Invariant differential operators
Dobrev, Vladimir K
2016-01-01
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Invariant Differential Operators for Non-Compact Lie Groups: the Reduced SU(4,4) Multiplets
Dobrev, V K
2014-01-01
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $su(n,n)$. Earlier were given the main multiplets of indecomposable elementary representations for $n\\leq 4$, and the reduced ones for $n=2,3$. Here we give all reduced multiplets containing physically relevant representations including the minimal ones for $n=4$. Due to the recently established parabolic relations the results are valid also for the algebras $sl(8,\\mathbb{R})$ and $su^*(8)$ with suitably chosen maximal parabolic subalgebras.
Invariant differential operators for non-compact Lie groups: the reduced SU(3,3) multiplets
Dobrev, V. K.
2014-12-01
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras su( n, n). Earlier were given the main multiplets of indecomposable elementary representations for n ≤ 4, and the reduced ones for n = 2. Here we give all reduced multiplets containing physically relevant representations including the minimal ones for the algebra su(3, 3). Due to the recently established parabolic relations the results are valid also for the algebra sl(6, ℝ) with suitably chosen maximal parabolic subalgebra.
On twistor transformations and invariant differential operator of simple Lie group G2(2)
Wang, Wei
2013-01-01
The twistor transformations associated to the simple Lie group G2 are described explicitly. We consider the double fibration G_2/P_2 xleftarrow {η } {G_2/B} xrArr {tau }G_2/P_1, where P1 and P2 are two parabolic subgroups of G2 and B is a Borel subgroup, and its local version: H^*_2 xleftarrow {η } F xrArr {tau } H_1, where H_1 is the Heisenberg group of dimension 5 embedded in the coset space G2/P1, F = {CP}^1 × H_1 and H^*_2 contains the nilpotent Lie group H_2 of step three. The Baker-Campbell-Hausdorff formula is used to parametrize the coset spaces, coordinates charts, their transition functions and the fibers of the projection η as complex curves. We write down the relative De-Rham sequence on F along the fibers and push it down to H_1 to get a family of matrix-valued differential operators {D}_k. Then we establish a kind of Penrose correspondence for G2: the kernel of {D}_k is isomorphic to the first cohomology of the sheaf {O} (-k ) over H^*_2. We also give the Penrose-type integral transformation u = Pf for fin {O} (-k ), which gives solutions to equations {D}_ku=0. When restricted to the real Heisenberg group, the differential operators are invariant under the action of G2(2). Exchanging P1 and P2, we derive corresponding results on H_2.
Dobrev, V K
2013-01-01
In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduce the new notion of {\\it parabolic relation} between two non-compact semisimple Lie algebras g and g' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E_{7(7)} which is parabolically related to the CLA E_{7(-25)}, the parabolic subalgebras including E_{6(6)} and E_{6(-6)} . Other interesting examples are the orthogonal algebras so(p,q) all of which are parabolically related to the conformal algebra so(n,2) with p+q=n+2, the parabolic subalgebras including the Lorentz subalgebra so(n-1,1) and its analogs so(p-1,...
Dobrev, V K
2013-01-01
In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of {\\it parabolic relation} between two non-compact semisimple Lie algebras $\\cal G$ and $\\cal G'$ that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra $E_{7(7)}$ which is parabolically related to the CLA $E_{7(-25)}$. Other interesting examples are the orthogonal algebras $so(p,q)$ all of which are parabolically related to the conformal algebra $so(n,2)$ with $p+q=n+2$, the parabolic subalgebras including the Lorentz subalgebra $so(n-1,1)$ and its analogs ...
The Lie Algebraic Structure of Differential Operators Admitting Invariant Spaces of Polynomials
Finkel, F; Finkel, Federico; Kamran, Niky
1996-01-01
We prove that the scalar and $2\\times 2$ matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental Lie algebraic structure. Our approach is based on a general graphical method which does not require the modules to be irreducible under the action of the corresponding Lie (super)algebra. This method can be generalized to modules of polynomials in an arbitrary number of variables. We give generic examples of partially solvable differential operators which are not Lie algebraic. We show that certain vector-valued modules give rise to new realizations of finite-dimensional Lie superalgebras by first-order differential operators.
DEFF Research Database (Denmark)
Möllers, Jan; Ørsted, Bent; Zhang, Genkai
2016-01-01
on the nilpotent radicals $N$ and $N_1$ of the minimal parabolics in $G$ and $G_1$, respectively. The groups $N$ and $N_1$ are of H-type and we construct explicitly invariant differential operators between $N$ and $N_1$. These operators induce the projections onto the discrete components. Our construction...... of the invariant differential operators is carried out uniformly in the framework of H-type groups and also works for those H-type groups which do not occur as nilpotent radical of a parabolic subgroup in a semisimple group....
Operator equations and invariant subspaces
Directory of Open Access Journals (Sweden)
Valentin Matache
1994-05-01
Full Text Available Banach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A2=B2 and if A has nontrivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.
Simple Algebras of Invariant Operators
Institute of Scientific and Technical Information of China (English)
Xiaorong Shen; J.D.H. Smith
2001-01-01
Comtrans algebras were introduced in as algebras with two trilinear operators, a commutator [x, y, z] and a translator , which satisfy certain identities. Previously known simple comtrans algebras arise from rectangular matrices, simple Lie algebras, spaces equipped with a bilinear form having trivial radical, spaces of hermitian operators over a field with a minimum polynomial x2+1. This paper is about generalizing the hermitian case to the so-called invariant case. The main result of this paper shows that the vector space of n-dimensional invariant operators furnishes some comtrans algebra structures, which are simple provided that certain Jordan and Lie algebras are simple.
Kubo, Toshihisa
2011-01-01
In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the existence of such a system was left open in two cases, namely, the $\\Omega_3$ system for type $A_2$ and type $D_4$. Here, such a system is shown to exist for both cases. The construction of the system may also be interpreted as giving an explicit homomorphism between generalized Verma modules.
Differential invariants of second-order ordinary differential equations
Rosado Maria, Maria Eugenia
2011-01-01
The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.
Integration using invariant operators Conformally flat radiation metrics
Edgar, S B
1999-01-01
A new method is presented for obtaining the general conformally flat radiation metric by using the differential operators of Machado Ramos and Vickers (a generalisation of the GHP operators) which are invariant under null rotations and spin and boosts. The solution is found by constructing involutive tables of these derivatives applied to the quantities which arise in the Karlhede classification of metrics.
Nonlinear Differential Systems with Prescribed Invariant Sets
DEFF Research Database (Denmark)
Sandqvist, Allan
1999-01-01
We present a class of nonlinear differential systems for which invariant sets can be prescribed.Moreover,we show that a system in this class can be explicitly solved if a certain associated linear homogeneous system can be solved.As a simple application we construct a plane autonomous system having...
On the hierarchy of partially invariant submodels of differential equations
Energy Technology Data Exchange (ETDEWEB)
Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru
2008-07-04
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
Differential invariants of feedback transformations for quasi-harmonic oscillation equations
Gritsenko, Dmitry S.; Kiriukhin, Oleg M.
2017-03-01
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie pseudo-group of local feedback transformations. In particular, considered class describes behavior of conservative mechanical systems. We construct the class of rational differential invariants that separate regular orbits. It is well known that differential invariants form algebra with respect to the operation of addition and multiplication (Alekseevskij et al. 1991) [20]. In our case, constructed rational differential operators form a field (in algebraic sense). Rational differential invariants were studied by Rosenlicht (1956, 1963) [25,26], Kruglikov and Lychagin (2011) [24].
The Invar tensor package: Differential invariants of Riemann
Martín-García, J. M.; Yllanes, D.; Portugal, R.
2008-10-01
The long standing problem of the relations among the scalar invariants of the Riemann tensor is computationally solved for all 6ṡ10 objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within seconds a canonical form for any of those objects in terms of a basis. The process is as follows: (1) an invariant is converted in real time into a canonical form with respect to the permutation symmetries of the Riemann tensor; (2) Invar reads a database of more than 6ṡ10 relations and applies those coming from the cyclic symmetry of the Riemann tensor; (3) then applies the relations coming from the Bianchi identity, (4) the relations coming from commutations of covariant derivatives, (5) the dimensionally-dependent identities for dimension 4, and finally (6) simplifies invariants that can be expressed as product of dual invariants. Invar runs on top of the tensor computer algebra systems xTensor (for Mathematica) and Canon (for Maple). Program summaryProgram title:Invar Tensor Package v2.0 Catalogue identifier:ADZK_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_v2_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:3 243 249 No. of bytes in distributed program, including test data, etc.:939 Distribution format:tar.gz Programming language:Mathematica and Maple Computer:Any computer running Mathematica versions 5.0 to 6.0 or Maple versions 9 and 11 Operating system:Linux, Unix, Windows XP, MacOS RAM:100 Mb Word size:64 or 32 bits Supplementary material:The new database of relations is much larger than that for the previous version and therefore has not been included in
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V
2007-01-01
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given.
Rearrangement invariant optimal range for Hardy type operators
Soria, Javier; Tradacete, Pedro
2013-01-01
We characterize, in the context of rearrangement invariant spaces, the optimal range space for a class of monotone operators related to the Hardy operator. The connection between optimal range and optimal domain for these operators is carefully analyzed.
Riccati equations for second order spatially invariant partial differential systems
Curtain, Ruth F.
Recently, the class of spatially invariant systems was introduced with motivating examples of partial differential equations on an infinite domain. For these it was shown that by taking Fourier transforms, one obtains infinitely many finite-dimensional systems with a scalar parameter. The idea is
Spectral invariants of operators of Dirac type on partitioned manifolds
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Bleecker, D.
2004-01-01
We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators of Dirac type on closed manifolds and manifolds with bou...
Fermionic quantum operations: a computational framework I. Basic invariance properties
Lakos, Gyula
2015-01-01
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this first part we study how the basic invariance properties of FQ operations ($n=2$) are reflected in their formal power series expansions.
Singular conformally invariant trilinear forms and generalized Rankin Cohen operators
Jean-Louis, Clerc
2011-01-01
The most singular residues of the standard meromorphic family of trilinear conformally invariant forms on $\\mathcal C^\\infty_c(\\mathbb R^d)$ are computed. Their expression involves covariant bidifferential operators (generalized Rankin Cohen operators), for which new formul\\ae \\ are obtained. The main tool is a Bernstein-Sato identity for the kernel of the forms.
Energy Technology Data Exchange (ETDEWEB)
Christe, P.; Flume, R.
1987-04-09
We investigate the structure of the linear differential operators whose solutions determine the four-point correlations of primary operators in the d=2 conformally invariant SU(2) sigma-model with Wess-Zumino term and the d=2 critical statistical systems with central Virasoro charge smaller than one. Factorisation properties of the differential operators are related to a finite closure of the operator algebras. We recover the selection and fusion rules of Fateev, Zamolodchikov and Gepner, Witten for the SU(2) sigma-model. It is outlined how the results of the SU(2) model can be used for the identification of closed operator algebras in the statistical model.
Energy Technology Data Exchange (ETDEWEB)
Christe, P.; Flume, R.
1986-10-01
We investigate the structure of the linear differential operators whose solutions determine the four point correlations of primary operators in the d=2 conformally invariant SU(2) sigma-model with Wess-Zumino term and the d=2 critical statistical systems with central Virasoro charge smaller than one. Factorisation properties of the differential operators are related to a finite closure of the operator algebras. We recover the selection and fusion rules of Fateev, Zamolodchikov and Gepner, Witten for the SU(2) sigma-model. It is outlined how the results of the SU(2) model can be used for the identification of closed operator algebras in the statistical model.
Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations
2014-07-01
non- linear hybrid systems by linear algebraic methods. In Radhia Cousot and Matthieu Martel, editors, SAS, volume 6337 of LNCS, pages 373–389. Springer...Tarski. A decision method for elementary algebra and geometry. Bulletin of the American Mathematical Society, 59, 1951. [36] Wolfgang Walter. Ordinary...Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations Khalil Ghorbal1 Andrew Sogokon2 André Platzer1 July 2014
Zhou, Long-Qiao; Meleshko, Sergey V.
2017-01-01
A linear thermoviscoelastic model for homogeneous, aging materials with memory is established. A system of integro-differential equations is obtained by using two motions (a one-dimensional motion and a shearing motion) for this model. Applying the group analysis method to the system of integro-differential equations, the admitted Lie group is determined. Using this admitted Lie group, invariant and partially invariant solutions are found. The present paper gives a first example of application of partially invariant solutions to integro-differential equations.
J2 invariant relative orbits via differential correction algorithm
Institute of Scientific and Technical Information of China (English)
Ming Xu; Shijie Xu
2007-01-01
This paper describes a practical method for finding the invariant orbits in J2 relative dynamics. Working with the Hamiltonian model of the relative motion in cludingthe J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth's orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite,and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configurationis proposed. The influences of measure errors on the invariantorbit are also investigated by the Monte-Carlo simulation.
Hitchin's connection, Toeplitz operators, and symmetry invariant deformation quantization
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard
2012-01-01
We introduce the notion of a rigid family of Kähler structures on a symplectic manifold. We then prove that a Hitchin connection exists for any rigid holomorphic family of Kähler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints....... Using Toeplitz operators we prove that the Hitchin connection induces a unique formal connection on smooth functions on the symplectic manifold. Parallel transport of this formal connection produces equivalences between the corresponding Berezin–Toeplitz deformation quantizations. In the cases where...... the Hitchin connection is projectively flat, the formal connections will be flat and we get a symmetry-invariant formal quantization. If a certain cohomological condition is satisfied a global trivialization of this algebra bundle is constructed. As a corollary we get a symmetry-invariant deformation...
Invariant Hermitian Operator and Density Operator for the Adiabatically Time-Dependent System
Institute of Scientific and Technical Information of China (English)
YAN Feng-Li; YANG Lin-Guang
2001-01-01
The density operator is approximately expressed as a function of the invariant Hermitian operator for the adiabatically time-dependent system. Using this method, the calculation of the density operator for the Heisenberg spin system in a weakly time-dependent magnetic field is exemplified. By virtue of the density operator, we obtain equilibrium.``
One-loop potential with scale invariance and effective operators
Ghilencea, D M
2016-01-01
We study quantum corrections to the scalar potential in classically scale invariant theories, using a manifestly scale invariant regularization. To this purpose, the subtraction scale $\\mu$ of the dimensional regularization is generated after spontaneous scale symmetry breaking, from a subtraction function of the fields, $\\mu(\\phi,\\sigma)$. This function is then uniquely determined from general principles showing that it depends on the dilaton only, with $\\mu(\\sigma)\\sim \\sigma$. The result is a scale invariant one-loop potential $U$ for a higgs field $\\phi$ and dilaton $\\sigma$ that contains an additional {\\it finite} quantum correction $\\Delta U(\\phi,\\sigma)$, beyond the Coleman Weinberg term. $\\Delta U$ contains new, non-polynomial effective operators like $\\phi^6/\\sigma^2$ whose quantum origin is explained. A flat direction is maintained at the quantum level, the model has vanishing vacuum energy and the one-loop correction to the mass of $\\phi$ remains small without tuning (of its self-coupling, etc) bey...
Gauge invariant composite operators of QED in the exact renormalization group formalism
Sonoda, Hidenori
2013-01-01
Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ``gauge fixing parameter independence,'' we show that any gauge independent composite operators can be made ``gauge fixing parameter independent'' by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A. Zee.
On a class of invariant coframe operators with application to gravity
Itin, Yakov; Kaniel, Shmuel
2000-09-01
Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives and quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The article exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity, exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the geodesic postulate, we find all the equations that are experimentally (by the three classical tests) indistinguishable from Einstein field equations. This family also includes, of course, Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the article is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations.
Manifestly scale-invariant regularization and quantum effective operators
Ghilencea, D.M.
2016-01-01
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this symmetry explicitly. We show how to avoid this problem and study the implications of a manifestly scale invariant regularization in (classical) scale invariant theories. We use a dilaton-dependent subtraction function $\\mu(\\sigma)$ which after spontaneous breaking of scale symmetry generates the usual DR subtraction scale $\\mu(\\langle\\sigma\\rangle)$. One consequence is that "evanescent" interactions generated by scale invariance of the action in $d=4-2\\epsilon$ (but vanishing in $d=4$), give rise to new, finite quantum corrections. We find a (finite) correction $\\Delta U(\\phi,\\sigma)$ to the one-loop scalar potential for $\\phi$ and $\\sigma$, beyond the Coleman-Weinberg term. $\\Delta U$ is due to an evanescent correction ($\\propto\\epsilon$) to the field-dependent masses (of...
Institute of Scientific and Technical Information of China (English)
白永强; 刘震; 裴明
2008-01-01
The theory of moving frames developed by Peter J Olver and M Fels has importaut applications to geometry,classical invariant theory.We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.
ATTRACTING AND QUASI-INVARIANT SETS OF STOCHASTIC NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Dingshi LI; Daoyi XU
2013-01-01
In this article,we investigate a class of stochastic neutral partial functional differential equations.By establishing new integral inequalities,the attracting and quasi-invariant sets of stochastic neutral partial functional differential equations are obtained.The results in [15,16] are generalized and improved.
SPECTRAL PROPERTIES OF SECOND ORDER DIFFERENTIAL OPERATORS ON TWO-STEP NILPOTENT LIE GROUPS
Institute of Scientific and Technical Information of China (English)
Niu Pengcheng
2000-01-01
In this paper, spectral properties of certain left invariant differential operators on two-step nilpotent Lie groups are completely described by using the theory of unitary irreducible representations and the Plancherel formulae on nilpotent Lie groups.
Invariance of visual operations at the level of receptive fields.
Lindeberg, Tony
2013-01-01
The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the
Differential operators and automorphism schemes
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The ring of global differential operators of a variety is in closed and deep relation with its automorphism scheme.This relation can be applied to the study of homogeneous schemes,giving some criteria of homogeneity,a generalization of Serre-Lang theorem,and some consequences about abelian varieties.
ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES
Institute of Scientific and Technical Information of China (English)
J.M.BISMUT
2005-01-01
The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.
Differential invariants for Hirota-Ramani equation and Drinfel'd-Sokolov-Wilson system
Li, Wei; Li, Wenting; Wang, Fei; Zhang, Hongqing
2013-04-01
In this paper, the differential invariants of Lie symmetry groups of Hirota-Ramani (HR) equation and Drinfel'd-Sokolov-Wilson (DSW) system are obtained and their syzygies and recurrence relations are classified. The algorithms are based on the method of equivariant moving frames.
Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Classes of Invariant Subspaces for Some Operator Algebras
Hamhalter, Jan; Turilova, Ekaterina
2014-10-01
New results showing connections between structural properties of von Neumann algebras and order theoretic properties of structures of invariant subspaces given by them are proved. We show that for any properly infinite von Neumann algebra M there is an affiliated subspace such that all important subspace classes living on are different. Moreover, we show that can be chosen such that the set of σ-additive measures on subspace classes of are empty. We generalize measure theoretic criterion on completeness of inner product spaces to affiliated subspaces corresponding to Type I factor with finite dimensional commutant. We summarize hitherto known results in this area, discuss their importance for mathematical foundations of quantum theory, and outline perspectives of further research.
Formal theory for differential-difference operators
Faber, B.F.; Put, M. van der
2001-01-01
Differential-difference operators are linear operators involving both d/dz and the shift z ↦ z + 1 (or z(d/dz) and z ↦ qz). The aim is to give a formal classification and to provide solutions for these equations. Differential-difference operators can be considered as formal differential operators of
Wavelet Subspaces Invariant Under Groups of Translation Operators
Indian Academy of Sciences (India)
Biswaranjan Behera; Shobha Madan
2003-05-01
We study the action of translation operators on wavelet subspaces. This action gives rise to an equivalence relation on the set of all wavelets. We show by explicit construction that each of the associated equivalence classes is non-empty.
A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets
2014-11-01
linear hybrid systems by linear algebraic methods. In SAS, volume 6337 of LNCS, pages 373–389. Springer, 2010. [19] E. W. Mayr. Membership in polynomial...383–394, 2009. [31] A. Tarski. A decision method for elementary algebra and geometry. Bull. Amer. Math. Soc., 59, 1951. [32] A. Tiwari. Abstractions...A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets Khalil Ghorbal1 Andrew Sogokon2 André Platzer1 November 2014 CMU
Energy Technology Data Exchange (ETDEWEB)
Li Xicheng; Xu Mingyu [Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100 (China); Wang Shaowei [Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)], E-mail: xichengli@yahoo.com.cn
2008-04-18
In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given.
Chiral differential operators and topology
Cheung, Pokman
2010-01-01
The first part of this paper provides a new formulation of chiral differential operators (CDOs) in terms of global geometric quantities. The main result is a recipe to define essentially all sheaves of smooth CDOs on a cs-manifold; its ingredients consist of an affine connection and an even 3-form that trivializes the first Pontrjagin form. With the connection fixed, two suitable 3-forms define isomorphic sheaves of CDOs if and only if their difference is exact. Moreover, conformal structures are in one-to-one correspondence with even 1-forms that trivialize the first Chern form. The second part of this paper concerns the construction of what may be called "chiral Dolbeault complexes". The classical Dolbeault complex of a complex manifold M may be viewed as the functions on an associated cs-manifold with the action of an odd vector field Q that satisfies Q^2=0. Motivated by this, we study the condition under which a conformal sheaf of CDOs on that cs-manifold admits an odd derivation Q' that extends Q and sat...
Differential and holomorphic differential operators on noncommutative algebras
Beggs, E.
2015-07-01
This paper deals with sheaves of differential operators on noncommutative algebras, in a manner related to the classical theory of D-modules. The sheaves are defined by quotienting the tensor algebra of vector fields (suitably deformed by a covariant derivative). As an example we can obtain enveloping algebra like relations for Hopf algebras with differential structures which are not bicovariant. Symbols of differential operators are defined, but not studied. These sheaves are shown to be in the center of a category of bimodules with flat bimodule covariant derivatives. Also holomorphic differential operators are considered.
A Maple package to find first order differential invariants of 2ODEs via a Darboux approach
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.
2014-01-01
Here we present an implementation of a semi-algorithm to find elementary first order differential invariants (elementary first integrals) of a class of rational second order ordinary differential equations (rational 2ODEs). The algorithm was developed in Duarte and da Mota (2009) [18]; it is based on a Darboux-type procedure, and it is an attempt to construct an analog (generalization) of the method built by Prelle and Singer (1983) [6] for rational first order ordinary differential equations (rational 1ODEs). to deal, this time, with 2ODEs. The FiOrDi package presents a set of software routines in Maple for dealing with rational 2ODEs. The package presents commands permitting research investigations of some algebraic properties of the ODE that is being studied.
Two-loop scale-invariant scalar potential and quantum effective operators
Energy Technology Data Exchange (ETDEWEB)
Ghilencea, D.M. [National Institute of Physics and Nuclear Engineering (IFIN-HH), Theoretical Physics Department, Bucharest (Romania); CERN, Theory Division, Geneva 23 (Switzerland); Lalak, Z.; Olszewski, P. [University of Warsaw, Faculty of Physics, Institute of Theoretical Physics, Warsaw (Poland)
2016-12-15
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a Higgs-like scalar φ in theories in which scale symmetry is broken only spontaneously by the dilaton (σ). Its VEV left angle σ right angle generates the DR subtraction scale (μ ∝ left angle σ right angle), which avoids the explicit scale symmetry breaking by traditional regularizations (where μ = fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking (μ = fixed scale). These operators have the form φ{sup 6}/σ{sup 2}, φ{sup 8}/σ{sup 4}, etc., which generate an infinite series of higher dimensional polynomial operators upon expansion about left angle σ right angle >> left angle φ right angle, where such hierarchy is arranged by one initial, classical tuning. These operators emerge at the quantum level from evanescent interactions (∝ ε) between σ and φ that vanish in d = 4 but are required by classical scale invariance in d = 4 - 2ε. The Callan-Symanzik equation of the two-loop potential is respected and the two-loop beta functions of the couplings differ from those of the same theory regularized with μ = fixed scale. Therefore the running of the couplings enables one to distinguish between spontaneous and explicit scale symmetry breaking. (orig.)
On weakly D-differentiable operators
DEFF Research Database (Denmark)
Christensen, Erik
2016-01-01
Let DD be a self-adjoint operator on a Hilbert space HH and aa a bounded operator on HH. We say that aa is weakly DD-differentiable, if for any pair of vectors ξ,ηξ,η from HH the function 〈eitDae−itDξ,η〉〈eitDae−itDξ,η〉 is differentiable. We give an elementary example of a bounded operator aa, suc...
On invariant analysis of some time fractional nonlinear systems of partial differential equations. I
Singla, Komal; Gupta, R. K.
2016-10-01
An investigation of Lie point symmetries for systems of time fractional partial differential equations including Ito system, coupled Burgers equations, coupled Korteweg de Vries equations, Hirota-Satsuma coupled KdV equations, and coupled nonlinear Hirota equations has been done. Using the obtained symmetries, each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving Erdélyi-Kober fractional differential operator depending on a parameter α.
Differential operator multiplication method for fractional differential equations
Tang, Shaoqiang; Ying, Yuping; Lian, Yanping; Lin, Stephen; Yang, Yibo; Wagner, Gregory J.; Liu, Wing Kam
2016-08-01
Fractional derivatives play a very important role in modeling physical phenomena involving long-range correlation effects. However, they raise challenges of computational cost and memory storage requirements when solved using current well developed numerical methods. In this paper, the differential operator multiplication method is proposed to address the issues by considering a reaction-advection-diffusion equation with a fractional derivative in time. The linear fractional differential equation is transformed into an integer order differential equation by the proposed method, which can fundamentally fix the aforementioned issues for select fractional differential equations. In such a transform, special attention should be paid to the initial conditions for the resulting differential equation of higher integer order. Through numerical experiments, we verify the proposed method for both fractional ordinary differential equations and partial differential equations.
Hyperbolic differential operators and related problems
Ancona, Vincenzo
2003-01-01
Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the top
Aizawa, N.; Kuznetsova, Z.; Toppan, F.
2016-04-01
Conformal Galilei algebras (CGAs) labeled by d, ℓ (where d is the number of space dimensions and ℓ denotes a spin-ℓ representation w.r.t. the 𝔰𝔩(2) subalgebra) admit two types of central extensions, the ordinary one (for any d and half-integer ℓ) and the exotic central extension which only exists for d = 2 and ℓ ∈ ℕ. For both types of central extensions, invariant second-order partial differential equations (PDEs) with continuous spectrum were constructed by Aizawa et al. [J. Phys. A 46, 405204 (2013)]. It was later proved by Aizawa et al. [J. Math. Phys. 3, 031701 (2015)] that the ordinary central extensions also lead to oscillator-like PDEs with discrete spectrum. We close in this paper the existing gap, constructing a new class of second-order invariant PDEs for the exotic centrally extended CGAs; they admit a discrete and bounded spectrum when applied to a lowest weight representation. These PDEs are markedly different with respect to their ordinary counterparts. The ℓ = 1 case (which is the prototype of this class of extensions, just like the ℓ = /1 2 Schrödinger algebra is the prototype of the ordinary centrally extended CGAs) is analyzed in detail.
Institute of Scientific and Technical Information of China (English)
P.S. Vyas; FAN Hong-Yi; P.N. Gajjar; WU Hao; B.Y. Thakore; A.R. Jani
2008-01-01
We show that the recently proposed invariant eigen-operator (IEO) method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.
Two-loop scale-invariant scalar potential and quantum effective operators
Ghilencea, D.M.
2016-01-01
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\\sigma$). Its vev $\\langle\\sigma\\rangle$ generates the DR subtraction scale ($\\mu\\sim\\langle\\sigma\\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\\mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\\mu$=fixed scale). These operators have the form: $\\phi^6/\\sigma^2$, $\\phi^8/\\sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $\\langle\\sigma\\rangle\\gg \\langle\\phi\\rangle$, where such hierarchy is arranged by {\\it one} initial, classical tuning. These operators emerge at the quantum...
Institute of Scientific and Technical Information of China (English)
ZHA Xin-Wei; MA Gang-Long
2011-01-01
It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication (SLOCC) invariants. Verstraete et al.[Phys. Rev. A 65 (2002)052112] showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement classes. Li et al.[Phys.Rev. A 76 (2007)052311] showed that there are at least 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and semi-invariant. We give 16 different entanglement classes for four qubits by means of basic SLOCC invariants.%@@ It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication (SLOCC) invariants.Verstraete et al.[Phys.Rev.A 65(2002)052112] showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement classes.Li et al.[Phys.Rev.A 76(2007)052311] showed that there are at least 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and semi-invariant.We give 16 different entanglement classes for four qubits by means of basic SLOCC invariants.
Pei, Bo; Zhao, Meng; Miller, Brian C; Véla, Jose Luis; Bruinsma, Monique W; Virgin, Herbert W; Kronenberg, Mitchell
2015-06-15
Autophagy regulates cell differentiation, proliferation, and survival in multiple cell types, including cells of the immune system. In this study, we examined the effects of a disruption of autophagy on the differentiation of invariant NKT (iNKT) cells. Using mice with a T lymphocyte-specific deletion of Atg5 or Atg7, two members of the macroautophagic pathway, we observed a profound decrease in the iNKT cell population. The deficit is cell-autonomous, and it acts predominantly to reduce the number of mature cells, as well as the function of peripheral iNKT cells. In the absence of autophagy, there is reduced progression of iNKT cells in the thymus through the cell cycle, as well as increased apoptosis of these cells. Importantly, the reduction in Th1-biased iNKT cells is most pronounced, leading to a selective reduction in iNKT cell-derived IFN-γ. Our findings highlight the unique metabolic and genetic requirements for the differentiation of iNKT cells.
