On the geometry of supermanifolds with even and odd Kählerian structures

Even and odd Kählerian structures are constructed on supermanifolds associated with the tangent bundles of Kählerian manifolds. Mechanics that are bi-Hamiltonian with respect to the corresponding Poisson brackets are found; they determine Killing vectors of the Kählerian structures. An analog of the operator in the Batalin—Vilkovisky quantization method is constructed; it corresponds to the divergence operator of the base manifold.Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 96, No. 1, pp. 140–149, July, 1993.     

Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc.     

1,2,4-Triazole-Based Hybrid Heterocyclic Carbaldehyde Hydrazones and Their Effect on DNA Methylation Level

Russian Journal of Organic Chemistry - While developing new approaches to the design of biologically active compounds based on 1,2,4-triazole, a number of new hydrazones containing...     

Exact results in the two-dimensional U(1)-symmetric Thirring model

A systematic study of the ground state, excitation spectrum, and “isospin-magnetic” properties of the U(1)-Thirring model, based on its exact (Bethe-ansatz) solution, is presented. The exact results obtained for the renormalized mass spectrum in all sectors of the phase diagram of the model allow us to observe a continuous transition from the weak-coupling theory into a strong-coupling (asymptotically free) regime, taking place by varying the coupling constants, g and g. Some questions concerning universality and the relation to other models are discussed.     

Lagrangian model of a massless particle on spacelike curves

We consider a model of a massless particle in a D-dimensional space with the Lagrangian proportional to the Nth extrinsic curvature of the world line. We present the Hamiltonian formulation of the system and show that its trajectories are spacelike curves satisfying the conditions k _N+a =k _N-a and k _2N =0, a=1,,N-1, where N[(D-2)/2]. The first N curvatures take arbitrary values, which is a manifestation of N+1 gauge degrees of freedom; the corresponding gauge symmetry forms an algebra of the W type. This model describes D-dimensional massless particles, whose helicity matrix has N coinciding nonzero weights, while the remaining [(D-2)/2]-N weights are zero. We show that the model can be extended to spaces with nonzero constant curvature. It is the only system with the Lagrangian dependent on the world-line extrinsic curvatures that yields irreducible representations of the Poincaré group.     

Penetration depth and pinning effects in high-Tc superconductors La-Sr-Cu-O and (Er,Ho)-Ba-Cu-O studies by μSR

We report the results of μSR investigations of the ceramic samples La_2-xSr_xCuO_4-σ (x=0.1, 0.15, 0.25) and ReBa₂Cu₃O_7-σ (Re=Er, Ho, Y_0.5Ho_0.5) in the external magnetic field 0–800 Oe. The measurements were performed by the ZFC and FC methods. The irreversibility effects were studied at several temperatures by measuring the mean value and the width of the magnetic field distribution on the muon in the step by step procedure of increasing and subsequent decreasing of the external field. The temperature dependences of the magnetic penetration depth perpendicular to the basal plane λ_⊥ were obtained. For the lanthanum sample with 0.15 of Sr its value at the zero temperature is λ_⊥ (0)=2400 Å, for Er-Ba-Cu-O λ_⊥ (0)=1600 Å.     

Hamiltonian formalism for particles with a generalized rigidity

The Hamiltonian formalism is developed for mechanical systems described by reparametrization-invariant Lagrangians dependent on the external curvatures of a world line. The complete sets of constraints are constructed for the Lagrangians quadratic in the external curvatures, the Lagrangians proportional to an arbitrary external curvature, and the Lagrangians linear in the first two curvatures. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 1, pp. 130–139, October, 1998.     

Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications

We prove that the Schrödinger equation is approximately controllable in Sobolev spaces Hs$H^s$, s>0$s>0$, generically with respect to the potential. We give two applications of this result. First, in the case of one space dimension, combining our result with a local exact controllability property, we get the global exact controllability of the system in higher Sobolev spaces. Then we prove that the Schrödinger equation with a potential which has a random time-dependent amplitude admits at most one stationary measure on the unit sphere S   in L²$L^2$.     

Spinful fermionic ladders at incommensurate filling: Phase diagram,local perturbations,and ionic potentials

We study the effect of external potential on transport properties of the fermionic two-leg ladder model. The response of the system to a local perturbation is strongly dependent on the ground state properties of the system and especially on the dominant correlations. We categorize all phases and transitions in the model (for incommensurate filling) and introduce “hopping-driven transitions” that the system undergoes as the inter-chain hopping is increased from zero. We also describe the response of the system to an ionic potential. The physics of this effect is similar to that of the single impurity, except that the ionic potential can affect the bulk properties of the system and in particular induce true long range order.