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Consider an absolutely simple abelian variety A defined over a number field K. For most places v of K, we study how the reduction Av of A modulo v splits up to isogeny. Assumingthe Mumford–Tate conjec...
Old and new reductions of dispersionless Toda hierarchy
dispersionless Toda hierarchy finite-variable reduction waterbag model Landau-Ginzburg potential Lowner equations
2012/6/21
Two types of finite-variable reductions of the dispersionless Toda hierarchy are considered in the geometric perspectives. The reductions are formulated in terms of "Landau-Ginzburg potentials" that p...
Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy
Dunajski-Tod equation reductions of the generalized dispersionless 2DTL hierarchy Exactly Solvable and Integrable Systems
2012/4/26
We transfer the scheme for constructing differential reductions recently developed for the Manakov-Santini hierarchy to the case of the two-component generalization of dispersionless 2DTL hierarchy. W...
On some curve singularity invariants and reductions
adeles motivic integration reduction of algebraic curves zeta functions
2011/8/24
Abstract: This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta functio...
Minimal Reductions and Cores of Edge Ideals
edge ideal even cycles minimal reductions core
2011/2/28
We study minimal reductions of edge ideals of graphs containing a unique even cycle, and determine restrictions on the coefficients of the generators of these minimal reductions.
Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
non-recursive form symmetry factorization semi-invertible map criterion
2010/12/28
A higher order difference equation may be generally defined in an arbitrary nonempty set S as:
fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
non-recursive form symmetry factorization semi-invertible map criterion
2011/3/4
A higher order difference equation may be generally defined in an arbitrary nonempty set S as:
fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
Thirty years of studies of integrable reductions of Einstein's field equations
integrable reductions Einstein's field equations
2010/12/27
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made...
Homotopy invariance for homology of linear groups: reductions and the rank two case
linear groups the rank two case
2010/11/24
We discuss the problem of homotopy invariance for homology of linear groups. Some reductions we are able to make show that homotopy invariance for linear groups follows from contractibility of a cert...
Interpolating' differential reductions of multidimensional integrable hierarchies
differential reductions multidimensional integrable hierarchies
2010/11/10
We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the ...
Thirty years of studies of integrable reductions of Einstein's field equations
Einstein equations string gravity supergravity integrability
2010/12/20
More than thirty years passed since the first discoveries of various aspects of integrability
of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein- Maxwell equations were made...
Inducing Barbero-Immirzi Connections along SU(2)-reductions of Bundles on Spacetime
Barbero-Immirzi Connections Bundles Spacetime
2010/12/20
We shall present here a general apt technique to induce connections along bundle reductions
which is different from the standard restriction. The technique is a generalization of the mechanism presen...
Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions
illiquid market nonlinearity explicit solutions Liegroup analysis
2010/4/27
We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study t...
New Reductions and Nonlinear Systems for 2D Schrodinger Operators
Nonlinear Systems Dubrovin, I.Krichever, S.Novikov 2D Schrodinger Operators
2010/4/1
New Completely Integrable (2+1)-System is studied. It is based on the so-called L-A-B-triples $L_t=[H,L]-fL$ where L is a 2D Schrodinger Operator. This approach was invented by S.Manakov and B.Dubrovi...
Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models
multicomponent nonlinear Schrodinger equations scattering method soliton interactions
2010/4/1
We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces and their reductions. We briefly outline the direct and the inverse scat...