55,905 research outputs found
A Generic Framework for Higher-Order Generalizations
We consider a generic framework for anti-unification of simply typed lambda terms. It helps to compute generalizations which contain maximally common top part of the input expressions, without nesting generalization variables. The rules of the corresponding anti-unification algorithm are formulated, and their soundness and termination are proved. The algorithm depends on a parameter which decides how to choose terms under generalization variables. Changing the particular values of the parameter, we obtained four new unitary variants of higher-order anti-unification and also showed how the already known pattern generalization fits into the schema
Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity
Models of cosmological inflation resembling the Starobinsky R + R^2 model
emerge naturally among the effective potentials derived from no-scale
SU(N,1)/SU(N) x U(1) supergravity when N > 1. We display several examples in
the SU(2,1)/SU(2) x U(1) case, in which the inflaton may be identified with
either a modulus field or a matter field. We discuss how the modulus field may
be stabilized in models in which a matter field plays the role of the inflaton.
We also discuss models that generalize the Starobinsky model but display
different relations between the tilt in the spectrum of scalar density
perturbations, n_s, the tensor-to-scalar ratio, r, and the number of e-folds,
N_*. Finally, we discuss how such models can be probed by present and future
CMB experiments.Comment: 23 pages, 3 figure
Classical R-Operators and Integrable Generalizations of Thirring Equations
We construct different integrable generalizations of the massive Thirring
equations corresponding loop algebras in
different gradings and associated ''triangular'' -operators. We consider the
most interesting cases connected with the Coxeter automorphisms, second order
automorphisms and with ''Kostant-Adler-Symes'' -operators. We recover a
known matrix generalization of the complex Thirring equations as a partial case
of our construction.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Non-Abelian fields in AdS spacetime: axially symmetric, composite configurations
We construct new finite energy regular solutions in Einstein-Yang-Mills-SU(2)
theory. They are static, axially symmetric and approach at infinity the anti-de
Sitter spacetime background. These configurations are characterized by a pair
of integers , where is related to the polar angle and to the
azimuthal angle, being related to the known flat space monopole-antimonopole
chains and vortex rings. Generically, they describe composite configurations
with several individual components, possesing a nonzero magnetic charge, even
in the absence of a Higgs field. Such Yang-Mills configurations exist already
in the probe limit, the AdS geometry supplying the attractive force needed to
balance the repulsive force of Yang-Mills gauge interactions. The gravitating
solutions are constructed by numerically solving the elliptic
Einstein-DeTurck--Yang-Mills equations. The variation of the gravitational
coupling constant reveals the existence of two branches of gravitating
solutions which bifurcate at some critical value of . The lower energy
branch connects to the solutions in the global AdS spacetime, while the upper
branch is linked to the generalized Bartnik-McKinnon solutions in
asymptotically flat spacetime. Also, a spherically symmetric, closed form
solution is found as a perturbation around the globally anti-de Sitter vacuum
state.Comment: 30 pages, 15 figure
Integrable Euler top and nonholonomic Chaplygin ball
We discuss the Poisson structures, Lax matrices, -matrices, bi-hamiltonian
structures, the variables of separation and other attributes of the modern
theory of dynamical systems in application to the integrable Euler top and to
the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio
Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials
The concept of cyclic tridiagonal pairs is introduced, and explicit examples
are given. For a fairly general class of cyclic tridiagonal pairs with
cyclicity N, we associate a pair of `divided polynomials'. The properties of
this pair generalize the ones of tridiagonal pairs of Racah type. The algebra
generated by the pair of divided polynomials is identified as a higher-order
generalization of the Onsager algebra. It can be viewed as a subalgebra of the
q-Onsager algebra for a proper specialization at q the primitive 2Nth root of
unity. Orthogonal polynomials beyond the Leonard duality are revisited in light
of this framework. In particular, certain second-order Dunkl shift operators
provide a realization of the divided polynomials at N=2 or q=i.Comment: 32 pages; v2: Appendices improved and extended, e.g. a proof of
irreducibility is added; v3: version for Linear Algebra and its Applications,
one assumption added in Appendix about eq. (A.2
On bi-integrable natural Hamiltonian systems on the Riemannian manifolds
We introduce the concept of natural Poisson bivectors, which generalizes the
Benenti approach to construction of natural integrable systems on the
Riemannian manifolds and allows us to consider almost the whole known zoo of
integrable systems in framework of bi-hamiltonian geometry.Comment: 24 pages, LaTeX with AMSfonts (some new references were added
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