Function Theory Research Articles

Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory

In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fej\' er Interpolation Problem for matrix rational functions. We then extend the $H^\infty$-functional calculus to an $\overline{H^\infty}+H^\infty$-functional calculus for the compressions of the shift. Next, we consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5; we then establish a matrix-valued version of Abrahamse's Theorem. We also solve a subnormal Toeplitz completion problem of $2\times 2$ partial block Toeplitz matrices. Further, we establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols, and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.

Spectral approximations of strongly degenerate elliptic differential operators

We establish analytical estimates of spectral approximations errors for strongly degenerate elliptic differential operators in the Lebesgue space $L_q(\Omega)$ on a bounded domain $\Omega$. Elliptic operators have coefficients with strong degeneration near boundary. Their spectrum consists of isolated eigenvalues of finite multiplicity and the linear span of the associated eigenvectors is dense in $L_q(\Omega)$. The received results are based on an appropriate generalization of Bernstein-Jackson inequalities with explicitly calculated constants for quasi-normalized Besov-type approximation spaces which are associated with the given elliptic operator. The approximation spaces are determined by the functional $E\left(t,u\right)$, which characterizes the shortest distance from an arbitrary function ${u\in L_q(\Omega)}$ to the closed linear span of spectral subspaces of the given operator, corresponding to the eigenvalues such that not larger than fixed ${t>0}$. Such linear span of spectral subspaces coincides with the subspace of entire analytic functions of exponential type not larger than ${t>0}$. The approximation functional $E\left(t,u\right)$ in our cases plays a similar role as the modulus of smoothness in the functions theory.

Analysis of Dynamic Parameters of a Railway Bridge

This article analyses the dispersion of vibration accelerations of a railway bridge during the passage of a train, and presents an analysis of their parameters after the application of the theory of covariance functions. The measurements of vibration accelerations at the fixed points of the beams of the overlay of the bridge were recorded in the time scale as digital arrays (matrices). The values of inter-covariance functions of the arrays of data of measurements of digital vibration accelerations and the values of auto-covariance functions of the individual arrays, changing the quantization interval in the time scale, were calculated. The compiled software Matlab 7 in the operator package environment was used in calculations. This article aims at determining the interdependencies of results of vibrations of bridge points rather than at the impact which a train makes on a bridge without emphasizing the modal parameters of the bridge. The aforementioned interdependencies make it possible to predict the results of hard-to-reach points.

A Primal Framework for Indefinite Kernel Learning

Kernel methods have been widely applied in machine learning to solve complex nonlinear problems. Kernel selection is one of the key issues in kernel methods, since it is vital for improving generalization performance. Traditionally, the selection of kernel is restricted to be positive definite which makes their applicability partially limited. Actually, in many real applications such as gene identification and object recognition, indefinite kernels frequently emerge and can achieve better performance. However, compared to positive definite ones, indefinite kernels are more complicated due to the non-convexity of the subsequent optimization problems, which leads to the incapability of most existing kernel algorithms. Some indefinite kernel methods have been proposed based on the dual of support vector machine (SVM), which mostly emphasize on how to transform the non-convex optimization to be convex by using positive definite kernels to approximate indefinite ones. In fact, the duality gap in SVM usually exists in the case of indefinite kernels and therefore these algorithms do not indeed solve the indefinite kernel problems themselves. In this paper, we present a novel framework for indefinite kernel learning derived directly from the primal of SVM, which establishes several new models not only for single indefinite kernel but also extends to multiple indefinite kernel scenarios. Several algorithms are developed to handle the non-convex optimization problems in these models. We further provide a constructive approach for kernel selection in the algorithms by using the theory of similarity functions. Experiments on real world datasets demonstrate the superiority of our models.

Notes on the ideology of international organizations law: The International Organization for Migration, state-making, and the market for migration

AbstractThis article discusses the law and practice of the International Organization for Migration (IOM), a little-known but important international organization. The article aims to illuminate what it is the IOM does; how it influences its member state practices while simultaneously working on member state assignments; and how this affects the dominant theory underpinning the law of international organizations, i.e., the theory of functionalism. The article concludes that the IOM takes functionalist thought to extremes, and in doing so makes visible the latter’s ideological nature.

