Authors:A.-K. Gallagher; J. Lebl; K. Ramachandran Abstract: Abstract Let \(\Omega \) be an unbounded domain in \(\mathbb {R}\times \mathbb {R}^{d}.\) A positive harmonic function u on \(\Omega \) that vanishes on the boundary of \(\Omega \) is called a Martin function. In this note, we show that, when \(\Omega \) is convex, the superlevel sets of a Martin function are also convex. As a consequence we obtain that if in addition \(\Omega \) has certain symmetry with respect to the t-axis, and \(\partial \Omega \) is sufficiently flat, then the maximum of any Martin function along a slice \(\Omega \cap (\{t\}\times \mathbb {R}^d)\) is attained at (t, 0). PubDate: 2018-01-12 DOI: 10.1007/s13324-017-0207-3

Authors:Rodica Cimpoiasu Abstract: Abstract In this paper some travelling wave solutions and conservation laws for the 2D Ricci flow model in conformal gauge are investigated. A guideline able to classify the types of solutions according to the values of some parameters is provided by making use of two versions of the auxiliary equation method. The key feature of these approaches is to take a second order linear ordinary differential equation (ODE), respectively a first order nonlinear ODE with at most an eighth-degree nonlinear term as auxiliary equations. Conserved forms of the travelling wave equation for the Ricci flow are derived through three specific approaches, namely the variational approach, the Ibragimov method for nonlinear self-adjoint differential equations and the one based upon a relationship between conserved forms and their associated symmetries. The former two methods generated similar results, while the latter one has revealed new conserved densities. PubDate: 2018-01-03 DOI: 10.1007/s13324-017-0206-4

Authors:A. Rahimi; Z. Darvishi; B. Daraby Pages: 335 - 348 Abstract: Abstract Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may not be defined. To overcome this problem, the new concept namely Q-dual for c-fusion frames will be defined and some of its properties will be investigated. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0146-4 Issue No:Vol. 7, No. 4 (2017)

Authors:Boris Rubin Pages: 349 - 375 Abstract: Abstract We transfer the results of Part I related to the modified support theorem and the kernel description of the hyperplane Radon transform to totally geodesic transforms on the sphere and the hyperbolic space, the spherical slice transform, and the spherical mean transform for spheres through the origin. The assumptions for functions are formulated in integral terms and close to minimal. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0145-5 Issue No:Vol. 7, No. 4 (2017)

Authors:Alessandro Michelangeli; Alessandro Olgiati Pages: 377 - 416 Abstract: Abstract We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schrödinger dynamics is effectively described by a system of coupled cubic non-linear Schrödinger equations, one for each component. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0147-3 Issue No:Vol. 7, No. 4 (2017)

Authors:S. Rahman; T. Hayat; B. Ahmad Pages: 417 - 435 Abstract: Abstract The flow of Sisko fluid in an annular pipe is considered. The governing nonlinear equation of an incompressible Sisko fluid is modelled. The purpose of present paper is to obtain the global classical solutions for unsteady flow of magnetohydrodynamic Sisko fluid in terms of the bounded mean oscillations norm. Uniqueness of solution is also verified. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0148-2 Issue No:Vol. 7, No. 4 (2017)

Authors:Farid Messelmi Pages: 437 - 447 Abstract: Abstract We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray–Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0151-7 Issue No:Vol. 7, No. 4 (2017)

Authors:Sergey Tychkov Pages: 449 - 458 Abstract: Abstract A two-dimensional Buckley–Leverett system governing motion of two-phase flow is considered. Travelling-wave solutions for these equations are found. Wavefronts of these solutions may be circles, lines and parabolae. Values of pressure and saturation on the wave fronts are found. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0152-6 Issue No:Vol. 7, No. 4 (2017)

Authors:Der-Chen Chang; Sheng-Ya Feng Pages: 459 - 477 Abstract: Abstract This paper is focused on the approximate procedures for the periodic solutions of the nonlinear Hamilton equation with Gaussian potential. We propose a modified rational harmonic balance method to treat conservative nonlinear equations without the requirements on small perturbation or small parameter. The different approximating orders of this scheme illustrate the excellent agreement of the approximate frequencies with the exact ones. All the numerical results reveal that this effective method can be widely applied to many other truly nonlinear differential equations. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0149-1 Issue No:Vol. 7, No. 4 (2017)

Authors:F. Soleyman; M. Masjed-Jamei; I. Area Pages: 479 - 492 Abstract: Abstract In this paper, a class of finite q-orthogonal polynomials is studied whose weight function corresponds to the inverse gamma distribution as \(q \rightarrow 1\) . Via Sturm–Liouville theory in q-difference spaces, the orthogonality of this class is proved and its norm square value is computed. Also, its general properties such as q-weight function, q-difference equation and the basic hypergeometric representation are recovered in the continuous case. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0150-8 Issue No:Vol. 7, No. 4 (2017)

Authors:Arash Ghaani Farashahi Pages: 493 - 508 Abstract: This paper presents the abstract notion of Poisson summation formulas for homogeneous spaces of compact groups. Let G be a compact group, H be a closed subgroup of G, and \(\mu \) be the normalized G-invariant measure over the left coset space G / H associated to the Weil’s formula. We prove that the abstract Fourier transform over G / H satisfies a generalized version of the Poisson summation formula. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0156-2 Issue No:Vol. 7, No. 4 (2017)

