Conjugation Operator Research Articles

Estimates of -Harmonic Conjugate Operator

We define the -harmonic conjugate operator and prove that for , there is a constant such that for all if and only if the nonnegative weight satisfies the -condition. Also, we prove that if there is a constant such that for all , then the pair of weights satisfies the -condition.

TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives.

On the structure of the continuity set of the solution to a boundary-value problem for the radiation transfer equation

In this paper, we study the continuity properties of the solution to a boundary-value problem for the radiation transfer equation with generalized conjugation conditions at the interface of media. We establish the solvability of the boundary-value problem and obtain estimates of the maximum principle type. It is shown that the Fresnel component in the conjugation operator significantly complicates the structure of the set on which the solution of the boundary-value problem is continuous.

ELKO SPINOR FIELDS: LAGRANGIANS FOR GRAVITY DERIVED FROM SUPERGRAVITY

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong — together with Majorana spinor fields — to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein–Hilbert, the Einstein–Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that — in particular — the Einstein–Hilbert, Einstein–Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator — leading ELKO Lagrangian into the Dirac Lagrangian — is also pointed out, together with its relationship to the instanton Hopf fibration.

Analytic solutions of a class of nonlinear partial differential equations

An approach is presented for computing the adjoint operator vector of a class of nonlinear (that is, partial-nonlinear) operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear (partial-nonlinear and including all linear) and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations.

Application of the dual operator method to an equation describing the behavior of a boundary function

The dual operator is an analogue of the conjugate operator in linear theory. In this study the dual operator is applied to a second-order differential equation describing the behavior of the zero-order boundary function in the boundary function method used to derive the asymptotic solution of the singularly perturbed integro-differential plasma-sheath equation. This approach produces is a three-point difference scheme. The results of a numerical solution of the Cauchy problem are reported.

Strategies for ARQ in 2x2 MIMO Systems

Packet retransmission strategies are presented for 2x2 MIMO spatial multiplexing systems. Antennas for retransmission are selected to maximize an approximation of the throughput of the system. A sign change or conjugate operation is allowed for retransmitted packets. The proposed scheme performs selection of retransmission antennas based on the CSI at the receiver: only 1 bit of feedback is additionally required, along with the acknowledgement bits. When 2 packets are decoded with errors, retransmission follows a space time block code structure, allowing a seamless switching between spatial multiplexing and space time block coding.

Spectral Theory for the Standard Model of Non-Relativistic QED

For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy. As corollaries we derive local decay estimates for the photon dynamics, and we prove absence of (excited) eigenvalues and absolute continuity of the energy spectrum near the ground state energy, a region of the spectrum not understood in previous investigations. The conjugate operator in our Mourre estimate is the second quantized generator of dilatations on Fock space.

The comparative analysis of two solutions of Pekeris boundary problem

The solution of the reduced Pekeris boundary problem, satisfying to the generalized radiation condition on an impedance interface is obtained. Mode part of the solution is presented by series expansion on the total system of regular normal waves, of generalized normal waves and of leakage normal waves. The principle of the continuous continuation of the obtained solution in physical half‐space with validity of boundedness condition is formulated. Expansion of the solution on physical half‐space in a class of generalized functions is constructed. The obtained generalized solution includes canonical series expansion on the set of eigenfunctions of both conjugate operators corresponding an initial not self‐conjugate boundary problem, the associated eigenfunctions of a waveguide with two soft boundaries, the associated eigenfunctions of a waveguide with upper soft boundary and lower rigid boundary and a set of spherical components. Results of the comparative analysis of the classical solution and generalized solution are given.

Transferring Boundedness from Conjugate Operators Associated with Jacobi, Laguerre, and Fourier–Bessel Expansions to Conjugate Operators in the Hankel Setting

In this paper we establish transference results showing that the boundedness of the conjugate operator associated with Hankel transforms on Lorentz spaces can be deduced from the corresponding boundedness of the conjugate operators defined on Laguerre, Jacobi, and Fourier–Bessel settings. Our result also allows us to characterize the power weights in order that conjugation associated with Laguerre, Jacobi, and Fourier–Bessel expansions define bounded operators between the corresponding weighted Lp spaces.

An AM Radio Receiver Designed With a Genetic Algorithm Based on a Bacterial Conjugation Genetic Operator

Most methods in evolutionary computation are biologically inspired by chromosome crossover and mutation, two of the main sources of genetic variability in biological populations, as well as in genetic algorithms. In fact, this is a very important feature of the biological populations and their counterpart in genetic algorithms since the efficiency of the Darwinian natural selection depends on the degree of genetic variation that is achieved with the genetic mechanism or operator responsible for the population variability. Furthermore, in Nature, several other genetic mechanisms are used by populations as sources of variability such as bacterial conjugation, that is the transfer of genetic material between bacteria. In this paper, we introduce a biologically inspired conjugation operator simulating the genetic mechanism exhibited by bacterial colonies. The efficiency of the bacterial conjugation operator is illustrated designing with a genetic algorithm based on this operator an AM radio receiver, optimizing the main features of the electronic components of the AM radio circuit, as well as those of the radio enclosure.

Algebraic polymorphisms

AbstractIn this paper we consider a special class of polymorphisms with invariant measure, the algebraic polymorphisms of compact groups. A general polymorphism is—by definition—a many-valued map with invariant measure, and the conjugate operator of a polymorphism is a Markov operator (i.e. a positive operator on L2 of norm 1 which preserves the constants). In the algebraic case a polymorphism is a correspondence in the sense of algebraic geometry, but here we investigate it from a dynamical point of view. The most important examples are the algebraic polymorphisms of a torus, where we introduce a parametrization of the semigroup of toral polymorphisms in terms of rational matrices and describe the spectra of the corresponding Markov operators. A toral polymorphism is an automorphism of $\mathbb {T}^m$ if and only if the associated rational matrix lies in $\mathrm {GL}(m,\mathbb {Z})$. We characterize toral polymorphisms which are factors of toral automorphisms.

