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When considering initial stress field in geomaterial, nonzero resultant of shallow tunnel excavation exists, which produces logarithmic items in complex potentials, and would further lead to a unique displacement singularity at infinity to violate geo-engineering fact in real world. The mechanical and mathematical reasons of such a unique displacement singularity in the existing mechanical models are elaborated, and a new mechanical model is subsequently proposed to eliminate this singularity by constraining far-field ground surface displacement, and the original unbalanced resultant problem is converted into an equilibrium one with mixed boundary conditions. To solve stress and displacement in the new model, the analytic continuation is applied to transform the mixed boundary conditions into a homogenerous Riemann-Hilbert problem with extra constraints, which is then solved using an approximate and iterative method with good numerical stability. The Lanczos filtering is applied to the stress and displacement solution to reduce the Gibbs phenomena caused by abrupt change of the boundary conditions along ground surface. Several numerical cases are conducted to verify the proposed mechanical model and the results strongly validate that the proposed mechanical model successfully eliminates the displacement singularity caused by unbalanced resultant with good convergence and accuracy to obtain stress and displacement for shallow tunnel excavation. A parametric investigation is subsequently conducted to study the influence of tunnel depth, lateral coefficient, and free surface range on stress and displacement distribution in geomaterial. • A new mechanical model is proposed to obtain reasonable stress and displacement for shallow tunnel excavation. • The displacement singularity caused by unbalanced resultant of shallow tunnel excavation is eliminated. • Solution convergence is guaranteed using an approximate and iterative method. [ABSTRACT FROM AUTHOR]

We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of imaginary-time correlation functions computed by quantum Monte Carlo simulations. After reviewing the conventional maximum-entropy approach and established stochastic analytic continuation methods, we present several new developments in which the configurational entropy of the sampled spectrum plays a key role. Parametrizing the spectrum as a large number of δ -functions in continuous frequency space, an exact calculation of the entropy lends support to a simple goodness-of-fit criterion for the optimal sampling temperature. We also compare spectra sampled in continuous frequency with those from amplitudes sampled on a fixed frequency grid. Insights into the functional form of the entropy in different cases allow us to demonstrate equivalence in a generalized thermodynamic limit (large number of degrees of freedom) of the average spectrum and the maximum-entropy solution, with different parametrizations corresponding to different forms of the entropy in the prior probability. These results revise prevailing notions of the maximum-entropy method and its relationship to stochastic analytic continuation. In further developments of the sampling approach, we explore various adjustable (optimized) constraints that allow sharp low-temperature spectral features to be resolved, in particular at the lower frequency edge. The constraints, e.g., the location of the edge or the spectral weight of a quasi-particle peak, are optimized using a statistical criterion based on entropy minimization under the condition of optimal fit. We show with several examples that this method can correctly reproduce both narrow and broad quasi-particle peaks. We next introduce a parametrization for more intricate spectral functions with sharp edges, e.g., power-law singularities. We present tests with synthetic data as well as with real simulation data for the spin-1/2 Heisenberg chain, where a divergent edge of the dynamic structure factor is due to deconfined spinon excitations. Our results demonstrate that distortions of sharp edges or quasi-particle peaks, which arise with other analytic continuation methods, propagate and cause artificial spectral features also at higher energies. The constrained sampling methods overcome this problem and allow analytic continuation of spectra with sharp edge features at unprecedented fidelity. We present results for S = 1 / 2 Heisenberg 2-leg and 3-leg ladders to illustrate the ability of the methods to resolve spectral features arising from both elementary and composite excitations. Finally, we also propose how the methods developed here could be used as "pre processors" for analytic continuation by machine learning. Edge singularities and narrow quasi-particle peaks being ubiquitous in quantum many-body systems, we expect the new methods to be broadly useful and take numerical analytic continuation to a new quantitative level in many applications. [ABSTRACT FROM AUTHOR]

An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution T on d -dimensional Euclidean space. This is a holomorphic function on a right half-plane. If T is a (uniform) double-layer on a compact smooth hypersurface, then the beta function has an analytic continuation to the complex plane as a meromorphic function, and the residues are integrals of invariants of the second fundamental form. The first few residues are computed when d = 2 and d = 3. [ABSTRACT FROM AUTHOR]