Authors:Zaitao Liang; Fanchao Kong Pages: 509 - 524 Abstract: Abstract We study the existence and multiplicity of positive periodic wave solutions for one-dimensional non-Newtonian filtration equations with singular nonlinear sources. We discuss both the attractive singular case and the repulsive singular case. The proof is based on an extension of the continuation theorem of coincidence degree theory. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0153-5 Issue No:Vol. 7, No. 4 (2017)

Authors:Mazhar Hussain Tiwana; Rab Nawaz; Amer Bilal Mann Pages: 525 - 548 Abstract: Abstract This article examines sound radiation from a hard semi-infinite duct placed symmetrically inside an acoustically lined duct. We introduce a wake on right handed region of the duct configuration to analyze sound radiation process for the trailing edge situation. The integral transforms together with Wiener–Hopf techniques render the solution of underlying problem. However expressions for field intensity involve infinite sums/products that enable solution using truncation approach. The sound radiation analysis is then observed graphically while using different choice of some pertinent parameters. It is worth mentioning that results of leading edge situation can be recovered as a limiting case. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0154-4 Issue No:Vol. 7, No. 4 (2017)

Authors:Vitor Balestro; Ákos G. Horváth; Horst Martini Pages: 549 - 575 Abstract: Abstract In this paper a special group of bijective maps of a normed plane (or, more generally, even of a plane with a suitable Jordan curve as unit circle) is introduced which we call the group of general rotations of that plane. It contains the isometry group as a subgroup. The concept of general rotations leads to the notion of flexible motions of the plane, and to the concept of Minkowskian roulettes. As a nice consequence of this new approach to motions the validity of strong analogues to the Euler-Savary equations for Minkowskian roulettes is proved. PubDate: 2017-12-01 DOI: 10.1007/s13324-016-0155-3 Issue No:Vol. 7, No. 4 (2017)

Authors:Laurent Bétermin Abstract: Abstract We study the local optimality of simple cubic, body-centred-cubic and face-centred-cubic lattices among Bravais lattices of fixed density for some finite energy per point. Following the work of Ennola (Math Proc Camb 60:855–875, 1964), we prove that these lattices are critical points of all the energies, we write the second derivatives in a simple way and we investigate the local optimality of these lattices for the theta function and the Lennard–Jones-type energies. In particular, we prove the local minimality of the FCC lattice (resp. BCC lattice) for large enough (resp. small enough) values of its scaling parameter and we also prove the fact that the simple cubic lattice is a saddle point of the energy. Furthermore, we prove the local minimality of the FCC and the BCC lattices at high density (with an optimal explicit bound) and its local maximality at low density in the Lennard–Jones-type potential case. We then show the local minimality of FCC and BCC lattices among all the Bravais lattices (without a density constraint). The largest possible open interval of density’s values where the simple cubic lattice is a local minimizer is also computed. PubDate: 2017-12-29 DOI: 10.1007/s13324-017-0205-5

Authors:Walter Bergweiler; Alexandre Eremenko Abstract: Abstract We give upper and lower bounds for the number of solutions of the equation \(p(z)\log z +q(z)=0\) with polynomials p and q. PubDate: 2017-12-27 DOI: 10.1007/s13324-017-0204-6

Authors:Yehonatan Salman Abstract: Abstract In the article of Kunyansky (Inverse Probl 23(1):373–383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in \({\mathbb {R}}^{n}\) . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in \({\mathbb {R}}^{2}\) . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates. PubDate: 2017-12-20 DOI: 10.1007/s13324-017-0203-7

Authors:Björn Gustafsson; Mihai Putinar Abstract: Abstract Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz reflection and line bundles defined on the Schottky double of a planar domain is briefly discussed in the same context. PubDate: 2017-12-13 DOI: 10.1007/s13324-017-0201-9

Authors:Zouhaïr Mouayn Abstract: Abstract We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and \( \varepsilon >0\) by replacing the coefficients \(z^{n}/\sqrt{n!}\) of the canonical coherent states by polyanalytic functions. These states solve the identity of the states Hilbert space of the harmonic oscillator at the limit \(\varepsilon \rightarrow 0^{+}\) and obey a thermal stability property. Their wavefunctions are obtained in a closed form and their associated Bargmann-type transform is also discussed. PubDate: 2017-12-09 DOI: 10.1007/s13324-017-0202-8

Authors:Cheng Chen; Yao-Lin Jiang Abstract: Abstract In this paper Lie symmetry analysis method is applied to study nonlinear generalized Zakharov system which is the coupled nonlinear system of Schrödinger equations. With the aid of Lie point symmetry, nonlinear generalized Zakharov system is reduced into the ODEs and some group invariant solutions are obtained where some solutions are new, which are not reported in literatures. Then the bifurcation theory and qualitative theory are employed to investigate nonlinear generalized Zakharov system. Through the analysis of phase portraits, some Jacobi-elliptic function solutions are found, such as the periodic-wave solutions, kink-shaped and bell-shaped solitary-wave solutions. PubDate: 2017-11-08 DOI: 10.1007/s13324-017-0200-x