Bajorath, Jürgen
2014-08-01
Profiling of compound libraries against arrays of targets has become an important approach in pharmaceutical research. The prediction of multi-target compound activities also represents an attractive task for machine learning with potential for drug discovery applications. Herein, we have explored activity prediction in high-dimensional target space. Different types of models were derived to predict multi-target activities. The models included naïve Bayesian (NB) and support vector machine (SVM) classifiers based upon compound structure information and NB models derived on the basis of activity profiles, without considering compound structure. Because the latter approach can be applied to incomplete training data and principally depends on the feature independence assumption, SVM modeling was not applicable in this case. Furthermore, iterative hybrid NB models making use of both activity profiles and compound structure information were built. In high-dimensional target space, NB models utilizing activity profile data were found to yield more accurate activity predictions than structure-based NB and SVM models or hybrid models. An in-depth analysis of activity profile-based models revealed the presence of correlation effects across different targets and rationalized prediction accuracy. Taken together, the results indicate that activity profile information can be effectively used to predict the activity of test compounds against novel targets. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Energy Technology Data Exchange (ETDEWEB)
Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)
2014-12-01
In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)
Directory of Open Access Journals (Sweden)
Marshall Naylor
2018-01-01
Full Text Available Prominent approaches to the problems of evil assume that even if the Anselmian God exists, some worlds are better than others, all else being equal. But the assumptions that the Anselmian God exists and that some worlds are better than others cannot be true together. One description, by Mark Johnston and Georg Cantor, values God’s existence as exceeding any transfinite cardinal value. For any finite or infinite amount of goodness in any possible world, God’s value infinitely exceeds that amount. This conception is not obviously inconsistent with the Anselmian God. As a result, the prominent approaches to the problems of evil are mistaken. The elimination of evil does not, in fact, improve the value of any world as commonly thought. Permitting evil does not, in fact, diminish the value of any world as commonly thought.
Horizontal biases in rats’ use of three-dimensional space
Jovalekic, Aleksandar; Hayman, Robin; Becares, Natalia; Reid, Harry; Thomas, George; Wilson, Jonathan; Jeffery, Kate
2011-01-01
Rodent spatial cognition studies allow links to be made between neural and behavioural phenomena, and much is now known about the encoding and use of horizontal space. However, the real world is three dimensional, providing cognitive challenges that have yet to be explored. Motivated by neural findings suggesting weaker encoding of vertical than horizontal space, we examined whether rats show a similar behavioural anisotropy when distributing their time freely between vertical and horizontal movements. We found that in two- or three-dimensional environments with a vertical dimension, rats showed a prioritization of horizontal over vertical movements in both foraging and detour tasks. In the foraging tasks, the animals executed more horizontal than vertical movements and adopted a “layer strategy” in which food was collected from one horizontal level before moving to the next. In the detour tasks, rats preferred the routes that allowed them to execute the horizontal leg first. We suggest three possible reasons for this behavioural bias. First, as suggested by Grobety and Schenk [5], it allows minimisation of energy expenditure, inasmuch as costly vertical movements are minimised. Second, it may be a manifestation of the temporal discounting of effort, in which animals value delayed effort as less costly than immediate effort. Finally, it may be that at the neural level rats encode the vertical dimension less precisely, and thus prefer to bias their movements in the more accurately encoded horizontal dimension. We suggest that all three factors are related, and all play a part. PMID:21419172
Jiang, Shidong; Xu, Minzhong
2005-01-01
The analytical solutions for the general-four-wave-mixing hyperpolarizabilities $\\chi^{(3)}(-(w_1+w_2+w_3);w_1,w_2,w_3)$ on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained through the scheme of dipole-dipole correlation. Analytical expressions of DC Kerr effect $\\chi^{(3)}(-w;0,0,w)$, DC-induced second harmonic generation $\\chi^{(3)}(-2w;0,w,w)$, optical Kerr effect $\\chi^{(3)}(-w;w,-w,w)$ and DC-electric-field-induced optica...
