Analytic T matrices for Coulomb plus rational separable potentials

Mirror maps, modular relations and hypergeometric series II

In this article , we explore the properties and relations of the hypergeometric superhyberbolic functions in terms of generalized hypergeometric functions. Then we express the hypergeometric superhyberbolic functions with the help of hypergeometric functions to obtain an integral representation related to classical results within the theory of generalized hypergeometric functions. The work emphasises conditions of convergence, and special cases where the results can be expressed in a simple form and provide a unified framework for evaluating integrals involving hypergeometric functions.

We establish a common structure of all two-body off-shell scattering quantities (expressed in momentum space or coordinate space) associated with Coulomb plus rational separable potentials. We present expressions in so-called maximal-reduced closed form, including new formulas: (i) for the off-shell Jost state for the Coulomb potential, (ii) for the off-shell Jost function associated with the Coulomb plus Yamaguchi potential, and (iii) for the scattering, regular, and Jost states in coordinate representation for Coulomb plus simple separable potentials for all l.

We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first illustrate covariance properties on order-two linear differential operators associated with identities relating the same hypergeometric function with different rational pullbacks. These rational transformations are solutions of a differentially algebraic equation that already emerged in a paper by Casale on the Galoisian envelopes. We provide two new and more general results of the previous covariance by rational functions: a new Heun function example and a higher genus hypergeometric function example. We then focus on identities relating the same hypergeometric function with two different algebraic pullback transformations: such remarkable identities correspond to modular forms, the algebraic transformations being solution of another differentially algebraic Schwarzian equation that also emerged in Casale’s paper. Further, we show that the first differentially algebraic equation can be seen as a subcase of the last Schwarzian differential condition, the restriction corresponding to a factorization condition of some associated order-two linear differential operator. Finally, we also explore generalizations of these results, for instance, to , hypergeometric functions, and show that one just reduces to the previous cases through a Clausen identity. The question of the reduction of these Schwarzian conditions to modular correspondences remains an open question. In a hypergeometric framework the Schwarzian condition encapsulates all the modular forms and modular equations of the theory of elliptic curves, but these two conditions are actually richer than elliptic curves or hypergeometric functions, as can be seen on the Heun and higher genus example. This work is a strong incentive to develop more differentially algebraic symmetry analysis in physics.

A study of the n-n interaction from a complete experiment of the n + d break-up at 14.5 MeV

Charged-particle off-shell scattering: The T matrix for the pure Coulomb potential and for Coulomb plus simple separable potentials for all partial waves

An assessment of some closed-form expressions for the Voigt function II: Utilizing rational approximations for the Gauss function

Logarithmic connections with vanishing [formula omitted]-curvature

We present a method for solution of linear ill-posed equations in function spaces based on the use of continuousJ-fractions. We obtain a meromorphic solution of regularized equations and indicate some cases where a solution can be represented in terms of rational functions.

This article presents theoretical investigations on techniques for the improvement of the dynamic characteristics of slender bridges under wind action. Aerodynamically effective control shields are applied as controlled actuators. The first part of the article describes the modelling of the uncontrolled aeroelastic system. Acting aerodynamic forces are consistently characterised using linear time-invariant transfer elements in terms of rational functions. On this basis, two configuration levels of the uncontrolled system are represented with linear time-invariant state-space models and investigated. The second part of the article addresses controller design and the behaviour of the controlled aeroelastic system. Both fundamental limits for stabilisation and the efficiency for attenuating the influence of gusts are described for different actuator mechanisms. The results are derived and discussed with methods of control theory.

Synthetic division based integration of rational functions of bivariate polynomial numerators with linear denominators over a unit triangle {0⩽ ξ, η⩽1, ξ+ η⩽1} in the local parametric space ( ξ, η)

Electromagnetic transients resulting from voltage dips not only present challenges for low-voltage ride-through (LVRT) of doubly fed induction generators (DFIGs) in wind turbines (WTs) but also introduce complications for protective relays in power systems. Analysis of the voltage-dip response is a fundamental requirement for methodologies targeting LVRT performance and is also useful for power system development. To date, it has not been feasible to take into account the interval between voltage dip and crowbar triggering, and, consequently, the accuracy of the analytical results has been compromised. In this paper, a concept of equivalent fault source is presented with which the transient process during voltage dips is decomposed into one response to the equivalent stator fault source and the other response to the equivalent rotor fault source. The former results from dips in the supply voltage, while the latter arises from variations in both the rotor resistance and the control voltage produced by crowbar activation. This makes it feasible to incorporate the interval, i.e., the triggering delay, into the analytical solution. Additionally, this decomposition approach allows for the physical mechanisms behind the individual transient components to be more clearly understood. With the explicit analytical formulas, some intrinsic characteristics of the transients are identified. The comparative accuracy and advantages of this analytical method over the conventional approaches is demonstrated through simulations using a 2-MW DFIG for commercial WTs and further verified experimentally on a laboratory-scale test rig.

Proceeding from the earlier constructed solution of the scalar free boundary value problem (BVP) for the Earth’s potential, several kinds of new formulas are presented for the spectral characteristics of the geopotential. An explicit analytical formula is derived for a geopotential harmonic coefficient as a function of the surface gravity anomaly, Earth’s figure ellipticity and terrain topography. Then several basic linear relations are constructed, as well, between the whole set of the harmonic coefficients and gravity anomaly data. These relations can be applied for constructing BVP spectral solution by collocation technique. They can be also used for solving an inverse problem, i.e. the determination of the gravity anomaly on the basis of a known geopotential model.

A Theoretical Model of Erosion and Macromolecular Drug Release from Biodegrading Microspheres

A technique, simple and easy to use, is presented to design the optimum gain pyramidal horn. The optimum gain pyramidal horn design equation available in the literature is improved. Design parameters are computed from the simple and explicit analytical formulas. The pyramidal horn gain is determined with no path length error approximation. Several design examples are given to show the performance of the improved design technique. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 188–193, 2001.