Pre-processing the nuclear many-body problem

The solution of the nuclear A-body problem encounters severe limitations from the size of many-body operators. These limitations are typically related to both the (iterative) storing of the associated tensors and to the computational time related to their multiple contractions in the calculation of various quantities of interest. However, not all the degrees of freedom encapsulated into these tensors equally contribute to the description of many-body observables. Identifying systematic and dominating patterns, a relevant objective is to achieve an \emph{a priori} reduction to the most relevant degrees of freedom via a pre-processing of the A-body problem. The present paper is dedicated to the analysis of two different paradigms to do so. The factorization of tensors in terms of lower-rank ones, whose know-how has been recently transferred to the realm of nuclear structure, is compared to a reduction of the tensors' index size based on an importance truncation. While the objective is to eventually utilize these pre-processing tools in the context of non-perturbative many-body methods, benchmark calculations are presently performed within the frame of perturbation theory. More specifically, we employ the recently introduced Bogoliubov many-body perturbation theory that is systematically applicable to open-shell nuclei displaying strong correlations. This extended perturbation theory serves as a jumpstart for non-perturbative Bogoliubov coupled cluster and Gorkov self-consistent Green's function theories. Results obtained in "small" model spaces are equally encouraging for tensor factorization and importance truncation techniques. While the former requires significant numerical developments to be applied in large model spaces, the latter is presently applied in this context and demonstrates great potential to enable high-accuracy calculations at a much reduced computational cost.

Applications of a Functionalist Theory of Gender: A Response to Reflections and a Research Agenda

Applications of a Functionalist Theory of Gender: A Response to Reflections and a Research Agenda

A Revenge of the Generals. The Rebalancing of the Civil-military Relations in France

ABSTRACTWhile academic debate on the political control of military forces tends to oppose the poles of ‘integration’ or ‘separation’, the French military tradition is most often described as a case of subordination to political authorities. I examine the indicators of the rebalance of power in favour of the military by adopting an inductive approach based on the observation of the institutionalization of Civil-Military Cooperation (CIMIC). The focus on officers’ professional trajectories and collective resources, gives an alternative explanation of the adaptation of the military organizations to the security environment, that no longer only relies on usual realist and functionalist theories.

Method of Riemann surfaces for an inverse antiplane problem in an n-connected domain

ABSTRACTAn inverse problem of the theory of harmonic functions for an n-connected domain is analyzed. The problem is equivalent to a problem of antiplane elasticity on determination of the profiles of n uniformly stressed inclusions. The inclusions are in ideal contact with the surrounding matrix, the stress field inside the inclusions is uniform, and at infinity the body is subjected to antiplane uniform shear. The exterior of the inclusions, an n-connected domain, is treated as the image by a conformal map of an n-connected slit domain with the slits lying in the same line. The inverse problem is solved by quadratures by reducing it to two Riemann-Hilbert problems on a Riemann surface of genus n−1. Samples of two and three symmetric and non-symmetric uniformly stressed inclusions are reported.

Robust finite-time control of descriptor Markovian jump systems with impulsive

In this paper, we obtain sufficient conditions ensuring stability of the robust finite-time for descriptor Markovian jump systems with impulsive effects and time-varying norm-bounded disturbance, especially, when the system is in actuator saturation. Using the theory of Lyapunov functions and the concept of convex hull-based representation of saturation function. We design the state feedback controller and obtain estimation of domain of attraction, extending the results to convex optimization problems; the solvability condition of the controller can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). Finally, we present some numerical examples showing the effectiveness of the obtained theoretical results.