A new static equilibrium mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface, and a mixed boundary value problem thus forms with elimination of displacement singularity at infinity. By applying analytic continuation, the mixed boundaries are transformed to a homogeneous Riemann–Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface to obtain more reasonable results. Several numerical cases are conducted to intensively verify the proposed solution by examining the utilization of Lanczos filtering, the elimination of displacement singularity, and solution convergence of constraining arc and truncation number, and comparisons with existing solutions, and all the results are in good agreements. Finally, more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery considering different tunnel geometries, lateral coefficients, and tunnel depths. Further discussions on the defects of the proposed solution are also conducted for objectivity. [Display omitted] • A new mechanical model is proposed for noncircular shallow tunnelling. • Far-field ground surface is constrained to equilibrate unbalanced resultant due to tunnelling. • Displacement singularity at infinity caused by unbalanced resultant is eliminated. • The solution simultaneously gives correct stress and reasonable displacement. [ABSTRACT FROM AUTHOR]

We establish the existence of an internal uniform hydrostatic state of stress inside a coated non-parabolic open elastic inhomogeneity when the surrounding matrix is subjected to a concentrated couple and uniform remote in-plane stresses. The proof of existence is accomplished through analytic continuation and the introduction of a specialized form of the conformal mapping function containing an infinite number of first-order poles. The complex constants appearing in the mapping function can be uniquely determined from a resulting set of non-linear recurrence relations for given material, geometric and loading parameters. The convergence criterion for the series in the mapping function is rigorously established. A simple condition on the remote loading in the matrix is found for given elastic constants of the inhomogeneity and the matrix in order to ensure that the internal stresses inside the non-parabolic inhomogeneity are uniform and hydrostatic. The analysis indicates that the internal uniform hydrostatic stress field, the constant mean stress in the coating and the constant hoop stress along the inhomogeneity-coating interface on the coating side are all independent of the specific open shapes of the two interfaces and are also independent of the existence of the nearby concentrated couple. However, the non-parabolic open shapes of the two interfaces are significantly influenced by the concentrated couple. We also accomplish the design of an uncoated non-parabolic harmonic elastic inhomogeneity in the presence of an arbitrary number of concentrated couples applied in the matrix. [ABSTRACT FROM AUTHOR]

• The proposition of a restarting process is applied to the HELM, designated RHELM. • The computations are performed explicitly on a low-order Padé approximant. • The RHELM has showed a performance superior to the traditional NR method. • The lower-order Padé approximants provides the initial data for the restarting process. • The work is implemented with usual numerical precision computations. The holomorphic embedding load-flow model (HELM) is a noniterative method based on the computation of a Taylor power series that is a function of an embedded parameter. In this method, a continuous function based on a Padé approximant is used to replace this series, extending the radius of convergence. However, depending on the problem and how it is solved, the convergence can demand a high-order series or have a stagnated solution for the case of the continued equivalent function. In this paper, a restarted HELM (RHELM) is introduced. The method works with a very much reduced number of coefficients of the bus voltage Taylor series, different from HELM. Additionally, in the problem formulation, the power balance equations (PBEs) are embedded, considering a parameter and an estimated bus-injected power. This injected power is computed from a voltage estimate whose value is updated at every restarting point. The restart process allows for an approximate solution of the voltages computed via Padé approximation to be used as a new starting point. It is expected that at a new restarting point, the estimated power tends to converge toward the effective power injection of the bus. Tests to accept a given result for a voltage are evaluated for each of two consecutive new coefficient power series that are calculated. The coefficients are calculated until a given specified power mismatch is achieved. In the event that this tolerance is not reached up to a user-defined number of coefficients, the process is then restarted. The method's performance is evaluated for a wide variety of test systems including a 13659-bus network model. The obtained results reveal that in comparison with the traditional iterative methods based on Newton's method and the HELM, the proposed formulation is very efficient for computations involving large-scale systems and presents fast convergence. [ABSTRACT FROM AUTHOR]

