Counterexamples in probability
Stoyanov, Jordan M
2013-01-01
While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix.
Steen, Lynn Arthur
1978-01-01
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.
Abortion: Strong's counterexamples fail
DEFF Research Database (Denmark)
Di Nucci, Ezio
2009-01-01
This paper shows that the counterexamples proposed by Strong in 2008 in the Journal of Medical Ethics to Marquis's argument against abortion fail. Strong's basic idea is that there are cases--for example, terminally ill patients--where killing an adult human being is prima facie seriously morally......'s scenarios have some valuable future or admitted that killing them is not seriously morally wrong. Finally, if "valuable future" is interpreted as referring to objective standards, one ends up with implausible and unpalatable moral claims....
Finite-dimensional division algebras over fields
Jacobson, Nathan
2009-01-01
Finite-Dimensional Division Algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called 'multiplication algebras of Riemann matrices'. The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of parti
Lectures on counterexamples in several complex variables
Fornæss, John Erik
2007-01-01
Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornæss and Stensønes look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampère equations, CR geometry, function theory, and the \\bar\\
Supraclassical consequence relations: Tolerating rare counterexamples
CSIR Research Space (South Africa)
Labuschagne, W
2013-12-01
Full Text Available We explore a family of supraclassical consequence relations obtained by varying the criteria according to which counterexamples to classical entailment may be deemed tolerable. This provides a different perspective on the rational consequence...
Computations in finite-dimensional Lie algebras
Directory of Open Access Journals (Sweden)
A. M. Cohen
1997-12-01
Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.
The Socle and finite dimensionality of some Banach algebras
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
It follows that µ = 0. By Proposition 1, we have Soc(L1(G)) = Soc(M(G)). In the following Theorem we will provide some conditions on A and A∗∗ that are sufficient to guarantee finite dimensionality. Theorem 1. Let A be a Banach algebra with a bounded approximate identity. If. Soc(A∗∗) = A∗∗. , then A is finite dimensional.
Finite-Dimensional Representations for Controlled Diffusions with Delay
Energy Technology Data Exchange (ETDEWEB)
Federico, Salvatore, E-mail: salvatore.federico@unimi.it [Università di Milano, Dipartimento di Economia, Management e Metodi Quantitativi (Italy); Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr [Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires (France)
2015-02-15
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.
Wigner distributions for finite dimensional quantum systems: An ...
Indian Academy of Sciences (India)
2005-07-11
Jul 11, 2005 ... physics pp. 981–993. Wigner distributions for finite dimensional quantum systems: An algebraic approach. S CHATURVEDI1,∗, E ERCOLESSI2, G MARMO3, G MORANDI4, ... Abstract. We discuss questions pertaining to the definition of 'momentum', 'momentum space' ..... multiple of the parity operator.
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)
Integrable finite-dimensional systems related to Lie algebras
International Nuclear Information System (INIS)
Olshanetsky, M.A.; Perelomov, A.M.
1979-01-01
Some solvable finite-dimensional classical and quantum systems related to the Lie algebras are considered. The dynamics of these systems is closely related to free motion on symmetric spaces. In specific cases the systems considered describe the one-dimensional n-body problem recently considered by many authors. The review represents from general and universal point of view the results obtained during the last few years. Besides, it contains some results both of physical and mathematical type
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....
Incoherent systems and coverings in finite dimensional Banach spaces
Energy Technology Data Exchange (ETDEWEB)
Temlyakov, V N [Steklov Mathematical Institute of the Russian Academy of Sciences (Russian Federation)
2014-05-31
We discuss the construction of coverings of the unit ball of a finite dimensional Banach space. There is a well-known technique based on comparing volumes which gives upper and lower bounds on covering numbers. However, this technique does not provide a method for constructing good coverings. Here we study incoherent systems and apply them to construct good coverings. We use the following strategy. First, we build a good covering using balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We shall concentrate mainly on the first step of this strategy. Bibliography: 14 titles.
Ordering, symbols and finite-dimensional approximations of path integrals
International Nuclear Information System (INIS)
Kashiwa, Taro; Sakoda, Seiji; Zenkin, S.V.
1994-01-01
We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of O(ε), where ε of is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of pq- and qp-ordering. As an explicit example the fermionic oscillator is considered in detail. (author)
Gauge theory for finite-dimensional dynamical systems
International Nuclear Information System (INIS)
Gurfil, Pini
2007-01-01
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently ''disordered'' flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory
Discrete coherent states and probability distributions in finite-dimensional spaces
Energy Technology Data Exchange (ETDEWEB)
Galetti, D.; Marchiolli, M.A.
1995-06-01
Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well know results. (author). 20 refs, 2 figs.
Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras
Cheng, Shun-Jen; Kwon, Jae-Hoon
2016-09-01
We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra {{q}(n)}. It is given in terms of the Brundan's work on finite-dimensional integer weight {{q}(n)}-modules by means of Lusztig's canonical basis. Using this viewpoint we compute the characters of the finite-dimensional half-integer weight irreducible modules. For a large class of irreducible modules whose highest weights are of special types (i.e., totally connected or totally disconnected) we derive closed-form character formulas that are reminiscent of the Kac-Wakimoto character formula for basic Lie superalgebras.
Automatic proofs and counterexamples for some ortholattice identities.
Energy Technology Data Exchange (ETDEWEB)
McCune, W.; Mathematics and Computer Science
1998-01-01
This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, and the other two are proved to hold by EQP, an equational theorem proven. The problems, from work in quantum logic, were given to us by Norman Megill.
Two kinds of finite-dimensional integrable reduction to the Harry-Dym hierarchy
Chen, Jinbing
2016-11-01
In this paper, two kinds of finite-dimensional integrable reduction are studied for the Harry-Dym (HD) hierarchy. From the nonlinearization of Lax pair, the HD hierarchy is reduced to a class of finite-dimensional Hamiltonian systems (FDHSs) in view of a Bargmann map and a set of Neumann type systems by a Neumann map, which separate temporal and spatial variables on the symplectic space (ℝ2N,ω2) and the tangent bundle of ellipsoid (TSN-1,ω2), respectively. It turns out that involutive solutions of the resulted finite-dimensional integrable systems (FDISs) directly give rise to finite parametric solutions of HD hierarchy through the Bargmann and Neumann maps. The finite-gap potential to the high-order stationary HD equation is obtained that cuts out a finite-dimensional invariant subspace for the HD flows. Finally, some comparisons of two kinds of integrable reductions are then discussed.
A new (in)finite-dimensional algebra for quantum integrable models
International Nuclear Information System (INIS)
Baseilhac, Pascal; Koizumi, Kozo
2005-01-01
A new (in)finite-dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite-dimensional representations are constructed and mutually commuting quantities-which ensure the integrability of the system-are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan-Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite-dimensional algebra is a 'q-deformed' analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models
A finite-dimensional reduction method for slightly supercritical elliptic problems
Directory of Open Access Journals (Sweden)
Riccardo Molle
2004-01-01
Full Text Available We describe a finite-dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite-dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.
Finite-dimensional effects and critical indices of one-dimensional quantum models
International Nuclear Information System (INIS)
Bogolyubov, N.M.; Izergin, A.G.; Reshetikhin, N.Yu.
1986-01-01
Critical indices, depending on continuous parameters in Bose-gas quantum models and Heisenberg 1/2 spin antiferromagnetic in two-dimensional space-time at zero temperature, have been calculated by means of finite-dimensional effects. In this case the long-wave asymptotics of the correlation functions is of a power character. Derivation of man asymptotics terms is reduced to the determination of a central charge in the appropriate Virassoro algebra representation and the anomalous dimension-operator spectrum in this representation. The finite-dimensional effects allow to find these values
Reparametrization in the path integral over finite dimensional manifold with a time-dependent metric
International Nuclear Information System (INIS)
Storchak, S.N.
1988-01-01
The path reparametrization procedure in the path integral is considered using the methods of stochastic processes for diffusion on finite dimensional manifold with a time-dependent metric. the reparametrization Jacobian has been obtained. The formulas of reparametrization for a symbolic presentation of the path integral have been derived
International Nuclear Information System (INIS)
Santhanam, T.S.; Jagannathan, R.
1986-12-01
Finite dimensional matrix representations of differential operators are discussed. The determinental form of polynomials is used to relate their zeros to the eigenvalues of Jacobi's tridiagonal matrix for the case of special functions. The distribution of these zeros is analyzed. (author)
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)
Finite-dimensional output feedback regulator for a mono-tubular heatexchanger process
Xu, Xiaodong; Dubljevic, Stevan
2016-01-01
In this work, we consider the output tracking and disturbance rejection problems of a mono-tubular heat exchanger process and a novel finite-dimensional output feedback regulator is developed. In the proposed output feedback regulator design, measurements available for the regulator do not belong to the set of controlled outputs. In other words, design emphasizes that other than controlled output is used as input signal to the regulator. The proposed output feedback regulator with only plant ...
Absolute continuity of autophage measures on finite-dimensional vector spaces
International Nuclear Information System (INIS)
Raja, C.R.E.
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 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)
Quantum limits to information about states for finite dimensional Hilbert space
International Nuclear Information System (INIS)
Jones, K.R.W.
1990-01-01
A refined bound for the correlation information of an N-trial apparatus is developed via an heuristic argument for Hilbert spaces of arbitrary finite dimensionality. Conditional upon the proof of an easily motivated inequality it was possible to find the optimal apparatus for large ensemble quantum Inference, thereby solving the asymptotic optimal state determination problem. In this way an alternative inferential uncertainty principle, is defined which is then contrasted with the usual Heisenberg uncertainty principle. 6 refs
Energy conservation with non-symplectic methods: examples and counter-examples
Faou, Erwan; Hairer, Ernst; Pham, Truong-Linh
2004-01-01
Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented.
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
Berlyand, Leonid; Owhadi, Houman
2010-11-01
We consider linear divergence-form scalar elliptic equations and vectorial equations for elasticity with rough ( L ∞(Ω), {Ω subset mathbb R^d}) coefficients a( x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most general case of arbitrary bounded coefficients. For such problems, we introduce explicit and optimal finite dimensional approximations of solutions that can be viewed as a theoretical Galerkin method with controlled error estimates, analogous to classical homogenization approximations. In particular, this approach allows one to analyze a given medium directly without introducing the mathematical concept of an {ɛ} family of media as in classical homogenization. We define the flux norm as the L 2 norm of the potential part of the fluxes of solutions, which is equivalent to the usual H 1-norm. We show that in the flux norm, the error associated with approximating, in a properly defined finite-dimensional space, the set of solutions of the aforementioned PDEs with rough coefficients is equal to the error associated with approximating the set of solutions of the same type of PDEs with smooth coefficients in a standard space (for example, piecewise polynomial). We refer to this property as the transfer property. A simple application of this property is the construction of finite dimensional approximation spaces with errors independent of the regularity and contrast of the coefficients and with optimal and explicit convergence rates. This transfer property also provides an alternative to the global harmonic change of coordinates for the homogenization of elliptic operators that can be extended to elasticity equations. The proofs of these homogenization results are based on a new class of elliptic inequalities. These inequalities play the same role in our approach
International Nuclear Information System (INIS)
Barrios, Dolores; Lopez, Guillermo L; Martinez-Finkelshtein, A; Torrano, Emilio
1999-01-01
The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established
International Nuclear Information System (INIS)
Castellani, Marco; Giuli, Massimiliano
2016-01-01
We study pseudomonotone and quasimonotone quasivariational inequalities in a finite dimensional space. In particular we focus our attention on the closedness of some solution maps associated to a parametric quasivariational inequality. From this study we derive two results on the existence of solutions of the quasivariational inequality. On the one hand, assuming the pseudomonotonicity of the operator, we get the nonemptiness of the set of the classical solutions. On the other hand, we show that the quasimonoticity of the operator implies the nonemptiness of the set of nonzero solutions. An application to traffic network is also considered
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
International Nuclear Information System (INIS)
Ivashchuk, V.D.
2017-01-01
A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants q s , s = 1,.., n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ s over a proper 2d submanifold are finite and obey the relations q s Φ s = 4πn s h s , where the h s > 0 are certain constants (related to dilatonic coupling vectors) and the n s are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s = 1,.., n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A 1 , A 2 , A 3 , C 2 , G 2 and A 1 + A 1 are presented. (orig.)
Reductions in finite-dimensional integrable systems and special points of classical r-matrices
Skrypnyk, T.
2016-12-01
For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
Energy Technology Data Exchange (ETDEWEB)
Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Institute of Gravitation and Cosmology, Moscow (Russian Federation)
2017-10-15
A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions H{sub s}(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants q{sub s}, s = 1,.., n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ{sup s} over a proper 2d submanifold are finite and obey the relations q{sub s} Φ{sup s} = 4πn{sub s}h{sub s}, where the h{sub s} > 0 are certain constants (related to dilatonic coupling vectors) and the n{sub s} are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s = 1,.., n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A{sub 1}, A{sub 2}, A{sub 3}, C{sub 2}, G{sub 2} and A{sub 1} + A{sub 1} are presented. (orig.)
Computational Topology Counterexamples with 3D Visualization of Bézier Curves
Directory of Open Access Journals (Sweden)
J. Li
2012-10-01
Full Text Available For applications in computing, Bézier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R3 and yields a smooth polynomial curve C embedded in R3. It is of interest to understand when L and C have the same embeddings. One class ofc ounterexamples is shown for L being unknotted, while C is knotted. Another class of counterexamples is created where L is equilateral and simple, while C is self-intersecting. These counterexamples were discovered using curve visualizing software and numerical algorithms that produce general procedures to create more examples.
International Nuclear Information System (INIS)
Nguyen Buong.
1992-11-01
The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs
Ko, Yi-Yin; Knuth, Eric J.
2013-01-01
Validating proofs and counterexamples across content domains is considered vital practices for undergraduate students to advance their mathematical reasoning and knowledge. To date, not enough is known about the ways mathematics majors determine the validity of arguments in the domains of algebra, analysis, geometry, and number theory--the domains…
Ko, Yi-Yin; Knuth, Eric
2009-01-01
In advanced mathematical thinking, proving and refuting are crucial abilities to demonstrate whether and why a proposition is true or false. Learning proofs and counterexamples within the domain of continuous functions is important because students encounter continuous functions in many mathematics courses. Recently, a growing number of studies…
Numerical and algebraic studies for the control of finite-dimensional quantum systems
Energy Technology Data Exchange (ETDEWEB)
Sander, Uwe
2010-11-18
In this thesis, two aspects of control theory, namely controllability and optimal control, are applied to quantum systems. The presented results are based on group theoretical techniques and numerical studies. By Lie-algebraic analysis, the controllability properties of systems with an arbitrary topology are described and related to the symmetries existing in these systems. We find that symmetry precludes full controllability. Our work investigates well-known control systems and gives rules for the design of new systems. Furthermore, theoretical and numerical concepts are instrumental to studying quantum channels: Their capacities are optimised using gradient flows on the unitary group in order to find counterexamples to a long-established additivity conjecture. The last part of this thesis presents and benchmarks a modular optimal control algorithm known as GRAPE. Numerical tests show how the interplay of its modules can be optimised for higher performance, and how the algorithm performs in comparison to a Krotov-type optimal control algorithm. It is found that GRAPE performs particularly well when aiming for high qualities. (orig.)
Finite dimensional approximation of a class of constrained nonlinear optimal control problems
Gunzburger, Max D.; Hou, L. S.
1994-01-01
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.
Partially-massless higher-spin algebras and their finite-dimensional truncations
International Nuclear Information System (INIS)
Joung, Euihun; Mkrtchyan, Karapet
2016-01-01
The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS d+1 are studied. The algebras involving PM generators up to depth 2 (ℓ−1) are defined as the maximal symmetries of free conformal scalar field with 2 ℓ order wave equation in d dimensions. We review the construction of these algebras by quotienting certain ideals in the universal enveloping algebra of (A)dS d+1 isometries. We discuss another description in terms of Howe duality and derive the formula for computing trace in these algebras. This enables us to explicitly calculate the bilinear form for this one-parameter family of algebras. In particular, the bilinear form shows the appearance of additional ideal for any non-negative integer values of ℓ−d/2 , which coincides with the annihilator of the one-row ℓ-box Young diagram representation of so d+2 . Hence, the corresponding finite-dimensional coset algebra spanned by massless and PM generators is equivalent to the symmetries of this representation.
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.
One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control
Taasan, Shlomo
1991-01-01
The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.
Counterexamples to regularity of Mañé projections in the theory of attractors
International Nuclear Information System (INIS)
Eden, Al'p; Zelik, Sergey V; Kalantarov, Varga K
2013-01-01
This paper is a study of global attractors of abstract semilinear parabolic equations and their embeddings in finite-dimensional manifolds. As is well known, a sufficient condition for the existence of smooth (at least C 1 -smooth) finite-dimensional inertial manifolds containing a global attractor is the so-called spectral gap condition for the corresponding linear operator. There are also a number of examples showing that if there is no gap in the spectrum, then a C 1 -smooth inertial manifold may not exist. On the other hand, since an attractor usually has finite fractal dimension, by Mañé's theorem it projects bijectively and Hölder-homeomorphically into a finite-dimensional generic plane if its dimension is large enough. It is shown here that if there are no gaps in the spectrum, then there exist attractors that cannot be embedded in any Lipschitz or even log-Lipschitz finite-dimensional manifold. Thus, if there are no gaps in the spectrum, then in the general case the inverse Mañé projection of the attractor cannot be expected to be Lipschitz or log-Lipschitz. Furthermore, examples of attractors with finite Hausdorff and infinite fractal dimension are constructed in the class of non-linearities of finite smoothness. Bibliography: 35 titles.
Czech Academy of Sciences Publication Activity Database
de Montigny, M.; Niederle, Jiří; Nikitin, A. G.
2006-01-01
Roč. 39, - (2006), s. 9365-9385 ISSN 0305-4470 R&D Projects: GA MŠk 1P04LA211 Grant - others:NSF PHY-0244261 Institutional research plan: CEZ:AV0Z10100502 Keywords : indecomposable finite dimensional representations * homogeneous Galilei group * Pauli anomalous interaction * Darwin and spin-orbit couplings Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 1.577, year: 2006
Euler equations on finite-dimensional Lie coalgebras, arising in problems of mathematical physics
Bogoyavlenskii, O. I.
1992-02-01
CONTENTSIntroductionChapter I. Euler equations on finite-dimensional Lie coalgebras, arising in physical problems §1. Classical investigations of the Euler equations of the rotation of an n-dimensional rigid body §2. Euler equations on Lie coalgebras, connected with the dynamics of a rigidbody around a fixed point and with the dynamics of a rigid body in an ideal incompressible fluid §3. Algebraic and Hamiltonian structure of the equations of rotation of a satellite around the mass centre §4. Physical applications of Euler equations on the direct sum of n Lie coalgebras SO(3)Chapter II. Integration of the dynamics of an arbitrary rigid body in the Newtonian gravitational field with an arbitrary quadratic potential §1. History of the problem §2. Integrability in the Liouville sense of the equations of rotation of a rigid body around a fixed mass centre in the field of remote attractive objects §3. Integrability in the Liouville sense of the equations of the translational-rotational dynamics of a rigid body in the Newtonian gravitational field with an arbitrary quadratic potential §4. The integrability of the dynamics in terms of Riemann theta-functions §5. Dynamics of a symmetric rigid body in the Newtonian gravitational field with an arbitrary quadratic potential §6. Integrable cases of equations of rotation of a rigid body in non-linear gravitational fields §7. Integrability of the n-dimensional analogue of the problem of rotation of a rigid body in the Newtonian gravitational field with an arbitrary quadratic potential §8. Lagrangian structure of the Kirchhoff equationsChapter III. General integrable problems of classical mechanics §1. Introduction and summary §2. Complete integrability of the dynamics of a C1-central configuration §3. General integrable problems of classical mechanics §4. Hidden symmetry of the inertial dynamics §5. Reductions and integrable cases of rotation of a Ck-central configuration around a fixed point in Newtonian
Nazarov, Anton
2012-11-01
In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent
Manukure, Solomon
2018-04-01
We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.
International Nuclear Information System (INIS)
Shan-Shan, Xu; Shu-Min, Li; Jamal, Berakdar
2009-01-01
As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell–Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces. (general)
Mendizabal, J E; Nowack, W J
1996-10-01
The topic of transitory impairment of consciousness with spike wave bursts has been of interest to neurologists for years. Based on some early experiments, a 3-second rule was formulated and has found its way into the conventional wisdom of neurology. It states that, in order to result in impairment of consciousness, a spike-wave burst must be of at least 3 seconds' duration. We discuss a case which poses a clinical counterexample to that rule.
Energy Technology Data Exchange (ETDEWEB)
Marchiolli, M.A., E-mail: marcelo_march@bol.com.br [Avenida General Osório 414, Centro, 14.870-100 Jaboticabal, SP (Brazil); Mendonça, P.E.M.F., E-mail: pmendonca@gmail.com [Academia da Força Aérea, C.P. 970, 13.643-970 Pirassununga, SP (Brazil)
2013-09-15
We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar–Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener–Khinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelet bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar–Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory. -- Highlights: •Conception of a quantum-algebraic framework embracing a new uncertainty principle for unitary operators. •Determination of new restrictions upon the selective process of signals and wavelet bases. •Demonstration of looser bounds interpolating between the tightest bound and the Massar–Spindel inequality. •Construction of finite ground states properly describing the tightest bound. •Establishment of an important connection with the discrete Weyl function.
Broken bridges: a counter-example of the ER=EPR conjecture
Energy Technology Data Exchange (ETDEWEB)
Chen, Pisin; Wu, Chih-Hung; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: b02202007@ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2017-06-01
In this paper, we provide a counter-example to the ER=EPR conjecture. In an anti-de Sitter space, we construct a pair of maximally entangled but separated black holes. Due to the vacuum decay of the anti-de Sitter background toward a deeper vacuum, these two parts can be trapped by bubbles. If these bubbles are reasonably large, then within the scrambling time, there should appear an Einstein-Rosen bridge between the two black holes. Now by tracing more details on the bubble dynamics, one can identify parameters such that one of the two bubbles either monotonically shrinks or expands. Because of the change of vacuum energy, one side of the black hole would evaporate completely. Due to the shrinking of the apparent horizon, a signal of one side of the Einstein-Rosen bridge can be viewed from the opposite side. We analytically and numerically demonstrate that within a reasonable semi-classical parameter regime, such process can happen. Bubbles are a non-perturbative effect, which is the crucial reason that allows the transmission of information between the two black holes through the Einstein-Rosen bridge, even though the probability is highly suppressed. Therefore, the ER=EPR conjecture cannot be generic in its present form and its validity maybe restricted.
International Nuclear Information System (INIS)
Shaaban, M.; Azit, A.H.; Nor, K.M.
2011-01-01
Despite the abundance of natural gas reserves in Malaysia coupled with serious government thrusts to promote cogeneration, its (cogeneration) development pace lags far off expectations. There are widespread fallacies among potential cogeneration developers and concerned professionals that cogeneration is uncompetitive in Malaysia due to existing policies of subsidized gas prices and grid-connection charges. This paper exposes these fallacies through counterexamples of practical cogeneration system design and evaluation of some segments of the industrial and service sectors in Peninsular Malaysia. The electrical and thermal characteristics of the cogeneration were modeled based on heat rate characteristics at partial loading patterns. A hierarchical mathematical programming approach that uses mixed-integer nonlinear optimization and dynamic programming principle, if necessary, is employed to determine the optimal size of cogeneration and its related auxiliary equipment as well as the optimal operation schedule. Financial assessment is integrated at a later stage to assess the economic viability of the system. Analyses of the cogeneration potential for several facilities of miscellaneous activities were carried out using various gas and electricity prices. Results obtained consistently rebuff the perpetuated fallacies and confirm that there is no real barrier to cogeneration development in Malaysia under current policies of gas prices and electricity tariffs. - Highlights: → Mixed-integer nonlinear programming and dynamic programming are used in the design. → Various loading levels are modeled and hourly operation schedule is determined. → Standby electricity charge has a minimal impact on cogeneration feasibility. → Gas and electricity prices are interrelated and affect cogeneration investment. → Under existing policies, there is no barrier to cogeneration adoption in Malaysia.
Energy Technology Data Exchange (ETDEWEB)
Shaaban, M., E-mail: m.shaaban@fke.utm.my [Centre of Electrical Energy Systems, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia); Azit, A.H. [Tenaga Nasional Berhad, Wisma TNB, Jalan Timur, 46200 Petaling Jaya, Selangor (Malaysia); Nor, K.M. [Centre of Electrical Energy Systems, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia)
2011-09-15
Despite the abundance of natural gas reserves in Malaysia coupled with serious government thrusts to promote cogeneration, its (cogeneration) development pace lags far off expectations. There are widespread fallacies among potential cogeneration developers and concerned professionals that cogeneration is uncompetitive in Malaysia due to existing policies of subsidized gas prices and grid-connection charges. This paper exposes these fallacies through counterexamples of practical cogeneration system design and evaluation of some segments of the industrial and service sectors in Peninsular Malaysia. The electrical and thermal characteristics of the cogeneration were modeled based on heat rate characteristics at partial loading patterns. A hierarchical mathematical programming approach that uses mixed-integer nonlinear optimization and dynamic programming principle, if necessary, is employed to determine the optimal size of cogeneration and its related auxiliary equipment as well as the optimal operation schedule. Financial assessment is integrated at a later stage to assess the economic viability of the system. Analyses of the cogeneration potential for several facilities of miscellaneous activities were carried out using various gas and electricity prices. Results obtained consistently rebuff the perpetuated fallacies and confirm that there is no real barrier to cogeneration development in Malaysia under current policies of gas prices and electricity tariffs. - Highlights: > Mixed-integer nonlinear programming and dynamic programming are used in the design. > Various loading levels are modeled and hourly operation schedule is determined. > Standby electricity charge has a minimal impact on cogeneration feasibility. > Gas and electricity prices are interrelated and affect cogeneration investment. > Under existing policies, there is no barrier to cogeneration adoption in Malaysia.
Finite-dimensional linear algebra
Gockenbach, Mark S
2010-01-01
Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq
Energy Technology Data Exchange (ETDEWEB)
Ranade, Kedar S.
2009-02-04
This PhD thesis deals with quantum-cryptographic protocols which allow general finite-dimensional quantum systems (qudits) as carriers of information in contrast to the predominantly used two-dimensional quantum systems (qubits). The main focus of investigations is the maximum tolerable error rate of such protocols and its behaviour as a function of the dimension of the information carriers. For this purpose, several concepts are introduced which allow the treatment of this problem. In particular, protocols are presented which work up to a maximum tolerate error rate, and it is shown that a wide class of protocols cannot be used for higher error rates. Among other things, it turns out that the maximum tolerable error rate for two-basis protocols increases up to 50% for high dimensions. Apart from the above-mentioned main subjects of this thesis, some other results from the field of quantum information theory are given, which were achieved during this PhD project. (orig.)
Hyperreflexivity of finite-dimensional subspaces
Czech Academy of Sciences Publication Activity Database
Müller, Vladimír; Ptak, M.
2005-01-01
Roč. 218, č. 3 (2005), s. 395-408 ISSN 0022-1236 R&D Projects: GA ČR(CZ) GA201/03/0041 Institutional research plan: CEZ:AV0Z10190503 Keywords : reflexive subspaces * hyperreflexive subspace * hyperreflexive constant Subject RIV: BA - General Mathematics Impact factor: 0.806, year: 2005
Finite Dimensional Approximations for Continuum Multiscale Problems
Energy Technology Data Exchange (ETDEWEB)
Berlyand, Leonid [Pennsylvania State Univ., University Park, PA (United States)
2017-01-24
The completed research project concerns the development of novel computational techniques for modeling nonlinear multiscale physical and biological phenomena. Specifically, it addresses the theoretical development and applications of the homogenization theory (coarse graining) approach to calculation of the effective properties of highly heterogenous biological and bio-inspired materials with many spatial scales and nonlinear behavior. This theory studies properties of strongly heterogeneous media in problems arising in materials science, geoscience, biology, etc. Modeling of such media raises fundamental mathematical questions, primarily in partial differential equations (PDEs) and calculus of variations, the subject of the PI’s research. The focus of completed research was on mathematical models of biological and bio-inspired materials with the common theme of multiscale analysis and coarse grain computational techniques. Biological and bio-inspired materials offer the unique ability to create environmentally clean functional materials used for energy conversion and storage. These materials are intrinsically complex, with hierarchical organization occurring on many nested length and time scales. The potential to rationally design and tailor the properties of these materials for broad energy applications has been hampered by the lack of computational techniques, which are able to bridge from the molecular to the macroscopic scale. The project addressed the challenge of computational treatments of such complex materials by the development of a synergistic approach that combines innovative multiscale modeling/analysis techniques with high performance computing.