Dunkl–Darboux differential-difference operators
Khekalo, S. P.
2017-02-01
Using a natural generalization, we construct and study analogues of Dunkl differential-difference operators on the line. These analogues turn out to be closely connected with the so-called Burchnall– Chaundy–Adler–Moser polynomials and, therefore, with Darboux transforms. We find the eigenfunctions of these operators.
Neutral Operator and Neutral Differential Equation
Directory of Open Access Journals (Sweden)
Jingli Ren
2011-01-01
Full Text Available In this paper, we discuss the properties of the neutral operator (Ax(t=x(t−cx(t−δ(t, and by applying coincidence degree theory and fixed point index theory, we obtain sufficient conditions for the existence, multiplicity, and nonexistence of (positive periodic solutions to two kinds of second-order differential equations with the prescribed neutral operator.
Fermionic realisations of simple Lie algebras and their invariant fermionic operators
Azcarraga, J A D
2000-01-01
We study the representation D of a simple compact Lie algebra g of rank l constructed with the aid of the hermitian Dirac matrices of a ( dim g )-dimensional euclidean space. The irreducible representations of g contained in D are found by providing a general construction on suitable fermionic Fock spaces. We give full details not only for the simplest odd and even cases, namely su(2) and su(3) , but also for the next ( dim g )-even case of su(5) . Our results are far reaching: they apply to any g -invariant quantum mechanical system containing dim g fermions. Another reason for undertaking this study is to examine the role of the g -invariant fermionic operators that naturally arise. These are given in terms of products of an odd number of gamma matrices, and include, besides a cubic operator, l-1 fermionic scalars of higher order. The latter are constructed from the Lie algebra cohomology cocycles, and must be considered to be of theoretical significance similar to the cubic operator. In the ( dim g )-even ...
The commutant and similarity invariant of analytic Toeplitz operators on Bergman space
Institute of Scientific and Technical Information of China (English)
2007-01-01
The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator Mb(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. Prom the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K0-group term.
Differential geometric invariants for time-reversal symmetric Bloch-bundles: The "Real" case
De Nittis, Giuseppe; Gomi, Kiyonori
2016-05-01
Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related "Real" (resp. "Quaternionic") Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303-338 (2014)] for the "Real" case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1-55 (2015)] for the "Quaternionic" case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. De Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the "Real" case we generalize the Chern-Weil theory and we show that the assignment of a "Real" connection, along with the related differential Chern class and its holonomy, suffices for the classification of "Real" vector bundles in low dimensions.
Angiuli, Luciana
2010-01-01
In this paper we consider nonautonomous elliptic operators ${\\mathcal A}$ with nontrivial potential term defined in $I\\times\\mathbb R^d$, where $I$ is a right-halfline (possibly $I=\\mathbb R$). We prove that we can associate an evolution operator $(G(t,s))$ with ${\\mathcal A}$ in the space of all bounded and continuous functions on $\\mathbb R^d$. We also study the compactness properties of the operator $G(t,s)$. Finally, we provide sufficient conditions guaranteeing that each operator $G(t,s)$ preserves the usual $L^p$-spaces and $C_0(\\mathbb R^d)$.
Hyponormal differential operators with discrete spectrum
Directory of Open Access Journals (Sweden)
Zameddin I. Ismailov
2010-01-01
Full Text Available In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
Multipoint normal differential operators of first order
Directory of Open Access Journals (Sweden)
Zameddin I. Ismailov
2009-01-01
Full Text Available In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.
Selfadjoint extensions of multipoint singular differential operators
Directory of Open Access Journals (Sweden)
Zameddin I. Ismailov
2013-10-01
Full Text Available This article describes all selfadjoint extensions of the minimal operator generated by a linear singular multipoint symmetric differential-operator expression for first order in the direct sum of Hilbert spaces of vector-functions. This description is done in terms of the boundary values, and it uses the Everitt-Zettl and the Calkin-Gorbachuk methods. Also the structure of the spectrum of these extensions is studied.
Differential operators on Hermite Sobolev spaces
Indian Academy of Sciences (India)
Suprio Bhar; B Rajeev
2015-02-01
In this paper, we compute the Hilbert space adjoint * of the derivative operator on the Hermite Sobolev spaces $\\mathcal{S}_{q}$. We use this calculation to give a different proof of the ‘monotonicity inequality’ for a class of differential operators (, ) for which the inequality was proved in Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2(4) (2009) 515–591. We also prove the monotonicity inequality for (, ), when these correspond to the Ornstein–Uhlenbeck diffusion.
Matching of gauge invariant dimension 6 operators for $b\\to s$ and $b\\to c$ transitions
Aebischer, Jason; Fael, Matteo; Greub, Christoph
2016-01-01
New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are invariant under the Standard Model gauge group. In this article, we study the matching of the $SU(3)_C \\times SU(2)_L \\times U(1)_Y$ gauge invariant dim-6 operators on the standard $B$ physics Hamiltonian relevant for $b \\to s$ and $b\\to c$ transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, $W$, $Z$ and the Higgs particle. We first carry out the matching of the dim-6 operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter $b \\to s$ transitions already at tree level, but can give relevant one-loop matching effects.
Araújo, Ricardo de A
2010-12-01
This paper presents a hybrid intelligent methodology to design increasing translation invariant morphological operators applied to Brazilian stock market prediction (overcoming the random walk dilemma). The proposed Translation Invariant Morphological Robust Automatic phase-Adjustment (TIMRAA) method consists of a hybrid intelligent model composed of a Modular Morphological Neural Network (MMNN) with a Quantum-Inspired Evolutionary Algorithm (QIEA), which searches for the best time lags to reconstruct the phase space of the time series generator phenomenon and determines the initial (sub-optimal) parameters of the MMNN. Each individual of the QIEA population is further trained by the Back Propagation (BP) algorithm to improve the MMNN parameters supplied by the QIEA. Also, for each prediction model generated, it uses a behavioral statistical test and a phase fix procedure to adjust time phase distortions observed in stock market time series. Furthermore, an experimental analysis is conducted with the proposed method through four Brazilian stock market time series, and the achieved results are discussed and compared to results found with random walk models and the previously introduced Time-delay Added Evolutionary Forecasting (TAEF) and Morphological-Rank-Linear Time-lag Added Evolutionary Forecasting (MRLTAEF) methods.
Q-operators, Yangian invariance and the quantum inverse scattering method
Frassek, Rouven
2014-01-01
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author's original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the fun...
On chiral differential operators over homogeneous spaces
Directory of Open Access Journals (Sweden)
Vassily Gorbounov
2001-01-01
Full Text Available We give a classification and construction of chiral algebras of differential operators over semisimple algebraic groups G and over homogeneous spaces G/N and G/P where N is a nilpotent and P a parabolic subgroup.
Pointwise estimates of pseudo-differential operators
DEFF Research Database (Denmark)
Johnsen, Jon
2011-01-01
As a new technique it is shown how general pseudo-differential operators can be estimated at arbitrary points in Euclidean space when acting on functions u with compact spectra. The estimate is a factorisation inequality, in which one factor is the Peetre–Fefferman–Stein maximal function of u...
Pointwise estimates of pseudo-differential operators
DEFF Research Database (Denmark)
Johnsen, Jon
As a new technique it is shown how general pseudo-differential operators can be estimated at arbitrary points in Euclidean space when acting on functions u with compact spectra.The estimate is a factorisation inequality, in which one factor is the Peetre–Fefferman–Stein maximal function of u...
ALGEBRAIC METHODS IN PARTIAL DIFFERENTIAL OPERATORS
Institute of Scientific and Technical Information of China (English)
Djilali Behloul
2005-01-01
In this paper we build a class of partial differential operators L having the following property: if u is a meromorphic function in Cn and Lu is a rational function A/q, with q homogenous, then u is also a rational function.
Pseudo-differential operators and generalized functions
Toft, Joachim
2015-01-01
This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.
DEFF Research Database (Denmark)
Yoon, G. H.; Kim, Y. Y.; Bendsøe, Martin P.;
2004-01-01
In topology optimization applications for the design of compliant mechanisms, the formation of hinges is typically encountered. Often such hinges are unphysical artifacts that appear due to the choice of discretization spaces for design and analysis. The objective of this work is to present a new...... in the multiscale design space. To imbed the shrinkage method implicitly in the optimization formulation and thus facilitate sensitivity analysis, the shrinkage method is made differentiable by means of differentiable versions of logical operators. The validity of the present method is confirmed by solving typical...... two-dimensional compliant mechanism design problems....
Anisovich, A V; Sarantsev, A V
2016-01-01
Vertex operators for photo- and electro-production of baryon states with arbitrary spin-parity, $ \\gamma + N\\to B(J^P)$, are constructed. The operators obey gauge invariance and analyticity constraints. Analyticity is realized as a requirement of the generalized Siegert theorem for vertex form factors.
Operator calculus - the exterior differential complex
Harrison, Jenny
2011-01-01
This paper and its sequels lay the groundwork for an operator calculus based on a spectral pair ('B,O) where 'B is a complete locally convex topological vector space of "differential chains" and O is an algebra of continuous operators acting on 'B. The topological dual of 'B is isomorphic to the classical Fr\\'echet space B of differential forms with uniform bounds on each of its directional derivatives. In a sequel H. Pugh and the author show that 'B is not generally reflexive. Since basic operators sufficient for a full calculus described in this paper, and important products are closed in 'B, there is little need for the larger double dual space B'. The covariant, constructive viewpoint of chains takes precedence over the contravariant, abstract viewpoint of cochains. In other words, chains come first. Applications include the first proof of a solution to Plateau's problem for soap films, solving a two hundred year old problem.
Relativistic differential-difference momentum operators and noncommutative differential calculus
Mir-Kasimov, R. M.
2013-09-01
The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.
Spectral theory of ordinary differential operators
Weidmann, Joachim
1987-01-01
These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including th...
Pseudo-Differential Operators and Integrable Models
Sedra, M B
2009-01-01
The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra $\\Xi $ of nonlinear (local and nonlocal) differential operators, acting on the ring of analytic functions $u_{s}(x, t)$, is studied. It is shown in particular that this space splits into several classes of subalgebras $\\Sigma_{jr}, j=0,\\pm 1, r=\\pm 1$ completely specified by the quantum numbers: $s$ and $(p,q)$ describing respectively the conformal weight (or spin) and the lowest and highest degrees. The algebra ${\\huge \\Sigma}_{++}$ (and its dual $\\Sigma_{--}$) of local (pure nonlocal) differential operators is important in the sense that it gives rise to the explicit form of the second hamiltonian structure of the KdV system and that we call also the Gelfand-Dickey Poisson bracket. This is explicitly done in several previous studies, see for the moment \\cite{4, 5, 14}. Some results concerning the KdV and Boussinesq hierarchies are derived explicitly.
Representations of Inverse Covariances by Differential Operators
Institute of Scientific and Technical Information of China (English)
Qin XU
2005-01-01
In the cost function of three- or four-dimensional variational data assimilation, each term is weighted by the inverse of its associated error covariance matrix and the background error covariance matrix is usually much larger than the other covariance matrices. Although the background error covariances are traditionally normalized and parameterized by simple smooth homogeneous correlation functions, the covariance matrices constructed from these correlation functions are often too large to be inverted or even manipulated. It is thus desirable to find direct representations of the inverses of background errorcorrelations. This problem is studied in this paper. In particular, it is shown that the background term can be written into ∫ dx|Dv(x)|2, that is, a squared L2 norm of a vector differential operator D, called the D-operator, applied to the field of analysis increment v(x). For autoregressive correlation functions, the Doperators are of finite orders. For Gaussian correlation functions, the D-operators are of infinite order. For practical applications, the Gaussian D-operators must be truncated to finite orders. The truncation errors are found to be small even when the Gaussian D-operators are truncated to low orders. With a truncated D-operator, the background term can be easily constructed with neither inversion nor direct calculation of the covariance matrix. D-operators are also derived for non-Gaussian correlations and transformed into non-isotropic forms.
SymPix: A spherical grid for efficient sampling of rotationally invariant operators
Seljebotn, Dag Sverre
2015-01-01
We present SymPix, a special-purpose spherical grid optimized for efficient sampling of rotationally invariant linear operators. This grid is conceptually similar to the Gauss-Legendre (GL) grid, aligning sample points with iso-latitude rings located on Legendre polynomial zeros. Unlike the GL grid, however, the number of grid points per ring varies as a function of latitude, avoiding expensive over-sampling near the poles and ensuring nearly equal sky area per grid point. The ratio between the number of grid points in two neighbouring rings is required to be a low-order rational number (3, 2, 1, 4/3, 5/4 or 6/5) to maintain a high degree of symmetries. Our main motivation for this grid is to solve linear systems using multi-grid methods, and to construct efficient preconditioners through pixel-space sampling of the linear operator in question. The GL grid is not suitable for these purposes due to its massive over-sampling near the poles, leading to nearly degenerate linear systems, while HEALPix, another com...
Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations
Directory of Open Access Journals (Sweden)
Chunrong Zhu
2016-11-01
Full Text Available In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.
Convex functions, monotone operators and differentiability
Phelps, Robert R
1993-01-01
The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational princ...
[Operative differential therapy of rheumatic wrists].
Dinges, H; Fürst, M; Rüther, H; Schill, S
2007-09-01
The wrists are affected in the long-term in 90% of people with rheumatism and are often (42%) the first manifestation of a destructive disease. The functionality of the wrist and the whole hand is of great importance because in many cases loss of function of the wrists leads to severe limitations. Local and operative treatment of the wrist in rheumatoid arthritis (RA) is one of the main duties in rheuma-orthopaedics. For operative treatment there is a finely tuned differential therapeutic spectrum available. The diagnostic indications take the local and total pattern of affection, the current systemic therapy as well as patient wishes and patient compliance into consideration. In the early stages according to LDE (Larsen, Dale, Eek), soft tissues operations such as articulo-tenosynovectomy (ATS) are most commonly carried out. In further advanced stages osseus stabilisation must often be performed. At this point a smooth transition from partial arthrodesis to complete fixation is possible. After initial euphoria, arthroplasty of the wrist is being increasingly less used for operative treatment due to the unconvincing long-term results and high complication rate. With reference to the good long-term results of all operative procedures, in particular early ATS with respect to pain, function and protection of tendons, after failure of medicinal treatment and persistence of inflammatory activity in the wrist, patients should be transferred to an experienced rheuma-orthopaedic surgeon.
Yamazaki, Tatsuya; Hagiwara, Tomomichi
2014-08-01
A new stability analysis method of time-delay systems (TDSs) called the monodromy operator approach has been studied under the assumption that a TDS is represented as a time-delay feedback system consisting of a finite-dimensional linear time-invariant (LTI) system and a pure delay. For applying this approach to TDSs described by delay-differential equations (DDEs), the problem of converting DDEs into representation as time-delay feedback systems has been studied. With regard to such a problem, it was shown that, under discontinuous initial functions, it is natural to define the solutions of DDEs in two different ways, and the above conversion problem was solved for each of these two definitions. More precisely, the solution of a DDE was represented as either the state of the finite-dimensional part of a time-delay feedback system or a part of the output of another time-delay feedback system, depending on which definition of the DDE solution one is talking about. Motivated by the importance in establishing a thorough relationship between time-delay feedback systems and DDEs, this paper discusses the opposite problem of converting time-delay feedback systems into representation as DDEs, including the discussions about the conversion of the initial conditions. We show that the state of (the finite-dimensional part of) a time-delay feedback system can be represented as the solution of a DDE in the sense of one of the two definitions, while its 'essential' output can be represented as that of another DDE in the sense of the other type of definition. Rigorously speaking, however, it is also shown that the latter representation is possible regardless of the initial conditions, while some initial condition could prevent the conversion into the former representation. This study hence establishes that the representation of TDSs as time-delay feedback systems possesses higher ability than that with DDEs, as description methods for LTI TDSs with commensurate delays.
Analysis of linear partial differential operators
Hörmander , Lars
2005-01-01
This volume is an expanded version of Chapters III, IV, V and VII of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the monographs by Ehrenpreis and by Palamodov on this subject. The reader is assumed to be familiar with distribution theory as presented in Volume I. Most topics discussed here have in fact been encountered in Volume I in special cases, which should provide the necessary motivation and background for a more systematic and precise exposition. The main technical tool in this volume is the Fourier- Laplace transformation. More powerful methods for the study of operators with variable coefficients will be developed in Volume III. However, constant coefficient theory has given the guidance for all that work. Although the field...
Gibbs-Butzer differential operators on locally compact Vilenkin groups
Institute of Scientific and Technical Information of China (English)
苏维宜
1996-01-01
The concept of para-differential operators over locally compact Vilenkin groups is given and their properties are studied. By means of para-linearization theorem, efforts are made to establish the basic theory of Gibbs-Butzer differential operators.
Obtaining a class of Type N pure radiation metrics using invariant operators
Ramos, M P M
2004-01-01
We develop further the integration procedure in the generalised invariant formalism, and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A major addition to the technique is the introduction of non-intrinsic elements in generalised invariant formalism, which can be exploited to keep calculations manageable.
Abstract Operators and Higher-order Linear Partial Differential Equation
Institute of Scientific and Technical Information of China (English)
BI Guang-qing; BI Yue-kai
2011-01-01
We summarize several relevant principles for the application of abstract operators in partial differential equations,and combine abstract operators with the Laplace transform.Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations.
Convex functions, monotone operators and differentiability
Phelps, Robert R
1989-01-01
These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.
Dye, H A
2011-01-01
We construct two knot invariants. The first knot invariant is a sum constructed using linking numbers. The second is an invariant of flat knots and is a formal sum of flat knots obtained by smoothing pairs of crossings. This invariant can be used in conjunction with other flat invariants, forming a family of invariants. Both invariants are constructed using the parity of a crossing.
The Differential Virial Theorem with Gradient Formulas for the Operators
Finley, James P
2016-01-01
A gradient dependent formula is derived for the spinless one-particle density-matrix operator z from the differential virial theorem. A gradient dependent formula is also derived for a spinless one-particle density-matrix operator that can replace the two operators of the differential virial theorem that arise from the kinetic energy operator. Other operators are also derived that can replace the operators mentioned above in the differential virial theorem; these operators depend on the real part of spinless one-particle density-matrix.
Directory of Open Access Journals (Sweden)
V.M. Fedorchuk
2008-11-01
Full Text Available It is established which functional bases of the first-order differential invariants of the splitting and non-splitting subgroups of the Poincaré group $P(1,4$ are invariant under the subgroups of the extended Galilei group $widetilde G(1,3 subset P(1,4$. The obtained sets of functional bases are classified according to dimensions.
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational molecular spectra is explicitly proved and a connection of this Hamiltonian to the formalism of Amal'sky is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITOs) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved and a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced. Numerical tests against an experimental rotational band of HF are provided.
Vassiliev invariants a new framework for quantum gravity
Gambini, R; Pullin, J; Gambini, Rodolfo; Griego, Jorge; Pullin, Jorge
1998-01-01
We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of quantum gravity as geometrical operators acting on the space of Vassiliev invariants of spin nets. We show how to explicitly realize the diffeomorphism constraint on this space and present proposals for the construction of Hamiltonian constraints.
Conformal symmetry breaking operators for differential forms on spheres
Kobayashi, Toshiyuki; Pevzner, Michael
2016-01-01
This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vecto...
Afonso, S. M.; Bonotto, E. M.; Federson, M.; Schwabik, Š.
2011-04-01
In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times.
Directory of Open Access Journals (Sweden)
Hossein Jafari
2016-04-01
Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.
All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory
Fröb, Markus B; Hollands, Stefan
2015-01-01
We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfil suitable Ward identities. Our proof treats rigorously both all ultraviolet and infrared problems of the theory and provides, in the end, detailed analytical bounds on the correlation functions of an arbitrary number of composite local operators. These bounds are formulated in terms of certain weighted spanning trees extending between the insertion points of these operators. Our proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, combined with estimation techniques based on tree structures. Compared with previous mathematical treatments of massless theories without local gauge invariance [R. Guida and Ch. Kopper, arXiv:1103.5692; J. Holland, S. Hollands, and Ch. Kopper, arXiv:1411.1785] our constructions require seve...
Eigenvalues of singular differential operators by finite difference methods. I.
Baxley, J. V.
1972-01-01
Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.
Boolean linear differential operators on elementary cellular automata
Martín Del Rey, Ángel
2014-12-01
In this paper, the notion of boolean linear differential operator (BLDO) on elementary cellular automata (ECA) is introduced and some of their more important properties are studied. Special attention is paid to those differential operators whose coefficients are the ECA with rule numbers 90 and 150.
Pseudo-differential operators on manifolds with singularities
Schulze, B-W
1991-01-01
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
Bonaccio, Silvia; Reeve, Charlie L.
2006-01-01
This paper investigates the differentiation of cognitive abilities as a function of neuroticism. Specifically, we examine Eysenck and White's [Eysenck, H. J., and White, P. O. (1964). Personality and the measurement of intelligence. British Journal of Educational Psychology, 24, 197-201.] hypothesis that cognitive abilities are less differentiated…
Invariant manifolds and applications for functional differential equations of mixed type
Hupkes, Hermen Jan
2008-01-01
Differential equations posed on discrete lattices have by now become a popular modelling tool used in a wide variety of scientific disciplines. Such equations allow the inclusion of non-local interactions into models and lead to interesting dynamical and pattern-forming behaviour. Although many num
Pseudo-differential operators groups, geometry and applications
Zhu, Hongmei
2017-01-01
This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.
Krishnaswami, Govind S
2008-01-01
For a class of large-N multi-matrix models, we identify a group G that plays the same role as the group of loops on space-time does for Yang-Mills theory. G is the spectrum of a commutative shuffle-deconcatenation Hopf algebra that we associate to correlations. G is the exponential of the free Lie algebra. The generating series of correlations is a function on G and satisfies quadratic equations in convolution. These factorized Schwinger-Dyson or loop equations involve a collection of Schwinger-Dyson operators, which are shown to be right-invariant vector fields on G, one for each linearly independent primitive of the Hopf algebra. A large class of formal matrix models satisfying these properties are identified, including as special cases, the zero momentum limits of the Gaussian, Chern-Simons and Yang-Mills field theories. Moreover, the Schwinger-Dyson operators of the continuum Yang-Mills action are shown to be right-invariant derivations of the shuffle-deconcatenation Hopf algebra generated by sources labe...
Bilinear Pseudo-differential Operators on Local Hardy Spaces
Institute of Scientific and Technical Information of China (English)
Jiang Wei XIAO; Yin Sheng JIANG; Wen Hua GAO
2012-01-01
In this paper,the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type (1,0) in the sense of H(o)rmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.
An algebra of noncommutative differential operators and Sobolev spaces
Beggs, E J
2011-01-01
We consider differential operators over a noncommutative algebra $A$ generated by vector fields. This is shown to form an associative algebra of differential operators, and acts on $A$-modules $E$ with covariant derivative. For bimodule covariant derivatives on $E$, we consider a module map $U_E$ which classifies how similar to the classical case the bimodule covariant derivative is. If this module map vanishes, we give an action of differential operators on tensor products. This turns out to be quite simple, and is related to the braided shuffle product. However technical issues with tensor products mean that we are not yet able to give a form of Hopf algebroid structure to the algebra of differential operators. We end by using the repeated differentials given in the paper to give a definition of noncommutative Sobolev space.
Versal deformations of a Dirac type differential operator
1999-01-01
If we are given a smooth differential operator in the variable $x\\in {\\mathbb R}/2\\pi {\\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the $\\mbox{Diff}(S^1)$-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced $\\mb...
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators
Dasgupta, Keshav; Ramadevi, P; Tatar, Radu
2016-01-01
Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted N = 4 Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten's brane construction could lead, using certain well defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show th...
On two energy-like invariants of line graphs and related graph operations
Directory of Open Access Journals (Sweden)
Xiaodan Chen
2016-02-01
Full Text Available Abstract For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\\mu_{1}\\geq\\mu_{2}\\geq\\cdots\\geq\\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\\geq q_{2}\\geq\\cdots\\geq q_{n}\\geq0$ be its signless Laplacian eigenvalues. The Laplacian-energy-like invariant and incidence energy of G are defined as, respectively, LEL ( G = ∑ i = 1 n − 1 μ i and IE ( G = ∑ i = 1 n q i . $$\\mathit{LEL}(G=\\sum_{i=1}^{n-1}\\sqrt{ \\mu_{i}} \\quad\\mbox{and}\\quad \\mathit {IE}(G=\\sum_{i=1}^{n} \\sqrt{q_{i}}. $$ In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve previously known results. The main tools we use here are the Cauchy-Schwarz inequality and the Ozeki inequality.
Eigenvalues of singular differential operators by finite difference methods. II.
Baxley, J. V.
1972-01-01
Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.
Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential
Directory of Open Access Journals (Sweden)
Aleksandr Mikhailovich Kholkin
2016-01-01
Full Text Available A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained.
On almost automorphic solutions of linear operational-differential equations
Directory of Open Access Journals (Sweden)
Gaston M. N'Guérékata
2004-01-01
Full Text Available We prove almost periodicity and almost automorphy of bounded solutions of linear differential equations x′(t=Ax(t+f(t for some class of linear operators acting in a Banach space.
Directory of Open Access Journals (Sweden)
Muwei Li
Full Text Available Machine learning techniques, along with imaging markers extracted from structural magnetic resonance images, have been shown to increase the accuracy to differentiate patients with Alzheimer's disease (AD from normal elderly controls. Several forms of anatomical features, such as cortical volume, shape, and thickness, have demonstrated discriminative capability. These approaches rely on accurate non-linear image transformation, which could invite several nuisance factors, such as dependency on transformation parameters and the degree of anatomical abnormality, and an unpredictable influence of residual registration errors. In this study, we tested a simple method to extract disease-related anatomical features, which is suitable for initial stratification of the heterogeneous patient populations often encountered in clinical data. The method employed gray-level invariant features, which were extracted from linearly transformed images, to characterize AD-specific anatomical features. The intensity information from a disease-specific spatial masking, which was linearly registered to each patient, was used to capture the anatomical features. We implemented a two-step feature selection for anatomic recognition. First, a statistic-based feature selection was implemented to extract AD-related anatomical features while excluding non-significant features. Then, seven knowledge-based ROIs were used to capture the local discriminative powers of selected voxels within areas that were sensitive to AD or mild cognitive impairment (MCI. The discriminative capability of the proposed feature was measured by its performance in differentiating AD or MCI from normal elderly controls (NC using a support vector machine. The statistic-based feature selection, together with the knowledge-based masks, provided a promising solution for capturing anatomical features of the brain efficiently. For the analysis of clinical populations, which are inherently heterogeneous
On the reduction of the degree of linear differential operators
Bobieński, Marcin
2010-01-01
Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type.
Difference spaces and invariant linear forms
Nillsen, Rodney
1994-01-01
Difference spaces arise by taking sums of finite or fractional differences. Linear forms which vanish identically on such a space are invariant in a corresponding sense. The difference spaces of L2 (Rn) are Hilbert spaces whose functions are characterized by the behaviour of their Fourier transforms near, e.g., the origin. One aim is to establish connections between these spaces and differential operators, singular integral operators and wavelets. Another aim is to discuss aspects of these ideas which emphasise invariant linear forms on locally compact groups. The work primarily presents new results, but does so from a clear, accessible and unified viewpoint, which emphasises connections with related work.
On the formalism of local variational differential operators
Igonin, S.; Verbovetsky, A.V.; Vitolo, R.
2002-01-01
The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and com
On algebraically integrable differential operators on an elliptic curve
Etingof, Pavel
2010-01-01
We discuss explicit classification of algebraically integrable (i.e., finite gap) differential operators on elliptic curves with one and several poles. After giving a new exposition of some known results (based on differential Galois theory), we describe a conjectural classification of third order algebraically integrable operators with one pole (obtained using Maple), in particular discovering new "isolated" ones, living on special elliptic curves defined over $\\Bbb Q$. We also discuss algebraically integrable operators with several poles, with and without symmetries, and connect them to elliptic Calogero-Moser systems (in the case with symmetries, to the crystallographic ones, introduced recently by Felder, Ma, Veselov, and the first author).
SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence
Hollands, Stefan
2016-01-01
We propose a model for the dS/CFT correspondence. The model is constructed in terms of a "Yang-Baxter operator" $R$ for unitary representations of the deSitter group $SO(d,1)$. This $R$-operator is shown to satisfy the Yang-Baxter equation, unitarity, as well as certain analyticity relations, including in particular a crossing symmetry. With the aid of this operator we construct: a) A chiral (light-ray) conformal quantum field theory whose internal degrees of freedom transform under the given unitary representation of $SO(d,1)$. By analogy with the $O(N)$ non-linear sigma model, this chiral CFT can be viewed as propagating in a deSitter spacetime. b) A (non-unitary) Euclidean conformal quantum field theory on ${\\mathbb R}^{d-1}$, where $SO(d,1)$ now acts by conformal transformations in (Euclidean) spacetime. These two theories can be viewed as dual to each other if we interpret ${\\mathbb R}^{d-1}$ as conformal infinity of deSitter spacetime. Our constructions use semi-local generator fields defined in terms o...
spl(p,q) superalgebra and differential operators
Brihaye, Y; Kosinski, P; Brihaye, Yves; Giller, Stefan; Kosinski, Piotr
1997-01-01
Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general ingredients necessary to construct these representations and present examples related to spl(2,1) and spl(2,2). By revisiting the products of projectivised representations of sl(2), we are able to construct new sets of differential operators preserving some space of polynomials in two or more variables. In particular, this allows to express the representation of spl(2,1) in terms of matrix differential operators in two variables. The corresponding operators provide the building blocks for the construction of quasi exactly solvable systems of two and four equations in two variables. We also present a quommutator deformation of spl(2,1) which, by construction, provides an appropriate basis for analyzing the quasi exactly solvable systems of finite difference equations.
