International Nuclear Information System (INIS)
Feinsilver, Philip; Schott, Rene
2009-01-01
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.
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.
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...
Dialectica Interpretation with Marked Counterexamples
Directory of Open Access Journals (Sweden)
Trifon Trifonov
2011-01-01
Full Text Available Goedel's functional "Dialectica" interpretation can be used to extract functional programs from non-constructive proofs in arithmetic by employing two sorts of higher-order witnessing terms: positive realisers and negative counterexamples. In the original interpretation decidability of atoms is required to compute the correct counterexample from a set of candidates. When combined with recursion, this choice needs to be made for every step in the extracted program, however, in some special cases the decision on negative witnesses can be calculated only once. We present a variant of the interpretation in which the time complexity of extracted programs can be improved by marking the chosen witness and thus avoiding recomputation. The achieved effect is similar to using an abortive control operator to interpret computational content of non-constructive principles.
Quantum Finance: The Finite Dimensional Case
Chen, Zeqian
2001-01-01
In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of the binomial market. Furthermore, we re-deduce the Cox-Ross-Rubinstein binomial option pricing form...
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.
Biderivations of finite dimensional complex simple Lie algebras
Tang, Xiaomin
2016-01-01
In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In particular, we find a class of a non-inner and non-skewsymmetric biderivations. Furthermore, we also get the forms of linear commuting maps on the finite dimensional complex simple Lie algebra or general linear Lie algebra.
Vacuum counterexamples to the cosmic censorship hypothesis
International Nuclear Information System (INIS)
Miller, B.D.
1981-01-01
In cylindrically symmetric vacuum spacetimes it is possible to specify nonsingular initial conditions such that timelike singularities will (necessarily) evolve from these conditions. Examples are given; the spacetimes are somewhat analogous to one of the spherically symmetric counterexamples to the cosmic censorship hypothesis
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.
Finite-dimensional approximation for operator equations of Hammerstein type
International Nuclear Information System (INIS)
Buong, N.
1992-11-01
The purpose of this paper is to establish convergence rate for a method of finite-dimensional approximation to solve operator equation of Hammerstein type in real reflexive Banach space. In order to consider a numerical example an iteration method is proposed in Hilbert space. (author). 25 refs
A Simple Counterexample to the Bootstrap
Donald W.K. Andrews
1997-01-01
The bootstrap of the maximum likelihood estimator of the mean of a sample of iid normal random variables with mean mu and variance one is not asymptotically correct to first order when the mean is restricted to be nonnegative. The problem occurs when the true value of the mean mu equals zero. This counterexample to the bootstrap generalizes to a wide variety of estimation problems in which the true parameter may be on the boundary of the parameter space. We provide some alternatives to the bo...
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
Automata Learning through Counterexample Guided Abstraction Refinement
DEFF Research Database (Denmark)
Aarts, Fides; Heidarian, Faranak; Kuppens, Harco
2012-01-01
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...... are allowed. Our approach uses counterexample-guided abstraction refinement: whenever the current abstraction is too coarse and induces nondeterministic behavior, the abstraction is refined automatically. Using Tomte, a prototype tool implementing our algorithm, we have succeeded to learn – fully......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...
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....
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
The finite - dimensional star and grade star irreducible representation of SU(n/1)
International Nuclear Information System (INIS)
Han Qi-zhi.
1981-01-01
We derive the conditions of star and grade star representations of SU(n/1) and give some examples of them. We also give a brief review of the finite - dimensional irreducible representations of SU(n/1). (author)
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
International Nuclear Information System (INIS)
Nguyen Anh Ky.
1993-05-01
In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)] at generic deformation parameter q. As in the non-deformed case the finite-dimensional U q [gl(2/2)]-module W q obtained is irreducible and can be decomposed into finite-dimensional irreducible U q [l(2)+gl(2)]submodules V i q . (authohor). 32 refs
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
The structure of the Hamiltonian in a finite-dimensional formalism based on Weyl's quantum mechanics
International Nuclear Information System (INIS)
Santhanam, T.S.; Madivanane, S.
1982-01-01
Any discussion on finite-dimensional formulation of quantum mechanics involves the Sylvester matrix (finite Fourier transform). In the usual formulation, a remarkable relation exists that gives the Fourier transform as the exponential of the Hamiltonian of a simple harmonic oscillator. In this paper, assuming that such a relation holds also in the finite dimensional case, we extract the logarithm of the Sylvester matrix and in some cases this can be interpreted as the Hamiltonian of the truncated oscillator. We calculate the Hamiltonian matrix explicitly for some special cases of n = 3,4. (author)
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
Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2010-01-25
The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.
Quantum phase space points for Wigner functions in finite-dimensional spaces
Luis Aina, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.
Quantum phase space points for Wigner functions in finite-dimensional spaces
International Nuclear Information System (INIS)
Luis, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
International Nuclear Information System (INIS)
Bagchi, B.
1995-01-01
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.))
International Nuclear Information System (INIS)
Xia Tiecheng; Chen Xiaohong; Chen Dengyuan
2004-01-01
An eigenvalue problem and the associated new Lax integrable hierarchy of nonlinear evolution equations are presented in this paper. As two reductions, the generalized nonlinear Schroedinger equations and the generalized mKdV equations are obtained. Zero curvature representation and bi-Hamiltonian structure are established for the whole hierarchy based on a pair of Hamiltonian operators (Lenard's operators), and it is shown that the hierarchy of nonlinear evolution equations is integrable in Liouville's sense. Thus the hierarchy of nonlinear evolution equations has infinitely many commuting symmetries and conservation laws. Moreover the eigenvalue problem is nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalue functions. Finally finite-dimensional Liouville integrable system are found, and the involutive solutions of the hierarchy of equations are given. In particular, the involutive solutions are developed for the system of generalized nonlinear Schroedinger equations
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)
Fu, Yuchen; Shelley-Abrahamson, Seth
2016-06-01
We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for U_q(sl_N). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov.
Absolute continuity of autophage measures on finite-dimensional vector spaces
Energy Technology Data Exchange (ETDEWEB)
Raja, C R.E. [Stat-Math Unit, Indian Statistical Institute, Bangalore (India); [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]. E-mail: creraja@isibang.ac.in
2002-06-01
We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or Q{sub p} are infinitely divisible without idempotent factors and are absolutely continuous with bounded continuous density. We also show that certain semistable measures on such vector spaces are absolutely continuous. (author)
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
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.
Energy Technology Data Exchange (ETDEWEB)
Castellani, Marco; Giuli, Massimiliano, E-mail: massimiliano.giuli@univaq.it [University of L’Aquila, Department of Information Engineering, Computer Science and Mathematics (Italy)
2016-02-15
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.
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
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)
Marchiolli, M.A.; Ruzzi, M.
2012-01-01
We propose a self-consistent theoretical framework for a wide class of physical systems characterized by a finite space of states which allows us, within several mathematical virtues, to construct a discrete version of the Weyl–Wigner–Moyal (WWM) formalism for finite-dimensional discrete phase spaces with toroidal topology. As a first and important application from this ab initio approach, we initially investigate the Robertson–Schrödinger (RS) uncertainty principle related to the discrete coordinate and momentum operators, as well as its implications for physical systems with periodic boundary conditions. The second interesting application is associated with a particular uncertainty principle inherent to the unitary operators, which is based on the Wiener–Khinchin theorem for signal processing. Furthermore, we also establish a modified discrete version for the well-known Heisenberg–Kennard–Robertson (HKR) uncertainty principle, which exhibits additional terms (or corrections) that resemble the generalized uncertainty principle (GUP) into the context of quantum gravity. The results obtained from this new algebraic approach touch on some fundamental questions inherent to quantum mechanics and certainly represent an object of future investigations in physics. - Highlights: ► We construct a discrete version of the Weyl–Wigner–Moyal formalism. ► Coherent states for finite-dimensional discrete phase spaces are established. ► Discrete coordinate and momentum operators are properly defined. ► Uncertainty principles depend on the topology of finite physical systems. ► Corrections for the discrete Heisenberg uncertainty relation are also obtained.
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.
A complementarity-based approach to phase in finite-dimensional quantum systems
International Nuclear Information System (INIS)
Klimov, A B; Sanchez-Soto, L L; Guise, H de
2005-01-01
We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d-1 operators. One of these classes consists of diagonal operators that represent amplitudes (or inversions). By finite Fourier transformation, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss examples of qubits and qutrits, and show how these results generalize previous approaches
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.)
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
Numerical and algebraic studies for the control of finite-dimensional quantum systems
International Nuclear Information System (INIS)
Sander, Uwe
2010-01-01
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.)
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.)
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.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
Energy Technology Data Exchange (ETDEWEB)
Thapliyal, Kishore, E-mail: tkishore36@yahoo.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India)
2016-03-15
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Sergyeyev, Artur, E-mail: Artur.Sergyeyev@math.slu.cz [Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava (Czech Republic)
2012-06-04
In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.
International Nuclear Information System (INIS)
Sergyeyev, Artur
2012-01-01
In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.
International Nuclear Information System (INIS)
Nguyen Anh Ky; Stoilova, N.I.
1994-11-01
The construction approach proposed in the previous paper Ref.1 allows us there and in the present paper to construct at generic deformation parameter q all finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)]. The finite-dimensional U q [gl(2/2)]-modules W q constructed in Ref.1 are either irreducible or indecomposable. If a module W q is indecomposable, i.e. when the condition (4.41) in Ref.1 does not hold, there exists an invariant maximal submodule of W q , to say I q k , such that the factor-representation in the factor-module W q /I q k is irreducible and called nontypical. Here, in this paper, indecomposable representations and nontypical finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)] are considered and classified as their module structures are analyzed and the matrix elements of all nontypical representations are written down explicitly. (author). 23 refs
International Nuclear Information System (INIS)
Sun Yepeng; Chen Dengyuan
2006-01-01
A new spectral problem and the associated integrable hierarchy of nonlinear evolution equations are presented in this paper. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. An explicit symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the hierarchy. Moreover, the corresponding Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative, new finite-dimensional completely integrable Hamiltonian systems in the Liouville sense. Further, an involutive representation of solution of each equation in the hierarchy is given. Finally, expanding integrable models of the hierarchy are constructed by using a new Loop algebra
International Nuclear Information System (INIS)
Yan, Z.; Zhang, H.
2001-01-01
In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed
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)
Ranade, Kedar S.
2009-01-01
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.)
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)
Broken bridges: a counter-example of the ER=EPR conjecture
International Nuclear Information System (INIS)
Chen, Pisin; Wu, Chih-Hung; Yeom, Dong-han
2017-01-01
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.
Akibue, Seiseki; Kato, Go
2018-04-01
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a composite system consisting of N subsystems, where each subsystem is shared between two parties and the state of each subsystem is randomly sampled from a particular ensemble comprising the Bell states. We show that the success probability of perfectly identifying the state converges to 1 as N →∞ if the entropy of the probability distribution associated with the ensemble is less than 1, even if the success probability is less than 1 for any finite N . In other words, the nonlocality of the N -fold ensemble asymptotically disappears if the probability distribution associated with each ensemble is concentrated. Furthermore, we show that the disappearance of the nonlocality can be regarded as a remarkable counterexample of a fundamental open question in theoretical computer science, called a parallel repetition conjecture of interactive games with two classically communicating players. Measurements for the discrimination task include a projective measurement of one party represented by stabilizer states, which enable the other party to perfectly distinguish states that are sampled with high probability.
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.
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.
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.
Finite dimensional convexity and optimization
Florenzano, Monique
2001-01-01
The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.
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.)
Structures in dynamics finite dimensional deterministic studies
Broer, HW; van Strien, SJ; Takens, F
1991-01-01
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic
ON STATISTICALLY CONVERGENT IN FINITE DIMENSIONAL SPACES
GÜNCAN, Ayşe Nur
2009-01-01
Abstract: In this paper, the notion of statistical convergence, which was introduced by Steinhaus (1951), was studied in Rm ; and some concepts and theorems, whose statistical correspondence for the real number sequences were given, were carried to Rm . In addition, the concepts of the statistical limit point and the statistical cluster point were given and it was mentioned that these two concepts were'nt equal in Fridy's study in 1993. These concepts were given in Rm and the i...
The finite-dimensional Freeman thesis.
Rudolph, Lee
2008-06-01
I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.
Classical counterexamples to Bell's inequalities
International Nuclear Information System (INIS)
Orlov, Yuri F.
2002-01-01
This paper shows that a classical system containing a conventional yes/no decision-making component can behave like a quantum system of spin measurements in many ways (although it lacks a wave function) when, in principle, there are no deterministic decision procedures to govern the decision making, and when probabilistic decision procedures consistent with the system are introduced. Most notably, the system violates Bell's inequalities. Moreover, since the system is simple and macroscopic, its similarities to quantum systems arguably provide an insight into quantum mechanics and, in particular, EPR experiments. Thus, from the qualitative correspondences, decisions↔quantum measurements and the impossibility of deterministic decision procedures↔quantum noncommutativity, we conclude that the violation of Bell's inequalities in quantum mechanics does not require the existence of an unknown nonclassical nonlocality. It can merely be a result of local noncommutativity combined with nonlocalities of the classical type. The proposed classical decision-making system is a nonquantum theoretical construct possessing complementarity features in Bohr's sense
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.
Wigner distributions for finite dimensional quantum systems: An ...
Indian Academy of Sciences (India)
2005-07-11
Jul 11, 2005 ... 5Centre for High Energy Physics, Indian Institute of Science, Bangalore ... one has to take the Cartesian product of the elementary solutions. ... tor of translations in configuration space, with mass not playing an explicit role. .... with a distinguished 'origin' corresponding to the identity element e ∈ G. In turn,.
D-boundedness and D-compactness in finite dimensional ...
Indian Academy of Sciences (India)
closely modelled on the theory of (classical) normed spaces, and used to study the problem .... and the strong neighborhood system for V is the union ∪p∈V Np where Np ... is said to be strongly complete in the strong topology if and only if.
Infinite Dimensional Dynamical Systems and their Finite Dimensional Analogues.
1987-01-01
Rolla ____t___e ___o, __.Paul Steen Cornell Univ.Andrew Szeri Cornell Univ. ByEdriss Titi Univ. of Chicago _Distributi-on/ -S. Tsaltas Unvcrsity of...Cornell University Ithaca, NY 14853 Edriss Titi University of Chicago Dept. of Mathematics 5734 S. University Ave.Chicago, IL 60637 Spiros Tsaltas Dept
Approximation of the Frame Coefficients using Finite Dimensional Methods
DEFF Research Database (Denmark)
Christensen, Ole; Casazza, P.
1997-01-01
_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...
Finite-dimensional reductions of the discrete Toda chain
International Nuclear Information System (INIS)
Kazakova, T G
2004-01-01
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 Painleve equations dP III , dP V , dP VI . Lax representations for these discrete Painleve equations are found
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
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...
Cooperstock's counterexample to the gravitational-radiation quadrupole formula
International Nuclear Information System (INIS)
Walker, M.
1986-01-01
Cooperstock has recently modified the axially symmetric gravitational two-body problem previously analyzed by himself, Lim, and Hobill by introducing a new assumption, that ''The system undergoes a smooth transition from the static state to free-fall and the motion. . .consists of the two bodies accelerating towards each other while undergoing slow tidal deformation.'' This assumption is inconsistent with his solution of the field equations. The quadrupole formula correctly describes the radiation emitted
On Young's (1805) equation and Finn's (2006) 'counterexample'
International Nuclear Information System (INIS)
Shikhmurzaev, Yulii D.
2008-01-01
In 1805, Thomas Young considered the balance of forces acting on the contact line formed at the intersection of a liquid-fluid interface with a solid surface and introduced a macroscopic concept of 'contact angle'. From Young's reasoning it follows that in equilibrium the contact angle is a material property of the liquid/fluid/solid system independent of a particular configuration. Two centuries later, Robert Finn considered a model problem which seems to suggest that there is a fundamental flaw in Young's force diagram and the reasoning behind it. In the present note, we show that the apparent paradox in Finn's model problem disappears once Young's original concepts are applied in a correct way
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...