Feynmann diagrams in a finite dimensional setting
Neiss, Daniel
2012-01-01
This article aims to explain and justify the use of Feynmann diagrams as a computational tool in physics. The integrals discussed may be seen as a toybox version of the real physical case. It starts out with the basic one-dimensional Gaussian integral and then proceeds with examples of multidimensional cases. Correlators and their solutions through generating functions and Wick's theorem are shown, as well as some examples of how to relate the computations to diagrams and the corresponding ru...
Computations in finite-dimensional Lie algebras
Cohen, A.M.; Graaf, W.A. de; Rónyai, L.
1997-01-01
This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the packagecan be found in Cohen and de Graaf[1]. Since then, in a collaborative
Counterexamples to Segal's Measure Representation Theorem
Wakker, P.P.
1993-01-01
This article discusses relations between several notions of continuity in rank-dependent utility, and in the generalized version of rank-dependent utility as initiated by Segal. Primarily, examples are given to show logical independencies between these notions of continuity. This also leads to
Surprises and counterexamples in real function theory
Rajwade, A R
2007-01-01
This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis.Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II.This book will be useful for students and teachers alike.
Automata Learning through Counterexample Guided Abstraction Refinement
DEFF Research Database (Denmark)
Aarts, Fides; Heidarian, Faranak; Kuppens, Harco
2012-01-01
Abstraction is the key when learning behavioral models of realistic systems. Hence, in most practical applications where automata learning is used to construct models of software components, researchers manually define abstractions which, depending on the history, map a large set of concrete events...... to a small set of abstract events that can be handled by automata learning tools. In this article, we show how such abstractions can be constructed fully automatically for a restricted class of extended finite state machines in which one can test for equality of data parameters, but no operations on data...
D-boundedness and D-compactness in finite dimensional ...
Indian Academy of Sciences (India)
normed spaces were introduced by Šerstnev [9] in 1962 by means of a definition that was closely modelled on the theory of (classical) normed spaces, and used to study the problem of best approximation in statistics. In the sequel, we shall adopt the usual terminology, notation and conventions of the theory of probabilistic ...
Wigner distributions for finite dimensional quantum systems: An ...
Indian Academy of Sciences (India)
2005-07-11
Jul 11, 2005 ... a spin 1/2 angular momentum in quantum mechanics were used effectively. The treatment of the odd prime dimensional case has been geometric in spirit. From the start it is assumed that the phase space is a square array of points, namely that. 'momentum space' is of the same 'size' as 'position' or ...
Nambu-Poisson reformulation of the finite dimensional dynamical systems
International Nuclear Information System (INIS)
Baleanu, D.; Makhaldiani, N.
1998-01-01
A system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system is introduced. We found in two simplest cases the complete sets of the integrals of motion using Nambu-Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures
Approximation of the Frame Coefficients using Finite Dimensional Methods
DEFF Research Database (Denmark)
Christensen, Ole; Casazza, P.
1997-01-01
A frame is a family $\\{f_i \\}_{i=1}^{\\infty}$ of elements in aHilbert space $\\cal H $with the property that every element in $\\cal H $ can be written as a(infinite) linear combination of the frame elements. Frame theorydescribes how one can choose the corresponding coefficients, which arecalled......_i \\}_{i=1}^{n}$ of the frame and theorthogonal projection $P_n$ onto its span. For $f \\in \\h ,P_nf$ has a representation as a linear combination of $f_i , i=1,2,..n,$and the corresponding coefficients can be calculated using finite dimensionalmethods. We find conditions implying that those coefficients...... frame coefficients. From the mathematical point of view this is gratifying, but for applications it is a problem that the calculationrequires inversion of an operator on $\\cal H $. \\The projection method is introduced in order to avoid thisproblem. The basic idea is toconsider finite subfamilies $\\{f...
Finite-dimensional reductions of the discrete Toda chain
Kazakova, T. G.
2004-08-01
The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well-known discrete Painlevé equations dPIII, dPV, dPVI. Lax representations for these discrete Painlevé equations are found.
D-boundedness and D-compactness in finite dimensional ...
Indian Academy of Sciences (India)
Introduction and preliminaries. K Menger introduced the notion of a probabilistic metric space in 1942 and since then the theory of probabilistic metric spaces has developed in many directions [8]. The idea of. Menger was to use distribution functions instead of nonnegative real numbers as values of the metric. The notion of ...
Counterexamples from elementary calculus to the beginnings of analysis
Bourchtein, Andrei
2014-01-01
IntroductionCommentsOn the structure of this bookOn mathematical language and notationBackground (elements of theory)SetsFunctionsFUNCTIONS OF ONE REAL VARIABLEElementary properties of functionsElements of theoryFunction definitionBoundednessPeriodicityEven/odd functionsMonotonicityExtremaExercisesLimitsElements of theoryConceptsElementary properties (arithmetic and comparative)ExercisesContinuityElements of theoryLocal propertiesGlobal properties: general resultsGlobal properties: the famous theorems Mapping setsWeierstrass theoremsIntermediate Value theoremUniform continuityExercisesDifferentiationElements of theoryConceptsLocal propertiesGlobal propertiesApplicationsTangent lineMonotonicity and local extremaConvexity and inflectionAsymptotesL'Hospital's ruleExercisesIntegralsElements of theoryIndefinite integralDefinite (Riemann) integralImproper integralsApplicationsExercisesSequences and seriesElements of theoryNumerical sequencesNumerical series: convergence and elementary propertiesNumerical series: co...
Examples and counter-examples of log-symplectic manifolds
Cavalcanti, Gil R.
We study topological properties of log-symplectic structures and produce examples of compact manifolds with such structures. Notably, we show that several symplectic manifolds do not admit bona fide log-symplectic structures and several bona fide log-symplectic manifolds do not admit symplectic
A counter-example in linear feature selection theory
Brown, D. R.; Omalley, M. J.
1976-01-01
The paper shows that it is possible to construct two k x n matrices, both of which maximize divergence in the transformed space of the linear feature selection problem in multiclass pattern recognition, and which are not row equivalent. Thus, even under extremely strong conditions, it is not possible to assume that all matrix solutions which maximize transformed divergence are row equivalent.
COUNTEREXAMPLE IN COGNITIVE CONFLICT AS FACTOR INFLUENCING CONCEPTUAL CHANGE
Sutopo Sutopo
2014-01-01
When a teacher trying to use anomaly phenomenon to encourage conceptual change, he/she will use model process cognitive conflict to anticipate how students may experience cognitive conflict. It can help teacher not to let students have conflict. Conflict Cognitive defined as conflict between structure cognitive (i.e, structure organized knowledge in brain) with the environment (for example, an experiment, demonstration, opinions of peers, books, or other), or conflict between concept in the c...
Coarsening at random: characterizations, conjectures and counter-examples
Gill, R.D.; Laan, M.J. van der; Robins, J.M.
1997-01-01
The notion of coarsening at random CAR was introduced by Heitjan and Rubin to describe the most general form of randomly grouped censored or missing data for which the coarsening mechanism can be ignored when making likelihoodbased inference about the parameters of the distribution of the variable
Counterexamples to the B-spline Conjecture for Gabor Frames
DEFF Research Database (Denmark)
Lemvig, Jakob; Nielsen, Kamilla Haahr
2016-01-01
The frame set conjecture for B-splines Bn, n≥2, states that the frame set is the maximal set that avoids the known obstructions. We show that any hyperbola of the form ab=r, where r is a rational number smaller than one and a and b denote the sampling and modulation rates, respectively, has infin...
A Parametric Counterexample Refinement Approach for Robust Timed Specifications
Directory of Open Access Journals (Sweden)
Louis-Marie Traonouez
2012-07-01
Full Text Available Robustness analyzes the impact of small perturbations in the semantics of a model. This allows to model hardware imprecision and therefore it has been applied to determine implementability of timed automata. In a recent paper, we extend this problem to a specification theory for real-timed systems based on timed input/output automata, that are interpreted as two-player games. We propose a construction that allows to synthesize an implementation of a specification that is robust under a given timed perturbation, and we study the impact of these perturbations when composing different specifications. To complete this work we present a technique that evaluates the greatest admissible perturbation. It consists in an iterative process that extracts a spoiling strategy when a game is lost, and through a parametric analysis refines the admissible values for the perturbation. We demonstrate this approach with a prototype implementation.
A Single Counterexample Leads to Moral Belief Revision.
Horne, Zachary; Powell, Derek; Hummel, John
2015-11-01
What kind of evidence will lead people to revise their moral beliefs? Moral beliefs are often strongly held convictions, and existing research has shown that morality is rooted in emotion and socialization rather than deliberative reasoning. In addition, more general issues-such as confirmation bias-further impede coherent belief revision. Here, we explored a unique means for inducing belief revision. In two experiments, participants considered a moral dilemma in which an overwhelming majority of people judged that it was inappropriate to take action to maximize utility. Their judgments contradicted a utilitarian principle they otherwise strongly endorsed. Exposure to this scenario led participants to revise their belief in the utilitarian principle, and this revision persisted over several hours. This method provides a new avenue for inducing belief revision. Copyright © 2015 Cognitive Science Society, Inc.
The role of diffeomorphisms in the integration over a finite dimensional space of geometries
International Nuclear Information System (INIS)
Menotti, P.
1998-01-01
Starting from the De Witt supermetric and limiting ourselves to a family of geometries characterized by a finite number of geometric invariants we extract the unique integration measure. Such a measure turns out to be a geometric invariant, i.e. independent of the gauge fixed metric used for describing the geometries. The measure is also invariant in form under an arbitrary change of parameters describing the geometries. The additional functional integration on the conformal factor makes the measure independent of the free parameter intervening in the De Witt supermetric. The differences between the case D=2 and D>2 are evidenced. (orig.)
Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
Czech Academy of Sciences Publication Activity Database
Chueshov, I.; Rezunenko, Oleksandr
2015-01-01
Roč. 14, č. 5 (2015), s. 1685-1704 ISSN 1534-0392 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic evolution equations * state-dependent delay * global attractor * finite-dimension * exponential attractor Subject RIV: BC - Control Systems Theory Impact factor: 0.926, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf
1991-01-01
multigrid methods , for the state and costate equations at each step of a descent algorithm. This may result in a significant saving in computa- tional time...to that of A the same fast solver can be used in all the steps. The operator A is assumed to be elliptic and therefore calls for multigrid methods . Assume...indefinite and nearly singular problems. Multigrnd Methods II, Lecture Notes in Mathe- matics 1228, Springer Verlag, 1985. [Ti] S. Ta’asan : Multigrid methods for
Finite-dimensional colored fluctuation-dissipation theorem for spin systems
Nicolis, Stam; Thibaudeau, Pascal; Tranchida, Julien
2017-05-01
When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin equation, for mapping the noise to the dynamical degrees of freedom. When the spin dynamics is discretized in time, a general fluctuation-dissipation theorem, valid for non-Markovian noise, can be established, even when zero modes are present. We discuss the subtleties that arise, when Gilbert damping is present and the mapping between noise and spin degrees of freedom is non-linear.
The Dynamics of Finite-Dimensional Systems Under Nonconservative Position Forces
Lobas, L. G.
2001-01-01
General theorems on the stability of stationary states of mechanical systems subjected to nonconservative position forces are presented. Specific mechanical problems on gyroscopic systems, a double-link pendulum with a follower force and elastically fixed upper tip, multilink pneumowheel vehicles, a monorail car, and rail-guided vehicles are analyzed. Methods for investigation of divergent bifurcations and catastrophes of stationary states are described
Alfven-wave particle interaction in finite-dimensional self-consistent field model
International Nuclear Information System (INIS)
Padhye, N.; Horton, W.
1998-01-01
A low-dimensional Hamiltonian model is derived for the acceleration of ions in finite amplitude Alfven waves in a finite pressure plasma sheet. The reduced low-dimensional wave-particle Hamiltonian is useful for describing the reaction of the accelerated ions on the wave amplitudes and phases through the self-consistent fields within the envelope approximation. As an example, the authors show for a single Alfven wave in the central plasma sheet of the Earth's geotail, modeled by the linear pinch geometry called the Harris sheet, the time variation of the wave amplitude during the acceleration of fast protons
Finite-dimensional attractor for a composite system of wave/plate equations with localized damping
International Nuclear Information System (INIS)
Bucci, Francesca; Toundykov, Daniel
2010-01-01
The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping
DEFF Research Database (Denmark)
Tatu, Aditya Jayant; Lauze, Francois Bernard; Sommer, Stefan Horst
2010-01-01
This paper deals with restricting curve evolution to a finite and not necessarily flat space of curves, obtained as a subspace of the infinite dimensional space of planar curves endowed with the usual but weak parametrization invariant curve L 2-metric.We first show how to solve differential...... of a 3-sphere and then a series of examples on a highly non-linear subspace of the space of closed spline curves, where we have restricted mean curvature motion, Geodesic Active contours and compute geodesic between two curves....
LÖwner evolution and finite-dimensional reductions of integrable systems
Pavlov, M. V.; Prokhorov, D. V.; Vasil'ev, A. Yu.; Zakharov, A. M.
2014-10-01
The Löwner equation is known as the one-dimensional reduction of the Benney chain and also as the dispersionless KP hierarchy. We propose a reverse process and show that time splitting in the Löwner or the Löwner-Kufarev equation leads to some known integrable systems.
On the intersection of irreducible components of the space of finite-dimensional Lie algebras
International Nuclear Information System (INIS)
Gorbatsevich, Vladimir V
2012-01-01
The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra is considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.
Tam, Bit-Shun
2001-01-01
This is a review of a coherent body of knowlegde, which perhaps deserves the name of the geometric spectral theory of positive linear operators (in finite dimension), developed by this author and his co-author Hans Schncider (or S.F. Wu) over the past decade. The following topics are covered, besides others: combinatorial spectral theory of nonnegative matrices, Collatz-Wielandt sets (or numbers) associated with a cone-preserving map, distinguished eigenvalues, cone-solvability theorems...
Conditional reasoning, frequency of counterexamples, and the effect of response modality.
Markovits, Henry; Forgues, Hugues Lortie; Brunet, Marie-Laurence
2010-06-01
Geiger and Oberauer (2007) found that when asked to reason with conditionals, people are very sensitive to information about the relative frequency of exceptions to conditional rules and quite insensitive to the relative number of disabling conditions. They asked participants to rate their degree of certainty in a conclusion. In the following studies, we investigated the possibility that this kind of response encourages a more probabilistic mode of processing compared with the usual dichotomous response. In Study 1, participants were given a variant of the problems used by Geiger and Oberauer with either the same scaled response format or a dichotomous categorical response. The results with the scaled response were identical to those of Geiger and Oberauer. However, the results with the categorical response presented a very different profile. In Study 2, we presented similar problems using only frequency information, followed by a set of abstract conditional reasoning problems. The participants who performed better on the abstract problems showed a significantly different response profile than those who did worse on the abstract problems in the categorical response condition. No such difference was observed in the scaled response condition. These results show that response modality strongly affects the way in which information is processed in otherwise identical inferential problems and they are consistent with the idea that scaled responses promote a probabilistic mode of processing.
Weber, Keith
2009-01-01
This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…
A Counterexample Guided Abstraction Refinement Framework for Verifying Concurrent C Programs
2005-05-24
Davis and Hilary Putnam . A computing procedure for quantification theory. Journal of the ACM (JACM), 7(3):201–215, June 1960. [53] C. Demartini, R... Putnam -Loveland [51, 52] algorithm that handles these constraints directly. PBS accepts as input standard CNF formulas augmented with pseudo-Boolean
Item Purification Does Not Always Improve DIF Detection: A Counterexample with Angoff's Delta Plot
Magis, David; Facon, Bruno
2013-01-01
Item purification is an iterative process that is often advocated as improving the identification of items affected by differential item functioning (DIF). With test-score-based DIF detection methods, item purification iteratively removes the items currently flagged as DIF from the test scores to get purified sets of items, unaffected by DIF. The…
Diagrammatical display of the counter-example to non-Abelian Bloch-Nordsieck conjecture
International Nuclear Information System (INIS)
Yoshida, Nobuo
1981-01-01
The reason why the Bloch-Nordsieck theorem breaks down in the Drell-Yan process is shown through a simple diagrammatical calculation. The uncancelled contribution is from the retarded soft gluons, and the colour weight different for each ''double cut diagram'' interrupts the cancellation analogous to QED. (author)
Czech Academy of Sciences Publication Activity Database
Cavazos-Cadena, R.; Montes-de-Oca, R.; Sladký, Karel
2014-01-01
Roč. 163, č. 2 (2014), s. 674-684 ISSN 0022-3239 Grant - others:PSF Organization(US) 012/300/02; CONACYT (México) and ASCR (Czech Republic)(MX) 171396 Institutional support: RVO:67985556 Keywords : Strong sample-path optimality * Lyapunov function condition * Stationary policy * Expected average reward criterion Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.509, year: 2014 http://library.utia.cas.cz/separaty/2014/E/sladky-0432661.pdf
Energy Technology Data Exchange (ETDEWEB)
Raj, Sunny [Univ. of Central Florida, Orlando, FL (United States); Jha, Sumit Kumar [Univ. of Central Florida, Orlando, FL (United States); Pullum, Laura L. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Ramanathan, Arvind [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2017-05-01
Validating the correctness of human detection vision systems is crucial for safety applications such as pedestrian collision avoidance in autonomous vehicles. The enormous space of possible inputs to such an intelligent system makes it difficult to design test cases for such systems. In this report, we present our tool MAYA that uses an error model derived from a convolutional neural network (CNN) to explore the space of images similar to a given input image, and then tests the correctness of a given human or object detection system on such perturbed images. We demonstrate the capability of our tool on the pre-trained Histogram-of-Oriented-Gradients (HOG) human detection algorithm implemented in the popular OpenCV toolset and the Caffe object detection system pre-trained on the ImageNet benchmark. Our tool may serve as a testing resource for the designers of intelligent human and object detection systems.
Universal Solutions of Quantum Dynamical Yang-Baxter Equations
Arnaudon, Daniel; Ragoucy, E; Roche, P; Roche, Ph.
1998-01-01
We construct a universal trigonometric solution of the Gervais-Neveu-Felder equation in the case of finite dimensional simple Lie algebras and finite dimensional contragredient simple Lie superalgebras.
Tracking Deforming Objects using Particle Filtering for Geometric Active Contours
National Research Council Canada - National Science Library
Rathi, Yogesh; Vaswani, Namrata; Tannenbaum, Allen; Yezzi, Anthony
2007-01-01
.... Tracking algorithms using Kalman filters or particle filters have been proposed for finite dimensional representations of shape, but these are dependent on the chosen parametrization and cannot...
Meaningful Intuitions: The Evidential Role of Intuitions in the Study of Language
Maynes, Jeffrey
2012-01-01
Philosophical theories are often repudiated, or taken to be repudiated, by identifying counter-examples. These counter-examples are typically based upon our natural response to a real or hypothetical scenario, also called our intuition about the scenario. This methodology of appealing to intuition has been the focus of recent debates about…
Linear systems and operators in Hilbert space
Fuhrmann, Paul A
2014-01-01
A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.
H-infinity Tracking Problems for a Distributed Parameter System
DEFF Research Database (Denmark)
Larsen, Mikael
1997-01-01
The thesis considers the problem of finding a finite dimensional controller for an infinite dimensional system (A tunnel Pasteurizer) combinedwith a rubustness analysis.......The thesis considers the problem of finding a finite dimensional controller for an infinite dimensional system (A tunnel Pasteurizer) combinedwith a rubustness analysis....
Dimension of the c-nilpotent multiplier of Lie algebras
Indian Academy of Sciences (India)
By a Lie algebra we mean a vector space over a field F with the Lie bracket [ , ]. The finite dimensional Lie algebra analogous to the Schur multiplier was developed in. [4, 5] and has been studied by various authors [7, 8, 14]. Let L be a finite dimensional. Lie algebra, its Schur multiplier, M(L), can be defined as a second ...
Zero cycles on certain surfaces in arbitrary characteristic
Indian Academy of Sciences (India)
Let be a field of arbitrary characteristic. Let be a singular surface defined over with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation S ¯ is finite dimensional. We give numerical conditions under which the Chow group of zero cycles of is finite dimensional.
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
Let be a field of arbitrary characteristic. Let be a singular surface defined over with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation S ¯ is finite dimensional. We give numerical conditions under which the Chow group of zero cycles of is finite dimensional.
A new description of orthogonal bases
Coecke, Bob; Pavlovic, Dusko; Vicary, Jamie
2012-01-01
We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative †-Frobenius monoid in the category FdHilb, which has finite-dimensional Hilbert spaces as objects and continuous linear maps as morphisms, and tensor product for the monoidal
Diagnosis, Synthesis and Analysis of Probabilistic Models
Han, Tingting
2009-01-01
This dissertation considers three important aspects of model checking Markov models: diagnosis — generating counterexamples, synthesis — providing valid parameter values and analysis — verifying linear real-time properties. The three aspects are relatively independent while all contribute to
Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space
Crisford, Toby; Santos, Jorge E.
2017-05-01
We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.
Simple properties of some ideals of compact operators in algebras of unbounded operators
International Nuclear Information System (INIS)
Timmermann, W.
1977-01-01
Several ideals of compact and completely continuous operators in algebras of unbounded operators are defined. Simple properties as the density of the finite dimensional operators are discussed. The connection with the approximation problem is indicated
Multiplexing of spatial modes in the mid-IR region
CSIR Research Space (South Africa)
Gailele, Lucas M
2017-02-01
Full Text Available ceiling in the near future. Communications using orbital angular momentum (OAM) carrying modes offers in finite dimensional states, providing means to increase link capacity by multiplexing spatially overlapping modes in both the azimuthal and radial...
Directory of Open Access Journals (Sweden)
G. Kondrat'ev
1999-10-01
Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.
Constructing canonical bases of quantized enveloping algebras
Graaf, W.A. de
2001-01-01
An algorithm for computing the elements of a given weight of the canonical basis of a quantized enveloping algebra is described. Subsequently, a similar algorithm is presented for computing the canonical basis of a finite-dimensional module.
Differential calculus and its applications
Field, Michael J
2013-01-01
Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.
Path integral and quasiclassical asymptotics of the Lie group
International Nuclear Information System (INIS)
Karasev, M.V.
1977-01-01
Solution of the Cauchy problem for the right-invariant differential operator on the Lie group is represented as a formal path integral. Finite-dimensional approximations of this integral and its quasiclassical asymptotics are written down
Existence of high-energy solutions for supercritical fractional Schrodinger equations in R^N
Directory of Open Access Journals (Sweden)
Lu Gan
2016-12-01
Full Text Available In this article, we study supercritical fractional Schr\\"odinger equations. Applying the finite-dimensional reduction method and the penalization method, we obtain the high-energy solutions for this equation.
Semiprojectivity of universal -algebras generated by algebraic elements
DEFF Research Database (Denmark)
Shulman, Tatiana
2012-01-01
Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given....
Directory of Open Access Journals (Sweden)
D. Bahuguna
2005-01-01
Full Text Available We consider a retarded differential equation with applications to population dynamics. We establish the convergence of a finite-dimensional approximations of a unique solution, the existence and uniqueness of which are also proved in the process.
Character and Dimension Formulae for Queer Lie Superalgebra
Su, Yucai; Zhang, R. B.
2015-02-01
Closed formulae are constructed for the characters and dimensions of the finite dimensional simple modules of the queer Lie superalgebra . This is achieved by refining Brundan's algorithm for computing simple -characters.
Degenerate representations from quantum kinematical constraints
International Nuclear Information System (INIS)
Iosifescu, M.; Scutaru, H.
1987-11-01
We present a systematization of previous results concerning the finite-dimensional irreducible L-modules, for semisimple Lie algebras, on which the second-degree irreducible tensors from the enveloping algebra U(L) vanish.(authors)
Variational calculus on Banach spaces
International Nuclear Information System (INIS)
Uglanov, A V
2000-01-01
The problem of variational calculus is considered in a (variable) subdomain of a Banach space. Analogues of the basic principles of the finite-dimensional theory are derived: the main formula for variations of a functional, necessary conditions of an extremum, Noether's theorem. All the results obtained are dimension-invariant and become the classical ones in the finite-dimensional setting. The main tool of the analysis is the theory of surface integration in Banach spaces
Pakuliak, S.; Sergeev, S.
2002-01-01
We investigate an N-state spin model called quantum relativistic Toda chain and based on the unitary finite-dimensional representations of the Weyl algebra with q being Nth primitive root of unity. Parameters of the finite-dimensional representation of the local Weyl algebra form the classical discrete integrable system. Nontrivial dynamics of the classical counterpart corresponds to isospectral transformations of the spin system. Similarity operators are constructe...
On the Hochschild coho-mology groups of endomorphism algebras of exceptional sequences
Hailou Yao; Lihong Huang
2004-01-01
Let $ A $ be a finite dimensional associative algebra over an algebraically closed field $ k $, and $\\mod A$ be the category of finite dimensional left $ A $-module and $ X_1,X_2,\\ldots,X_n$ in $\\mod A$ be a complete exceptional sequence, then we investigate the Hochschild Cohomology groups of endomorphism algebra of exceptional sequence $ {X_1,X_2, \\ldots,X_n}$ in this paper.
Parumasur, N.; Willie, R.
2008-09-01
We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.
Geometric derivation of the quantum speed limit
International Nuclear Information System (INIS)
Jones, Philip J.; Kok, Pieter
2010-01-01
The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum-mechanical processes in nature since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for nonunitary evolution.
Decomposition of a hierarchy of nonlinear evolution equations
International Nuclear Information System (INIS)
Geng Xianguo
2003-01-01
The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations
Classification of flexible composition algebras, I
Energy Technology Data Exchange (ETDEWEB)
Okubo, S.
1982-06-01
The following theorem has been proven. Let A be a finite-dimensional flexible composition algebra over a field F of characteristic not equal to 2, and not equal to 3. Then, A must be either a Hurwitz, or a para-Hurwitz, or a pseudo-octonion algebra. If the field F is of characteristic 2, then the dimension of a composition algebra is arbitrary in contrast to the standard dimensionality of 1, 2, 4, or 8. Finally, it is shown that any finite-dimensional flexible composition algebra over a field F of any characteristic is automatically a Malcev-admissible algebra.
Binary classification of real sequences by discrete-time systems
Kaliski, M. E.; Johnson, T. L.
1979-01-01
This paper considers a novel approach to coding or classifying sequences of real numbers through the use of (generally nonlinear) finite-dimensional discrete-time systems. This approach involves a finite-dimensional discrete-time system (which we call a real acceptor) in cascade with a threshold type device (which we call a discriminator). The proposed classification scheme and the exact nature of the classification problem are described, along with two examples illustrating its applicability. Suggested approaches for further research are given.
The smooth entropy formalism for von Neumann algebras
International Nuclear Information System (INIS)
Berta, Mario; Furrer, Fabian; Scholz, Volkher B.
2016-01-01
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra
Economic-mathematical methods and models under uncertainty
Aliyev, A G
2013-01-01
Brief Information on Finite-Dimensional Vector Space and its Application in EconomicsBases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector SpacePiecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector SpacePiecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a PlaneBases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Comp
Blocks of tame representation type and related algebras
Erdmann, Karin
1990-01-01
This monograph studies algebras that are associated to blocks of tame representation type. Over the past few years, a range of new results have been obtained and a comprehensive account of these is provided here to- gether with some new proofs of known results. Some general theory of algebras is also presented, as a means of understanding the subject. The book is addressed to researchers and graduate students interested in the links between representations of finite-dimensional algebras and modular group representation theory. The basic properties of modules and finite-dimensional algebras are assumed known.
International Nuclear Information System (INIS)
Huang Hualin; Li Libin; Ye Yu
2004-07-01
We study pointed graded self-dual Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras. Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional coradically graded pointed self-dual Hopf algebras are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider and may help to classify finite dimensional self-dual pointed Hopf algebras
The smooth entropy formalism for von Neumann algebras
Energy Technology Data Exchange (ETDEWEB)
Berta, Mario, E-mail: berta@caltech.edu [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States); Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp [Department of Physics, Graduate School of Science, University of Tokyo, Tokyo, Japan and Institute for Theoretical Physics, Leibniz University Hanover, Hanover (Germany); Scholz, Volkher B., E-mail: scholz@phys.ethz.ch [Institute for Theoretical Physics, ETH Zurich, Zurich (Switzerland)
2016-01-15
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.
Representations of the algebra Uq'(son) related to quantum gravity
International Nuclear Information System (INIS)
Klimyk, A.U.