International Nuclear Information System (INIS)
Ganapol, B.D.; Kornreich, D.E.
1997-01-01
Because of the requirement of accountability and quality control in the scientific world, a demand for high-quality analytical benchmark calculations has arisen in the neutron transport community. The intent of these benchmarks is to provide a numerical standard to which production neutron transport codes may be compared in order to verify proper operation. The overall investigation as modified in the second year renewal application includes the following three primary tasks. Task 1 on two dimensional neutron transport is divided into (a) single medium searchlight problem (SLP) and (b) two-adjacent half-space SLP. Task 2 on three-dimensional neutron transport covers (a) point source in arbitrary geometry, (b) single medium SLP, and (c) two-adjacent half-space SLP. Task 3 on code verification, includes deterministic and probabilistic codes. The primary aim of the proposed investigation was to provide a suite of comprehensive two- and three-dimensional analytical benchmarks for neutron transport theory applications. This objective has been achieved. The suite of benchmarks in infinite media and the three-dimensional SLP are a relatively comprehensive set of one-group benchmarks for isotropically scattering media. Because of time and resource limitations, the extensions of the benchmarks to include multi-group and anisotropic scattering are not included here. Presently, however, enormous advances in the solution for the planar Green's function in an anisotropically scattering medium have been made and will eventually be implemented in the two- and three-dimensional solutions considered under this grant. Of particular note in this work are the numerical results for the three-dimensional SLP, which have never before been presented. The results presented were made possible only because of the tremendous advances in computing power that have occurred during the past decade
Guiding spoof surface plasmon polaritons by infinitely thin grooved metal strip
Directory of Open Access Journals (Sweden)
Xiang Wan
2014-04-01
Full Text Available In this paper, the propagation characteristics of spoof surface plasmon polaritons (SPPs on infinitely thin corrugated metal strips are theoretically analyzed. Compared with the situations of infinitely thick lateral thickness, the infinitely thin lateral thickness leads to lower plasma frequency according to the analyses. The propagation lengths and the binding capacity of the spoof SPPs are evaluated based on the derived dispersion equation. The effects of different lateral thicknesses are also investigated. At the end, a surface wave splitter is presented using infinitely thin corrugated metal strip. Other functional planar or flexible devices can also be designed using these metal strips in microwave or terahertz regimes.
An Infinite Sequence of Full AFL-Structures, Each of Which Possesses an Infinite Hierarchy
Asveld, P.R.J.
1999-01-01
We investigate different sets of operations on languages which results in corresponding algebraic structures, viz.\\ in different types of full AFL's (full Abstract Family of Languages). By iterating control on ETOL-systems we show that there exists an infinite sequence ${\\cal C}_m$ ($m\\geq1$) of
An Infinite Sequence of Full AFL-structures, Each of Which Possesses an Infinite Hierarchy
Asveld, P.R.J.; Martin-Vide, C.; Mitrana, V.
2001-01-01
We investigate different sets of operations on languages which results in corresponding algebraic structures, viz.\\ in different types of full AFL's (full Abstract Family of Languages). By iterating control on ETOL-systems we show that there exists an infinite sequence ${\\cal C}_m$ ($m\\geq1$) of
Directory of Open Access Journals (Sweden)
L.V. Arun Shalin
2016-01-01
Full Text Available Clustering is a process of grouping elements together, designed in such a way that the elements assigned to similar data points in a cluster are more comparable to each other than the remaining data points in a cluster. During clustering certain difficulties related when dealing with high dimensional data are ubiquitous and abundant. Works concentrated using anonymization method for high dimensional data spaces failed to address the problem related to dimensionality reduction during the inclusion of non-binary databases. In this work we study methods for dimensionality reduction for non-binary database. By analyzing the behavior of dimensionality reduction for non-binary database, results in performance improvement with the help of tag based feature. An effective multi-clustering anonymization approach called Discrete Component Task Specific Multi-Clustering (DCTSM is presented for dimensionality reduction on non-binary database. To start with we present the analysis of attribute in the non-binary database and cluster projection identifies the sparseness degree of dimensions. Additionally with the quantum distribution on multi-cluster dimension, the solution for relevancy of attribute and redundancy on non-binary data spaces is provided resulting in performance improvement on the basis of tag based feature. Multi-clustering tag based feature reduction extracts individual features and are correspondingly replaced by the equivalent feature clusters (i.e. tag clusters. During training, the DCTSM approach uses multi-clusters instead of individual tag features and then during decoding individual features is replaced by corresponding multi-clusters. To measure the effectiveness of the method, experiments are conducted on existing anonymization method for high dimensional data spaces and compared with the DCTSM approach using Statlog German Credit Data Set. Improved tag feature extraction and minimum error rate compared to conventional anonymization
Collapsing perfect fluid in self-similar five dimensional space-time and cosmic censorship
International Nuclear Information System (INIS)
Ghosh, S.G.; Sarwe, S.B.; Saraykar, R.V.