An Examination of Counterexamples in Proofs and Refutations
Bağçe, Samet; Başkent, Can
2011-01-01
Dans son influent Proofs and Refutations (Preuves et Réfutations), Lakatos introduit les méthodes de preuves et de réfutations en discutant l’histoire et le développement de la formule V — E+F = 2 d’Euler pour les polyèdres en 3 dimensions. Lakatos croyait, en effet, que l’histoire du polyèdre présentait un bon exemple pour sa philosophie et sa méthodologie des mathématiques, incluant la géométrie. Le présent travail met l’accent sur les propriétés mathématiques et topologiques qui sont incor...
Numerical simulation of a possible counterexample to cosmic censorship
International Nuclear Information System (INIS)
Garfinkle, David
2004-01-01
A numerical simulation is presented here of the evolution of initial data of the kind that was conjectured by Hertog, Horowitz, and Maeda to be a violation of cosmic censorship. Those initial data are essentially a thick domain wall connecting two regions of anti-de Sitter space. The initial data have a free parameter that is the initial size of the wall. The simulation shows no violation of cosmic censorship, but rather the formation of a small black hole. The simulation described here is for a moderate wall size and leaves open the possibility that cosmic censorship might be violated for larger walls
Highly arc-transitive digraphs -- counterexamples and structure
DeVos, Matt; Mohar, Bojan; Šámal, Robert
2011-01-01
We resolve two problems of [Cameron, Praeger, and Wormald -- Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica 1993]. First, we construct a locally finite highly arc-transitive digraph with universal reachability relation. Second, we provide constructions of 2-ended highly arc transitive digraphs where each `building block' is a finite bipartite graph that is not a disjoint union of complete bipartite graphs. This was conjectured impossible in the above pa...
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.
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2011-05-09
A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. - Highlights: A new family of Poisson structures is globally characterized and analyzed. Such family is globally defined for arbitrary values of the dimension and the rank. Global construction of Casimir invariants and Darboux canonical form is provided. Very diverse and previously known solutions of physical interest are generalized.
Representation theory of 2-groups on finite dimensional 2-vector spaces
Elgueta, Josep
2004-01-01
In this paper, the 2-category $\\mathfrak{Rep}_{{\\bf 2Mat}_{\\mathbb{C}}}(\\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces is studied. In particular, the set of equivalence classes of representations is computed in terms of the invariants $\\pi_0(\\mathbb{G})$, $\\pi_1(\\mathbb{G})$ and $[\\alpha]\\in H^3(\\pi_0(\\mathbb{G}),\\pi_1(\\mathbb{G}))$ classifying $\\mathbb{G}$. Also the categ...
International Nuclear Information System (INIS)
Hernandez-Bermejo, Benito
2011-01-01
A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. - Highlights: → A new family of Poisson structures is globally characterized and analyzed. → Such family is globally defined for arbitrary values of the dimension and the rank. → Global construction of Casimir invariants and Darboux canonical form is provided. → Very diverse and previously known solutions of physical interest are generalized.
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
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
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
On the rate of convergence of the alternating projection method in finite dimensional spaces
Galántai, A.
2005-10-01
Using the results of Smith, Solmon, and Wagner [K. Smith, D. Solomon, S. Wagner, Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math. Soc. 83 (1977) 1227-1270] and Nelson and Neumann [S. Nelson, M. Neumann, Generalizations of the projection method with application to SOR theory for Hermitian positive semidefinite linear systems, Numer. Math. 51 (1987) 123-141] we derive new estimates for the speed of the alternating projection method and its relaxed version in . These estimates can be computed in at most O(m3) arithmetic operations unlike the estimates in papers mentioned above that require spectral information. The new and old estimates are equivalent in many practical cases. In cases when the new estimates are weaker, the numerical testing indicates that they approximate the original bounds in papers mentioned above quite well.
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
International Nuclear Information System (INIS)
Dzheparov, F.S.
1977-01-01
The integral H tilde (lambda) = ∫sub(0)sup(infinity) dt exp[-(lambda-iF)t]Xexp(-iHt) and the solution of the matrix equation iX tilde (lambda)H+(lambda-iF)Xtilde (lambda)=X, where F and H are hermitian matrices with dimensions M and N, respectively, are represented as a polynomial of the (M-1) degree in F and of the (N-1) degree in H whose coefficients are found from the characteristic polynomials of the F and H matrices
Plate falling in a fluid: Regular and chaotic dynamics of finite-dimensional models
Kuznetsov, Sergey P.
2015-05-01
Results are reviewed concerning the planar problem of a plate falling in a resisting medium studied with models based on ordinary differential equations for a small number of dynamical variables. A unified model is introduced to conduct a comparative analysis of the dynamical behaviors of models of Kozlov, Tanabe-Kaneko, Belmonte-Eisenberg-Moses and Andersen-Pesavento-Wang using common dimensionless variables and parameters. It is shown that the overall structure of the parameter spaces for the different models manifests certain similarities caused by the same inherent symmetry and by the universal nature of the phenomena involved in nonlinear dynamics (fixed points, limit cycles, attractors, and bifurcations).
Energy Technology Data Exchange (ETDEWEB)
Sergyeyev, Artur [Mathematical Institute, Silesian University in Opava, Na RybnIcku 1, 746 01 Opava (Czech Republic); Blaszak, Maciej [Institute of Physics, A Mickiewicz University, Umultowska 85, 61-614 Poznan (Poland)], E-mail: Artur.Sergyeyev@math.slu.cz, E-mail: blaszakm@amu.edu.pl
2008-03-14
We present a multiparameter generalization of the Staeckel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized Staeckel transform preserves Liouville integrability, noncommutative integrability and superintegrability. The corresponding transformation for the equations of motion proves to be nothing but a reciprocal transformation of a special form, and we investigate the properties of this reciprocal transformation. Finally, we show that the Hamiltonians of the systems possessing separation curves of apparently very different form can be related through a suitably chosen generalized Staeckel transform.
International Nuclear Information System (INIS)
Guo Boling
1994-01-01
We prove the existence of the global attractors for the generalized Landau-Lifshitz equation on compact manifold M, and give the upper and lower estimates of their Hausdorff and fractal dimensions. (author). 18 refs
International Nuclear Information System (INIS)
Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.
1984-01-01
The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed
1988-06-01
loop equations can be written in terms of the extended space XE = h ., where . C 7, to get SA = + G 0w(54 ) X K C A- BK - KfC j [0 K] 7] or in terms...C where in LQG notation C, = l,(sJ - (A - BK, - AfC))-’kj C = K (sl - (A - BK, - KfC ))-1K ! 44 Uy Recall that only Kf has to be approximated in...the oper- ators A-BK, and A- KfC both generate stable semigroups [24]. If (A+AA-BK) and (A + AA - 1’fC) also generale stable semigroups, then the
Collapse of the random-phase approximation: Examples and counter-examples from the shell model
International Nuclear Information System (INIS)
Johnson, Calvin W.; Stetcu, Ionel
2009-01-01
The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a 'phase transition' in the literature). The order of the transition is important when one applies the random-phase approximation (RPA) to the of the Hartree-Fock wave function: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as 'collapse' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time nontrivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.
A Counterexample Guided Abstraction Refinement Framework for Verifying Concurrent C Programs
2005-05-24
source code are routinely executed. The source code is written in languages ranging from C/C++/Java to ML/ Ocaml . These languages differ not only in...from the difficulty to model computer programs—due to the complexity of programming languages as compared to hardware description languages —to...intermediate specification language lying between high-level Statechart- like formalisms and transition systems. Actions are encoded as changes in
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)
The Zak transform and some counterexamples in time-frequency analysis
Janssen, A.J.E.M.
1992-01-01
It is shown how the Zak transform can be used to find nontrivial examples of functions f, g e L2(R) with f × g ¿ 0 ¿ F × G, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, k e L2(R), h ¿ k, such that |h| = |k|, |H| = |K|. A
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…
About one counterexample of applying method of splitting in modeling of plating processes
Solovjev, D. S.; Solovjeva, I. A.; Litovka, Yu V.; Korobova, I. L.
2018-05-01
The paper presents the main factors that affect the uniformity of the thickness distribution of plating on the surface of the product. The experimental search for the optimal values of these factors is expensive and time-consuming. The problem of adequate simulation of coating processes is very relevant. The finite-difference approximation using seven-point and five-point templates in combination with the splitting method is considered as solution methods for the equations of the model. To study the correctness of the solution of equations of the mathematical model by these methods, the experiments were conducted on plating with a flat anode and cathode, which relative position was not changed in the bath. The studies have shown that the solution using the splitting method was up to 1.5 times faster, but it did not give adequate results due to the geometric features of the task under the given boundary conditions.
International Nuclear Information System (INIS)
Garcia-Parrado, Alfonso; Sanchez, Miguel
2005-01-01
Recently (Garcia-Parrado and Senovilla 2003 Class. Quantum Grav. 20 625-64) the concept of causal mapping between spacetimes, essentially equivalent in this context to the chronological map defined in abstract chronological spaces, and the related notion of causal structure, have been introduced as new tools to study causality in Lorentzian geometry. In the present paper, these tools are further developed in several directions such as (i) causal mappings-and, thus, abstract chronological ones-do not preserve two levels of the standard hierarchy of causality conditions (however, they preserve the remaining levels as shown in the above reference), (ii) even though global hyperbolicity is a stable property (in the set of all time-oriented Lorentzian metrics on a fixed manifold), the causal structure of a globally hyperbolic spacetime can be unstable against perturbations; in fact, we show that the causal structures of Minkowski and Einstein static spacetimes remain stable, whereas that of de Sitter becomes unstable, (iii) general criteria allow us to discriminate different causal structures in some general spacetimes (e.g. globally hyperbolic, stationary standard); in particular, there are infinitely many different globally hyperbolic causal structures (and thus, different conformal ones) on R 2 (iv) plane waves with the same number of positive eigenvalues in the frequency matrix share the same causal structure and, thus, they have equal causal extensions and causal boundaries
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-06-01
With any semisimple Lie algebra g we associate an infinite-dimensional Lie algebra AC(g) which is an analytic continuation of g from its root system to its root lattice. The manifest expressions for the structure constants of analytic continuations of the symplectic Lie algebras sp2 n are obtained by Poisson-bracket realizations method and AC(g) for g=sl n and so n are discussed. The representations, central extension, supersymmetric and higher spin generalizations are considered. The Virasoro theory is a particular case when g=sp 2 . (author). 9 refs
S.N.M. Ruijsenaars (Simon)
1995-01-01
textabstractWe present an explicit construction of an action-angle map for the nonrelativistic N-particle Sutherland system and for two different generalizations thereof, one of which may be viewed as a relativistic version. We use the map to obtain detailed information concerning dynamical issues
BALTOS, Georgios; VIDAKIS, Ioannis G.; BALODIS, Janis
2017-01-01
CC BY 3.0 Copyright © MCSER-Mediterranean Center of Social and Educational Research This paper aims to provide a functional assessment of a country’s dynamics at a regional power level, through the development of a tool which shall examine the working hypothesis of a given country’s “candidacy” to emerge as a regional power. The power equation applied in order to have such an evaluation has been formulated in a visually enriched and prototype format, given that particularly the geopolitics...
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
International Nuclear Information System (INIS)
Bellissard, J.
1981-07-01
We exhibit an example of a one-dimensional discrete Schroedinger operator with an almost periodic potential for which the steps of the density of states do not belong to the frequency module. This example is suggested by the K-theory
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.
Guzzo, H.; Hernández, I.; Sánchez-Valenzuela, O. A.
2014-09-01
Finite dimensional semisimple real Lie superalgebras are described via finite dimensional semisimple complex Lie superalgebras. As an application of these results, finite dimensional real Lie superalgebras mathfrak {m}=mathfrak {m}_0 oplus mathfrak {m}_1 for which mathfrak {m}_0 is a simple Lie algebra are classified up to isomorphism.
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
Groups acting on CAT(0) cube complexes
Niblo, Graham A.; Reeves, Lawrence
1997-01-01
We show that groups satisfying Kazhdan's property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(-1) Riemannian manifold which is not homotopy equivalent to any finite dimensional, locally CAT(0) cube complex.
International Nuclear Information System (INIS)
Aizawa, N; Chakrabarti, R
2007-01-01
We note that the recently introduced fuzzy torus can be regarded as a q-deformed parafermion. Based on this picture, classification of the Hermitian representations of the fuzzy torus is carried out. The result involves Fock-type representations and new finite-dimensional representations for q being a root of unity as well as already known finite-dimensional ones
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....
Further notes on convergence of the Weiszfeld algorithm
Directory of Open Access Journals (Sweden)
Brimberg Jack
2003-01-01
Full Text Available The Fermat-Weber problem is one of the most widely studied problems in classical location theory. In his previous work, Brimberg (1995 attempts to resolve a conjecture posed by Chandrasekaran and Tamir (1989 on a convergence property of the Weiszfeld algorithm, a well-known iterative procedure used to solve this problem. More recently, Canovas, Marin and Canavate (2002 provide counterexamples that appear to reopen the question. However, they do not attempt to reconcile their counterexamples with the previous work. We now show that in the light of these counterexamples, the proof is readily modified and the conjecture of Chandrasekaran and Tamir reclosed. .
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.
Diffeomorphisms Holder conjugate to Anosov diffeomorphisms
Gogolev, Andrey
2008-01-01
We show by means of a counterexample that a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to $C^3$. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is Anosov itself provided that Holder exponents of the conjugacy and its inverse are sufficiently large.
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...
Migliorati, Giovanni; Nobile, Fabio; Tempone, Raul
2015-01-01
We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability
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.
An Angle Criterion for Riesz Bases
DEFF Research Database (Denmark)
Lindner, Alexander M; Bittner, B.
1999-01-01
We present a characterization of Riesz bases in terms ofthe angles between certain finite dimensional subspaces. Correlationsbetween the bounds of the Riesz basis and the size of the angles arederived....
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.
Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces
International Nuclear Information System (INIS)
Arai, A.
1985-01-01
We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)
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.
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.
Interpolation in Spaces of Functions
Directory of Open Access Journals (Sweden)
K. Mosaleheh
2006-03-01
Full Text Available In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces
International Nuclear Information System (INIS)
Berezin, F.A.
1977-01-01
The Laplace-Cazimir operators on the Lie supergroups are defined, and their radial parts are calculated under some general assumptions on supergroup. Under the same assumptions the characters of nondegenerate irreducible finite-dimensional representations are found
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)
Existence a jednoznačnost rozdělení náhodné míry na základě konečněrozměrných projekcí
Jurčo, Adam
2015-01-01
Title: Existence and uniqueness of the distribution of a random measure given by finite dimensional projections Author: Adam Jurčo Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jan Rataj, CSc., Department of Probability and Mathe- matical Statistics Abstract: This thesis deals with the existence and uniqueness of the distribu- tion of a random measure given a system of finite-dimensional distributions. A random measure can be interpreted as a partic...
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.......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....
Barth, Timothy J.
2014-01-01
Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.
Quantization of a Hamiltonian system with an infinite number of degrees of freedom
International Nuclear Information System (INIS)
Zhidkov, P.E.
1994-01-01
We propose a method of quantization of a discrete Hamiltonian system with an infinite number of degrees of freedom. Our approach is analogous to the usual finite-dimensional quantum mechanics. We construct an infinite-dimensional Schroedinger equation. We show that it is possible to pass from the finite-dimensional quantum mechanics to our construction in the limit when the number of particles tends to infinity. In the paper rigorous mathematical methods are used. 9 refs. (author)
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians
Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan
2018-02-01
Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.
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.
Projective measure without projective Baire
DEFF Research Database (Denmark)
Schrittesser, David; Friedman, Sy David
We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a ∆13 set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.......We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a ∆13 set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal....
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.