Using analytic continuation, we derive a new analytical solution for a screw dislocation in an N -phase laminate composed of N −2 intermediate elastic layers of equal thickness encased in two semi-infinite elastic media. The number of phases comprising the laminate can be arbitrarily large. The solution can be interpreted in terms of image screw dislocations, the magnitudes of which are determined by solving an algebraic equation of order N −2. We also obtain an elementary expression for the image force acting on the screw dislocation in terms of a single real function. Several specific examples are presented to demonstrate the solution. Analytic continuation is also applied to solve the related problem of a screw dislocation interacting with a multicoated circular elastic inhomogeneity. • New analytical solution for a screw dislocation in an N -phase laminate. • Number of phases comprising the laminate can be arbitrarily large. • Solution can be interpreted in terms of image screw dislocations. • Image force acting on screw dislocation in terms of a single real function. • Screw dislocation interacting with multicoated circular elastic inhomogeneity. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study some classes of generalized singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions. Such equations can be transformed into Riemann boundary value problems with two unknown functions on two parallel straight lines via Fourier transformation. The general solutions and the conditions of solvability are obtained by means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation. This paper will be of great significance for the study of improving and developing complex analysis, integral equation and boundary value problem. Therefore, the classic Riemann boundary value problem is extended further. [ABSTRACT FROM AUTHOR]

Highlights • Historically, obtaining closed-form approximations required trial and error. • We show such approximations can be derived without iterative trial and error. • After impedance approximations we successfully test our method on Green's functions. • The method can be used on any series or integral that has no closed form solution. Abstract Engineering approximations of physical systems sometimes produce models in which real-valued model-based physical-distances are added to complex-valued distances and/or (for electrical systems), real-valued current/charge image intensities are replaced with complex-valued quantities. These models are arrived at often using ad hoc approximations that allow infinite integrals or series to be approximated in closed form. Arriving at accurate ad hoc approximations in a compatible analytic form is often the difficult step in the derivation of these approximations. In this paper, we show that this difficult ad hoc step can be replaced for many classes of functions with the use of analytic continuation via Padé approximants, along with some reasonable engineering judgement. We apply our approach to several existing approximations in the electrical engineering field (overhead transmission line impedance, underground cable impedance and Green's functions used in ground potential rise calculations) and show that these approximations can be derived elegantly, without the need for grand leaps of insight, and provide a basis for both distance parameters and current/charge intensities that are complex-valued. [ABSTRACT FROM AUTHOR]

Abstract We present recent results on in-medium spectral functions of vector and axial-vector mesons, the electromagnetic (EM) spectral function and dilepton rates using the Functional Renormalization Group (FRG) approach. Our method is based on an analytic continuation procedure that allows us to calculate real-time quantities like spectral functions at finite temperature and chemical potential. As an effective low-energy model for Quantum Chromodynamics (QCD) we use an extended linear-sigma model including quarks where (axial-)vector mesons as well as the photon are introduced as gauge bosons. In particular, it is shown how the ρ and the a 1 spectral function become degenerate at high temperatures or chemical potentials due to the restoration of chiral symmetry. Preliminary results for the EM spectral function and the dilepton production rate are discussed with a focus on the possibility to identify signatures of the chiral crossover and the critical endpoint (CEP) in the QCD phase diagram. [ABSTRACT FROM AUTHOR]

We consider a circular elastic inclusion embedded in an infinite matrix each from a particular class of compressible hyperelastic materials of harmonic type. A concentrated couple is applied either inside the circular inclusion or in the matrix. Closed-form solutions of the corresponding boundary value problems are obtained using complex variable methods, in particular the principle of analytic continuation. Our analysis reveals several interesting conclusions including: the sum σ 11 + σ 22 of the normal stresses inside the inclusion remains constant when the concentrated couple is located in the surrounding matrix; the sum of the normal stresses is zero everywhere in the matrix when the concentrated couple is located inside the inclusion. [ABSTRACT FROM AUTHOR]