Solution for bending of a polygonal plate with cracks by the linear conjugate method

Stress–strain state of a polygonal multiply connected plate under bending is considered. The plate under the action of different force factors (bending moment M and uniformly distributed load of intensity q) is also carried out. Similar problems for a simple configuration plates were solved by different authors. But the bending problem for a plate with different length through cracks is considered first. Using the theory of a complex variable function and analytic functions (Kolosov-Muskheleshvili potential) the problem is solved by the linear conjugate method. Such plates (slabs) are widely used in shipbuilding (hull-deck of ships), in construction (interfloor slabs, balcony flooring slabs) in mechanical engineering, aircraft building, etc. Therewith, at first boundary condition for an entire plate (without cracks) under the action of the applied loads, (M and q) and then a problem on bending of a plate with cracks under the action of loads applied to crack faces and that are determined from the problem on entire plate (using the uniqueness of displacements $$v+iv$$ and uniqueness of the flexure w), are used. The obtained elliptic integrals F(x) and E(x) are calculated by the methods known from references. As a result for determining integral constants $$C_1 ,C_2 ,\ldots ,C_j $$ , we get a system of equations for the considered cases of applied loads. Some numerical examples are solved.

On the Convergence Rate of the Continuous Newton Method

In this paper we study the convergence of the continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on recent progress in the geometric theory of spiral-like functions. We prove convergence theorems and illustrate them by numerical simulations.

Thomson scattering from dense inhomogeneous plasmas.

X-ray Thomson scattering experiments in the soft and hard x-ray regime yield information on fundamental parameters of high-density systems. Pump-probe experiments with variable time delay provide insight into the excitation and relaxation dynamics in dense plasmas. On short time scales, a local thermodynamic equilibrium description might not be sufficient. Besides nonequilibrium effects on the electron distribution function, spatial inhomogeneities influence the scattering signal. Generalizing previous approaches of Belyi [Phys. Rev. E 97, 053204 (2018)2470-004510.1103/PhysRevE.97.053204] and Kozlowski etal. [Sci. Rep. 6, 24283 (2016)2045-232210.1038/srep24283], we discuss implications for Thomson scattering spectra for inhomogeneous plasmas in the warm dense matter regime based on a gradient expansion within real-time Green's-functions theory. Especially in the collective scattering regime, Thomson scattering spectra are modifed substantially by spatial inhomogeneities. Within a first-order gradient expansion, the dispersion relation for plasmons is determined. In particular, the ratio of the heights of the plasmon peaks is changed which prevents a simple estimation of the plasma temperature from the detailed balance relation.

The Pragmatic Force of Making an Argument

Making arguments makes reasons apparent. Sometimes those reasons may affect audiences’ relationships to claims (e.g., accept, adhere). But an over-emphasis on audience effects encouraged by functionalist theories of argumentation distracts attention from other things that making arguments can accomplish. We advance the normative pragmatic program on argumentation through two case studies of how early advocates for women’s suffrage in the U.S. made reasons apparent in order to show that what they were doing wasn’t ridiculous. While it might be possible to identify this as a new function of argumentation, we encourage instead attention to a more important question: explaining how all the diverse uses of argument have pragmatic force.

An Elementary Approach to the Study of Somos Sequences

An elementary approach (not involving the theory of elliptic functions) is proposed to the proof of the main properties of the Somos-4 sequence.

Electronic energy transfer studied by many-body Green's function theory.

We present a combination of many-body Green's function theory and Förster-Dexter theory to estimate the excitation energy transfer (EET) coupling in both the isolated and condensed systems. This approach employs the accurate wave functions of excitons, which are derived from the Bethe-Salpeter equation, in the donor and acceptor to set up the electronic coupling terms. Dexter coupling, which arises from the exchange-correlation effect, is evaluated based on the GW method which is a state-of-the-art ab initio theory for the description of self-energy. This approach is applicable to various situations, especially for periodic systems. The approach is tested on some model molecular dimers and compared with other high-level quantum chemistry methods together with the exact supermolecule scheme. Finally, we apply it to study the EET between periodic single-walled carbon nanotubes, exploring the dependence of EET on the chirality of nanotubes and the type of excitation transferred, finding that dark states play key roles in the EET between nanotubes. The EET rate falls as ∼D-12 approximately with the distance D between nanotubes for small D, much faster than the traditional Förster model.

