2,616 research outputs found
Functionals of the Peierls - Froehlich type and the variational principle for the Whitham equation
No full textHyperelliptic Kleinian functions and applications by V. M. Buchstaber, V. Z. Enolskii, and D. V. Leikin Functionals of the Peierls-Frohlich type and the variational principle for the Whitham equations by B. Dubrovin Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples by I. A. Dynnikov An invariant of integral homology 3-spheres which is universal for all finite type invariants by T. Q. Le Krichever-Novikov algebras and the cohomology of the algebra of meromorphic vector fields by D. V. Millionshchikov Exactly solvable two-dimensional Schrodinger operators and Laplace transformations by S. P. Novikov and A. P. Veselov Modified Novikov-Veselov equation and differential geometry of surfaces by I. A. Taimanov Supermanifold forms and integration. A dual theory by T. Voronov On hyperplane sections of periodic surfaces by A. Zorich
On the Morse–Novikov Cohomology of blowing up complex manifolds
Get PDFInspired by the recent works of S. Rao–S. Yang–X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse–Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse–Novikov cohomology by introducing the relative Morse–Novikov cohomology group via sheaf cohomology theory and presenting the explicit isomorphism therein
Complexes and exactness of certain Artin groups
No full textIn his work on the Novikov conjecture, Yu introduced Property A as a readily verified criterion implying coarse embeddability. Studied subsequently as a property in its own right, Property A for a discrete group is known to be equivalent to C*-exactness of the reduced C*-algebra, and to the amenability of the action of the group on its Stone-Cech compactification. In this paper we study exactness for groups acting on a finite dimensional CAT(0) cube complex. We apply our methods to show that Artin groups of type FC are exact. While many discrete groups are known to be exact the question of whether every Artin group is exact remains open
Automorphic Lie algebras with dihedral symmetry
No full textThe concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. Automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl2(C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits
Selective transannular ring transformations in azirino-fused eight-membered O,N- or S,N-heterocycles
No full textThe first examples of transannular ring transformations in azirino-fused eight-membered O,N- or S,N-heterocycles involving selective aziridine ring opening and medium-sized ring contraction are described, which provide an access to functionalized 1,4-benzox(thi)azines or 1,3-benzox(thi)azoles
On a Solution of the Optimal Stopping Problem for Processes with Independent Increments
Get PDFWe discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time through a level defined as the largest root of the Appell function associated with the maximum of the underlying process.
Flag Manifolds and the Landweber-Novikov Algebra
No full textWe investigate geometrical interpretations of various structure maps associated with the Landweber{Novikov algebra S and its integral dual S . In particular, we study the coproduct and antipode in S , together with the left and right actions of S on S which underly the construction of the quantum (or Drinfeld) double D(S). We set our realizations in the context of double complex cobordism, utilizing certain manifolds of bounded flags which generalize complex projective space and may be canonically expressed as toric varieties. We discuss their cell structure by analogy with the classical Schubert decomposition, and detail the implications for Poincare duality with respect to double cobordism theory; these lead directly to our main results for the Landweber-Novikov algebra
Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets
Get PDFInternational audienceWe compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin–Novikov type with independent variables. We find that the second and third cohomology groups are generically non-vanishing in . Hence, in contrast with the case, the deformation theory in the multivariable case is non-trivial
Fermionic Novikov algebras admitting invariant non-degenerate symmetric bilinear forms
Get PDFsummary:Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian superoperator in a supervariable. In this paper, we show that fermionic Novikov algebras equipped with invariant non-degenerate symmetric bilinear forms are Novikov algebras
1,3-dipolar cycloaddition of difluoro-substituted azomethine ylides. Synthesis and transformations of 2-fluoro-4,5-dihydropyrroles
No full text2-Fluoro-4,5-dihydropyrrole-3,4-dicarboxylic acid derivatives were obtained by reaction of difluorocarbene with N-substituted ketone imines in the presence of fumaronitrile, maleonitrile, or dimethyl maleate. The reaction involves intermediate formation of azomethine ylides and their subsequent cycloaddition at the double bond. 11H-Dibenz[b,e]azepine and 3,.4-dihydroisoquinolines react with difluorocarbene in the presence of fumaronitrile to give fluoro-substituted dibenzo[c,f]pyrrolo[1,2-a]azepine and pyrrolo[2,1-a]-isoquinoline derivatives. Treatment of 2-fluoro-4,5-dihydropyrrole-3,4-dicarbonitrile with amines and alkoxides affords the corresponding 2-amino- and 2-alkoxy derivatives, while its reactions with hydrazine hydrate and benzimidamide lead to formation of substituted pyrrolo[2,3-c]pyrazole and pyrrolo[2,3-d]pyrimidine derivatives
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