2002-01-01
We investigate the occurrence and nature of naked singularities in the gravitational collapse of a self-similar adiabatic perfect fluid in a five dimensional space-time. The naked singularities are found to be gravitationally strong in the sense of Tipler and thus violate the cosmic censorship conjecture
A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space
International Nuclear Information System (INIS)
Le, Van-Hoang; Nguyen, Thanh-Son
2011-01-01
We establish an explicit form of a non-Abelian SO(8) monopole in a 9-dimensional space and show that it is indeed a direct generalization of Dirac and Yang monopoles. Using the generalized Hurwitz transformation, we have found a connection between a 16-dimensional harmonic oscillator and a 9-dimensional hydrogenlike atom in the field of the SO(8) monopole (MICZ-Kepler problem). Using the built connection the group of dynamical symmetry of the 9-dimensional MICZ-Kepler problem is found as SO(10, 2).
Chemical potential of one-dimensional simple harmonic oscillators
International Nuclear Information System (INIS)
Mungan, Carl E
2009-01-01
Expressions for the chemical potential of an Einstein solid, and of ideal Fermi and Bose gases in an external one-dimensional oscillatory trap, are calculated by two different methods and are all found to share the same functional form. These derivations are easier than traditional textbook calculations for an ideal gas in an infinite three-dimensional square well. Furthermore, the results indicate some important features of chemical potential that could promote student learning in an introductory course in statistical mechanics at the undergraduate level.
Topological phases of interacting fermions in one-dimensional superconductor - normal metal geometry
Energy Technology Data Exchange (ETDEWEB)
Meidan, Dganit [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universitaet Berlin, 14195 Berlin (Germany); Romito, Alessandro; Brouwer, Piet W. [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)
2015-07-01
One-dimensional superconductors can be in non-trivial topological phases harboring Majorana end-states, which possess non-abelian statistics. It has been recently established that in the presence of interactions the classification of topological superconducting phases can be significantly altered. Specifically, for one-dimensional superconductors possessing a time reversal symmetry (BDI class), interactions reduce the infinitely many non-interacting phases (Z topological index) to eight distinct ones (Z{sub 8} topological index). In this talk I will consider multi-mode superconducting wires in such BDI class when probed by an external contact, and discuss their low temperature and voltage bias transport properties. I will first show that the Andreev reflection component of the scattering matrix of the probing lead provides a topological index, r=-4,.., 4, which distinguish the eight topological phases. The two topologically equivalent phases with r= 4,-4 support emergent many-body end states, which are identified to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops.
Infinite games and $sigma$-porosity
Czech Academy of Sciences Publication Activity Database
Doležal, Martin; Preiss, D.; Zelený, M.
