We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky’s (2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity of the hierarchy, which is related to the vertex operator representation of the toroidal Lie algebra sl 2 .

We present the main ideas of the proof of the following result: The characteristic function of the unit disc in R is the symbol of a bounded bilinear multiplier operator from L1(R) × L2(R) into L(R) when 2 ≤ p1, p2 < ∞ and 1 < p = p1p2 p1+p2 ≤ 2.

Four-point correlation functions of hypermultiplet bilinear composites are analysed in N = 2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is shown that the complete amplitude is determined by a single arbitrary function of the two conformal cross-ratios of the space-time variables.

We complete the one loop renormalization of the HQET lagrangian at O(1/m3Q) including four fermion operators with two heavy and two light quark fields in the operator basis. It is shown that as a consequence the short distance coefficients of the operators bilinear in the heavy quark field receive nontrivial corrections. email: [email protected]

A concept of quantum triad and its solution is introduced. It represents a common framework for several situations where we have a quantale with a right module and a left module, provided with a bilinear inner product. Examples include Van den Bossche quantaloids, quantum frames, simple and Galois quantales, operator algebras, or orthomodular lattices.

We present first results from a simulation of quenched overlap fermions with improved gauge field action. Among the quantities we study are the spectral properties of the overlap operator, the chiral condensate and topological charge, quark and hadron masses, and selected nucleon matrix elements. To make contact with continuum physics, we compute the renormalization constants of quark bilinear ...

C. Muscalu, J. Pipher, T. Tao and C. Thiele proved in [27] that the standard bilinear and bi-parameter Hilbert transform does not satisfy any L estimates. They also raised a question asking if a bilinear and bi-parameter multiplier operator defined by Tm(f1, f2)(x) := ∫ R m(ξ, η)f̂1(ξ1, η1)f̂2(ξ2, η2)e 1122dξdη satisfies any L estimates, where the symbol m satisfies |∂ ξ ∂ ηm(ξ, η)| . 1 dist(ξ,Γ1...

(defined for Schwarzt test functions f and g in ) extends to a bounded bilinear operator from Lp1 (R)×Lp2 (R) into Lp3 (R). The theory of these multipliers has been tremendously developed after the results proved by Lacey and Thiele (see [16, 18, 17]) which establish that m(ξ,ν) = sign(ξ +αν) is a (p1, p2)-multiplier for each triple (p1, p2, p3) such that 1 < p1, p2 ≤∞, p3 > 2/3, and each α∈R \...

We consider the Schr\"odinger operator on halfline with potential $(m^2-\frac14)\frac1{x^2}$, often called Bessel operator. assume that $m$ is complex. study domains of various closed homogeneous realizations In particular, we prove domain its minimal realization for $|\Re(m)|<1$ and unique $\Re(m)>1$ coincide second order Sobolev space. On other hand, if $\Re(m)=1$ space a subspace infinite co...

As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...