Perturbation of sectorial projections of elliptic pseudo-differential operators
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Chen, Guoyuan; Lesch, Matthias;
2012-01-01
Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We showthat it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology whichwe...... explicitly describe. Our main application deals with a continuous curve of arbitrary first order linear elliptic differential operators over a compact manifold with boundary. Under the additional assumption of the weak inner unique continuation property, we derive the continuity of a related curve...... of Calderón projections and hence of the Cauchy data spaces of the original operator curve. In the Appendix, we describe a topological obstruction against a verbatim use of R. Seeley’s original argument for the complex powers, which was seemingly overlooked in previous studies of the sectorial projection....
SUB-SIGNATURE OPERATORS, η-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES
Institute of Scientific and Technical Information of China (English)
张伟平
2004-01-01
The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2, 3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants.
On modular invariant partition functions of conformal field theories with logarithmic operators
Flohr, M A
1995-01-01
We extend the definitions of characters and partition functions to the case of conformal field theories which contain operators with logarithmic correlation functions. As an example we consider the theories with central charge c = c(p,1) = 13-6(p+1/p), the ``border'' of the discrete minimal series. We show that there is a slightly generalized form of the property of rationality for such logarithmic theories. In particular, we obtain a classification of theories with c = c(p,1) which is similar to the A-D-E classification of c = 1 models.
On multipartite invariant states
Chruscinski, D; Chruscinski, Dariusz; Kossakowski, Andrzej
2006-01-01
We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states: separability criteria and multi-PPT conditions.
Directory of Open Access Journals (Sweden)
Phil Diamond
2003-01-01
Full Text Available Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.
On Two Kinds of Differential Operators on General Smooth Surfaces
Xie, Xi-Lin
2013-01-01
Two kinds of differential operators that can be generally defined on an arbitrary smooth surface in a finite dimensional Euclid space are studied, one is termed as surface gradient and the other one as Levi-Civita gradient. The surface gradient operator is originated from the differentiability of a tensor field defined on the surface. Some integral and differential identities have been theoretically studied that play the important role in the studies on continuous mediums whose geometrical configurations can be taken as surfaces and on interactions between fluids and deformable boundaries. The definition of Levi-Civita gradient is based on Levi-Civita connections generally defined on Riemann manifolds. It can be used to set up some differential identities in the intrinsic/coordiantes-independent form that play the essential role in the theory of vorticity dynamics for two dimensional flows on general fixed smooth surfaces.
Wavelet operational matrix method for solving the Riccati differential equation
Li, Yuanlu; Sun, Ning; Zheng, Bochao; Wang, Qi; Zhang, Yingchao
2014-03-01
A Haar wavelet operational matrix method (HWOMM) was derived to solve the Riccati differential equations. As a result, the computation of the nonlinear term was simplified by using the Block pulse function to expand the Haar wavelet one. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. The capability and the simplicity of the proposed method was demonstrated by some examples and comparison with other methods.
Explicit fundamental solutions of some second order differential operators on Heisenberg groups
Cardoso, Isolda
2012-01-01
Let $p,q,n$ be natural numbers such that $p+q=n$. Let $\\FF$ be either $\\CC$, the complex numbers field, or $\\HH$, the quaternionic division algebra. We consider the Heisenberg group $N(p,q,\\FF)$ defined as $N(p,q,\\FF)=\\FF^{n}\\times \\mathfrak{Im}\\FF$, with group law given by $$(v,\\zeta)(v',\\zeta')=(v+v', \\zeta+\\zeta'-{1/2} \\mathfrak{Im} B(v,v')),$$ where $B(v,w)=\\sum_{j=1}^{p} v_{j}\\bar{w_{j}} - \\sum_{j=p+1}^{n} v_{j}\\bar{w_{j}}$. Let $U(p,q,\\FF)$ be the group of $n\\times n$ matrices with coefficients in $\\FF$ that leave invariant the form $B$. In this work we compute explicit fundamental solutions of some second order differential operators on $N(p,q,\\FF)$ which are canonically associated to the action of $U(p,q,\\FF)$.
Fiorentini, M A L Capri D; Mintz, B W; Palhares, L F; Sorella, S P
2016-01-01
We address the issue of the renormalizability of the gauge-invariant non-local dimension-two operator $A^2_{\\rm min}$, whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator $A^2_{\\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A^2_{\\rm min}$ turns out to be independent from the gauge parameter $\\alpha$ entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator $A^2$ in the Landau gauge.
Differential evolution with ranking-based mutation operators.
Gong, Wenyin; Cai, Zhihua
2013-12-01
Differential evolution (DE) has been proven to be one of the most powerful global numerical optimization algorithms in the evolutionary algorithm family. The core operator of DE is the differential mutation operator. Generally, the parents in the mutation operator are randomly chosen from the current population. In nature, good species always contain good information, and hence, they have more chance to be utilized to guide other species. Inspired by this phenomenon, in this paper, we propose the ranking-based mutation operators for the DE algorithm, where some of the parents in the mutation operators are proportionally selected according to their rankings in the current population. The higher ranking a parent obtains, the more opportunity it will be selected. In order to evaluate the influence of our proposed ranking-based mutation operators on DE, our approach is compared with the jDE algorithm, which is a highly competitive DE variant with self-adaptive parameters, with different mutation operators. In addition, the proposed ranking-based mutation operators are also integrated into other advanced DE variants to verify the effect on them. Experimental results indicate that our proposed ranking-based mutation operators are able to enhance the performance of the original DE algorithm and the advanced DE algorithms.
Repeated morphine treatment influences operant and spatial learning differentially
Institute of Scientific and Technical Information of China (English)
Mei-Na WANG; Zhi-Fang DONG; Jun CAO; Lin XU
2006-01-01
Objective To investigate whether repeated morphine exposure or prolonged withdrawal could influence operant and spatial learning differentially. Methods Animals were chronically treated with morphine or subjected to morphine withdrawal. Then, they were subjected to two kinds of learning: operant conditioning and spatial learning.Results The acquisition of both simple appetitive and cued operant learning was impaired after repeated morphine treatment. Withdrawal for 5 weeks alleviated the impairments. Single morphine exposure disrupted the retrieval of operant memory but had no effect on rats after 5-week withdrawal. Contrarily, neither chronic morphine exposure nor 5-week withdrawal influenced spatial learning task of the Morris water maze. Nevertheless, the retrieval of spatial memory was impaired by repeated morphine exposure but not by 5-week withdrawal. Conclusion These observations suggest that repeated morphine exposure can influence different types of learning at different aspects, implicating that the formation of opiate addiction may usurp memory mechanisms differentially.
Nonlocal Problems for Fractional Differential Equations via Resolvent Operators
Directory of Open Access Journals (Sweden)
Zhenbin Fan
2013-01-01
Full Text Available We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.
Spectrum of a Differential Operator with Periodic Generalized Potential
Directory of Open Access Journals (Sweden)
Mehmet Sahin
2007-01-01
Full Text Available We study some spectral problems for a second-order differential operator with periodic potential. Notice that the given potential is a sum of zero- and first-order generalized functions. It is shown that the spectrum of the investigated operator consists of infinite number of gaps whose length limit unlike the classic case tends to nonzero constant in some place and to infinity in other place.
Selfadjoint singular differential operators of first order and their spectrum
Directory of Open Access Journals (Sweden)
Zameddin I. Ismailov
2016-01-01
Full Text Available Based on Calkin-Gorbachuk method, we describe all selfadjoint extensions of the minimal operator generated by linear multipoint singular symmetric differential-operator, as a direct sum of weighted Hilbert space of vector-functions. Another approach to the investigation of this problem has been done by Everitt, Zettl and Markus. Also we study the structure of spectrum of these extensions.
On conditions for invertibility of difference and differential operators in weight spaces
Energy Technology Data Exchange (ETDEWEB)
Bichegkuev, Mairbek S [North-Ossetia State University, Vladikavkaz (Russian Federation)
2011-08-31
We obtain necessary and sufficient conditions for the invertibility of the difference operator D{sub E}:D(D{sub E}) subset of l{sup p}{sub {alpha}}{yields}l{sup p}{sub {alpha}}, (D{sub E} x)(n)=x(n+1)-Bx(n), n element of Z{sub +}, whose domain D(D{sub E}) is given by the condition x(0) element of E, where l{sup p}{sub {alpha}}=l{sup p}{sub {alpha}}(Z{sub +},X), p element of [1,{infinity}], is the Banach space of sequences (of vectors in a Banach space X) summable with weight {alpha}:Z{sub +}{yields}(0,{infinity}) for p element of [1,{infinity}) and bounded with respect to {alpha} for p={infinity}, B:X{yields}X is a bounded linear operator, and E is a closed B-invariant subspace of X. We give applications to the invertibility of differential operators with an unbounded operator coefficient (the generator of a strongly continuous operator semigroup) in weight spaces of functions.
Proton spin: A topological invariant
Tiwari, S. C.
2016-11-01
Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein-Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to ℏ 2, i.e. proton spin decomposition has no meaning in this approach.
On invariants and scalar chiral correlation functions in N=1 superconformal field theories
Knuth, Holger
2010-01-01
A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomi...
A differential operator for integrating one-loop scattering equations
Chen, Gang; Wang, Tianheng; Xu, Feng
2016-01-01
We propose a differential operator for computing the residues associated with a class of meromorphic $n$-forms that frequently appear in the Cachazo-He-Yuan form of the scattering amplitudes. This differential operator is conjectured to be uniquely determined by the local duality theorem and the intersection number of the divisors in the $n$-form. We use the operator to evaluate the tree-level amplitude of $\\phi^3$ theory and the one-loop integrand of Yang-Mills theory from their CHY forms. The method can reduce the complexity of the calculation. In addition, the expression for the 1-loop four-point Yang-Mills integrand obtained in our approach has a clear correspondence with the Q-cut results.
Globally nilpotent differential operators and the square Ising model
Energy Technology Data Exchange (ETDEWEB)
Bostan, A [INRIA Rocquencourt, Domaine de Voluceau, BP 105 78153 Le Chesnay Cedex (France); Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida (Algeria); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M [LPTMC, CNRS, Universite de Paris, Tour 24, 4eme etage, Case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Weil, J-A [LACO, XLIM, Universite de Limoges, 123 Avenue Albert Thomas, 87060 Limoges Cedex (France)], E-mail: alin.bostan@inria.fr, E-mail: boukraa@mail.univ-blida.dz, E-mail: maillard@lptmc.jussieu.fr, E-mail: jacques-arthur.weil@unilim.fr, E-mail: njzenine@yahoo.com
2009-03-27
We recall various multiple integrals with one parameter, related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their {lambda}-extensions. The univariate analytic functions defined by these integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations, as well as their Russian-doll and direct sum structures. These differential operators are selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. We also display miscellaneous examples of globally nilpotent operators emerging from enumerative combinatorics problems for which no integral representation is yet known. Focusing on the factorized parts of all these operators, we find out that the global nilpotence of the factors (resp. p-curvature nullity) corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, curves of genus five, six,..., and even a remarkable weight-1 modular form emerging in the three-particle contribution {chi}{sup (3)} of the magnetic susceptibility of the square Ising model. Noticeably, this associated weight-1 modular form is also seen in the factors of the differential operator for another n-fold integral of the Ising class, {phi}{sup (3)}{sub H}, for the staircase polygons counting, and in Apery's study of {zeta}(3). G-functions naturally occur as solutions of globally nilpotent operators. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or {infinity}) that correspond to the confluence of singularities in the scaling limit
A novel fully differential telescopic operational transconductance amplifier
Energy Technology Data Exchange (ETDEWEB)
Li Tianwang; Jiang Jinguang [Department of Integrated Circuits and Communication Software, International School of Software, Wuhan University, Wuhan 430079 (China); Ye Bo, E-mail: jgjiang95@yahoo.com.c [Faculty of Computer and Information Engineering, Shanghai University of Electric Power, Shanghai 200090 (China)
2009-08-15
A novel fully differential telescopic operational transconductance amplifier (OTA) is proposed. An additional PMOS differential pair is introduced to improve the unit-gain bandwidth of the telescopic amplifier. At the same time, the slew rate is enhanced by the auxiliary slew rate boost circuits. The proposed OTA is designed in a 0.18{mu}m CMOS process. Simulation results show that there is a 49% improvement in the unit-gain bandwidth compared to that of a conventional OTA; moreover, the DC gain and the slew rate are also enhanced. (semiconductor integrated circuits)
Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
Directory of Open Access Journals (Sweden)
Mahmut Mak
2014-01-01
Full Text Available We consider hyperbolic rotation (G0, hyperbolic translation (G1, and horocyclic rotation (G2 groups in H3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of G0 in H3. Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator in H3.
Operator splitting for partial differential equations with Burgers nonlinearity
Holden, Helge; Risebro, Nils Henrik
2011-01-01
We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+u u_x$ where $A$ is a linear differential operator such that the equation is well-posed. Particular examples include the viscous Burgers' equation, the Korteweg-de Vries (KdV) equation, the Benney-Lin equation, and the Kawahara equation. We show that the Strang splitting method converges with the expected rate if the initial data are sufficiently regular. In particular, for the KdV equation we obtain second-order convergence in $H^r$ for initial data in $H^{r+5}$ with arbitrary $r\\ge 1$.
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; TANG Xu-Bing
2006-01-01
Using the "Pseudo-invariant eigen-operator" method we find the energy-gap of the Jaynes-Cummings Hamiltonian model of an atom-cavity system. This model takes the atomic centre-of-mass motion into account. The supersymmetric structure is involved in the Hamiltonian of an atom-cavity system. By selecting suitable supersymmetric generators and using supersymmetric transformation the Hamiltonian is diagonalized and energy eigenvectors are obtained.
Spectral analysis of difference and differential operators in weighted spaces
Energy Technology Data Exchange (ETDEWEB)
Bichegkuev, M S [North-Ossetia State University, Vladikavkaz (Russian Federation)
2013-11-30
This paper is concerned with describing the spectrum of the difference operator K:l{sub α}{sup p}(Z,X)→l{sub α}{sup p}(Z......athscrKx)(n)=Bx(n−1), n∈Z, x∈l{sub α}{sup p}(Z,X), with a constant operator coefficient B, which is a bounded linear operator in a Banach space X. It is assumed that K acts in the weighted space l{sub α}{sup p}(Z,X), 1≤p≤∞, of two-sided sequences of vectors from X. The main results are obtained in terms of the spectrum σ(B) of the operator coefficient B and properties of the weight function. Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given. Bibliography: 23 titles.
Differential evolution enhanced with multiobjective sorting-based mutation operators.
Wang, Jiahai; Liao, Jianjun; Zhou, Ying; Cai, Yiqiao
2014-12-01
Differential evolution (DE) is a simple and powerful population-based evolutionary algorithm. The salient feature of DE lies in its mutation mechanism. Generally, the parents in the mutation operator of DE are randomly selected from the population. Hence, all vectors are equally likely to be selected as parents without selective pressure at all. Additionally, the diversity information is always ignored. In order to fully exploit the fitness and diversity information of the population, this paper presents a DE framework with multiobjective sorting-based mutation operator. In the proposed mutation operator, individuals in the current population are firstly sorted according to their fitness and diversity contribution by nondominated sorting. Then parents in the mutation operators are proportionally selected according to their rankings based on fitness and diversity, thus, the promising individuals with better fitness and diversity have more opportunity to be selected as parents. Since fitness and diversity information is simultaneously considered for parent selection, a good balance between exploration and exploitation can be achieved. The proposed operator is applied to original DE algorithms, as well as several advanced DE variants. Experimental results on 48 benchmark functions and 12 real-world application problems show that the proposed operator is an effective approach to enhance the performance of most DE algorithms studied.
Differential spacecraft charging on the geostationary operational environmental satellites
Farthing, W. H.; Brown, J. P.; Bryant, W. C.
1982-01-01
Subsystems aboard the Geostationary Operational Environmental Satellites 4 and 5 showed instances of anomalous changes in state corresponding to false commands. Evidence linking the anomalous changes to geomagnetic activity, and presumably static discharges generated by spacecraft differential charging induced by substorm particle injection events is presented. The anomalies are shown to be correlated with individual substorms as monitored by stations of the North American Magnetometer Chain. The relative frequency of the anomalies is shown to be a function of geomagnetic activity. Finally a least squares fit to the time delay between substorm initiation and spacecraft anomaly as a function of spacecraft local time is shown to be consistent with injected electron populations with energy in the range 10 keV to 15 keV, in agreement with present understanding of the spacecraft charging mechanism. The spacecraft elements responsible for the differential charging were not satisfactorily identified. That question is currently under investigation.
Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications
Directory of Open Access Journals (Sweden)
F. Toutounian
2013-01-01
Full Text Available This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized Pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solution of Pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods.
On invariants and scalar chiral correlation functions in N=1 superconformal field theories
Knuth, Holger
2010-01-01
A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d>2 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.
On Invariants and Scalar Chiral Correlation Functions in { n} = 1 Superconformal Field Theories
Knuth, Holger
A general expression for the four-point function with vanishing total R-charge of antichiral and chiral superfields in { N} = 1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross-ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d > 1 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.
Quantum-mechanical tunneling differential operators, zeta-functions and determinants
Casahorrán, J
2002-01-01
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral method. Once we perform the Wick rotation, the euclidean equation of motion is the same as the usual one for the point particle in real time, except that the potential at issue is turned upside down. In doing so, our double-well potential becomes a two-humped potential. As required by the semiclassical approximation we may study the quadratic fluctuations over the instanton which represents in this context the localised finite-action solutions of the euclidean equation of motion. The determinants of the quadratic differential operators are evaluated by means of the zeta-function method. We write in closed form the eigenfunctions as well as the energy eigenvalues corresponding to such operators by using the shape-invariance symmetry. The effect of the multi-instantons configu...
An -Dimensional Pseudo-Differential Operator Involving the Hankel Transformation
Indian Academy of Sciences (India)
R S Pathak; Akhilesh Prasad; Manish Kumar
2012-02-01
An -dimensional pseudo-differential operator (p.d.o.) involving the -dimensional Hankel transformation is defined. The symbol class $H^m$ is introduced. It is shown that p.d.o.'s associated with symbols belonging to this class are continuous linear mappings of the -dimensional Zemanian space $H_(I^n)$ into itself. An integral representation for the p.d.o. is obtained. Using the Hankel convolution, it is shown that the p.d.o. satisfies a certain 1-norm inequality.
Fundamental solutions of linear partial differential operators theory and practice
Ortner, Norbert
2015-01-01
This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics...
Nonlinear evolution operators and semigroups applications to partial differential equations
Pavel, Nicolae H
1987-01-01
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.
Inverse spectral analysis for singular differential operators with matrix coefficients
Directory of Open Access Journals (Sweden)
Nour el Houda Mahmoud
2006-02-01
Full Text Available Let $L_alpha$ be the Bessel operator with matrix coefficients defined on $(0,infty$ by $$ L_alpha U(t = U''(t+ {I/4-alpha^2over t^2}U(t, $$ where $alpha$ is a fixed diagonal matrix. The aim of this study, is to determine, on the positive half axis, a singular second-order differential operator of $L_alpha+Q$ kind and its various properties from only its spectral characteristics. Here $Q$ is a matrix-valued function. Under suitable circumstances, the solution is constructed by means of the spectral function, with the help of the Gelfund-Levitan process. The hypothesis on the spectral function are inspired on the results of some direct problems. Also the resolution of Fredholm's equations and properties of Fourier-Bessel transforms are used here.
Sugimoto, Chie; Mituyama, Toutai; Wakao, Hiroshi
2017-01-01
Mucosal-associated invariant T cells (MAITs) are innate-like T cells that play a pivotal role in the host defense against infectious diseases, and are also implicated in autoimmune diseases, metabolic diseases, and cancer. Recent studies have shown that induced pluripotent stem cells (iPSCs) derived from MAITs selectively redifferentiate into MAITs without altering their antigen specificity. Such a selective differentiation is a prerequisite for the use of MAITs in cell therapy and/or regenerative medicine. However, the molecular mechanisms underlying this phenomenon remain unclear. Here, we performed methylome and transcriptome analyses of MAITs during the course of differentiation from iPSCs. Our multi-omics analyses revealed that recombination-activating genes (RAG1 and RAG2) and DNA nucleotidylexotransferase (DNTT) were highly methylated with their expression being repressed throughout differentiation. Since these genes are essential for V(D)J recombination of the T cell receptor (TCR) locus, this indicates that nascent MAITs are kept from further rearrangement that may alter their antigen specificity. Importantly, we found that the repression of RAGs was assured in two layers: one by the modulation of transcription factors for RAGs, and the other by DNA methylation at the RAG loci. Together, our study provides a possible explanation for the unaltered antigen specificity in the selective differentiation of MAITs from iPSCs. PMID:28346544
Stoker, J J
2011-01-01
This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis.
Directory of Open Access Journals (Sweden)
Sotirios K. Goudos
2015-01-01
Full Text Available This paper addresses the problem of designing shaped beam patterns with arbitrary arrays subject to constraints. The constraints could include the sidelobe level suppression in specified angular intervals, the mainlobe halfpower beamwidth, and the predefined number of elements. In this paper, we propose a new Differential Evolution algorithm, which combines Composite DE with an eigenvector-based crossover operator (CODE-EIG. This operator utilizes eigenvectors of covariance matrix of individual solutions, which makes the crossover rotationally invariant. We apply this novel design method to shaped beam pattern synthesis for linear and conformal arrays. We compare this algorithm with other popular algorithms and DE variants. The results show CODE-EIG outperforms the other DE algorithms in terms of statistical results and convergence speed.
Conformal projective invariants in the problem of image recognition.
Directory of Open Access Journals (Sweden)
Надежда Григорьевна Коновенко
2014-11-01
Full Text Available In this paper we reduce local classification of differential 1-forms on the plane with respect to group SL_2(C of Mobius transformations. We find the field of rational conformal differential invariants and show that the field is generated by two differential invariant derivations and by differential invariants of the first and second orders.
Frank, Steven A.
2016-01-01
In nematodes, environmental or physiological perturbations alter death’s scaling of time. In human cancer, genetic perturbations alter death’s curvature of time. Those changes in scale and curvature follow the constraining contours of death’s invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death’s scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.
Directory of Open Access Journals (Sweden)
Shuichi Kitayama
2016-02-01
Full Text Available Vα24 invariant natural killer T (iNKT cells are a subset of T lymphocytes implicated in the regulation of broad immune responses. They recognize lipid antigens presented by CD1d on antigen-presenting cells and induce both innate and adaptive immune responses, which enhance effective immunity against cancer. Conversely, reduced iNKT cell numbers and function have been observed in many patients with cancer. To recover these numbers, we reprogrammed human iNKT cells to pluripotency and then re-differentiated them into regenerated iNKT cells in vitro through an IL-7/IL-15-based optimized cytokine combination. The re-differentiated iNKT cells showed proliferation and IFN-γ production in response to α-galactosylceramide, induced dendritic cell maturation and downstream activation of both cytotoxic T lymphocytes and NK cells, and exhibited NKG2D- and DNAM-1-mediated NK cell-like cytotoxicity against cancer cell lines. The immunological features of re-differentiated iNKT cells and their unlimited availability from induced pluripotent stem cells offer a potentially effective immunotherapy against cancer.
Institute of Scientific and Technical Information of China (English)
YIN Yajun; WU Jiye; YIN Jie
2008-01-01
To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry.The conventional second fundamental tensor is replaced by the so-called conjugate fundamental tensor.Because the differential properties of the conjugate fundamental tensor and the first fundamental tensor are symmetrical, the symmetrical analytical system including the symmetrical differential operators, symmetrical differential characteristics, and symmetrical integral theorems for tensor fields defined on curved surfaces can be constructed. From the symmetrical analytical system, the symmetrical integral theorems for mean curvature and Gauss curvature, with which the symmetrical Minkowski integral formulas are easily deduced just as special cases, can be derived. The applications of this symmetrical analytical system to biology not only display its simplicity and beauty, but also show its powers in depicting the symmetrical patterns of net-works of biomembrane nanotubes. All these symmetrical patterns in soft matters should be just the reason-able and natural results of the symmetrical analytical system.
Gauge-invariant approach to quark dynamics
Sazdjian, H
2016-01-01
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's functions is presented, and the relevance of Wilson loops for the representation of the interaction is emphasized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are then presented. An integro-differential equation is obtained for the quark Green's function defined with a phase factor along a single, straight line segment. It is solved exactly and analytically in the case of two-dimensional QCD in the large $N_c$ limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.
The shape operator for differential analysis of images.
Avants, Brian; Gee, James
2003-07-01
This work provides a new technique for surface oriented volumetric image analysis. The method makes no assumptions about topology, instead constructing a local neighborhood from image information, such as a segmentation or edge map, to define a surface patch. Neighborhood constructions using extrinsic and intrinsic distances are given. This representation allows one to estimate differential properties directly from the image's Gauss map. We develop a novel technique for this purpose which estimates the shape operator and yields both principal directions and curvatures. Only first derivatives need be estimated, making the method numerically stable. We show the use of these measures for multi-scale classification of image structure by the mean and Gaussian curvatures. Finally, we propose to register image volumes by surface curvature. This is particularly useful when geometry is the only variable. To illustrate this, we register binary segmented data by surface curvature, both rigidly and non-rigidly. A novel variant of Demons registration, extensible for use with differentiable similarity metrics, is also applied for deformable curvature-driven registration of medical images.
On Frame-Invariance in Electrodynamics
Romano, Giovanni
2012-01-01
The Faraday and Ampere-Maxwell laws of electrodynamics in space-time manifold are formulated in terms of differential forms and exterior and Lie derivatives. Due to their natural behavior with respect to push-pull operations, these geometric objects are the suitable tools to deal with the space-time observer split of the events manifold and with frame-invariance properties. Frame-invariance is investigated in complete generality, referring to any automorphic transformation in space-time, in accord with the spirit of general relativity. A main result of the new geometric theory is the assessment of frame-invariance of space-time electromagnetic differential forms and induction laws and of their spatial counterparts under any change of frame. This target is reached by a suitable extension of the formula governing the correspondence between space-time and spatial differential forms in electrodynamics to take relative motions in due account. The result modifies the statement made by Einstein in the 1905 paper on ...
Transformation invariant sparse coding
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel Nørgaard
2011-01-01
Sparse coding is a well established principle for unsupervised learning. Traditionally, features are extracted in sparse coding in specific locations, however, often we would prefer invariant representation. This paper introduces a general transformation invariant sparse coding (TISC) model....... The model decomposes images into features invariant to location and general transformation by a set of specified operators as well as a sparse coding matrix indicating where and to what degree in the original image these features are present. The TISC model is in general overcomplete and we therefore invoke...... sparse coding to estimate its parameters. We demonstrate how the model can correctly identify components of non-trivial artificial as well as real image data. Thus, the model is capable of reducing feature redundancies in terms of pre-specified transformations improving the component identification....
Directory of Open Access Journals (Sweden)
Kyoko Nakamura
Full Text Available Thymocytes expressing the invariant Vγ5 γδT-cell receptor represent progenitors of dendritic epidermal T-cells (DETC that play an important immune surveillance role in the skin. In contrast to the bulk of αβT-cell development, Vγ5(+ DETC progenitor development occurs exclusively in fetal thymus. Whilst αβT-cell development is known to require chemokine receptor mediated migration through distinct thymus regions, culminating in medullary entry and thymic egress, the importance and control of intrathymic migration for DETC progenitors is unclear. We recently revealed a link between Vγ5(+ DETC progenitor development and medullary thymic epithelial cells expressing Aire, a known regulator of thymic chemokine expression, demonstrating that normal Vγ5(+ DETC progenitor development requires regulated intramedullary positioning. Here we investigate the role of chemokines and their receptors during intrathymic Vγ5(+ DETC progenitor development and establishment of the DETC pool in the skin. We report that thymic medullary accumulation of Vγ5(+ DETC progenitors is a G-protein coupled receptor dependent process. However, this process occurs independently of Aire's influences on intrathymic chemokines, and in the absence of CCR4 and CCR7 expression by DETC progenitors. In contrast, analysis of epidermal γδT-cells at neonatal and adult stages in CCR4(-/- mice reveals that reduced numbers of DETC in adult epidermis are not a consequence of diminished intrathymic embryonic development, nor deficiencies in initial epidermal seeding in the neonate. Collectively, our data reveal differences in the chemokine receptor requirements for intrathymic migration of αβ and invariant γδT-cells, and highlight a differential role for CCR4 in the maintenance, but not initial seeding, of DETC in the epidermis.