We consider the problem of numerical analytic continuation of an analytic function f ( z ) = f ( x + i y ) on a strip domain Ω + = { z = x + i y ∈ C | x ∈ R , 0 < y < y 0 } , where the data is given approximately only on the line y = 0 . This is a severely ill-posed problem. Motivated by the advantage of iterative methods for solving ill-posed problems, we propose a new modified iterative method to solve this problem under both a priori and a posteriori parameter choice rules. Moreover, some sharp error estimates between the exact solution and its approximation are proved. Some interesting numerical examples are conducted for showing that the newly-developed method works well. [ABSTRACT FROM AUTHOR]

In this work we show how by using a Padé type analytical continuation scheme, based on the Schlessinger point method, it is possible to find higher production thresholds in hadron physical problems. Recently, an extension of this numerical approach to the complex energy plane enabled the calculations of auto-ionization decay resonance poles in atomic and molecular systems. Here we use this so-called Resonances via Padé (RVP) method, to show its convergence beyond the singular point in hadron physical problems. In order to demonstrate the capabilities of the RVP method, two illustrations for the ability to identify singularities and branch points are given. In addition, two applications for hadron physical problems are given. In the first one, we identify the decay thresholds from a numerically calculated spectral function. In the second one, we use experimental data. First, we calculate the resonance pole of the f 0 ( 500 ) or σ meson using the S 0 partial wave amplitude for ππ scattering in very good agreement with the literature. Second, we use data on the cross section ratio R ( s ) for e + e − collisions and discuss the prediction of decay thresholds which proves to be difficult if the data is noisy. [ABSTRACT FROM AUTHOR]

A new scheme is put forward to determine the wetting temperature ( T w ) by utilizing the adaptation of arc-length continuation algorithm to classical density functional theory (DFT) used originally by Frink and Salinger, and its advantages are summarized into four points: (i) the new scheme is applicable whether the wetting occurs near a planar or a non-planar surface, whereas a zero contact angle method is considered only applicable to a perfectly flat solid surface, as demonstrated previously and in this work, and essentially not fit for non-planar surface. (ii) The new scheme is devoid of an uncertainty, which plagues a pre-wetting extrapolation method and originates from an unattainability of the infinitely thick film in the theoretical calculation. (iii) The new scheme can be similarly and easily applied to extreme instances characterized by lower temperatures and/or higher surface attraction force field, which, however, can not be dealt with by the pre-wetting extrapolation method because of the pre-wetting transition being mixed with many layering transitions and the difficulty in differentiating varieties of the surface phase transitions. (iv) The new scheme still works in instance wherein the wetting transition occurs close to the bulk critical temperature; however, this case completely can not be managed by the pre-wetting extrapolation method because near the bulk critical temperature the pre-wetting region is extremely narrow, and no enough pre-wetting data are available for use of the extrapolation procedure. [ABSTRACT FROM AUTHOR]

We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve. We show that all what is required is just the analytic continuation of these two periods. We present an explicit formula for the two periods for all values of t ∈ R . Furthermore, the nome q of the elliptic curve satisfies over the complete range in t the inequality | q | ≤ 1 , where | q | = 1 is attained only at the singular points t ∈ { m 2 , 9 m 2 , ∞ } . This ensures the convergence of the q -series expansion of the ELi-functions and provides a fast and efficient evaluation of these Feynman integrals. [ABSTRACT FROM AUTHOR]