Deductive Updating Is Not Bayesian
Markovits, Henry; Brisson, Janie; de Chantal, Pier-Luc
2015-01-01
One of the major debates concerning the nature of inferential reasoning is between counterexample-based theories such as mental model theory and probabilistic theories. This study looks at conclusion updating after the addition of statistical information to examine the hypothesis that deductive reasoning cannot be explained by probabilistic…
Logical reasoning versus information processing in the dual-strategy model of reasoning.
Markovits, Henry; Brisson, Janie; de Chantal, Pier-Luc
2017-01-01
One of the major debates concerning the nature of inferential reasoning is between counterexample-based strategies such as mental model theory and statistical strategies underlying probabilistic models. The dual-strategy model, proposed by Verschueren, Schaeken, & d'Ydewalle (2005a, 2005b), which suggests that people might have access to both kinds of strategy has been supported by several recent studies. These have shown that statistical reasoners make inferences based on using information about premises in order to generate a likelihood estimate of conclusion probability. However, while results concerning counterexample reasoners are consistent with a counterexample detection model, these results could equally be interpreted as indicating a greater sensitivity to logical form. In order to distinguish these 2 interpretations, in Studies 1 and 2, we presented reasoners with Modus ponens (MP) inferences with statistical information about premise strength and in Studies 3 and 4, naturalistic MP inferences with premises having many disabling conditions. Statistical reasoners accepted the MP inference more often than counterexample reasoners in Studies 1 and 2, while the opposite pattern was observed in Studies 3 and 4. Results show that these strategies must be defined in terms of information processing, with no clear relations to "logical" reasoning. These results have additional implications for the underlying debate about the nature of human reasoning. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
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.
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.
Li, Xiangzheng
2018-06-01
A counterexample is given to show that the product rule of the Caputo fractional derivatives does not hold except on a special point. The function-expansion method of separation variable proposed by Rui[Commun Nonlinear Sci Numer Simulat 47 (2017) 253-266] based on the product rule must be modified.
On Modal Refinement and Consistency
DEFF Research Database (Denmark)
Nyman, Ulrik; Larsen, Kim Guldstrand; Wasowski, Andrzej
2007-01-01
Almost 20 years after the original conception, we revisit several fundamental question about modal transition systems. First, we demonstrate the incompleteness of the standard modal refinement using a counterexample due to Hüttel. Deciding any refinement, complete with respect to the standard...
Humphreys, Michael S.; And Others
1989-01-01
An associative theory of memory is proposed to serve as a counterexample to claims that dissociations among episodic, semantic, and procedural memory tasks necessitate separate memory systems. The theory is based on task analyses of matching (recognition and familiarity judgments), retrieval (cued recall), and production (free association). (TJH)
Building Program Verifiers from Compilers and Theorem Provers
2015-05-14
Checking with SMT UFO • LLVM-based front-end (partially reused in SeaHorn) • Combines Abstract Interpretation with Interpolation-Based Model Checking • (no...assertions Counter-examples are long Hard to determine (from main) what is relevant Assertion Main 35 Building Verifiers from Comp and SMT Gurfinkel, 2015
Isospectral graphs with identical nodal counts
International Nuclear Information System (INIS)
Oren, Idan; Band, Ram
2012-01-01
According to a recent conjecture, isospectral objects have different nodal count sequences (Gnutzmann et al 2005 J. Phys. A: Math. Gen. 38 8921–33). We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counterexamples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs. (paper)
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
Temporal logic runtime verification of dynamic systems
CSIR Research Space (South Africa)
Seotsanyana, M
2010-07-01
Full Text Available , this paper provides a novel framework that automatically and verifiably monitors these systems at runtime. The main aim of the framework is to assist the operator through witnesses and counterexamples that are generated during the execution of the system...
Sequential models for coarsening and missingness
Gill, R.D.; Robins, J.M.
1997-01-01
In a companion paper we described what intuitively would seem to be the most general possible way to generate Coarsening at Random mechanisms a sequential procedure called randomized monotone coarsening Counterexamples showed that CAR mechanisms exist which cannot be represented in this way Here we
Conservative interacting particles system with anomalous rate of ergodicity
Brzeźniak, Zdzislaw; Flandoli, Franco; Neklyudov, Misha; Zegarliński, Boguslaw
2010-01-01
We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence.
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...
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
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...
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...
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...
When can a language have adjectives? An implicational universal
DEFF Research Database (Denmark)
Rijkhoff, Jan
1999-01-01
Data from a representative sample of the world's languages indicate that adjectives only occur in languages in which the numeral is in a direct construction with a noun (i.e. the numeral does not occur with a sortal classifier). In my sample Hmong Njua is the only counterexample, but I will show ...
When can a language have adjectives? An implicational universal
DEFF Research Database (Denmark)
Rijkhoff, Jan
2000-01-01
Data from a representative sample of the world's languages indicate that adjectives only occur in languages in which the numeral is in a direct construction with a noun (i.e. the numeral does not occur with a sortal classifier). In my sample Hmong Njua is the only counterexample, but I will show ...
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…
Greenslade, Thomas B.
2010-04-01
Students all know that reflection from a plane mirror produces an image that is reversed right to left and so cannot be read by anyone but Leonardo da Vinci, who kept his notes in mirror writing. A useful counter-example is the Porro prism, which produces an image that is not reversed.
Frenette, Micheline
Trying to change the predictive rule for the sinking and floating phenomena, students have a great difficulty in understanding density and they are insensitive to empirical counter-examples designed to challenge their own rule. The purpose of this study is to examine the process whereby students from sixth and seventh grades relinquish their…
Meaning in Life and the Metaphysics of Value
Evers, Daan
2017-01-01
According to subjectivist views about a meaningful life, one's life is meaningful in virtue of desire satisfaction or feelings of fulfilment. Standard counterexamples consist of satisfaction found through trivial or immoral tasks. In response to such examples, many philosophers require that the
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
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...
A Primer on the Pathway to Scholarly Writing: Helping Nascent Writers to Unlearn Conditioned Habits
McDougall, Dennis; Ornelles, Cecily; Rao, Kavita
2015-01-01
In this article, we identify eight common error patterns of nascent writers when they attempt to navigate the pathway to scholarly writing. We illustrate each error pattern via examples and counter-examples (corrections). We also describe how to identify such patterns, why those patterns might occur and persist, and why each pattern is…
Papapetrou's naked singularity is a strong curvature singularity
Energy Technology Data Exchange (ETDEWEB)
Hollier, G.P.
1986-11-01
Following Papapetrou (1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)), a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture.
Variability-Specific Abstraction Refinement for Family-Based Model Checking
DEFF Research Database (Denmark)
Dimovski, Aleksandar; Wasowski, Andrzej
2017-01-01
and property, while the number of possible scenarios is very large. In this work, we present an automatic iterative abstraction refinement procedure for family-based model checking. We use Craig interpolation to refine abstract variational models based on the obtained spurious counterexamples (traces...
Logical Reasoning versus Information Processing in the Dual-Strategy Model of Reasoning
Markovits, Henry; Brisson, Janie; de Chantal, Pier-Luc
2017-01-01
One of the major debates concerning the nature of inferential reasoning is between counterexample-based strategies such as mental model theory and statistical strategies underlying probabilistic models. The dual-strategy model, proposed by Verschueren, Schaeken, & d'Ydewalle (2005a, 2005b), which suggests that people might have access to both…
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.
Topics in Corpus-Based Dutch Syntax
Beek, Leonoor Johanneke van der
2005-01-01
In this dissertation, corpus data is applied in various kinds of linguistic analyses. The data serves as a source of examples and counterexamples in a theoretical linguistic analysis of the Dutch cleft construction, as the source of quantitative data in a probabilistic account of the dative
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
On the nature of naked singularities in Vaidya spacetimes
Energy Technology Data Exchange (ETDEWEB)
Dwivedi, I.H. (Aligarh Muslim Univ. (India). Dept. of Physics); Joshi, P.S. (Tata Inst. of Fundamental Research, Bombay (India))
1989-11-01
The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author).
Papapetrou's naked singularity is a strong curvature singularity
International Nuclear Information System (INIS)
Hollier, G.P.
1986-01-01
Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)
On the nature of naked singularities in Vaidya spacetimes
International Nuclear Information System (INIS)
Dwivedi, I.H.
1989-01-01
The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author)
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 ...
Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations
International Nuclear Information System (INIS)
Xu Xixiang
2012-01-01
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. (general)
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
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
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
From racks to pointed Hopf algebras
Andruskiewitsch, Nicolás; Graña, Matı́as
2003-01-01
A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided vector spaces arising from groups is the class of braided vector spaces (CX, c^q), where C is the field of complex numbers, X is a rack and q is a 2-cocycle on X with values in C^*. Racks and cohomology of racks appeared also in the work of topologists. This...
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
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.
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.
An L∞/L1-Constrained Quadratic Optimization Problem with Applications to Neural Networks
International Nuclear Information System (INIS)
Leizarowitz, Arie; Rubinstein, Jacob
2003-01-01
Pattern formation in associative neural networks is related to a quadratic optimization problem. Biological considerations imply that the functional is constrained in the L ∞ norm and in the L 1 norm. We consider such optimization problems. We derive the Euler-Lagrange equations, and construct basic properties of the maximizers. We study in some detail the case where the kernel of the quadratic functional is finite-dimensional. In this case the optimization problem can be fully characterized by the geometry of a certain convex and compact finite-dimensional set
Simple 2-representations and Classification of Categorifications
DEFF Research Database (Denmark)
Agerholm, Troels
We consider selfadjoint functors defined on categories of modules over finite dimensional algebras and classify those that satisfy some simple relations. In particular we classify self- adjoint idempotents and selfadjoint squareroots of a multiple of the identity functor. This is related to the t......We consider selfadjoint functors defined on categories of modules over finite dimensional algebras and classify those that satisfy some simple relations. In particular we classify self- adjoint idempotents and selfadjoint squareroots of a multiple of the identity functor. This is related...
Extreme cognitions are associated with diminished ability to use disconfirming evidence.
Haigh, Matthew; Dodd, Alyson L
2017-03-01
An Integrative Cognitive Model of mood swings and bipolar disorder proposes that cognitive styles characterized by extreme self-referent appraisals of internal states (e.g., 'If I have a bad night's sleep it means that I am about to have a breakdown') interfere with mood regulation. The aim of this study is to determine whether strong endorsement of such appraisals is predicted by a diminished ability to access disconfirming counterexamples. We examined whether the ability to access two different categories of counterexample (known as Disabling Conditions and Alternative Causes) would predict endorsement of extreme appraisals (measured by the Hypomanic Attitudes and Positive Predictions Inventory; HAPPI) and mania risk (measured by the Hypomanic Personality Scale; HPS). A non-clinical sample of 150 students completed the HAPPI, the HPS and a conditional reasoning task that indexed the ability to access Disabling Conditions and Alternative Causes. Current mood was controlled for using the Internal States Scale. The ability to make use of disabling counterexamples during the reasoning task was inversely related with scores on the HAPPI (r = -.19, p referent appraisals to a greater extent. There was no association between the use of alternative cause counterexamples and the HAPPI, and no association between either measure of counterexample generation and the HPS. A diminished ability to use disconfirming evidence when reasoning about the world may reinforce problematic cognitive styles such as extreme, personalized appraisals of experience, which can interfere with mood regulation. Problematic cognitive styles such as extreme, personalized appraisals of experience may be reinforced by the inability to produce or access evidence that disconfirms these maladaptive beliefs. This reasoning bias may be associated with cognitive styles underlying psychopathology. There may be clinical utility in exploring the use of disabler generation in psychological interventions, to
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.
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
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.
Testing a parametric function against a nonparametric alternative in IV and GMM settings
DEFF Research Database (Denmark)
Gørgens, Tue; Wurtz, Allan
This paper develops a specification test for functional form for models identified by moment restrictions, including IV and GMM settings. The general framework is one where the moment restrictions are specified as functions of data, a finite-dimensional parameter vector, and a nonparametric real ...
Locally semisimple algebras. Combinatorial theory and the K0-functor
International Nuclear Information System (INIS)
Vershik, A.M.; Kerov, S.V.
1987-01-01
Survey is devoted to theory of locally finite algebras and approximately finite-dimensional absolute value of AF- C*-algebras which has been developed intensively in recent years. It can serve as an introduction to the subject. Both known and new results are contained in it
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
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.
Amenable crossed product Banach algebras associated with a class of C*-dynamical systems
Jeu, de M.F.E.; Elharti, R.; Pinto, P.R.
2017-01-01
We prove that the crossed product Banach algebra ℓ1(G,A;α) that is associated with a C∗-dynamical system (A,G,α) is amenable if G is a discrete amenable group and A is a commutative or finite dimensional C∗-algebra. Perspectives for further developments are indicated.
q-structure algebra of Uq(g-circumflex) from its adjoint action
International Nuclear Information System (INIS)
El Hassouni, A.; Hassouni, Y.; Zakkari, M.
1994-08-01
We prove that the adjoint action of the quantum affine Lie algebra U q (g-circumflex), where g is a simple finite dimensional Lie algebra, reproduces the q-commutation relationship of U q (g-circumflex) if and only if g is of type A n , n ≥ 1. (author). 4 refs
The Finite-Horizon Singular H∞ Control Problem With Dynamic Measurement Feedback
Stoorvogel, A.A.; Trentelman, H.L.
1993-01-01
This paper is concerned with the finite-horizon version of the H∞ problem with measurement feedback. Given a finite-dimensional linear, time-varying system, together with a positive real number γ, we obtain necessary and sufficient conditions for the existence of a possibly time-varying dynamic
Circular arc snakes and kinematic surface generation
Barton, Michael; Shi, Ling; Kilian, Martin; Wallner, Johannes; Pottmann, Helmut
2013-01-01
of circular arcs is well suited for such purposes, and allows us to reduce evolution of curves to the evolution of a control point collection in a certain finite-dimensional shape space. We approach this evolution by a 2-step process: linearized evolution via
Safety Verification of Piecewise-Deterministic Markov Processes
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer; Bujorianu, Manuela
2016-01-01
the moment method, we can translate the infinite-dimensional optimisation problem searching for the largest set of p-safe states to a finite dimensional polynomial optimisation problem. We have implemented this technique on top of GloptiPoly and show how to apply it to a numerical example....
Moment Restriction-based Econometric Methods: An Overview
N. Kunitomo (Naoto); M.J. McAleer (Michael); Y. Nishiyama (Yoshihiko)
2010-01-01
textabstractMoment restriction-based econometric modelling is a broad class which includes the parametric, semiparametric and nonparametric approaches. Moments and conditional moments themselves are nonparametric quantities. If a model is specified in part up to some finite dimensional parameters,
On the structure of transitively differential algebras
Post, Gerhard F.
1999-01-01
We study finite-dimensional Lie algebras of polynomial vector fields in $n$ variables that contain the vector fields ${\\partial}/{\\partial x_i} \\; (i=1,\\ldots, n)$ and $x_1{\\partial}/{\\partial x_1}+ \\dots + x_n{\\partial}/{\\partial x_n}$. We derive some general results on the structure of such Lie
On the structure of graded transitive Lie algebras
Post, Gerhard F.
2000-01-01
We study finite-dimensional Lie algebras ${\\mathfrak L}$ of polynomial vector fields in $n$ variables that contain the vector fields $\\dfrac{\\partial}{\\partial x_i} \\; (i=1,\\ldots, n)$ and $x_1\\dfrac{\\partial}{\\partial x_1}+ \\dots + x_n\\dfrac{\\partial}{\\partial x_n}$. We show that the maximal ones
On selfadjoint functors satisfying polynomial relations
DEFF Research Database (Denmark)
Agerholm, Troels; Mazorchuk, Volodomyr
2011-01-01
We study selfadjoint functors acting on categories of finite dimen- sional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint func- tors satisfying several easy relations, in particular, idempotents and square roots of a sum...