Operating principles of tristable circuits regulating cellular differentiation
Jia, Dongya; Jolly, Mohit Kumar; Harrison, William; Boareto, Marcelo; Ben-Jacob, Eshel; Levine, Herbert
2017-06-01
Many cell-fate decisions during embryonic development are governed by a motif comprised of two transcription factors (TFs) A and B that mutually inhibit each other and may self-activate. This motif, called as a self-activating toggle switch (SATS), can typically have three stable states (phenotypes)—two corresponding to differentiated cell fates, each of which has a much higher level of one TF than the other—≤ft(A,~B\\right)=≤ft(1,~0\\right) or ≤ft(0,~1\\right) —and the third state corresponding to an ‘undecided’ stem-like state with similar levels of both A and B—≤ft(A,~B\\right)=≤ft(1/2,1/2\\right) . Furthermore, two or more SATSes can be coupled together in various topologies in different contexts, thereby affecting the coordination between multiple cellular decisions. However, two questions remain largely unanswered: (a) what governs the co-existence and relative stability of these three stable states? (b) What orchestrates the decision-making of coupled SATSes? Here, we first demonstrate that the co-existence and relative stability of the three stable states in an individual SATS can be governed by the relative strength of self-activation, external signals activating and/or inhibiting A and B, and mutual degradation between A and B. Simultaneously, we investigate the effects of these factors on the decision-making of two coupled SATSes. Our results offer novel understanding into the operating principles of individual and coupled tristable self-activating toggle switches (SATSes) regulating cellular differentiation and can yield insights into synthesizing three-way genetic circuits and understanding of cellular reprogramming.
Wavelet analysis on adeles and pseudo-differential operators
Khrennikov, A Yu; Shelkovich, V M
2011-01-01
This paper is devoted to wavelet analysis on adele ring $\\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of adeles $\\bA$ by using infinite tensor products of Hilbert spaces. The adele ring is roughly speaking a subring of the direct product of all possible ($p$-adic and Archimedean) completions $\\bQ_p$ of the field of rational numbers $\\bQ$ with some conditions at infinity. Using our technique, we prove that $L^2(\\bA)=\\otimes_{e,p\\in\\{\\infty,2,3,5,...}}L^2({\\bQ}_{p})$ is the infinite tensor product of the spaces $L^2({\\bQ}_{p})$ with a stabilization $e=(e_p)_p$, where $e_p(x)=\\Omega(|x|_p)\\in L^2({\\bQ}_{p})$, and $\\Omega$ is a characteristic function of the unit interval $[0,\\,1]$, $\\bQ_p$ is the field of $p$-adic numbers, $p=2,3,5,...$; $\\bQ_\\infty=\\bR$. This description allows us to construct an infinite family of Haar wavelet bases on $L^2(\\bA)$ which can be obtained by shifts...
Invariant measures for Chebyshev maps
Directory of Open Access Journals (Sweden)
Abraham Boyarsky
2001-01-01
Full Text Available Let Tλ(x=cos(λarccosx, −1≤x≤1, where λ>1 is not an integer. For a certain set of λ's which are irrational, the density of the unique absolutely continuous measure invariant under Tλ is determined exactly. This is accomplished by showing that Tλ is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed as the unique left eigenvector of a matrix.
Properties of Caputo Operator and Its Applications to Linear Fractional Differential Equations
Directory of Open Access Journals (Sweden)
B. R. Sontakke,
2015-05-01
Full Text Available The purpose of this paper is to demonstrate the power of two mostly used definitions for fractional differentiation, namely, the Riemann-Liouville and Caputo fractional operator to solve some linear fractionalorder differential equations. The emphasis is given to the most popular Caputo fractional operator which is more suitable for the study of differential equations of fractional order..Illustrative examples are included to demonstrate the procedure of solution of couple of fractional differential equations having Caputo operator using Laplace transformation. Itshows that the Laplace transforms is a powerful and efficient technique for obtaining analytic solution of linear fractional differential equations
On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0, +∞)
Institute of Scientific and Technical Information of China (English)
Jian Ye AN; Jiong SUN
2004-01-01
In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, +∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.
Baev, Denis V; Caielli, Simone; Ronchi, Francesca; Coccia, Margherita; Facciotti, Federica; Nichols, Kim E; Falcone, Marika
2008-07-15
The regulatory function of invariant NKT (iNKT) cells for tolerance induction and prevention of autoimmunity is linked to a specific cytokine profile that comprises the secretion of type 2 cytokines like IL-4 and IL-10 (NKT2 cytokine profile). The mechanism responsible for iNKT cell differentiation toward a type 2 phenotype is unknown. Herein we show that costimulatory signals provided by the surface receptor signaling lymphocytic activation molecule (SLAM) on myeloid dendritic cells (mDC) to iNKT cells is crucial for NKT2 orientation. Additionally, we demonstrate that the impaired acquisition of an NKT2 cytokine phenotype in nonobese diabetic (NOD) mice that spontaneously develop autoimmune diabetes is due to defective SLAM-induced signals generated by NOD mDC. Mature mDC of C57BL/6 mice express SLAM and induce C57BL/6 or NOD iNKT cells to acquire a predominant NKT2 cytokine phenotype in response to antigenic stimulation with the iNKT cell-specific Ag, the alpha-galactosylceramide. In contrast, mature NOD mDC express significantly lower levels of SLAM and are unable to promote GATA-3 (the SLAM-induced intracellular signal) up-regulation and IL-4/IL-10 production in iNKT cells from NOD or C57BL/6 mice. NOD mice carry a genetic defect of the Slamf1 gene that is associated with reduced SLAM expression on double-positive thymocytes and altered iNKT cell development in the thymus. Our data suggest that the genetic Slamf1 defect in NOD mice also affects SLAM expression on other immune cells such as the mDC, thus critically impairing the peripheral differentiation of iNKT cells toward a regulatory NKT2 type.
Undergraduate Students' Mental Operations in Systems of Differential Equations
Whitehead, Karen; Rasmussen, Chris
2003-01-01
This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…
Solving evolutionary-type differential equations and physical problems using the operator method
Zhukovsky, K. V.
2017-01-01
We present a general operator method based on the advanced technique of the inverse derivative operator for solving a wide range of problems described by some classes of differential equations. We construct and use inverse differential operators to solve several differential equations. We obtain operator identities involving an inverse derivative operator, integral transformations, and generalized forms of orthogonal polynomials and special functions. We present examples of using the operator method to construct solutions of equations containing linear and quadratic forms of a pair of operators satisfying Heisenberg-type relations and solutions of various modifications of partial differential equations of the Fourier heat conduction type, Fokker-Planck type, Black-Scholes type, etc. We demonstrate using the operator technique to solve several physical problems related to the charge motion in quantum mechanics, heat propagation, and the dynamics of the beams in accelerators.
Besov continuity for pseudo-differential operators on compact homogeneous manifolds
Cardona, Duván
2016-01-01
In this paper we study the Besov continuity of pseudo-differential operators on compact homogeneous manifolds $M=G/K.$ We use the global quantization of these operators in terms of the representation theory of compact homogeneous manifolds.
Viability, invariance and applications
Carja, Ovidiu; Vrabie, Ioan I
2007-01-01
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In th...
Operators on Differential Form Spaces for Riemann Surfaces
Institute of Scientific and Technical Information of China (English)
Guang Fu CAO; Xiao Feng WANG
2007-01-01
In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator Cρ is Fredholm if and only if it is invertible if and only ifρ is invertible for some special cases. In addition,the Toeplitz operators on ∧12 a (M) for Riemann surface M are defined and some properties of these operators are discussed.
Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation
Institute of Scientific and Technical Information of China (English)
LIU Chang; JIA Yi-Feng; ZHU Na; CHEN Yu-Fu; MEI Feng-Xiang; GUO Yong-Xin
2008-01-01
In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.
Spectral Properties of Integral Differential Operators Applied in Linear Antenna Modeling
Bekers, D.J.; Eijndhoven, S.J.L. van
2012-01-01
The current on a linear strip or wire solves an equation governed by a linear integro-differential operator that is the composition of the Helmholtz operator and an integral operator with a logarithmically singular displacement kernel. Investigating the spectral behaviour of this classical operator,
Institute of Scientific and Technical Information of China (English)
Veli B SHAKHMUROV
2008-01-01
The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued Lp-spaces are studied. To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations, the sufficient conditions are founded. By using these facts, the unique continuation properties are established. In the application part, the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.
Invariant Scattering Convolution Networks
Bruna, Joan
2012-01-01
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear modulus and averaging operators. The first network layer outputs SIFT-type descriptors whereas the next layers provide complementary invariant information which improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State of the art classification results are obtained for handwritten digits and texture discrimination, using a Gaussian kernel SVM and a generative PCA classifier.
Permutationally invariant state reconstruction
Moroder, Tobias; Toth, Geza; Schwemmer, Christian; Niggebaum, Alexander; Gaile, Stefanie; Gühne, Otfried; Weinfurter, Harald
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a non-linear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed n...
Invariants for Parallel Mapping
Institute of Scientific and Technical Information of China (English)
YIN Yajun; WU Jiye; FAN Qinshan; HUANG Kezhi
2009-01-01
This paper analyzes the geometric quantities that remain unchanged during parallel mapping (i.e., mapping from a reference curved surface to a parallel surface with identical normal direction). The second gradient operator, the second class of integral theorems, the Gauss-curvature-based integral theorems, and the core property of parallel mapping are used to derive a series of parallel mapping invadants or geometri-cally conserved quantities. These include not only local mapping invadants but also global mapping invari-ants found to exist both in a curved surface and along curves on the curved surface. The parallel mapping invadants are used to identify important transformations between the reference surface and parallel surfaces. These mapping invadants and transformations have potential applications in geometry, physics, biome-chanics, and mechanics in which various dynamic processes occur along or between parallel surfaces.
Relative boundedness and compactness theory for second-order differential operators
Directory of Open Access Journals (Sweden)
Don B. Hinton
1997-01-01
Full Text Available The problem considered is to give necessary and sufficient conditions for perturbations of a second-order ordinary differential operator to be either relatively bounded or relatively compact. Such conditions are found for three classes of operators. The conditions are expressed in terms of integral averages of the coefficients of the perturbing operator.
Lie group invariant finite difference schemes for the neutron diffusion equation
Energy Technology Data Exchange (ETDEWEB)
Jaegers, P.J.
1994-06-01
Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.
2010-01-01
properties governing the mechanics of grasping and manipulation would also be preserved. For example, as we shall see later in this paper, if O is a...focus on the actual finger form. Dollar and Howe [6] survey 20 different designs of compliant and underactuated hands, and all employ cylindrical or...fundamental existence and uniqueness theorem for solutions of systems of differential equations [12]. 6 Alberto Rodriguez and Matthew T. Mason 3.2 General
Invariants and submanifolds in almost complex geometry
Kruglikov, Boris
2007-01-01
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds.
An abstract approach to some spectral problems of direct sum differential operators
Directory of Open Access Journals (Sweden)
Maksim S. Sokolov
2003-07-01
Full Text Available In this paper, we study the common spectral properties of abstract self-adjoint direct sum operators, considered in a direct sum Hilbert space. Applications of such operators arise in the modelling of processes of multi-particle quantum mechanics, quantum field theory and, specifically, in multi-interval boundary problems of differential equations. We show that a direct sum operator does not depend in a straightforward manner on the separate operators involved. That is, on having a set of self-adjoint operators giving a direct sum operator, we show how the spectral representation for this operator depends on the spectral representations for the individual operators (the coordinate operators involved in forming this sum operator. In particular it is shown that this problem is not immediately solved by taking a direct sum of the spectral properties of the coordinate operators. Primarily, these results are to be applied to operators generated by a multi-interval quasi-differential system studied, in the earlier works of Ashurov, Everitt, Gesztezy, Kirsch, Markus and Zettl. The abstract approach in this paper indicates the need for further development of spectral theory for direct sum differential operators.
A CLASS OF REACTION-DIFFUSION EQUATIONS WITH HYSTERESIS DIFFERENTIAL OPERATOR
Institute of Scientific and Technical Information of China (English)
XuLongfeng
2002-01-01
In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.
The Symmetry of Singular Hamiltonian Differential Operators and Properties of Deficiency Indices
Institute of Scientific and Technical Information of China (English)
Jian Gang QI
2006-01-01
The symmetry of singular Hamiltonian differential operators is proved under the standard "definiteness condition", which is strictly weaker than the densely definite condition used by A. M.Krall. Meanwhile, some properties of deficiency indices are given.
A weighted identity for stochastic partial differential operators and its applications
2015-01-01
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and inverse problems for some deterministic/stochastic partial differential equations. Based on this identity, one can deduce all the known Carleman estimates and observability results, for some deterministic partial differential equations, stochastic heat equation...
Construction and Operation of a Differential Hall Element Magnetometer
Calkins, Matthew W.; Javernick, Philip D.; Quintero, Pedro A.; Calm, Yitzi M.; Meisel, Mark W.
2012-02-01
A Differential Hall Element Magnetometer (DHEM) was constructed to measure the magnetic saturation and coercive fields of small samples consisting of magnetic nanoparticles that may have biomedical applications. The device consists of two matched Hall elements that can be moved through the room temperature bore of a 9 Tesla superconducting magnet. The Hall elements are wired in opposition such that a null response, to within a small offset, is measured in the absence of a sample that may be located on top of one unit. A LabVIEW program controls the current through the Hall elements and measures the net Hall voltage while simultaneously moving the probe through the magnetic field by regulating a linear stepper motor. Ultimately, the system will be tested to obtain a figure of merit using successively smaller samples. Details of the apparatus will be provided along with preliminary data.
Directory of Open Access Journals (Sweden)
Zhinan Xia
2015-07-01
Full Text Available In this article, we show sufficient conditions for the existence, uniqueness and attractivity of piecewise weighted pseudo almost periodic classical solution of nonlinear impulsive integro-differential equations. The working tools are based on the fixed point theorem and fractional powers of operators. An application to impulsive integro-differential equations is presented.
Directory of Open Access Journals (Sweden)
Hossein Jafari
2016-04-01
Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte
2015-07-01
This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)
Extension theory for elliptic partial differential operators with pseudodifferential methods
DEFF Research Database (Denmark)
Grubb, Gerd
2012-01-01
This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n >1. The theory of pseudodifferential boundary problems has turned out to be very useful here, not only as a formulational framework, but also...... for the solution of specific questions. We recall some elements of that theory, and show its application in several cases (including new results), namely to the lower boundedness question, and the question of spectral asymptotics for differences between resolvents....
Farber, M S; Farber, Michael S.; Levine, Jerome P.
1994-01-01
We study the eta-invariant, defined by Atiyah-Patodi-Singer a real valued invariant of an oriented odd-dimensional Riemannian manifold equipped with a unitary representation of its fundamental group. When the representation varies analytically, the corresponding eta-invariant may have an integral jump, known also as the spectral flow. The main result of the paper establishes a formula for this spectral jump in terms of the signatures of some homological forms, defined naturally by the path of representations. These signatures may also be computed by means of a spectral sequence of Hermitian forms,defined by the deformation data. Our theorem on the spectral jump has a generalization to arbitrary analytic families of self-adjoint elliptic operators. As an application we consider the problem of homotopy invariance of the rho-invariant. We give an intrinsic homotopy theoretic definition of the rho-invariant, up to indeterminacy in the form of a locally constant function on the space of unitary representations. In...
Institute of Scientific and Technical Information of China (English)
Veli; B; SHAKHMUROV
2008-01-01
The unique continuation theorems for the anisotropic partial differential-operator equations with variable coeffcients in Banach-valued Lp-spaces are studied.To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations,the suffcient conditions are founded.By using these facts,the unique continuation properties are established.In the application part,the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.
Deficiency indices of a differential operator satisfying certain matching interface conditions
Directory of Open Access Journals (Sweden)
Pallav Kumar Baruah
2005-03-01
Full Text Available A pair of differential operators with matching interface conditions appears in many physical applications such as: oceanography, the study of step index fiber in optical fiber communication, and one dimensional scattering in quantum theory. Here we initiate the study the deficiency index theory of such operators which precedes the study of the spectral theory.
On differential subordinations for a class of analytic functions defined by a linear operator
Directory of Open Access Journals (Sweden)
V. Ravichandran
2004-01-01
Full Text Available We obtain several results concerning the differential subordination between analytic functions and a linear operator defined for a certain family of analytic functions which are introduced here by means of these linear operators. Also, some special cases are considered.
Palmer, T N
2016-01-01
Invariant Set Theory (IST) is a realistic, locally causal theory of fundamental physics which assumes a much stronger synergy between cosmology and quantum physics than exists in contemporary theory. In IST the (quasi-cyclic) universe $U$ is treated as a deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. In this approach, the geometry of $I_U$, and not a set of differential evolution equations in space-time $\\mathcal M_U$, provides the most primitive description of the laws of physics. As such, IST is non-classical. The geometry of $I_U$ is based on Cantor sets of space-time trajectories in state space, homeomorphic to the algebraic set of $p$-adic integers, for large but finite $p$. In IST, the non-commutativity of position and momentum observables arises from number theory - in particular the non-commensurateness of $\\phi$ and $\\cos \\phi$. The complex Hilbert Space and the relativistic Dirac Equation respectively are shown to describe $I_U$...
Operational Solution of Non-Integer Ordinary and Evolution-Type Partial Differential Equations
Directory of Open Access Journals (Sweden)
Konstantin V. Zhukovsky
2016-12-01
Full Text Available A method for the solution of linear differential equations (DE of non-integer order and of partial differential equations (PDE by means of inverse differential operators is proposed. The solutions of non-integer order ordinary differential equations are obtained with recourse to the integral transforms and the exponent operators. The generalized forms of Laguerre and Hermite orthogonal polynomials as members of more general Appèl polynomial family are used to find the solutions. Operational definitions of these polynomials are used in the context of the operational approach. Special functions are employed to write solutions of DE in convolution form. Some linear partial differential equations (PDE are also explored by the operational method. The Schrödinger and the Black–Scholes-like evolution equations and solved with the help of the operational technique. Examples of the solution of DE of non-integer order and of PDE are considered with various initial functions, such as polynomial, exponential, and their combinations.
Spectrum of a class of fourth order left-definite differential operators
Institute of Scientific and Technical Information of China (English)
GAO Yun-lan; SUN Jiong
2008-01-01
The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators,the following conclusions are obtained: if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite,then all its eigenvalues are real,and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above,have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0＜0＜λ0≤λ1≤λ2≤…
An approach to dark energy problem through linear invariants
Institute of Scientific and Technical Information of China (English)
Jeong Ryeol Choi
2011-01-01
The time evolution of vacuum energy density is investigated in the coherent states of inflationary universe using a linear invariant approach. The linear invariants we derived are represented in terms of annihilation operators. On account of the fact that
Complex J-Symplectic Geometry With Application to Ordinary Differential Operators
Institute of Scientific and Technical Information of China (English)
王万义
2001-01-01
@@In this paper, we deal with complex J-symplectic geometry with application to ordinary differential operators. We define complex J-symplectic spaces and their J-Lagrangian subspaces and complete J-Lagrangian subspaces, and then we discuss their basic algebraic properties. Then we apply them to the theory of J-selfadjoint operators and give J-symplectic geometry complete characterizations of J-selfadjoint extensions of J-symmetric operators.
Permutationally invariant state reconstruction
DEFF Research Database (Denmark)
Moroder, Tobias; Hyllus, Philipp; Tóth, Géza;
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale opti......Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large...... likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex...
Wilson loop invariants from WN conformal blocks
Directory of Open Access Journals (Sweden)
Oleg Alekseev
2015-12-01
Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.
On multipartite invariant states II. Orthogonal symmetry
Chruściński, Dariusz; Kossakowski, Andrzej
2006-01-01
We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper "On multipartite invariant states I. Unitary symmetry". We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.
On multipartite invariant states II. Orthogonal symmetry
Chruscinski, D; Chruscinski, Dariusz; Kossakowski, Andrzej
2006-01-01
We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper "On multipartite invariant states I. Unitary symmetry". We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.
Form invariance for systems of generalized classical mechanics
Institute of Scientific and Technical Information of China (English)
张毅; 梅凤翔
2003-01-01
This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. According to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and establishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is given to illustrate the application of the results.
Symplectic Covariance Properties for Shubin and Born-Jordan Pseudo-Differential Operators
de Gosson, Maurice A
2011-01-01
Among all classes of pseudo-differential operators only the Weyl operators enjoy the property of symplectic covariance with respect to conjugation by elements of the metaplectic group. In this paper we show that there is, however, a weaker form of symplectic covariance for Shubin's {\\tau}-dependent operators, in which the intertwiners no longer are metaplectic, but still are invertible non-unitary operators. We also study the case of Born--Jordan operators, which are obtained by averaging the {\\tau}-operators over the interval [0,1] (such operators have recently been studied by Boggiatto and his collaborators). We show that metaplectic covariance still hold for these operators, with respect top a subgroup of the metaplectic group.
Pseudo-differential Operators with Semi-Quasielliptic Symbols Over p-adic Fields
Galeano-Penaloza, J
2011-01-01
In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable functions with respect to a semi-quasielliptic operator. By using these spaces we show the existence of a regularization effect for certain parabolic equations over p-adics.
Directory of Open Access Journals (Sweden)
Ammar Ali Neamah
2014-01-01
Full Text Available The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.
Nagaya, Yasunobu
2014-06-01
The methods to calculate the kinetics parameters of βeff and Λ with the differential operator sampling have been reviewed. The comparison of the results obtained with the differential operator sampling and iterated fission probability approaches has been performed. It is shown that the differential operator sampling approach gives the same results as the iterated fission probability approach within the statistical uncertainty. In addition, the prediction accuracy of the evaluated nuclear data library JENDL-4.0 for the measured βeff/Λ and βeff values is also examined. It is shown that JENDL-4.0 gives a good prediction except for the uranium-233 systems. The present results imply the need for revisiting the uranium-233 nuclear data evaluation and performing the detailed sensitivity analysis.
Operational method of solution of linear non-integer ordinary and partial differential equations.
Zhukovsky, K V
2016-01-01
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.
Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation
Directory of Open Access Journals (Sweden)
S. Balaji
2014-01-01
Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
Feng, Sheng-Ya
2011-01-01
In this paper, we study a class of second order differential operators with quadratic potentials $L$ and its principal part $L_{S}$. Thanks to Hamiltonian formalism and a multiplier technique, we first obtain heat kernel of $L_{S}$, then we, by use of the action function and volume element, solve a matrix Riccati equations and a scalar differential equation which leads us to the heat kernel of $L$ via a probabilistic ansatz. As application, we finally recover and generalise several classical results on celebrated operators.
Realization of the N(odd)-Dimensional Quantum Euclidean Space by Differential Operators
Institute of Scientific and Technical Information of China (English)
LI Yun; JING Si-Cong
2004-01-01
The quantum Euclidean space RNq is a kind of noncommutative space that is obtained from ordinary Euclidean space RN by deformation with parameter q. When N is odd, the structure of this space is similar to R3q.Motivated by realization ofR3q by differential operators in R3, we give such realization for R5q and R7q cases and generalize our results to RNq (N odd) in this paper, that is, we show that the algebra of RNq can be realized by differential operators acting on C∞ functions on undeformed space RN.
RELATIONS OF DERIVATIVE ALGEBRA AND RING OF DIFFERENTIAL OPERATORS IN CHARACTERISTIC p>0
Institute of Scientific and Technical Information of China (English)
张江峰
2002-01-01
Let K be a field of characteristic p>0. We prove that the derivative algebra of K[x1,…,xn] is a proer subring of the ring of differential operators of K[x1,…,xn]. A concrete example is given to show that there is a differential operator of order p that does not belong to the derivative algebra. By these results, is follows that the derivative algebra is Morita equivalent to K[xp1,…,xpn], and hence its global homological dimension, Krull dimension, K0 group and some other properties are got.
Differential operators and spectral theory M. Sh. Birman's 70th anniversary collection
Buslaev, V; Yafaev, D
1999-01-01
This volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman. The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrödinger operator, which is within Birman's current scope of interests and re
A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Kaplitskii, V M [Southern Federal University, Rostov-on-Don (Russian Federation)
2014-08-01
The function Ψ(x,y,s)=e{sup iy}Φ(−e{sup iy},s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L{sub 2}(Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles.
Diethelm, Kai
2010-01-01
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Computational invariant theory
Derksen, Harm
2015-01-01
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...
Spectral theory of differential operators M. Sh. Birman 80th anniversary collection
Suslina, T
2009-01-01
This volume is dedicated to Professor M. Sh. Birman in honor of his eightieth birthday. It contains original articles in spectral and scattering theory of differential operators, in particular, Schrodinger operators, and in homogenization theory. All articles are written by members of M. Sh. Birman's research group who are affiliated with different universities all over the world. A specific feature of the majority of the papers is a combination of traditional methods with new modern ideas.
Projectively related metrics, Weyl nullity, and metric projectively invariant equations
Gover, A Rod
2015-01-01
A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity condition. The analysis is simplified by a fundamental and canonical 2-tensor invariant that we discover. It leads to a new canonical tractor connection for these geometries which is defined on a rank $(n+1)$-bundle. We show this connection is linked to the metrisability equations that govern the existence of metrics compatible with the structure. The fundamental 2-tensor also leads to a new class of invariant linear differential operators that are canonically associated to these geometries; included is a third equation studied by Gallot et al. We apply the results to study the metrisability equation, in the nullity setting described. We obtain strong local and global results on the nature of solutions and also on the nature of the geometries admitting such solutions, obtaining ...
From scale invariance to Lorentz symmetry
Sibiryakov, Sergey
2014-01-01
It is shown that a unitary translationally invariant field theory in (1+1) dimensions satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators and the requirement that signals propagate with finite velocity possesses an infinite dimensional symmetry given by one or a product of several copies of conformal algebra. In particular, this implies presence of one or several Lorentz groups acting on the operator algebra of the theory.
Directory of Open Access Journals (Sweden)
Kunio Ichinobe
2015-01-01
Full Text Available We study the \\(k\\-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in \\(t\\. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.
Expansion by eigenvectors in case of simple eigenvalues of singular differential operator
Directory of Open Access Journals (Sweden)
O. V. Makhnei
2011-06-01
Full Text Available The asymptotic formulas with large values of parameter for solutions of singular differential equation allow us to estimate Green's function of the boundary-value problem. With the help of this estimation the expansion of singular dierential operator by eigenvectors in the case of simple eigenvalues is constructed.
Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods
Energy Technology Data Exchange (ETDEWEB)
Kiedrowski, Brian C [Los Alamos National Laboratory; Brown, Forrest B [Los Alamos National Laboratory
2010-01-01
Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.
van Eck, H. J. N.; Koppers, W. R.; van Rooij, G. J.; W. J. Goedheer,; Engeln, R.; D.C. Schram,; Cardozo, N. J. L.; Kleyn, A. W.
2009-01-01
The direct simulation Monte Carlo (DSMC) method was used to investigate the efficiency of differential pumping in linear plasma generators operating at high gas flows. Skimmers are used to separate the neutrals from the plasma beam, which is guided from the source to the target by a strong axial mag
Model reduction for nonlinear systems based on the differential eigenstructure of Hankel operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.
2001-01-01
This paper offers a new input-normal output-diagonal realization and model reduction procedure for nonlinear systems based on the differential eigenstructure of Hankel operators. Firstly, we refer to the preliminary results on input-normal realizations with original singular value functions and the
Existence of solutions to fractional differential inclusions with p-Laplacian operator
Directory of Open Access Journals (Sweden)
Ahmet Yantir
2014-12-01
Full Text Available In this article, we prove the existence of solutions for three-point fractional differential inclusions with p-Laplacian operator. We use fixed point theory for set valued upper semi-continuous maps for obtaining the solutions.
Morita invariance of the filter dimension and of the inequality of Bernstein
Bavula, V.V.; Hinchcliffe, V.
2006-01-01
It is proved that the filter dimenion is Morita invariant. A direct consequence of this fact is the Morita invariance of the inequality of Bernstein: if an algebra $A$ is Morita equivalent to the ring $\\CD (X)$ of differential operators on a smooth irreducible affine algebraic variety $X$ of dimension $n\\geq 1$ over a field of characteristic zero then the Gelfand-Kirillov dimension $ \\GK (M)\\geq n = \\frac{\\GK (A)}{2}$ for all nonzero finitely generated $A$-modules $M$. In fact, a more strong ...
Invariance and stability for bounded uncertain systems.
Peng, T. K. C.
1972-01-01
The positive limit sets of the solutions of a contingent differential equation are shown to possess an invariance property. In this connection the 'invariance principle' in the theory of Lyapunov stability is extended to systems with unknown, bounded, time-varying parameters, and thus to a large and important class of nonautonomous systems. Asymptotic stability criteria are obtained and applied to guaranteed cost control problems.
Institute of Scientific and Technical Information of China (English)
郭新伟; 吕延芳; 齐海涛
2014-01-01
讨论了完备可分距离空间上一类 Markov-Feller 算子的遍历性质，给出了存在不变测度的充分必要条件以及唯一不变测度的充分条件，研究了此类算子轨道的稠密性质。%The ergodic property of the Markov-Feller operators on complete separable spaces is discussed. The exist-ence and uniqueness of invariant probability measures for the Markov-Feller operators with equicontinuous dual op-erators is given. In addition,the dense trajectories for the operators is studied.
Directory of Open Access Journals (Sweden)
Jian Wang
2014-01-01
Full Text Available A large-scale parallel-unit seawater reverse osmosis desalination plant contains many reverse osmosis (RO units. If the operating conditions change, these RO units will not work at the optimal design points which are computed before the plant is built. The operational optimization problem (OOP of the plant is to find out a scheduling of operation to minimize the total running cost when the change happens. In this paper, the OOP is modelled as a mixed-integer nonlinear programming problem. A two-stage differential evolution algorithm is proposed to solve this OOP. Experimental results show that the proposed method is satisfactory in solution quality.