2002-01-01
The aim of this paper is to review our results on finite dimensional irreducible representations of the nonstandard q-deformation U q ' (so n ) of the universal enveloping algebra U(so(n)) of the Lie algebra so(n) which does not coincide with the Drinfeld-Jimbo quantum algebra U q (so n ).This algebra is related to algebras of observables in quantum gravity and to algebraic geometry.Irreducible finite dimensional representations of the algebra U q ' (so n ) for q not a root of unity and for q a root of unity are given
Theory of control systems described by differential inclusions
Han, Zhengzhi; Huang, Jun
2016-01-01
This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Luré systems. They also introduce the elemental theory of finite dimensional differential inclusions, and the properties and designs of the control systems described by differential inclusions. Addressing the material with clarity and simplicity, the book includes recent research achievements and spans all concepts, concluding with a critical mathematical framework. This book is intended for researchers, teachers and postgraduate students in the area of automatic control engineering.
Supercharacters of queer Lie superalgebras
Cheng, Shun-Jen
2017-06-01
Let g =g0 ¯ ⊕ g1 ¯ be the queer Lie superalgebra and let L be a finite-dimensional non-trivial irreducible g -module. Restricting the g -action on L to g0 ¯, we show that the space of g0 ¯-invariants Lg0 ¯ is trivial. As a consequence, we establish a conjecture first formulated by Gorelik, Grantcharov and Mazorchuk on the triviality of the supercharacter of irreducible g -modules in the case when the modules are finite dimensional.
Holomorphic two-spheres in the complex Grassmann manifold G(k, n)
Indian Academy of Sciences (India)
of Sciences, Beijing 100049, People's Republic of China. 2Department of Mathematics, University of Science and Technology of China, Hefei, ..... author's knowledge is concerned, there is no corresponding example or counterexample. Example. Through direct calculations, one can show that f : S2 −→ G(k, 2k) defined by.
Interfaces - a new perspective on the implementation of language in the brain
DEFF Research Database (Denmark)
Christensen, Ken Ramshøj
A large number of studies of syntax and the brain, both aphasia studies and neuroimaging experiments, have shown that there is a correlation between phrasal movement (word-order variation) and activation in Brocas area. Some studies, however, have reported counterexamples to this correlation...
Robust Adaptive Control of Multivariable Nonlinear Systems
2011-03-28
On the commercial side, the implementation of L1 adaptive controller on NASA’s subscale generic transport model (GTM) aircraft demonstrated...I. Gregory, L. Valavani, Experimental Validation of 1L Adaptive Control: Rohrs ’ Counterexample in Flight, Submitted to AIAA Journal of Guidance
Adamek, J.; Rosicky, Jiri; Vitale, Enrico
2010-01-01
Sifted colimits, important for algebraic theories, are "almost" just the combination of filtered colimits and reflexive coequalizers. For example, given a finitely cocomplete category $cal A$, then a functor with domain $cal A$ preserves sifted colimits iff it preserves filtered colimits and reflexive coequalizers. But for general categories $cal A$ that statement is not true: we provide a counter-example.
Role Shifts and Role Strains Entailed in Moving from Participant to Observer.
Kapinus, Barbara
The purpose of this study was exploration of the role shift from participant to observer in educational research and evaluation. Examples and counter-examples of graduate students who were experiencing the role shift were explored. Generalizations were made in order to abstract the data, and draw the conclusion that ethnographic approaches…
An Instructional Model for Teaching Proof Writing in the Number Theory Classroom
Schabel, Carmen
2005-01-01
I discuss an instructional model that I have used in my number theory classes. Facets of the model include using small group work and whole class discussion, having students generate examples and counterexamples, and giving students the opportunity to write proofs and make conjectures in class. The model is designed to actively engage students in…
Generalized monotone convergence and Radon-Nikodym theorems
Gudder, S.; Zerbe, J.
1981-11-01
A measure and integration theory is presented in the quantum logic framework. A generalization of the monotone convergence theorem is proved. Counterexamples are used to show that the dominated convergence theorem, Fatou's lemma, Egoroff's theorem, and the additivity of the integral do not hold in this framework. Finally, a generalization of the Radon-Nikodym theorem is proved.
Theory of Endorsements and Reasoning with Uncertainty
1990-02-01
reductionistic. An obvious counterexample is the work of Jean Piaget , whose structuralist psychology (or, as he preferred, "genetic epistemology") has much...Journal of Automated Reasoning, volume 1, pages 49-74, 1985. [Boden, 1979] Margaret A. Boden. Jean Piaget . Penguin Books, New York, 1979. [Boose and
Page 1 Sinclair 39 ROOT TRANSFORMATIONS AS A WASTE ...
African Journals Online (AJOL)
friend. Emonds. ·however, denies SUBJECT-AUXILIARY INVERSION the status of an actual counter-example to the SPC. This he (1976, p.24, note 2) does by claiming that the clauses in (5) in which SUBJECT-AUXILIARY INVERSION has applied, are root S's. (6). "The auxiliary inversion that occurs in 'sentence relatives'.
Students' Misconceptions about Random Variables
Kachapova, Farida; Kachapov, Ilias
2012-01-01
This article describes some misconceptions about random variables and related counter-examples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for discrete and continuous cases. The focus is on post-calculus probability courses. (Contains 2 figures.)
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Semilocal and electroweak strings
Achucarro, A; Vachaspati, T
We review a class of non-topological defects in the standard electroweak model, and their implications. Starting with the semilocal string, which provides a counterexample to many well-known properties of topological vortices, we discuss electroweak strings and their stability with and without
The planar cubic cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
AFP Algorithm and a Canonical Normal Form for Horn Formulas
Majdoddin, Ruhollah
2014-01-01
AFP Algorithm is a learning algorithm for Horn formulas. We show that it does not improve the complexity of AFP Algorithm, if after each negative counterexample more that just one refinements are performed. Moreover, a canonical normal form for Horn formulas is presented, and it is proved that the output formula of AFP Algorithm is in this normal form.
Deriving minimal models for resource utilization
te Brinke, Steven; Bockisch, Christoph; Bergmans, Lodewijk; Malakuti Khah Olun Abadi, Somayeh; Aksit, Mehmet; Katz, Shmuel
2013-01-01
We show how compact Resource Utilization Models (RUMs) can be extracted from concrete overly-detailed models of systems or sub-systems in order to model energy-aware software. Using the Counterexample-Guided Abstraction Refinement (CEGAR) approach, along with model-checking tools, abstract models
Asymptotic completeness of scattering in the nonlinear Lamb system for nonzero mass
Komech, A. I.; Merzon, A. E.
2017-07-01
We establish the asymptotic completeness in the nonlinear Lamb system with nonzero mass for hyperbolic stationary states. For the proof, we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic stationary point, using the Banach space Inverse Function Theorem and a priori estimates. We give a counterexample showing that the hyperbolicity condition is essential.
Intersections of adelic groups on a surface
International Nuclear Information System (INIS)
Budylin, R Ya; Gorchinskiy, S O
2013-01-01
We solve a technical problem related to adeles on an algebraic surface. Given a finite set of natural numbers, one can associate with it an adelic group. We show that this operation commutes with taking intersections if the surface is defined over an uncountable field, and we provide a counterexample otherwise. Bibliography: 12 titles
Creating Büchi automata for multi-valued model checking
Vijzelaar, Stefan J.J.; Fokkink, Wan J.
2017-01-01
In explicit state model checking of linear temporal logic properties, a Büchi automaton encodes a temporal property. It interleaves with a Kripke model to form a state space, which is searched for counterexamples. Multi-valued model checking considers additional truth values beyond the Boolean true
Soft α-Open Sets and Soft α-Continuous Functions
Directory of Open Access Journals (Sweden)
Metin Akdag
2014-01-01
Full Text Available We introduce soft α-sets on soft topological spaces and study some of their properties. We also investigate the concepts of soft α-continuous and soft α-open functions and discuss their relationships with soft continuous and other weaker forms of soft continuous functions. Also counterexamples are given to show the noncoincidence of these functions.
A study of frontier and semifrontier in intuitionistic fuzzy topological spaces.
Kharal, Athar
2014-01-01
Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms.
Type 1,1-operators defined by vanishing frequency modulation
DEFF Research Database (Denmark)
Johnsen, Jon
This paper presents a general definition of pseudo-differential operators of type 1,1; the definition is shown to be the largest one that is both compatible with negligible operators and stable under vanishing frequency modulation. Elaborating counter-examples of Ching andHörmander, type 1...
Type 1,1-operators defined by vanishing frequency modulation
DEFF Research Database (Denmark)
Johnsen, Jon
2009-01-01
This paper presents a general definition of pseudo-differential operators of type 1,1; the definition is shown to be the largest one that is both compatible with negliible operators and stable under vanishing frequency modulation. Elaborating counter-examples of Ching, Hörmander and Parenti...
Equilibria of Chinese Auctions
DEFF Research Database (Denmark)
Branzei, Simina; Forero, Clara; Larson, Kate
are symmetric when both valuations and budgets are symmetric. We also study Chinese auctions with discrete budgets, for which we give both existence results and counterexamples. While the literature on rent-seeking contests traditionally focuses on continuous costly tickets, the discrete variant is very natural...
Reinstatement and Specificty in Argumentation Systems
Directory of Open Access Journals (Sweden)
Claudio Andres Alessio
2016-12-01
Full Text Available Reinstatement is a principle of argumentation systems that enables the justification of a defeated argument when all its defeaters are in turn ultimately defeated. Some counterexamples to reinstatement have been offered in the literature. Specifically, counterexamples suggest that reinstatement cannot be taken as a general principle of defeasible argumentation because the reinstated arguments may support incorrect conclusions. Some authors argued that the problems are not due to reinstatement but to the formalization of those examples. Then, the solution is to make the language expressive enough to obtain the correct results. They also warn that one should avoid tinkering with the formalization in concrete examples just to get a desired outcome. Therefore, this approach should be combined with the search of general principles for choosing the proper formalization. Taking into account that finding general principles of representation could be a hard enterprise, the goal of this thesis is to identify some criterion that allows i. neutralize the counterexamples, ii. preserve the original formal language as much as possible, and iii. maintain reinstatement as a general principle. To identify that criterion, counterexamples are analyzed and possible causes of the problem are detected. As a result it is found that the preference by specificity among arguments can be used to obtain that criterion. Three approaches based on specificity are proposed and evaluated. Two of them introduce alternative defeat relations among arguments. The third one is based on filtering the non maximally specific arguments.
Revisiting Weak Simulation for Substochastic Markov Chains
DEFF Research Database (Denmark)
Jansen, David N.; Song, Lei; Zhang, Lijun
2013-01-01
of the logic PCTL\\x, and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness...
Indian Academy of Sciences (India)
The construction shows the existence of an infinite group which is finitely generated and all of whose elements have finite p-power order for some prime p. The orders of the elements are unbounded, and thus, this is not a counterexample to the Burnside problem where the torsion is bounded. Burnside's contributions to ...
Misunderstandings concerning income distribution policies
J. Tinbergen (Jan)
1981-01-01
textabstractIn this essay in honour of Professor P. Hennipman the latter's clarity and precision of expression are chosen as an example of how to avoid misunderstanding of his publications. As counterexamples some twenty-odd misunderstandings are set out by the essay's author in the field of income
Iterated Hamiltonian type systems and applications
Tiba, Dan
2018-04-01
We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.
Zassenhaus conjecture for A6 A6 A6
Indian Academy of Sciences (India)
It remains not only unsolved but also lacking in plausible means of either proof or counter-example. Only a few non-solvable groups G are known to satisfy (ZC1); in this note, the conjecture is verified for the alternating group A6. In 1988, Luthar and Passi [17] started investigations in this field when dealing with A5, thereby ...
Suing One's Sense Faculties for Fraud: 'Justifiable Reliance' in the ...
African Journals Online (AJOL)
The law requires that plaintiffs in fraud cases be 'justified' in relying on a misrepresentation. I deploy the accumulated intuitions of the law to defend externalist accounts of epistemic justification and knowledge against Laurence BonJour's counterexamples involving clairvoyance. I suggest that the law can offer a ...
On an ideal in algebras of unbounded operators
International Nuclear Information System (INIS)
Timmermann, W.
1977-01-01
The closure of the set of finite dimensional operators with respect to different topologies is considered. The obtained ideals have many properties similar to those of the ideal of completely continuous operators on the Hilbert space. For example, on some appropriate assumptions all continuous functionals are normal, irreducible representations are equivalent to the identical representation and so on
Shilov, Georgi E
1977-01-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Quantum groups and double quiver algebras
International Nuclear Information System (INIS)
Huang Hualin; Yang Shilin
2004-07-01
For a finite dimensional sernisimple Lie algebra g and a root q of unity in a field k we associate to these data a double quiver Q-bar. It is shown that a restricted version of the quantized enveloping algebras U q (g) is a quotient of the double quiver algebra kQ-bar. (author)
Variational analysis and generalized differentiation I basic theory
Mordukhovich, Boris S
2006-01-01
Contains a study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces. This title presents many applications to problems in optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, and more.
Conformal higher-spin symmetries in twistor string theory
Directory of Open Access Journals (Sweden)
D.V. Uvarov
2014-12-01
Full Text Available It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains psl(4|4,R superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to SL(4|4,R one.
Tame-wild dichotomy for derived categories
Bekkert, Viktor I.; Drozd, Yuriy A.
2003-01-01
We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular, that any degeneration of a derived wild algebra is derived wild; respectively, any deformation of a derived tame algebra is derived tame.
DEFF Research Database (Denmark)
Haahr Andersen, Henning; Kaneda, Masaharu
Let $U_q$ denote the quantum group associated with a finite dimensional semisimple Lie algebra. Assume that $q$ is a complex root of unity of odd order and that $U_q$ is %the quantum group version obtained via Lusztig's $q$-divided powers construction. We prove that all regular projective (tilting...
Exceptional groups and elementary-particle structures
International Nuclear Information System (INIS)
Biedenharn, L.C.; Truini, P.
1981-09-01
A new finite-dimensional quantum mechanical space is constructed over the complex octonionic plane using the recently developed algebraic techniques of Jordan pairs and inner ideals. The automorphism group of this structure is E 6 x U(1), realized on precisely two E 6 irreps which is abstracted as a (topless) model for grand unification
Exceptional groups and elementary-particle structures
Energy Technology Data Exchange (ETDEWEB)
Biedenharn, L.C.; Truini, P.
1981-09-01
A new finite-dimensional quantum mechanical space is constructed over the complex octonionic plane using the recently developed algebraic techniques of Jordan pairs and inner ideals. The automorphism group of this structure is E/sub 6/ x U(1), realized on precisely two E/sub 6/ irreps which is abstracted as a (topless) model for grand unification.
Nonlinear elliptic differential equations with multivalued nonlinearities
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
Nonlinear elliptic differential equations with multivalued ... has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth .... A is upper semicontinuous (as a set-valued map) from every finite dimensional subspace of X into ...
Indian Academy of Sciences (India)
48 E. C. G. SUDARSHAN. Since is furnishes a lepresentation of the complete Lorentz group (which is in general reducible and not necessarily unitary) is also furnishes a repre- sentation of the Lorentz group. For any collection of finite dimensional representations, if is equivalent to the representation furnished by di.
Indian Academy of Sciences (India)
both finite-dimensional and continuum nonlinear dynamical systems, modelled by difference, ordinary and partial differential equations and their applications in diverse areas such as hydrodynamics, nonlinear optics, magnetism, spintronics, field theory, quantum systems, and Bose–Einstein condensates. About 20 experts.
The planar algebra of a semisimple and cosemisimple Hopf algebra
Indian Academy of Sciences (India)
M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22
[TngGlk] Etingof Pavel and Gelaki Shlomo, On finite-dimensional semisimple and cosemisimple Hopf algebras in positive characteristic. Int. Math. Res. Notices,. 16 (1998) 851–864. [DasKdy] Das Paramita and Vijay Kodiyalam, Planar algebras and the Ocneanu–. Szymanski theorem, Proc. AMS, 133 (2005) 2751–2759.
A note on the Campbell-Hausdorff formula
Veldkamp, Ferdinand D
1980-01-01
In his book (“Lie Algebras,” Interscience, 1962) Jacobson proves the Campbell-Hausdorff formula for formal power series in Lie algebras. In this short note we shall prove it for finite-dimensional Lie groups making use of parts of Jacobson's proof.
A note on the Campbell-Hausdorff formula
Veldkamp, F.D.
In his book (“Lie Algebras,” Interscience, 1962) Jacobson proves the Campbell-Hausdorff formula for formal power series in Lie algebras. In this short note we shall prove it for finite-dimensional Lie groups making use of parts of Jacobson's proof.
Weak Darboux property and transitivity of linear mappings on topological vector spaces
Directory of Open Access Journals (Sweden)
V. K. Maslyuchenko
2013-06-01
Full Text Available It is shown that every linear mapping ontopological vector spaces always has weak Darboux property, therefore, it is continuous ifand only if it is transitive. For finite-dimensional mapping $f$ with values in Hausdorfftopological vector space the following conditions are equivalent: (i $f$ iscontinuous; (ii graph of $f$ is closed; (iii kernel of $f$ is closed; (iv $f$ istransition map.
Structure Preserving Port-Hamiltonian Discretization of a 1-D Inflatable Space Reflector
Voß, T.; Scherpen, J.M.A.
2009-01-01
In this paper we show how to spatially discretize a distributed port-Hamiltonian (pH) system, which describes the dynamics of an 1-D piezoelectric Euler-Bernoulli beam. Standard spatial discretization schemes for PDE systems have the disadvantage that they typically lead to a finite dimensional
Symmetric webs, Jones-Wenzl recursions and q-Howe duality
DEFF Research Database (Denmark)
Rose, David; Tubbenhauer, Daniel
We define and study the category of symmetric sl2-webs. This category is a combinatorial description of the category of all finite dimensional quantum sl2-modules. Explicitly, we show that (the additive closure of) the symmetric sl2-spider is (braided monoidally) equivalent to the latter. Our main...
Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed
DEFF Research Database (Denmark)
Matsushita, Hiroshi; Miyata, T.; Christiansen, Lasse Engbo
2002-01-01
The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests...
Classifying spaces with virtually cyclic stabilizers for linear groups
DEFF Research Database (Denmark)
Degrijse, Dieter Dries; Köhl, Ralf; Petrosyan, Nansen
2015-01-01
We show that every discrete subgroup of GL(n, ℝ) admits a finite-dimensional classifying space with virtually cyclic stabilizers. Applying our methods to SL(3, ℤ), we obtain a four-dimensional classifying space with virtually cyclic stabilizers and a decomposition of the algebraic K-theory of its...
Approximation of the inverse G-frame operator
Indian Academy of Sciences (India)
... projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
Lie algebras and linear differential equations.
Brockett, R. W.; Rahimi, A.
1972-01-01
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
On the range of completely bounded maps
Directory of Open Access Journals (Sweden)
Richard I. Loebl
1978-01-01
Full Text Available It is shown that if every bounded linear map from a C*-algebra α to a von Neumann algebra β is completely bounded, then either α is finite-dimensional or β⫅⊗Mn, where is a commutative von Neumann algebra and Mn is the algebra of n×n complex matrices.
Unitary operator bases and Q-deformed algebras
Energy Technology Data Exchange (ETDEWEB)
Galetti, D.; Pimentel, B.M. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Lima, C.L. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica. Grupo de Fisica Nuclear e Teorica e Fenomenologia de Particulas Elementares; Lunardi, J.T. [Universidade Estadual de Ponta Grossa, PR (Brazil). Dept. de Matematica e Estatistica
1998-03-01
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-know q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root of unity. (author)
Unitary operator bases and q-deformed algebras
Energy Technology Data Exchange (ETDEWEB)
Galleti, D.; Lunardi, J.T.; Pimentel, B.M. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Lima, C.L. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica
1995-11-01
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-know q-deformed communication relation is shown to emergence in a natural way, when the deformation parameter is a root of unity. (author). 14 refs.
Nurbekyan, Levon
2017-03-11
Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
In this paper, we examine bases for finite index inclusion of I I 1 factors and connected inclusion of finite dimensional C ∗ -algebras. These bases behave nicely with respect to basic construction towers. As applications we have studied automorphisms of the hyperfinite I I 1 factor R which are 'compatible with respect to the ...
Equivariant K-theory, groupoids and proper actions
Cantarero, Jose
2008-01-01
In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant CW-complexes. We also establish an analogue of the completion theorem of Atiyah and Segal. Some examples are discussed.
Three Solvable Matrix Models of a Quantum Catastrophe
Czech Academy of Sciences Publication Activity Database
Levai, G.; Růžička, František; Znojil, Miloslav
2014-01-01
Roč. 53, č. 9 (2014), s. 2875-2890 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : quantum theory * PT symmetry * Finite-dimensional non-Hermitian Hamiltonians * exceptional-point localization * quantum theory of catastrophes * methods of computer algebra Subject RIV: BE - Theoretical Physics Impact factor: 1.184, year: 2014
Rosestolato, M.; Święch, A.
2017-02-01
We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C 1 + α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance.
Star order and topologies on von Neumann algebras
Bohata, Martin
2017-01-01
The goal of the paper is to study a topology generated by the star order on von Neumann algebras. In particular, it is proved that the order topology under investigation is finer than $\\sigma$-strong* topology. On the other hand, we show that it is comparable with the norm topology if and only if the von Neumann algebra is finite-dimensional.
Greiner, G.; Heesterbeek, J.A.P.; Metz, J.A.J.
1994-01-01
In this paper we present a generalization of a finite dimensional singular perturbation theorem to Banach spaces. From this we obtain sufficient conditions under which a faithful simplification by a time-scale argument is justified for age-structured models of slowly growing populations. An explicit
1989-07-01
sample paths Track D Room B239 Diffusion and Partial Differential Equations 2:00 - 2:20 p.m. G. Galeazzi Uniqueness of viscosity solutions of Ham...V.S.) OF HAMILTON-JACOBI--BELLMAN (IB) EQUATIONS FOR CONTROLLED DIFFUSIONS ON FINITE-DIMENSIONAL RIEMANNIAN MANIFOLDS WITH BOUNDARY Giuliano Galeazzi
Simple mathematical models of symmetry breaking. Application to particle physics
International Nuclear Information System (INIS)
Michel, L.
1976-01-01
Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)
An algorithm to compute the canonical basis of an irreducible Uq(g)-module
de Graaf, W. A.
2002-01-01
An algorithm is described to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for modules that are constructed as a submodule of a tensor product of modules with known canonical bases.
Transfinite C2 interpolant over triangles
International Nuclear Information System (INIS)
Alfeld, P.; Barnhill, R.E.
1984-01-01
A transfinite C 2 interpolant on a general triangle is created. The required data are essentially C 2 , no compatibility conditions arise, and the precision set includes all polynomials of degree less than or equal to eight. The symbol manipulation language REDUCE is used to derive the scheme. The scheme is discretized to two different finite dimensional C 2 interpolants in an appendix
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
The quantum symmetry of rational field theories
International Nuclear Information System (INIS)
Fuchs, J.
1993-12-01
The quantum symmetry of a rational quantum field theory is a finite-dimensional multi-matrix algebra. Its representation category, which determines the fusion rules and braid group representations of superselection sectors, is a braided monoidal C*-category. Various properties of such algebraic structures are described, and some ideas concerning the classification programme are outlined. (orig.)
On the Hausdorff distance and some openings between Banach ...
African Journals Online (AJOL)
... coding of separable Banach spaces as closed subspaces of C(Δ) endowed with the Effros-Borel structure. Also, we discuss the Borel complexity of the Banach-Mazur distance, and we show that its restriction to finite dimensional Banach spaces is Borel. Keywords: Effros-Borel structure, Vietoris topology, Hausdorff metric, ...
Codes in W*-Metric Spaces: Theory and Examples
Bumgardner, Christopher J.
2011-01-01
We introduce a "W*"-metric space, which is a particular approach to non-commutative metric spaces where a "quantum metric" is defined on a von Neumann algebra. We generalize the notion of a quantum code and quantum error correction to the setting of finite dimensional "W*"-metric spaces, which includes codes and error correction for classical…
Perturbation of operators and approximation of spectrum
Indian Academy of Sciences (India)
compact subsets by the sequence of eigenvalue functions of A(x)n. ... functions. Also, some spectral gap prediction results are proved using the finite dimensional truncations. We should mention that gap related problems were studied ...... perturbation is Lipschitz continuous, then the number δ that appears in Theorem 3.10.
An Iterative Method for the Approximation of Fibers in Slow-Fast Systems
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Brøns, Morten; Starke, Jens
2014-01-01
In this paper we extend a method for iteratively improving slow manifolds so that it also can be used to approximate the fiber directions. The extended method is applied to general finite-dimensional real analytic systems where we obtain exponential estimates of the tangent spaces to the fibers...
Critical properties of a three dimension p-spin model
International Nuclear Information System (INIS)
Franz, S.; Parisi, G.
2000-03-01
In this paper we study the critical properties of a finite dimensional generalization of the p-spin model. We find evidence that in dimension three, contrary to its mean field limit, the glass transition is associated to a diverging susceptibility (and correlation length). (author)
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 ...
Affine Kac-Moody algebras and their representations
International Nuclear Information System (INIS)
Slansky, R.
1988-01-01
Highest weight representation theory of finite dimensional and affine Kac-Moody algebras is summarized from a unified point of view. Lattices of discrete additive quantum numbers and the presentation of Lie algebras on Cartan matrices are the central points of departure for the analysis. (author)
The supersymmetric Pegg-Barnett oscillator
International Nuclear Information System (INIS)
Shen, Jian Qi
2005-01-01
The su(n) Lie algebraic structure of the Pegg-Barnett oscillator that possesses a finite-dimensional number-state space is demonstrated. The supersymmetric generalization of the Pegg-Barnett oscillator is suggested. it is shown that such a supersymmetric Pegg-Barnett oscillator may have some potential applications, e.g., the mass spectrum of the charged leptons
Elliptic Quadratic Operator Equations
Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor
2017-01-01
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.
Dimension of the c-nilpotent multiplier of Lie algebras
Indian Academy of Sciences (India)
Abstract. The purpose of this paper is to derive some inequalities for dimension of the c-nilpotent multiplier of finite dimensional Lie algebras and their factor Lie algebras. We further obtain an inequality between dimensions of c-nilpotent multiplier of Lie algebra L and tensor product of a central ideal by its abelianized factor ...
Subanalytic Bundles and Tubular Neighbourhoods of Zero-Loci
Indian Academy of Sciences (India)
We introduce the natural and fairly general notion of a subanalytic bundle (with a finite dimensional vector space of sections) on a subanalytic subset of a real analytic manifold , and prove that when is compact, there is a Baire subset of sections in whose zero-loci in have tubular neighbourhoods, ...
Port-Hamiltonian discretization for open channel flows
Ramkrishna Pasumarthy, R.P.; Ambati, V.R.; van der Schaft, Arjan
2010-01-01
A finite-dimensional Port-Hamiltonian formulation for the dynamics of smooth open channel flows is presented. A numerical scheme based on this formulation is developed for both the linear and nonlinear shallow water equations. The scheme is verified against exact solutions and has the advantage of
The sample autocorrelation function of non-linear time series
Basrak, Bojan
2000-01-01
When studying a real-life time series, it is frequently reasonable to assume, possibly after a suitable transformation, that the data come from a stationary time series (Xt). This means that the finite-dimensional distributions of this sequence are invariant under shifts of time. Various stationary
Phase-Field Relaxation of Topology Optimization with Local Stress Constraints
DEFF Research Database (Denmark)
Stainko, Roman; Burger, Martin
2006-01-01
inequality constraints. We discretize the problem by finite elements and solve the arising finite-dimensional programming problems by a primal-dual interior point method. Numerical experiments for problems with local stress constraints based on different criteria indicate the success and robustness...
Transformations Based on Continuous Piecewise-Affine Velocity Fields
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Batmanghelich, Kayhan
2017-01-01
We propose novel finite-dimensional spaces of well-behaved transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume...
On exterior variational calculus
International Nuclear Information System (INIS)
Aldrovandi, R.; Kraenkel, R.A.
1987-01-01
Exterior variational calculus is introduced through examples in field theory. It provides a very simple technique to decide on the existence of Lagrangians for given equations of motions and, in the case, to find them. Only local aspects are discussed but the analogy to exterior calculus on finite dimensional manifolds is complete, strongly suggesting its suitability to the study of topological aspects. (Author) [pt
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
Hamiltonian systems (especially in increasing the stability region). Furthermore, the norm can also serve as a measure to compute the 'distance' between two symplectic maps. Now the symmetry group for the linear part ˆM for n degrees of freedom is the finite dimensional non-compact real symplectic group Sp(2n, R).
When to call a linear system nonnegative
Nieuwenhuis, J.W.
1998-01-01
In this paper we will consider discrete time invariant linear systems that allow for an input-state-output representation with a finite dimensional state space, and that have a finite number of inputs and outputs. The basic issue in this paper is when to call these systems nonnegative. An important
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.
Port Hamiltonian formulation of infinite dimensional systems I. Modeling
Macchelli, Alessandro; Macchelli, A.; van der Schaft, Arjan; 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 multivariable case.