Comparison of Poisson structures and Poisson-Lie dynamical r-matrices
Enriquez, B.; Etingof, P.; Marshall, I.
2004-01-01
We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices of Balog-Feher-Palla.
Directory of Open Access Journals (Sweden)
Khvedelidze Arsen
2018-01-01
Full Text Available The generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. In particular, we consider the generation of random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.
Description of the electron-hydrogen collision by the Coulomb Fourier transform method
International Nuclear Information System (INIS)
Levin, S.B.
2005-01-01
A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals
Quadratic brackets from symplectic forms
International Nuclear Information System (INIS)
Alekseev, Anton Yu.; Todorov, Ivan T.
1994-01-01
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))
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.
Precuantización en difeologías suaves
Directory of Open Access Journals (Sweden)
Carlos Torre
2009-02-01
Full Text Available We define a prequantization in the category of smooth diffeological spaces ( a category which includes finite an infinite dimensional systems, in the case where the symplectic form is exact, extending, for this case, the results of Kirillov, Kostant and Souriau which are devoloped for finite dimensional Physical systems.
Twisting products in Hopf algebras and the construction of the quantum double
International Nuclear Information System (INIS)
Ferrer Santos, W.R.
1992-04-01
Let H be a finite dimensional Hopf algebra and B an (H, H*)-comodule algebra. The purpose of this note is to present a construction in which the product of B is twisted by the given actions. The constructions of the smash product and of the Quantum Double appear as special cases. (author). 7 refs
Quantum Riemann surfaces. Pt. 2; The discrete series
Energy Technology Data Exchange (ETDEWEB)
Klimek, S. (Dept. of Mathematics, IUPUI, Indianapolis, IN (United States)); Lesniewski, A. (Dept. of Physics, Harvard Univ., Cambridge, MA (United States))
1992-02-01
We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of C{sup *}-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional C{sup *}-algebras. (orig.).
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 ...
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
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.
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
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 ...
Nurbekyan, Levon
2017-01-01
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.
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.
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., volum...
Turing patterns and long-time behavior in a three-species food-chain model
Parshad, Rana D.; Kumari, Nitu Krishna; Kasimov, Aslan R.; Ait Abderrahmane, Hamid
2014-01-01
We consider a spatially explicit three-species food chain model, describing generalist top predator-specialist middle predator-prey dynamics. We investigate the long-time dynamics of the model and show the existence of a finite dimensional global
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.
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.
Weierstrass preparation and division theorems for the ring of germs of superanalytic functions
International Nuclear Information System (INIS)
Yankov, C.L.
1989-11-01
The aim of this paper is to show that Weierstrass preparation and division theorems hold for the ring of germs of superanalytic functions at a given point. This ring is the tensor product of the ring of germs of analytic functions at that point and a finite-dimensional complex Grassmann algebra. 7 refs
A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter
Brigo, D.; Hanzon, B.; LeGland, F.
1998-01-01
This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is
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
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.)
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...
Alternative Hamiltonian description for quantum systems
International Nuclear Information System (INIS)
Dubrovin, B.A.; Marno, G.; Simoni, A.
1990-01-01
The existence of time-invariant Kahler structures is analyzed in both Classical and Quantum Mechanics. In Quantum Mechanics, a family of such Kahler structures is found, in the finite-dimensional case it is proven that this family is complete
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
Port-based modeling of a flexible link
Macchelli, A.; Macchelli, A.; Hirohika, A.; Lynch, K.; Melchiorri, C.; Park, F.C.; Stramigioli, Stefano; Parker, L.E.
In this paper, a simple way to model flexible robotic links is presented. This is different from classical approaches and from the Euler–Bernoulli or Timoshenko theory, in that the proposed model is able to describe large deflections in 3-D space and does not rely on any finite-dimensional
Duality in non-linear programming
Jeyalakshmi, K.
2018-04-01
In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.
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.
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.
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.
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.
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.
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...
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
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 actions of algebraic groups | Omokaro | Journal of the Nigerian ...
African Journals Online (AJOL)
In [6] we discussed the Lie Algebra associated with an algebraic group G. In this work, we employ morphical action of G to obtain a necessary and sufficient condition for a finite dimensional subspace F of K[X] to be stable under all translations where K[X] denotes the set of polynomials in the variables x1,x2, …, xn.
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 ...
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.)
The Heun equation and the Calogero-Moser-Sutherland system II: Perturbation and algebraic solution
Directory of Open Access Journals (Sweden)
Kouichi Takemura
2004-02-01
Full Text Available We apply a method of perturbation for the $BC_1$ Inozemtsev model from the trigonometric model and show the holomorphy of perturbation. Consequently, the convergence of eigenvalues and eigenfuncions which are expressed as formal power series is proved. We investigate also the relationship between $L^2$ space and some finite dimensional space of elliptic functions.
Representation theory of current algebra and conformal field theory on Riemann surfaces
International Nuclear Information System (INIS)
Yamada, Yasuhiko
1989-01-01
We study conformal field theories with current algebra (WZW-model) on general Riemann surfaces based on the integrable representation theory of current algebra. The space of chiral conformal blocks defined as solutions of current and conformal Ward identities is shown to be finite dimensional and satisfies the factorization properties. (author)
Physical states in Quantum Einstein-Cartan Gravity
Cianfrani, Francesco
2016-01-01
The definition of physical states is the main technical issue of canonical approaches towards Quantum Gravity. In this work, we outline how those states can be found in Einstein-Cartan theory via a continuum limit and they are given by finite dimensional representations of the Lorentz group.
The construction of representations of Lie supergroups U(p,q) and C(m,n)
International Nuclear Information System (INIS)
Berezin, F.A.
1977-01-01
The construction of finite-dimensional representations of the Lie supergroups under some general assumptions is given. It is shown that U(p,q) and C(m,n) supergroups satisfy these assumptions. The detailed study of representations of U(p,q) supergroup is given
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
Some functional solutions of the Yang-Baxter equation
International Nuclear Information System (INIS)
Stoyanov, D.Ts.
1994-09-01
A general functional definition of the infinite dimensional quantum R-matrix satisfying the Yang-Baxter equation is given. A procedure for extracting a finite dimensional R-matrix from the general definition is demonstrated in a particular case when the group SU(2) takes place. (author). 6 refs
Quantum operations that cannot be implemented using a small mixed environment
International Nuclear Information System (INIS)
Zalka, Christof; Rieffel, Eleanor
2002-01-01
To implement any quantum operation (a.k.a. ''superoperator'' or ''CP map'') on a d-dimensional quantum system, it is enough to apply a suitable overall unitary transformation to the system and a d 2 -dimensional environment which is initialized in a fixed pure state. It has been suggested that a d-dimensional environment might be enough if we could initialize the environment in a mixed state of our choosing. In this note we show with elementary means that certain explicit quantum operations cannot be realized in this way. Our counterexamples map some pure states to pure states, giving strong and easily manageable conditions on the overall unitary transformation. Everything works in the more general setting of quantum operations from d-dimensional to d ' -dimensional spaces, so we place our counterexamples within this more general framework
The Argument Form "Appeal to Galileo": A Critical Appreciation of Doury’s Account
Directory of Open Access Journals (Sweden)
Maurice A Finocchiaro
2015-09-01
Full Text Available Following a linguistic-descriptivist approach, Marianne Doury has studied debates about “parasciences” (e.g. astrology, discovering that “parascientists” frequently argue by “appeal to Galileo” (i.e., defend their views by comparing themselves to Galileo and their opponents to the Inquisition; opponents object by criticizing the analogy, charging fallacy, and appealing to counter-examples. I argue that Galilean appeals are much more widely used, by creationists, global-warming skeptics, advocates of “settled science”, great scientists, and great philosophers. Moreover, several subtypes should be distinguished; critiques questioning the analogy are proper; fallacy charges are problematic; and appeals to counter-examples are really indirect critiques of the analogy.
Logic, Probability, and Human Reasoning
2015-01-01
accordingly suggest a way to integrate probability and deduction. The nature of deductive reasoning To be rational is to be able to make deductions...3–6] and they underlie mathematics, science, and tech- nology [7–10]. Plato claimed that emotions upset reason- ing. However, individuals in the grip...fundamental to human rationality . So, if counterexamples to its principal predictions occur, the theory will at least explain its own refutation
On a total function which overtakes all total recursive functions
da Costa, N. C. A.; Doria, F. A.
2001-01-01
This paper discusses a function that is frequently presented as a simile or look-alike of the so-called ``counterexample function to P=NP,'' that is, the function that collects all first instances of a problem in NP where a poly machine incorrectly `guesses' about the instance. We state and give in full detail a crucial result on the computation of Goedel numbers for some families of poly machines.
A simple necessary decoherence condition for a set of histories
International Nuclear Information System (INIS)
Scherer, Artur; Soklakov, Andrei N.; Schack, Ruediger
2004-01-01
Within the decoherent histories formulation of quantum mechanics, we investigate necessary conditions for decoherence of arbitrarily long histories. We prove that fine-grained histories of arbitrary length decohere for all classical initial states if and only if the unitary evolution preserves classicality of states (using a natural formal definition of classicality). We give a counterexample showing that this equivalence does not hold for coarse-grained histories
On the Partiality of Procreative Beneficence
DEFF Research Database (Denmark)
Petersen, Thomas Søbirk
2015-01-01
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...... 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....
EOG feature relevance determination for microsleep detection
Golz Martin; Wollner Sebastian; Sommer David; Schnieder Sebastian
2017-01-01
Automatic relevance determination (ARD) was applied to two-channel EOG recordings for microsleep event (MSE) recognition. 10 s immediately before MSE and also before counterexamples of fatigued, but attentive driving were analysed. Two type of signal features were extracted: the maximum cross correlation (MaxCC) and logarithmic power spectral densities (PSD) averaged in spectral bands of 0.5 Hz width ranging between 0 and 8 Hz. Generalised learn-ing vector quantisation (GRLVQ) was used as ARD...
Bounds and maximum principles for the solution of the linear transport equation
International Nuclear Information System (INIS)
Larsen, E.W.
1981-01-01
Pointwise bounds are derived for the solution of time-independent linear transport problems with surface sources in convex spatial domains. Under specified conditions, upper bounds are derived which, as a function of position, decrease with distance from the boundary. Also, sufficient conditions are obtained for the existence of maximum and minimum principles, and a counterexample is given which shows that such principles do not always exist
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...
Imperfect Commitment and the Revelation Principle: the Multi-Agent Case with Transferable Utility
Evans, R.; Reich, S.
2007-01-01
Bester and Strausz (2000) showed that the revelation principle of Bester and Strausz (2001) does not apply in a setting of many agents and no commitment. In their counterexample only one agent has private information. We show that if the parties can make ex ante transfers the revelation principle does extend to this setting. However, we show that it does not extend to a setting in which more than one agent has private information.
2013-08-01
in a linear scaling with vehicle weight. • Counter-examples to linear scaling, such as torsion rods , account only for a small fraction (< 10%) of...at the maximum cabin height comes out to be 61 cm which is consistent with previous designs. We wish to keep as much flexibility for the designer...the ground via the track shoe(s). If we assume the track is perfectly flexible , one can estimate the sinkage by:10 0 = 6 5 √
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
Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation
Wu, Lei
2014-01-01
We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.
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.
Evidence for an electrifying violation of cosmic censorship
International Nuclear Information System (INIS)
Horowitz, Gary T; Santos, Jorge E; Way, Benson
2016-01-01
We present a plausible counterexample to cosmic censorship in four-dimensional Einstein–Maxwell theory with asymptotically anti-de Sitter boundary conditions. Smooth initial data evolves to a region of arbitrarily large curvature that is visible to distant observers. Our example is based on a holographic model of an electrically charged, localised defect which was previously studied at zero temperature. We partially extend those results to nonzero temperatures. (paper)
Thin charged shells and the violation of the third law of black hole mechanics
International Nuclear Information System (INIS)
Proszynski, M.
1983-01-01
The collapse of an infinitely thin spherical shell of charged matter, which surrounds a spherically symmetric black hole or has a flat interior, is analyzed in connection with the laws of black hole mechanics and the cosmic censorship hypothesis. An effective potential is introduced to describe the motion of the shell. The process, proposed by Farrugia and Hajicek as a counterexample to the third law, is discussed and generalized to the case of nondust shells. (author)
Risteski, Ice B.
2010-01-01
In this article, the author discovers a paradox of balancing chemical equations. The many counterexamples illustrate that the considered procedure of balancing chemical equations given in the paper1 is inconsistent. A new complex vector method for paradox resolution is given too. V članku avtor opisuje paradoks pri uravnoteženju kemijskih reakcij. Več primerov dokazuje, da je procedura uravnoteženja kemijskih reakcij v viru1 inkonsistentna. Predstavljena je nova kompleksna vektorska metoda...
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)
Reasoning strategies modulate gender differences in emotion processing.
Markovits, Henry; Trémolière, Bastien; Blanchette, Isabelle
2018-01-01
The dual strategy model of reasoning has proposed that people's reasoning can be understood asa combination of two different ways of processing information related to problem premises: a counterexample strategy that examines information for explicit potential counterexamples and a statistical strategy that uses associative access to generate a likelihood estimate of putative conclusions. Previous studies have examined this model in the context of basic conditional reasoning tasks. However, the information processing distinction that underlies the dual strategy model can be seen asa basic description of differences in reasoning (similar to that described by many general dual process models of reasoning). In two studies, we examine how these differences in reasoning strategy may relate to processing very different information, specifically we focus on previously observed gender differences in processing negative emotions. Study 1 examined the intensity of emotional reactions to a film clip inducing primarily negative emotions. Study 2 examined the speed at which participants determine the emotional valence of sequences of negative images. In both studies, no gender differences were observed among participants using a counterexample strategy. Among participants using a statistical strategy, females produce significantly stronger emotional reactions than males (in Study 1) and were faster to recognize the valence of negative images than were males (in Study 2). Results show that the processing distinction underlying the dual strategy model of reasoning generalizes to the processing of emotions. Copyright © 2017 Elsevier B.V. All rights reserved.
Os anulabilismos de Klein e de Swain e o problema de Gettier
Directory of Open Access Journals (Sweden)
Emerson Carlos Valcarenghi
2010-08-01
Full Text Available In this essay, we intend to show that Peter Klein and Marshall Swain defeasibility theories do not resolve the Gettier problem. Klein postulates, to any Gettier counterexample, that there is a true proposition which, when associated with evidence-e of S, genuinely defeats the justification of p to S. Swain postulates that, to any Gettier-type counterexample, there is a true proposition which, when associated with the set of reasons-R of S, ultimately defeats the justification of S to believe p. To show that Klein an Swain proposals do not resolve that problem, this essay presents two Gettier-type counterexamples for which there are no genuine defeaters of justification of p by e to S and there are no defeaters not ultimately defeated of the justification of the belief of S that p by R. After doing that, we try to show that the obtained conclusion regarding Klein and Swain defeasibility theories can be extended to any defeasibility theory of knowledge.
Directory of Open Access Journals (Sweden)
Joe Milburn
2015-05-01
Full Text Available http://dx.doi.org/10.5007/1808-1711.2015v19n2p183 We can call any reductive account of knowledge that appeals to both safety and ability conditions a mixed account of knowledge. Examples of mixed accounts of knowledge include Pritchard’s (2012 Anti-Luck Virtue Epistemology, Kelp’s (2013 Safe-Apt account of knowledge, and Turri’s (2011 Ample belief account of knowledge. Mixed accounts of knowledge are motivated by well-known counterexamples to pure safety and pure ability accounts of knowledge. It is thought that by combining both safety and ability conditions we can give an extensionally adequate reductive account of knowledge. In this paper I argue that the putative counterexamples to pure safety and pure ability accounts of knowledge fail to motivate mixed accounts of knowledge. In particular, I argue that if the putative counterexamples are problematic for safety accounts they are problematic for ability accounts and vice-versa. The reason for this, I argue, is that the safety condition and ability condition should be understood as alternative expressions of the same intuition — that knowledge must come from a reliable source.