Directory of Open Access Journals (Sweden)
Mohsen Alipour
2013-01-01
Full Text Available We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs. In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD, and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI. The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1.
Embedded graph invariants in Chern-Simons theory
Major, Seth A.
1998-01-01
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines - an embedded graph invariant. Using a slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order ...
McCarthy, S.; Rachinskii, D.
2011-01-01
We describe two Euler type numerical schemes obtained by discretisation of a stochastic differential equation which contains the Preisach memory operator. Equations of this type are of interest in areas such as macroeconomics and terrestrial hydrology where deterministic models containing the Preisach operator have been developed but do not fully encapsulate stochastic aspects of the area. A simple price dynamics model is presented as one motivating example for our studies. Some numerical evidence is given that the two numerical schemes converge to the same limit as the time step decreases. We show that the Preisach term introduces a damping effect which increases on the parts of the trajectory demonstrating a stronger upwards or downwards trend. The results are preliminary to a broader programme of research of stochastic differential equations with the Preisach hysteresis operator.
VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
Poghosyan, Gabriel
2016-01-01
In this short notes using AGT correspondence we express simplest fully degenerate primary fields of Toda field theory in terms an analogue of Baxter's $Q$-operator naturally emerging in ${\\cal N}=2$ gauge theory side. This quantity can be considered as a generating function of simple trace chiral operators constructed from the scalars of the ${\\cal N}=2$ vector multiplets. In the special case of Liouville theory, exploring the second order differential equation satisfied by conformal blocks including a degenerate at the second level primary field (BPZ equation) we derive a mixed difference-differential relation for $Q$-operator. Thus we generalize the $T$-$Q$ difference equation known in Nekrasov-Shatashvili limit of the $\\Omega$-background to the generic case.
Recovery of partial differential operators on classes of periodic functions with mixed smoothness
Balgimbayeva, Sholpan
2016-08-01
We consider the problem of optimal linear recovery for mixed partial differential operator A on the unit ball SBpθ r(Tn) of the Nikol'skii-Besov space of periodic functions with mixed smoothness. We find error bounds sharp in order for optimal linear recovery of operator A on class SBpθ r(Tn) . As information IMδ(f ) about the functions f from class SBpθ r(Tn) we shall use Fourier coefficients with numbers from step "hyperbolic" cross. As the linear method using the information about Fourier coefficients, we shall consider action of the mixed partial differential operator A on the special "private" sum of decomposition on system (type as wavelets) trigonometric polynomials.
Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces
Institute of Scientific and Technical Information of China (English)
Veli B. SHAKHMUROV
2006-01-01
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators Dα from this space to Eα -valued Lp,γ spaces is proved. These results are applied to partial differential-operator equationswith parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.
A basis in an invariant subspace of analytic functions
Energy Technology Data Exchange (ETDEWEB)
Krivosheev, A S [Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa (Russian Federation); Krivosheeva, O A [Bashkir State University, Ufa (Russian Federation)
2013-12-31
The existence problem for a basis in a differentiation-invariant subspace of analytic functions defined in a bounded convex domain in the complex plane is investigated. Conditions are found for the solvability of a certain special interpolation problem in the space of entire functions of exponential type with conjugate diagrams lying in a fixed convex domain. These underlie sufficient conditions for the existence of a basis in the invariant subspace. This basis consists of linear combinations of eigenfunctions and associated functions of the differentiation operator, whose exponents are combined into relatively small clusters. Necessary conditions for the existence of a basis are also found. Under a natural constraint on the number of points in the groups, these coincide with the sufficient conditions. That is, a criterion is found under this constraint that a basis constructed from relatively small clusters exists in an invariant subspace of analytic functions in a bounded convex domain in the complex plane. Bibliography: 25 titles.
Oancea, Alexandru
2011-01-01
This is an overview of some of the invariants that were discovered by Welschinger in the context of enumerative real algebraic geometry. Their definition finds a natural setup in real symplectic geometry. In particular, they can be studied using techniques from symplectic field theory, of which we also give a sample. Welschinger invariants are real analogues of certain Gromov-Witten invariants. This article is an extended set of notes for a talk at the Bourbaki seminar in April 2011.
Cores for Feller semigroups with an invariant measure
Albanese, A. A.; Mangino, E. M.
Let A=∑i,j=1Na(x)D+∑i=1Nb(x)D be an elliptic differential operator with unbounded coefficients on R and assume that the associated Feller semigroup (T( has an invariant measure μ. Then (T( extends to a strongly continuous semigroup (T( on L(μ)=L(R,μ) for every 1⩽p<∞. We prove that, under mild conditions on the coefficients of A, the space of test functions Cc∞(R) is a core for the generator (A,D) of (T( in L(μ) for 1⩽p<∞.
Lorenzo, C F; Hartley, T T; Malti, R
2013-05-13
A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Tianwang, Li; Bo, Ye; Jinguang, Jiang
2009-08-01
A novel fully differential telescopic operational transconductance amplifier (OTA) is proposed. An additional PMOS differential pair is introduced to improve the unit-gain bandwidth of the telescopic amplifier. At the same time, the slew rate is enhanced by the auxiliary slew rate boost circuits. The proposed OTA is designed in a 0.18μm CMOS process. Simulation results show that there is a 49% improvement in the unit-gain bandwidth compared to that of a conventional OTA; moreover, the DC gain and the slew rate are also enhanced.
Energy Technology Data Exchange (ETDEWEB)
Lukkassen, D.
1996-12-31
When partial differential equations are set up to model physical processes in strongly heterogeneous materials, effective parameters for heat transfer, electric conductivity etc. are usually required. Averaging methods often lead to convergence problems and in homogenization theory one is therefore led to study how certain integral functionals behave asymptotically. This mathematical doctoral thesis discusses (1) means and bounds connected to homogenization of integral functionals, (2) reiterated homogenization of integral functionals, (3) bounds and homogenization of some particular partial differential operators, (4) applications and further results. 154 refs., 11 figs., 8 tabs.
The Differential Dimension Polynomial for Characterizable Differential Ideals
Lange-Hegermann, Markus
2014-01-01
We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it decides equality of characterizable differential ideals contained in each other.
Hrstka, O; 10.1016/S0965-9978(03)00113-3
2009-01-01
This paper presents several types of evolutionary algorithms (EAs) used for global optimization on real domains. The interest has been focused on multimodal problems, where the difficulties of a premature convergence usually occurs. First the standard genetic algorithm (SGA) using binary encoding of real values and its unsatisfactory behavior with multimodal problems is briefly reviewed together with some improvements of fighting premature convergence. Two types of real encoded methods based on differential operators are examined in detail: the differential evolution (DE), a very modern and effective method firstly published by R. Storn and K. Price, and the simplified real-coded differential genetic algorithm SADE proposed by the authors. In addition, an improvement of the SADE method, called CERAF technology, enabling the population of solutions to escape from local extremes, is examined. All methods are tested on an identical set of objective functions and a systematic comparison based on a reliable method...
Directory of Open Access Journals (Sweden)
Ying Lu
2013-12-01
Full Text Available To study the problem about the optimal combination of postponement operations in the context of supply chain network, a decision-making model is developed. In the model two kinds of product differentiations and three types of postponement operations are considered. Then a procedure for solving this model is proposed. By using a numerical example, we analyze the effect of cost structure on the decision about postponement operations. The results show that if customizing cost is high, no customizing operation should be adopted, if the subassembly-related costs are large assembling directly the components is more sensible, as well as if lead time is tight and penalty cost is high, only manufacturing postponement should be adopted
Ashyralyev, Allaberen; Tetikoglu, Fatih Sabahattin
2015-09-01
In this study, the Green's function of the second order differential operator Ax defined by the formula Axu =-a (x )ux x(x )+δ u (x ), δ ≥0 , a (x )=a (x +2 π ), x ∈ℝ1 with domain D (Ax)={ u (x ):u (x ),u '(x ),u″(x )∈C (ℝ1),u (x )=u (x +2 π ), x ∈ℝ1,∫0 2 π u (x )d x =0 } is presented. The estimates for the Green's function and it's derivative are obtained. The positivity of the operator Ax is proved.
q-differential operator representation of the quantum superalgebra Uq(sl(M+1|N+1))
Kimura, K
1996-01-01
A representation of the quantum superalgebra Uq(sl(M+1|N+1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates correspond to the local ones of the flag manifold. This realization provides us with a guide to construct the free field realization for the quantum affine superalgebra Uq^(sl(M+1|N+1)) at arbitrary level.
Inverse-Definiteness of the Fourth-Order Symmetric Differential Operator (Ⅰ)
Institute of Scientific and Technical Information of China (English)
Wei Yin YE
2004-01-01
We give a linear symmetric differential operator L defined by L := D4 + bD2 + aIin the 2π-periodic function space, and study the inverse-definiteness property of L. We obtain a complete result about the inverse-definiteness property of L with real constants a and b when b2 -4a ＞ 0and a- bk2 + k4 ≠ 0 for any k ∈ {1,2,3,...}.
Relativistic kinetic momentum operators, half-rapidities and noncommutative differential calculus
Mir-Kasimov, R. M.
2012-09-01
It is shown that the generating function for the matrix elements of irreps of Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions in the Relativistic Configuration Space (RCS). These derivatives commute and can be interpreted as the quantum mechanical operators of the relativistic momentum corresponding to the half of the non-Euclidean distance in the Lobachevsky momentum space (the mass shell).
On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces
Directory of Open Access Journals (Sweden)
Sobhy El-Sayed Ibrahim
2003-01-01
order, with complex coefficients and its formal adjoint Mp+ on any finite number of intervals Ip=(ap,bp, p=1,…, N, are considered in the setting of the direct sums of Lwp2(ap,bp-spaces of functions defined on each of the separate intervals. And a number of results concerning the location of the point spectra and regularity fields of general differential operators generated by such expressions are obtained.
Scale invariance of parity-invariant three-dimensional QED
Karthik, Nikhil; Narayanan, Rajamani
2016-09-01
We present numerical evidences using overlap fermions for a scale-invariant behavior of parity-invariant three-dimensional QED with two flavors of massless two-component fermions. Using finite-size scaling of the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator, we rule out the presence of a bilinear condensate and estimate the mass anomalous dimension. The eigenvectors associated with these low-lying eigenvalues suggest critical behavior in the sense of a metal-insulator transition. We show that there is no mass gap in the scalar and vector correlators in the infinite-volume theory. The vector correlator does not acquire an anomalous dimension. The anomalous dimension associated with the long-distance behavior of the scalar correlator is consistent with the mass anomalous dimension.
Local and gauge invariant observables in gravity
Khavkine, Igor
2015-01-01
It is well known that General Relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observables. We propose a generalized notion of local observables, which retain the most important properties that follow from the standard definition of locality, yet is flexible enough to admit a large class of diffeomorphism invariant observables in GR. The generalization comes at a small price, that the domain of definition of a generalized local observable may not cover the entire phase space of GR and two such observables may have distinct domains. However, the subset of metrics on which generalized local observables can be defined is in a sense generic (its open interior is non-empty in the Whitney strong topology). Moreover, generalized local gauge invariant observables are sufficient to separate diffeomorphism orbits on this admissible subset of the phase space. Connecting the construction with the notion of differential invariants, gives a general scheme for...
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement instrume
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement instrume
Measurement invariance versus selection invariance: Is fair selection possible?
Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement instrume
Measurement invariance versus selection invariance: Is fair selection possible?
Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equation
Institute of Scientific and Technical Information of China (English)
Chen Xiang-Wei; Liu Cui-Mei; Li Yan-Min
2006-01-01
Based on the invariance of differential equations under infinitesimal transformations,Lie symmetry,laws of conservations,perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed.The conditions for existence of the exact invariants and adiabatic invariants are proved,and their forms are also given.In addition,an example is presented to illustrate these results.
A scale invariant covariance structure on jet space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo
2005-01-01
This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part...... of the derivation, we introduce a blurring operator At that acts on jet space contrary to doing spatial filtering and a scaling operator Ss. The stochastic Brownian image model is an example of a class of functions which are scale invariant with respect to the operators At and Ss. This paper also includes empirical...
Finite type invariants and fatgraphs
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry
2010-01-01
–Murakami–Ohtsuki of the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an isomorphism...... from an appropriate vector space of homology cylinders to a certain algebra of Jacobi diagrams. Via composition for any pair of fatgraph spines G,G′ of Σ, we derive a representation of the Ptolemy groupoid, i.e., the combinatorial model for the fundamental path groupoid of Teichmüller space, as a group...... of automorphisms of this algebra. The space comes equipped with a geometrically natural product induced by stacking cylinders on top of one another and furthermore supports related operations which arise by gluing a homology handlebody to one end of a cylinder or to another homology handlebody. We compute how G...
Invariant tensors for simple groups
Energy Technology Data Exchange (ETDEWEB)
De Azcarraga, J.A.; Macfarlane, A.J.; Mountain, A.J.; Perez Bueno, J.C. [Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics (DAMTP)
1998-01-26
The forms of the invariant primitive tensors for the simple Lie algebras A{sub l}, B{sub l}, C{sub l} and D{sub l} are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A{sub l} algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given. (orig.). 34 refs.
Lie symmetries and invariants of constrained Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Liu Rong-Wan; Chen Li-Qun
2004-01-01
According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.
Domains of pseudo-differential operators: a case for the Triebel-Lizorkin spaces
Directory of Open Access Journals (Sweden)
Jon Johnsen
2005-01-01
Full Text Available The main result is that every pseudo-differential operator of type 1, 1 and order d is continuous from the Triebel-Lizorkin space Fp,1d to Lp, 1≤p≺∞, and that this is optimal within the Besov and Triebel-Lizorkin scales. The proof also leads to the known continuity for s≻d, while for all real s the sufficiency of Hörmander's condition on the twisted diagonal is carried over to the Besov and Triebel-Lizorkin framework. To obtain this, type 1, 1-operators are extended to distributions with compact spectrum, and Fourier transformed operators of this type are on such distributions proved to satisfy a support rule, generalising the rule for convolutions. Thereby the use of reduced symbols, as introduced by Coifman and Meyer, is replaced by direct application of the paradifferential methods. A few flaws in the literature have been detected and corrected.
Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V
1999-01-01
This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical
Lorentz invariance with an invariant energy scale
Magueijo, J; Magueijo, Joao; Smolin, Lee
2002-01-01
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a non-linear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants, and we highlight the similarities between the group action found and a transformation previously proposed by Fock. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
Bytsenko, A A
2016-01-01
In this paper we analyze the quantum homological invariants (the Poincar\\'e polynomials of the $\\mathfrak{sl}_N$ link homology). In the case when the dimensions of homologies of appropriate topological spaces are precisely known, the procedure of the calculation of the Kovanov-Rozansky type homology, based on the Euler-Poincar\\'e formula can be appreciably simplified. We express the formal character of the irreducible tensor representation of the classical groups in terms of the symmetric and spectral functions of hyperbolic geometry. On the basis of Labastida-Mari\\~{n}o-Ooguri-Vafa conjecture, we derive a representation of the Chern-Simons partition function in the form of an infinite product in terms of the Ruelle spectral functions (the cases of a knot, unknot, and links have been considered). We also derive an infinite-product formula for the orthogonal Chern-Simons partition functions and analyze the singularities and the symmetry properties of the infinite-product structures.
Adaptivity and group invariance in mathematical morphology
Roerdink, Jos B.T.M.
2009-01-01
The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements depe
Speed-variable Switched Differential Pump System for Direct Operation of Hydraulic Cylinders
DEFF Research Database (Denmark)
Schmidt, Lasse; Roemer, Daniel Beck; Pedersen, Henrik Clemmensen
2015-01-01
proportional valves, this design allows to control the lower chamber pressure levels, throttling excess compression flow to tank. The resulting design introduces additional losses due to throttling of excess compression flow, but also improves the dynamic properties of the system significantly. The proposed...... differential cylinders. The main idea was here to utilize an electric rotary drive, with the shaft interconnected to two antiparallel fixed displacement gear pumps, to actuate a differential cylinder. With the design carried out such that the area ratio of the cylinder matches the displacement ratio of the two...... may seriously influence the dynamics and hence the performance during operation. This paper presents an analysis of these properties, and a redesign of the hydraulic system concept is proposed. Here the area- and displacement ratios are deliberately mismatched, causing inherent pressure build...
Reservoir Flood Control Operation Based on Adaptive Immune Differential Evolution Algorithm
Zou, Qiang; Lu, Jun; Yu, Shan
2017-05-01
Reservoir flood control operation (RFCO) is a high dimensional complex problem with multi-stages, multi-variables and multi-constraints, and its optimal solution is not easy to get. Differential evolution algorithm (DE) can be applied in RFCO, but its species diversity may sharply decline at the last evolution and lead into local optimal. Therefore, based on the adaptively controlling for mutation factor and crossover factor in each generation and immune clonal selection for better individuals, then adaptive immune differential evolution algorithm (AIDE) was proposed. And test function simulation verified the feasibility and efficiency of AIDE. Finally, AIDE was employed for RFCO and case study showed that AIDE could get better flood control benefit with fast convergence and high accuracy, moreover the outcomes of this research provided an effective way for RFCO.
Solving the Interval Riccati differential equation by Wavelet operational matrix method
Directory of Open Access Journals (Sweden)
N. Ahangari Ghadimi
2016-03-01
Full Text Available Riccati differential equation is an important equation, in many fields of engineering and applied sciences, so recently lots of methods have been proposed to solve this equation. Haar Wavelet operational matrix,is one of the effective methods to solve this equation, that is very simple and easy, compared to other orders. In this paper, we want to solve the nonlinear riccati differential equation in interval initial condition. first we simplify it by using the block pulse function to expand the Haar wavelet one. we have three cases for each interval, but now it can be solved for positive interval Haar coefficients. The results reveal that the proposed method is very effective and simple.
Analysis of an operator-differential model for magnetostrictive energy harvesting
Davino, D.; Krejčí, P.; Pimenov, A.; Rachinskii, D.; Visone, C.
2016-10-01
We present a model of, and analysis of an optimization problem for, a magnetostrictive harvesting device which converts mechanical energy of the repetitive process such as vibrations of the smart material to electrical energy that is then supplied to an electric load. The model combines a lumped differential equation for a simple electronic circuit with an operator model for the complex constitutive law of the magnetostrictive material. The operator based on the formalism of the phenomenological Preisach model describes nonlinear saturation effects and hysteresis losses typical of magnetostrictive materials in a thermodynamically consistent fashion. We prove well-posedness of the full operator-differential system and establish global asymptotic stability of the periodic regime under periodic mechanical forcing that represents mechanical vibrations due to varying environmental conditions. Then we show the existence of an optimal solution for the problem of maximization of the output power with respect to a set of controllable parameters (for the periodically forced system). Analytical results are illustrated with numerical examples of an optimal solution.
Invariants of polarization transformations.
Sadjadi, Firooz A
2007-05-20
The use of polarization-sensitive sensors is being explored in a variety of applications. Polarization diversity has been shown to improve the performance of the automatic target detection and recognition in a significant way. However, it also brings out the problems associated with processing and storing more data and the problem of polarization distortion during transmission. We present a technique for extracting attributes that are invariant under polarization transformations. The polarimetric signatures are represented in terms of the components of the Stokes vectors. Invariant algebra is then used to extract a set of signature-related attributes that are invariant under linear transformation of the Stokes vectors. Experimental results using polarimetric infrared signatures of a number of manmade and natural objects undergoing systematic linear transformations support the invariancy of these attributes.
Algorithms in invariant theory
Sturmfels, Bernd
2008-01-01
J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
Cosmological disformal invariance
Domènech, Guillem; Sasaki, Misao
2015-01-01
The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a d...
Manifold invariants affect dynamics in ADS gravity
Liko, Tomas
2013-01-01
The first-order Holst action with negative cosmological constant is rendered finite by requiring functional differentiability on the configuration space of tetrads and connections. The surface terms that arise in the action for ADS gravity are equivalent to the Euler and Pontryagin densities with fixed weight factors; these terms modify the Noether charges that arise from diffeomorphism invariance of the action.
Invariant algebraic surfaces for a virus dynamics
Valls, Claudia
2015-08-01
In this paper, we provide a complete classification of the invariant algebraic surfaces and of the rational first integrals for a well-known virus system. In the proofs, we use the weight-homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.
Determinantal invariant gravity
Pirinccioglu, Nurettin
2016-01-01
Einstein-Hilbert action with a determinantal invariant has been considered. The obtained field equation contains the \\texttt{inverse Ricci tensor}, $\\Re_{\\alpha\\beta}$. The linearized solution of invariant has been examined, and constant curvature space-time metric solution of the field equation gives different curvature constant for each values of $\\sigma$. $\\sigma=0$ gives a trivial solution for constant curvature, $R_{0}$.
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Baire classes of Lyapunov invariants
Bykov, V. V.
2017-05-01
It is shown that no relations exist (apart from inherent ones) between Baire classes of Lyapunov transformation invariants in the compact- open and uniform topologies on the space of linear differential systems. It is established that if a functional on the space of linear differential systems with the compact-open topology is the repeated limit of a multisequence of continuous functionals, then these can be chosen to be determined by the values of system coefficients on a finite interval of the half-line (one for each functional). It is proved that the Lyapunov exponents cannot be represented as the limit of a sequence of (not necessarily continuous) functionals such that each of these depends only on the restriction of the system to a finite interval of the half-line. Bibliography: 28 titles.
Ćurgus, Branko; Read, Thomas T.
Necessary and sufficient conditions and also simple sufficient conditions are given for the self-adjoint operators associated with the second-order linear differential expression τ(y)= {1}/{w}(-(py')'+qy) on [ a, b) to have discrete spectrum. Here the coefficients of τ are non-negative and satisfy minimal smoothness conditions. These results follow from compact embedding theorems from a weighted one-dimensional Sobolev space with norm∫ ab( p∣ f'∣ r+ q∣ f∣ r)) 1/ r into a weighted Banach space with norm(∫ abw∣ f∣ s) 1/ s .
Directory of Open Access Journals (Sweden)
S. C. Lim
2012-01-01
Full Text Available A new direct operational inversion method is introduced for solving coupled linear systems of ordinary fractional differential equations. The solutions so-obtained can be expressed explicitly in terms of multivariate Mittag-Leffler functions. In the case where the multiorders are multiples of a common real positive number, the solutions can be reduced to linear combinations of Mittag-Leffler functions of a single variable. The solutions can be shown to be asymptotically oscillatory under certain conditions. This technique is illustrated in detail by two concrete examples, namely, the coupled harmonic oscillator and the fractional Wien bridge circuit. Stability conditions and simulations of the corresponding solutions are given.
On the harmonic superspace language adapted to the Gelfand-Dickey algebra of differential operators
Hssaini, M; Maroufi, B; Sedra, M B
2000-01-01
Methods developed for the analysis of non-linear integrable models are used in the harmonic superspace (HS) framework. These methods, when applied to the HS, can lead to extract more information about the meaning of integrability in non-linear physical problems. Among the results obtained, we give the basic ingredients towards building in the HS language the analogue of the G.D. algebra of pseudo-differential operators. Some useful convention notations and algebraic structures are also introduced to make the use of the harmonic superspace techniques more accessible.
Directory of Open Access Journals (Sweden)
Emran Tohidi
2013-01-01
Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.
On the q-deformed differential operators and induced su(n)-Toda field theory
Hssaini, M; Maroufi, B; Sedra, M B
2000-01-01
We build in this paper the algebra of q-deformed pseudo-differential operators shown to be an essential step towards setting a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the q-analogues of the generalised KdV hierarchy. We focus in particular the first leading orders of this q-deformed hierarchy namely the q-KdV and q- Boussinesq integrable systems. We present also the q-generalisation of the conformal transformations of the currents and discuss the primarity condition of the fields by using the Volterra gauge group transformations for the q-covariant Lax operators. An induced su(n)-Toda(su(2)-Liouville) field theory construction is discussed and other important features are presented.
Kemper, Gregor; Körding, Elmar; Malle, Gunter; Matzat, B. Heinrich; Vogel, Denis; Wiese, Gabor
2001-01-01
We announce the creation of a database of invariant rings. This database contains a large number of invariant rings of finite groups, mostly in the modular case. It gives information on generators and structural properties of the invariant rings. The main purpose is to provide a tool for researchers in invariant theory.
Gauge Invariant Fractional Electromagnetic Fields
Lazo, Matheus Jatkoske
2011-01-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.
Directory of Open Access Journals (Sweden)
Guo Feng
2008-01-01
Full Text Available Abstract We consider the classes of periodic functions with formal self-adjoint linear differential operators , which include the classical Sobolev class as its special case. With the help of the spectral of linear differential equations, we find the exact values of Bernstein -width of the classes in the for .
On the optimal determination of differential rates in the presence of higher-dimensional operators
Fichet, Sylvain; Rebello Teles, Patricia
2017-08-03
When the Standard Model is interpreted as the renormalizable sector of a low-energy effective theory, the effects of new physics are encoded into a set of higher-dimensional operators. These operators potentially deform the shapes of Standard Model differential distributions of final states observable at colliders. We describe a simple and systematic method to obtain optimal estimations of these deformations when using numerical tools, like Monte Carlo simulations. A crucial aspect of this method is minimization of the estimation uncertainty: we demonstrate how the operator coefficients have to be set in the simulations in order to get optimal results. The uncertainty on the interference term turns out to be the most difficult to control and grows very quickly when the interference is suppressed. We exemplify our method by computing the deformations induced by the ${\\cal O}_{3W}$ operator in $W^+W^-$ production at the LHC, and by deriving a bound on ${\\cal O}_{3W}$ using 8 TeV CMS data.
Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Shoufeng SHEN; ChangZheng QU; Yongyang JIN; Lina JI
2012-01-01
In this paper,the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions.It is shown that if the two-component nonlinear vector differential operator F =(F1,F2) with orders {k1,k2} (k1 ≥ k2) preserves the invariant subspace W1n1 × W2n2 (n1 ≥ n2),then n1 - n2 ≤ k2,n1 ≤ 2(k1 + k2) + 1,where Wqnq is the space generated by solutions of a linear ordinary differential equation of order nq (q =1,2).Several examples including the (1+1)-dimensional diffusion system and It(o)'s type,Drinfel'd-Sokolov-Wilson's type and Whitham-Broer-Kaup's type equations are presented to illustrate the result.Furthermore,the estimate of dimension for m-component nonlinear systems is also given.
Invariant distances and metrics in complex analysis
Jarnicki, Marek
2013-01-01
As in the field of ""Invariant Distances and Metrics in Complex Analysis"" there was and is a continuous progress this is the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other met
The decomposition of global conformal invariants
Alexakis, Spyros
2012-01-01
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Dese
On logarithmic extensions of local scale-invariance
Energy Technology Data Exchange (ETDEWEB)
Henkel, Malte, E-mail: malte.henkel@ijl.nancy-universite.fr [Groupe de Physique Statistique, Département de Physique de la Matière et des Matériaux, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506 Vandoeuvre lès Nancy Cedex (France)
2013-04-11
Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena.
Chern-Simons Invariants of Torus Knots and Links
Stevan, Sébastien
2010-01-01
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
Supersymmetric invariant theories
Esipova, S R; Radchenko, O V
2013-01-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Supersymmetric invariant theories
Esipova, S. R.; Lavrov, P. M.; Radchenko, O. V.
2014-04-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Pérez-Nadal, Guillem
2016-01-01
We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates "scaling like time" is generically greater than one. We propose the Cartesian product of two curved spaces, with the metric of each space parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry.
Institute of Scientific and Technical Information of China (English)
WU; Jianhua; WANG; Zhaohui
2009-01-01
Digital libraries are complex systems and this brings difficulties for their evaluation.This paper proposes a hierarchical model to solve this problem,and puts the entangled matters into a clear-layered structure.Firstly,digital libraries(DLs thereafter)are classified into 5 groups in ascending gradations,i.e.mini DLs,small DLs,medium DLs,large DLs,and huge DLs by their scope of operation.Then,according to the characteristics of DLs at different operational scope and level of sophistication,they are further grouped into unitary DLs,union DLs and hybrid DLs accordingly.Based on this simulated structure,a hierarchical model for digital library evaluation is introduced,which evaluates DLs differentiatingly within a hierarchical scheme by using varying criteria based on their specific level of operational complexity such as at the micro-level,medium-level,and/or at the macro-level.Based on our careful examination and analysis of the current literature about DL evaluation system,an experiment is conducted by using the DL evaluation model along with its criteria for unitary DLs at micro-level.The main contents resulting from this evaluation experimentation and also those evaluation indicators and relevant issues of major concerns for DLs at medium-level and macro-level are also to be presented at some length.
Generalized invariance principles and the theory of stability.
Lasalle, J. P.
1971-01-01
Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Objective: To explore the patterns of Syndrome Differentiation (SD) of coronary heart disease (CHD) patients in peri-operative stage of coronary artery bypass graft (CABG). Methods: One week after operation, thirty-seven CHD patients, who received CABG of internal mammary artery or great saphena vein under conventional general anesthesia with low or middle temperature extracorporeal circulation were differentiated as various syndromes, with the pre- or post-operational EKG, color Doppler echocardiography were done during and after operation. The hemodynamic parameters were monitored. Results: In the CHD patients, 64.9% were differentiated as Qi-Yin deficiency, 67.6% were complicated with phlegm syndrome and 62.2% with blood stasis, suggesting that Qi-deficiency, phlegm and stasis are the basic pathogenetic factors in patients with CABG. Moreover, the peri-operative syndrome was correlated with the condition of coronary artery lesion, heart and lung functions before operation, and the extracorporeal circulation time during the operation. Conclusion: TCM SD conducting in peri-operative stage might be useful in exploring the patterns of syndrome alteration which provided a basis for preventing peri-operative complications and elevating success rate of operation.
