the purpose of this paper is to introduce the concept of l-fuzzybilinear operators. we obtain a decomposition theorem for l-fuzzy bilinearoperators and then prove that a l-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by s.e.rodabaugh (1991).finally we discuss the continuity of l-fuzzy bilinear operators.

This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...

Let Ω be a bounded domain in C. Let R(Ω) (usually A(Ω) or H(Ω)) be a ring of holomorphic functions that contains the polynomials, and let p = (p1, . . . , pn) be a point in Ω. Recall the Gleason problem, cf. [8]: is the maximal ideal in R(Ω) consisting of functions vanishing at p, generated by the coordinate functions (z1 − p1), . . . , (zn − pn) ? One says that a domain Ω has the Gleason R-pro...

In the present paper, we are with integrable discretization of a modified Camassa–Holm (mCH) equation linear dispersion term. The key construction is semidiscrete analog for set bilinear equations mCH equation. First, show that these and their determinant solutions either in Gram-type or Casorati-type can be reduced from discrete Kadomtsev–Petviashvili (KP) through Miwa transformation. Then, by...

Stabilizer states and graph find application in quantum error correction, measurement-based computation various other concepts information theory. In this work, we study party-local Clifford (PLC) transformations among stabilizer states. These arise as a physically motivated extension of local operations networks with access to bipartite entanglement between some the nodes network. First, show ...

The equivalence of continuous-/discrete-time autoregressive-moving average (ARMA) systems is considered in this paper. For the integer-order cases, interrelations between defined by continuous-time (CT) differential and discrete-time (DT) difference equations are found, leading to formulae relating partial fractions continuous discrete transfer functions. Simple transformations presented allow ...

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.