2016-01-01
Roč. 215, č. 1 (2016), s. 441-457 ISSN 0021-2172 Institutional support: RVO:67985840 Keywords : infinite games Subject RIV: BA - General Mathematics Impact factor: 0.796, year: 2016 http://link.springer.com/article/10.1007%2Fs11856-016-1383-9
International Nuclear Information System (INIS)
Leverrier, A; Karpov, E; Cerf, N J; Grangier, P
2009-01-01
Proving the unconditional security of quantum key distribution (QKD) is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A possible strategy to address this problem is to make an extensive use of the symmetries of the protocol. In this paper, we investigate a rotation symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de Finetti theorem that would exploit this symmetry and provide a powerful tool to assess the security of continuous-variable protocols. As a first step, a single-party asymptotic version of this quantum de Finetti theorem in phase space is derived.
Borel hierarchies in infinite products of Polish spaces
Indian Academy of Sciences (India)
with two product topologies: (i) the product of copies of the Polish topology on X, so that H is again a Polish space and (ii) the product of copies of the discrete topology on X. Define now the Borel hierarchy in the larger topology on H. To do so, we need some notation. An element of H will be denoted by h = (x1,x2,...,xn,.
Comments on the integrability of the loop-space chiral equations
International Nuclear Information System (INIS)
Gu, C.; Wang, L.L.C.
1980-01-01
A demonstration is given how the ordinary space chiral equations provide the existence conditions for the infinite number of conserved currents and how these currents are related to the so-called inverse-scattering equations, whose integrability is provided by the original chiral equations. Loop-space chiral equations are introduced. The integrability conditions of the non-local currents in two possible different situations are discussed. In the first case, the generating functions are functionals of the loop alone. The integrability conditions are not satisfied and higher order conserved non-local currents do not exist. In the second case, the generating functions are functionals of the loop as well as a parameter the integrability conditions at a restricted point of the parameter are satisfied, however there is an infinite fold of arbitrariness. It indicates that additional guiding principles are needed in addition to the original loop-space chiral equation in order to uniquely determine the infinite conserved non-local currents as functionals of the loop and the parameter
Photons in Fock space and beyond
Honegger, Reinhard
2015-01-01
The three-volume major reference "Photons in Fock Space and Beyond" undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantu...
Ramsey theory for product spaces
Dodos, Pandelis
2016-01-01
Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics. This book is devoted to one of the most important areas of Ramsey theory-the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales-Jewett theorem. This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, ...
Internal space-time symmetries of massive and massless particles and their unification
International Nuclear Information System (INIS)
Kim, Y.S.
2001-01-01
It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted also that, while the rotational degree of freedom for a massless particle leads to its helicity, the two translational degrees of freedom correspond to its gauge degrees of freedom. It is shown that the E(2)-like symmetry of of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like symmetry of massive particles. This mechanism is illustrated in terms of a sphere elongating into a cylinder. In this way, the helicity degree of freedom remains invariant under the Lorentz boost, but the transverse rotational degrees of freedom become contracted into the gauge degree of freedom
Automated Analysis of Infinite Scenarios
DEFF Research Database (Denmark)
Buchholtz, Mikael
2005-01-01
The security of a network protocol crucially relies on the scenario in which the protocol is deployed. This paper describes syntactic constructs for modelling network scenarios and presents an automated analysis tool, which can guarantee that security properties hold in all of the (infinitely many...
International Nuclear Information System (INIS)
Christodoulakis, T; Doulis, G; Terzis, Petros A; Melas, E; Grammenos, Th; Papadopoulos, G O; Spanou, A
2010-01-01
The canonical decomposition of all 3+1 geometries admitting two-dimensional space-like surfaces is exhibited as a generalization of a previous work. A proposal, consisting of a specific renormalization Assumption and an accompanying Requirement, which has been put forward in the 2+1 case is now generalized to 3+1 dimensions. This enables the canonical quantization of these geometries through a generalization of Kuchar's quantization scheme in the case of infinite degrees of freedom. The resulting Wheeler-DeWitt equation is based on a renormalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, a fact that is entirely new to the present case. This is made possible through the exploitation of the residual freedom in the choice of the third functional, which is left by the imposition of the Requirement, and is proven to correspond to a general coordinate transformation in the renormalized manifold.