Local and gauge invariant observables in gravity
Khavkine, Igor
2015-09-01
It is well known that general relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observable. We propose a generalized notion of local observables, which retain the most important properties that follow from the standard definition of locality, yet is flexible enough to admit a large class of diffeomorphism invariant observables in GR. The generalization comes at a small price—that the domain of definition of a generalized local observable may not cover the entire phase space of GR and two such observables may have distinct domains. However, the subset of metrics on which generalized local observables can be defined is in a sense generic (its open interior is non-empty in the Whitney strong topology). Moreover, generalized local gauge invariant observables are sufficient to separate diffeomorphism orbits on this admissible subset of the phase space. Connecting the construction with the notion of differential invariants gives a general scheme for defining generalized local gauge invariant observables in arbitrary gauge theories, which happens to agree with well-known results for Maxwell and Yang-Mills theories.
Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2014-01-01
Full Text Available The nonlocal boundary value problem for the parabolic differential equation v'(t+A(tv(t=f(t (0≤t≤T, v(0=v(λ+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β of all Eα-β-valued continuous functions φ(t on [0,T] satisfying a Hölder condition with a weight (t+τγ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.
Wang, Ruey-Lue; Fu, Chien-Cheng; Yu, Chi; Wu, Wei-De; Chuang, Yan-Tse; Lin, Chen-Fu; Liao, Hsin-Hao; Tsai, Hann-Huei; Juang, Ying-Zong
2014-01-01
In this paper, a CMOS multisensor readout circuit is presented. A multiple differential-input operational amplifier (MDI-OPA) with three distinct positive inputs and one common negative input is designed to make one of the three inputs to act as a general differential-input OPA through a built-in multiplexer. A voltage-to-current converter and a current-controlled oscillator are integrated with the MDI-OPA so that the selected analog input voltage can be used to generate a pulse output whose frequency is linearly proportional to the selected input voltage. The linearity of the transfer characteristic is at least 99.99% for input voltages below 1.44 V. An added current-offset structure is used to modify the transfer characteristic that usually varies owing to process variation. The measured output transfer characteristics of three input channels show nearly the same sensitivity of 90 Hz/mV or so with a linearity of at least 99.99% with the assistance of the current-offset mechanism.
Magoon, Michael A; Critchfield, Thomas S; Merrill, Dustin; Newland, M Christopher; Schneider, W Joel
2017-01-01
Although theoretical discussions typically assume that positive and negative reinforcement differ, the literature contains little unambiguous evidence that they produce differential behavioral effects. To test whether the two types of consequences control behavior differently, we pitted money-gain positive reinforcement and money-loss-avoidance negative reinforcement, scheduled through identically programmed variable-cycle schedules, against each other in concurrent schedules. Contingencies of response-produced feedback, normally different in positive and negative reinforcement, were made symmetrical. Steeper matching slopes were produced compared to a baseline consisting of all positive reinforcement. This free-operant differential outcomes effect supports the notion that that stimulus-presentation positive reinforcement and stimulus-elimination negative reinforcement are functionally "different." However, a control experiment showed that the feedback asymmetry of more traditional positive and negative reinforcement schedules also is sufficient to create a "difference" when the type of consequence is held constant. We offer these findings as a small step in meeting the very large challenge of moving negative reinforcement theory beyond decades of relative quiescence.
Deehan, Gerald A; Palmatier, Matthew I; Cain, Mary E; Kiefer, Stephen W
2011-04-01
Exposing rats to differential rearing conditions during early postweaning development has been shown to produce changes in a number of behaviors displayed during adulthood. The purpose of the present studies was to investigate whether rearing alcohol-preferring (P) and nonpreferring (NP) rats in an environmental enrichment condition (EC), a social condition (SC), or an impoverished condition (IC) would differentially affect self-administration of 10% ethanol. In Experiment 1, rats were tested for consumption of 10% ethanol in limited- and free-access tests. For Experiment 2, rats were trained to respond in an operant chamber for ethanol and then provided concurrent access to 10% ethanol and water. Each solution was presented in a separate liquid dipper after meeting the schedule of reinforcement on distinct levers. After concurrent access tests, the water lever/dipper was inactivated and a progressive ratio (PR) schedule was initiated. Three successive solutions (10% ethanol, 15% ethanol, and 10% sucrose) were tested under the PR. For P rats, rearing in an EC reduced ethanol consumption, preference, and motivation to obtain ethanol, relative to P rats reared in an IC. Thus, exposure to a novel environment immediately after weaning acted to decrease the reinforcing properties of ethanol in an animal model for alcoholism.
Differential gene expression in the rat hippocampus during learning of an operant conditioning task.
Rapanelli, M; Frick, L R; Zanutto, B S
2009-11-10
Changes in transcription levels of brain-derived neurotrophic factor (BDNF), cyclic adenosine monophosphate (cAMP) response element binding (CREB), Synapsin I, Ca(2+)/calmodulin-dependent protein kinase II (CamKII), activity-regulated cytoskeleton-associated protein (Arc), c-jun and c-fos have been associated to several learning paradigms in different brain areas. In this study, we measured mRNA expression in the hippocampus by real time (RT)-PCR mRNA levels of BDNF, CREB, Synapsin I, CamKII, Arc, c-jun and c-fos, during learning and operant conditioning task. Experimental groups were as follows: control (C, the animals never left the bioterium), when the animals reached 50-65% of the expected response (Incompletely Trained, IT), when animals reached 100% of the expected response with a latency time lower than 5 s (Trained, Tr), Box Control of Incompletely Trained (BCIT), animals spent the same time as the IT in the operant conditioning box and Box Control of Trained (BCTr) animals spent the same time as the Tr in the operant conditioning box. All rats were killed at the same time by cervical dislocation 15 min after training and hippocampi were removed and processed. We found increments of mRNA levels of most genes (BDNF, CREB, Synapsin I, Arc, c-jun and c-fos) in IT and Tr groups compared to their box controls, but increments in Tr were smaller compared with IT. These results describe a differential gene expression in the rat hippocampus when the animals are learning and when animals have already learned. Taking together the results presented herein with the known functions of these genes, we propose a link between changes in gene expression in the hippocampus and different degrees of cellular activation and plasticity during learning of an operant conditioning task.
Kobayashi, Tatsuo; Urakawa, Yuko
2016-01-01
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field $T$ whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by $T$. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential $V_{ht}$, but it also has a non-negligible deviation from $V_{ht}$. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still po...
Energy Technology Data Exchange (ETDEWEB)
Kobayashi, Tatsuo [Department of Physics, Hokkaido University,Kita, Sapporo, 060-0810 (Japan); Nitta, Daisuke; Urakawa, Yuko [Department of Physics and Astrophysics, Nagoya University,Chikusa, Nagoya 464-8602 (Japan)
2016-08-08
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential V{sub ht}, but it also has a non-negligible deviation from V{sub ht}. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.
LUNISOLAR INVARIANT RELATIVE ORBITS
Walid Ali Rahoma
2013-01-01
The present study deal with constructing an analytical model within Hamiltonian formulation to design invariant relative orbits due to the perturbation of J2 and the lunisolar attraction. To fade the secular drift separation over the time between two neighboring orbits, two second order conditions that guarantee that drift are derived and enforced to be equal.
Kobayashi, Tatsuo; Nitta, Daisuke; Urakawa, Yuko
2016-08-01
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential Vht, but it also has a non-negligible deviation from Vht. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.
Tanaka, Ken'ichiro; Murashige, Sunao
2012-01-01
We present the convergence rates and the explicit error bounds of Hill's method, which is a numerical method for computing the spectra of ordinary differential operators with periodic coefficients. This method approximates the operator by a finite dimensional matrix. On the assumption that the operator is selfadjoint, it is shown that, under some conditions, we can obtain the convergence rates of eigenvalues with respect to the dimension and the explicit error bounds. Numerical examples demon...
Multipartite invariant states. II. Orthogonal symmetry
Chruściński, Dariusz; Kossakowski, Andrzej
2006-06-01
We construct a class of multipartite states possessing orthogonal symmetry. This new class contains multipartite states which are invariant under the action of local unitary operations introduced in our preceding paper [Phys. Rev. A 73, 062314 (2006)]. We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.
Testing local Lorentz invariance with gravitational waves
Kostelecky, Alan
2016-01-01
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
Testing local Lorentz invariance with gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Kostelecký, V. Alan, E-mail: kostelec@indiana.edu [Physics Department, Indiana University, Bloomington, IN 47405 (United States); Mewes, Matthew [Physics Department, California Polytechnic State University, San Luis Obispo, CA 93407 (United States)
2016-06-10
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
Joint Local Quasinilpotence and Common Invariant Subspaces
Indian Academy of Sciences (India)
A Fernández Valles
2006-08-01
In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for -tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
OBJECTIVE To examine the ultrastructure of gastric cancer cells by the electron microscope, in order to assess the relationship between neuroendocrine differentiation and post-operative survival time.METHODS NSE, Syn and CgA immunohistochemical labeling was conducted in 168 cases with a common-type of gastric cancer. Electron microscopy was performed in 80 cases with positive immunohistochemical labeling.These cases were followed-up for over 5 years and the post-operative survival data analyzed.RESULTS Neuroendocrine granules were found by electron microscopy in 39 cases. The rate of neuroendocrine differentiation found was 23% (39/168), using routine diagnostic criteria and electron microscopy (REM).The post-operative survival time of gastric cancer patients with neuroendocrine differentiation was significantly shorter (P=0.0032) compared to those without neuroendocrine differentiation.CONCLUSION It is of significant clinical importance to determine if the neuroendocrine cells are differentiated in gastric cancers. The gastric cancer patients with neuroendocrine differentiation have a shorter post-operative survival time and a poorer prognosis. Electron microscopy is a reliable method of providing a diagnosis.
Exact invariants and adiabatic invariants of the singular Lagrange system
Institute of Scientific and Technical Information of China (English)
陈向炜; 李彦敏
2003-01-01
Based on the theory of symmetries and conserved quantities of the singular Lagrange system,the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed.Firstly,the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed.Then,the conditions for the existence of the exact invariants and adiabatic invariants are proved,and their forms are given.Finally,an example is presented to illustrate these results.
Hojman Exact Invariants and Adiabatic Invariants of Hamilton System
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higherorder adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of the results.
Measurement Invariance versus Selection Invariance: Is Fair Selection Possible?
Borsman, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement instrument is used and group differences are present in…
Scaling theory of {{{Z}}_{2}} topological invariants
Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P.
2016-09-01
For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
Unitarily invariant norms related to factors
Fang, Junsheng
2007-01-01
Let $\\M$ be a semi-finite von Neumann algebra and $\\J(\\M)$ be the set of operators in $\\M$ with finite range projections. In this paper we obtain a representation theorem for unitarily invariant norms on $\\J(\\M)$ of semi-finite factors $\\M$ in terms of Ky Fan norms. As an application, we prove that the class of unitarily invariant norms on $\\J(\\M)$ of a type ${\\rm II}\\sb \\infty$ (or type ${\\rm I}\\sb \\infty$) factor $\\M$ coincides with the class of symmetric gauge norms on $\\J(L^\\infty[0,\\infty))$ (or $\\J(l^\\infty(\
Continuous Integrated Invariant Inference Project
National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...
Reducing Lookups for Invariant Checking
DEFF Research Database (Denmark)
Thomsen, Jakob Grauenkjær; Clausen, Christian; Andersen, Kristoffer Just;
2013-01-01
This paper helps reduce the cost of invariant checking in cases where access to data is expensive. Assume that a set of variables satisfy a given invariant and a request is received to update a subset of them. We reduce the set of variables to inspect, in order to verify that the invariant is sti...
Vollmer, Gerhard
2010-10-01
Scientific knowledge should not only be true, it should be as objective as possible. It should refer to a reality independent of any subject. What can we use as a criterion of objectivity? Intersubjectivity (i.e., intersubjective understandability and intersubjective testability) is necessary, but not sufficient. Other criteria are: independence of reference system, independence of method, non-conventionality. Is there some common trait? Yes, there is: invariance under some specified transformations. Thus, we say: A proposition is objective only if its truth is invariant against a change in the conditions under which it was formulated. We give illustrations from geometry, perception, neurobiology, relativity theory, and quantum theory. Such an objectivist position has many advantages.
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Cheng, Miranda C N; Harrison, Sarah M; Kachru, Shamit
2015-01-01
In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau--Zaslow (capturing the Euler characters of the moduli spaces of D2-branes on curves of given genus), together with their refinements to carry additional quantum numbers by Katz--Klemm--Vafa (KKV), and Katz--Klemm--Pandharipande (KKP). We show that these invariants can be reproduced by studying the Ramond ground states of an auxiliary chiral superconformal field theory which has recently been observed to give rise to mock modular moonshine for a variety of sporadic simple groups that are subgroups of Conway's group. We also study equivariant versions of these invariants. A K3 sigma model is specified by a choice of 4-plane in the K3 D-brane charge lattice. Symmetries of K3 sigma models are naturally identified with 4-plane preserving subgroups of the Conway group, according to the work of Gaberdiel--Hoheneg...
Braaten, Eric
2015-01-01
XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the X(3872) resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly conserved in the transition D*0 --> D0 pi0. The transitions D*0 --> D0 pi0 and X --> D0 D0-bar pi0 are described explicitly in XEFT. The effects of the decay D*0 --> D0 gamma and of short-distance decay modes of the X(3872), such as J/psi --> pi+ pi-, can be taken into account by using complex on-shell renormalization schemes for the D*0 propagator and for the D*0 D0-bar propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the D*0 D0-bar scattering length to next-to-leading order. Galilean invariance ensures the cancellation of ultraviolet divergences without the need for truncating an expansion in powers of the ratio of the pion and charm meson masses.
Kiryakova, Virginia S.
2012-11-01
The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order
The left invariant metric in the general linear group
Andruchow, Esteban; Recht, Lazaro; Varela, Alejandro
2011-01-01
Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general lineal group. By means of the Euler-Lagrange equations, existence and uniqueness of extremal paths for the length functional are established, and regularity properties of these extremal paths are obtained. Minimizing paths in the group are shown to have a velocity with constant singular values and multiplicity. In several special cases, these geodesic paths are computed explicitly. In particular the Riemannian geodesics, corresponding to the case p=2, are characterized as the product of two one-parameter groups. It is also shown that geodesics are one-parameter groups if and only if the initial velocity is a normal matrix. These results are further extended to the context of compact operators with p-summable spectrum, where a differential equation for the spectral projections of the velocity vector of an extremal path is obtained.
Generalized scale invariance, clouds and radiative transfer on multifractal clouds
Energy Technology Data Exchange (ETDEWEB)
Lovejoy, S.; Schertzer, D. [Univ. Pierre et Marie Curie, Paris (France)
1995-09-01
Recent systematic satellite studies (LANDSAT, AVHRR, METEOSAT) of cloud radiances using (isotropic) energy spectra have displayed excellent scaling from at least about 300m to about 4000km, even for individual cloud pictures. At first sight, this contradicts the observed diversity of cloud morphology, texture and type. The authors argue that the explanation of this apparent paradox is that the differences are due to anisotropy, e.g. differential stratification and rotation. A general framework for anisotropic scaling expressed in terms of isotropic self-similar scaling and fractals and multifractals is needed. Schertzer and Lovejoy have proposed Generalized Scale Invariance (GSI) in response to this need. In GSI, the statistics of the large and small scales of system can be related to each other by a scale changing operator T{sub {lambda}} which depends only on the scale ratio {lambda}{sub i} there is no characteristic size. 3 refs., 1 fig.
A HIGH PERFORMANCE FULLY DIFFERENTIAL PURE CURRENT MODE OPERATIONAL AMPLIFIER AND ITS APPLICATIONS
Directory of Open Access Journals (Sweden)
SEYED JAVAD AZHARI
2012-08-01
Full Text Available In this paper a novel high performance all current-mode fully-differential (FD Current mode Operational Amplifier (COA in BIPOLAR technology is presented. The unique true current mode simple structure grants the proposed COA the largest yet reported unity gain frequency while providing low voltage low power operation. Benefiting from some novel ideas, it also exhibits high gain, high common mode rejection ratio (CMRR, high power supply rejection ratio (PSRR, high output impedance, low input impedance and most importantly high current drive capability. Its most important parameters are derived and its performance is proved by PSPICE simulations using 0.8 μm BICMOS process parameters at supply voltage of ±1.2V indicating the values of 82.4 dB,52.3º, 31.5 Ω, 31.78 MΩ, 179.2 dB, 2 mW and 698 MHz for gain, phase margin, input impedance, output impedance, CMRR, power and unity gain frequency respectively. Its CMRR also shows very high frequency of 2.64 GHz at zero dB. Its very high PSRR+/PSRR- of 182 dB/196 dB makes the proposed COA a highly suitable block in Mixed-Mode (SOC chips. Most favourably it can deliver up to ±1.5 mA yielding a high current drive capability exceeding 25. To demonstrate the performance of the proposed COA, it is used to realize a constant bandwidth voltage amplifier and a high performance Rm amplifier.
Computation of whiskered invariant tori and their associated manifolds: new fast algorithms
Huguet, Gemma; Sire, Yannick
2010-01-01
In this paper we present efficient algorithms for the computation of several invariant objects for Hamiltonian dynamics. More precisely, we consider KAM tori (i.e diffeomorphic copies of the torus such that the motion on them is conjugated to a rigid rotation) both Lagrangian tori (of maximal dimension) and whiskered tori (i.e. tori with hyperbolic directions which, together with the tangents to the torus and the symplectic conjugates span the whole tangent space). In the case of whiskered tori, we also present algorithms to compute the invariant splitting and the invariant manifolds associated to the splitting. We present them both for the case of discrete time and for differential equations. The algorithms are based on a Newton method to solve an appropriately chosen functional equation that expresses invariance. The algorithms are efficient: if we discretize the objects by $N$ elements, one step of the Newton method requires only O(N) storage and $O(N \\ln(N))$ operations. Furthermore, if the object we cons...
Cardinal invariants on Boolean algebras
Monk, J Donald
2014-01-01
This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the...
Inflation and classical scale invariance
Racioppi, Antonio
2014-01-01
BICEP2 measurement of primordial tensor modes in CMB suggests that cosmological inflation is due to a slowly rolling inflaton taking trans-Planckian values and provides further experimental evidence for the absence of large $M_{\\rm P}$ induced operators. We show that classical scale invariance solves the problem and allows for a remarkably simple scale-free inflaton model without any gauge group. Due to trans-Planckian inflaton values and VEVs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio $r$ in a large range. Precise determination of $r$ in future experiments will allow to test the proposed field-theoretic framework.
S. A. Effiong; J. O. Udoayang; A. I. Asuquo
2011-01-01
The study investigated the correlation and differential influence of historical cost and current cost profits on the operating capabilities of the firm. The financial statements of thirty-one Nigerian Companies were surveyed and adjusted for effects of price changes using the Consumers¡¯ Price Index (CPI). Correlation influence between the historical cost profits on the operating ability of the firm was measured and established on one hand and that of current cost profit on the other hand. Di...
Quadratic relativistic invariant and metric form in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Pissondes, Jean-Claude [DAEC, Observatoire de Paris-Meudon, Meudon (France)
1999-04-16
The Klein-Gordon equation is recovered in the framework of the theory of scale-relativity, first in the absence, then in the presence of an electromagnetic field. In this framework, spacetime at quantum scales is characterized by non-differentiability and continuity, which involves the introduction of explicit resolution-dependent fractal coordinates. Such a description leads to the notion of scale-covariance and its corresponding tool, a scale-covariant; derivative operator {theta}/ds. Due to it, the Klein-Gordon equation is written as an equation of free motion and interpreted as a geodesic equation in fractal spacetime. However, we obtain a new form for the corresponding relativistic invariant, which differs from that of special and general relativity. Characterizing quantum mechanics in the present approach, it is not simply quadratic in terms of velocities, but contains an extra term of divergence, which is intrinsically present in its expression. Moreover, in spite of the scale-covariance statements of the present theory, we find an extra term of current in addition to the Lorentz force, within the equations of motion with electromagnetic field written in this framework. Finally, we introduce another tool - a 'symmetric product' - from the requirement of recovering the usual form of the Leibniz rule written with the operator {theta}/ds. This tool allows us to write most equations in this framework in their usual classical form; in particular the simple rules of differentiation, the equations of motion with field and also our new relativistic invariant. (author)
Riccati group invariants of linear hamiltonian systems
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.
Notes on Group Invariants and Positivity of Density Matrices and Superoperators
Byrd, M S; Byrd, Mark S.; Khaneja, Navin
2003-01-01
In this paper, we construct a distinguished class of unitary invariants, the Casimir invariants, in terms of the generalized coherence vector representation of the density operator. Using a tensor product basis, we show how to extract local information about the density operator and the n-positivity of maps from density operators to density operators (superoperators). We then discuss some applications and implications.
Invariant functionals in higher-spin theory
Vasiliev, M. A.
2017-03-01
A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell AdS4 higher-spin theory we identify a four-form conjectured to represent the generating functional for 3d boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for 3d boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in AdS4. The peculiarity of the spinorial formulation of the on-shell AdS3 higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function F* (B (x)) in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space-time points of the factors of B (x), which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.
Finding Mutual Exclusion Invariants in Temporal Planning Domains
Bernardini, Sara; Smith, David E.
2011-01-01
We present a technique for automatically extracting temporal mutual exclusion invariants from PDDL2.2 planning instances. We first identify a set of invariant candidates by inspecting the domain and then check these candidates against properties that assure invariance. If these properties are violated, we show that it is sometimes possible to refine a candidate by adding additional propositions and turn it into a real invariant. Our technique builds on other approaches to invariant synthesis presented in the literature, but departs from their limited focus on instantaneous discrete actions by addressing temporal and numeric domains. To deal with time, we formulate invariance conditions that account for both the entire structure of the operators (including the conditions, rather than just the effects) and the possible interactions between operators. As a result, we construct a technique that is not only capable of identifying invariants for temporal domains, but is also able to find a broader set of invariants for non-temporal domains than the previous techniques.
EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS
Institute of Scientific and Technical Information of China (English)
陈向炜; 尚玫; 梅凤翔
2001-01-01
A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.
Link Invariants from Classical Chern-Simons Theory
Leal, L C
2002-01-01
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present this expressions in a manifestly diffeomorphism-invariant form, we introduce a set of differential forms associated with submanifolds in Euclidean three-space that allow us to write the link invariants as a kind of surface-dependent diffeomorphism-invariants that present certain Abelian gauge symmetry.
Noncommutative Field Theory With General Translation Invariant Star Products
Rivera, Manolo
2015-01-01
We compute the two-point and four-point Green's function of the noncommutative $\\phi^{4}$ field theory; first with the s-ordered star products and then with a general translation invariant star product. We derive the differential expression for any translation invariant star product, and with the help of this expression we show that any of these products can be written in terms of a twist. Finally, using the notion of the twisted action of the infinitesimal Poincar\\'e transformations, we show that the commutator between the coordinate functions is invariant under Poincar\\'e transformations at a deformed level.
Directory of Open Access Journals (Sweden)
Roman Urban
2003-08-01
Full Text Available We consider the Green functions for second order non-coercive differential operators on homogeneous manifolds of negative curvature, being a semi-direct product of a nilpotent Lie group $N$ and $A=mathbb{R}^+$. We obtain estimates for the mixed derivatives of the Green functions that complements a previous work by the same author [17].
Singularities of invariant connections
Energy Technology Data Exchange (ETDEWEB)
Amores, A.M. (Universidad Complutense, Madrid (Spain)); Gutierrez, M. (Universidad Politecnica, Madrid (Spain))
1992-12-01
A reductive homogeneous space M = P/G is considered, endowed with an invariant connection, i.e., such that all left translations of M induced by members of P preserve it. The authors study the set of singularities of such connections giving sufficient conditions for it to be empty, or, in other cases, familities of b-incomplete curves converging to singularities. A full description of the b-completion of a connection with M = R[sup m] (or a quotient of it) is given with information on its topology. 5 refs.
Invariant connections and vortices
García-Prada, Oscar
1993-10-01
We study the vortex equations on a line bundle over a compact Kähler manifold. These are a generalization of the classical vortex equations over ℝ2. We first prove an invariant version of the theorem of Donaldson, Uhlenbeck and Yau relating the existence of a Hermitian-Yang-Mills metric on a holomorphic bundle to the stability of such a bundle. We then show that the vortex equations are a dimensional reduction of the Hermitian-Yang-Mills equation. Using this fact and the theorem above we give a new existence proof for the vortex equations and describe the moduli space of solutions.
Anistropic Invariant FRW Cosmology
Chagoya, J F
2015-01-01
In this paper we study the effects of including anisotropic scaling invariance in the minisuperspace Lagrangian for a universe modelled by the Friedman-Robertson-Walker metric, a massless scalar field and cosmological constant. We find that canonical quantization of this system leads to a Schroedinger type equation, thus avoiding the frozen time problem of the usual Wheeler-DeWitt equation. Furthermore, we find numerical solutions for the classical equations of motion, and we also find evidence that under some conditions the big bang singularity is avoided in this model.
On the Discreteness Spectrum of the J-selfadjoint Euler Differential Operator%J-自伴Euler微分算子谱的离散性
Institute of Scientific and Technical Information of China (English)
高鹏飞; 王忠
2001-01-01
讨论了2n阶Euler微分算式生成的J-对称微分算子，得到了J-自伴Euler微分算子的谱是离散的充分条件.%The spectra of 2n order Euler differential operators with complexcoefficients are discussed.We obtain some sufficient conditions for discreteness of the spectrum of J-selfadjoint differential operators associated with J-symmetric Euler differential operators.
Sylvester and algebraic invariant theory%西尔维斯特与代数不变量理论
Institute of Scientific and Technical Information of China (English)
金英姬; 白宏刚
2013-01-01
文中利用文献研读与历史分析法,系统研究和探讨了西尔维斯特(James Joseph Sylvester,1814-1897)创立代数不变量理论的相关思想及其贡献:西尔维斯特建立了代数不变量理论的学科语言；发明了计算不变量的一般方法——复合换位法；引进微分算子,建立了不变量零化子理论；尝试利用施图姆函数的合冲关系解决不变量的合冲问题；证明了凯莱定理.西尔维斯特的工作奠定了代数不变量的理论基础,反映了19世纪英国不变量理论研究的主要轨迹及特点.%In this paper,by using the method of the literature review and historic analysis,the thought and contribution of the algebria invariant theory are systematically investigated and discussed,which was found by Sylvester (James Joseph Sylvester,1814-1897):the language of the algebria invariant theory was established by Sylvester,the general method of calculating the invariants-Compound Commutants Method was devised,the theory of the invariant annihilator was established by introducing the differential operators,the syzygy problems of the invariants was attempt to solve by using the syzygetic relations of Strurm functions,Cayley's theorem was proved.Sylvester's work laid the foundation of the algebria invariant theory,and reflected the main research track and feature of the British algebria invariant theory in the 19th century.
Tanaka, Ken'ichiro
2012-01-01
We present the convergence rates and the explicit error bounds of Hill's method, which is a numerical method for computing the spectra of ordinary differential operators with periodic coefficients. This method approximates the operator by a finite dimensional matrix. On the assumption that the operator is selfadjoint, it is shown that, under some conditions, we can obtain the convergence rates of eigenvalues with respect to the dimension and the explicit error bounds. Numerical examples demonstrate that we can verify these conditions using Gershgorin's theorem for some real problems. Main theorems are proved using the Dunford integrals which project an eigenvector to the corresponding eigenspace.
Directory of Open Access Journals (Sweden)
Dumitru Baleanu
2013-01-01
Full Text Available We obtain the approximate analytical solution for the fractional quadratic Riccati differential equation with the Riemann-Liouville derivative by using the Bernstein polynomials (BPs operational matrices. In this method, we use the operational matrix for fractional integration in the Riemann-Liouville sense. Then by using this matrix and operational matrix of product, we reduce the problem to a system of algebraic equations that can be solved easily. The efficiency and accuracy of the proposed method are illustrated by several examples.
VEV of Baxter’s Q-operator in N=2 gauge theory and the BPZ differential equation
Energy Technology Data Exchange (ETDEWEB)
Poghosyan, Gabriel; Poghossian, Rubik [Yerevan Physics Institute,Alikhanian Br. 2, AM-0036 Yerevan (Armenia)
2016-11-09
In this short note using AGT correspondence we express the simplest fully degenerate primary fields of Toda field theory in terms of an analogue of Baxter’s Q-operator naturally emerging on the N=2 gauge theory side. This quantity can be considered as a generating function of certain chiral operators constructed from the scalars of the N=2 vector multiplets. In the special case of Liouville theory, exploring the second order differential equation satisfied by conformal blocks including a primary field which is degenerate at the second level (BPZ equation) we derive a mixed difference-differential relation for Q-operator. Thus we generalize the T-Q difference equation known in Nekrasov-Shatashvili limit of the Ω-background to the generic case.
Entanglement, Invariants, and Phylogenetics
Sumner, J. G.