Distributed port-Hamiltonian formulation of infinite dimensional systems
Macchelli, Alessandro; Macchelli, A.; van der Schaft, Arjan; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control 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
Wave-particle duality in a quark model
International Nuclear Information System (INIS)
Gudder, S.P.
1984-01-01
A quark model based on finite-dimensional quantum mechanics is presented. Observables associated with color, flavor, charge, and spin are considered. Using these observables, quark and baryon Hamiltonians are constructed. Wave-particle dualities in this model are pointed out. (Auth.)
On the maximal dimension of a completely entangled subspace for ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
K R PARTHASARATHY. Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg,. New Delhi 110 016, India. E-mail: krp@isid.ac.in. MS received 19 March 2004; revised 16 August 2004. Abstract. Let Hi be a finite dimensional complex Hilbert space of dimension di associated with a finite level quantum system Ai ...
A non-Archimedean approach to prolongation theory
van Eck, H.N.
1986-01-01
Some evolution equations possess infinite-dimensional prolongation Lie algebras which can be made finite-dimensional by using a bigger (non-Archimedean) field. The advantage of this is that convergence problems hardly exist in such a field. Besides that, the accompanying Lie groups can be easily
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences. K R Parthasarathy. Articles written in Proceedings – Mathematical Sciences. Volume 113 Issue 1 February 2003 pp 3-13. A Remark on the Unitary Group of a Tensor Product of Finite-Dimensional Hilbert Spaces · K R Parthasarathy · More Details Abstract Fulltext ...
Indian Academy of Sciences (India)
2016-09-28
Sep 28, 2016 ... sponding Lie group is finite-dimensional. However, such systems may be described in terms of ASD quater- nion–Kahler four-manifolds, or equivalently ASD Ein- stein manifolds, are locally determined by one scalar function subject to Przanowski's equation (see [1,2] and references therein). In this case ...
Leibniz Algebras and Lie Algebras
Directory of Open Access Journals (Sweden)
Geoffrey Mason
2013-10-01
Full Text Available This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.
On the structure of the space of geometric product-form models
Bayer, Nimrod; Boucherie, Richardus J.
2002-01-01
This article deals with Markovian models defined on a finite-dimensional discrete state space and possess a stationary state distribution of a product-form. We view the space of such models as a mathematical object and explore its structure. We focus on models on an orthant [script Z]+n, which are
Pramana – Journal of Physics | Indian Academy of Sciences
Indian Academy of Sciences (India)
pp 981-993 Research Articles. Wigner distributions for finite dimensional quantum systems: An algebraic approach · S Chaturvedi E Ercolessi G Marmo G Morandi N Mukunbda R Simon · More Details Abstract Fulltext PDF. We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space' ...
Algorithms for global total least squares modelling of finite multivariable time series
Roorda, Berend
1995-01-01
In this paper we present several algorithms related to the global total least squares (GTLS) modelling of multivariable time series observed over a finite time interval. A GTLS model is a linear, time-invariant finite-dimensional system with a behaviour that has minimal Frobenius distance to a given
Geometric structures on loop and path spaces
Indian Academy of Sciences (India)
∗Departamento de Geometrıa y Topologıa, Facultad de Matemáticas,. Universidad Complutense de Madrid, 28040 Madrid, Spain. †Instituto de Ciencias ..... To finish, let us check that the familiar finite dimensional picture translates to this case. PROPOSITION 4.2. Let (M,g) be a Riemannian manifold which has a locally ...
Conformal higher-spin symmetries in twistor string theory
Energy Technology Data Exchange (ETDEWEB)
Uvarov, D.V., E-mail: d_uvarov@hotmail.com
2014-12-15
It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains psl(4|4,R) superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to SL(4|4,R) one.
DEFF Research Database (Denmark)
Gundersen, Eline Busck
2011-01-01
Response-dependence theses are usually formulated in terms of a priori true biconditionals of roughly the form ‘something, x, falls under the concept ‘F’ « x would elicit response R from subjects S under conditions C’. Such formulations are vulnerable to conditional fallacy problems; counterexamp......Response-dependence theses are usually formulated in terms of a priori true biconditionals of roughly the form ‘something, x, falls under the concept ‘F’ « x would elicit response R from subjects S under conditions C’. Such formulations are vulnerable to conditional fallacy problems...... to the truth of the biconditional. I argue that this move leaves the equations vulnerable to counterexamples of a slightly different kind: Cases where the change is triggered, not by the C-conditions’ coming to obtain, but by the response. I consider two ways to resist these counterexamples, and argue...
Filtrated K-theory for real rank zero C*-algebras
DEFF Research Database (Denmark)
Arklint, Sara Esther; Restorff, Gunnar; Ruiz, Efren
2012-01-01
The smallest primitive ideal spaces for which there exist counterexamples to the classification of non-simple, purely infinite, nuclear, separable C*-algebras using filtrated K-theory, are four-point spaces. In this article, we therefore restrict to real rank zero C*-algebras with four-point prim......The smallest primitive ideal spaces for which there exist counterexamples to the classification of non-simple, purely infinite, nuclear, separable C*-algebras using filtrated K-theory, are four-point spaces. In this article, we therefore restrict to real rank zero C*-algebras with four......-point primitive ideal spaces. Up to homeomorphism, there are ten different connected T0-spaces with exactly four points. We show that filtrated K-theory classifies real rank zero, tight, stable, purely infinite, nuclear, separable C*-algebras that satisfy that all simple subquotients are in the bootstrap class...
Fouquet, Jean-Luc; Vanherpe, Jean-Marie
2008-01-01
A conjecture of Fan and Raspaud [3] asserts that every bridgeless cubic graph con-tains three perfect matchings with empty intersection. Kaiser and Raspaud [6] sug-gested a possible approach to this problem based on the concept of a balanced join in an embedded graph. We give here some new results concerning this conjecture and prove that a minimum counterexample must have at least 32 vertices.
1990-01-01
as a teacher at the United States Air Force Academy. This change gave me the unique opportunity to develop a formal theoretical structure for thinking...trivial counter-example of an adult stutterer who foresees the inevitable result of his speech, but ’struggles against the unwanted but practically...Yet without a distinction between intended and foreseen outcomes, we are forced to conclude that the stuttering is nevertheless an integral part of
Global smoothness preservation and the variation-diminishing property
Directory of Open Access Journals (Sweden)
Gavrea Ioan
1999-01-01
Full Text Available In the center of our paper are two counterexamples showing the independence of the concepts of global smoothness preservation and variation diminution for sequences of approximation operators. Under certain additional assumptions it is shown that the variation-diminishing property is the stronger one. It is also demonstrated, however, that there are positive linear operators giving an optimal pointwise degree of approximation, and which preserve global smoothness, monotonicity and convexity, but are not variation-diminishing.
On supersymmetry at high temperature
International Nuclear Information System (INIS)
Bajc, B.; Senjanovic, G.; Melfo, A.
1996-08-01
While it is possible to find examples of field theories with a spontaneously broken symmetry at high temperature, in renormalizable supersymmetric models any internal symmetry always get restored. Recently, a counterexample was suggested in the context of nonrenormalizable supersymmetric theories. We show that non negligible higher loop effects actually restore the symmetry, without compromising the validity of perturbation theory. We give some arguments as to why the proposed mechanism should not work in general. (author). 13 refs, 1 fig
Resource Curse or Destructive Creation: A Tale of Crony Capitalism in Transition
Vuong, Quan-Hoang; Napier, Nancy K.
2012-01-01
This paper explores the “resource curse” problem as a counter-example of creative performance and innovation by examining reliance on capital and physical resources, showing the gap between expectations and ex-post actual performance became clearer under conditions of economic turmoil. The analysis employs logistic regressions with dichotomous response and predictor variables, showing significant results.Several findings that have use for economic and business practice follow. First, in a tra...
Three-space problems in Banach space theory
Castillo, Jesús M F
1997-01-01
This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.
Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels
Directory of Open Access Journals (Sweden)
Benoît Collins
2010-06-01
Full Text Available Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.
Pearls in graph theory a comprehensive introduction
Hartsfield, Nora
2003-01-01
""Innovative introductory text . . . clear exposition of unusual and more advanced topics . . . Develops material to substantial level.""--American Mathematical Monthly""Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples.""--American Mathematical Monthly"" . . . An excellent textbook for an undergraduate course.""--Australian Computer JournalA stimulating view of mathematics that appeals to students as well as teachers, this undergraduate-level text is written
VERIFICATION OF PARALLEL AUTOMATA-BASED PROGRAMS
M. A. Lukin
2014-01-01
The paper deals with an interactive method of automatic verification for parallel automata-based programs. The hierarchical state machines can be implemented in different threads and can interact with each other. Verification is done by means of Spin tool and includes automatic Promela model construction, conversion of LTL-formula to Spin format and counterexamples in terms of automata. Interactive verification gives the possibility to decrease verification time and increase the maxi...
Blumson, Ben
2016-01-01
Whereas the analysis of meaning in terms of intention is orthodoxy in the philosophy of language, it is highly controversial in the philosophy of art. So even if it is agreed that inserting resemblance into the analysis of speaker meaning in terms of intention escapes counterexamples to the sufficiency of resemblance for depiction, it’s likely to be argued that defining depiction as a kind of intentional representation draws too close an analogy between depiction and description. Counterexamp...
Modal Subordination in Type Theoretic Dynamic Logic
Qian, Sai; De Groote, Philippe; Amblard, Maxime
2016-01-01
International audience; Classical theories of discourse semantics, such as Discourse Representation Theory (DRT), Dynamic Predicate Logic (DPL), predict that an indefinite noun phrase cannot serve as antecedent for an anaphor if the noun phrase is, but the anaphor is not, in the scope of a modal expression. However, this prediction meets with counterexamples. The phenomenon modal subordination is one of them. In general, modal subordination is concerned with more than two modalities, where th...
Compensatory lengthening and structure preservation revisited yet again
Kavitskaya, Darya
2017-01-01
In their seminal paper, deChene (1979) make a strong claim that pre-existing vowel length contrast is a necessary condition for the phonologization of vowel length through compensatory lengthening. Compensatory lengthening is thus predicted to be always a structure-preserving change. Since that time, the claim has been challenged in numerous works (Gess 1998, Hock1986, Morin 1992), among others). A closer examination of the cited counterexamples to de Chene and Anderson's claim reveals certa...
Integrating Testing and Interactive Theorem Proving
Directory of Open Access Journals (Sweden)
Harsh Raju Chamarthi
2011-10-01
Full Text Available Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often spend considerable effort examining the theorem prover's output before realizing this. We present a synergistic integration of testing with theorem proving, implemented in the ACL2 Sedan (ACL2s, for automatically generating concrete counterexamples. Our method uses the full power of the theorem prover and associated libraries to simplify conjectures; this simplification can transform conjectures for which finding counterexamples is hard into conjectures where finding counterexamples is trivial. In fact, our approach even leads to better theorem proving, e.g. if testing shows that a generalization step leads to a false conjecture, we force the theorem prover to backtrack, allowing it to pursue more fruitful options that may yield a proof. The focus of the paper is on the engineering of a synergistic integration of testing with interactive theorem proving; this includes extending ACL2 with new functionality that we expect to be of general interest. We also discuss our experience in using ACL2s to teach freshman students how to reason about their programs.
Sufficient conditions for uniqueness of the weak value
International Nuclear Information System (INIS)
Dressel, J; Jordan, A N
2012-01-01
We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average using the contextual values formalism introduced in Dressel, Agarwal and Jordan (2010 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.104.240401). We also respond to criticism of our work by Parrott (arXiv:1105.4188v1) concerning a proposed counter-example to the uniqueness of the definition of the generalized weak value. The counter-example does not satisfy our prescription in the case of an underspecified measurement context. We show that when the contextual values formalism is properly applied to this example, a natural interpretation of the measurement emerges and the unique definition in the weak limit holds. We also prove a theorem regarding the uniqueness of the definition under our sufficient conditions for the general case. Finally, a second proposed counter-example by Parrott (arXiv:1105.4188v6) is shown not to satisfy the sufficiency conditions for the provided theorem. (paper)
Geometrical aspects of operator ordering terms in gauge invariant quantum models
International Nuclear Information System (INIS)
Houston, P.J.
1990-01-01
Finite-dimensional quantum models with both boson and fermion degrees of freedom, and which have a gauge invariance, are studied here as simple versions of gauge invariant quantum field theories. The configuration space of these finite-dimensional models has the structure of a principal fibre bundle and has defined on it a metric which is invariant under the action of the bundle or gauge group. When the gauge-dependent degrees of freedom are removed, thereby defining the quantum models on the base of the principal fibre bundle, extra operator ordering terms arise. By making use of dimensional reduction methods in removing the gauge dependence, expressions are obtained here for the operator ordering terms which show clearly their dependence on the geometry of the principal fibre bundle structure. (author)
Identification of a Discontinuous Parameter in Stochastic Parabolic Systems
International Nuclear Information System (INIS)
Aihara, S. I.
1998-01-01
The purpose of this paper is to study the identification problem for a spatially varying discontinuous parameter in stochastic diffusion equations. The consistency property of the maximum likelihood estimate (M.L.E.) and a generating algorithm for M.L.E. have been explored under the condition that the unknown parameter is in a sufficiently regular space with respect to spatial variables. In order to prove the consistency property of the M.L.E. for a discontinuous diffusion coefficient, we use the method of sieves, i.e., first the admissible class of unknown parameters is projected into a finite-dimensional space and next the convergence of the derived finite-dimensional M.L.E. to the infinite-dimensional M.L.E. is justified under some conditions. An iterative algorithm for generating the M.L.E. is also proposed with two numerical examples
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Moser, Martin
2013-01-01
We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting on...... on the point processes of the normalized jump sizes, we prove that the maximum increment of the random walk converges in distribution to a Fréchet distributed random variable.......We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting...
Conditional quantum entropy power inequality for d-level quantum systems
Jeong, Kabgyun; Lee, Soojoon; Jeong, Hyunseok
2018-04-01
We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert et al (2016 J. Math. Phys. 57 052202). Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.
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.)
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.
On the Number of Mather Measures of Lagrangian Systems
Bernard, Patrick
2010-09-01
In 1996, Ricardo Ricardo Mañé discovered that Mather measures are in fact the minimizers of a “universal” infinite dimensional linear programming problem. This fundamental result has many applications, of which one of the most important is to the estimates of the generic number of Mather measures. Mañé obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able, with Gonzalo Contreras, to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest.
International Nuclear Information System (INIS)
Daskaloyannis, C.
2000-01-01
The integrals of motion of the classical two-dimensional superintegrable systems close in a restrained polynomial Poisson algebra, whose general form is discussed. Each classical superintegrable problem has a quantum counterpart, a quantum superintegrable system. The polynomial Poisson algebra is deformed to a polynomial associative algebra, the finite-dimensional representations of this algebra are calculated by using a deformed parafermion oscillator technique. It is conjectured that the finite-dimensional representations of the polynomial algebra are determined by the energy eigenvalues of the superintegrable system. The calculation of energy eigenvalues is reduced to the solution of algebraic equations, which are universal for a large number of two-dimensional superintegrable systems. (author)
Static properties of 2D spin-ice as a sixteen-vertex model
International Nuclear Information System (INIS)
Foini, Laura; Levis, Demian; Cugliandolo, Leticia F; Tarzia, Marco
2013-01-01
We present a thorough study of the static properties of 2D models of spin-ice type on the square lattice or, in other words, the sixteen-vertex model. We use extensive Monte Carlo simulations to determine the phase diagram and critical properties of the finite-dimensional system. We put forward a suitable mean-field approximation, by defining the model on carefully chosen trees. We employ the cavity (Bethe–Peierls) method to derive self-consistent equations, the fixed points of which yield the equilibrium properties of the model on the tree-like graph. We compare mean-field and finite-dimensional results. We discuss our findings in the context of experiments in artificial two-dimensional spin-ice. (paper)
Topological characteristics of non-smooth functionals
International Nuclear Information System (INIS)
Klimov, V S
1998-01-01
We establish infinite-dimensional variants of the Poincare-Hopf theorem for many-valued vector fields generated by operators of monotonic type. We suggest conditions for the stabilization of the homology groups of closed subsets of a Banach space when approximated by finite-dimensional sections. Emphasis is given to the study of topological characteristics of Lebesgue sets of Lipschitz functionals defined on a closed convex subset of a reflexive space
Energy Technology Data Exchange (ETDEWEB)
Ferrari, Frank, E-mail: frank.ferrari@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); Klevtsov, Semyon, E-mail: semyon.klevtsov@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); ITEP, B. Cheremushkinskaya 25, Moscow 117218 (Russian Federation); Zelditch, Steve, E-mail: zelditch@math.northwestern.edu [Department of Mathematics, Northwestern University, Evanston, IL 60208 (United States)
2013-04-01
The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a Kaehler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of Kaehler metrics. We use the theory of large deviations to decide when a sequence of probability measures on the spaces of Bergman metrics tends to a limit measure on the space of all Kaehler metrics. Several examples are considered.
Irreducible representation basis for unitary groups
International Nuclear Information System (INIS)
Babutsidze, T.D.; Machabeli, I.Z.
1982-01-01
A general method is presented for construction of a complete basis for finite-dimensional irreducible representations of those subgroups of the general linear group GLsub(n) for which irreps of GLsub(n) remain irreducible after the contraction from GLsub(n) to the subgroup in view. Using the constructed basis, the reduction coefficients for contraction of irreps of the group to those of its subgroups are calculated, as well as matrix elements for some physical operators [ru
Physics-compatible numerical methods
Barry, Koren; Abgrall, Remi; Pavel, Bochev; Jason, Frank; Blair, Perrot
2014-01-01
International audience; Physics-compatible numerical methods are methods that aim to preserve key mathematical and physical properties of continuum physics models in their finite-dimensional algebraic representations. They include methods which preserve properties such as energy, monotonicity, maximum principles, symmetries, and involutions of the continuum models. Examples are mimetic methods for spatial discretizations, variational and geometric integrators, conservative finite-volume and f...
Computation of optimal transport and related hedging problems via penalization and neural networks
Eckstein, Stephan; Kupper, Michael
2018-01-01
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, martingale optimal transport, portfolio optimization under uncertainty and generative adversa...
2016-09-13
Polak, E., Da Cunha, N.O.: Constrainedminimization under vector valued-criteria in finite dimensional spaces. J. Math . Anal. Appl. 19(1), 103–124...1969) 12. Pironneau, O., Polak, E.: On the rate of convergence of certain methods of centers. Math . Program. 2(2), 230–258 (1972) 13. Polak, E., Sargent...D.Q.: First order, strong variations algorithms for optimal control problems with terminal inequality constraints. J. Optim. Theory Appl. 16(3/4
Baker-Campbell-Hausdorff relations and unitarity of SU(2) and SU(1,1) squeeze operators
International Nuclear Information System (INIS)
Truax, D.R.
1985-01-01
For squeeze operators, an alternative to the matrix derivations of Baker-Campbell-Hausdorff relations is presented for the groups SU(2) and SU(1,1). The technique involves the solution of a system of nonlinear, first-order differential equations. By this method, criteria for unitarity of the representations are established, and these apply to both infinite- and to finite-dimensional representations of these groups
An example of higher weight superpotential interaction in the heterotic string on orbifolds
International Nuclear Information System (INIS)
Erdenebayar, D.
1994-11-01
An explicit orbifold example of the non-zero correlation functions related to the additional contribution to the induced mass term for Higgs particles at low energies is given. We verify that they form finite dimensional representations of the target space modular transformation SL 2 (Z). This action of the modular group is shown to be consistent with its action on the fixed points set defining the twisted fields. (author). 11 refs
Degenerate odd Poisson bracket on Grassmann variables
International Nuclear Information System (INIS)
Soroka, V.A.
2000-01-01
A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is proposed. It is revealed that this bracket has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, second and third orders with respect to the Grassmann derivatives. It is shown that these Δ-like operators, together with the Grassmann-odd nilpotent Casimir function of this bracket, form a finite-dimensional Lie superalgebra
Probability theory and mathematical statistics for engineers
Pugachev, V S
1984-01-01
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Control electron beam oscillation regimes in Pierce diode with overcritical current
International Nuclear Information System (INIS)
Rempen, I.S.; Khramov, A.E.
2001-01-01
The effect of the delayed feedback on the complex oscillation regimes in the electron flux with the overcritical current in the Pierce diode is studied. The possibility of controlling the oscillation regimes through changing the feedback parameters is shown. The finite-dimensional model, describing the behavior of the electron flux in the Pierce diode hydrodynamic model, is constructed. Its behavior under the effect of the delayed feedback is studied [ru
Dynamics of second order in time evolution equations with state-dependent delay
Czech Academy of Sciences Publication Activity Database
Chueshov, I.; Rezunenko, Oleksandr
123-124, č. 1 (2015), s. 126-149 ISSN 0362-546X R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Second order evolution equations * State dependent delay * Nonlinear plate * Finite-dimensional attractor Subject RIV: BD - Theory of Information Impact factor: 1.125, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf
Energy Technology Data Exchange (ETDEWEB)
Azevedo, Fabio Souto de, E-mail: fabio.azevedo@ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Inst. de Matematica; Sauter, Esequia, E-mail: esequia.sauter@canoas.ifrs.edu.b [Instituto Federal do Rio Grande do Sul (IFRS), Canoas, RS (Brazil); Thompson, Mark; Vilhena, Marco Tulio B., E-mail: mark.thompson@mat.ufrgs.b, E-mail: vilhena@mat.ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2011-07-01
In this work we apply the Green Function Decomposition Method the radiative transport equation in a slab. The method consists in converting the radiative transport equation into a integral equation and projecting the integral operators involved into a finite dimensional space. This methodology does not involve an a priori discretization on the angular variable {mu}, requiring only that the kernel is numerically integrated on {mu}. Numerical results are provided for isotropic, linearly anisotropic, and Rayleigh scattering near the unitary albedo. (author)
On General Off-Shell Representations of World Line (1D Supersymmetry
Directory of Open Access Journals (Sweden)
Charles F. Doran
2014-02-01
Full Text Available Every finite-dimensional unitary representation of the N-extended world line supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets that are identifiable with representations of the Clifford algebra. The data specifying this procedure is a sequence of subspaces of the direct sum of Adinkras, which then opens an avenue for the classification of the continuum of the so-constructed off-shell supermultiplets.
Diamond lemma for the group graded quasi-algebras
Indian Academy of Sciences (India)
the basis for 고 = J/I, where I is the ideal generated by the elements Wσ − fσ ,. (Wσ ,fσ ) ∈ S. The first step in the classification project of quasi-quantum groups [5, 6] is to say whether the subalgebra (in a graded quiver Majid algebra) generated by the paths having unit of the group as the source vertex, is finite dimensional or ...
Chaos of discrete dynamical systems in complete metric spaces
International Nuclear Information System (INIS)
Shi Yuming; Chen Guanrong
2004-01-01
This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces
Large $N$ QCD and $q$-Deformed Quantum Field Theories
Aref'eva, I. Ya.
1996-01-01
A construction of master field describing multicolour QCD is presented. The master fields for large N matrix theories satisfy to standard equations of relativistic field theory but fields are quantized according $q$-deformed commutation relations with $q=0$. These commutation relations are realized in the Boltzmannian Fock space. The master field for gauge theory does not take values in a finite-dimensional Lie algebra, however, there is a non-Abelian gauge symmetry and BRST-invariance.
Process Convergence of Self-Normalized Sums of i.i.d. Random ...
Indian Academy of Sciences (India)
... either of tightness or finite dimensional convergence to a non-degenerate limiting distribution does not hold. This work is an extension of the work by Csörgő et al. who showed Donsker's theorem for Y n , 2 ( ⋅ p ) , i.e., for p = 2 , holds i f f =2 and identified the limiting process as a standard Brownian motion in sup norm.
Classifying Linear Canonical Relations
Lorand, Jonathan
2015-01-01
In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary introduction to the theory of linear canonical relations and present partial results toward the classification problem. This exposition should be accessible to undergraduate students with a basic familiarity with linear algebra.
Adiabatic Theorem without a Gap Condition
International Nuclear Information System (INIS)
Avron, J.E.; Elgar, A.
1999-01-01
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. She general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate
Structure of biprojective Banach algebras with non-trivial radical
International Nuclear Information System (INIS)
Aristov, O Yu
2008-01-01
We study the structure of biprojective Banach algebras. In contrast to earlier results of Selivanov, we admit the presence of nilpotent ideals in the algebras under consideration, and the structure theorem covers almost all known examples. As a corollary, we obtain a complete classification of finite-dimensional biprojective Banach algebras. A major role in the proof is played by the approximation property for certain Banach spaces related to the algebras under consideration
Banach C*-algebras not containing a subspace isomorphic to C0
International Nuclear Information System (INIS)
Basit, B.
1989-09-01
If X is a locally Hausdorff space and C 0 (X) the Banach algebra of continuous functions defined on X vanishing at infinity, we showed that a subalgebra A of C 0 (X) is finite dimensional if it does not contain a subspace isomorphic to the Banach space C 0 of convergent to zero complex sequences. In this paper we extend this result to noncommutative Banach C*-algebras and Banach* algebras. 10 refs
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
International Nuclear Information System (INIS)
Gel'man, B D
2002-01-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed
Absolute Continuity of Stable Foliations for Mappings of Banach Spaces
Blumenthal, Alex; Young, Lai-Sang
2017-09-01
We prove the absolute continuity of stable foliations for mappings of Banach spaces satisfying conditions consistent with time- t maps of certain classes of dissipative PDEs. This property is crucial for passing information from submanifolds transversal to the stable foliation to the rest of the phase space; it is also used in proofs of ergodicity. Absolute continuity of stable foliations is well known in finite dimensional hyperbolic theory. On Banach spaces, the absence of nice geometric properties poses some additional difficulties.
Robust Manipulation and Computation for Inhomogeneous Quantum Ensembles
2013-07-01
stimulus [33]. Phase models are widely employed in physics, chemistry, and biology [34] to study rhythmic systems where the oscillatory phase, but not the...due to their long duration. This has prompted a surge of theoretical and experimental activities to find shortcuts to adiabaticity in quantum systems... Academy of Sciences, Vol. 108, No. 5, pp. 1879-1884, 2011. 12. J.-S. Li, “Ensemble Control of Finite-Dimensional Time-Varying Linear Systems”, IEEE
A representative individual from Arrovian aggregation of parametric individual utilities
Herzberg, Frederik
2011-01-01
This article investigates the representative-agent hypothesis for an infinite population which has to make a social choice from a given finite-dimensional space of alternatives. It is assumed that some class of admissible strictly concave utility functions is exogenously given and that each individual's preference ordering can be represented cardinally through some admissible utility function. In addition, we assume that (i) the class of admissible utility functions allows for a smooth parame...
The Domain of Normal Attraction of an Operator-Stable Law
Hudson, William N.; Mason, J. David; Veeh, Jerry Alan
1983-01-01
The idea of the domain of normal attraction was earlier extended to probabilities on a finite-dimensional inner-product space. We obtain a necessary and sufficient condition that a probability be in the domain of normal attraction of a given probability in terms of their covariance operators and of a limit involving the Levy measure. This condition appears to be the natural generalization of the corresponding univariate condition. We also show that the domains of normal attraction of two prob...
An introduction to associative geometry with applications to integrable systems
Tacchella, Alberto
2017-08-01
The aim of these notes is to provide a reasonably short and ;hands-on; introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory associative geometry. We argue that this formalism sheds a new light on some classic solution methods in the theory of finite-dimensional integrable dynamical systems.
Harnad, J.; Loutsenko, I.; Yermolayeva, O.
2005-11-01
Finite-dimensional reductions of the two-dimensional dispersionless Toda hierarchy constrained by the "string equation" are studied. These include solutions determined by polynomial, rational, or logarithmic functions, which are of interest in relation to the "Laplacian growth" or Hele-Shaw problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derived.
A Constructive Sharp Approach to Functional Quantization of Stochastic Processes
Junglen, Stefan; Luschgy, Harald
2010-01-01
We present a constructive approach to the functional quantization problem of stochastic processes, with an emphasis on Gaussian processes. The approach is constructive, since we reduce the infinite-dimensional functional quantization problem to a finite-dimensional quantization problem that can be solved numerically. Our approach achieves the sharp rate of the minimal quantization error and can be used to quantize the path space for Gaussian processes and also, for example, Lévy processes.
Relaxation periodic solutions of one singular perturbed system with delay
Kashchenko, A. A.
2017-12-01
In this paper, we consider a singularly perturbed system of two differential equations with delay, simulating two coupled oscillators with a nonlinear compactly supported feedback. We reduce studying nonlocal dynamics of initial system to studying dynamics of special finite-dimensional mappings: rough stable (unstable) cycles of these mappings correspond to exponentially orbitally stable (unstable) relaxation solutions of initial problem. We show that dynamics of initial model depends on coupling coefficient crucially. Multistability is proved.