Tensor products of quantized tilting modules
International Nuclear Information System (INIS)
Andersen, H.H.
1992-01-01
Let U k denote the quantized enveloping algebra corresponding to a finite dimensional simple complex Lie algebra L. Assume that the quantum parameter is a root of unity in k of order at least the Coxeter number for pound. Also assume that this order is odd and not divisible by 3 if type G 2 occurs. We demonstrate how one can define a reduced tensor product on the family F consisting of those finite dimensional simple U k -modules which are deformations of simple L-modules and which have non-zero quantum dimension. This together with the work of Reshetikhin-Turaev and Turaev-Wenzl prove that (U k , F) is a modular Hopf algebra and hence produces invariants of 3-manifolds. Also by recent work of Duurhus, Jakobsen and Nest it leads to a general topological quantum field theory. The method of proof explores quantized analogues of tilting modules for algebraic groups. (orig.)
The Pegg–Barnett phase operator and the discrete Fourier transform
International Nuclear Information System (INIS)
Perez-Leija, Armando; Szameit, Alexander; Andrade-Morales, Luis A; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M
2016-01-01
In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg–Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London–Susskind–Glogower phase operator, whose natural logarithm gives rise to the Pegg–Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties. (invited comment)
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.
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
Infinite-dimensional Z2sup(k)-supermanifolds
International Nuclear Information System (INIS)
Molotkov, V.
1984-10-01
In this paper the theory of finite-dimensional supermanifolds of Berezin, Leites and Kostant is generalized in two directions. First, we introduce infinite-dimensional supermanifolds ''locally isomorphic'' to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped with some additional structure) from the category of finite-dimensional Grassman superalgebras into the category of the corresponding smooth manifolds (Banach or locally convex). As examples, flag supermanifolds of Banach superspaces as well as unitary supergroups of Hilbert superspaces are constructed. Second, we define ''generalized'' supermanifolds, graded by Abelian groups Z 2 sup(k), instead of the group Z 2 (Z 2 sup(k)-supermanifolds). The corresponding superfields, describing, potentially, particles with more general statistics than Bose + Fermi, generally speaking, turn out to have an infinite number of components. (author)
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)
International Nuclear Information System (INIS)
Kong Linghua; Hong Jialin; Liu Ruxun
2008-01-01
In this paper, we propose a family of symplectic structure-preserving numerical methods for the coupled Klein-Gordon-Schroedinger (KGS) system. The Hamiltonian formulation is constructed for the KGS. We discretize the Hamiltonian system in space first with a family of canonical difference methods which convert an infinite-dimensional Hamiltonian system into a finite-dimensional one. Next, we discretize the finite-dimensional system in time by a midpoint rule which preserves the symplectic structure of the original system. The conservation laws of the schemes are analyzed in succession, including the charge conservation law and the residual of energy conservation law, etc. We analyze the truncation errors and global errors of the numerical solutions for the schemes to end the theoretical analysis. Extensive numerical tests show the accordance between the theoretical and numerical results
Dynamical decoupling of unbounded Hamiltonians
Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin
2018-03-01
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
Partition function expansion on region graphs and message-passing equations
International Nuclear Information System (INIS)
Zhou, Haijun; Wang, Chuang; Xiao, Jing-Qing; Bi, Zedong
2011-01-01
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)
A Monte Carlo simulation model for stationary non-Gaussian processes
DEFF Research Database (Denmark)
Grigoriu, M.; Ditlevsen, Ove Dalager; Arwade, S. R.
2003-01-01
includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second...... athe proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes. Keywords: Monte Carlo simulation, non-Gaussian processes, sampling theorem, stochastic processes, translation processes......A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes...
State-independent error-disturbance trade-off for measurement operators
International Nuclear Information System (INIS)
Zhou, S.S.; Wu, Shengjun; Chau, H.F.
2016-01-01
In general, classical measurement statistics of a quantum measurement is disturbed by performing an additional incompatible quantum measurement beforehand. Using this observation, we introduce a state-independent definition of disturbance by relating it to the distinguishability problem between two classical statistical distributions – one resulting from a single quantum measurement and the other from a succession of two quantum measurements. Interestingly, we find an error-disturbance trade-off relation for any measurements in two-dimensional Hilbert space and for measurements with mutually unbiased bases in any finite-dimensional Hilbert space. This relation shows that error should be reduced to zero in order to minimize the sum of error and disturbance. We conjecture that a similar trade-off relation with a slightly relaxed definition of error can be generalized to any measurements in an arbitrary finite-dimensional Hilbert space.
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.
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.)
DEFF Research Database (Denmark)
Tatu, Aditya Jayant
This thesis deals with two unrelated issues, restricting curve evolution to subspaces and computing image patches in the equivalence class of Histogram of Gradient orientation based features using nonlinear projection methods. Curve evolution is a well known method used in various applications like...... tracking interfaces, active contour based segmentation methods and others. It can also be used to study shape spaces, as deforming a shape can be thought of as evolving its boundary curve. During curve evolution a curve traces out a path in the infinite dimensional space of curves. Due to application...... specific requirements like shape priors or a given data model, and due to limitations of the computer, the computed curve evolution forms a path in some finite dimensional subspace of the space of curves. We give methods to restrict the curve evolution to a finite dimensional linear or implicitly defined...
Optimal control of tokamak and stellarator plasma behaviour
International Nuclear Information System (INIS)
Rastovic, Danilo
2007-01-01
The control of plasma transport, laminar and turbulent, is investigated, using the methods of scaling, optimal control and adaptive Monte Carlo simulations. For this purpose, the asymptotic behaviour of kinetic equation is considered in order to obtain finite-dimensional invariant manifolds, and in this way the finite-dimensional theory of control can be applied. We imagine the labyrinth of open doors and after applying self-similarity, the motion moved through all the desired doors in repeatable ways as Brownian motions. We take local actions for each piece of contractive ergodic motion, and, after self-organization in adaptive invariant measures, the optimum movement of particles is obtained according to the principle of maximum entropy. This is true for deterministic and stochastic cases that serve as models for plasma dynamics
International Nuclear Information System (INIS)
Ferrie, Christopher; Emerson, Joseph
2008-01-01
Several finite-dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite-dimensional quantum systems. Moreover, we show that any quasi-probability representation is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus. (fast track communication)
An embedding of the universal Askey-Wilson algebra into Uq (sl2) ⊗Uq (sl2) ⊗Uq (sl2)
Huang, Hau-Wen
2017-09-01
The Askey-Wilson algebras were used to interpret the algebraic structure hidden in the Racah-Wigner coefficients of the quantum algebra Uq (sl2). In this paper, we display an injection of a universal analog △q of Askey-Wilson algebras into Uq (sl2) ⊗Uq (sl2) ⊗Uq (sl2) behind the application. Moreover we establish the decomposition rules for 3-fold tensor products of irreducible Verma Uq (sl2)-modules and of finite-dimensional irreducible Uq (sl2)-modules into the direct sums of finite-dimensional irreducible △q-modules. As an application, we derive a formula for the Racah-Wigner coefficients of Uq (sl2).
An embedding of the universal Askey–Wilson algebra into Uq(sl2⊗Uq(sl2⊗Uq(sl2
Directory of Open Access Journals (Sweden)
Hau-Wen Huang
2017-09-01
Full Text Available The Askey–Wilson algebras were used to interpret the algebraic structure hidden in the Racah–Wigner coefficients of the quantum algebra Uq(sl2. In this paper, we display an injection of a universal analog △q of Askey–Wilson algebras into Uq(sl2⊗Uq(sl2⊗Uq(sl2 behind the application. Moreover we establish the decomposition rules for 3-fold tensor products of irreducible Verma Uq(sl2-modules and of finite-dimensional irreducible Uq(sl2-modules into the direct sums of finite-dimensional irreducible △q-modules. As an application, we derive a formula for the Racah–Wigner coefficients of Uq(sl2.
Maximum principles and sharp constants for solutions of elliptic and parabolic systems
Kresin, Gershon
2012-01-01
The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
Land of Addicts? An Empirical Investigation of Habit-Based Asset Pricing Behavior
Xiaohong Chen; Sydney C. Ludvigson
2004-01-01
This paper studies the ability of a general class of habit-based asset pricing models to match the conditional moment restrictions implied by asset pricing theory. We treat the functional form of the habit as unknown, and to estimate it along with the rest of the model's finite dimensional parameters. Using quarterly data on consumption growth, assets returns and instruments, our empirical results indicate that the estimated habit function is nonlinear, the habit formation is better described...
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 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....
Selfdual strings and loop space Nahm equations
International Nuclear Information System (INIS)
Gustavsson, Andreas
2008-01-01
We give two independent arguments why the classical membrane fields should be take values in a loop algebra. The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations. The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as su(N) for any N) that satisfies the algebraic structure of the membrane theory
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
On δ-derivations of n-ary algebras
International Nuclear Information System (INIS)
Kaygorodov, Ivan B
2012-01-01
We give a description of δ-derivations of (n+1)-dimensional n-ary Filippov algebras and, as a consequence, of simple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero. We also give new examples of non-trivial δ-derivations of Filippov algebras and show that there are no non-trivial δ-derivations of the simple ternary Mal'tsev algebra M 8 .
Robust Performance And Dissipation of Stochastic Control Systems
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro
and topology on the space of supply rates. For instance, we give conditions under which the available storage is a continuous convex function of the supply rate. Dissipation theory in the existing literature applies only to deterministic systems. This is unfortunate since robust control applications typically...... is a prototype of robust adaptive control problems. We show that the optimal (minimax) controller for this problem is finite dimensional but not based on certainty equivalence, and we discuss the heuristic certainty equivalence controller....
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 mai...... tool is a quantum version of symmetric Howe duality. As a corollary of our construction, we provide new insight into Jones-Wenzl projectors and the colored Jones polynomials....
2016-09-13
lems arising, for example, after discretization of optimal control problems. Lucien developed a general framework for quantifying near-optimality...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
Gelfand-Dikii Hamiltonian operator and co-ad joint representation of the Volterra group
International Nuclear Information System (INIS)
Lebedev, D.R.; Manin, Yu.I.
1978-01-01
It is shown that the Gelfand-Dikii Hamiltonian structure is an analogue of a very special class of finite-dimensional symplectic structures, namely, the Kirillow structures on the orbits of the co-adjoint representation of the Lie groups. The Lie group is represented by the Volterra operators. The main interest lies in the possibility of application of the ideology of ''geometric quantization'' to the Lax equations
Grassmannian frames with applications to coding and communication
Strohmer, Thomas; Heath Jr., Robert W
2003-01-01
For a given class ${\\cal F}$ of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation $||$ among all frames $\\{f_k\\}_{k \\in {\\cal I}} \\in {\\cal F}$. We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These...
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.
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)
An algorithm for the basis of the finite Fourier transform
Santhanam, Thalanayar S.
1995-01-01
The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.
Multivariate fractional Poisson processes and compound sums
Beghin, Luisa; Macci, Claudio
2015-01-01
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.
The Maslov index in symplectic Banach spaces
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all...... for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds....
Condition for unambiguous state discrimination using local operations and classical communication
International Nuclear Information System (INIS)
Chefles, Anthony
2004-01-01
We obtain a necessary and sufficient condition for a finite set of states of a finite-dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition is valid for states which may be mixed, entangled, or both. When the support of the set of states is the entire multiparticle Hilbert space, this condition is found to have an intriguing connection with the theory of entanglement witnesses
Solving Conic Systems via Projection and Rescaling
Pena, Javier; Soheili, Negar
2015-01-01
We propose a simple projection and rescaling algorithm to solve the feasibility problem \\[ \\text{ find } x \\in L \\cap \\Omega, \\] where $L$ and $\\Omega$ are respectively a linear subspace and the interior of a symmetric cone in a finite-dimensional vector space $V$. This projection and rescaling algorithm is inspired by previous work on rescaled versions of the perceptron algorithm and by Chubanov's projection-based method for linear feasibility problems. As in these predecessors, each main it...
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.
Quantal Response: Nonparametric Modeling
2017-01-01
capture the behavior of observed phenomena. Higher-order polynomial and finite-dimensional spline basis models allow for more complicated responses as the...flexibility as these are nonparametric (not constrained to any particular functional form). These should be useful in identifying nonstandard behavior via... deviance ∆ = −2 log(Lreduced/Lfull) is defined in terms of the likelihood function L. For normal error, Lfull = 1, and based on Eq. A-2, we have log
System theory as applied differential geometry. [linear system
Hermann, R.
1979-01-01
The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.
The existence of periodic solutions for nonlinear beam equations on Td by a para-differential method
Chen, Bochao; Li, Yong; Gao, Yixian
2018-05-01
This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the non-resonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.
Toeplitz quantization of Kaehler manifolds and gl(N), N [yields] [infinity] limits
Energy Technology Data Exchange (ETDEWEB)
Bordemann, M. (Dept. of Physics, Univ. of Freiburg (Germany)); Meinrenken, E. (Dept. of Mathematics, M.I.T., Cambridge, MA (United States)); Schlichenmaier, M. (Dept. of Mathematics and Computer Science, Univ. of Mannheim (Germany))
1994-10-01
For general compact Kaehler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finite-dimensional matrix algebras gl(N), N [yields] [infinity]. (orig.)
Highly-Expressive Spaces of Well-Behaved Transformations: Keeping It Simple
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Batmanghelich, Kayhan
We propose novel finite-dimensional spaces of Rn → Rn transformations, n ∈ {1, 2, 3}, derived from (continuously-defined) parametric stationary velocity fields. Particularly, we obtain these transformations, which are diffeomorphisms, by fast and highly-accurate integration of continuous piecewise...... transformations). Its applications include, but are not limited to: unconstrained optimization over monotonic functions; modeling cumulative distribution functions or histograms; time warping; image registration; landmark-based warping; real-time diffeomorphic image editing....
From Koszul duality to Poincaré duality
Indian Academy of Sciences (India)
2012-06-09
Jun 9, 2012 ... Our aim here is to describe elements of the formulation of the Koszul duality and ... Throughout this paper K denotes a (commutative) field and all vector ... the form A = T(E)/I where E is a finite-dimensional vector space and I is a finitely gen- .... for any n ∈ N. The Koszul complex of A is then defined to be the ...
Discrete Wigner function and quantum-state tomography
Leonhardt, Ulf
1996-05-01
The theory of discrete Wigner functions and of discrete quantum-state tomography [U. Leonhardt, Phys. Rev. Lett. 74, 4101 (1995)] is studied in more detail guided by the picture of precession tomography. Odd- and even-dimensional systems (angular momenta and spins, bosons, and fermions) are considered separately. Relations between simple number theory and the quantum mechanics of finite-dimensional systems are pointed out. In particular, the multicomplementarity of the precession states distinguishes prime dimensions from composite ones.
All unitary ray representations of the conformal group SU(2,2) with positive energy
International Nuclear Information System (INIS)
Mack, G.
1975-12-01
We find all those unitary irreducible representations of the infinitely - sheeted covering group G tilde of the conformal group SU(2,2)/Z 4 which have positive energy P 0 >= O. They are all finite component field representations and are labelled by dimension d and a finite dimensional irreducible representation (j 1 , j 2 ) of the Lorentz group SL(2C). They all decompose into a finite number of unitary irreducible representations of the Poincare subgroup with dilations. (orig.) [de
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.
r-Matrix Structure for a Restricted Flow with Bargmann Constraint
International Nuclear Information System (INIS)
Chen Jinbing; Geng Xianguo
2005-01-01
This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R 2N . Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.
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...
Feedback control using only quantum back-action
International Nuclear Information System (INIS)
Jacobs, Kurt
2010-01-01
The traditional approach to feedback control is to apply deterministic forces to a system by modifying the Hamiltonian. Here we show that finite-dimensional quantum systems can be controlled purely by exploiting the random quantum back-action of a continuous weak measurement. We demonstrate that, quite remarkably, the quantum back-action of such an adaptive measurement is just as effective at controlling quantum systems as traditional feedback.
