the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...

It is shown that any real and even function of the phase (time) operator has a self-adjoint extension and its relation to the general phase operator problem is analyzed. Typeset using REVTEX E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]

We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on F is order continuous. We prove as well that if S : E → E is dominated by a disjointly strictly singular operator, then S2 is disjointly strictly singular.

Let M be a complete Riemannian manifold and D : C∞ 0 (E) → C∞ 0 (F ) a first order differential operator acting between sections of the hermitian vector bundles E, F . Moreover, let V : C∞(E) → L∞ loc (E) be a self–adjoint zero order differential operator. We give a sufficient condition for the Schrödinger operator H = DD + V to be essentially self–adjoint. This generalizes recent work of I. Ol...

where E: D(E) —• S, D(E) C S, is a linear not necessarily bounded operator in a real Hilbert space S with 1 < dim W < °°, W = ketE, and N: S —> S is a continuous nonlinear operator. In terms of the alternative method (see Cesari [1] , [2]), let P: S —> S be the orthogonal projector with range PS = S0 = W = ker E, let St = (I -P)S, and let S1 be also the range of E. Let H: Sx -—• 5'1 denote a li...

We derive a differential equation for the modified Feynman propagator describing timedependent measurements or histories continuous in time. We obtain an exact series solution and its applications. Suppose the system is initially in a state with density operator ρ(0) and the projection operator E(t) = U(t)EU (t) is measured continuously from t = 0 to T , where E is a projector obeying Eρ(0)E = ...

THEOREM 4. Let a be an arbitrarily often differentiable function on the real line having countably many isolated zeros s1, S2, . . . offinite orders ml, M2, ..., respectively. Denote by A the multiplication operator mapping x into Ax = ax and let E be any linear space satisfying X = E (3 R*. Then there is a unique continuous linear op rator A-l :X -X whose range is orthogonal to E and is such t...

For the approximation of fixed points of a nonexpansive operator T in a uniformly convex Banach space E the convergence of the Mann-Toeplitz iteration x„+1 = a„T(x„) + (1 a„)xñ is studied. Strong convergence is established for a special class of operators T. Via regularization this result can be used for general nonexpansive operators, if E possesses a weakly sequentially continuous duality map...