The application of analytic continuation in quantum field theory (QFT) is juxtaposed to T-duality and mirror symmetry in string theory. Analytic continuation—a mathematical transformation that takes the time variable t to negative imaginary time— it —was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean approaches within mainstream QFT (e.g., Wilsonian renormalization group methods, lattice gauge theories) and the Euclidean field theory program for rigorously constructing non-perturbative models of interacting QFTs. A crucial difference between theories related by duality transformations and those related by analytic continuation is that the former are judged to be physically equivalent while the latter are regarded as physically inequivalent. There are other similarities between the two cases that make comparing and contrasting them a useful exercise for clarifying the type of argument that is needed to support the conclusion that dual theories are physically equivalent. In particular, T-duality and analytic continuation in QFT share the criterion for predictive equivalence that two theories agree on the complete set of expectation values and the mass spectra and the criterion for formal equivalence that there is a “translation manual” between the physically significant algebras of observables and sets of states in the two theories. The analytic continuation case study illustrates how predictive and formal equivalence are compatible with physical inequivalence, but not in the manner of standard underdetermination cases. Arguments for the physical equivalence of dual theories must cite considerations beyond predictive and formal equivalence. The analytic continuation case study is an instance of the strategy of developing a physical theory by extending the formal or mathematical equivalence with another physical theory as far as possible. That this strategy has resulted in developments in pure mathematics as well as theoretical physics is another feature that this case study has in common with dualities in string theory. [ABSTRACT FROM AUTHOR]

Voltage stability studies have been progressively gaining importance in the power engineering community. Predicting the saddle-node bifurcation point (SNBP) of a power system has become more critical as the power-system loading has increased in many places without a concomitant increase in transmission resources. Since a Newton–Raphson power-flow method is inherently unstable near the SNBP, adaptations such as continuation methods have been used as stabilizers. A new class of nonlinear equation solvers known as the holomorphic embedding method (HEM) is theoretically guaranteed to find the high-voltage solution to the power-flow problem, if one exists, up to the SNBP, provided sufficient precision is used and the conditions of Stahl’s theorem are satisfied by the equation set. In this paper, four different HEM-based methods to estimate the saddle-node bifurcation point of a power system, are proposed and compared in terms of accuracy as well as computational efficiency. [ABSTRACT FROM AUTHOR]

We prove the conjecture of Sfetsos, Siampos and Thompson that suitable analytic continuations of the Poisson–Lie T-duals of the bi-Yang–Baxter sigma models coincide with the recently introduced generalized λ -models. We then generalize this result by showing that the analytic continuation of a generic σ -model of “universal WZW-type” introduced by Tseytlin in 1993 is nothing but the Poisson–Lie T-dual of a generic Poisson–Lie symmetric σ -model introduced by Klimčík and Ševera in 1995. [ABSTRACT FROM AUTHOR]

It is shown that the general 3-point function 〈 Φ c Φ b Φ a 〉 , with continuous values of charges a , b , c of a statistical model operators, and the 3-point function of the Liouville model, could all be obtained by successive analytical continuations starting from the 3-point function of the minimal model. [ABSTRACT FROM AUTHOR]

This paper investigates axisymmetric shapes of an incompressible inviscid fluid bubble in a uniform flow. Approximate solutions are constructed for the governing nonlinear boundary value problem using the domain perturbation method. Bifurcation and turning points are located by applying a special type of Hermite–Padé approximation. [ABSTRACT FROM AUTHOR]

Let c be a characteristic form of degree k which is defined on a Kähler manifold of real dimension m > 2 k . Taking the inner product with the Kähler form Ω k gives a scalar invariant which can be considered as a generalized Lovelock functional. The associated Euler–Lagrange equations are a generalized Einstein–Gauss–Bonnet gravity theory; this theory restricts to the canonical formalism if c = c 2 is the second Chern form. We extend previous work studying these equations from the Kähler to the pseudo-Kähler setting. [ABSTRACT FROM AUTHOR]

We present the crossover line between the quark gluon plasma and the hadron gas phases for small real chemical potentials. First we determine the effect of imaginary values of the chemical potential on the transition temperature using lattice QCD simulations. Then we use various formulas to perform an analytic continuation to real values of the baryo-chemical potential. Our data set maintains strangeness neutrality to match the conditions of heavy ion physics. The systematic errors are under control up to μ B ≈ 300 MeV . For the curvature of the transition line we find that there is an approximate agreement between values from three different observables: the chiral susceptibility, chiral condensate and strange quark susceptibility. The continuum extrapolation is based on N t = 10 , 12 and 16 lattices. By combining the analysis for these three observables we find, for the curvature, the value κ = 0.0149 ± 0.0021 . [ABSTRACT FROM AUTHOR]