ON A PROLONGATION CONSTRUCTION FOR LOCAL NON-DIVERGENT VECTOR FIELDS ON Rn
Directory of Open Access Journals (Sweden)
A. M. Lukatsky
2015-01-01
Full Text Available The problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This construction allows to move from the Euler equations for the ideal incompressible fluid to the Euler equations on finite-dimensional Lie groups.
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
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
Some connections between classical and quantum anholonomy
International Nuclear Information System (INIS)
Giavarini, G.; Rohrlich, D.; Thacker, W.D.
1988-08-01
In this paper we study the interplay between the classical and quantum anholonomy effects (Hannay's angle and Berry's phase). When a finite-dimensional quantum system has a Berry phase, it has a nonzero Hannay angle. We show how infinite-dimensional systems can evade this correspondence, and find some necessary conditions for a system with a Berry phase to have no Hannay angle. (orig.)
Friedan-Shenker bundle from Chern-Simons theory
International Nuclear Information System (INIS)
Falceto, F.
1990-01-01
In this letter we present a proof of the invariance of the space of quantum states of the Chern-Simons (CS) theory in the presence of Wilson lines under parallel transport with respect to the Knizhnik-Zamolodchikov (KZ) connection for the case of a simple, simply connected, finite-dimensional group and genus-zero surface. The proof is based on the polynomial realization of the space of tensors in which these quantum states take values. (orig.)
International Nuclear Information System (INIS)
Arnlind, Joakim; Hofer, Laurent; Hoppe, Jens; Bordemann, Martin; Shimada, Hidehiko
2009-01-01
We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.
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
Grunspan, C.
2003-01-01
This text gives some results about quantum torsors. Our starting point is an old reformulation of torsors recalled recently by Kontsevich. We propose an unification of the definitions of torsors in algebraic geometry and in Poisson geometry. Any quantum torsor is equipped with two comodule-algebra structures over Hopf algebras and these structures commute with each other. In the finite dimensional case, these two Hopf algebras share the same finite dimension. We show that any Galois extension...
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
Numerical modelling of elastic space tethers
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P. L.; Roberts, R. M.
2012-01-01
In this paper the importance of the ill-posedness of the classical, non-dissipative massive tether model on an orbiting tether system is studied numerically. The computations document that via the regularisation of bending resistance a more reliable numerical integrator can be produced. Furthermo....... It is also shown that on the slow manifold the dynamics of the satellites are well-approximated by the finite dimensional slack-spring model....
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.
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
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 ...
Remarks on Chern-Simons Invariants
Cattaneo, Alberto S.; Mnëv, Pavel
2010-02-01
The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.
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
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
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.)
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.
Unitary representations of basic classical Lie superalgebras
International Nuclear Information System (INIS)
Gould, M.D.; Zhang, R.B.
1990-01-01
We have obtained all the finite-dimensional unitary irreps of gl(mvertical stroken) and C(n), which also exhaust such irreps of all the basic classical Lie superalgebras. The lowest weights of such irreps are worked out explicitly. It is also shown that the contravariant and covariant tensor irreps of gl(mvertical stroken) are unitary irreps of type (1) and type (2) respectively, explaining the applicability of the Young diagram method to these two types of tensor irreps. (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.)
International Nuclear Information System (INIS)
Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H F
2013-01-01
We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation ϕ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with ϕ, we can completely characterize the kinds of quantum states that are fixed by ϕ. Our work has several applications. It gives a simple proof of the structural characterization of a unital quantum operation that acts on finite-dimensional quantum states—a result not explicitly mentioned in earlier studies. It also provides a necessary and sufficient condition for determining what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of Størmer by giving a proof of a reduction theorem on the unassisted and entanglement-assisted classical capacities, coherent information, and minimal output Renyi entropy of a unital channel acting on a finite-dimensional quantum state. (paper)
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...
Gauged supergravities from M-theory reductions
Katmadas, Stefanos; Tomasiello, Alessandro
2018-04-01
In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.
Local equivalence, surface-code states, and matroids
International Nuclear Information System (INIS)
Sarvepalli, Pradeep; Raussendorf, Robert
2010-01-01
Recently, Ji et al. disproved the local-unitary-local Clifford (LU-LC) conjecture and showed that the local unitary (LU) and local Clifford (LC) equivalence classes of the stabilizer states are not always the same. Despite the fact that this settles the LU-LC conjecture, a sufficient condition for stabilizer states that violate the LU-LC conjecture is not known. In this paper, we investigate further the properties of stabilizer states with respect to local equivalence. Our first result shows that there exist infinitely many stabilizer states that violate the LU-LC conjecture. In particular, we show that for all numbers of qubits n≥28, there exist distance-two stabilizer states which are counterexamples to the LU-LC conjecture. We prove that, for all odd n≥195, there exist stabilizer states with distance greater than two that are LU equivalent but not LC equivalent. Two important classes of stabilizer states that are of great interest in quantum computation are the cluster states and stabilizer states of the surface codes. We show that, under some minimal restrictions, both these classes of states preclude any counterexamples. In this context, we also show that the associated surface codes do not have any encoded non-Clifford transversal gates. We characterize the Calderbank-Shor-Steane (CSS) surface-code states in terms of a class of minor closed binary matroids. In addition to making a connection to an important open problem in binary matroid theory, this characterization does in some cases provide an efficient test for CSS states that are not counterexamples.
Limits in the application of harmonic analysis to pulsating stars
Pascual-Granado, J.; Garrido, R.; Suárez, J. C.
2015-09-01
Using ultra-precise data from space instrumentation, we found that the underlying functions of stellar light curves from some AF pulsating stars are non-analytic, and consequently their Fourier expansion is not guaranteed. This result demonstrates that periodograms do not provide a mathematically consistent estimator of the frequency content for this type of variable stars. More importantly, this constitutes the first counterexample against the current paradigm, which considers that any physical process is described by a continuous (band-limited) function that is infinitely differentiable.
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.
Analytic Hypoellipticity and the Treves Conjecture
Directory of Open Access Journals (Sweden)
Marco Mughetti
2016-12-01
Full Text Available We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, P, (firstly appeared and studied in [3] having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem.
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.
Visual Temporal Logic as a Rapid Prototying Tool
DEFF Research Database (Denmark)
Fränzle, Martin; Lüth, Karsten
2001-01-01
Within this survey article, we explain real-time symbolic timing diagrams and the ICOS tool-box supporting timing-diagram-based requirements capture and rapid prototyping. Real-time symbolic timing diagrams are a full-fledged metric-time temporal logic, but with a graphical syntax reminiscent...... of the informal timing diagrams widely used in electrical engineering. ICOS integrates a variety of tools, ranging from graphical specification editors over tautology checking and counterexample generation to code generators emitting C or VHDL, thus bridging the gap from formal specification to rapid prototype...
Development and necessary norms of reasoning
Markovits, Henry
2014-01-01
The question of whether reasoning can, or should, be described by a single normative model is an important one. In the following, I combine epistemological considerations taken from Piaget’s notion of genetic epistemology, a hypothesis about the role of reasoning in communication and developmental data to argue that some basic logical principles are in fact highly normative. I argue here that explicit, analytic human reasoning, in contrast to intuitive reasoning, uniformly relies on a form of validity that allows distinguishing between valid and invalid arguments based on the existence of counterexamples to conclusions. PMID:24904501
THEORETICAL FLAWS IN THE USE OF THE CAPM FOR INVESTMENT DECISIONS
Magni, Carlo Alberto
2005-01-01
This paper uses counterexamples and simple formalization to show that the standard CAPM-based Net Present Value may not be used for investment valuations. The reason is that the standard CAPM-based capital budgeting criterion implies a notion of value which does not comply with the principle of additivity. Framing effects arise in decisions so that different descriptions of the same problem lead to different choices. As a result, the CAPM-based NPV as a tool for valuing projects and making in...
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...
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
Miles-Ezzell's WACC Approach Yields Arbitrage
Löffler, Andreas
2002-01-01
A simple counterexample shows the the widely used WACC approach to value leverage firms developed by Miles and Ezzell can create an arbitrage opportunity. The only consequence to be drawn is that their WACC approach cannot be applied under the circumstances assumed by Miles and Ezzell. We show how the WACC has to be modified in order to obtain proper results. We develop a theory in continuous as well as discrete time. In discrete time it turns out that with a further assumption on the cash fl...
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.
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.
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.
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.
Interfaces - a new perspective on the implementation of language in the brain
DEFF Research Database (Denmark)
Christensen, Ken Ramshøj
suggesting that the data should be accounted for with e.g. working memory or canonicity. Furthermore, several neuroimaging studies have reported Brocas area to be activated by semantic or pragmatic anomaly and implausibility. I present data from a neuroimaging study using fMRI on pragmatic anomaly and two......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...
Parts-of-speech systems and word order
DEFF Research Database (Denmark)
Hengeveld, Kees; Rijkhoff, Jan; Siewierska, Anna
2004-01-01
are rather restricted in these languages. Counterexamples to the latter claim all involve cases in which identifiability is ensured by morphological rather than syntactic means. This shows that there is a balanced trade-off between the syntactic, morphological, and lexical structure of a language.......), the identifiability of these slots is ensured by the nature of the lexical items (e.g. adjectives) themselves. As a result, word order possibilities are relatively unrestricted in these languages. In languages in which lexical items are not specialized for certain syntactic slots, in that these items combine...
Vanishing of cohomology over Cohen–Macaulay rings
DEFF Research Database (Denmark)
Christensen, Lars Winther; Holm, Henrik Granau
2012-01-01
A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings—colloquially called AC rings—that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational......, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen–Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our...
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
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
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.
International Nuclear Information System (INIS)
Celerier, Marie-Noeelle; Szekeres, Peter
2002-01-01
Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated by Szekeres and Iyer, we identify two classes of peculiar interest: focusing timelike singularity solutions with the stress-energy tensor of a radiative perfect fluid (equation of state: p=(1/3)ρ) and a set of null singularity classes verifying identical properties. We consider two important applications of these results: to cosmology, as regards the possibility of solving the horizon problem with no need to resort to any inflationary scenario, and to the strong cosmic censorship hypothesis to which we propose a class of physically consistent counterexamples
Is it really naked? On cosmic censorship in string theory
International Nuclear Information System (INIS)
Frolov, Andrei V.
2004-01-01
We investigate the possibility of cosmic censorship violation in string theory using a characteristic double-null code, which penetrates horizons and is capable of resolving the spacetime all the way to the singularity. We perform high-resolution numerical simulations of the evolution of negative mass initial scalar field profiles, which were argued to provide a counterexample to cosmic censorship conjecture for AdS-asymptotic spacetimes in five-dimensional supergravity. In no instances formation of naked singularity is seen. Instead, numerical evidence indicates that black holes form in the collapse. Our results are consistent with earlier numerical studies, and explicitly show where the 'no black hole' argument breaks
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
Reasoning from an incompatibility: False dilemma fallacies and content effects.
Brisson, Janie; Markovits, Henry; Robert, Serge; Schaeken, Walter
2018-03-23
In the present studies, we investigated inferences from an incompatibility statement. Starting with two propositions that cannot be true at the same time, these inferences consist of deducing the falsity of one from the truth of the other or deducing the truth of one from the falsity of the other. Inferences of this latter form are relevant to human reasoning since they are the formal equivalent of a discourse manipulation called the false dilemma fallacy, often used in politics and advertising in order to force a choice between two selected options. Based on research on content-related variability in conditional reasoning, we predicted that content would have an impact on how reasoners treat incompatibility inferences. Like conditional inferences, they present two invalid forms for which the logical response is one of uncertainty. We predicted that participants would endorse a smaller proportion of the invalid incompatibility inferences when more counterexamples are available. In Study 1, we found the predicted pattern using causal premises translated into incompatibility statements with many and few counterexamples. In Study 2A, we replicated the content effects found in Study 1, but with premises for which the incompatibility statement is a non-causal relation between classes. These results suggest that the tendency to fall into the false dilemma fallacy is modulated by the background knowledge of the reasoner. They also provide additional evidence on the link between semantic information retrieval and deduction.
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.)
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...
Interpolant Tree Automata and their Application in Horn Clause Verification
Directory of Open Access Journals (Sweden)
Bishoksan Kafle
2016-07-01
Full Text Available This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this paper. The role of an interpolant tree automaton is to provide a generalisation of a spurious counterexample during refinement, capturing a possibly infinite set of spurious counterexample traces. In our approach these traces are then eliminated using a transformation of the Horn clauses. We compare this approach with two other methods; one of them uses interpolant tree automata in an algorithm for trace abstraction and refinement, while the other uses abstract interpretation over the domain of convex polyhedra without the generalisation step. Evaluation of the results of experiments on a number of Horn clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead.
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.
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.
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.
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In 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. PMID:26919740
Poisson traces, D-modules, and symplectic resolutions.
Etingof, Pavel; Schedler, Travis
2018-01-01
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.
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.
Frame approximation of pseudo-inverse operators
DEFF Research Database (Denmark)
Christensen, Ole
2001-01-01
Let T denote an operator on a Hilbert space (H, [.,.]), and let {f(i)}(i=1)(infinity) be a frame for the orthogonal complement of the kernel NT. We construct a sequence of operators {Phi (n)} of the form Phi (n) (.) = Sigma (n)(i=1) [., g(t)(n)]f(i) which converges to the psuedo-inverse T+ of T i...... in the strong operator topology as n --> infinity. The operators {Phi (n)} can be found using finite-dimensional methods. We also prove an adaptive iterative version of the result. (C) 2001 Academic Press....
Estimates for Solutions of Differential Equations in a Banach Space via Commutators
Directory of Open Access Journals (Sweden)
Gil’ Michael
2018-02-01
Full Text Available In a Banach space we consider the equation dx(t/dt = (A + B(t×(t (t ≥ 0, where A is a constant bounded operator, and B(t is a bounded variable operator.Norm estimates for the solutions of the considered equation are derived in terms of the commutator AB(t − B(tA. These estimates give us sharp stability conditions. Our results are new even in the finite dimensional case.We also discuss applications of the obtained results to a class of integro-differential equations.
Lie Quasi-Bialgebras and Cohomology of Lie algebra
International Nuclear Information System (INIS)
Bangoura, Momo
2010-05-01
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, μ, γ, φ), corresponds one Lie algebra structure on D = G + G*, called the double of the given Lie quasi-bialgebra. We show that there exist on ΛG, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between ΛD and End(ΛG), D acting on ΛD by the adjoint action. (author) [fr
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.)
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...
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.
Non-linear sigma model on the fuzzy supersphere
International Nuclear Information System (INIS)
Kurkcuoglu, Seckin
2004-01-01
In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S (2,2) . In hep-th/0212133 Bott projectors have been used to obtain the fuzzy C P 1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super)-projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model. (author)
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.
A quantum group approach to cL > 1 Liouville gravity
International Nuclear Information System (INIS)
Suzuki, Takashi.
1995-03-01
A candidate of c L > 1 Liouville gravity is studied via infinite dimensional representations of U q sl(2, C) with q at a root of unity. We show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from finite dimensional representations of U q sl(2, C). Expressions of correlation functions and transition amplitudes are presented. We discuss about our results and find an intimate relation between our quantization of the Liouville theory and the geometric quantization of moduli space of Riemann surfaces. An interpretation of quantum space-time is also given within this formulation. (author)
Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
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)
Density character of subgroups of topological groups
Leiderman, Arkady; Morris, Sidney A.; Tkachenko, Mikhail G.
2015-01-01
A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie groups which consists of projective limits of finite-dimensional Lie groups and proved that it contains all compact groups, locally compact abelian groups and connected locally compact groups and is closed under products and closed subgroups. A topological group...
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...... conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear...
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.