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...
Millward, Raymond
2011-01-01
In this thesis we show that the finite element error for the high contrast elliptic interface problem is independent of the contrast in the material coefficient under certain assumptions. The error estimate is proved using a particularly technical proof with construction of a specific function from the finite dimensional space of piecewise linear functions.We review the multiscale finite element method of Chu, Graham and Hou to give clearer insight. We present some generalisations to extend t...
A generalized biharmonic equation and its applications to ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
complex conjugate of w) and integrate each term of the resulting equation over the range of z by parts a ...... matrix C2(x) being Hermitian in a finite dimensional space, the spectral theorem gives that these form an orthonormal basis to Cn for each x in V i.e., u† i (x)uj (x) = δij . We thus have an expression χ(x) = n. ∑ i=1.
Real Orthogonal Projections as Quantum Logic
Matvejchuk, Marjan
2017-12-01
In this paper, we study linear operators on real and complex Euclidean spaces which are real-orthogonal projections. It is a generalization of such standard (complex) orthogonal projections for which only the real part of scalar product vanishes. We can compare some partial order properties of the orthogonal and of the R-orthogonal projections. We prove that the set of all R-orthogonal projections in finite-dimensional complex space is a quantum logic.
On characterisation of Markov processes via martingale problems
Indian Academy of Sciences (India)
the finite dimensional distributions of the (unique in law) solution to the (A, δx) martingale problem that is continuous in probability. We have seen in the proof above that x −→ µx(= −1. (x)) is Borel measurable and hence for all t1,t2,...,tm, m ≥ 1 x −→ µm x (t1,t2,...,tm) is Borel measurable. (3.6). The next step is to prove that ...
On Casimir elements of simple Lie algebras
International Nuclear Information System (INIS)
El Houari, M.
1996-08-01
In this letter, we recall briefly the generalized Casimir elements of a finite dimensional Lie algebra. We specify those of orders two and three: when the Lie algebra is simple (even semisimple), we begin by normalizing the former (the quadratic), and then we study some actions of the latter (the cubic). In particular, we introduce a graphical formalism, translating rigorously the tensorial calculus. This allows us to prove the main theorem in a graphic theoretic manner. (author). 11 refs, 1 tab
Stochastic processes and filtering theory
Jazwinski, Andrew H
1970-01-01
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
Let H i , 1 ≤ i ≤ n be complex finite-dimensional Hilbert spaces of dimension d i , 1 ≤ i ≤ n respectively with d i ≥ 2 for every . By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on ...
Highest Weight Modules Over Quantum Queer Superalgebra {U_q(mathfrak {q}(n))}
Grantcharov, Dimitar; Jung, Ji Hye; Kang, Seok-Jin; Kim, Myungho
2010-06-01
In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra {U_q(mathfrak {q}(n))}. The key ingredients are the triangular decomposition of {U_q(mathfrak {q}(n))} and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for {U_q(mathfrak {q}(n))}-modules in the category {mathcal {O}q^{≥ 0}}.
Renault, Vincent
2016-01-01
The aim of this thesis is to propose different mathematical neuron models that take into account Optogenetics, and study their optimal control. We first define a controlled version of finite-dimensional, deterministic, conductance based neuron models. We study a minimal time problem for a single-input affine control system and we study its singular extremals. We implement a direct method to observe the optimal trajectories and controls. The optogenetic control appears as a new way to assess t...
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.)
Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields
International Nuclear Information System (INIS)
Albeverio, S.; Brzezniak, Z.
1994-01-01
We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)
Quantum Channels, Wavelets, Dilations and Representations of $O_n$
Kribs, David W.
2003-01-01
We show that the representations of the Cuntz C$^\\ast$-algebras $O_n$ which arise in wavelet analysis and dilation theory can be classified through a simple analysis of completely positive maps on finite-dimensional space. Based on this analysis, an application in quantum information theory is obtained; namely, a structure theorem for the fixed point set of a unital quantum channel. We also include some open problems motivated by this work.
A Risk Comparison of Ordinary Least Squares vs Ridge Regression
Dhillon, Paramveer S.; Foster, Dean P.; Kakade, Sham M.; Ungar, Lyle H.
2011-01-01
We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.
Codimensions of generalized polynomial identities
International Nuclear Information System (INIS)
Gordienko, Aleksei S
2010-01-01
It is proved that for every finite-dimensional associative algebra A over a field of characteristic zero there are numbers C element of Q + and t element of Z + such that gc n (A)∼Cn t d n as n→∞, where d=PI exp(A) element of Z + . Thus, Amitsur's and Regev's conjectures hold for the codimensions gc n (A) of the generalized polynomial identities. Bibliography: 6 titles.
Twistor fibrations giving primitive harmonic maps of finite type
Directory of Open Access Journals (Sweden)
Rui Pacheco
2005-01-01
Full Text Available Primitive harmonic maps of finite type from a Riemann surface M into a k-symmetric space G/H are obtained by integrating a pair of commuting Hamiltonian vector fields on certain finite-dimensional subspaces of loop algebras. We will clarify and generalize Ohnita and Udagawa's results concerning homogeneous projections p:G/H→G/K, with H⊂K, preserving finite-type property for primitive harmonic maps.
Optimal control of ODEs and DAEs
Gerdts, Matthias
2011-01-01
The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations. An emphasis is placed on the interplay between the continuous optimal control problem, which typically is defined and analyzed in a Banach space setting, and discrete optimal control problems, which are obtained by discretization and lead to finite dimensional optimization problems.
Superalgebras, their quantum deformations and the induced representation method
International Nuclear Information System (INIS)
Nguyen Anh Ky.
1996-08-01
In this paper some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Up to now, based on the Kac representation theory we have succeeded in constructing representations of several higher rank superalgebras. When representations of quantum superalgebras are concerned, we develop a method which can be applied not only to the one-parametric quantum deformations but also to the multi-parametric ones. Here, being illustrations of the above-mentioned methods, the superalgebra gl(2/1) and its (one-parametric) quantum deformation U q [gl(2/1)] are considered as their finite-dimensional representations are investigated in detail and constructed explicitly. Also, it is shown that the finite-dimensional representations obtained constitute classes of all irreducible (typical and non-typical) finite-dimensional representations of gl(2/1) and U q [gl(2/1)]. Some of the detailed results may be simple but they are given for the first time. (author). 64 refs
Strade, Helmut
2004-01-01
The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question during the last 35 years has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the...
Discretization of variational regularization in Banach spaces
International Nuclear Information System (INIS)
Pöschl, Christiane; Resmerita, Elena; Scherzer, Otmar
2010-01-01
Consider a nonlinear ill-posed operator equation F(u) = y, where F is defined on a Banach space X. In this paper we analyze finite-dimensional variational regularization, which takes into account operator approximations and noisy data. As shown in the literature, depending on the setting, convergence of the regularized solutions of the finite-dimensional problems can be with respect to the strong or just a weak topology. In this paper our contribution is twofold. First, we derive convergence rates in terms of Bregman distances in the convex regularization setting under appropriate sourcewise representation of a solution of the equation. Secondly, for particular regularization realizations in nonseparable Banach spaces, we discuss the finite-dimensional approximations of the spaces and the type of convergence, which is needed for the convergence analysis. These considerations lay the fundament for efficient numerical implementation. In particular, we emphasize on the space X of finite total variation functions and analyze in detail the cases when X is the space of the functions of finite bounded deformation and the L ∞ -space. The latter two settings are of interest in numerous problems arising in optimal control, machine learning and engineering
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-05-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.
A dynamic approach to quadrilateral definitions
Directory of Open Access Journals (Sweden)
Rajendran Govender
2004-10-01
Full Text Available This study examined 18 prospective secondary mathematics teachers' understanding of the nature of definitions, and their use of the dynamic geometry software Sketchpad to improve not only their understanding of definitions but also their ability to define geometric concepts themselves. Results indicated that the evaluation of definitions by accurate construction and measurement enabled students to achieve a better understanding of necessary and sufficient conditions, as well as the ability to more readily find counter-examples, and to recognise and improve on uneconomical definitions.
Shared intention and the doxastic single end condition
DEFF Research Database (Denmark)
Blomberg, Olle
2016-01-01
end condition captures a feature at the very heart of the phenomenon of intentional joint action. For instance, just as several simple actions are only unified into a complex intentional singular activity if the agent believes or assumes that there is a single end that each action is directed to, so...... this condition only if participants must intend to contribute to the end under the same conception. While such a requirement successfully rules out some counterexamples, it also makes the accounts unable to appropriately accommodate and explain clear cases of intentional joint action that they ought to be able...
Quantum Physics Without Quantum Philosophy
Dürr, Detlef; Zanghì, Nino
2013-01-01
It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Is Justified True Belief Knowledge? / ¿Una creencia verdadera justificada es conocimiento?
Directory of Open Access Journals (Sweden)
Edmund L. Gettier
2013-12-01
Full Text Available [ES] En este breve trabajo, se presenta una edición bilingüe de Is Justified True Belief Knowledge? (1963, de Edmund L. Gettier, donde se presentan contraejemplos a la definición de «conocimiento» como «creencia verdadera justificada». [ES] In this brief text, a bilingual edition of Is Justified True Belief Knowledge?, (1963 by Edmund L. Gettier, some counterexamples are presented to the definition of «knowledge» as «justified true belief».
Refinement monoids, equidecomposability types, and boolean inverse semigroups
Wehrung, Friedrich
2017-01-01
Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
Zero nouns with and without objects
Directory of Open Access Journals (Sweden)
Antonio Fábregas
2012-05-01
Full Text Available One of the main topics on the study of the relationship between syntax and morphology is (deverbal nominalizations. In this area, several generalizations that tie the morphological make-up with the syntactic structure have been made. Most relevantly, it has been argued that only overt nominalizations (those that include a nominalizer like -ation or ‑ment are allowed to have internal arguments introduced in their structural representation. In this paper, we address some previously unexplained apparent counterexamples to this generalization, and we argue that they can be captured if particular restrictions on the spell out of the syntactic structure are taken into consideration.
Mach's principle and rotating universes
International Nuclear Information System (INIS)
King, D.H.
1990-01-01
It is shown that the Bianchi 9 model universe satisfies the Mach principle. These closed rotating universes were previously thought to be counter-examples to the principle. The Mach principle is satisfied because the angular momentum of the rotating matter is compensated by the effective angular momentum of gravitational waves. A new formulation of the Mach principle is given that is based on the field theory interpretation of general relativity. Every closed universe with 3-sphere topology is shown to satisfy this formulation of the Mach principle. It is shown that the total angular momentum of the matter and gravitational waves in a closed 3-sphere topology universe is zero
N=4 Multi-Particle Mechanics, WDVV Equation and Roots
Directory of Open Access Journals (Sweden)
Olaf Lechtenfeld
2011-03-01
Full Text Available We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U. The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed flat Yang-Mills connections. Three- and four-particle solutions are presented. The covector ansatz turns the WDVV equation into an algebraic condition, for which we give a formulation in terms of partial isometries. Three ideas for classifying WDVV solutions are developed: ortho-polytopes, hypergraphs, and matroids. Various examples and counterexamples are displayed.
Remarks on the conformally flat submanifolds satisfying the R.C-condition or the C.R-condition
International Nuclear Information System (INIS)
Zafindratafa, G.K.
1988-06-01
The hypersurfaces of E n+1 have been studied for the particular case when they satisfy the R.C-condition or the C.R-condition. One objective is to generalize this situation to a higher codimension. More precisely, we consider the case of dimension 4, and replace the condition of quasiumbilicity by the conformal flatness. In this way, we construct an example of 4-submanifold of IE 6 which is conformally flat at a particular point without being quasiumbilical. That such submanifolds exist, was asserted without proof. Thus, we present another counter-example. (author). 4 refs
CSIR Research Space (South Africa)
Booth, R
2011-08-01
Full Text Available kernel base contraction operator. The converse, however, does not hold, i.e., there exist kernel base contraction operators which are not partial meet base contraction operators (see [28, p91]) for a counterexample, and [18] for more on the relation... to infer that Tweety can fly. But given the additional evidence that Tweety is an ostrich, we should abandon our conclusion about Tweety?s flying capabilities. While there are many approaches to nonmonotonic reasoning (see e.g., [53, 46]), we consider...
On how to interpret the role of the future within the abortion debate
DEFF Research Database (Denmark)
Di Nucci, Ezio
2009-01-01
In a previous paper, I had argued that Strong's counterexamples to Marquis's argument against abortion-according to which terminating fetuses is wrong because it deprives them of a valuable future-fail either because they have no bearing on Marquis's argument or because they make unacceptable cla...... ours" and "valuable future" are interchangeable; and that, rather, it is exactly by replacing "future like ours" with "valuable future" that I construct my argument against Strong. I conclude with some remarks on how Marquis's concept of "future like ours" should be interpreted....
Putting the horse before the cart: a pragmatist analysis of knowledge
Directory of Open Access Journals (Sweden)
Luís M. Augusto
2011-01-01
Full Text Available The definition of knowledge as justified true belief is the best we presently have. However, the canonical tripartite analysis of knowledge does not do justice to it due to a Platonic conception of a priori truth that puts the cart before the horse. Within a pragmatic approach, I argue that by doing away with a priori truth, namely by submitting truth to justification, and by accordingly altering the canonical analysis of knowledge, this is a fruitful definition. So fruitful indeed that it renders the Gettier counterexamples vacuous, allowing positive work in epistemology and related disciplines.
Radial solutions of equations and inequalities involving the -Laplacian
Directory of Open Access Journals (Sweden)
Reichel Wolfgang
1997-01-01
Full Text Available Several problems for the differential equation are considered. For , the operator is the radially symmetric -Laplacian in . For the initial value problem with given data various uniqueness conditions and counterexamples to uniqueness are given. For the case where is increasing in , a sharp comparison theorem is established; it leads to maximal solutions, nonuniqueness and uniqueness results, among others. Using these results, a strong comparison principle for the boundary value problem and a number of properties of blow-up solutions are proved under weak assumptions on the nonlinearity .
On topological groups admitting a base at identity indexed with $\\omega^\\omega$
Leiderman, Arkady G.; Pestov, Vladimir G.; Tomita, Artur H.
2015-01-01
A topological group $G$ is said to have a local $\\omega^\\omega$-base if the neighbourhood system at identity admits a monotone cofinal map from the directed set $\\omega^\\omega$. In particular, every metrizable group is such, but the class of groups with a local $\\omega^\\omega$-base is significantly wider. The aim of this article is to better understand the boundaries of this class, by presenting new examples and counter-examples. Ultraproducts and non-arichimedean ordered fields lead to natur...
Risk Management and Insurance Decisions under Ambiguity
DEFF Research Database (Denmark)
Martínez-Correa, Jimmy
a counterexample to a classical result in insurance economics where an insurance contract with straight deductible is dominated by a coinsurance contract. Finally, I find that a modified Borch rule characterizes the optimal insurance contract with bilateral risk and ambiguity attitudes and heterogeneity in beliefs....... and ambiguity attitudes interact in nontrivial ways to determine the change of coinsurance demand. I derive sufficient conditions to guarantee that the optimal coinsurance demand is decreasing in wealth. When a non-traded asset is introduced, my model predicts behavior that is inconsistent with the classical...
Testing the weak gravity-cosmic censorship connection
Crisford, Toby; Horowitz, Gary T.; Santos, Jorge E.
2018-03-01
A surprising connection between the weak gravity conjecture and cosmic censorship has recently been proposed. In particular, it was argued that a promising class of counterexamples to cosmic censorship in four-dimensional Einstein-Maxwell-Λ theory would be removed if charged particles (with sufficient charge) were present. We test this idea and find that indeed if the weak gravity conjecture is true, one cannot violate cosmic censorship this way. Remarkably, the minimum value of charge required to preserve cosmic censorship appears to agree precisely with that proposed by the weak gravity conjecture.
DEFF Research Database (Denmark)
Schlichtkrull, Anders; Villadsen, Jørgen
2016-01-01
Reference Library Volume 110: Towards Paraconsistent Engineering (Springer 2016). We formalize a paraconsistent many-valued logic that we motivated and described in a special issue on logical approaches to paraconsistency (Journal of Applied Non-Classical Logics 2005). We limit ourselves...... to the propositional fragment of the higher-order logic. The logic is based on so-called key equalities and has a countably infinite number of truth values. We prove theorems in the logic using the definition of validity. We verify truth tables and also counterexamples for non-theorems. We prove meta-theorems about...
Minimalism and Speakers’ Intuitions
Directory of Open Access Journals (Sweden)
Matías Gariazzo
2011-08-01
Full Text Available Minimalism proposes a semantics that does not account for speakers’ intuitions about the truth conditions of a range of sentences or utterances. Thus, a challenge for this view is to offer an explanation of how its assignment of semantic contents to these sentences is grounded in their use. Such an account was mainly offered by Soames, but also suggested by Cappelen and Lepore. The article criticizes this explanation by presenting four kinds of counterexamples to it, and arrives at the conclusion that minimalism has not successfully answered the above-mentioned challenge.
An extension of the mixed Novikov-Kazamaki condition
Chikvinidze, B.
Given a continuous local martingale M, the associated stochastic exponential ℰ(M) =exp{M ‑1 2〈M〉} is a local martingale, but not necessarily a true martingale. To know whether ℰ(ℳ) is a true martingale is important for many applications, e.g., if Girsanov’s theorem is applied to perform a change of measure. We give several generalizations of Kazamaki’s results and finally construct a counterexample which does not satisfy the mixed Novikov-Kazamaki condition, but satisfies our conditions.
Introduction to stochastic dynamic programming
Ross, Sheldon M; Lukacs, E
1983-01-01
Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the
The lambda sigma calculus and strong normalization
DEFF Research Database (Denmark)
Schack-Nielsen, Anders; Schürmann, Carsten
Explicit substitution calculi can be classified into several dis- tinct categories depending on whether they are confluent, meta-confluent, strong normalization preserving, strongly normalizing, simulating, fully compositional, and/or local. In this paper we present a variant of the λσ-calculus......, which satisfies all seven conditions. In particular, we show how to circumvent Mellies counter-example to strong normalization by a slight restriction of the congruence rules. The calculus is implemented as the core data structure of the Celf logical framework. All meta-theoretic aspects of this work...
Instability of the Kaluza-Klein vacuum
International Nuclear Information System (INIS)
Witten, E.
1982-01-01
It is argued that the ground state of the Kaluza-Klein unified theory is unstable against a process of semiclassical barrier penetration. This is related to the fact that the positive energy conjecture does not hold for the Kaluza-Klein theory; an explicit counter-example is given. The reasoning presented here assumes that in general relativity one should include manifolds of non-vacuum topology. It is argued that the existence of elementary fermions (not present in the original Kaluza-Klein theory) would stabilize the Kaluza-Klein vacuum. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Sanchis-Ojeda, Roberto; Isaacson, Howard; Marcy, Geoffrey W.; Weiss, Lauren [Department of Astronomy, University of California, Berkeley, CA 94720 (United States); Winn, Joshua N.; Dai, Fei [Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Howard, Andrew W.; Sinukoff, Evan [Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822 (United States); Petigura, Erik; Rogers, Leslie [Department of Astronomy and Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 (United States); Albrecht, Simon [Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C (Denmark); Hirano, Teruyuki, E-mail: sanchisojeda@berkeley.edu [Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2015-10-10
We have detected the Rossiter–Mclaughlin effect during a transit of WASP-47b, the only known hot Jupiter with close planetary companions. By combining our spectroscopic observations with Kepler photometry, we show that the projected stellar obliquity is λ = 0° ± 24°. We can firmly exclude a retrograde orbit for WASP-47b, and rule out strongly misaligned prograde orbits. Low obliquities have also been found for most of the other compact multiplanet systems that have been investigated. The Kepler-56 system, with two close-in gas giants transiting their subgiant host star with an obliquity of at least 45{sup ◦}, remains the only clear counterexample.
The Quantitative Linear-Time–Branching-Time Spectrum
DEFF Research Database (Denmark)
Thrane, Claus; Fahrenberg, Uli; Legay, Axel
2011-01-01
We present a distance-agnostic approach to quantitative verification. Taking as input an unspecified distance on system traces, or executions, we develop a game-based framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance....... Thus we extend the classic linear-time–branching-time spectrum to a quantitative setting, parametrized by trace distance. We also prove a general transfer principle which allows us to transfer counterexamples from the qualitative to the quantitative setting, showing that all system distances...
Directory of Open Access Journals (Sweden)
Robert E Kelly
2010-11-01
Full Text Available The War on Terror encourages a moral rigidity that all terrorism is automatically normatively wrong. Yet conceivable counter-examples, such as terrorism against Nazi wartime installations or African National Congress (ANC behavior in the apartheid struggle, suggest otherwise. Asymmetric terrorism is a tactic generally found morally repugnant, but we leaven our normative judgment of it by three more factors: 1 the target, 2 the regime-type, and 3 the ideological goal. That we cross-reference these four vectors in our normative judgment of terrorism generates the moral complexity of, e.g., the 'freedom fighter' problem in terrorism studies.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan
2016-01-01
In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional
Hamiltonian quantization of Chern-Simons theory with SL(2, C) group
Energy Technology Data Exchange (ETDEWEB)
Buffenoir, E; Noui, K; Roche, Ph [Laboratoire de Physique Mathematique et Theorique, Universite Montpellier 2, 34000 Montpellier (France)
2002-10-07
We analyse the Hamiltonian quantization of Chern-Simons theory associated with the real group SL(2, C){sub R}, universal covering group of the Lorentz group SO(3, 1). The algebra of observables is generated by finite-dimensional spin networks drawn on a punctured topological surface. Our main result is a construction of a unitary representation of this algebra. For this purpose, we use the formalism of combinatorial quantization of Chern-Simons theory, i.e., we quantize the algebra of polynomial functions on the space of flat SL(2, C){sub R} connections on a topological surface {sigma} with punctures. This algebra, the so-called moduli algebra, is constructed along the lines of Fock-Rosly, Alekseev-Grosse-Schomerus, Buffenoir-Roche using only finite-dimensional representations of U{sub q}(sl(2, C){sub R}). It is shown that this algebra admits a unitary representation acting on a Hilbert space which consists of wave packets of spin networks associated with principal unitary representations of U{sub q}(sl(2, C){sub R}). The representation of the moduli algebra is constructed using only Clebsch-Gordan decomposition of a tensor product of a finite-dimensional representation with a principal unitary representation of U{sub q}(sl(2, C){sub R}). The proof of unitarity of this representation is nontrivial and is a consequence of the properties of U{sub q}(sl(2, C){sub R}) intertwiners which are studied in depth. We analyse the relationship between the insertion of a puncture coloured with a principal representation and the presence of a worldline of a massive spinning particle in de Sitter space.
Poisson traces, D-modules, and symplectic resolutions
Etingof, Pavel; Schedler, Travis
2018-03-01
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.
Geometric MCMC for infinite-dimensional inverse problems
Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.
2017-04-01
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.
New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials
Energy Technology Data Exchange (ETDEWEB)
Marquette, Ian [School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072 (Australia); Quesne, Christiane [Physique Nucleaire Theorique et Physique Mathematique, Universite Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2013-04-15
In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequences of EOP.
Witten, Edward
2008-01-01
I sketch what it is supposed to mean to quantize gauge theory, and how this can be made more concrete in perturbation theory and also by starting with a finite-dimensional lattice approximation. Based on real experiments and computer simulations, quantum gauge theory in four dimensions is believed to have a mass gap. This is one of the most fundamental facts that makes the Universe the way it is. This article is the written form of a lecture presented at the conference "Geometric Analysis: Past and Future" (Harvard University, August 27-September 1, 2008), in honor of the 60th birthday of S.-T. Yau.
Algebraic properties of compatible Poisson brackets
Zhang, Pumei
2014-05-01
We discuss algebraic properties of a pencil generated by two compatible Poisson tensors A( x) and B( x). From the algebraic viewpoint this amounts to studying the properties of a pair of skew-symmetric bilinear forms A and B defined on a finite-dimensional vector space. We describe the Lie group G P of linear automorphisms of the pencil P = { A + λB}. In particular, we obtain an explicit formula for the dimension of G P and discuss some other algebraic properties such as solvability and Levi-Malcev decomposition.
Safety Analysis of Stochastic Dynamical Systems
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2015-01-01
This paper presents a method for verifying the safety of a stochastic system. In particular, we show how to compute the largest set of initial conditions such that a given stochastic system is safe with probability p. To compute the set of initial conditions we rely on the moment method that via...... Haviland's theorem allows an infinite dimensional optimization problem on measures to be formulated as a polynomial optimization problem. Subsequently, the moment sequence is truncated (relaxed) to obtain a finite dimensional polynomial optimization problem. Finally, we provide an illustrative example...
International Nuclear Information System (INIS)
Wang Ling; Dong Zhongzhou; Liu Xiqiang
2008-01-01
By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation (ANNV). Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.
Notes on Whitehead space of an algebra
Directory of Open Access Journals (Sweden)
M. Arian-Nejad
2002-01-01
the number of simple components of R. More precisely, we show that when R is algebraic over F and Char F=0, then the number of simple components of R is greater than or equal to dimF R/[R,R], and when R is finite dimensional over F or is locally finite over F in the case of Char F=0, then the number of simple components of R is equal to dimF R/[R,R].
Belkhatir, Zehor
2015-11-23
This paper discusses the estimation of distributed Cerebral Blood Flow (CBF) using spatiotemporal traveling wave model. We consider a damped wave partial differential equation that describes a physiological relationship between the blood mass density and the CBF. The spatiotemporal model is reduced to a finite dimensional system using a cubic b-spline continuous Galerkin method. A Kalman Filter with Unknown Inputs without Direct Feedthrough (KF-UI-WDF) is applied on the obtained reduced differential model to estimate the source term which is the CBF scaled by a factor. Numerical results showing the performances of the adopted estimator are provided.
Jorgensen, Palle E T
1987-01-01
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
The universal Racah-Wigner symbol for U{sub q}(osp(1 vertical stroke 2))
Energy Technology Data Exchange (ETDEWEB)
Pawelkiewicz, Michal; Schomerus, Volker [DESY Hamburg (Germany). Theory Group; Suchanek, Paulina [DESY Hamburg (Germany). Theory Group; Wroclaw Univ. (Poland). Inst. for Theoretical Physics
2013-10-15
We propose a new and elegant formula for the Racah-Wigner symbol of self-dual continuous series of representations of U{sub q}(osp(1 vertical stroke 2)). It describes the entire fusing matrix for both NS and R sector of N=1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in an earlier paper (L. Hadaz, M. Pawelkiewicz, and V. Schomerus, arXiv:1305.4596[hep-th]). Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the Racah-Wigner coefficients of finite dimensional representations.
Geometry and dynamics in Gromov hyperbolic metric spaces with an emphasis on non-proper settings
Das, Tushar; Urbański, Mariusz
2016-01-01
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Simulation of conditional diffusions via forward-reverse stochastic representations
Bayer, Christian
2015-01-07
We derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval,conditioned on the terminal state. The conditioning can be with respect to a fixed measurement point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced by Milstein, Schoenmakers and Spokoiny in the context of density estimation. The corresponding Monte Carlo estimators have essentially root-N accuracy, and hence they do not suffer from the curse of dimensionality. We also present an application in statistics, in the context of the EM algorithm.
Linear operators in Clifford algebras
International Nuclear Information System (INIS)
Laoues, M.
1991-01-01
We consider the real vector space structure of the algebra of linear endomorphisms of a finite-dimensional real Clifford algebra (2, 4, 5, 6, 7, 8). A basis of that space is constructed in terms of the operators M eI,eJ defined by x→e I .x.e J , where the e I are the generators of the Clifford algebra and I is a multi-index (3, 7). In particular, it is shown that the family (M eI,eJ ) is exactly a basis in the even case. (orig.)
Relativistic covariant wave equations and acausality in external fields
International Nuclear Information System (INIS)
Pijlgroms, R.B.J.
1980-01-01
The author considers linear, finite dimensional, first order relativistic wave equations: (βsup(μ)ideltasub(μ)-β)PSI(x) = 0 with βsup(μ) and β constant matrices. Firstly , the question of the relativistic covariance conditions on these equations is considered. Then the theory of these equations with β non-singular is summarized. Theories with βsup(μ), β square matrices and β singular are also discussed. Non-square systems of covariant relativistic wave equations for arbitrary spin > 1 are then considered. Finally, the interaction with external fields and the acausality problem are discussed. (G.T.H.)
Multilevel ensemble Kalman filtering
Hoel, Hakon
2016-06-14
This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.
Nonlinear analysis of flexible plates lying on elastic foundation
Directory of Open Access Journals (Sweden)
Trushin Sergey
2017-01-01
Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.