We show that the so-called λ deformed σ -model as well as the η deformed one belong to a class of the E -models introduced in the context of the Poisson–Lie-T-duality. The λ and η theories differ solely by the choice of the Drinfeld double; for the λ model the double is the direct product G × G while for the η model it is the complexified group G C . As a consequence of this picture, we prove for any G that the target space geometries of the λ -model and of the Poisson–Lie T-dual of the η -model are related by a simple analytic continuation. [ABSTRACT FROM AUTHOR]

We study the analytical properties of the Laplace transform of the lognormal distribution. Two integral expressions for the analytic continuation of the Laplace transform of the lognormal distribution are provided, one of which takes the form of a Mellin–Barnes integral. As a corollary, we obtain an integral expression for the characteristic function. We present two approximations for the Laplace transform of the lognormal distribution, both valid in ℂ ∖ (− ∞ , 0 ]. In the last section, we discuss how one may use our results to compute the density of a sum of independent lognormal random variables. [ABSTRACT FROM AUTHOR]

In this paper, we consider the evaluation of two kinds of oscillatory integrals with a Hankel function as kernel. We first rewrite these integrals as the integrals of Fourier-type. By analytic continuation, these Fourier-type integrals can be transformed into the integrals on [0, +∞), the integrands of which are not oscillatory, and decay exponentially fast. Consequently, the transformed integrals can be efficiently computed by using the generalized Gauss–Laguerre quadrature rule. Moreover, the error analysis for the presented methods is given. The efficiency and accuracy of the methods have been demonstrated by both numerical experiments and theoretical results. [ABSTRACT FROM AUTHOR]

We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities, asymptotics for large values of the variable and asymptotic location of zeros. [ABSTRACT FROM AUTHOR]

We use analytic continuation to derive the Euler–Lagrange equations associated to the Pfaffian in indefinite signature ( p , q ) directly from the corresponding result in the Riemannian setting. We also use analytic continuation to derive the Chern–Gauss–Bonnet theorem for pseudo-Riemannian manifolds with boundary directly from the corresponding result in the Riemannian setting. Complex metrics on the tangent bundle play a crucial role in our analysis and we obtain a version of the Chern–Gauss–Bonnet theorem in this setting for certain complex metrics. [ABSTRACT FROM AUTHOR]

• The generation mechanism of off-critical zeros starting from special critical zeros is revealed for Epstein zeta-functions. • The exact analysis of the Epstein zeta-functions is made for dimensions going to 0 and to infinity. • The existence of real off-critical zeros is proved for dimensions larger than 9.24555. We study the Epstein zeta-function formulated on the d -dimensional hypercubic lattice ζ (d) (s) = 1 2 ∑ ′ n 1 , ... , n d (n 1 2 + ... + n d 2) − s / 2 where the real part ℜ (s) > d and the summation runs over all integers except of the origin (0 , 0 , ... , 0). An analytical continuation of the Epstein zeta-function to the whole complex s -plane is constructed for the spatial dimension d being a continuous variable ranging from 0 to ∞. Zeros of the Epstein zeta-function ρ = ρ x + i ρ y are defined by ζ (d) (ρ) = 0. The nontrivial zeros split into the "critical" zeros (on the critical line) with ρ x = d 2 and the "off-critical" zeros (off the critical line) with ρ x ≠ d 2. Numerical calculations reveal that the critical zeros form closed or semi-open curves ρ y (d) which enclose disjunctive regions of the plane (ρ x = d 2 , ρ y). Each curve involves a number of left/right edge points ρ * = (d * 2 , ρ y *) , defined by a divergent tangent d ρ y / d d | ρ * . Every edge point gives rise to two conjugate tails of off-critical zeros with continuously varying dimension d which exhibit a singular expansion around the edge point, in analogy with critical phenomena for second-order phase transitions. For each dimension d > 9.24555 ... there exists a conjugate pair of real off-critical zeros which tend to the boundaries 0 and d of the critical strip in the limit d → ∞. As a by-product of the formalism, we derive an exact formula for lim d → 0 ζ (d) (s) / d. An equidistant distribution of critical zeros along the imaginary axis is obtained for large d , with spacing between the nearest-neighbour zeros vanishing as 2 π / ln d in the limit d → ∞. [ABSTRACT FROM AUTHOR]

