Homomorphism-Homogeneous Partially Ordered Sets

A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Nešetřil introduced a relaxed version of homogeneity: we say that a structure is homomorphism-homogeneous if every homomorphism between finite substructures of the structure extends to an endomorphism of the structure. In this paper we characterize homomorphism-homogeneous partially ordered sets (where a homomorphism between partially ordered sets A and B is a mapping f : A →B satisfying ). We show that there are five types of homomorphism-homogeneous partially ordered sets: partially ordered sets whose connected components are chains; trees; dual trees; partially ordered sets which split into a tree and a dual tree; and X ₅-dense locally bounded partially ordered sets. Supported by the Ministry od Science and Environmental Protection of the Republic of Serbia, Grant No. 144017.     

An exact (2 + 1)-dimensional optical soliton with spatially modulated nonlinearity and an external potential

An exact (2 + 1)-dimensional spatial optical soliton of the nonlinear Schrödinger equation with a spatially modulated nonlinearity and a special external potential is discovered in an inhomogeneous nonlinear medium, by utilizing the similarity transformation. Exact analytical solutions are constructed by the products of Whittaker functions and the bright and dark soliton solutions of the standard stationary nonlinear Schrödinger equation. Some examples of such composed solutions are given, in which these spatial solitons display different localized structures. Numerical calculation shows that the soliton is stable in propagating over long distances, thus also confirming the validity of the exact solution.     

Reply to the Comment on¶Low temperature specific heat of blue bronze K0.30MoO3

Eur. Phys. J. B 24, 315 (2001) In our Reply to the Comment [#!1!#] we refute the “straightforward” interpretation of the excess low-temperature specific heat, C_p, contribution we have measured in our study of CDW systems K_0.3MoO₃ and (TaSe₄)₂I [#!2!#] as originating solely from normal phonon modes. The specific sensitivity of the bump in C _p / T ³ at low temperatures to the impurity content is consistent with the increased value of the phason pinning gap while the dispersion of normal phonons remains unaffected. We ascribe at least this part of the anomaly to the phason contribution. As stated in reference [3] that the phonon density of states extracted from neutron scattering measurements is the least reliable in this energy range (<0.5 meV), we conclude that C_p measurements are more accurate for detecting the phason contribution. Received 17 April 2002 Published online 19 July 2002     

Dirac Cohomology for Lie Superalgebras

Dirac cohomology is a new tool to study representations of semisimple Lie groups and Lie algebras. The aim of this paper is to define a Dirac operator for a Lie superalgebra of Riemannian type and show that this Dirac operator has similar nature as the one for semisimple Lie algebras. As a consequence, we show how to determine the infinitesimal character of a representation by the infinitesimal character of its Dirac cohomology.     

The sixth moment of the family of Γ<Subscript>1</Subscript>(<Emphasis Type="Italic">q</Emphasis>)-automorphic <Emphasis Type="Italic">L</Emphasis>-functions

In this paper we investigate the sixth moment of the family of L-functions associated to holomorphic modular forms on GL ₂ with respect to a congruence subgroup Γ₁(q). The bound for central values averaged over the family, consistent with the Lindelöf hypothesis, is obtained for prime levels q.     

Asymptotic Behavior of the Fourth Painlevé Transcendents in the Space of Initial Values

We study the asymptotic behavior of solutions of the fourth Painlevé equation as the independent variable goes to infinity in its space of (complex) initial values, which is a generalization of phase space described by Okamoto. We show that the limit set of each solution is compact and connected and, moreover, that any solution that is not rational has an infinite number of poles and infinite number of zeros.     

Quantum Hamiltonians with Weak Random Abstract Perturbation. I. Initial Length Scale Estimate

We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube size, and consequently the number of parameters as well, tends to infinity, we derive deterministic and probabilistic variational bounds on the lowest eigenvalue, i.e., the spectral minimum, as well as exponential off-diagonal decay of the Green function at energies above, but close to the overall spectral bottom.     

Barzilai–Borwein method with variable sample size for stochastic linear complementarity problems

A smoothing method for solving stochastic linear complementarity problems is proposed. The expected residual minimization reformulation of the problem is considered, and it is approximated by the sample average approximation (SAA). The proposed method is based on sequential solving of a sequence of smoothing problems where each of the smoothing problems is defined with its own sample average approximation. A nonmonotone line search with a variant of the Barzilai–Borwein (BB) gradient direction is used for solving each of the smoothing problems. The BB search direction is efficient and low cost, particularly suitable for nonmonotone line search procedure. The variable sample size scheme allows the sample size to vary across the iterations and the method tends to use smaller sample size far away from the solution. The key point of this strategy is a good balance between the variable sample size strategy, the smoothing sequence and nonmonotonicity. Eventually, the maximal sample size is used and the SAA problem is solved. Presented numerical results indicate that the proposed strategy reduces the overall computational cost.     

Extensions of the Fill–Fishkind formula and the infimum – parallel sum relation

Recently, in (Arias ML, Corach G, Maestripieri A. Range additivity, shorted operator and the Sherman–Morrison–Woodburry formula, Linear Algebra Appl. 2015;467), authors gave a generalization of a formula by Fill and Fishkind, regarding the Moore–Penrose inverse of the sum of two matrices, in the setting of arbitrary Hilbert spaces. We consider this formula under some weaker assumptions and derive certain conclusions generalizing the mentioned result. We also extend a formula connecting the infimum of two orthogonal projections and their parallel sum to a formula connecting the star-infimum and the parallel sum of operators which need not be positive, using the concept of parallel sum that was introduced in (Antezana J, Corach G, Stojanoff D. Bilateral shorted operators and parallel sums. Linear Algebra Appl. 2006;414).