Active Learning Method (ALM) is a soft computing method used for modeling and control based on fuzzy logic. All operators defined for fuzzy sets must serve as either fuzzy S-norm or fuzzy T-norm. Despite being a powerful modeling method, ALM does not possess operators which serve as S-norms and T-norms which deprive it of a profound analytical expression/form. This paper introduces two new oper...

For any non-negative integer v we construct explicitly ⌊v2⌋+1 independent covariant bilinear differential operators from Jk,m × Jk′,m′ to Jk+k′+v,m+m′ . As an application we construct a covariant bilinear differential operator mapping S (2) k ×S (2) k′ to S (2) k+k′+v. Here Jk,m denotes the space of Jacobi forms of weight k and index m and S (2) k the space of Siegel modular forms of degree 2 a...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

and Applied Analysis 3 Lemma 5. The operators S α and A α have the following properties: (i) for any fixed t ≥ 0 and any x ∈ X β , one has the operators S α (t) and A α (t) which are linear and bounded operators; that is, for any x ∈ X β , 󵄩󵄩󵄩󵄩Sα (t) x 󵄩󵄩󵄩󵄩β ≤ M‖x‖β, 󵄩󵄩󵄩󵄩Aα (t) x 󵄩󵄩󵄩󵄩β ≤ M Γ (α) ‖x‖ β ; (12) (ii) the operatorsS α (t) andA α (t) are strongly continuous for all t ≥ 0; (iii) S α (...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

Part I proved that for every quasivariety K of structures (which may have both operations and relations) there is a semilattice S with operators such that the lattice of quasiequational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+, 0,F). It is known that if S is a join semilattice with 0 (and no operators), then there is a quasivariety Q such that ...

In order to study vertex operators for the Type IIB superstring on AdS space, we derive supersymmetric constraint equations for the vertex operators in AdS3 × S backgrounds with Ramond-Ramond flux, using Berkovits-Vafa-Witten variables. These constraints are solved to compute the vertex operators and show that they satisfy the linearized D = 6, N = (2, 0) equations of motion for a supergravity ...

We prove a generalization to the case of s × s matrix linear differential operators of the classical theorem of E. Cotton giving necessary and sufficient conditions for equivalence of eigenvalue problems for scalar linear differential operators. The conditions for equivalence to a matrix Schrödinger operator are derived and formulated geometrically in terms of vanishing conditions on the curvat...