Abstract: Planar central configurations of point masses that have one or more clusters of bodies are created by analytic continuation. The singularity of the gravitational interaction is removed from the continuation equations by algebraic means. The continuation splits a single body into several, and the initial mass of the single body can be nonzero. Necessary conditions are derived for these continuations that may be useful in addressing the question of finiteness of central configurations. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of numerical evaluation of a class of highly oscillatory integrals , where and , has been discussed. Based on analytic continuation, the integrals are transformed into the problems of integrating the forms on with the integrand does not oscillate and decays exponentially fast, which can be efficiently computed by using general Gauss–Laguerre quadrature rule. Theoretical results and numerical experiments perform that the method is very efficient in obtaining very high precision approximations if ω is sufficiently large. [Copyright &y& Elsevier]

Abstract: The aim of this work is to study the analytic continuation of the doubly-periodic Barnes zeta function. By using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic Barnes zeta function to the entire complex plane in terms of a real integral containing the Hurwitz zeta function and the first Jacobi theta function. These allow us to explicitly give expressions for the derivative at all non-positive integer points. [Copyright &y& Elsevier]

We apply analytic continuation and conformal mapping techniques to investigate, in detail, the elastic interaction of a screw dislocation and subsequently an edge dislocation with a locally rough bimaterial interface. In the case of a screw dislocation, the locations and Burgers vectors of the image screw dislocations for the half-plane containing the real screw dislocation are determined in an analytical manner. The image force acting on the screw dislocation is then expediently obtained using the Peach-Koehler formula. A sufficiently accurate closed-form expression for the image force is proposed. For the case of an edge dislocation, it is assumed that the two half-planes have identical shear moduli but distinct Poisson's ratios. An exact closed-form expression for the image force acting on the edge dislocation is obtained. The image force is found to vary with the direction of the Burgers vector of the edge dislocation due to the influence of interface roughness. [ABSTRACT FROM AUTHOR]

We prove that it is possible to maintain an internal uniform hydrostatic stress field within a non-elliptical inhomogeneity in the neighborhood of a non-circular inhomogeneity when the surrounding matrix is subjected to uniform remote in-plane stresses. The non-circular inhomogeneity and the matrix have a common shear modulus but distinct Poisson's ratios. The given non-circular shapes of the inhomogeneity include a Booth's lemniscate, a generalized Booth's lemniscate and a cardioid. Our analysis indicates that the uniform hydrostatic field inside the non-elliptical inhomogeneity is unaffected by the existence of the nearby non-circular inhomogeneity whereas the non-elliptical shape of the inhomogeneity is caused solely by the presence of the non-circular inhomogeneity. Numerical examples are presented to demonstrate the general solutions obtained in each of the three non-circular shapes of the inhomogeneity. • Internal uniform stress in non-elliptic inhomogeneity near non-circular inhomo. • Non-circular shapes include Booth's leminiscate and cardoid. • Uniform field in non-elliptical inhomogeneity unaffected by nearby inhomogeneity. • Non-elliptical shape of inhomogeneity caused by presence of non-circular inhomo. • Numerical examples are presented for three non-circular shapes of inhomogeneity. [ABSTRACT FROM AUTHOR]

Highlights: [•] The anions are stabilized by additional charges on the nuclei. [•] The energy dependence of anions and neutrals on nuclear charges are calculated by ab initio methods. [•] Resonance energies and widths are obtained from the energy data by analytical continuation with Padé approximation. [•] The resonance energies and widths of amino acids are compared with Nestmann–Peyerimhoff’s method and with experiment. [•] The resonance energies and (widths) of formic acid monomer and dimer are 2.09 (0.33)eV and 1.7 (0.13)eV, respectively. [ABSTRACT FROM AUTHOR]