Designing energy spectra in finite phase plane

In recent years the finite phase plane has been used to accommodate spin 1/2 particles which play a decisive role as a tool in quantum computing [1]. For this, one often uses conjugate operators in the framework of the Wigner function approach. Conjugate variables are important both in classical and quantum mechanics. The best known example of such operators are the coordinate x and the momentu p [2]. In elementary quantum mechanics there are very few such pairs of conjugate operators. One of the striking results in a finite phase plane of dimension M is that there exist more than one pair of conjugate operators in the xp-plane. In this talk we show how to build 2 conjugate kq-representations (k-quasimomentum, q- quasicoordinte) [3]. These conjugate representations are then applied to Harper-like Hamiltonians, and it's shown how to design physical systems with energy spectra with any desired number of discrete energy levels, and with prescribed degeneracy. A general theory of quantum mechanics in finite phase plane was developed by Schwinger [4].

On the existence of a generalized solution of the conjugation problem for the Navier-Stokes system

By the conjugation problem we mean the problem of finding a solution u(t) of a non-stationary Navier-Stokes system in some domain on some time interval [0,T] such that the solution must satisfy certain conditions. Namely, the value of the solution at the boundary is equal to zero, and a conjugation condition is given which consists in the requirement that the initial value of the solution be connected with its values on the entire time interval by some linear operator defined on solutions: . In the special case where the values of the solution at the ends of the time interval coincide, we obtain the problem about a periodic solution.For the conjugation problem we establish the existence of a generalized solution in the case of bounded and unbounded domains of arbitrary dimension under various assumptions about the conjugation operator. A peculiarity of unbounded domains is the fact that a solution of the conjugation problem may not be quadratically integrable.Bibliography: 8 titles.

Spectral theory of certain unbounded Jacobi matrices

Using the conjugate operator method of Mourre we study the spectral theory of a class of unbounded Jacobi matrices. We especially focus on the case where the off-diagonal entries a n = n α ( 1 + o ( 1 ) ) and diagonal ones b n = λ n α ( 1 + o ( 1 ) ) with α > 0 , λ ∈ R .

Statistical Modeling of Epistasis and Linkage Decay using Logic Regression

AbstractLogic regression has been recognized as a tool that can identify and model non-additive genetic interactions using Boolean logic groups. Logic regression, TASSEL-GLM and SAS-GLM were compared for analytical precision using a previously characterized model system to identify the best genetic model explaining epistatic interaction for vernalization-sensitivity in barley. A genetic model containing two molecular markers identified in vernalization response in barley was selected using logic regression while both TASSEL-GLM and SAS-GLM included spurious associations in their models. The results also suggest the logic regression can be used to identify dominant/recessive relationships between epistatic alleles through its use of conjugate operators.

From Dirac spinor fields to eigenspinoren des ladungskonjugationsoperators

Dual-helicity eigenspinors of the charge conjugation operator [eigenspinoren des ladungskonjugationsoperators (ELKO) spinor fields] belong—together with Majorana spinor fields—to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class (5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three, respectively, corresponding to flagpole, flag-dipole, and Weyl spinor fields. This paper is devoted to investigate and provide the necessary and sufficient conditions to map Dirac spinor fields to ELKO, in order to naturally extend the standard model to spinor fields possessing mass dimension 1. As ELKO is a prime candidate to describe dark matter, an adequate and necessary formalism is introduced and developed here, to better understand the algebraic, geometric, and physical properties of ELKO spinor fields, and their underlying relationship to Dirac spinor fields.

Geometry of spaces of compact operators

We introduce the notion of compactly locally reflexive Banach spaces and show that a Banach space X is compactly locally reflexive if and only if $\mathcal{K}(Y,X^{**})\subseteq\mathcal{K}(Y,X)^{**}$ for all reflexive Banach spaces Y. We show that X* has the approximation property if and only if X has the approximation property and is compactly locally reflexive. The weak metric approximation property was recently introduced by Lima and Oja. We study two natural weak compact versions of this property. If X is compactly locally reflexive then these two properties coincide. We also show how these properties are related to the compact approximation property and the compact approximation property with conjugate operators for dual spaces.

Conjugate operators that preserve the nonconvergence of bounded martingales

We show that the conjugate T ∗ of an operator T : X → Y , with X and Y Banach spaces, satisfies the following dichotomy: either T ∗ preserves the nonconvergence of bounded martingales in Y ∗ , or there exists a compact operator K : X → Y such that the kernel N ( T ∗ + K ∗ ) fails the Radon–Nikodým property.

Factorization of singular integral operators with a Carleman shift via factorization of matrix functions: the anticommutative case

AbstractThis paper deals with what we call modified singular integral operators. When dealing with (pure) singular integral operators on the unit circle with coefficients belonging to a decomposing algebra of continuous functions it is known that a factorization of the symbol induces a factorization of the original operator, which is a representation of the operator as a product of three singular integral operators where the outer operators in that representation are invertible.The main purpose of this paper is to obtain a similar operator factorization for the case of singular integral operators with a backward shift and to extract from there some consequences for their Fredholm characteristics. At the end of the paper it is shown that the operator factorization is also possible for other classes of singular integral operators, namely those including either a conjugation operator or a composition of a conjugation with a forward shift operator. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)