2007-10-01
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units from biomolecular sequence data. The techniques of mathematical physics are plethora and have been developed for some time. The Markov model of phylogenetics and its analysis is a relatively new technique where most progress to date has been achieved by using discrete mathematics. This thesis takes a group theoretical approach to the problem by beginning with a remarkable mathematical parallel to the process of scattering in particle physics. This is shown to equate to branching events in the evolutionary history of molecular units. The major technical result of this thesis is the derivation of existence proofs and computational techniques for calculating polynomial group invariant functions on a multi-linear space where the group action is that relevant to a Markovian time evolution. The practical results of this thesis are an extended analysis of the use of invariant functions in distance based methods and the presentation of a new reconstruction technique for quartet trees which is consistent with the most general Markov model of sequence evolution.
From dynamical scaling to local scale-invariance: a tutorial
Henkel, Malte
2016-01-01
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, ind...
Tractors, Mass and Weyl Invariance
Gover, A R; Waldron, A
2008-01-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus--a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner--Freedman stability bounds for Anti de Sitter theories arise na...
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Di Bartolo, Cayetano; Leal, Lorenzo
2012-01-01
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
Implications of conformal invariance in momentum space
Energy Technology Data Exchange (ETDEWEB)
Bzowski, Adam [Institute for Theoretical Physics,K.U. Leuven, Celestijnenlaan 200D, 3000 Leuven (Belgium); McFadden, Paul [Perimeter Institute for Theoretical Physics,31 Caroline St. N. Waterloo, N2L 2Y5 Ontario (Canada); Skenderis, Kostas [Mathematical Sciences, University of Southampton,Highfield, SO17 1BJ Southampton (United Kingdom)
2014-03-25
We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (‘triple-K integrals’). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. In odd dimensions 3-point functions are finite without renormalisation while in even dimensions non-trivial renormalisation in required. In this paper we restrict ourselves to odd dimensions. A comprehensive analysis of renormalisation will be discussed elsewhere. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple-K integrals while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper.
Tractors, mass, and Weyl invariance
Gover, A. R.; Shaukat, A.; Waldron, A.
2009-05-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus—a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner-Freedman stability bounds for Anti-de Sitter theories arise naturally as do direct derivations of the novel Weyl invariant theories given by Deser and Nepomechie. In constant curvature spaces, partially massless theories—which rely on the interplay between mass and gauge invariance—are also generated by our method. Another simple consequence is conformal invariance of the maximal depth partially massless theories. Detailed examples for spins s⩽2 are given including tractor and component actions, on-shell and off-shell approaches and gauge invariances. For all spins s⩾2 we give tractor equations of motion unifying massive, massless, and partially massless theories.
Directory of Open Access Journals (Sweden)
Waleed M. Abd-Elhameed
2016-09-01
Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.
Permutation centralizer algebras and multimatrix invariants
Mattioli, Paolo; Ramgoolam, Sanjaye
2016-03-01
We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.
Gromov-Witten Invariants and Quantum Cohomology
Indian Academy of Sciences (India)
Amiya Mukherjee
2006-11-01
This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December 20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture was meant for a general audience, and also prospective research students, the idea of the quantum cohomology based on the Gromov-Witten invariants. Of course there are many important aspects that are not discussed here.
Directory of Open Access Journals (Sweden)
J. Golenia
2004-01-01
Full Text Available The structure properties of multidimensional Delsarte transmutation operators in parametric functional spaces are studied by means of differential-geometric tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in soliton theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.
Invariant and Absolute Invariant Means of Double Sequences
Directory of Open Access Journals (Sweden)
Abdullah Alotaibi
2012-01-01
Full Text Available We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.
Lorentz invariant intrinsic decoherence
Milburn, G J
2003-01-01
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schr\\"{o}dinger dynamics based on discrete time intervals with an intrinsic uncertainty. The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, in a way consistent with other modifications suggested by quantum grav...
Wulan, Hasi
2017-01-01
This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.
Smooth Frechet subalgebras of *-algebras defined by first order differential seminorms
Indian Academy of Sciences (India)
Subhash J Bhatt
2016-02-01
The differential structure in a *-algebra defined by a dense Frechet subalgebra whose topology is defined by a sequence of differential seminorms of order 1 is investigated. This includes differential Arens–Michael decomposition, spectral invariance, closure under functional calculi as well as intrinsic spectral description. A large number of examples of such Frechet algebras are exhibited; and the smooth structure defined by an unbounded self-adjoint Hilbert space operator is discussed.
Alcock-Zeilinger, Judith
2016-01-01
In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young projection operators derived in a companion paper. We show that the Hermitian Young projection operators together with their transition operators constitute a fully orthogonal basis for the algebra of invariants of $V^{\\otimes m}$ that exhibits a systematically simplified multiplication table. We discuss the full algebra of invariants over $V^{\\otimes 3}$ and $V^{\\otimes 4}$ as explicit examples. In our presentation we make use of various standard concepts such as Young projection operators, Clebsch-Gordan operators, and invariants (in birdtrack notation). We tie these perspectives together and use them to shed light on each other.
Well-posedness of nonlocal parabolic differential problems with dependent operators.
Ashyralyev, Allaberen; Hanalyev, Asker
2014-01-01
The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 parabolic equations with dependent coefficients are established.
Branson, T P; Vasilevich, D V
1998-01-01
Let M be a compact Riemannian manifold with smooth boundary. We study the vacuum expectation value of an operator Q by studying Tr Qe^{-tD}, where D is an operator of Laplace type on M, and where Q is a second order operator with scalar leading symbol; we impose Dirichlet or modified Neumann boundary conditions.
Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories
Mattioli, Paolo
2016-01-01
In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
Directory of Open Access Journals (Sweden)
B. Thamaraikannan
2014-01-01
Full Text Available This paper studies in detail the background and implementation of a teaching-learning based optimization (TLBO algorithm with differential operator for optimization task of a few mechanical components, which are essential for most of the mechanical engineering applications. Like most of the other heuristic techniques, TLBO is also a population-based method and uses a population of solutions to proceed to the global solution. A differential operator is incorporated into the TLBO for effective search of better solutions. To validate the effectiveness of the proposed method, three typical optimization problems are considered in this research: firstly, to optimize the weight in a belt-pulley drive, secondly, to optimize the volume in a closed coil helical spring, and finally to optimize the weight in a hollow shaft. have been demonstrated. Simulation result on the optimization (mechanical components problems reveals the ability of the proposed methodology to find better optimal solutions compared to other optimization algorithms.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
Liu, Chengshi
2010-08-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
Gauge invariance properties and singularity cancellations in a modified PQCD
Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos
2006-01-01
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.
Isospin Invariance and the Vacuum Polarization Energy of Cosmic Strings
Weigel, H; Graham, N
2016-01-01
We corroborate the previously applied spectral approach to compute the vacuum polarization energy of string configurations in models similar to the standard model of particle physics. The central observation underlying this corroboration is the existence of a particular global isospin transformation of the string configuration. Under this transformation the single particle energies of the quantum fluctuations are invariant, while the inevitable implementation of regularization and renormalization requires operations that are not invariant. We verify numerically that all such variances eventually cancel, and that the vacuum polarization energy obtained in the spectral approach is indeed gauge invariant.
Omran, Hesham
2016-10-06
We propose a successive-approximation capacitive sensor readout circuit that achieves 35fJ/Step energy efficiency FoM, which represents 4× improvement over the state-of-the-art. A fully differential architecture is employed to provide robustness against common mode noise and errors. An inverter-based amplifier with near-threshold biasing provides robust, fast, and energy-efficient operation. Quasi-dynamic operation is used to maintain the energy efficiency for a scalable sample rate. A hybrid coarse-fine capacitive DAC achieves 11.7bit effective resolution in a compact area. © 2016 IEEE.
Muhammad Yunus Amar
2015-01-01
In the last decade, many researchers have conducted studies on the efforts to improve corporate performance through the stimulation of specific business strategy approach. This study aims to analyze the effect of product differentiation strategy on operating performance of the company. The study was conducted on industrial of SMEs in South Sulawesi, Indonesia using a survey method with the sample of 75 respondents. The data were collected through questionnaires, and processed by the method of...
Robust Image Hashing Using Radon Transform and Invariant Features
Directory of Open Access Journals (Sweden)
Y.L. Liu
2016-09-01
Full Text Available A robust image hashing method based on radon transform and invariant features is proposed for image authentication, image retrieval, and image detection. Specifically, an input image is firstly converted into a counterpart with a normalized size. Then the invariant centroid algorithm is applied to obtain the invariant feature point and the surrounding circular area, and the radon transform is employed to acquire the mapping coefficient matrix of the area. Finally, the hashing sequence is generated by combining the feature vectors and the invariant moments calculated from the coefficient matrix. Experimental results show that this method not only can resist against the normal image processing operations, but also some geometric distortions. Comparisons of receiver operating characteristic (ROC curve indicate that the proposed method outperforms some existing methods in classification between perceptual robustness and discrimination.
Hidden scale invariance of metals
DEFF Research Database (Denmark)
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.
2015-01-01
available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...... of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were......Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...
Invariant Measures for Cherry Flows
Saghin, Radu; Vargas, Edson
2013-01-01
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.
Physical Invariants of Intelligence
Zak, Michail
2010-01-01
A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai; Chen Xiang-Wei; Guo Yong-Xin
2007-01-01
Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries,exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
Stable evaluation of differential operators and linear and nonlinear multi-scale filtering
Directory of Open Access Journals (Sweden)
Otmar Scherzer
1997-09-01
Full Text Available Diffusion processes create multi--scale analyses, which enable the generation of simplified pictures, where for increasing scale the image gets sketchier. In many practical applications the ``scaled image'' can be characterized via a variational formulation as the solution of a minimization problem involving unbounded operators. These unbounded operators can be evaluated by regularization techniques. We show that the theory of stable evaluation of unbounded operators can be applied to efficiently solve these minimization problems.
Speed-variable Switched Differential Pump System for Direct Operation of Hydraulic Cylinders
DEFF Research Database (Denmark)
Schmidt, Lasse; Roemer, Daniel Beck; Pedersen, Henrik Clemmensen;
2015-01-01
Efforts to overcome the inherent loss of energy due to throttling in valve driven hydraulic systems are many, and various approaches have been proposed by research communities as well as the industry. Recently, a so-called speed-variable differential pump was proposed for direct drive of hydraulic...... differential cylinders. The main idea was here to utilize an electric rotary drive, with the shaft interconnected to two antiparallel fixed displacement gear pumps, to actuate a differential cylinder. With the design carried out such that the area ratio of the cylinder matches the displacement ratio of the two...... gear pumps, the throttling losses are confined to cross port leakage in the cylinder and leakage of the pumps. However, it turns out that the volumetric pump losses and the pressure dynamics of the cylinder and connecting pipes may cause pressure increase- or decrease in the cylinder chambers, which...
Complete Pick Positivity and Unitary Invariance
Bhattacharya, Angshuman
2009-01-01
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\\ow)^{-1}$ for $|z|, |w| < 1$, by means of $(1/k_S)(T,T^*) \\ge 0$, we consider an arbitrary open connected domain $\\Omega$ in $\\BC^n$, a complete Nevanilinna-Pick kernel $k$ on $\\Omega$ and a tuple $T = (T_1, ..., T_n)$ of commuting bounded operators on a complex separable Hilbert space $\\clh$ such that $(1/k)(T,T^*) \\ge 0$. For a complete Pick kernel the $1/k$ functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with $T$. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples $T$.
Field redefinition invariance in quantum field theory
Apfeldorf, K M; Apfeldorf, Karyn M; Ordonez, Carlos
1994-01-01
We investigate the consequences of field redefinition invariance in quantum field theory by carefully performing nonlinear transformations in the path integral. We first present a ``paradox'' whereby a 1+1 freemassless scalar theory on a Minkowskian cylinder is reduced to an effectively quantum mechanical theory. We perform field redefinitions both before and after reduction to suggest that one should not ignore operator ordering issues in quantum field theory. We next employ a discretized version of the path integral for a free massless scalar quantum field in d dimensions to show that beyond the usual jacobian term, an infinite series of divergent ``extra'' terms arises in the action whenever a nonlinear field redefinition is made. The explicit forms for the first couple of these terms are derived. We evaluate Feynman diagrams to illustrate the importance of retaining the extra terms, and conjecture that these extra terms are the exact counterterms necessary to render physical quantities invariant under fie...
Spherical harmonics, invariant theory and Maxwell's poles
Dowker, J S
2008-01-01
I discuss the relation between harmonic polynomials and invariant theory and show that homogeneous, harmonic polynomials correspond to ternary forms that are apolar to a base conic (the absolute). The calculation of Schlesinger that replaces such a form by a polarised binary form is reviewed. It is suggested that Sylvester's theorem on the uniqueness of Maxwell's pole expression for harmonics is renamed the Clebsch-Sylvester theorem. The relation between certain constructs in invariant theory and angular momentum theory is enlarged upon and I resurrect the Joos--Weinberg matrices. Hilbert's projection operators are considered and their generalisations by Story and Elliott are related to similar, more recent constructions in group theory and quantum mechanics, the ternary case being equivalent to SU(3).
More Modular Invariant Anomalous U(1) Breaking
Gaillard, Mary Katherin; Gaillard, Mary K.; Giedt, Joel
2002-01-01
We consider the case of several scalar fields, charged under a number of U(1) factors, acquiring vacuum expectation values due to an anomalous U(1). We demonstrate how to make redefinitions at the superfield level in order to account for tree-level exchange of vector supermultiplets in the effective supergravity theory of the light fields in the supersymmetric vacuum phase. Our approach builds upon previous results that we obtained in a more elementary case. We find that the modular weights of light fields are typically shifted from their original values, allowing an interpretation in terms of the preservation of modular invariance in the effective theory. We address various subtleties in defining unitary gauge that are associated with the noncanonical Kahler potential of modular invariant supergravity, the vacuum degeneracy, and the role of the dilaton field. We discuss the effective superpotential for the light fields and note how proton decay operators may be obtained when the heavy fields are integrated o...
Conformal invariant saturation
Navelet, H
2002-01-01
We show that, in onium-onium scattering at (very) high energy, a transition to saturation happens due to quantum fluctuations of QCD dipoles. This transition starts when the order alpha^2 correction of the dipole loop is compensated by its faster energy evolution, leading to a negative interference with the tree level amplitude. After a derivation of the the one-loop dipole contribution using conformal invariance of the elastic 4-gluon amplitude in high energy QCD, we obtain an exact expression of the saturation line in the plane (Y,L) where Y is the total rapidity and L, the logarithm of the onium scale ratio. It shows universal features implying the Balitskyi - Fadin - Kuraev - Lipatov (BFKL) evolution kernel and the square of the QCD triple Pomeron vertex. For large L, only the higher BFKL Eigenvalue contributes, leading to a saturation depending on leading log perturbative QCD characteristics. For initial onium scales of same order, however, it involves an unlimited summation over all conformal BFKL Eigen...
Gauge invariants, correlators and holography in bosonic and fermionic tensor models
de Mello Koch, Robert; Gossman, David; Tribelhorn, Laila
2017-09-01
Motivated by the close connection of tensor models to the SYK model, we use representation theory to construct the complete set of gauge invariant observables for bosonic and fermionic tensor models. Correlation functions of the gauge invariant operators in the free theory are computed exactly. The gauge invariant operators close a ring. The structure constants of the ring are described explicitly. Finally, we construct a collective field theory description of the bosonic tensor model.
Natroshvili, David; Shargorodsky, Eugene; Wendland, Wolfgang
2017-01-01
This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.
Convergence of eigenvalues for a highly non-self-adjoint differential operator
Davies, E B
2008-01-01
In this paper we study a family of operators dependent on a small parameter $\\epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\\epsilon \\to 0$, even though, for fixed $\\epsilon > 0$, the eigenvalue asymptotics are quadratic.
Houwen, P.J. van der; Sommeijer, B.P.; Wubs, F.W.
1990-01-01
A smoothing technique for the “preconditioning” of the right-hand side of semidiscrete partial differential equations is analyzed. For a parabolic and a hyperbolic model problem, optimal smoothing matrices are constructed which result in a substantial amplification of the maximal stable integration
Translationally invariant conservation laws of local Lindblad equations
Energy Technology Data Exchange (ETDEWEB)
Žnidarič, Marko [Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana (Slovenia); Benenti, Giuliano; Casati, Giulio [CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell' Insubria, Via Valleggio 11, 22100 Como (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano (Italy)
2014-02-15
We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator (e.g., particle density) there exist Lindblad dissipators that conserve that operator, while on the other hand we prove that among 2-local operators (e.g., energy density) only trivial ones of the Ising type can be conserved, while all the other cannot be conserved, neither locally nor globally, by any 2- or 3-local translationally invariant Lindblad equation. Our statements hold for rings of any finite length larger than some minimal length determined by the locality of Lindblad equation. These results show in particular that conservation of energy density in interacting systems is fundamentally more difficult than conservation of 1-local quantities.
On density of the Vassiliev invariants
DEFF Research Database (Denmark)
Røgen, Peter
1999-01-01
The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...
On density of the Vassiliev invariants
DEFF Research Database (Denmark)
Røgen, Peter
1999-01-01
The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...
QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS
Institute of Scientific and Technical Information of China (English)
Ai-guo Xiao; Shou-fu Li; Min Yang
2001-01-01
In this paper, we present some invariants and conservation laws of general linear methods applied to differential equation systems. We show that the quadratic invariants and symplecticity of the systems can be extended to general linear methods by a tensor product, and show that general linear methods with the matrix M=0 inherit in an extended sense the quadratic invariants possessed by the differential equation systems being integrated and preserve in an extended sense the symplectic structure of the phase space in the integration of Hamiltonian systems. These unify and extend existing relevant results on Runge-Kutta methods, linear multistep methods and one-leg methods. Finally, as special cases of general linear methods, we examine multistep Runge-Kutta methods, one-leg methods and linear two-step methods in detail.
Generalized Formalism in Gauge-Invariant Gravitational Perturbations
Cai, Rong-Gen
2013-01-01
By use of the gauge-invariant variables proposed by Kodama and Ishibashi, we obtain the most general perturbation equations in the $(m+n)$-dimensional spacetime with a warped product metric. These equations do not depend on the spectral expansions of the Laplace-type operators on the $n$-dimensional Einstein manifold. These equations enable us to have a complete gauge-invariant perturbation theory and a well-defined spectral expansion for all modes and the gauge invariance is kept for each mode. By studying perturbations of some projections of Weyl tensor in the case of $m=2$, we define three Teukolsky-like gauge-invariant variables and obtain the perturbation equations of these variables by considering perturbations of the Penrose wave equations in the $(2+n)$-dimensional Einstein spectime. In particular, we find the relations between the Teukolsky-like gauge-invariant variables and the Kodama-Ishibashi gauge-invariant variables. These relations imply that the Kodama-Ishibashi gauge-invariant variables all c...
Mechanized derivation of linear invariants.
Cavender, J A
1989-05-01
Linear invariants, discovered by Lake, promise to provide a versatile way of inferring phylogenies on the basis of nucleic acid sequences (the method that he called "evolutionary parsimony"). A semigroup of Markov transition matrices embodies the assumptions underlying the method, and alternative semigroups exist. The set of all linear invariants may be derived from the semigroup by using an algorithm described here. Under assumptions no stronger than Lake's, there are greater than 50 independent linear invariants for each of the 15 rooted trees linking four species.
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.
Bayesian tests of measurement invariance.
Verhagen, A J; Fox, J P
2013-11-01
Random item effects models provide a natural framework for the exploration of violations of measurement invariance without the need for anchor items. Within the random item effects modelling framework, Bayesian tests (Bayes factor, deviance information criterion) are proposed which enable multiple marginal invariance hypotheses to be tested simultaneously. The performance of the tests is evaluated with a simulation study which shows that the tests have high power and low Type I error rate. Data from the European Social Survey are used to test for measurement invariance of attitude towards immigrant items and to show that background information can be used to explain cross-national variation in item functioning.
Invariant and semi-invariant probabilistic normed spaces
Energy Technology Data Exchange (ETDEWEB)
Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com
2009-10-15
Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.
Directory of Open Access Journals (Sweden)
Muhammad Yunus Amar
2015-12-01
Full Text Available In the last decade, many researchers have conducted studies on the efforts to improve corporate performance through the stimulation of specific business strategy approach. This study aims to analyze the effect of product differentiation strategy on operating performance of the company. The study was conducted on industrial of SMEs in South Sulawesi, Indonesia using a survey method with the sample of 75 respondents. The data were collected through questionnaires, and processed by the method of path analysis. The results show that the strategy of product differentiation (vertical and horizontal affects the operational performance of industrial of the SMEs significantly and negatively. It has implications such as in the early stages of the implementation of this strategy; the company can issue additional production costs in the form of material costs, and more failing products without being accompanied by an increase in new customers. This study can be continued to further examine the relationship of differentiation strategy implementation and performance of the company involving a moderator variable lag-time and the role of production technology in the research model.
Directory of Open Access Journals (Sweden)
Serguei I. Iakovlev
2013-01-01
Full Text Available It is shown that any \\(\\mu \\in \\mathbb{C}\\ is an infinite multiplicity eigenvalue of the Steklov smoothing operator \\(S_h\\ acting on the space \\(L^1_{loc}(\\mathbb{R}\\. For \\(\\mu \
Ulam stability for fractional differential equations in the sense of Caputo operator
Directory of Open Access Journals (Sweden)
Rabha W. Ibrahim
2012-12-01
Full Text Available In this paper, we consider the Hyers-Ulam stability for the following fractional differential equations, in the sense ofcomplex Caputo fractional derivative defined, in the unit disk: cDßzf(z=G(f(z, cDázf(z,zf‘(z;z 0<á<1<ß<2 . Furthermore,a generalization of the admissible functions in complex Banach spaces is imposed and applications are illustrated.
Wigner Function of Thermo-Invariant Coherent State
Institute of Scientific and Technical Information of China (English)
XU Xue-Fen; ZHU Shi-Qun
2008-01-01
@@ By using the thermal Winger operator of thermo-field dynamics in the coherent thermal state |ξ> representation and the technique of integration within an ordered product of operators, the Wigner function of the thermo-invariant coherent state |z, n> is derived. The nonclassical properties of state |z, n> is discussed based on the negativity of the Wigner function.
Local Scale Invariance and Inflation
Singh, Naveen K
2016-01-01
We study the inflation and the cosmological perturbations generated during the inflation in a local scale invariant model. The local scale invariant model introduces a vector field $S_{\\mu}$ in this theory. In this paper, for simplicity, we consider the temporal part of the vector field $S_t$. We show that the temporal part is associated with the slow roll parameter of scalar field. Due to local scale invariance, we have a gauge degree of freedom. In a particular gauge, we show that the local scale invariance provides sufficient number of e-foldings for the inflation. Finally, we estimate the power spectrum of scalar perturbation in terms of the parameters of the theory.
Scaling Equation for Invariant Measure
Institute of Scientific and Technical Information of China (English)
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Invariants from classical field theory
Diaz, Rafael
2007-01-01
We introduce a method that generates invariant functions from classical field theories depending on external parameters. We apply our method to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory.
Invariant measures for Cherry flows
Saghin, Radu
2011-01-01
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we discuss some situations when there exists another invariant measure supported on the quasi-minimal set, which is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.
Invariant foliations for parabolic equations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
It is proved for parabolic equations that under certain conditions the weak (un-)stable manifolds possess invariant foliations, called strongly (un-)stable foliations. The relevant results on center manifolds are generalized to weak hyperbolic manifolds.
Invariance on the NEO PI-R Neuroticism Scale.
Reise, Steven P.; Smith, Larissa; Furr, R. Michael
2001-01-01
Explored between-gender invariance on the NEO PI-R Neuroticism scale (Costa and McCrae, 1992) with a sample of 1,056 undergraduates. Several items displayed significant differential item functioning (DIF), but it was difficult to associate DIF with specific aspects of item content, and findings indicate that item-level DIF does not necessarily…
Invariant Measures for Monotone SPDEs with Multiplicative Noise Term
Energy Technology Data Exchange (ETDEWEB)
Es-Sarhir, Abdelhadi, E-mail: a.es-sarhir@uiz.ac.ma [Universite Ibn Zohr, Departement de Mathematiques, Faculte des Sciences (Morocco); Scheutzow, Michael, E-mail: ms@math.tu-berlin.de; Toelle, Jonas M., E-mail: jonasmtoelle@gmail.com [Technische Universitaet Berlin, Fakultaet II, Institut fuer Mathematik (Germany); Gaans, Onno van, E-mail: vangaans@math.leidenuniv.nl [Universiteit Leiden, Mathematisch Instituut (Netherlands)
2013-10-15
We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of the solution to show existence of an invariant measure. As an application we discuss stochastic reaction diffusion equations.
Selected papers on harmonic analysis, groups, and invariants
Nomizu, Katsumi
1997-01-01
This volume contains papers that originally appeared in Japanese in the journal Sūgaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including representation theory, differential geometry, invariant theory, and complex analysis.
Directory of Open Access Journals (Sweden)
Nemat Dalir
2014-01-01
Full Text Available Singular nonlinear initial-value problems (IVPs in first-order and second-order partial differential equations (PDEs arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.
Invariants of broken discrete symmetries
Kalozoumis, P.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic ...
Invariants of broken discrete symmetries
Kalozoumis, P; Diakonos, F K; Schmelcher, P
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Invariant Manifolds and Collective Coordinates
Papenbrock, T
2001-01-01
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.
Classification of simple current invariants
Gato-Rivera, Beatriz
1992-01-01
We summarize recent work on the classification of modular invariant partition functions that can be obtained with simple currents in theories with a center (Z_p)^k with p prime. New empirical results for other centers are also presented. Our observation that the total number of invariants is monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk presented in the parallel session on string theory of the Lepton-Photon/EPS Conference, Geneva, 1991.)
Current forms and gauge invariance
Energy Technology Data Exchange (ETDEWEB)
Lopez, M Castrillon [Departemento de GeometrIa y TopologIa, Facultad de Matematicas, Universidad Complutense de Madrid, 28040-Madrid (Spain); Masque, J Munoz [Instituto de FIsica Aplicada, CSIC, C/Serrano 144, 28006-Madrid (Spain)
2004-05-14
Let C be the bundle of connections of a principal G-bundle {pi}:P {yields} M, and let V be the vector bundle associated with P by a linear representation G {yields} GL(V) on a finite-dimensional vector space V. The Lagrangians on J{sup 1}(C x {sub M}V) whose current form is gauge invariant, are described and the gauge-invariant Lagrangians on J{sup 1}(V) are classified.
Z2 Invariants of Topological Insulators as Geometric Obstructions
Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca
2016-05-01
We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2 d, the obstruction to the existence of such a frame is shown to be encoded in a Z_2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3 d, instead, four Z_2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.
Permutation Centralizer Algebras and Multi-Matrix Invariants
Mattioli, Paolo
2016-01-01
We introduce a class of permutation centralizer algebras which underly the combinatorics of multi-matrix gauge invariant observables. One family of such non-commutative algebras is parametrised by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of 2-matrix models. The structure of the algebra, notably its dimension, its centre and its maximally commuting sub-algebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The centre of the algebra allows efficient computation of a sector of multi-matrix correlator...
The Teodorescu Operator in Clifford Analysis
Institute of Scientific and Technical Information of China (English)
F.BRACKX; H.De SCHEPPER; M.E.LUNA-ELIZARRAR(A)S; M.SHAPIRO
2012-01-01
Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions,i.e.,null solutions to a first order vector valued rotation invariant differential operator (θ) called the Dirac operator.More recently,Hermitian Clifford analysis has emerged as a new branch,offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions,called Hermitian monogenic functions,to two Hermitian Dirac operators (θ)z_ and (θ)z_(+) which are invariant under the action of the unitary group.In Euclidean Clifford analysis,the Teodorescu operator is the right inverse of the Dirac operator (θ).In this paper,Teodorescu operators for the Hermitian Dirac operators (θ)z_ and (θ)z(+) are constructed.Moreover,the structure of the Euclidean and Hermitian Teodorescu operators is revealed by analyzing the more subtle behaviour of their components.Finally,the obtained inversion relations are still refined for the differential operators issuing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts.Their relationship with several complex variables theory is discussed.
Kang, Yoonjeong; McNeish, Daniel M.; Hancock, Gregory R.
2016-01-01
Although differences in goodness-of-fit indices (?GOFs) have been advocated for assessing measurement invariance, studies that advanced recommended differential cutoffs for adjudicating invariance actually utilized a very limited range of values representing the quality of indicator variables (i.e., magnitude of loadings). Because quality of…
Translational invariance in nucleation theories: Theoretical formulation
Energy Technology Data Exchange (ETDEWEB)
Drossinos, Y.; Kevrekidis, P. G.; Georgopoulos, P. G.
2001-03-01
The consequences of spontaneously broken translational invariance on the nucleation-rate statistical prefactor in theories of first-order phase transitions are analyzed. A hybrid, semiphenomenological approach based on field-theoretic analyses of condensation and modern density-functional theories of nucleation is adopted to provide a unified prescription for the incorporation of translational-invariance corrections to nucleation-rate predictions. A connection between these theories is obtained starting from a quantum-mechanical Hamiltonian and using methods developed in the context of studies on Bose-Einstein condensation. An extremum principle is used to derive an integro-differential equation for the spatially nonuniform mean-field order-parameter profile; the appropriate order parameter becomes the square root of the fluid density. The importance of the attractive intermolecular potential is emphasized, whereas the repulsive two-body potential is approximated by considering hard-sphere collisions. The functional form of the degenerate translational eigenmodes in three dimensions is related to the mean-field order parameter, and their contribution to the nucleation-rate prefactor is evaluated. The solution of the Euler-Lagrange variational equation is discussed in terms of either a proposed variational trial function or the complete numerical solution of the associated boundary-value integro-differential problem. Alternatively, if the attractive potential is not explicitly known, an approach that allows its formal determination from its moments is presented.
