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Перегляд Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11, випуск за цей рік за назвою

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Перегляд Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11, випуск за цей рік за назвою

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  • A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation 
    Ujino, H.; Yajima, T. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    The s2s-OVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV) model and the slow-to-start (s2s) model, which is introduced in the framework of the ultradiscretization method. Inverse ultradiscretization as ...
  • A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian 
    Rösler, M.; Voit, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials ...
  • A Classical Limit of Noumi's q-Integral Operator 
    Borodin, A.; Corwin, I.; Remenik, D. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We demonstrate how a known Whittaker function integral identity arises from the t=0 and q→1 limit of the Macdonald polynomial eigenrelation satisfied by Noumi's q-integral operator.
  • A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have Q-Forms 
    Morris, D.W. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact ...
  • A Combinatorial Formula for Certain Elements of Upper Cluster Algebras 
    Lee, K.; Li, L.; Mills, M.R. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using ...
  • Algebro-Geometric Solutions of the Generalized Virasoro Constraints 
    Plaza Martín, F.J. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We will describe algebro-geometric solutions of the KdV hierarchy whose τ-functions in addition satisfy a generalization of the Virasoro constraints (and, in particular, a generalization of the string equation). We show ...
  • Ambiguities in a Problem in Planar Geodesy 
    Schicho, J.; Gallet, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining ...
  • An Asymmetric Noncommutative Torus 
    Dąbrowski, L.; Sitarz, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the ...
  • An Integrability Condition for Simple Lie Groups II 
    Min-Oo, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    It is shown that a simple Lie group G (≠SL₂) can be locally characterised by an integrability condition on an Aut(g) structure on the tangent bundle, where Aut(g) is the automorphism group of the Lie algebra of G. The ...
  • A Perturbation of the Dunkl Harmonic Oscillator on the Line 
    Álvarez López, J.A.; Calaza, M.; Franco, C. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    Let Jσ be the Dunkl harmonic oscillator on R (σ>−1/2. For 0<u<1 and ξ>0, it is proved that, if σ>u−1/2, then the operator U=Jσ+ξ|x|⁻²u, with appropriate domain, is essentially self-adjoint in L²(R,|x|²σdx), the Schwartz ...
  • BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras 
    Graziani, G.; Makhlouf, A.; Menini, C.; Panaite, F. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β:A→A such that α(a)(bc)=(ab)β(c), for all a,b,c∈A. This concept arose in the study of algebras in so-called ...
  • Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity 
    Kasman, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    A wave function of the N-component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN-dimensional space of finitely-supported vector distributions. This wave ...
  • Bosonizations of sl₂ and Integrable Hierarchies 
    Bakalov, B.; Fleisher, D. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We construct embeddings of sl₂ in lattice vertex algebras by composing the Wakimoto realization with the Friedan-Martinec-Shenker bosonization. The Kac-Wakimoto hierarchy then gives rise to two new hierarchies of integrable, ...
  • Certain Integrals Arising from Ramanujan's Notebooks 
    Berndt, B.C.; Straub, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    In his third notebook, Ramanujan claims the specific. In a following cryptic line, which only became visible in a recent reproduction of Ramanujan's notebooks, Ramanujan indicates that a similar relation exists if logx ...
  • Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A 
    Kanakubo, Y.; Nakashima, T. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    Let G be a simply connected simple algebraic group over C, B and B− be two opposite Borel subgroups in G and W be the Weyl group. For u, v∈W, it is known that the coordinate ring C[Gu,v] of the double Bruhat cell Gu,v=BuB∩B−vB− ...
  • (Co)isotropic Pairs in Poisson and Presymplectic Vector Spaces 
    Lorand, J.; Weinstein, А. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of finite-dimensional Poisson vector spaces. For this it is convenient to dualize; we work with pairs of isotropic subspaces of ...
  • Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras 
    Magazev, A.A.; Mikheyev, V.V.; Shirokov, I.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    Methods of construction of the composition function, left- and right-invariant vector fields and differential 1-forms of a Lie group from the structure constants of the associated Lie algebra are proposed. It is shown that ...
  • Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials 
    Grandati, Y.; Quesne, C. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    We construct rational extensions of the Darboux-Pöschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are ...
  • Constructing Involutive Tableaux with Guillemin Normal Form 
    Smith, A.D. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan-Kähler theorem. Guillemin normal form establishes ...
  • Cyclic Homology and Quantum Orbits 
    Maszczyk, T.; Sütlü, S. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    A natural isomorphism between the cyclic object computing the relative cyclic homology of a homogeneous quotient-coalgebra-Galois extension, and the cyclic object computing the cyclic homology of a Galois coalgebra with ...

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