N-point and higher-genus osp(1|2) fusion
International Nuclear Information System (INIS)
Rasmussen, Joergen
2003-01-01
We study affine osp(1|2) fusion, the fusion in osp(1|2) conformal field theory, for example. Higher-point and higher-genus fusion is discussed. The fusion multiplicities are characterized as discretized volumes of certain convex polytopes, and are written explicitly as multiple sums measuring those volumes. We extend recent methods developed to treat affine su(2) fusion. They are based on the concept of generalized Berenstein-Zelevinsky triangles and virtual couplings. Higher-point tensor products of finite-dimensional irreducible osp(1|2) representations are also considered. The associated multiplicities are computed and written as multiple sums
The finite section method and problems in frame theory
DEFF Research Database (Denmark)
Christensen, Ole; Strohmer, T.
2005-01-01
The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also...... solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz...
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.
International Nuclear Information System (INIS)
Zhang Honghao; Yan Wenbin; Li Xuesong
2008-01-01
By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to chiral perturbation theory and general relativity
Irrational free field resolutions for W(sl(n)) and extended Sugawara construction
International Nuclear Information System (INIS)
Niedermaier, M.
1991-03-01
The existence of Miura-type free field realizations is established for the extended conformal algebras W(sl(n)) at irrational values of the screening parameter. The problem of the 'closure' of the algebra is reduced to a finite dimensional quantum group problem. The structure of the Fock space resolution and the character formulae are obtained for the irreducible modules. They are shown to be isomorphic to the space of sl(n) singlets in sl(n) affine affine level 1 modules. The isomorphism is given by the Φβγ free field realization of sl(n). (orig.)
The core of a class of non-atomic games which arise in economic applications
Einy, Ezra; Moreno, Diego; Shitovitz, Benyamin
1997-01-01
We prove a representation theorem for the core of a non-atomic game of the form v = fOil, where Il is a finite dimensional vector of non-atomic measures and f is a non-decreasing continuous concave function on the range of Il. The theorem is stated in terms of the sub gradients of the function f. As a consequence of this theorem we show that the game v is balanced (i. e., has a non-empty core) iff the function f is homogeneous of degree one along the diagonal of the range of Il, and it is tot...
Quantum mechanics on spaces with finite fundamental group
International Nuclear Information System (INIS)
Giulini, D.
1995-01-01
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that arise from the non-simply connectedness of the classical configuration space. We define the quantum theory on the universal cover but restrict the algebra of observables O to the commutant of the algebra generated by deck-transformations. We apply standard superselection principles and construct the corresponding sectors. We emphasize the relevance of all sectors and not just the abelian ones. (orig.)
CLASSIFICATION OF 4-DIMENSIONAL GRADED ALGEBRAS
Armour, Aaron; Chen, Hui-Xiang; ZHANG, Yinhuo
2009-01-01
Let k be an algebraically closed field. The algebraic and geometric classification of finite dimensional algebras over k with ch(k) not equal 2 was initiated by Gabriel in [6], where a complete list of nonisomorphic 4-dimensional k-algebras was given and the number of irreducible components of the variety Alg(4) was discovered to be 5. The classification of 5-dimensional k-algebras was done by Mazzola in [10]. The number of irreducible components of the variety Alg(5) is 10. With the dimensio...
On the normality of orbit closures which are hypersurfaces
Indian Academy of Sciences (India)
fi : Vi → Wi, i ∈ Q0, such that ft(α)Vα = Wαfs(α) for each α ∈ Q1. The category of representations of Q is an abelian k-linear category, which is naturally equivalent to the category mod (kQ) of finite-dimensional left kQ-modules (see section III.1 of [1]). For a path ω = αr ...α1 and a representation V of Q, we define. Vω = Vαr ◦ .
Computing faithful representations for nilpotent Lie algebras
Burde, Dietrich; Eick, Bettina; de Graaf, Willem
2008-01-01
We describe three methods to determine a faithful representation of small dimension for a finite-dimensional nilpotent Lie algebra over an arbitrary field. We apply our methods in finding bounds for the smallest dimension $\\mu(\\Lg)$ of a faithful $\\Lg$-module for some nilpotent Lie algebras $\\Lg$. In particular, we describe an infinite family of filiform nilpotent Lie algebras $\\Lf_n$ of dimension $n$ over $\\Q$ and conjecture that $\\mu(\\Lf_n) > n+1$. Experiments with our algorithms suggest th...
Fast Implicit Methods For Elliptic Moving Interface Problems
2015-12-11
rules. 2 Theory 2.1 Abstract formulation In this section the problem of evaluating a general continuous bilinear form on a pair of Banach spaces is...cases such as the L2 and H1 inner products. Definition 2.1. Let F and G be real Banach spaces . Then a bilinear quadrature of order (m,n) on F ×G is a...B(L1f, L2g). Definition 2.2. Let F ,G be real Banach spaces with a continuous bilinear form 〈·, ·〉 : F × G → R. Finite-dimensional subspaces F0 ⊂ F
Numerical signatures of non-self-adjointness in quantum Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Ruf, M; Mueller, C [Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg (Germany); Grobe, R, E-mail: matthias.ruf@mpi-hd.mpg.de, E-mail: carsten.mueller@mpi-hd.mpg.de, E-mail: grobe@phy.ilstu.edu [Intense Laser Physics Theory Unit and Department of Physics, Illinois State University, Normal, IL 61790-4560 (United States)
2011-08-26
Non-self-adjoint quantum mechanical operators do not necessarily possess eigenvalues. Finite N x N matrix representations of these operators, however, can be hermitian and therefore have a finite set of N real eigenvalues. Using the momentum operator, the kinetic energy operator, and the relativistic Hamiltonian of the Coulomb problem for the Klein-Gordon equation as examples, we examine analytically and also numerically the properties of the spectrum and eigenvectors in finite dimensional Hilbert spaces. We study the limit of N {yields} {infinity} for which some eigenvalues cease to exist as the corresponding operators are not self-adjoint. (paper)
Alimov, A. R.
2017-07-01
In a broad class of finite-dimensional Banach spaces, we show that a closed set with lower semicontinuous metric projection is a strict sun, admits a continuous selection of the metric projection operator onto it, has contractible intersections with balls, and its (nonempty) intersection with any closed ball is a retract of this ball. For sets with continuous metric projection, a number of new results relating the solarity of such sets to the stability of the operator of best approximation are obtained. Bibliography 25 titles.
Maximal L2 regularity for Ornstein-Uhlenbeck equation in convex sets of Banach spaces
Cappa, G.
2016-06-01
We study the elliptic equation λu -LΩ u = f in an open convex subset Ω of an infinite dimensional separable Banach space X endowed with a centered non-degenerate Gaussian measure γ, where LΩ is the Ornstein-Uhlenbeck operator. We prove that for λ > 0 and f ∈L2 (Ω , γ) the weak solution u belongs to the Sobolev space W 2 , 2 (Ω , γ). Moreover we prove that u satisfies the Neumann boundary condition in the sense of traces at the boundary of Ω. This is done by finite dimensional approximation.
Homotopies and the Universal Fixed Point Property
DEFF Research Database (Denmark)
Szymik, Markus
2015-01-01
. To even specify the problem, we introduce the universal fixed point property. Our results apply in particular to the analysis of convex subspaces of Banach spaces, to the topology of finite-dimensional manifolds and CW complexes, and to the combinatorics of Kolmogorov spaces associated with finite posets.......A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points that is continuous whenever the self-map varies continuously...
Regularization by discretization in Banach spaces
Hämarik, Uno; Kaltenbacher, Barbara; Kangro, Urve; Resmerita, Elena
2016-03-01
We consider ill-posed linear operator equations with operators acting between Banach spaces. For solution approximation, the methods of choice here are projection methods onto finite dimensional subspaces, thus extending existing results from Hilbert space settings. More precisely, general projection methods, the least squares method and the least error method are analyzed. In order to appropriately choose the dimension of the subspace, we consider a priori and a posteriori choices by the discrepancy principle and by the monotone error rule. Analytical considerations and numerical tests are provided for a collocation method applied to a Volterra integral equation in one-dimension space.
Automorphism modular invariants of current algebras
International Nuclear Information System (INIS)
Gannon, T.; Walton, M.A.
1996-01-01
We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some untwisted affine Lie algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac-Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension. (orig.). With 3 tabs
Fermionic quantum mechanics and superfields
International Nuclear Information System (INIS)
Marnelius, R.
1990-01-01
The explicit forms of consistent eigenstate representations for finite dimensional fermionic quantum theories are considered in detail. In particular are the possible Grassmann characters of the eigenstates determined. A straightforward Schrodinger representation is shown to exist if they are even or odd. For an odd number of real eigenvalues, the eigenstates cannot be even or odd. Still a consistent Schrodinger picture is shown to exist provided the basic canonical operators are antilinearly represented. Since the wave functions within the Schrodinger picture are super-fields, the class of superfields which also are first quantized wave functions is determined
Bäcklund transformations and Hamiltonian flows
International Nuclear Information System (INIS)
Zullo, Federico
2013-01-01
In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)
Chaotic Maps Dynamics, Fractals, and Rapid Fluctuations
Chen, Goong
2011-01-01
This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a
Jet schemes of the closure of nilpotent orbits
Moreau, Anne; Yu, Rupert W. T.
2014-01-01
39 pages in English. Final version, to appear in Pacific J. of Math.; We study in this paper the jet schemes of the closure of nilpotent orbits in a finite-dimensional complex reductive Lie algebra. For the nilpotent cone, which is the closure of the regular nilpotent orbit, all the jet schemes are irreducible. This was first observed by Eisenbud and Frenkel, and follows from a strong result of Musta ˘ t (2001). Using induction and restriction of "little" nilpotent orbits in reductive Lie alg...
International Nuclear Information System (INIS)
Ferrari, Frank; Klevtsov, Semyon; Zelditch, Steve
2013-01-01
The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a Kähler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of Kähler metrics. We use the theory of large deviations to decide when a sequence of probability measures on the spaces of Bergman metrics tends to a limit measure on the space of all Kähler metrics. Several examples are considered.
Fractional Number Operator and Associated Fractional Diffusion Equations
Rguigui, Hafedh
2018-03-01
In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.
Lectures given at the C.I.M.E. Summer School
2003-01-01
This volume aims to disseminate a number of new ideas that have emerged in the last few years in the field of numerical simulation, all bearing the common denominator of the "multiscale" or "multilevel" paradigm. This covers the presence of multiple relevant "scales" in a physical phenomenon; the detection and representation of "structures", localized in space or in frequency, in the solution of a mathematical model; the decomposition of a function into "details" that can be organized and accessed in decreasing order of importance; and the iterative solution of systems of linear algebraic equations using "multilevel" decompositions of finite dimensional spaces.
Analysis of nonlinear parabolic equations modeling plasma diffusion across a magnetic field
International Nuclear Information System (INIS)
Hyman, J.M.; Rosenau, P.
1984-01-01
We analyse the evolutionary behavior of the solution of a pair of coupled quasilinear parabolic equations modeling the diffusion of heat and mass of a magnetically confined plasma. The solutions's behavior, due to the nonlinear diffusion coefficients, exhibits many new phenomena. In short time, the solution converges into a highly organized symmetric pattern that is almost completely independent of initial data. The asymptotic dynamics then become very simple and take place in a finite dimensional space. These conclusions are backed by extensive numerical experimentation
The universal Racah-Wigner symbol for Uq(osp(1|2))
International Nuclear Information System (INIS)
Pawelkiewicz, Michal; Schomerus, Volker; Suchanek, Paulina; Wroclaw Univ.
2013-10-01
We propose a new and elegant formula for the Racah-Wigner symbol of self-dual continuous series of representations of U q (osp(1 vertical stroke 2)). It describes the entire fusing matrix for both NS and R sector of N=1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in an earlier paper (L. Hadaz, M. Pawelkiewicz, and V. Schomerus, arXiv:1305.4596[hep-th]). Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the Racah-Wigner coefficients of finite dimensional representations.
Weyl modules, demazure modules, KR-modules, crystals, fusion products and limit constructions
Fourier, G.; Littelmann, P.
2007-01-01
We study finite dimensional representations of current algebras, loop algebras and their quantized versions. For the current algebra of a simple Lie algebra of type {\\tt ADE}, we show that Kirillov-Reshetikhin modules and Weyl modules are in fact all Demazure modules. As a consequence one obtains an elementary proof of the dimension formula for Weyl modules for the current and the loop algebra. Further, we show that the crystals of the Weyl and the Demazure module are the same up to some addi...
Representations of centrally extended Lie superalgebra psl(2|2)
Energy Technology Data Exchange (ETDEWEB)
Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3854 CE Utrecht (Netherlands); Molev, Alexander, E-mail: alexander.molev@sydney.edu.au [School of Mathematics and Statistics, University of Sydney, NSW 2006 (Australia)
2014-09-15
The symmetries provided by representations of the centrally extended Lie superalgebra psl(2|2) are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory correspondence and one-dimensional Hubbard model. We give a complete description of finite-dimensional irreducible representations of this superalgebra thus extending the work of Beisert which deals with a generic family of representations. Our description includes a new class of modules with degenerate eigenvalues of the central elements. Moreover, we construct explicit bases in all irreducible representations by applying the techniques of Mickelsson–Zhelobenko algebras.
Construction of a Blow-Up Solution for the Complex Ginzburg-Landau Equation in a Critical Case
Nouaili, Nejla; Zaag, Hatem
2017-12-01
We construct a solution for the Complex Ginzburg-Landau equation in a critical case which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile. The proof relies on the reduction of the problem to a finite dimensional one, and the use of index theory to conclude. The interpretation of the parameters of the finite dimension problem in terms of the blow-up point and time allows us to prove the stability of the constructed solution.
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.
Mean-square filter design for stochastic polynomial systems with Gaussian and Poisson noises
Basin, Michael; Rodriguez-Ramirez, Pablo
2014-07-01
This paper addresses the mean-square finite-dimensional filtering problem for polynomial system states with both, Gaussian and Poisson, white noises over linear observations. A constructive procedure is established to design the mean-square filtering equations for system states described by polynomial equations of an arbitrary finite degree. An explicit closed form of the designed filter is obtained in case of a third-order polynomial system. The theoretical result is complemented with an illustrative example verifying performance of the designed filter.
Long time behavior of a PDE model for invasive species control
Parshad, R.D.
2011-01-01
The Trojan Y Chromosome strategy (TYC) is a theoretical method for eradication of invasive species. It requires constant introduction of artificial individuals into a target population, causing a shift in the sex ratio, that ultimately leads to local extinction. In this work we consider a modified version of the TYC system. We first demonstrate the existence of a unique weak solution to the system. Furthermore, we prove the existence of a compact finite dimensional global attractor for the modified system, in L 2(Ω) × L 2(Ω)× L 2(Ω).
Identity for propagator in four-fermion theory
International Nuclear Information System (INIS)
Karnaukhov, S.
1993-08-01
The method of exact evaluation of quantum partition function (QPF) in some four fermion models is proposed. The calculations are carried out by the path integral method. The integral is evaluated by introducing the additional fields (called Hubbard-Stratanovich transformation in some models), integration over fermionic variables, and considering the finite-dimensional approximation of the rest integral over bosonic fields in the infinite limit. The non-standard representation of propagator is proposed for the Fermi-theory of four-fermion interaction. This representation seems to be more convenient for the nonperturbative analysis. (author). 7 refs
Holographic space-time from the Big Bang to the de Sitter era
Banks, Tom
2009-07-01
I review the holographic theory of space-time and its applications to cosmology. Much of this has appeared before, but this discussion is more unified and concise. I also include some material on work in progress, whose aim is to understand compactification in terms of finite-dimensional super-algebras. This is an expanded version of a lecture I gave at the conference on Liouville Quantum Gravity and Statistical Systems, in memory of Alexei Zamolodchikov, at the Poncelet Institute in Moscow, 21-24 June 2008.
Holographic space-time from the Big Bang to the de Sitter era
Energy Technology Data Exchange (ETDEWEB)
Banks, Tom [Deptartment of Physics/SCIPP, University of California, Santa Cruz, CA 95064 (United States); Deptartment of Physics and Astronomy/NHETC, Rutgers University, Piscataway, NJ 08854 (United States)
2009-07-31
I review the holographic theory of space-time and its applications to cosmology. Much of this has appeared before, but this discussion is more unified and concise. I also include some material on work in progress, whose aim is to understand compactification in terms of finite-dimensional super-algebras. This is an expanded version of a lecture I gave at the conference on Liouville Quantum Gravity and Statistical Systems, in memory of Alexei Zamolodchikov, at the Poncelet Institute in Moscow, 21-24 June 2008.
Lie theory and control systems defined on spheres
Brockett, R. W.
1972-01-01
It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.
Reduction method for representations of queer Lie superalgebras
Chen, Chih-Whi
2016-05-01
We develop a reduction procedure which provides an equivalence from an arbitrary block of the BGG category for the queer Lie superalgebra 𝔮(n) to a "ℤ ± s-weights" (s ∈ ℂ) block of a BGG category for finite direct sum of queer Lie superalgebras. We give descriptions of blocks. We also establish equivalences between certain maximal parabolic subcategories for 𝔮(n) and blocks of atypicality-one of the category of finite-dimensional modules for 𝔤𝔩(ℓ|n - ℓ).
Statistical analysis of elastic beam with unilateral frictionless supports
International Nuclear Information System (INIS)
Feijoo, R.A.; Barbosa, H.J.C.
1983-06-01
A variational formulation of the elastic beam problem with unilateral frictionless supports is presented. It is shown that the solution of this problem can be characterized as the solution of a variational inequality or as the solution of the constrained minimum of the total potential energy of the structure. THe finite dimensional counterpart of this variational formulation is obtained using the finite element method, and the Gauss-Seidel method with projection and overrelaxation can be used to obtain an approximate solution. In order to show the numerical performance of the present approach some numerical examples are also presented. (Author) [pt
On the Pontryagin maximum principle for systems with delays. Economic applications
Kim, A. V.; Kormyshev, V. M.; Kwon, O. B.; Mukhametshin, E. R.
2017-11-01
The Pontryagin maximum principle [6] is the key stone of finite-dimensional optimal control theory [1, 2, 5]. So beginning with opening the maximum principle it was important to extend the maximum principle on various classes of dynamical systems. In t he paper we consider some aspects of application of i-smooth analysis [3, 4] in the theory of the Pontryagin maximum principle [6] for systems with delays, obtained results can be applied by elaborating optimal program controls in economic models with delays.
Soliton cellular automata associated with crystal bases
International Nuclear Information System (INIS)
Hatayama, Goro; Kuniba, Atsuo; Takagi, Taichiro
2000-01-01
We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U' q (g-circumflex n ). They have solitons labeled by crystals of the smaller algebra U' q (g-circumflex n-1 ). We prove stable propagation of one soliton for g-circumflex n =A (2) 2n-1 ,A (2) 2n ,B (1) n ,C (1) n ,D (1) n and D (2) n+1 . For g-circumflex n =C (1) n , we also prove that the scattering matrices of two solitons coincide with the combinatorial R matrices of U' q (C (1) n-1 )-crystals
Scaling theory of pore growth in a reactive solid
International Nuclear Information System (INIS)
Kerstein, A.R.; Bug, A.L.R.
1986-01-01
Pores in a reactive solid are modeled as a randomly selected fraction p of the bonds of a lattice. Solid bonds adjacent to the open porosity are consumed, leading to the opening of previously closed pores. Just above the pore percolation threshold p/sub c/, exact analysis of the Bethe lattice indicates that the solid is consumed in a time t 0 --ln[ln(1/epsilon)], where epsilon = p-p/sub c/. A scaling argument, supported by computational results, gives t 0 --ln(1/epsilon) for finite-dimensional lattices. Aspects of the time-varying morphology of the solid are examined analytically and computationally
Distribution of interference in the presence of decoherence
International Nuclear Information System (INIS)
Arnaud, Ludovic; Braun, Daniel
2009-01-01
We study the statistics of quantum interference for completely positive maps. We calculate analytically the mean interference and its second moment for finite-dimensional quantum systems interacting with a simple environment consisting of one or several spins (qudits). The joint propagation of the entire system is taken as unitary with an evolution operator drawn from the circular unitary ensemble (CUE). We show that the mean interference decays with a power law as function of the dimension of the Hilbert space of the environment, with a power that depends on the temperature of the environment.
Semigroup theory and numerical approximation for equations in linear viscoelasticity
Fabiano, R. H.; Ito, K.
1990-01-01
A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.
Complexity L0-Penalized M-Estimation: Consistency in More Dimensions
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Gerhard Winkler
2013-07-01
Full Text Available We study the asymptotics in L2 for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains—e.g., images—by piecewise smooth functions. We introduce a fairly general setting, which comprises most of the presently popular partitions of signal or image domains, like interval, wedgelet or related partitions, as well as Delaunay triangulations. Then, we prove consistency and derive convergence rates. Finally, we illustrate by way of relevant examples that the abstract results are useful for many applications.
Helix-Hopes on Finite Hyperfields
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Thomas Vougiouklis
2016-12-01
Full Text Available Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We study the helix-hyperstructures on the representations using ordinary fields. The related theory can be faced by defining the hyperproduct on the set of non square matrices. The main tools of the Hyperstructure Theory are the fundamental relations which connect the largest class of hyperstructures, the Hv-structures, with the corresponding classical ones. We focus on finite dimensional helix-hyperstructures and on small Hv-fields, as well.
Differentiation Theory over Infinite-Dimensional Banach Spaces
Directory of Open Access Journals (Sweden)
Claudio Asci
2016-01-01
Full Text Available We study, for any positive integer k and for any subset I of N⁎, the Banach space EI of the bounded real sequences xnn∈I and a measure over RI,B(I that generalizes the k-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables’ formula for the integration of the measurable real functions on RI,B(I. This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms.
A multigrid method for variational inequalities
Energy Technology Data Exchange (ETDEWEB)
Oliveira, S.; Stewart, D.E.; Wu, W.
1996-12-31
Multigrid methods have been used with great success for solving elliptic partial differential equations. Penalty methods have been successful in solving finite-dimensional quadratic programs. In this paper these two techniques are combined to give a fast method for solving obstacle problems. A nonlinear penalized problem is solved using Newton`s method for large values of a penalty parameter. Multigrid methods are used to solve the linear systems in Newton`s method. The overall numerical method developed is based on an exterior penalty function, and numerical results showing the performance of the method have been obtained.
Real-Space Application of the Mean-Field Description of Spin-Glass Dynamics
International Nuclear Information System (INIS)
Barrat, Alain; Berthier, Ludovic
2001-01-01
The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard 'mean-field theory' versus 'droplet picture' debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed
Osborn, J
1989-01-01
During the academic year 1987-1988 the University of Wisconsin in Madison hosted a Special Year of Lie Algebras. A Workshop on Lie Algebras, of which these are the proceedings, inaugurated the special year. The principal focus of the year and of the workshop was the long-standing problem of classifying the simple finite-dimensional Lie algebras over algebraically closed field of prime characteristic. However, other lectures at the workshop dealt with the related areas of algebraic groups, representation theory, and Kac-Moody Lie algebras. Fourteen papers were presented and nine of these (eight research articles and one expository article) make up this volume.
Learning from uncertain curves
DEFF Research Database (Denmark)
Mallasto, Anton; Feragen, Aasa
2017-01-01
We introduce a novel framework for statistical analysis of populations of nondegenerate Gaussian processes (GPs), which are natural representations of uncertain curves. This allows inherent variation or uncertainty in function-valued data to be properly incorporated in the population analysis....... Using the 2-Wasserstein metric we geometrize the space of GPs with L2 mean and covariance functions over compact index spaces. We prove uniqueness of the barycenter of a population of GPs, as well as convergence of the metric and the barycenter of their finite-dimensional counterparts. This justifies...
On the partiality of procreative beneficence: a critical note.
Petersen, Thomas Søbirk
2015-09-01
The aim of this paper is to criticise the well-discussed principle of Procreative Beneficence (PB) lately refined by Julian Savulescu and Guy Kahane. First, it is argued that advocates of PB leave us with an implausible justification for the moral partiality towards the child (or children) which reproducers decide to bring into existence as compared with all other individuals. This is implausible because the reasons given in favour of the partiality of PB, which are based on practical reason and common-sense morality, can just as well be used to guide reproducers to make choices that do not support partiality towards one's possible children. This seems to be true as least in some situations. Second, it is argued that Jakob Elster's recent critique of PB is problematic and specifically that a counterexample designed by Elster to criticise PB because of its partiality towards one's own children misses the target. Finally, a genuine counterexample to PB is developed in order to show that the partiality of PB leads to the wrong answer in a specific case. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.
DEFF Research Database (Denmark)
Broncano-Berrocal, Fernando
2014-01-01
In “Knowledge Under Threat” (Philosophy and Phenomenological Research 2012), Tomas Bogardus proposes a counterexample to the safety condition for knowledge. Bogardus argues that the case demonstrates that unsafe knowledge is possible. I argue that the case just corroborates the well-known require......In “Knowledge Under Threat” (Philosophy and Phenomenological Research 2012), Tomas Bogardus proposes a counterexample to the safety condition for knowledge. Bogardus argues that the case demonstrates that unsafe knowledge is possible. I argue that the case just corroborates the well......-known requirement that modal conditions like safety must be relativized to methods of belief formation. I explore several ways of relativizing safety to belief-forming methods and I argue that none is adequate: if methods were individuated in those ways, safety would fail to explain several much-discussed cases. I...... then propose a plausible externalist principle of method individuation. On the one hand, relativizing safety to belief-forming methods in the way suggested allows the defender of safety to account for the cases. On the other hand, it shows that the target known belief of Bogardus’s example is safe. Finally, I...
Rhodes, Carl; Morari, Manfred; Wiggins, Stephen
2006-12-01
Flockerzi and Heineken [Chaos 16, 048101 (2006)] present two examples with the goal of elucidating issues related to the Maas and Pope method for identifying low dimensional "slow" manifolds in systems with a time-scale separation. The goal of their first example is to show that the result claimed by Rhodes et al. [Chaos 9, 108-123 (1999)] that the Maas and Pope algorithm identifies the slow invariant manifold in the situation in which there is finite time-scale separation is incorrect. We show that their arguments result from an incomplete understanding of the situation and that, in fact, their example supports, and is completely consistent with, the result in Rhodes et al.. Their second example claims to be a counterexample to a conjecture in Rhodes et al. that away from the slow manifold the criterion of Maas and Pope [Combust. Flame 88, 239-264 (1992)] will never be fulfilled. While this conjecture may indeed be false, we argue that it is not clear that the example presented by Flockerzi and Heineken is indeed a counterexample.
Drell-Yan process with jet vetoes: breaking of generalized factorization
International Nuclear Information System (INIS)
Zeng, Mao
2015-01-01
Resummation of hadron collision cross sections, when the measurement imposes a hierarchy of scales, relies on factorization. Cancellation of Glauber/Coulomb gluons is a necessary condition for factorization. For Drell-Yan-like processes, the known proofs of cancellation of Glauber gluons are not applicable when jet vetoes are introduced, via jet algorithms or event shape variables such as the beam thrust. A priori, this does not rule out the possibility that an unknown new cancellation mechanism exists, or the possibility that a generalized factorization formalism is correct. To resolve the questions, we construct a direct counter-example in QCD with scalar quarks, contradicting any form of factorization in which the two collinear sectors are decoupled from each other. In the counter-example, decoupling of the two collinear sectors implies zero dependence of the beam thrust distribution on the longitudinal spin of the incoming hadrons, but we find a non-zero spin asymmetry at leading power due to Glauber gluons exchanged between spectators. We discuss implications for resumming large logarithms from jet vetoes.
International Nuclear Information System (INIS)
Sylvester, G.S.
1980-01-01
In the Ising-type models of statistical mechanics and the related quantum field theories, an inequality of Ginibre implies useful positivity and monotonicity properties: the Griffiths correlation inequalities. Essentially, the Ginibre inequality states that certain functions on the cycle group of a graph are positive definite. This has been proved for arbitrary graphs when the spin dimensions is 1 or 2 (classical Ising or plane rotator models). We give a counterexample to show that these spin dimensions are the only ones for which the Ginibre inequality is generally true: there are graphs for which it never holds when the spin dimension is at least 3. On the other hand, we show that for any graph the inequality holds for the apparent leading term in the large-spin-dimension limit. (The leading term vanishes in the graph of the counterexample.) Based on these results, one expects the Ginibre inequality to be true in most instances, with infrequent exceptions. A numerical survey supports this. The surprising failure of the Ginibre inequality in higher dimensions need not necessarily mean the Griffiths inequalities fail as well, but a different approach to them is required. (orig.)