Nonmeasurable sets and functions
Kharazishvili, Alexander
2004-01-01
The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-measurable cardinals;3. The theory of invariant (quasi-invariant)extensions of invariant (quasi-invaria
A representation theoretic approach to the WZW Verlinde formula
Fuchs, J
1997-01-01
By exploring the description of chiral blocks in terms of co-invariants, a proof of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine Lie algebras. In contrast to other proofs of the Verlinde formula, this approach works for all untwisted affine Lie algebras. As a by-product we obtain a homological interpretation of the Verlinde multiplicities, as Euler characteristics of complexes built from invariant tensors of finite-dimensional simple Lie algebras.
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.
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.)
Simple expression for the quantum Fisher information matrix
Šafránek, Dominik
2018-04-01
Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality, quantum phase transitions, coherence, entanglement, and irreversibility. We derive a surprisingly simple formula for this quantity, which, unlike previously known general expression, does not require diagonalization of the density matrix, and is provably at least as efficient. With a minor modification, this formula can be used to compute QFIM for any finite-dimensional density matrix. Because of its simplicity, it could also shed more light on the quantum information geometry in general.
Expansion of the Lie algebra and its applications
International Nuclear Information System (INIS)
Guo Fukui; Zhang Yufeng
2006-01-01
We take the Lie algebra A1 as an example to illustrate a detail approach for expanding a finite dimensional Lie algebra into a higher-dimensional one. By making use of the late and its resulting loop algebra, a few linear isospectral problems with multi-component potential functions are established. It follows from them that some new integrable hierarchies of soliton equations are worked out. In addition, various Lie algebras may be constructed for which the integrable couplings of soliton equations are obtained by employing the expanding technique of the the Lie algebras
Necessity of negativity in quantum theory
International Nuclear Information System (INIS)
Ferrie, Christopher; Morris, Ryan; Emerson, Joseph
2010-01-01
A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require negative probability in either the states or the effects. In this article we extend those results to Hilbert spaces of infinite dimension, for which the celebrated Wigner function is a special case. Hence, this article presents a unified framework for describing the set of possible quasiprobability representations of quantum theory, and a proof that the presence of negativity is a necessary feature of such representations.
Global dynamics and control of a comprehensive nonlinear beam equation
International Nuclear Information System (INIS)
You Yuncheng; Taboada, M.
1994-01-01
A nonlinear hinged extensible elastic beam equation with the structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures. It is proved that there exists an absorbing set in the energy space and that there exist inertial manifolds whose exponential attracting rates however are nonuniform. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite-dimensional feedback control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to uncertainty in the structural parameters. (author). 5 refs
Comment on 'Immirzi parameter in quantum general relativity'
International Nuclear Information System (INIS)
Samuel, Joseph
2001-01-01
The Immirzi parameter is a free parameter which appears in the physical predictions of loop quantum gravity and is sometimes viewed as a quantization ambiguity. Interpretations have been offered for the Immirzi ambiguity, but there does not appear to be a clear understanding or even a consensus about its origin and significance. We show that a previously discussed example containing a 'finite dimensional analogue' of the Immirzi ambiguity is fallacious, in the sense that the ambiguity in this example is not intrinsic to the system, but introduced artificially by compactifying the configuration space
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.
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.
Simulation of conditional diffusions via forward-reverse stochastic representations
Bayer, Christian
2015-01-01
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.
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.
BRST operator quantization of generally covariant gauge systems
International Nuclear Information System (INIS)
Ferraro, R.; Sforza, D.M.
1997-01-01
The BRST generator is realized as a Hermitian nilpotent operator for a finite-dimensional gauge system featuring a quadratic super-Hamiltonian and linear supermomentum constraints. As a result, the emerging ordering for the Hamiltonian constraint is not trivial, because the potential must enter the kinetic term in order to obtain a quantization invariant under scaling. Namely, BRST quantization does not lead to the curvature term used in the literature as a means to get that invariance. The inclusion of the potential in the kinetic term, far from being unnatural, is beautifully justified in light of the Jacobi's principle. copyright 1997 The American Physical Society
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
International Nuclear Information System (INIS)
Arias, Alvaro; Gudder, Stan
2004-01-01
Quantum effects are represented by operators on a Hilbert space satisfying 0≤A≤I, and sharp quantum effects are represented by projection operators. We say that an effect A is almost sharp if A=PQP for projections P and Q. We give simple characterizations of almost sharp effects. We also characterize effects that can be written as longer products of projections. For generality we first work in the formalism of von Neumann algebras. We then specialize to the full operator algebra B(H) and to finite dimensional Hilbert spaces
Topological quantum theories and integrable models
International Nuclear Information System (INIS)
Keski-Vakkuri, E.; Niemi, A.J.; Semenoff, G.; Tirkkonen, O.
1991-01-01
The path-integral generalization of the Duistermaat-Heckman integration formula is investigated for integrable models. It is shown that for models with periodic classical trajectories the path integral reduces to a form similar to the finite-dimensional Duistermaat-Heckman integration formula. This provides a relation between exactness of the stationary-phase approximation and Morse theory. It is also argued that certain integrable models can be related to topological quantum theories. Finally, it is found that in general the stationary-phase approximation presumes that the initial and final configurations are in different polarizations. This is exemplified by the quantization of the SU(2) coadjoint orbit
Conformal Nets II: Conformal Blocks
Bartels, Arthur; Douglas, Christopher L.; Henriques, André
2017-08-01
Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.
An Integrable Approximation for the Fermi Pasta Ulam Lattice
Rink, Bob
This contribution presents a review of results obtained from computations of approximate equations of motion for the Fermi-Pasta-Ulam lattice. These approximate equations are obtained as a finite-dimensional Birkhoff normal form. It turns out that in many cases, the Birkhoff normal form is suitable for application of the KAM theorem. In particular, this proves Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal Birkhoff normal form computations of Nishida, the KAM theorem and discrete symmetry considerations.
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.
International Nuclear Information System (INIS)
Bliokh, Yu.P.; Fajnberg, Ya.B.; Lyubarskij, M.G.; Podobinskij, V.O.
1994-01-01
Certain distributed dynamical systems describing the well-known beam generators of UHF oscillations are organized very simple: the nonlinear functional, which determines the current state of the system with respect to its behaviour in the past, is represented as a composition of the linear functional and the nonlinear finite-dimensional map. This property made it possible to find the mechanisms of auto modulation and stochastization of the signals from beam generators and to define corresponding range of parameters values. 12 refs., 6 figs
On derived groups of division rings II
International Nuclear Information System (INIS)
Mahdavi Hezavehi, M.; Akbari Feyzaabaadi, S.; Mehraabaadi, M.; Hajie Abolhassan, H.
1995-05-01
Let D be a division ring with centre F and denote by D' the derived group (commutator subgroup) of D * = D - {0}. It is shown that if each element of D' is algebraic over F, then D is algebraic over F. It is also proved that each finite separable extension of F in D is of the form F(c) for some element c in the derived group D'. Using these results, it is shown that if each element of the derived group D' is of bounded degree over F, then D is finite dimensional over F. (author). 5 refs
Directory of Open Access Journals (Sweden)
Wakako Nakai
2007-07-01
Full Text Available We study the Jacobi-Trudi-type determinant which is conjectured to be the $q$-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type $C_n$. Like the $D_n$ case studied by the authors recently, applying the Gessel-Viennot path method with an additional involution and a deformation of paths, we obtain an expression by a positive sum over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.
The finite section method and problems in frame theory
DEFF Research Database (Denmark)
Christensen, Ole; Strohmer, T.
2005-01-01
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......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...
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
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.
Universal R-matrix for quantized (super) algebras
International Nuclear Information System (INIS)
Khoroshkin, S.M.; Tolstoj, V.N.
1991-01-01
For quantum deformations of finite-dimensional contragredient Lie (super)algebras an explicit formula for the universal R-matrix is given. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A.N. Kirillov and N. Reshetikhin, Yas.S. Soibelman and S.Z. Levendorskii. Approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties of q-exponential functions. Quantum Weyl group is not used. 19 refs.; 2 tabs
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.
Indirect control of quantum systems via an accessor: pure coherent control without system excitation
International Nuclear Information System (INIS)
Fu, H C; Dong Hui; Sun, C P; Liu, X F
2009-01-01
A pure indirect control of quantum systems via a quantum accessor is investigated. In this control scheme, we do not apply any external classical excitation fields on the controlled system and we control a quantum system via a quantum accessor and classical control fields control the accessor only. Complete controllability is investigated for arbitrary finite-dimensional quantum systems and exemplified by two- and three-dimensional systems. The scheme exhibits some advantages; it uses less qubits in the accessor and does not depend on the energy-level structure of the controlled system
Quantum control in infinite dimensions
International Nuclear Information System (INIS)
Karwowski, Witold; Vilela Mendes, R.
2004-01-01
Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite-dimensional control Lie algebra. Here we show that by adding a discrete operation to a Lie algebra it is possible to obtain full control in infinite dimensions with a small number of control operators
Most energetic passive states.
Perarnau-Llobet, Martí; Hovhannisyan, Karen V; Huber, Marcus; Skrzypczyk, Paul; Tura, Jordi; Acín, Antonio
2015-10-01
Passive states are defined as those states that do not allow for work extraction in a cyclic (unitary) process. Within the set of passive states, thermal states are the most stable ones: they maximize the entropy for a given energy, and similarly they minimize the energy for a given entropy. Here we find the passive states lying in the other extreme, i.e., those that maximize the energy for a given entropy, which we show also minimize the entropy when the energy is fixed. These extremal properties make these states useful to obtain fundamental bounds for the thermodynamics of finite-dimensional quantum systems, which we show in several scenarios.
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
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
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...
On Optimal Feedback Control for Stationary Linear Systems
International Nuclear Information System (INIS)
Russell, David L.
2010-01-01
We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.
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.
Truncated conformal space approach to scaling Lee-Yang model
International Nuclear Information System (INIS)
Yurov, V.P.; Zamolodchikov, Al.B.
1989-01-01
A numerical approach to 2D relativstic field theories is suggested. Considering a field theory model as an ultraviolet conformal field theory perturbed by suitable relevant scalar operator one studies it in finite volume (on a circle). The perturbed Hamiltonian acts in the conformal field theory space of states and its matrix elements can be extracted from the conformal field theory. Truncation of the space at reasonable level results in a finite dimensional problem for numerical analyses. The nonunitary field theory with the ultraviolet region controlled by the minimal conformal theory μ(2/5) is studied in detail. 9 refs.; 17 figs
Spectral gaps, inertial manifolds and kinematic dynamos
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es
2005-10-17
Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.
The stochastic energy-Casimir method
Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.
2018-04-01
In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"
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
Quantum information theory with Gaussian systems
Energy Technology Data Exchange (ETDEWEB)
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Root Fernando-Kac subalgebras of finite type
Milev, Todor
2010-01-01
Let $\\mathfrak{g}$ be a finite-dimensional Lie algebra and $M$ be a $\\mathfrak{g}$-module. The Fernando-Kac subalgebra of $\\mathfrak{g}$ associated to $M$ is the subset $\\mathfrak{g}[M]\\subset\\mathfrak{g}$ of all elements $g\\in\\mathfrak{g}$ which act locally finitely on $M$. A subalgebra $\\mathfrak{l}\\subset\\mathfrak{g}$ for which there exists an irreducible module $M$ with $\\mathfrak{g}[M]=\\mathfrak{l}$ is called a Fernando-Kac subalgebra of $\\mathfrak{g}$. A Fernando-Kac subalgebra of $\\mat...
On One Means of Hard Excitation of Oscillations in Nonlinear Flutter Systems
Directory of Open Access Journals (Sweden)
S. D. Glyzin
2014-01-01
Full Text Available Considered are so-called finite-dimensional flutter systems, i.e. systems of ordinary differential equations, arising from Galerkin approximations of certain boundary value problems of aeroelasticity theory as well as from a number of radiophysics applications. We study small oscillations of these equations in case of 1 : 3 resonance. By combining analytical and numerical methods, it is concluded that the mentioned resonance can cause a hard excitation of oscillations. Namely, for flutter systems shown is the possibility of coexistence, along with the stable zero state, of stable invariant tori of arbitrary finite dimension as well as chaotic attractors.
Regularization by Functions of Bounded Variation and Applications to Image Enhancement
International Nuclear Information System (INIS)
Casas, E.; Kunisch, K.; Pola, C.
1999-01-01
Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating subspaces consisting of piecewise constant functions. Algorithms based on a primal-dual framework that exploit the structure of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images with very high noise
Wigner tomography of multispin quantum states
Leiner, David; Zeier, Robert; Glaser, Steffen J.
2017-12-01
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015), 10.1103/PhysRevA.91.042122]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.
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......We introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase-field method. In the basic formulation we have a PDE-constrained optimization problem, where the finite element and design analysis are solved simultaneously...
Vertex operators of ghost number three in Type IIB supergravity
International Nuclear Information System (INIS)
Mikhailov, Andrei
2016-01-01
We study the cohomology of the massless BRST complex of the Type IIB pure spinor superstring in flat space. In particular, we find that the cohomology at the ghost number three is nontrivial and transforms in the same representation of the supersymmetry algebra as the solutions of the linearized classical supergravity equations. Modulo some finite dimensional spaces, the ghost number three cohomology is the same as the ghost number two cohomology. We also comment on the difference between the naive and semi-relative cohomology, and the role of b-ghost.
Fixed Points in Grassmannians with Applications to Economic Equilibrium
DEFF Research Database (Denmark)
Keiding, Hans
2017-01-01
In some applications of equilibrium theory, the fixed point involves not only a state and a value of a parameter in the dual of the state space, but also a particular subspace of the state space. Since the set of all subspaces of a finite-dimensional Euclidean space has a structure which does...... not allow immediate application of fixed point theorems, the problem must be reformulated using a suitable parametrization of subspaces. One such parametrization, the Plücker coordinates, is used here to prove a general equilibrium existence theorem. Applications to economic problems involving hierarchies...... of consumers or incomplete markets with real assets are outlined....
Multilevel ensemble Kalman filtering
Hoel, Hakon; Law, Kody J. H.; Tempone, Raul
2016-01-01
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.
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
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.)
Quantum information theory with Gaussian systems
International Nuclear Information System (INIS)
Krueger, O.
2006-01-01
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
On the discrete Frobenius-Perron operator of the Bernoulli map
International Nuclear Information System (INIS)
Bai Zaiqiao
2006-01-01
We study the spectra of a finite-dimensional Frobenius-Perron operator (matrix) of the Bernoulli map derived from phase space discretization. The eigenvalues and (right and left) eigenvectors are analytically calculated, which are closely related to periodic orbits on the partition points. In the degenerate case, Jordan decomposition of the matrix is explicitly constructed. Except for the isolated eigenvalue 1, there is no definite limit with respect to eigenvalues when n → ∞. The behaviour of the eigenvectors is discussed in the limit of large n
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
Helix-Hopes on Finite Hyperfields
Directory of Open Access Journals (Sweden)
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.
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).
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
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.
Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye
2018-04-01
The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
Matveev, Vladimir S.; Miranda, Eva; Rubtsov, Vladimir; Przybylska, Maria; Tabachnikov, Sergei
2017-05-01
This Special Issue of Journal of Geometry and Physics gathers several contributions to the conference FDIS 2015 3-rd Conference on Finite Dimensional Integrable Systems in Geometry and Mathematical Physics which took place in Będlewo in July 12 to 17, 2015. It also contains other contributions by specialists in the field of integrable systems and related subjects. This is the second special issue which corresponds to the third installment of a series of Workshops called FDIS, which take place every other year.
Principles of quantum interference
International Nuclear Information System (INIS)
Jones, K.R.W.
1990-01-01
A new approach to quantum state determination is developed using data in the form of observed eigenvectors. An exceedingly natural inversion of such data results when the quantum probability rule is recognised as a conditional. The reversal of this conditional via Bayesian methods results in an inferred probability density over states which readily reduces to a density matrix estimator. The inclusion of concepts drawn from communication theory then defines an optimal state determination problem which is explored on Hilbert spaces of arbitrary finite dimensionality. 33 refs
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.
