In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

In this paper, we classify almost cosymplectic 3-manifolds with pseudo-parallel characteristic Jacobi operator. The only simply connected and complete non-cosymplectic 3-manifold pseudo parallel operator is the Minkowski motion group.

We define the notion of weak relative pseudo-complement on meet semi-lattices, and we show that it is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main result is that if a complete lattice L is meet-continuous, then every closure operator on L admits weak relative pseudo-complements with respect to continuous closure operators on L.

Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce in this paper its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling and solving systems of linear differe...

In the present work we show that joint probability distribution of eigenvalues can be expressed in terms a differential operator acting on some other matrix quantities. Those quantities might diagonal or pseudo-diagonal entries as it is case for Hermitian matrices. These representations are called derivative principles. We them additive spaces Hermitian, antisymmetric, anti-self-dual, and compl...

‎in the present paper‎, ‎by making use of the differential subordination and‎ ‎superordination results of miller and mocanu‎, ‎  ‎certain classes of admissible functions ‎are determined so that subordination as well as superordination implications‎ ‎of functions associated with an integral operator hold‎. ‎additionally‎, ‎differential sandwich-type result is obtained‎.

Abstract. We develop an algorithm for the canonical computation of general Fourier integral operators whose canonical relations are graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation of the action of such operators on data in the presence of caustics. The procedure consists in the construction of a universal operat...

We construct a new variety of N = 2 supersymmetric integrable systems by junction of pseudo-differential superspace Lax operators for a = 4, N = 2 KdV and multi-component N = 2 NLS hierarchies. As an important particular case, we obtain Lax operator for N = 4 super KdV system. A similar extension of one of N = 2 super Boussinesq hierarchies is given. We also present a minimal N = 4 supersymmetr...

The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this programme, the present paper shows under which conditions the introduction of pseudo-differential boundary operators in one-loop Euclidean quantum gravity is compat...