On the Representation of Linear Continuous Functionals in Spaces of Analytic Functions of the Hardy–Sobolev Type in a Polydisk

We describe dual spaces of classes of the Hardy–Sobolev type of functions holomorphic in a polydisk for 0 < p 1 and q (0, ) and for p (1, ) and q = 1.     

The ε-algorithm for the identification of a transfer-function model: some applications

The aim of this paper is to apply an algorithm related to the rational approximation for the identification of the lag structure in a transfer-function model. In fact, we apply the -algorithm proposed by Berlinet [3–5] to determine the polynomial orders in univariate and multivariate ARMA models. Furthermore, it has been proposed by Berlinet [5], González and Cano [13, 14] and González et al. [15] for a transfer-function model with one input and multiple inputs, respectively.The main contribution in this paper concerns the study of the relative significance of the elements in the -algorithm table, in the same way as that given by Berlinet and Francq [7] for ARMA models, to confirm the pattern used to specify the model. Two examples will be considered, namely, the sales series M [8] and a simulated model [20].A comparison is also made between the results of the -algorithm and the corner method generally used in the econometric literature. Although the -algorithm requires a more advanced theory in Numerical Analysis, it can be applied in a more simple way than the corner method.     

The Range of the Restriction Map for a Multiplicity Variety in Hörmander Algebras of Entire Functions

Characterizations of interpolating multiplicity varieties for Hörmander algebras ${A_p(\mathbb{C})}$ and ${A^0_p(\mathbb{C})}$ of entire functions were obtained by Berenstein and Li (J Geom Anal 5(1):1–48, 1995) and Berenstein et al. (Can J Math 47(1):28–43, 1995) for a radial subharmonic weight p with the doubling property. In this note we consider the case when the multiplicity variety is not interpolating, we compare the range of the associated restriction map for two weights ${q \leq p}$ and investigate when the range of the restriction map on ${A_p(\mathbb{C})}$ or ${A^0_p(\mathbb{C})}$ contains certain subspaces associated in a natural way with the smaller weight q.     

Asymptotic Behavior of Higher-Order Perturbations: Scaling Functions of the O(n)-Symmetric φ4-Theory in the (4−ε)-Expansion

We use an instantonic approach to calculate the asymptotic behavior of higher orders of the (4–)-expansion for the scaling function of the pair correlator of the O(n)-symmetric ⁴-theory in the minimal subtraction scheme. Our results differ substantially from the known exact expression for the ³ order of the expansion of the scaling function in the small- domain.     

Bifurcation Analysis of the Dynamics of Two Vortices in a Bose–Einstein Condensate. The Case of Intensities of Opposite Signs

This paper is concerned with a system two point vortices in a Bose–Einstein condensate enclosed in a trap. The Hamiltonian form of equations of motion is presented and its Liouville integrability is shown. A bifurcation diagram is constructed, analysis of bifurcations of Liouville tori is carried out for the case of opposite-signed vortices, and the types of critical motions are identified.     

Spectral Theory for a Mathematical Model of the Weak Interaction: The Decay of the Intermediate Vector Bosons W ��, II

We do the spectral analysis of the Hamiltonian for the weak leptonic decay of the gauge bosons W ^±. Using Mourre theory, it is shown that the spectrum between the unique ground state and the first threshold is purely absolutely continuous. Neither sharp neutrino high-energy cutoff nor infrared regularization is assumed.     

Operational Research in the U.K. in 1977: The Causes and Consequences of a Myth?

Instead of maintaining the original ideal of having a broad scientific basis for practical Operational Research, it is suggested that the O.R. community has uncritically accepted a myth which views O.R. as a "Hard" (Physical or even Mathematical) Science. It is argued that this has had profound consequences which explain the present difficulties O.R. workers have with problems involving major Social or Behavioural features. It is concluded that the "Hard" Science myth must be replaced, and a return made to the original conception of O.R., if we are to assist effectively in the complex social issues we face today.     

The Inequality Process Versus the Saved Wealth Model: Which Is the More Likely to Imply an Analogue of Thermodynamics in Social Science?

The Inequality Process (IP) and the Saved Wealth Model (SW) are theories of income distribution. The IP's social science metatheory requires its stationary distribution to fit the distribution of labor income conditioned on education. The SW is a modification of the particle system model of the kinetic theory of gases (KTG), the basis of gas thermodynamics. The IP is a particle system similar to the SW and KTG. This article shows that the IP passes the empirical test required of it by social science theory better than the SW. The IP's advantage increases as the U.S. labor force becomes more educated. The IP may the better bet to imply an analogue of thermodynamics in social science.     

The critical state in thin superconductors as a mixed boundary value problem: analysis and solution by means of the Erdélyi–Kober operators

With this paper, we provide an effective method to solve a large class of problems related to the electromagnetic behavior of thin superconductors. Here, all the problems are reduced to finding the weight functions for the Green integrals that represent the magnetic field components; these latter must satisfy the mixed boundary value conditions that naturally arise from the critical state assumptions. The use of the Erdélyi?CKober operators and of the Hankel transforms (and mostly the employment of their composition properties) is the keystone to unify the method toward the solution. In fact, the procedure consists always of the same steps and does not require any peculiar invention. For this reason, the method, here presented in detail for the simplest cases that can be handled in analytical way (two-part boundary), can be directly extended to many other more complex geometries (three or more parts), which usually will require a numerical treatment. In this paper, we use the operator technique to derive the current density and field distributions in perfectly conducting and superconducting thin discs and tapes subjected to a uniform magnetic field or carrying a transport current. Although analytical expressions for the field and current distributions have already been found by other authors in the past by using several other methods, their derivation is often cumbersome or missing key details, which makes it difficult for the reader to fully understand the derivation of the analytical formulas and, more importantly, to extend the same methods to solve similar new problems. On the contrary, the characterization of these cases as mixed boundary conditions has the advantage of referring to an immediate and na?ve translation of physics into a consistent mathematical formulation whose possible extension to other cases is self-evident.     

Homogenization of the boundary value problem for the Laplace operator in a domain perforated along (<Emphasis Type="Italic">n</Emphasis> – 1)-dimensional manifold with nonlinear Robin type boundary condition on the boundary of arbitrary shaped holes: Critical case

The asymptotic behavior of the solution to the boundary value problem for the Laplace operator in a domain perforated along an (n ? 1)-dimensional manifold is studied. A nonlinear Robin-type condition is assumed to hold on the boundary of the holes. The basic difference of this work from previous ones concerning this subject is that the domain is perforated not by balls, but rather by sets of arbitrary shape (more precisely, by sets diffeomorphic to the ball). A homogenized model is constructed, and the solutions of the original problem are proved to converge to the solution of the homogenized one.