Spectral theory of Sturm-Liouville differential operators: proceedings of the 1984 workshop
Energy Technology Data Exchange (ETDEWEB)
Kaper, H.G.; Zettl, A. (eds.)
1984-12-01
This report contains the proceedings of the workshop which was held at Argonne during the period May 14 through June 15, 1984. The report contains 22 articles, authored or co-authored by the participants in the workshop. Topics covered at the workshop included the asymptotics of eigenvalues and eigenfunctions; qualitative and quantitative aspects of Sturm-Liouville eigenvalue problems with discrete and continuous spectra; polar, indefinite, and nonselfadjoint Sturm-Liouville eigenvalue problems; and systems of differential equations of Sturm-Liouville type.
Directory of Open Access Journals (Sweden)
Huanhe Dong
2014-01-01
Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.
Arisawa, M
2010-01-01
A comparison principle for the integro-differential equation with the L{\\'e}vy operator corresponding to the spacial depending jump process is presented in this paper. The jump $\\beta(x,z)$ at a point $x$ and the L{\\'e}vy measure $dq(z)$ satisfy conditions given independently for each of them, which is a major difference from other works. Moreover, a useful form of the viscosity solution is presented, which is equivalent to more "classical" definitions, and is used to prove the comparison principle easily.
Differential Characteristics and Methods of Operation Underlying CAI/CMI Drill and Practice Systems.
Hativa, Nira
1988-01-01
Describes computer systems that combine drill and practice instruction with computer-managed instruction (CMI) and identifies system characteristics in four categories: (1) hardware, (2) software, (3) management systems, and (4) methods of daily operation. Topics discussed include microcomputer networks, graphics, feedback, degree of learner…
2010-10-01
...) representing interest on vessels shall be allocated to vessels and voyages in the same ratio that depreciation... forward necessary instructions and forms to be used. (f) Current financial reports. Each operator shall prepare current financial reports as specified in this paragraph and shall submit one copy each to...
Relations of 3D directional derivatives and expressions of typical differential operators
Institute of Scientific and Technical Information of China (English)
YIN Li; LV Gui-xia; SHEN Long-jun
2009-01-01
Relations of the 3D multi-directional derivatives are studied in this paper. These relations are applied to a general second-order linear elliptical operator and the corresponding expression are obtained. These relations and expressions play important roles in the meshless finite point method.
Differential Sandwich Theorems for some Subclasses of Analytic Functions Involving a Linear Operator
Directory of Open Access Journals (Sweden)
S. Sivasubramanian
2007-10-01
Full Text Available By making use of the familiar Carlson-Shaffer operator,the authors derive derive some subordination and superordination results for certain normalized analytic functions in the open unit disk. Relevant connections ofthe results, which are presented in this paper, with various other known results are also pointed out.
Dirac structures and boundary control systems associated with skew-symmetric differential operators
Le Gorrec, Y.; Zwart, H.J.; Maschke, B.
2005-01-01
Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated with this Dirac structure is an infinite-d
Dirac structures and boundary control systems associated with skew-symmetric differential operators
Le Gorrec, Y.; Zwart, H.J.; Maschke, B.
2004-01-01
Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated to this Dirac structure is infinite dimen
Institute of Scientific and Technical Information of China (English)
WANG Jing; LI Yuan-Cheng; HOU Qi-Bao; XIA Li-Li
2007-01-01
The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints.Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations,this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints.The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced.An example is given to illustrate the application of the results.
CPT violation implies violation of Lorentz invariance.
Greenberg, O W
2002-12-02
A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.
On Gauge Invariant Descriptions of Gluon Polarization
Guo, Zhi-Qiang
2012-01-01
We propose methods to construct gauge invariant decompositions of nucleon spin, especially gauge invariant descriptions of gluon polarization. We show that gauge invariant decompositions of nucleon spin can be derived naturally from the conserved current of a generalized Lorentzian transformation by Noether theorem. We also examine the problem of gauge dependence with a gauge invariant extension of the Chern-Simons current.
On higher rank Donaldson-Thomas invariants
Nagao, Kentaro
2010-01-01
We study higher rank Donaldson-Thomas invariants of a Calabi-Yau 3-fold using Joyce-Song's wall-crossing formula. We construct quivers whose counting invariants coincide with the Donaldson-Thomas invariants. As a corollary, we prove the integrality and a certain symmetry for the higher rank invariants.
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Suzuki, H
1999-01-01
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Conformal invariance in quantum field theory
Todorov, Ivan T; Petkova, Valentina B
1978-01-01
The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
The Axion Mass in Modular Invariant Supergravity
Butter, D; Butter, Daniel; Gaillard, Mary K.
2005-01-01
When supersymmetry is broken by condensates with a single condensing gauge group, there is a nonanomalous R-symmetry that prevents the universal axion from acquiring a mass. It has been argued that, in the context of supergravity, higher dimension operators will break this symmetry and may generate an axion mass too large to allow the identification of the universal axion with the QCD axion. We show that such contributions to the axion mass are highly suppressed in a class of models where the effective Lagrangian for gaugino and matter condensation respects modular invariance (T-duality).
Using wide area differential GPS to improve total system error for precision flight operations
Alter, Keith Warren
Total System Error (TSE) refers to an aircraft's total deviation from the desired flight path. TSE can be divided into Navigational System Error (NSE), the error attributable to the aircraft's navigation system, and Flight Technical Error (FTE), the error attributable to pilot or autopilot control. Improvement in either NSE or FTE reduces TSE and leads to the capability to fly more precise flight trajectories. The Federal Aviation Administration's Wide Area Augmentation System (WAAS) became operational for non-safety critical applications in 2000 and will become operational for safety critical applications in 2002. This navigation service will provide precise 3-D positioning (demonstrated to better than 5 meters horizontal and vertical accuracy) for civil aircraft in the United States. Perhaps more importantly, this navigation system, which provides continuous operation across large regions, enables new flight instrumentation concepts which allow pilots to fly aircraft significantly more precisely, both for straight and curved flight paths. This research investigates the capabilities of some of these new concepts, including the Highway-In-The Sky (HITS) display, which not only improves FTE but also reduces pilot workload when compared to conventional flight instrumentation. Augmentation to the HITS display, including perspective terrain and terrain alerting, improves pilot situational awareness. Flight test results from demonstrations in Juneau, AK, and Lake Tahoe, CA, provide evidence of the overall feasibility of integrated, low-cost flight navigation systems based on these concepts. These systems, requiring no more computational power than current-generation low-end desktop computers, have immediate applicability to general aviation flight from Cessnas to business jets and can support safer and ultimately more economical flight operations. Commercial airlines may also, over time, benefit from these new technologies.
Positive solutions for fractional differential equation with a p-Laplacian operator
Directory of Open Access Journals (Sweden)
Yunhong LI
2015-12-01
Full Text Available This paper studies the following Caputo fractional differential equation with p-Laplacian of higher-order multi-point: Dβ0+(p(Dα0+u(t+f(t,u(t=0,0≤t≤1,l-1<β≤l,n-1<α≤n,(p(Dα0+u(0(i=0,i=0,1,2,…,l-1,u(i(0=0,i=1,2,…,n-1,u(1=∑ m-2 i=1 aiu(ξi。 Using the Schauder fixed point theorem, the existence of positive solution is obtained for the above boundary value problems. An example is presented to illustrate our main theorem.
Directory of Open Access Journals (Sweden)
Marzena Pytel-Kudela
2006-01-01
Full Text Available The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bi-linear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
Sclafani, Anthony; Ackroff, Karen
2016-01-01
Intragastric (IG) flavor conditioning studies in rodents indicate that isocaloric sugar infusions differ in their reinforcing actions, with glucose and sucrose more potent than fructose. Here we determined if the sugars also differ in their ability to maintain operant self-administration by licking an empty spout for IG infusions. Food-restricted C57BL/6J mice were trained 1 h/day to lick a food-baited spout, which triggered IG infusions of 16% sucrose. In testing, the mice licked an empty spout, which triggered IG infusions of different sugars. Mice shifted from sucrose to 16% glucose increased dry licking, whereas mice shifted to 16% fructose rapidly reduced licking to low levels. Other mice shifted from sucrose to IG water reduced licking more slowly but reached the same low levels. Thus IG fructose, like water, is not reinforcing to hungry mice. The more rapid decline in licking induced by fructose may be due to the sugar's satiating effects. Further tests revealed that the Glucose mice increased their dry licking when shifted from 16% to 8% glucose, and reduced their dry licking when shifted to 32% glucose. This may reflect caloric regulation and/or differences in satiation. The Glucose mice did not maintain caloric intake when tested with different sugars. They self-infused less sugar when shifted from 16% glucose to 16% sucrose, and even more so when shifted to 16% fructose. Reduced sucrose self-administration may occur because the fructose component of the disaccharide reduces its reinforcing potency. FVB mice also reduced operant licking when tested with 16% fructose, yet learned to prefer a flavor paired with IG fructose. These data indicate that sugars differ substantially in their ability to support IG self-administration and flavor preference learning. The same post-oral reinforcement process appears to mediate operant licking and flavor learning, although flavor learning provides a more sensitive measure of sugar reinforcement.
Kemplin, Kate Rocklein; Bowling, F Young
Special Operations Forces (SOF) medics do not have preparation in research knowledge that enables them to independently initiate or generate their own studies. Thus, medics rely on evidence generated by others, who are removed from medics' practice environment. Here, salient literature on research self-efficacy and the genesis of institutional review boards (IRBs) are reviewed and interpreted for contextual applications to medics' practice and initiation of studies. More publications delving into research methods are warranted to promote medics' participation and initiation of selfdirected scientific investigation, in collaboration with research scientists. 2017.
Relativistic wave equations with fractional derivatives and pseudo-differential operators
Závada, P
2000-01-01
The class of the free relativistic covariant equations generated by the fractional powers of the D'Alambertian operator $(\\Box ^{1/n})$ is studied. Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac equations) are local in their nature, the multicomponent equations for arbitrary n>2 are non-local. It is shown, how the representation of generalized algebra of Pauli and Dirac matrices looks like and how these matrices are related to the algebra of SU(n) group. The corresponding representations of the Poincar\\'e group and further symmetry transformations on the obtained equations are discussed. The construction of the related Green functions is suggested.
Boundary value problems for second-order partial differential equations with operator coefficients
Eberhard Schock; Fayazov, Kudratillo S.
2001-01-01
Let $\\Omega_T$ be some bounded simply connected region in $\\mathbb{R}^2$ with $\\partial\\Omega_{T} = \\bar{\\Gamma}_{1}\\cap\\bar{\\Gamma}_{2}$ . We seek a function $u(x,t),((x,t)\\in\\Omega_{T})$ with values in a Hilbert space $H$ which satisfies the equation $ALu(x,t) = Bu(x,t) + f(x,t,u,u_{t}),(x,t)\\in\\Omega_{T}$ , where $A(x,t),B(x,t)$ are families of linear operators (possibly unbounded) with everywhere dense domain $D$ ( $D$ does not depend on $(x,t)$ ) in $H$ and $Lu...
From dynamical scaling to local scale-invariance: a tutorial
Henkel, Malte
2017-03-01
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schrödinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schrödinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.
Directory of Open Access Journals (Sweden)
Dongyuan Liu
2015-01-01
Full Text Available We consider the following state dependent boundary-value problem D0+αy(t-pD0+βg(t,y(σ(t+f(t,y(τ(t=0, 0
Invariant and energy analysis of an axially retracting beam
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Liu Ming; Zhang Wei; Roderick V.N. Melnik
2016-01-01
The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem. The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations (ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retrac-tion. The total energy varying with time has been investigated by numerical and analytical methods, and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method.
Test of Charge Conjugation Invariance
Nefkens, B. M.; Prakhov, S.; Gårdestig, A.; Allgower, C. E.; Bekrenev, V.; Briscoe, W. J.; Clajus, M.; Comfort, J. R.; Craig, K.; Grosnick, D.; Isenhower, D.; Knecht, N.; Koetke, D.; Koulbardis, A.; Kozlenko, N.; Kruglov, S.; Lolos, G.; Lopatin, I.; Manley, D. M.; Manweiler, R.; Marušić, A.; McDonald, S.; Olmsted, J.; Papandreou, Z.; Peaslee, D.; Phaisangittisakul, N.; Price, J. W.; Ramirez, A. F.; Sadler, M.; Shafi, A.; Spinka, H.; Stanislaus, T. D.; Starostin, A.; Staudenmaier, H. M.; Supek, I.; Tippens, W. B.
2005-02-01
We report on the first determination of upper limits on the branching ratio (BR) of η decay to π0π0γ and to π0π0π0γ. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(η→π0π0γ)<5×10-4 at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(η→π0π0π0γ)<6×10-5 at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions.
Invariant probabilities of transition functions
Zaharopol, Radu
2014-01-01
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of t...
Energy Technology Data Exchange (ETDEWEB)
Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu [Laboratoire J.-L. Lagrange, UMR CNRS/OCA/UCA 7293, Université Côte d’Azur, Observatoire de la Côte d’Azur, Bd de l’Observatoire CS 34229, 06304 Nice Cedex 4 (France); Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr [Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Institut de Physique et Chimie des Matériaux de Strasbourg, UMR CNRS/US 7504, Université de Strasbourg, 23 Rue du Loess, 67034 Strasbourg (France)
2016-08-15
Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original
Besse, Nicolas; Coulette, David
2016-08-01
Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic
Symmetries of the Gas Dynamics Equations Using the Differential Form Method
Schmidt, Joe; Ramsey, Scott; Baty, Roy
2016-11-01
A brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators - and corresponding EOS constraints - otherwise appearing in the existing literature are recovered through the application of and invariance under Lie derivative dragging operations.
Baryon non-invariant couplings in Higgs effective field theory
Energy Technology Data Exchange (ETDEWEB)
Merlo, Luca; Saa, Sara; Sacristan-Barbero, Mario [Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fsica Teorica, IFT-UAM/CSIC, Madrid (Spain)
2017-03-15
The basis of leading operators which are not invariant under baryon number is constructed within the Higgs effective field theory. This list contains 12 dimension six operators, which preserve the combination B - L, to be compared to only 6 operators for the standard model effective field theory. The discussion of the independent flavour contractions is presented in detail for a generic number of fermion families adopting the Hilbert series technique. (orig.)
Solutions of a partial differential equation related to the oplus operator
Directory of Open Access Journals (Sweden)
Wanchak Satsanit
2010-06-01
Full Text Available In this article, we consider the equation $$ oplus^ku(x=sum^{m}_{r=0}c_{r}oplus^{r}delta $$ where $oplus^k$ is the operator iterated k times and defined by $$ oplus^k=Big(Big(sum^p_{i=1}frac{partial^2}{partial x^2_i}Big^{4}-Big(sum^{p+q}_{j=p+1}frac{partial^2}{partial x^2_j}Big^{4}Big^k, $$ where $p+q=n$, $x=(x_1,x_2,dots,x_n$ is in the n-dimensional Euclidian space $mathbb{R}^n$, $c_{r}$ is a constant, $delta$ is the Dirac-delta distribution, $oplus^{0}delta=delta$, and $k=0,1,2,3,dots$. It is shown that, depending on the relationship between k and m, the solution to this equation can be ordinary functions, tempered distributions, or singular distributions.
First Integrals and Integral Invariants of Relativistic Birkhoffian Systems
Institute of Scientific and Technical Information of China (English)
LUOShao-Kai
2003-01-01
For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t~rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.
Test of charge conjugation invariance.
Nefkens, B M K; Prakhov, S; Gårdestig, A; Allgower, C E; Bekrenev, V; Briscoe, W J; Clajus, M; Comfort, J R; Craig, K; Grosnick, D; Isenhower, D; Knecht, N; Koetke, D; Koulbardis, A; Kozlenko, N; Kruglov, S; Lolos, G; Lopatin, I; Manley, D M; Manweiler, R; Marusić, A; McDonald, S; Olmsted, J; Papandreou, Z; Peaslee, D; Phaisangittisakul, N; Price, J W; Ramirez, A F; Sadler, M; Shafi, A; Spinka, H; Stanislaus, T D S; Starostin, A; Staudenmaier, H M; Supek, I; Tippens, W B
2005-02-04
We report on the first determination of upper limits on the branching ratio (BR) of eta decay to pi0pi0gamma and to pi0pi0pi0gamma. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(eta-->pi0pi0gamma)pi0pi0pi0gamma)<6 x 10(-5) at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions.
Invariants of Broken Discrete Symmetries
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Neutrino mixing and Lorentz invariance
Blasone, M; Pires-Pacheco, P; Blasone, Massimo; Magueijo, Joao; Pires-Pacheco, Paulo
2003-01-01
We use previous work on the Hilbert space for mixed fields to derive deformed dispersion relations for neutrino flavor states. We then discuss how these dispersion relations may be incorporated into frameworks encoding the breakdown of Lorentz invariance. We consider non-linear relativity schemes (of which doubly special relativity is an example), and also frameworks allowing for the existence of a preferred frame. In both cases we derive expressions for the spectrum and end-point of beta decay, which may be used as an experimental probe of the peculiar way in which neutrinos experience Lorentz invariance.
Invariant manifolds and collective coordinates
Energy Technology Data Exchange (ETDEWEB)
Papenbrock, T. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Institute for Nuclear Theory, University of Washington, Seattle, WA (United States); Seligman, T.H. [Centro Internacional de Ciencias, Cuernavaca, Morelos (Mexico); Centro de Ciencias Fisicas, University of Mexico (UNAM), Cuernavaca (Mexico)
2001-09-14
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction. (author)
Numeric invariants from multidimensional persistence
Energy Technology Data Exchange (ETDEWEB)
Skryzalin, Jacek [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Carlsson, Gunnar [Stanford Univ., Stanford, CA (United States)
2017-05-19
In this paper, we analyze the space of multidimensional persistence modules from the perspectives of algebraic geometry. We first build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence over one-dimensional persistence. We argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Lastly, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data.
Scale-invariance of parity-invariant three-dimensional QED
Karthik, Nikhil
2016-01-01
We present numerical evidences using overlap fermions for a scale-invariant behavior of parity-invariant three-dimensional QED with two flavors of massless two-component fermions. Using finite-size scaling of the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator, we rule out the presence of bilinear condensate and estimate the mass anomalous dimension. The eigenvectors associated with these low-lying eigenvalues suggest critical behavior in the sense of a metal-insulator transition. We show that there is no mass gap in the scalar and vector correlators in the infinite volume theory. The vector correlator does not acquire an anomalous dimension. The anomalous dimension associated with the long-distance behavior of the scalar correlator is consistent with the mass anomalous dimension.
Chronic sleep deprivation differentially affects short and long-term operant memory in Aplysia.
Krishnan, Harini C; Noakes, Eric J; Lyons, Lisa C
2016-10-01
The induction, formation and maintenance of memory represent dynamic processes modulated by multiple factors including the circadian clock and sleep. Chronic sleep restriction has become common in modern society due to occupational and social demands. Given the impact of cognitive impairments associated with sleep deprivation, there is a vital need for a simple animal model in which to study the interactions between chronic sleep deprivation and memory. We used the marine mollusk Aplysia californica, with its simple nervous system, nocturnal sleep pattern and well-characterized learning paradigms, to assess the effects of two chronic sleep restriction paradigms on short-term (STM) and long-term (LTM) associative memory. The effects of sleep deprivation on memory were evaluated using the operant learning paradigm, learning that food is inedible, in which the animal associates a specific netted seaweed with failed swallowing attempts. We found that two nights of 6h sleep deprivation occurring during the first or last half of the night inhibited both STM and LTM. Moreover, the impairment in STM persisted for more than 24h. A milder, prolonged sleep deprivation paradigm consisting of 3 consecutive nights of 4h sleep deprivation also blocked STM, but had no effect on LTM. These experiments highlight differences in the sensitivity of STM and LTM to chronic sleep deprivation. Moreover, these results establish Aplysia as a valid model for studying the interactions between chronic sleep deprivation and associative memory paving the way for future studies delineating the mechanisms through which sleep restriction affects memory formation.
Directory of Open Access Journals (Sweden)
M.H.T. Alshbool
2017-01-01
Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
Itkin, Andrey
2017-01-01
This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solvin...
Invariant Classification of Gait Types
DEFF Research Database (Denmark)
Fihl, Preben; Moeslund, Thomas B.
2008-01-01
This paper presents a method of classifying human gait in an invariant manner based on silhouette comparison. A database of artificially generated silhouettes is created representing the three main types of gait, i.e. walking, jogging, and running. Silhouettes generated from different camera angles...
A Many Particle Adiabatic Invariant
DEFF Research Database (Denmark)
Hjorth, Poul G.
1999-01-01
For a system of N charged particles moving in a homogeneous, sufficiently strong magnetic field, a many-particle adiabatic invariant constrains the collisional exchange of energy between the degrees of freedom perpendicular to and parallel to the magnetic field. A description of the phenomenon...
Conjectured enumeration of Vassiliev invariants
Broadhurst, D J
1997-01-01
These conjectures are motivated by successful enumerations of irreducible Euler sums. Predictions for $\\beta_{15,10}$, $\\beta_{16,12}$ and $\\beta_{19,16}$ suggest that the action of sl and osp Lie algebras, on baguette diagrams with ladder insertions, fails to detect an invariant in each case.
Scale invariance and superfluid turbulence
Energy Technology Data Exchange (ETDEWEB)
Sen, Siddhartha, E-mail: siddhartha.sen@tcd.ie [CRANN, Trinity College Dublin, Dublin 2 (Ireland); R.K. Mission Vivekananda University, Belur 711 202, West Bengal (India); Ray, Koushik, E-mail: koushik@iacs.res.in [Department of Theoretical Physics, Indian Association for the Cultivation of Science, Calcutta 700 032 (India)
2013-11-11
We construct a Schroedinger field theory invariant under local spatial scaling. It is shown to provide an effective theory of superfluid turbulence by deriving, analytically, the observed Kolmogorov 5/3 law and to lead to a Biot–Savart interaction between the observed filament excitations of the system as well.
Bayesian tests of measurement invariance
Verhagen, A.J.; Fox, J.P.
2013-01-01
Random item effects models provide a natural framework for the exploration of violations of measurement invariance without the need for anchor items. Within the random item effects modelling framework, Bayesian tests (Bayes factor, deviance information criterion) are proposed which enable multiple m
Galilean invariance in Lagrangian mechanics
Mohallem, J. R.
2015-10-01
The troublesome topic of Galilean invariance in Lagrangian mechanics is discussed in two situations: (i) A particular case involving a rheonomic constraint in uniform motion and (ii) the general translation of an entire system and the constants of motion involved. A widespread impropriety in most textbooks is corrected, concerning a condition for the equality h = E to hold.
Generalized Donaldson-Thomas invariants
Joyce, Dominic
2009-01-01
This is a summary of the much longer paper arXiv:0810.5645 with Yinan Song. Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers DT^a(t) which count stable sheaves with Chern character a on X, with respect to a Gieseker stability condition t. They are defined only for Chern characters a for which there are no strictly semistable sheaves on X. They have the good property that they are unchanged under deformations of X. Their behaviour under change of stability condition t was not understood until now. We discuss "generalized Donaldson-Thomas invariants" \\bar{DT}^a(t). These are rational numbers, defined for all Chern characters a, and are equal to DT^a(t) if there are no strictly semistable sheaves in class a. They are deformation-invariant, and have a known transformation law under change of stability condition. We conjecture they can be written in terms of integral "BPS invariants" \\hat{DT}^a(t) when the stability condition t is "generic". We extend the theory to abelian cat...
Gauge invariance and Weyl-polymer quantization
Strocchi, Franco
2016-01-01
The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magne...
Weights on cohomology and invariants of singularities
Arapura, Donu; Włodarczyk, Jarosław
2011-01-01
In this paper, we extract natural invariants of a singularity by using the Deligne weight filtration on the cohomology of an exceptional fibre of a resolution, and also on the intersection cohomology of the link. Our primary goal is to study and give natural bounds on the weights in terms of direct images of differential forms. These bounds can be made explicit for various standard classes such as rational, isolated normal Cohen-Macaulay and toroidal singularities, and lead to strong restrictions on the topology of these singularities. A secondary goal of this paper is to make the weight filtration, and related constructions, more widely accessible. So we have tried to make the presentation somewhat self contained. This is supersedes our earlier preprint arXiv:0902.4234.
Invariant conserved currents in generalized gravity
Obukhov, Yuri N; Puetzfeld, Dirk; Rubilar, Guillermo F
2015-01-01
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to non-Riemannian spacetime geometry and nonminimal coupling. We demonstrate that an arbitrary vector field on the spacetime manifold generates a current density that is conserved under certain conditions, and find the expression of the corresponding superpotential. For a family of models including nonminimal coupling between geometry and matter, we discuss in detail the differential conservation laws and the conserved quantities defined in terms of covariant multipole moments. We show that the equations of motion for the multipole moments of extended microstructured test bodies lead to conserved quantities that are closely related to the conserved currents derived in the field-theoretic framework.
Testing local Lorentz invariance with short-range gravity
Kostelecký, V. Alan; Mewes, Matthew
2017-03-01
The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.
Testing local Lorentz invariance with short-range gravity
Kostelecky, Alan
2016-01-01
The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.
Gauge-invariant quark and gluon fields in QCD: dynamics, topology, and the Gribov ambiguity
Energy Technology Data Exchange (ETDEWEB)
Haller, Kurt E-mail: khaller@uconnvm.uconn.edu
2002-04-01
We review the implementation, in a temporal-gauge formulation of QCD, of the non-Abelian Gauss's law and the construction of gauge-invariant gauge and matter fields. We then express the QCD Hamiltonian in terms of these gauge-invariant operator-valued fields, and discuss the relation of this Hamiltonian and the gauge-invariant fields to the corresponding quantities in a Coulomb gauge formulation of QCD. We argue that a representation of QCD in terms of gauge-invariant quantities could be particularly useful for understanding low-energy phenomenology. We present the results of an investigation into the topological properties of the gauge-invariant fields, and show that there are Gribov copies of these gauge-invariant gauge fields, which are constructed in the temporal gauge, even though the conditions that give rise to Gribov copies do not obtain for the gauge-dependent temporal-gauge fields.
Gauge-invariant description of Higgs phenomenon and quark confinement
Kondo, Kei-Ichi
2016-11-01
We propose a novel description for the Higgs mechanism by which a gauge boson acquires the mass. We do not assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. This enables us to discuss the confinement-Higgs complementarity from a new perspective. The "Abelian" dominance in quark confinement of the Yang-Mills theory is understood as a consequence of the gauge-invariant Higgs phenomenon for the relevant Yang-Mills-Higgs model.
Isotropic Scale-Invariant Dissipation of Solar Wind Turbulence
Kiyani, K H; Khotyaintsev, Yu V; Turner, A; Hnat, B; Sahraoui, F
2010-01-01
The anisotropic nature of solar wind magnetic fluctuations is investigated scale-by-scale using high cadence in-situ magnetic field measurements spanning five decades in scales from the inertial to dissipation ranges of plasma turbulence. We find an abrupt transition at ion kinetic scales to a single isotropic stochastic process that characterizes the dissipation range on all observable scales. In contrast to the inertial range, this is accompanied by a successive scale-invariant reduction in the ratio between parallel and transverse power. We suggest a possible phase space mechanism for this, based on nonlinear wave-particle interactions, operating in this scale-invariant isotropic manner.
Search for anisotropic Lorentz invariance violation with {\\gamma}-rays
Kislat, Fabian
2015-01-01
While Lorentz invariance, the fundamental symmetry of Einstein's theory of General Relativity, has been tested to a great level of detail, Grand Unified Theories that combine gravity with the other three fundamental forces may result in a violation of Lorentz symmetry at the Planck scale. These energies are unattainable experimentally. However, minute deviations from Lorentz invariance may still be present at much lower energies. These deviations can accumulate over large distances, making astrophysical measurements the most sensitive tests of Lorentz symmetry. One effect of Lorentz invariance violation is an energy dependent photon dispersion of the vacuum resulting in differences of the light travel time from distant objects. The Standard-Model Extension (SME) is an effective theory to describe the low-energy behaviour of a more fundamental Grand Unified Theory, including Lorentz and CPT violating terms. In the SME the Lorentz violating operators can in part be classified by their mass-dimension d, with the...
Shift-invariant optical associative memories
Energy Technology Data Exchange (ETDEWEB)
Psaltis, D.; Hong, J.
1987-01-01
Shift invariance in the context of associative memories is discussed. Two optical systems that exhibit shift invariance are described in detail with attention given to the analysis of storage capacities. It is shown that full shift invariance cannot be achieved with systems that employ only linear interconnections to store the associations.
Diassociative algebras and Milnor's invariants for tangles
Kravchenko, Olga
2010-01-01
We extend Milnor's mu-invariants of link homotopy to ordered tangles. Simple combinatorial formulas for mu-invariants are given in terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves corresponds to axioms of Loday's diassociative algebra. The relation of tangles to diassociative algebras is formulated in terms of a morphism of corresponding operads.
Invariant manifolds for flows in Banach Spaces
Energy Technology Data Exchange (ETDEWEB)
Lu Kening.
1989-01-01
The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.
Verifying Class Invariants in Concurrent Programs
Zaharieva, M.; Huisman, Marieke
2014-01-01
Class invariants are a highly useful feature for the verification of object-oriented programs, because they can be used to capture all valid object states. In a sequential program setting, the validity of class invariants is typically described in terms of a visible state semantics, i.e., invariants