Abstract: Further to a recent controversy on whether the differential transformation method (DTM) for solving a differential equation is purely and solely the traditional Taylor series method, it is emphasized that the DTM is currently used, often only, as a technique for (analytically) calculating the power series of the solution (in terms of the initial value parameters). Sometimes, a piecewise analytic continuation process is implemented either in a numerical routine (e.g., within a shooting method) or in a semi-analytical procedure (e.g., to solve a boundary value problem). Emphasized also is the fact that, at the time of its invention, the currently-used basic ingredients of the DTM (that transform a differential equation into a difference equation of same order that is iteratively solvable) were already known for a long time by the “traditional”-Taylor-method users (notably in the elaboration of software packages – numerical routines – for automatically solving ordinary differential equations). At now, the defenders of the DTM still ignore the, though much better developed, studies of the “traditional”-Taylor-method users who, in turn, seem to ignore similarly the existence of the DTM. The DTM has been given an apparent strong formalization (set on the same footing as the Fourier, Laplace or Mellin transformations). Though often used trivially, it is easily attainable and easily adaptable to different kinds of differentiation procedures. That has made it very attractive. Hence applications to various problems of the Taylor method, and more generally of the power series method (including noninteger powers) has been sketched. It seems that its potential has not been exploited as it could be. After a discussion on the reasons of the “misunderstandings” which have caused the controversy, the preceding topics are concretely illustrated. It is concluded that, for the sake of clarity, when the DTM is applied to ODEs, it should be mentioned that the DTM exactly coincides with the traditional Taylor method, contrary to what is currently written. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problem of numerical analytic continuation of an analytic function on a strip domain , where the data is given approximately only on the real axis . This problem is severely ill-posed: the solution does not depend continuously on the given data. A novel method (filtering) is used to solve this problem and an optimal error estimate with Hölder type is proved. Numerical examples show that this method works effectively. [Copyright &y& Elsevier]

Abstract: We compare and discuss the respective efficiency of three methods (with two variants for each of them), based respectively on Taylor (Maclaurin) series, Padé approximants and conformal mappings, for solving quasi-analytically a two-point boundary value problem of a nonlinear ordinary differential equation (ODE). Six configurations of ODE and boundary conditions are successively considered according to the increasing difficulties that they present. After having indicated that the Taylor series method almost always requires the recourse to analytical continuation procedures to be efficient, we use the complementarity of the two remaining methods (Padé and conformal mapping) to illustrate their respective advantages and limitations. We emphasize the importance of the existence of solutions with movable singularities for the efficiency of the methods, particularly for the so-called Padé–Hankel method. (We show that this latter method is equivalent to pushing a movable pole to infinity.) For each configuration, we determine the singularity distribution (in the complex plane of the independent variable) of the solution sought and show how this distribution controls the efficiency of the two methods. In general the method based on Padé approximants is easy to use and robust but may be awkward in some circumstances whereas the conformal mapping method is a very fine method which should be used when high accuracy is required. [Copyright &y& Elsevier]

Abstract: We investigate the light-front zero-mode contribution to the weak transition form factors between pseudoscalar and vector mesons using a covariant fermion field theory model in dimensions. In particular, we discuss the form factors and which have been suspected to have the zero-mode contribution in the frame. While the zero-mode contribution in principle depends on the form of the vector meson vertex , the form factor is found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor of the struck quark with the power . Although the form factor is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex term or from the other term just with a constant D (i.e. ), but not with the momentum-dependent denominator (i.e. with ). We identify the zero-mode contribution to and incorporate it as a convolution of the zero-mode operator with the initial- and final-state light-front wave functions. The covariance (i.e. frame independence) of our model has been checked by performing the light-front calculations both in the and frames. We present our numerical result of the transition for an explicit demonstration of our findings. [Copyright &y& Elsevier]

Abstract: Numerical analytic continuation is, in general, an ill-posed problem and some special regularization methods are needed. In this paper we apply the approximate inverse method to deal with the problem in a strip domain in complex plane, the data is known approximately only on the line . Error estimate between the exact and approximate solution with regularization parameter selected by both a priori and a posteriori strategy are provided, respectively. Numerical results show that the method works effectively, and can be a competitive alternative to existing method for the problem. [Copyright &y& Elsevier]