A Psychosocial Genealogy of LGBTQ+ Gender: An Empirically Based Theory of Gender and Gender Identity Cultures

In this invited article, I present an inclusive theory of gender that clarifies its interconnections with gender identity, gender expression, and sexuality. To support this functionalist theory, I summarize findings from an extensive body of mixed methods research on lesbian, gay, bisexual, transgender, queer, and other (LGBTQ+) genders in the United States. I use a feminist-intersectional lens to empirically base and historically situate a theory of gender that is grounded in research of LGBTQ+ communities (butch, femme, bear, leathermen, transgender, drag queens, and family/house systems). I define genders as either sets of personal qualities within a culture associated with physiological sex or sets of qualities that evolve in reaction to limitations of existing genders. The evolution of genders functions to meet needs in four domains: (1) psychological: an experience of fit between a core aspect of self and a gender construct; (2) cultural: the creation of an LGBTQ+ culture that asserts sets of gender characteristics, which were denied and stigmatized within preexisting cultural norms; (3) interpersonal: the communicating of affiliation and status to enhance safety; and (4) sexual: an erotic embodiment of signifiers of these needs via an aesthetic that structures sexual attraction. I detail how each function affects identity, security, belonging, and personal and social values. Online slides for instructors who want to use this article for teaching are available on PWQ's website at http://journals.sagepub.com/page/pwq/suppl/index

Predictive models for identification of gravitational waves by applying data from LIGO observatory

This paper explores the possibility of identifying gravitational waves by statistically processing data obtained from the experiment performed by the Laser Interferometer Gravitational-Wave Observatory (LIGO observatory). For an analysis of the measurement data arrays, the parameter z from the Doppler formula and the theory of covariance functions has been used. The trend of oscillation vectors of detectors obtained at the Hanford and Livingston observatories was assessed by applying the least square method. In addition, this procedure partially eliminates random errors in the data obtained from measurements carried out by the observatory. Upon assessment of the impact of gravitational waves on the changes in the values of the parameters of interferometer laser beams, the estimates of the auto-covariance and cross-covariance functions of vibration vectors of detectors measured at the observatories were calculated by varying the quantised interval on the time scale. The covariance of algebraic addition of relevant vectors and single vectors was used in the calculation of the estimates of covariance functions. The average value of the parameter z from the Doppler formula was calculated according to the formula created by using the expression of cross-covariance function of algebraic addition Hanford Gravitational Wave–Livingston Gravitational Wave (HGW−LGW) vector and single LGW vector. The speed and the direction of spread of the gravitational waves’ component HGW → LGW in respect of the vector of the gravitational waves were established. The calculations were performed using the author’s original software based on MATLAB procedures.

A Hilbert-type integral inequality under configuring free power and its applications

By using the method of weight function, the technique of real analysis, and the theory of special functions, a multi-parameter Hilbert-type integral inequality and its equivalent form are established, and their constant factors are proved to be the best possible. The expressions of operator with norm are given. As an application, relevant results in the references and some new inequalities are obtained by assigning some parameter values.

The Fekete–Szegö coefficient functional problems for q-starlike and q-convex functions related with lemniscate of Bernoulli

The area of [Formula: see text]-calculus has attracted the serious attention of researchers. This great interest is due its application in various branches of mathematics and physics. The application of [Formula: see text]-calculus was initiated by Jackson [Jackson, On [Formula: see text]-definite integrals, Quart. J. Pure Appl. Math. 41 (1910) 193–203; On [Formula: see text]-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh 46 (1908) 253–281.], who was the first to develop [Formula: see text]-integral and [Formula: see text]-derivative in a systematic way. In this paper, we make use of the concept of [Formula: see text]-calculus in the theory of univalent functions, to obtain the bounds for certain coefficient functional problems of [Formula: see text]-starlike and [Formula: see text]-convex functions. Further, we also obtain similar type of inequalities related to lemniscate of Bernoulli. The authors sincerely hope that this paper will revive this concept and encourage other researchers to work in this [Formula: see text]-calculus in the near-future in the area of complex function theory. Also, we present a direct and shortened proof for the estimates of [Formula: see text] found in [Mishra and Gochhayat, Fekete–Szego problem for [Formula: see text]-uniformly convex functions and for a class defined by Owa–Srivastava operator, J. Math. Anal. Appl. 347(2) (2008) 563–572] for [Formula: see text], [Formula: see text].