Directory of Open Access Journals (Sweden)
Yanjun Wang
2013-01-01
Full Text Available This paper considers a multiuser transmit beamforming problem under uncertain channel state information (CSI subject to SINR constraints in a downlink multiuser MISO system. A robust transmit beamforming formulation is proposed. This robust formulation is to minimize the transmission power subject to worst-case signal-to-interference-plus-noise ratio (SINR constraints on the receivers. The challenging problem is that the worst-case SINR constraints correspond to an infinite number of nonconvex quadratic constraints. In this paper, a natural semidifinite programming (SDP relaxation problem is proposed to solve the robust beamforming problem. The main contribution of this paper is to establish the tightness of the SDP relaxation problem under proper assumption, which means that the SDP relaxation problem definitely yields rank-one solutions under the assumption. Then the SDP relaxation problem provides globally optimum solutions of the primal robust transmit beamforming problem under proper assumption and norm-constrained CSI errors. Simulation results show the correctness of the proposed theoretical results and also provide a counterexample whose solutions are not rank one. The existence of counterexample shows that the guess that the solutions of the SDP relaxation problem must be rank one is wrong, except that some assumptions (such as the one proposed in this paper hold.
Nguyen, Nhan
2013-01-01
This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.
An Optimality-Theoretic Analysis of Scandinavian Object Shift and Remnant VP-Topicalisation
DEFF Research Database (Denmark)
Engels, Eva; Vikner, Sten
2006-01-01
Holmberg (1997, 1999) assumes that Holmberg's generalisation (HG) is derivational, prohibiting Object Shift (OS) across an intervening non-adverbial element at any point in the derivation. Counterexamples to this hypothesis are given in Fox & Pesetsky (2005) which show that remnant VP-topicalisat......Holmberg (1997, 1999) assumes that Holmberg's generalisation (HG) is derivational, prohibiting Object Shift (OS) across an intervening non-adverbial element at any point in the derivation. Counterexamples to this hypothesis are given in Fox & Pesetsky (2005) which show that remnant VP......-topicalisations are possible in Scandinavian as long as the VP-internal order relations are maintained. Extending the empirical basis concerning remnant VP-topicalisations, we argue that HG and the restrictions on object stranding result from the same, more general condition on order preservation. Considering this condition...... to be violable and to interact with various constraints on movement in an Optimality-theoretic fashion, we suggest an account for various asymmetries in the interaction between remnant VP-topicalisations and both OS and other movement operations (especially subject raising) as to their order preserving...
Simultaneous representations of semilattices by lattices with permutable congruences
Tuma, J; Tuma, Jiri; Wehrung, Friedrich
2001-01-01
The Congruence Lattice Problem (CLP), stated by R. P. Dilworth in the forties, asks whether every distributive {∨, 0}-semilatticeS is isomorphic to the semilattice Conc L of compact congruences of a lattice L. While this problem is still open, many partial solutions have been obtained, positive and negative as well. The solution to CLP is known to be positive for all S such that $|S|\\leq\\aleph\\_1$. Furthermore, one can then take L with permutable congruences. This contrasts with the case where $|S| \\geq\\aleph\\_2$, where there are counterexamples S for which L cannot be, for example, sectionally complemented. We prove in this paper that the lattices of these counterexamples cannot have permutable congruences as well. We also isolate ﬁnite, combinatorial analogues of these results. All the "ﬁnite" statements that we obtain are amalgamation properties of the Conc functor. The strongest known positive results, which originate in earlier work by the ﬁrst author, imply tha...
Commuting nonselfadjoint operators in Hilbert space two independent studies
Livšic, Moshe S
1987-01-01
Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S...
Generalized spin Sutherland systems revisited
Directory of Open Access Journals (Sweden)
L. Fehér
2015-04-01
Full Text Available We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n Yang–Mills theory on the cylinder and by constraining geodesic motion on the N-fold direct product of SU(n with itself, for any N>1. Our systems are in correspondence with the Dynkin diagram automorphisms of arbitrary connected and simply connected compact simple Lie groups. We give a finite-dimensional as well as an infinite-dimensional derivation and shed light on the mechanism whereby they lead to the same classical integrable systems. The infinite-dimensional approach, based on twisted current algebras (alias Yang–Mills with twisted boundary conditions, was inspired by the derivation of the spinless Sutherland model due to Gorsky and Nekrasov. The finite-dimensional method relies on Hamiltonian reduction under twisted conjugations of N-fold direct product groups, linking the quantum mechanics of the reduced systems to representation theory similarly as was explored previously in the N=1 case.
On the statistical mechanics of the 2D stochastic Euler equation
Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg
2011-12-01
The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.
2-regularity and 2-normality conditions for systems with impulsive controls
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Pavlova Natal'ya
2007-01-01
Full Text Available In this paper a controlled system with impulsive controls in the neighborhood of an abnormal point is investigated. The set of pairs (u,μ is considered as a class of admissible controls, where u is a measurable essentially bounded function and μ is a finite-dimensional Borel measure, such that for any Borel set B, μ(B is a subset of the given convex closed pointed cone. In this article the concepts of 2-regularity and 2-normality for the abstract mapping Ф, operating from the given Banach space into a finite-dimensional space, are introduced. The concepts of 2-regularity and 2-normality play a great role in the course of derivation of the first and the second order necessary conditions for the optimal control problem, consisting of the minimization of a certain functional on the set of the admissible processes. These concepts are also important for obtaining the sufficient conditions for the local controllability of the nonlinear systems. The convenient criterion for 2-regularity along the prescribed direction and necessary conditions for 2-normality of systems, linear in control, are introduced in this article as well.
International Nuclear Information System (INIS)
Potters, Max; Vaillant, Timothee; Bouchet, Freddy
2013-01-01
The 2D Euler equations are basic examples of fluid models for which a microcanonical measure can be constructed from first principles. This measure is defined through finite-dimensional approximations and a limiting procedure. Creutz’s algorithm is a microcanonical generalization of the Metropolis–Hastings algorithm (to sample Gibbs measures, in the canonical ensemble). We prove that Creutz’s algorithm can sample finite-dimensional approximations of the 2D Euler microcanonical measures (incorporating fixed energy and other invariants). This is essential as microcanonical and canonical measures are known to be inequivalent at some values of energy and vorticity distribution. Creutz’s algorithm is used to check predictions from the mean-field statistical mechanics theory of the 2D Euler equations (the Robert–Sommeria–Miller theory). We find full agreement with theory. Three different ways to compute the temperature give consistent results. Using Creutz’s algorithm, a first-order phase transition never observed previously and a situation of statistical ensemble inequivalence are found and studied. Strikingly, and in contrast to the usual statistical mechanics interpretations, this phase transition appears from a disordered phase to an ordered phase (with fewer symmetries) when the energy is increased. We explain this paradox. (paper)
Barth, Timothy J.
2014-01-01
This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.
The MUSIC algorithm for impedance tomography of small inclusions from discrete data
International Nuclear Information System (INIS)
Lechleiter, A
2015-01-01
We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images. (paper)
Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano
Falaize, Antoine; Hélie, Thomas
2017-03-01
This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis. Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed. This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.
Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems
Energy Technology Data Exchange (ETDEWEB)
Lee, Kookjin [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science; Carlberg, Kevin [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Elman, Howard C. [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Inst. for Advanced Computer Studies
2018-03-29
Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.
Emergent behaviors of the Schrödinger-Lohe model on cooperative-competitive networks
Huh, Hyungjin; Ha, Seung-Yeal; Kim, Dohyun
2017-12-01
We present several sufficient frameworks leading to the emergent behaviors of the coupled Schrödinger-Lohe (S-L) model under the same one-body external potential on cooperative-competitive networks. The S-L model was first introduced as a possible phenomenological model exhibiting quantum synchronization and its emergent dynamics on all-to-all cooperative networks has been treated via two distinct approaches, Lyapunov functional approach and the finite-dimensional reduction based on pairwise correlations. In this paper, we further generalize the finite-dimensional dynamical systems approach for pairwise correlation functions on cooperative-competitive networks and provide several sufficient frameworks leading to the collective exponential synchronization. For small systems consisting of three and four quantum subsystem, we also show that the system for pairwise correlations can be reduced to the Lotka-Volterra model with cooperative and competitive interactions, in which lots of interesting dynamical patterns appear, e.g., existence of closed orbits and limit-cycles.
Deformation Based Curved Shape Representation.
Demisse, Girum G; Aouada, Djamila; Ottersten, Bjorn
2017-06-02
In this paper, we introduce a deformation based representation space for curved shapes in Rn. Given an ordered set of points sampled from a curved shape, the proposed method represents the set as an element of a finite dimensional matrix Lie group. Variation due to scale and location are filtered in a preprocessing stage, while shapes that vary only in rotation are identified by an equivalence relationship. The use of a finite dimensional matrix Lie group leads to a similarity metric with an explicit geodesic solution. Subsequently, we discuss some of the properties of the metric and its relationship with a deformation by least action. Furthermore, invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function. Thereafter, two possible approaches are presented to solve the point correspondence estimation problem. Finally, we propose an adaptation of k-means clustering for shape analysis in the proposed representation space. Experimental results show that the proposed representation is robust to uninformative cues, e.g. local shape perturbation and displacement. In comparison to state of the art methods, it achieves a high precision on the Swedish and the Flavia leaf datasets and a comparable result on MPEG-7, Kimia99 and Kimia216 datasets.
Multiresolution Hilbert Approach to Multidimensional Gauss-Markov Processes
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Thibaud Taillefumier
2011-01-01
Full Text Available The study of the multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practically important Gauss-Markov processes, are ordinarily defined through the theory of stochastic integration. Here, inspired by the Lévy-Ciesielski construction of the Wiener process, we propose an alternative representation of multidimensional Gauss-Markov processes as expansions on well-chosen Schauder bases, with independent random coefficients of normal law with zero mean and unit variance. We thereby offer a natural multiresolution description of the Gauss-Markov processes as limits of finite-dimensional partial sums of the expansion, that are strongly almost-surely convergent. Moreover, such finite-dimensional random processes constitute an optimal approximation of the process, in the sense of minimizing the associated Dirichlet energy under interpolating constraints. This approach allows for a simpler treatment of problems in many applied and theoretical fields, and we provide a short overview of applications we are currently developing.
Two classes of spaces reflexive in the sense of Pontryagin
International Nuclear Information System (INIS)
Akbarov, S S; Shavgulidze, E T
2003-01-01
The Pontryagin-van Kampen duality for locally compact Abelian groups can be generalized in two ways to wider classes of topological Abelian groups: in the first approach the dual group X . is endowed with the topology of uniform convergence on compact subsets of X and in the second, with the topology of uniform convergence on totally bounded subsets of X. The corresponding two classes of groups 'reflexive in the sense of Pontryagin-van Kampen' are very wide and are so close to each other that it was unclear until recently whether they coincide or not. A series of counterexamples constructed in this paper shows that these classes do not coincide and also answer several other questions arising in this theory. The results of the paper can be interpreted as evidence that the second approach to the generalization of the Pontryagin duality is more natural
On the Optimality of Trust Network Analysis with Subjective Logic
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PARK, Y.
2014-08-01
Full Text Available Building and measuring trust is one of crucial aspects in e-commerce, social networking and computer security. Trust networks are widely used to formalize trust relationships and to conduct formal reasoning of trust values. Diverse trust network analysis methods have been developed so far and one of the most widely used schemes is TNA-SL (Trust Network Analysis with Subjective Logic. Recent papers claimed that TNA-SL always finds the optimal solution by producing the least uncertainty. In this paper, we present some counter-examples, which imply that TNA-SL is not an optimal algorithm. Furthermore, we present a probabilistic algorithm in edge splitting to minimize uncertainty.
Universality of the Hawking effect
International Nuclear Information System (INIS)
Unruh, William G.; Schuetzhold, Ralf
2005-01-01
Addressing the question of whether the Hawking effect depends on degrees of freedom at ultrahigh (e.g., Planckian) energies/momenta, we propose three rather general conditions on these degrees of freedom under which the Hawking effect is reproduced to lowest order. As a generalization of Corley's results, we present a rather general model based on nonlinear dispersion relations satisfying these conditions together with a derivation of the Hawking effect for that model. However, we also demonstrate counter-examples, which do not appear to be unphysical or artificial, displaying strong deviations from Hawking's result. Therefore, whether real black holes emit Hawking radiation remains an open question and could give nontrivial information about Planckian physics
Almost-commutative geometries beyond the standard model
International Nuclear Information System (INIS)
Stephan, Christoph A
2006-01-01
In Iochum et al (2004 J. Math. Phys. 45 5003), Jureit and Stephan (2005 J. Math. Phys. 46 043512), Schuecker T (2005 Preprint hep-th/0501181) and Jureit et al (2005 J. Math. Phys. 46 072303), a conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this paper, a counter-example will be given. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle, these new particles provide a novel dark matter candidate
Strange functions in real analysis
Kharazishvili, AB
2005-01-01
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nonintegrable Lebesgue measurable functions. While dubbed strange or "pathological," these functions are ubiquitous throughout mathematics and play an important role in analysis, not only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis.Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers e...
Conformal Killing vectors in Robertson-Walker spacetimes
International Nuclear Information System (INIS)
Maartens, R.; Maharaj, S.d.
1986-01-01
It is well known that Robertson-Walker spacetimes admit a conformal Killingl vector normal to the spacelike homogeneous hypersurfaces. Because these spacetimes are conformally flat, there are a further eight conformal Killing vectors, which are neither normal nor tangent to the homogeneous hypersurfaces. The authors find these further conformal Killing vectors and the Lie algebra of the full G 15 of conformal motions. Conditions on the metric scale factor are determined which reduce some of the conformal Killing vectors to homothetic Killing vectors or Killing vectors, allowing one to regain in a unified way the known special geometries. The non-normal conformal Killing vectors provide a counter-example to show that conformal motions do not, in general, map a fluid flow conformally. These non-normal vectors are also used to find the general solution of the null geodesic equation and photon Liouville equation. (author)
Weak cosmic censorship: as strong as ever.
Hod, Shahar
2008-03-28
Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the most important open questions in general relativity. In this Letter, we reanalyze extreme situations which have been considered as counterexamples to the weak cosmic censorship conjecture. In particular, we consider the absorption of scalar particles with large angular momentum by a black hole. Ignoring back reaction effects may lead one to conclude that the incident wave may overspin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when back reaction effects are properly taken into account, the stability of the black-hole event horizon is irrefutable. We therefore conclude that cosmic censorship is actually respected in this type of gedanken experiments.
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Béla FINTA
2017-12-01
Full Text Available The purpose of this paper is to give a negative answer to a possible generalization of an open question raised by Pál Erd˝os, concerning an inequality in acute triangles. We prove here that from a < b < c does not follow a 2k + l 2k a < b2k + l 2k b < c2k + l 2k c in every acute triangle ABC, nor the opposite chain of inequalities, where k ∈ N, k ≥ 2, and a, b, c denotes the length of the triangles sites , while la, lb, lc denotes the length of the interior angle bisectors, as usual. We achieve this by constructing effectively two counterexamples, one for each type of inequalities
Refining the classification of irreps of the 1D N-extended supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Kuznetsova, Zhanna [Universidade Federal de Juiz de Fora, MG (Brazil). Inst. de Ciencias Exatas; Toppan, Francesco. E-mail: zhanna@cbpf.br; toppan@cbpf.br
2007-01-15
In hep-th/0511274 the classification of the fields content of the linear finite irreducible representations of the algebra of the 1D N-Extended Supersymmetric Quantum Mechanics was given. In hep-th/0611060 it was pointed out that certain irreps with the same fields content can be regarded as inequivalent. This result can be understood in terms of the 'connectivity' properties of the graphs associated to the irreps. We present here a classification of the connectivity of the irreps, refining the hep-th/0511274 classification based on fields content. As a byproduct, we find a counterexample to the hep-th/0611060 claim that the connectivity is uniquely specified by the sources and targets of an irrep graph. We produce one pair of N=5 irreps and three pairs of N=6 irreps with the same number of sources and targets which, nevertheless, differ in connectivity. (author)
Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations
Anosov, Dmitry V.; Leksin, Vladimir P.
2011-02-01
This paper contains an account of A.A. Bolibrukh's results obtained in the new directions of research that arose in the analytic theory of differential equations as a consequence of his sensational counterexample to the Riemann-Hilbert problem. A survey of results of his students in developing topics first considered by Bolibrukh is also presented. The main focus is on the role of the reducibility/irreducibility of systems of linear differential equations and their monodromy representations. A brief synopsis of results on the multidimensional Riemann-Hilbert problem and on isomonodromic deformations of Fuchsian systems is presented, and the main methods in the modern analytic theory of differential equations are sketched. Bibliography: 69 titles.
‘Shining Indians’: Diaspora and Exemplarity in Bollywood
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Ingrid Therwath
2010-12-01
Full Text Available Commercial Hindi cinema plays a central role in the negotiation of national identity. For decades, the expatriate Indian served as a counter-example for acceptable behaviour, a living testimony of inappropriateness. In the mid-1990s, following the liberalization of the Indian economy, the rise of Hindu nationalism and the advent of a multiplex-going urban middle-class, the stereotype was turned around. The Non Resident Indian (NRI became the epitome of Indianness and embodied at once capitalist and consumerist modernity and patriarchal, Northern and Hindu traditionalism. This change was meant to cater to a lucrative niche market and reflected an uneasy transition period. In addition, the on screen NRI role models were seen as an instrument of Western modernity in India and of India's recognition as an international power in the West.
Indukcja, dedukcja i szlaki mamutów
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Mieszko Tałasiewicz
2007-06-01
Full Text Available The paper examines various instances of 'inductionism-deductionism' controversion (e.g. Popper vs Vienna Circle or the formulation of Laudan's argument against realism as pessimistic meta-induction vs. kind of deduction. The thesis is that the form of logical reconstruction of our reasoning (in every-day life as well as in science or meta-science as induction or deduction is irrelevant as to the rational evaluation of this reasoning. Thus the inductionism-deductionism controversion is claimed vacuous. Instead of formal logic a sort of evolutionary epistemology is called for adequate account, since - as it is argued for - the degree of sensitivity to counterexamples contradicting our theories and hypotheses is a kind of adaptation to environment.
Partially natural Two Higgs Doublet Models
Energy Technology Data Exchange (ETDEWEB)
Draper, Patrick [Department of Physics, University of California,Broida Hall, Santa Barbara, CA 93106 (United States); Haber, Howard E. [Santa Cruz Institute for Particle Physics, University of California,1156 High Street, Santa Cruz, CA 95064 (United States); Kavli Institute for Theoretical Physics, University of California,Kohn Hall, Santa Barbara, CA 93106 (United States); Ruderman, Joshua T. [Center for Cosmology and Particle Physics, Department of Physics, New York University,4 Washington Pl. New York, NY 10003 (United States)
2016-06-21
It is possible that the electroweak scale is low due to the fine-tuning of microscopic parameters, which can result from selection effects. The experimental discovery of new light fundamental scalars other than the Standard Model Higgs boson would seem to disfavor this possibility, since generically such states imply parametrically worse fine-tuning with no compelling connection to selection effects. We discuss counterexamples where the Higgs boson is light because of fine-tuning, and a second scalar doublet is light because a discrete symmetry relates its mass to the mass of the Standard Model Higgs boson. Our examples require new vectorlike fermions at the electroweak scale, and the models possess a rich electroweak vacuum structure. The mechanism that we discuss does not protect a small CP-odd Higgs mass in split or high-scale supersymmetry-breaking scenarios of the MSSM due to an incompatibility between the discrete symmetries and holomorphy.
Field, Michael
2017-01-01
This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal t...
The prime graph conjecture for integral group rings of some alternatings groups
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Mohamed Salim
2013-03-01
Full Text Available We investigate the classical Zassenhaus Conjecture (ZC for integral group rings of alternating groups A9 and A10. Even the question (ZC remains open as no counterexample is known up to date, it been confirmed for special types of groups such as nilpotent groups by Roggenkamp, Scot and Weiss. However, a new method based on the partial augmentation of torsion units been established by Luthar and Passi to confirm the (ZC for A5. Later a weaker version of (ZC was proposed in 2007, we call it the Prime Graph Conjecture (PGC about the Gruenberg-Kegel (prime graph of the group of all normalized units of the integral group ring of a finite group. Recently, the (PGC has a positive answer for solvable groups, Frobenius groups and several simple groups. Here, as a consequence of our results, we confirm the (PGC for integral group rings of alternating groups An for all n<11.
International Nuclear Information System (INIS)
Banerjee, Nabamita; Mandal, Ipsita; Sen, Ashoke
2009-01-01
Macroscopic entropy of an extremal black hole is expected to be determined completely by its near horizon geometry. Thus two black holes with identical near horizon geometries should have identical macroscopic entropy, and the expected equality between macroscopic and microscopic entropies will then imply that they have identical degeneracies of microstates. An apparent counterexample is provided by the 4D-5D lift relating BMPV black hole to a four dimensional black hole. The two black holes have identical near horizon geometries but different microscopic spectrum. We suggest that this discrepancy can be accounted for by black hole hair - degrees of freedom living outside the horizon and contributing to the degeneracies. We identify these degrees of freedom for both the four and the five dimensional black holes and show that after their contributions are removed from the microscopic degeneracies of the respective systems, the result for the four and five dimensional black holes match exactly.
Qutrit Dichromatic Calculus and Its Universality
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Quanlong Wang
2014-12-01
Full Text Available We introduce a dichromatic calculus (RG for qutrit systems. We show that the decomposition of the qutrit Hadamard gate is non-unique and not derivable from the dichromatic calculus. As an application of the dichromatic calculus, we depict a quantum algorithm with a single qutrit. Since it is not easy to decompose an arbitrary d by d unitary matrix into Z and X phase gates when d > 2, the proof of the universality of qudit ZX calculus for quantum mechanics is far from trivial. We construct a counterexample to Ranchin's universality proof, and give another proof by Lie theory that the qudit ZX calculus contains all single qudit unitary transformations, which implies that qudit ZX calculus, with qutrit dichromatic calculus as a special case, is universal for quantum mechanics.
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Gary R. Nicklason
2015-07-01
Full Text Available We consider center conditions for plane polynomial systems of Abel type consisting of a linear center perturbed by the sum of 2 homogeneous polynomials of degrees n and 2n-1 where $n \\ge 2$. Using properties of Abel equations we obtain two general systems valid for arbitrary values on n. For the cubic n=2 systems we find several sets of new center conditions, some of which show that the results in a paper by Hill, Lloyd and Pearson which were conjectured to be complete are in fact not complete. We also present a particular system which appears to be a counterexample to a conjecture by Zoladek et al. regarding rational reversibility in cubic polynomial systems.
Substantiation of a heuristic algorithm in the knapsack problem
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Н.В. KHalipovа
2012-12-01
Full Text Available Introduction: Formed knapsack problem in terms of set functions and is a heuristic algorithm. The goal: to prove that the heuristic algorithm is essential. Some facts from [2]. The equivalence of the limit order to E.Borelyu and convergence in measure. The theorem about the need to set a maximum of function. The situation is quite the algorithm: We present three cases where a heuristic algorithm is sufficient. Counterexample: An Rear take from [1], and given the addition heuristic algorithm, which allows to obtain the solution of the knapsack problem. Vector optimization: With the knapsack problem is tied vector optimization of investment activities. Conclusions: The proposed algorithm for solving the knapsack problem and for additive functions algorithm for Pareto solutions of vector optimization for the two indicators. Appendix: an agenda for the Maple solutions knapsack problem.
Tyson, Jon
2009-03-01
We compare several instances of pure-state Belavkin weighted square-root measurements from the standpoint of minimum-error discrimination of quantum states. The quadratically weighted measurement is proven superior to the so-called “pretty good measurement” (PGM) in a number of respects: (1) Holevo’s quadratic weighting unconditionally outperforms the PGM in the case of two-state ensembles, with equality only in trivial cases. (2) A converse of a theorem of Holevo is proven, showing that a weighted measurement is asymptotically optimal only if it is quadratically weighted. Counterexamples for three states are constructed. The cube-weighted measurement of Ballester, Wehner, and Winter is also considered. Sufficient optimality conditions for various weights are compared.
No turnover in lens lipids for the entire human lifespan.
Hughes, Jessica R; Levchenko, Vladimir A; Blanksby, Stephen J; Mitchell, Todd W; Williams, Alan; Truscott, Roger J W
2015-03-11
Lipids are critical to cellular function and it is generally accepted that lipid turnover is rapid and dysregulation in turnover results in disease (Dawidowicz 1987; Phillips et al., 2009; Liu et al., 2013). In this study, we present an intriguing counter-example by demonstrating that in the center of the human ocular lens, there is no lipid turnover in fiber cells during the entire human lifespan. This discovery, combined with prior demonstration of pronounced changes in the lens lipid composition over a lifetime (Hughes et al., 2012), suggests that some lipid classes break down in the body over several decades, whereas others are stable. Such substantial changes in lens cell membranes may play a role in the genesis of age-related eye disorders. Whether long-lived lipids are present in other tissues is not yet known, but this may prove to be important in understanding the development of age-related diseases.
Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species
Chen, Xiuqing; Daus, Esther S.; Jüngel, Ansgar
2018-02-01
The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.
Program Analysis as Model Checking
DEFF Research Database (Denmark)
Olesen, Mads Chr.
and abstract interpretation. Model checking views the program as a finite automaton and tries to prove logical properties over the automaton model, or present a counter-example if not possible — with a focus on precision. Abstract interpretation translates the program semantics into abstract semantics...... are considered, among others numerical analysis of c programs, and worst-case execution time analysis of ARM programs. It is shown how lattice automata allow automatic and manual tuning of the precision and efficiency of the verification procedure. In the case of worst-case execution time analysis a sound......Software programs are proliferating throughout modern life, to a point where even the simplest appliances such as lightbulbs contain software, in addition to the software embedded in cars and airplanes. The correct functioning of these programs is therefore of the utmost importance, for the quality...
The Pointer Assertion Logic Engine
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael Ignatieff
2001-01-01
in the logical tradition by encoding the programs and partial specifications as formulas in monadic second-order logic. Validity of these formulas is checked by the MONA tool, which also can provide explicit counterexamples to invalid formulas. To make verification decidable, the technique requires explicit loop...... restricted to simple special cases such as lists or trees. Even so, our current implementation is as fast as the previous specialized tools. Programs are annotated with partial specifications expressed in Pointer Assertion Logic, a new notation for expressing properties of the program store. We work......We present a new framework for verifying partial specifications of programs in order to catch type and memory errors and check data structure invariants. Our technique can verify a large class of data structures, namely all those that can be expressed as graph types. Earlier versions were...
SimCheck: An Expressive Type System for Simulink
Roy, Pritam; Shankar, Natarajan
2010-01-01
MATLAB Simulink is a member of a class of visual languages that are used for modeling and simulating physical and cyber-physical systems. A Simulink model consists of blocks with input and output ports connected using links that carry signals. We extend the type system of Simulink with annotations and dimensions/units associated with ports and links. These types can capture invariants on signals as well as relations between signals. We define a type-checker that checks the wellformedness of Simulink blocks with respect to these type annotations. The type checker generates proof obligations that are solved by SRI's Yices solver for satisfiability modulo theories (SMT). This translation can be used to detect type errors, demonstrate counterexamples, generate test cases, or prove the absence of type errors. Our work is an initial step toward the symbolic analysis of MATLAB Simulink models.
The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs
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Cranston Daniel W.
2014-11-01
Full Text Available The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms the conjectures for graphs with maximum average degree less than 8/3. The conjectures are already confirmed for larger families, but the structure theorems and reducibility results are of independent interest.
Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian
Benedikt, Jiří; Girg, Petr; Kotrla, Lukáš; Takáč, Peter
2016-01-01
The validity of the weak and strong comparison principles for degenerate parabolic partial differential equations with the p-Laplace operator Δp is investigated for p > 2. This problem is reduced to the comparison of the trivial solution (≡0, by hypothesis) with a nontrivial nonnegative solution u (x , t). The problem is closely related also to the question of uniqueness of a nonnegative solution via the weak comparison principle. In this article, realistic counterexamples to the uniqueness of a nonnegative solution, the weak comparison principle, and the strong maximum principle are constructed with a nonsmooth reaction function that satisfies neither a Lipschitz nor an Osgood standard ;uniqueness; condition. Nonnegative multi-bump solutions with spatially disconnected compact supports and zero initial data are constructed between sub- and supersolutions that have supports of the same type.
What questions can a placebo answer?
Hey, Spencer Phillips; Weijer, Charles
2016-03-01
The concept of clinical equipoise restricts the use of placebo controls in clinical trials when there already exists a proven effective treatment. Several critics of clinical equipoise have put forward alleged counter-examples to this restriction-describing instances of ethical placebo-controlled trials that apparently violate clinical equipoise. In this essay, we respond to these examples and show that clinical equipoise is not as restrictive of placebos as these authors assume. We argue that a subtler appreciation for clinical equipoise-in particular the distinction between de facto and de jure interpretations of the concept-allows the concept to explain when and why a placebo control may be necessary to answer a question of clinical importance.
