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 ...

(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 \...

Explicit counterexamples to bilinear estimates related to the Benjamin-Ono equation in the periodic setting are calculated for functions of zero mean value. As a consequence, certain bilinear estimates fail to hold in spite of the analyticity of the flow map. The latter has been shown recently by L. Molinet.

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 ...

We study L (or Lr,∞) boundedness for bilinear translation-invariant operators with nonnegative kernels acting on functions on R. We prove that if such operators are bounded on some products of Lebesgue spaces, then their kernels must necessarily be integrable functions on R, while via a counterexample we show that the converse statement is not valid. We provide certain necessary and some suffic...

We introduce a class of reductions the two-component KP hierarchy, which includes Hirota-Ohta system hierarchy. The description reduced hierarchies is based on Hirota bilinear identity and an extra relation characterising reduction. derive reduction conditions in terms Lax operator higher linear operators as well basic equations.

where A is the generator of a strongly continuous semigroup (S(t))t≥0 on the state space Z =: L(Ω) endowed with its natural inner product 〈·, ·〉, and the corresponding norm ‖ · ‖, B : Z → Z is a linear bounded operator, while u ∈ L[0, T ] is a control. The main result on the controllability of the system (1) is due to the pioneering work by Ball et al. (1982), which shows that, under the above-...

We are proving L(R) × L(R) → L(R) bounds for the bilinear Hilbert transform HΓ along curves Γ = (t,−γ(t)) with γ being a smooth “non-flat” curve near zero and infinity.