International Nuclear Information System (INIS)
Marquette, Ian
2015-01-01
Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions are related with Hermite and Laguerre exceptional orthogonal polynomials (EOP) of type III. We show that ladder operators obtained from alternative construction based on combinations of supercharges in the Krein-Adler and Darboux Crum (or state deleting and creating) approaches can be used to generate a set of integrals of motion and a corresponding polynomial algebra that provides an algebraic derivation of the full spectrum and total number of degeneracies. Such derivation is based on finite dimensional unitary representations (unirreps) and doesn't work for integrals build from standard ladder operators in supersymmetric quantum mechanics (SUSYQM) as they contain singlets isolated from excited states. In this paper, we also rely on a novel approach to obtain the finite dimensional unirreps based on the action of the integrals of motion on the wavefunctions given in terms of these EOP. We compare the results with those obtained from the Daskaloyannis approach and the realizations in terms of deformed oscillator algebras for one of the new families in the case of 1-step extension. This communication is a review of recent works. (paper)
Pro-Lie Groups: A Survey with Open Problems
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Karl H. Hofmann
2015-07-01
Full Text Available A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally-compact group that has a compact quotient group modulo its identity component and, thus, in particular, each compact and each connected locally-compact group; it also includes all locally-compact Abelian groups. This paper provides an overview of the structure theory and the Lie theory of pro-Lie groups, including results more recent than those in the authors’ reference book on pro-Lie groups. Significantly, it also includes a review of the recent insight that weakly-complete unital algebras provide a natural habitat for both pro-Lie algebras and pro-Lie groups, indeed for the exponential function that links the two. (A topological vector space is weakly complete if it is isomorphic to a power RX of an arbitrary set of copies of R. This class of real vector spaces is at the basis of the Lie theory of pro-Lie groups. The article also lists 12 open questions connected to pro-Lie groups.
On infinite-dimensional state spaces
International Nuclear Information System (INIS)
Fritz, Tobias
2013-01-01
It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V −1 U 2 V=U 3 , then finite-dimensionality entails the relation UV −1 UV=V −1 UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V −1 U 2 V=U 3 holds only up to ε and then yields a lower bound on the dimension.
Symmetric truncations of the shallow-water equations
International Nuclear Information System (INIS)
Rouhi, A.; Abarbanel, H.D.I.
1993-01-01
Conservation of potential vorticity in Eulerian fluids reflects particle interchange symmetry in the Lagrangian fluid version of the same theory. The algebra associated with this symmetry in the shallow-water equations is studied here, and we give a method for truncating the degrees of freedom of the theory which preserves a maximal number of invariants associated with this algebra. The finite-dimensional symmetry associated with keeping only N modes of the shallow-water flow is SU(N). In the limit where the number of modes goes to infinity (N→∞) all the conservation laws connected with potential vorticity conservation are recovered. We also present a Hamiltonian which is invariant under this truncated symmetry and which reduces to the familiar shallow-water Hamiltonian when N→∞. All this provides a finite-dimensional framework for numerical work with the shallow-water equations which preserves not only energy and enstrophy but all other known conserved quantities consistent with the finite number of degrees of freedom. The extension of these ideas to other nearly two-dimensional flows is discussed
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Sauri, Orimar; Szozda, Benedykt
In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master Lévy measure and the associated Lévy-Itô representation. We give the dilation criterion for selfdecomposa......In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master Lévy measure and the associated Lévy-Itô representation. We give the dilation criterion...... for selfdecomposability analogous to the classical one. Next, we give necessary and sufficient conditions (in terms of the kernel functions) for a Volterra field driven by a Lévy basis to be selfdecomposable. In this context we also study the so-called Urbanik classes of random fields. We follow this with the study...... of existence and selfdecomposability of integrated Volterra fields. Finally, we introduce infinitely divisible field-valued Lévy processes, give the Lévy-Itô representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of Lévy...
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Sauri, Orimar; Szozda, Benedykt
In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master L\\'evy measure and the associated L\\'evy-It\\^o representation. We give the dilation criterion for selfdec......In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master L\\'evy measure and the associated L\\'evy-It\\^o representation. We give the dilation criterion...... for selfdecomposability analogous to the classical one. Next, we give necessary and sufficient conditions (in terms of the kernel functions) for a Volterra field driven by a L\\'evy basis to be selfdecomposable. In this context we also study the so-called Urbanik classes of random fields. We follow this with the study...... of existence and selfdecomposability of integrated Volterra fields. Finally, we introduce infinitely divisible field-valued L\\'evy processes, give the L\\'evy-It\\^o representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of L...
Geometrical approach to fluid models
International Nuclear Information System (INIS)
Kuvshinov, B.N.; Schep, T.J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). copyright 1997 American Institute of Physics
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)
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.
Dynamic Self-Adaptive Reliability Control for Electric-Hydraulic Systems
Directory of Open Access Journals (Sweden)
Yi Wan
2015-02-01
Full Text Available The high-speed electric-hydraulic proportional control is a new development of the hydraulic control technique with high reliability, low cost, efficient energy, and easy maintenance; it is widely used in industrial manufacturing and production. However, there are still some unresolved challenges, the most notable being the requirements of high stability and real-time by the classical control algorithm due to its high nonlinear characteristics. We propose a dynamic self-adaptive mixed control method based on the least squares support vector machine (LSSVM and the genetic algorithm for high-speed electric-hydraulic proportional control systems in this paper; LSSVM is used to identify and adjust online a nonlinear electric-hydraulic proportional system, and the genetic algorithm is used to optimize the control law of the controlled system and dynamic self-adaptive internal model control and predictive control are implemented by using the mixed intelligent method. The internal model and the inverse control model are online adjusted together. At the same time, a time-dependent Hankel matrix is constructed based on sample data; thus finite dimensional solution can be optimized on finite dimensional space. The results of simulation experiments show that the dynamic characteristics are greatly improved by the mixed intelligent control strategy, and good tracking and high stability are met in condition of high frequency response.
Generalized spin Sutherland systems revisited
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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.
Fellner, Klemens; Tang, Bao Quoc
2018-06-01
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.
Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems
Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent
2018-05-01
We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.
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.
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)
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.
On infinite-dimensional state spaces
Fritz, Tobias
2013-05-01
It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.
2-regularity and 2-normality conditions for systems with impulsive controls
Directory of Open Access Journals (Sweden)
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.
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)
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. (author)
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 ...
Directory of Open Access Journals (Sweden)
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
A parabolic analogue of the higher-order comparison theorem of De Silva and Savin
Banerjee, Agnid; Garofalo, Nicola
2016-01-01
We show that the quotient of two caloric functions which vanish on a portion of the lateral boundary of a H k + α domain is H k + α up to the boundary for k ≥ 2. In the case k = 1, we show that the quotient is in H 1 + α if the domain is assumed to be space-time C 1 , α regular. This can be thought of as a parabolic analogue of a recent important result in [8], and we closely follow the ideas in that paper. We also give counterexamples to the fact that analogous results are not true at points on the parabolic boundary which are not on the lateral boundary, i.e., points which are at the corner and base of the parabolic boundary.
Galili, Tal; Meilijson, Isaac
2016-01-02
The Rao-Blackwell theorem offers a procedure for converting a crude unbiased estimator of a parameter θ into a "better" one, in fact unique and optimal if the improvement is based on a minimal sufficient statistic that is complete. In contrast, behind every minimal sufficient statistic that is not complete, there is an improvable Rao-Blackwell improvement. This is illustrated via a simple example based on the uniform distribution, in which a rather natural Rao-Blackwell improvement is uniformly improvable. Furthermore, in this example the maximum likelihood estimator is inefficient, and an unbiased generalized Bayes estimator performs exceptionally well. Counterexamples of this sort can be useful didactic tools for explaining the true nature of a methodology and possible consequences when some of the assumptions are violated. [Received December 2014. Revised September 2015.].
Directory of Open Access Journals (Sweden)
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.
Decoherence and quantum walks: Anomalous diffusion and ballistic tails
International Nuclear Information System (INIS)
Prokof'ev, N. V.; Stamp, P. C. E.
2006-01-01
The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasiclassical (in fact, diffusive) in the long time limit. We present here a counterexample, in which a particle makes quantum transitions between the sites of a d-dimensional hypercubic lattice while strongly coupled to a bath of two-level systems that 'record' the transitions. The long-time evolution of an initial wave packet is found to be most unusual: the mean square displacement of the particle density matrix shows long-range ballistic behavior, with 2 >∼t 2 , but simultaneously a kind of weakly localized behavior near the origin. This result may have important implications for the design of quantum computing algorithms, since it describes a class of quantum walks
Boundary perturbations coupled to core 3/2 tearing modes on the DIII-D tokamak
International Nuclear Information System (INIS)
Tobias, B; Yu, L; Domier, C W; Luhmann, N C Jr; Austin, M E; Paz-Soldan, C; Turnbull, A D; Classen, I G J
2013-01-01
High confinement (H-mode) discharges on the DIII-D tokamak are routinely subject to the formation of long-lived, non-disruptive magnetic islands that degrade confinement and limit fusion performance. Simultaneous, 2D measurement of electron temperature fluctuations in the core and edge regions allows for reconstruction of the radially resolved poloidal mode number spectrum and phase of the global plasma response associated with these modes. Coherent, n = 2 excursions of the plasma boundary are found to be the result of coupling to an n = 2, kink-like mode which arises locked in phase to the 3/2 island chain. This coupling dictates the relative phase of the displacement at the boundary with respect to the tearing mode. This unambiguous phase relationship, for which no counter-examples are observed, is presented as a test for modeling of the perturbed fields to be expected outside the confined plasma. (paper)
International Nuclear Information System (INIS)
Li, Risong; Wang, Hongqing
2014-01-01
Let (f n ) be a given sequence of continuous selfmaps of a compact metric space X which converges uniformly to a continuous selfmap f of the compact metric space X. In this note, we present a counterexample which shows that Theorems 3.9–3.11 obtained by us in [Chaos, Solitons and Fractals 45 (2012) 759–764] are not true and give the correct proofs of Theorems 3.4–3.7 in [Chaos, Solitons and Fractals 45 (2012) 759–764]. We also obtain a equivalence condition for the uniform map f to be syndetically sensitive or cofinitely sensitive or multi-sensitive or ergodically sensitive and a sufficient condition the uniform map f to be totally transitive or topologically weak mixing
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements
Guerini, Leonardo; Terra Cunha, Marcelo
2018-04-01
We address the problem of characterising the compatible tuples of measurements that admit a unique joint measurement. We derive a uniqueness criterion based on the method of perturbations and apply it to show that extremal points of the set of compatible tuples admit a unique joint measurement, while all tuples that admit a unique joint measurement lie in the boundary of such a set. We also provide counter-examples showing that none of these properties are both necessary and sufficient, thus completely describing the relation between the joint measurement uniqueness and the structure of the compatible set. As a by-product of our investigations, we completely characterise the extremal and boundary points of the set of general tuples of measurements and of the subset of compatible tuples.
International Nuclear Information System (INIS)
Zhikov, Vasilii V; Pastukhova, Svetlana E
2008-01-01
Elliptic equations of p(x)-Laplacian type are investigated. There is a well-known logarithmic condition on the modulus of continuity of the nonlinearity exponent p(x), which ensures that a Laplacian with variable order of nonlinearity inherits many properties of the usual p-Laplacian of constant order. One of these is the so-called improved integrability of the gradient of the solution. It is proved in this paper that this property holds also under a slightly more general condition on the exponent p(x), although then the improvement of integrability is logarithmic rather than power-like. The method put forward is based on a new generalization of Gehring's lemma, which relies upon the reverse Hoelder inequality 'with increased support and exponent on the right-hand side'. A counterexample is constructed that reveals the extent to which the condition on the modulus of continuity obtained is sharp. Bibliography: 28 titles.
Similarity problems and completely bounded maps
Pisier, Gilles
2001-01-01
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMO...
Learning using privileged information: SVM+ and weighted SVM.
Lapin, Maksim; Hein, Matthias; Schiele, Bernt
2014-05-01
Prior knowledge can be used to improve predictive performance of learning algorithms or reduce the amount of data required for training. The same goal is pursued within the learning using privileged information paradigm which was recently introduced by Vapnik et al. and is aimed at utilizing additional information available only at training time-a framework implemented by SVM+. We relate the privileged information to importance weighting and show that the prior knowledge expressible with privileged features can also be encoded by weights associated with every training example. We show that a weighted SVM can always replicate an SVM+ solution, while the converse is not true and we construct a counterexample highlighting the limitations of SVM+. Finally, we touch on the problem of choosing weights for weighted SVMs when privileged features are not available. Copyright © 2014 Elsevier Ltd. All rights reserved.
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
On the probability density interpretation of smoothed Wigner functions
International Nuclear Information System (INIS)
De Aguiar, M.A.M.; Ozorio de Almeida, A.M.
1990-01-01
It has been conjectured that the averages of the Wigner function over phase space volumes, larger than those of minimum uncertainty, are always positive. This is true for Gaussian averaging, so that the Husimi distribution is positive. However, we provide a specific counterexample for the averaging with a discontinuous hat function. The analysis of the specific system of a one-dimensional particle in a box also elucidates the respective advantages of the Wigner and the Husimi functions for the study of the semiclassical limit. The falsification of the averaging conjecture is shown not to depend on the discontinuities of the hat function, by considering the latter as the limit of a sequence of analytic functions. (author)
Gauging the cosmic acceleration with recent type Ia supernovae data sets
Velten, Hermano; Gomes, Syrios; Busti, Vinicius C.
2018-04-01
We revisit a model-independent estimator for cosmic acceleration based on type Ia supernovae distance measurements. This approach does not rely on any specific theory for gravity, energy content, nor parametrization for the scale factor or deceleration parameter and is based on falsifying the null hypothesis that the Universe never expanded in an accelerated way. By generating mock catalogs of known cosmologies, we test the robustness of this estimator, establishing its limits of applicability. We detail the pros and cons of such an approach. For example, we find that there are specific counterexamples in which the estimator wrongly provides evidence against acceleration in accelerating cosmologies. The dependence of the estimator on the H0 value is also discussed. Finally, we update the evidence for acceleration using the recent UNION2.1 and Joint Light-Curve Analysis samples. Contrary to recent claims, available data strongly favor an accelerated expansion of the Universe in complete agreement with the standard Λ CDM model.
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
A faster 1.375-approximation algorithm for sorting by transpositions.
Cunha, Luís Felipe I; Kowada, Luis Antonio B; Hausen, Rodrigo de A; de Figueiredo, Celina M H
2015-11-01
Sorting by Transpositions is an NP-hard problem for which several polynomial-time approximation algorithms have been developed. Hartman and Shamir (2006) developed a 1.5-approximation [Formula: see text] algorithm, whose running time was improved to O(nlogn) by Feng and Zhu (2007) with a data structure they defined, the permutation tree. Elias and Hartman (2006) developed a 1.375-approximation O(n(2)) algorithm, and Firoz et al. (2011) claimed an improvement to the running time, from O(n(2)) to O(nlogn), by using the permutation tree. We provide counter-examples to the correctness of Firoz et al.'s strategy, showing that it is not possible to reach a component by sufficient extensions using the method proposed by them. In addition, we propose a 1.375-approximation algorithm, modifying Elias and Hartman's approach with the use of permutation trees and achieving O(nlogn) time.
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.
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick
2014-01-01
We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of query-answer transformed clauses, and refinement by splitting...... in conjunction with specialisation for propagating constraints it can frequently solve challenging verification problems. This is a contribution in itself, but refinement is needed when it fails, and the question of how to refine convex polyhedral analyses has not been studied much. We present a refinement...... technique based on interpolants derived from a counterexample trace; these are used to drive a property-based specialisation that splits predicates, leading in turn to more precise convex polyhedral analyses. The process of specialisation, analysis and splitting can be repeated, in a manner similar...