Adaptive upscaling with the dual mesh method
Energy Technology Data Exchange (ETDEWEB)
Guerillot, D.; Verdiere, S.
1997-08-01
The objective of this paper is to demonstrate that upscaling should be calculated during the flow simulation instead of trying to enhance the a priori upscaling methods. Hence, counter-examples are given to motivate our approach, the so-called Dual Mesh Method. The main steps of this numerical algorithm are recalled. Applications illustrate the necessity to consider different average relative permeability values depending on the direction in space. Moreover, these values could be different for the same average saturation. This proves that an a priori upscaling cannot be the answer even in homogeneous cases because of the {open_quotes}dynamical heterogeneity{close_quotes} created by the saturation profile. Other examples show the efficiency of the Dual Mesh Method applied to heterogeneous medium and to an actual field case in South America.
Formal verification of dynamic hybrid systems: a NuSMV-based model checking approach
Directory of Open Access Journals (Sweden)
Xu Zhi
2018-01-01
Full Text Available Software security is an important and challenging research topic in developing dynamic hybrid embedded software systems. Ensuring the correct behavior of these systems is particularly difficult due to the interactions between the continuous subsystem and the discrete subsystem. Currently available security analysis methods for system risks have been limited, as they rely on manual inspections of the individual subsystems under simplifying assumptions. To improve this situation, a new approach is proposed that is based on the symbolic model checking tool NuSMV. A dual PID system is used as an example system, for which the logical part and the computational part of the system are modeled in a unified manner. Constraints are constructed on the controlled object, and a counter-example path is ultimately generated, indicating that the hybrid system can be analyzed by the model checking tool.
A further inquiry into FTR properties
International Nuclear Information System (INIS)
Benjamin, Richard
2010-01-01
William Hogan introduced financial transmission rights as a tool to hedge the locational risk inherent in locational marginal prices. FTRs are claimed to serve four main purposes: (1) provide a hedge for nodal price differences, (2) provide revenue sufficiency for contracts for differences, (3) distribute the merchandizing surplus an RTO accrues in market operations, and (4) provide a price signal for transmission and generation developers. This paper examines the hedging and redistributional properties of FTRs. It argues that FTR allocation has important distributional impacts and related implications for retail rates. This observation adds an additional explanation for rate increases in light of decreased production costs due to restructuring. This paper also shows that RTO practices have important implications for the hedging characteristics of FTRs. It further shows, via counterexample, that, even in theory, FTRs may not serve as a perfect hedge against congestion charges. The paper concludes with a series of recommendations for FTR allocation and the functions that FTRs should serve.
A Game-Theoretic Approach to Branching Time Abstract-Check-Refine Process
Wang, Yi; Tamai, Tetsuo
2009-01-01
Since the complexity of software systems continues to grow, most engineers face two serious problems: the state space explosion problem and the problem of how to debug systems. In this paper, we propose a game-theoretic approach to full branching time model checking on three-valued semantics. The three-valued models and logics provide successful abstraction that overcomes the state space explosion problem. The game style model checking that generates counter-examples can guide refinement or identify validated formulas, which solves the system debugging problem. Furthermore, output of our game style method will give significant information to engineers in detecting where errors have occurred and what the causes of the errors are.
Weak stability of Lagrangian solutions to the semigeostrophic equations
International Nuclear Information System (INIS)
Faria, Josiane C O; Lopes Filho, Milton C; Nussenzveig Lopes, Helena J
2009-01-01
In (Cullen and Feldman 2006 SIAM J. Math. Anal. 37 137–95), Cullen and Feldman proved the existence of Lagrangian solutions for the semigeostrophic system in physical variables with initial potential vorticity in L p , p > 1. Here, we show that a subsequence of the Lagrangian solutions corresponding to a strongly convergent sequence of initial potential vorticities in L 1 converges strongly in L q , q < ∞, to a Lagrangian solution, in particular extending the existence result of Cullen and Feldman to the case p = 1. We also present a counterexample for Lagrangian solutions corresponding to a sequence of initial potential vorticities converging in BM. The analytical tools used include techniques from optimal transportation, Ambrosio's results on transport by BV vector fields and Orlicz spaces
Kubrusly, Carlos S
2015-01-01
Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces. The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. Th...
Refining the classification of irreps of the 1D N-extended supersymmetry
International Nuclear Information System (INIS)
Kuznetsova, Zhanna; Toppan, Francesco.
2007-01-01
In hep-th/0511274 the classification of the fields content of the linear finite irreducible representations of the algebra of the 1D N-Extended Supersymmetric Quantum Mechanics was given. In hep-th/0611060 it was pointed out that certain irreps with the same fields content can be regarded as inequivalent. This result can be understood in terms of the 'connectivity' properties of the graphs associated to the irreps. We present here a classification of the connectivity of the irreps, refining the hep-th/0511274 classification based on fields content. As a byproduct, we find a counterexample to the hep-th/0611060 claim that the connectivity is uniquely specified by the sources and targets of an irrep graph. We produce one pair of N=5 irreps and three pairs of N=6 irreps with the same number of sources and targets which, nevertheless, differ in connectivity. (author)
Nonsymmorphic Weyl superconductivity in UPt3 based on E2 u representation
Yanase, Youichi
2016-11-01
We show that a heavy fermion superconductor UPt3 is a topological Weyl superconductor with tunable Weyl nodes. Adopting a generic order parameter in the E2 u representation allowed by nonsymmorphic crystal symmetry, we clarify unusual gap structure and associated topological properties. The pair creation, pair annihilation, and coalescence of Weyl nodes are demonstrated in the time-reversal symmetry broken B-phase. At most 98 point nodes compatible with Blount's theorem give rise to line-node-like behaviors in low-energy excitations, consistent with experimental results. We also show an arc node protected by the nonsymmorphic crystal symmetry on the Brillouin zone face, which is a counterexample of Blount's theorem.
The Fielding H. Garrison lecture: the aesthetic grounding of modern medicine.
Warner, John Harley
2014-01-01
This article focuses on visual choices that American physicians made in representing their profession, their work, and themselves during the decades when modern medical culture was set in place, the 1880s through the 1940s. Historians have emphasized the role that image played in the formation of modern medicine, but the visual images they have explored in connection to this process have tended to take a reductionist aesthetic identified with experimental laboratory science as emblematic of medical modernity. Explored here instead are several counterexamples-genres of self-representation in which medical students and physicians did not seek to link their identity with the laboratory and in some ways distanced themselves from the image and ideals of experimental science. The cultivation of these images invites us to see the cultural grounding of modern medicine as vastly more complex than a story scripted around the biomedical embrace of a stripped down, reductionist aesthetic.
The effect of channel decoherence on entangled coherent states: A theoretical analysis
International Nuclear Information System (INIS)
Yao, Yao; Li, Hong-Wei; Yin, Zhen-Qiang; Guo, Guang-Can; Han, Zheng-Fu
2011-01-01
Highlights: → We analyze decoherence properties of ECSs due to channel losses. → Our result gives a new counterexample of entanglement ordering. → ECSs with sufficient small amplitudes are more robust against channel decoherence than Bell states. -- Abstract: We analyze decoherence properties of entangled coherent states due to channel losses. Employing the concept of 'entanglement of formation', degradation of fidelity and degree of entanglement are calculated. We have obtained an explicit expression of concurrence concerning the symmetric noise channel and found our result is just incompatible with that of [K. Park, H. Jeong, Phys. Rev. A 82 (2010) 062325] measured by negativity in the limit of α→0. We demonstrate that entangled coherent states with sufficient small amplitudes are more robust against channel decoherence than Bell states.
SPEEDY: An Eclipse-based IDE for invariant inference
Directory of Open Access Journals (Sweden)
David R. Cok
2014-04-01
Full Text Available SPEEDY is an Eclipse-based IDE for exploring techniques that assist users in generating correct specifications, particularly including invariant inference algorithms and tools. It integrates with several back-end tools that propose invariants and will incorporate published algorithms for inferring object and loop invariants. Though the architecture is language-neutral, current SPEEDY targets C programs. Building and using SPEEDY has confirmed earlier experience demonstrating the importance of showing and editing specifications in the IDEs that developers customarily use, automating as much of the production and checking of specifications as possible, and showing counterexample information directly in the source code editing environment. As in previous work, automation of specification checking is provided by back-end SMT solvers. However, reducing the effort demanded of software developers using formal methods also requires a GUI design that guides users in writing, reviewing, and correcting specifications and automates specification inference.
Comment on ``Symmetries and Interaction Coefficients of Kelvin waves'' by Lebedev and L'vov
Kozik, E. V.; Svistunov, B. V.
2010-12-01
We comment on the claim by Lebedev and L’vov (J. Low Temp. Phys. 161, 2010) that the symmetry with respect to a tilt of a quantized vortex line does not yet prohibit coupling between Kelvin waves and the large-scale slope of the line. Ironically, the counterexample of an effective scattering vertex in the local induction approximation (LIA) attempted by Lebedev and L’vov invalidates their logic all by itself being a notoriously known example of how symmetries impose stringent constraints on kelvon kinetics—not only the coupling in question but the kinetics in general are absent within LIA. We further explain that the mistake arises from confusing symmetry properties of a specific mathematical representation in terms of the canonical vortex position field w( z)= x( z)+ iy( z), which explicitly breaks the tilt symmetry due to an arbitrary choice of the z-axis, with those of the real physical system recovered in final expressions.
Periodic Solutions to a Cahn-Hilliard-Willmore Equation in the Plane
Malchiodi, Andrea; Mandel, Rainer; Rizzi, Matteo
2017-12-01
In this paper we construct entire solutions to the phase field equation of Willmore type {-Δ(-Δ u+W^'(u))+W^''(u)(-Δ u+W^'(u))=0} in the Euclidean plane, where W(u) is the standard double-well potential {1/4 (1-u^2)^2} . Such solutions have a non-trivial profile that shadows a Willmore planar curve, and converge uniformly to {± 1} as {x_2 \\to ± ∞} . These solutions give a counterexample to the counterpart of Gibbons' conjecture for the fourth-order counterpart of the Allen-Cahn equation. We also study the x 2-derivative of these solutions using the special structure of Willmore's equation.
Vogel, Brant
2011-01-01
This article discusses an anonymous letter published in the Philosophical Transactions in 1676 that reports the theories of American colonists about the cause of their warming climate (cultivation and deforestation), and offers Ireland's colonial experience as a counterexample: Ireland was a colony with decreased cultivation, but the same perceived warming. That such an objection seemed necessary to the author shows that anthropogenic climate change could be a subject of debate and that the concept of climate was tied into theories of land use and to the colonial enterprise. Since he was liminal to both the Royal Society of London and the intellectual circles of Dublin, his skepticism, contextualized here, questions both the elite discourse and the discourse at the colonial periphery.
No simple dual to the causal holographic information?
Energy Technology Data Exchange (ETDEWEB)
Engelhardt, Netta [Department of Physics, Princeton University,Princeton, NJ, 08544 (United States); Wall, Aron C. [Institute for Advanced Study,Einstein Drive, Princeton, NJ, 08540 (United States)
2017-04-21
In AdS/CFT, the fine grained entropy of a boundary region is dual to the area of an extremal surface X in the bulk. It has been proposed that the area of a certain ‘causal surface’ C — i.e. the ‘causal holographic information’ (CHI) — corresponds to some coarse-grained entropy in the boundary theory. We construct two kinds of counterexamples that rule out various possible duals, using (1) vacuum rigidity and (2) thermal quenches. This includes the ‘one-point entropy’ proposed by Kelly and Wall, and a large class of related procedures. Also, any coarse-graining that fixes the geometry of the bulk ‘causal wedge’ bounded by C, fails to reproduce CHI. This is in sharp contrast to the holographic entanglement entropy, where the area of the extremal surface X measures the same information that is found in the ‘entanglement wedge’ bounded by X.
Structural realism beyond physics.
Tulodziecki, Dana
2016-10-01
The main purpose of this paper is to test structural realism against (one example from) the historical record. I begin by laying out an existing challenge to structural realism - that of providing an example of a theory exhibiting successful structures that were abandoned - and show that this challenge can be met by the miasma theory of disease. However, rather than concluding that this is an outright counterexample to structural realism, I use this case to show why it is that structural realism, in its current form, has trouble dealing with theories outside physics. I end by making some concrete suggestions for structural realists to pursue if, indeed, they are serious about extending structural realism to other domains. Copyright © 2016 Elsevier Ltd. All rights reserved.
Quantum fluctuations and coherence in high-precision single-electron capture.
Kashcheyevs, Vyacheslavs; Timoshenko, Janis
2012-11-21
The phase of a single quantum state is undefined unless the history of its creation provides a reference point. Thus, quantum interference may seem hardly relevant for the design of deterministic single-electron sources which strive to isolate individual charge carriers quickly and completely. We provide a counterexample by analyzing the nonadiabatic separation of a localized quantum state from a Fermi sea due to a closing tunnel barrier. We identify the relevant energy scales and suggest ways to separate the contributions of quantum nonadiabatic excitation and back tunneling to the rare noncapture events. In the optimal regime of balanced decay and nonadiabaticity, our simple electron trap turns into a single-lead Landau-Zener back tunneling interferometer, revealing the dynamical phase accumulated between the particle capture and leakage. The predicted "quantum beats in back tunneling" may turn the error of a single-electron source into a valuable signal revealing essentially nonadiabatic energy scales of a dynamic quantum dot.
Stress fluctuations and macroscopic stick-slip in granular materials.
Evesque, P; Adjémian, F
2002-11-01
This paper deals with the quasi-static regime of deformation of granular matter. It investigates the size of the Representative Elementary Volume (REV), which is the minimum packing size above which the macroscopic mechanical behaviour of granular materials can be defined from averaging. The first part uses typical results from recent literature and finds that the minimum REV contains in general 10 grains; this result holds true either for most experiments or for Discrete Element Method (DEM) simulation. This appears to be quite small. However, the second part gives a counterexample, which has been found when investigating uniaxial compression of glass spheres which exhibit stick-slip; we show in this case that the minimum REV becomes 10(7) grains. This makes the system not computable by DEM. Moreover, similarity between the Richter law of seism and the exponential statistics of stick-slip is stressed.
Integrative Production Technology for High-Wage Countries
2012-01-01
Industrial production in high-wage countries like Germany is still at risk. Yet, there are many counter-examples in which producing companies dominate their competitors by not only compensating for their specific disadvantages in terms of factor costs (e.g. wages, energy, duties and taxes) but rather by minimising waste using synchronising integrativity as well as by obtaining superior adaptivity on alternating conditions. In order to respond to the issue of economic sustainability of industrial production in high-wage countries, the leading production engineering and material research scientists of RWTH Aachen University together with renowned companies have established the Cluster of Excellence “Integrative Production Technology for High-Wage Countries”. This compendium comprises the cluster’s scientific results as well as a selection of business and technology cases, in which these results have been successfully implemented into industrial practice in close cooperation with more than 30 companies of ...
Greater learnability is not sufficient to produce cultural universals.
Rafferty, Anna N; Griffiths, Thomas L; Ettlinger, Marc
2013-10-01
Looking across human societies reveals regularities in the languages that people speak and the concepts that they use. One explanation that has been proposed for these "cultural universals" is differences in the ease with which people learn particular languages and concepts. A difference in learnability means that languages and concepts possessing a particular property are more likely to be accurately transmitted from one generation of learners to the next. Intuitively, this difference could allow languages and concepts that are more learnable to become more prevalent after multiple generations of cultural transmission. If this is the case, the prevalence of languages and concepts with particular properties can be explained simply by demonstrating empirically that they are more learnable. We evaluate this argument using mathematical analysis and behavioral experiments. Specifically, we provide two counter-examples that show how greater learnability need not result in a property becoming prevalent. First, more learnable languages and concepts can nonetheless be less likely to be produced spontaneously as a result of transmission failures. We simulated cultural transmission in the laboratory to show that this can occur for memory of distinctive items: these items are more likely to be remembered, but not generated spontaneously once they have been forgotten. Second, when there are many languages or concepts that lack the more learnable property, sheer numbers can swamp the benefit produced by greater learnability. We demonstrate this using a second series of experiments involving artificial language learning. Both of these counter-examples show that simply finding a learnability bias experimentally is not sufficient to explain why a particular property is prevalent in the languages or concepts used in human societies: explanations for cultural universals based on cultural transmission need to consider the full set of hypotheses a learner could entertain and all of
Greater learnability is not sufficient to produce cultural universals
Rafferty, Anna N.; Griffiths, Thomas L.; Ettlinger, Marc
2013-01-01
Looking across human societies reveals regularities in the languages that people speak and the concepts that they use. One explanation that has been proposed for these “cultural universals” is differences in the ease with which people learn particular languages and concepts. A difference in learnability means that languages and concepts possessing a particular property are more likely to be accurately transmitted from one generation of learners to the next. Intuitively, this difference could allow languages and concepts that are more learnable to become more prevalent after multiple generations of cultural transmission. If this is the case, the prevalence of languages and concepts with particular properties can be explained simply by demonstrating empirically that they are more learnable. We evaluate this argument using mathematical analysis and behavioral experiments. Specifically, we provide two counter-examples that show how greater learnability need not result in a property becoming prevalent. First, more learnable languages and concepts can nonetheless be less likely to be produced spontaneously as a result of transmission failures. We simulated cultural transmission in the laboratory to show that this can occur for memory of distinctive items: these items are more likely to be remembered, but not generated spontaneously once they have been forgotten. Second, when there are many languages or concepts that lack the more learnable property, sheer numbers can swamp the benefit produced by greater learnability. We demonstrate this using a second series of experiments involving artificial language learning. Both of these counter-examples show that simply finding a learnability bias experimentally is not sufficient to explain why a particular property is prevalent in the languages or concepts used in human societies: explanations for cultural universals based on cultural transmission need to consider the full set of hypotheses a learner could entertain and all
Directory of Open Access Journals (Sweden)
Seiya Nishiyama
2009-01-01
Full Text Available The maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a collective submanifold in which a canonicity condition makes the collective variables to be an orthogonal coordinate-system. For this aim we adopt a concept of curvature unfamiliar in the conventional time-dependent (TD self-consistent field (SCF theory. Our basic idea lies in the introduction of a sort of Lagrange manner familiar to fluid dynamics to describe a collective coordinate-system. This manner enables us to take a one-form which is linearly composed of a TD SCF Hamiltonian and infinitesimal generators induced by collective variable differentials of a canonical transformation on a group. The integrability condition of the system read the curvature C = 0. Our method is constructed manifesting itself the structure of the group under consideration. To go beyond the maximaly-decoupled method, we have aimed to construct an SCF theory, i.e., υ (external parameter-dependent Hartree-Fock (HF theory. Toward such an ultimate goal, the υ-HF theory has been reconstructed on an affine Kac-Moody algebra along the soliton theory, using infinite-dimensional fermion. An infinite-dimensional fermion operator is introduced through a Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent potential with a Υ-periodicity. A bilinear equation for the υ-HF theory has been transcribed onto the corresponding τ-function using the regular representation for the group and the Schur-polynomials. The υ-HF SCF theory on an infinite-dimensional Fock space F∞ leads to a dynamics on an infinite-dimensional Grassmannian Gr∞ and may describe more precisely such a dynamics on the group manifold. A finite-dimensional Grassmannian is identified with a Gr
An introduction to branching measure-valued processes
Dynkin, Eugene B
1994-01-01
For about half a century, two classes of stochastic processes-Gaussian processes and processes with independent increments-have played an important role in the development of stochastic analysis and its applications. During the last decade, a third class-branching measure-valued (BMV) processes-has also been the subject of much research. A common feature of all three classes is that their finite-dimensional distributions are infinitely divisible, allowing the use of the powerful analytic tool of Laplace (or Fourier) transforms. All three classes, in an infinite-dimensional setting, provide means for study of physical systems with infinitely many degrees of freedom. This is the first monograph devoted to the theory of BMV processes. Dynkin first constructs a large class of BMV processes, called superprocesses, by passing to the limit from branching particle systems. Then he proves that, under certain restrictions, a general BMV process is a superprocess. A special chapter is devoted to the connections between ...
Truncated predictor feedback for time-delay systems
Zhou, Bin
2014-01-01
This book provides a systematic approach to the design of predictor based controllers for (time-varying) linear systems with either (time-varying) input or state delays. Differently from those traditional predictor based controllers, which are infinite-dimensional static feedback laws and may cause difficulties in their practical implementation, this book develops a truncated predictor feedback (TPF) which involves only finite dimensional static state feedback. Features and topics: A novel approach referred to as truncated predictor feedback for the stabilization of (time-varying) time-delay systems in both the continuous-time setting and the discrete-time setting is built systematically Semi-global and global stabilization problems of linear time-delay systems subject to either magnitude saturation or energy constraints are solved in a systematic manner Both stabilization of a single system and consensus of a group of systems (multi-agent systems) are treated in a unified manner by applying the truncated pre...
Act-and-wait time-delayed feedback control of autonomous systems
Pyragas, Viktoras; Pyragas, Kestutis
2018-02-01
Recently an act-and-wait modification of time-delayed feedback control has been proposed for the stabilization of unstable periodic orbits in nonautonomous dynamical systems (Pyragas and Pyragas, 2016 [30]). The modification implies a periodic switching of the feedback gain and makes the closed-loop system finite-dimensional. Here we extend this modification to autonomous systems. In order to keep constant the phase difference between the controlled orbit and the act-and-wait switching function an additional small-amplitude periodic perturbation is introduced. The algorithm can stabilize periodic orbits with an odd number of real unstable Floquet exponents using a simple single-input single-output constraint control.
Dynamical systems generated by linear maps
Dolićanin, Ćemal B
2014-01-01
The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systems theory. However, for the dynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications. The considered problems are natural and look rather simple, but in reality in the course of investigation, they confront users with plenty of subtle questions, and their detailed analysis needs a substantial effort. The problems arising are related to linear algebra and dynamical systems theory, and therefore, the book can be considered as a natural amplification, refinement and supplement to linear algebra and dynamical systems theory textbooks.
Stochastic differential equations, backward SDEs, partial differential equations
Pardoux, Etienne
2014-01-01
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has...
Implementation of a partitioned algorithm for simulation of large CSI problems
Alvin, Kenneth F.; Park, K. C.
1991-01-01
The implementation of a partitioned numerical algorithm for determining the dynamic response of coupled structure/controller/estimator finite-dimensional systems is reviewed. The partitioned approach leads to a set of coupled first and second-order linear differential equations which are numerically integrated with extrapolation and implicit step methods. The present software implementation, ACSIS, utilizes parallel processing techniques at various levels to optimize performance on a shared-memory concurrent/vector processing system. A general procedure for the design of controller and filter gains is also implemented, which utilizes the vibration characteristics of the structure to be solved. Also presented are: example problems; a user's guide to the software; the procedures and algorithm scripts; a stability analysis for the algorithm; and the source code for the parallel implementation.
Construction of an exactly solvable model of the many-body problem
Energy Technology Data Exchange (ETDEWEB)
Zettili, N. [King Fahd Univ. of Petrolium and Minerals, Dhahran (Saudi Arabia). Dept. of Phys.]|[Institut de Physique, Universite de Blida, Blida (Algeria); Bouayad, N. [Institut de Physique, Universite de Blida, Blida (Algeria)
1996-11-11
We propose here a new model for the many-body problem that can be solved exactly through the diagonalization of its Hamiltonian. This model, which is founded on a Lie algebra, serves as a useful tool for testing the accuracy of many-body approximation methods. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct this model`s Hamiltonian by means of vector operators that are the generators of an SO(2,1) group and which satisfy a Lie algebra. We incorporate into the Hamiltonian a symmetry that yields a constant of the motion which, in turn, renders the size of the Hamiltonian matrix finite. The diagonalization of this finitely dimensional matrix gives the exact values of the energy spectrum. (orig.).
Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows
Barth, Timothy J.
2010-01-01
The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.
International Nuclear Information System (INIS)
Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio
2007-01-01
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1xM bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a, uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes
An introduction to quiver representations
Derksen, Harm
2017-01-01
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is su...
Applications of isotopy to real division algebras
Energy Technology Data Exchange (ETDEWEB)
Benkart, G. (Univ. of Wisconsin, Madison); Osborn, J.M.; Britten, D.
1981-02-01
In this paper we illustrate how the notion of isotopy can be used to solve various problems concerning finite-dimensional division algebras over the real numbers. In particular, we show that the 8-dimensional division algebras which have the same derivation algebra as the octonions, and hence which most resemble the octonions, are not in general isotopes of the octonions. Secondly, using a result of Hopf, we argue that every commutative division algebra is the reals or is isomorphic to a special kind of isotope of the complex numbers. Finally, by considering a certain class of algebras, we show how isotopy is a useful tool for determining necessary and sufficient conditions on the multiplication constants in order to have a division algebra.
Energy Technology Data Exchange (ETDEWEB)
Keim, M.
2005-07-01
In the present thesis response effects in interatomic collisions with two active electrons are studied in the range of non-relativistic collision energies. The starting point is the mapping of the time-dependent interacting many-electron sytem on an effective one-particle picture on the base of the time-dependent density functional theory (TDDFT). By means of the basis generator method the one-particle equations aring in the framework of the TDDFT concept are solved in a finite-dimensional model space. In the study of ionization cross section in the collisional systeem anti p+He it is shown that by response effects an essential diminuishing of the cross sections in comparison to the no-response case is reached. Analoguously the ionization cross sections for the collisional systems p-He, He{sup 2+}-He, Li{sup 3+}-He and p-Li{sup +} behave.
Ito, Kazufumi
1987-01-01
The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
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
Safety factor profile control in a tokamak
Bribiesca Argomedo, Federico; Prieur, Christophe
2014-01-01
Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The t...
Connes' embedding problem and winning strategies for quantum XOR games
Harris, Samuel J.
2017-12-01
We consider quantum XOR games, defined in the work of Regev and Vidick [ACM Trans. Comput. Theory 7, 43 (2015)], from the perspective of unitary correlations defined in the work of Harris and Paulsen [Integr. Equations Oper. Theory 89, 125 (2017)]. We show that the winning bias of a quantum XOR game in the tensor product model (respectively, the commuting model) is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game G with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.
Linear odd Poisson bracket on Grassmann variables
International Nuclear Information System (INIS)
Soroka, V.A.
1999-01-01
A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson bracket having the only Grassmann-odd nilpotent differential Δ-operator of the second order. It is shown that these Δ-like operators together with a Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
A Hamiltonian formulation for elasticity and thermoelasticity
Maugin, G A
2002-01-01
A Hamiltonian formulation for elasticity and thermoelasticity is proposed and its relation with the corresponding configurational setting is examined. Firstly, a variational principle, concerning the 'inverse motion' mapping, is formulated and the corresponding Euler-Lagrange equations are explored. Next, this Lagrangian formulation is used to define the Hamiltonian density function. The equations of Hamilton are derived in a form which is very similar to the one of the corresponding equations in particle mechanics (finite-dimensional case). From the Hamiltonian formulation it follows that the canonical momentum is identified with the pseudomomentum. Furthermore, a meaning for the Poisson bracket is defined and the entailed relations with the canonical variables as well as the balance laws are examined.
Notes on qubit phase space and discrete symplectic structures
International Nuclear Information System (INIS)
Livine, Etera R
2010-01-01
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.
Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing
2018-02-01
Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.
Computational physics an introduction to Monte Carlo simulations of matrix field theory
Ydri, Badis
2017-01-01
This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since 2010 to physics students at Annaba University. The second part is much more advanced and deals with the problem of how to set up working Monte Carlo simulations of matrix field theories which involve finite dimensional matrix regularizations of noncommutative and fuzzy field theories, fuzzy spaces and matrix geometry. The study of matrix field theory in its own right has also become very important to the proper understanding of all noncommutative, fuzzy and matrix phenomena. The second part, which consists of 9 simulations, was delivered informally to doctoral students who are working on various problems in matrix field theory. Sample codes as well as sample key solutions are also provided for convenience and completness. An appendix containing an executive arabic summary of t...
Loss of Energy Concentration in Nonlinear Evolution Beam Equations
Garrione, Maurizio; Gazzola, Filippo
2017-12-01
Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we introduce the notion of solutions with a prevailing mode for the nonlinear evolution beam equation u_{tt} + u_{xxxx} + f(u)= g(x, t) in bounded space-time intervals. We give a new definition of instability for these particular solutions, based on the loss of energy concentration on their prevailing mode. We distinguish between two different forms of energy transfer, one physiological (unavoidable and depending on the nonlinearity) and one due to the insurgence of instability. We then prove a theoretical result allowing to reduce the study of this kind of infinite-dimensional stability to that of a finite-dimensional approximation. With this background, we study the occurrence of instability for three different kinds of nonlinearities f and for some forcing terms g, highlighting some of their structural properties and performing some numerical simulations.