For a manifold $M$ endowed with Legendrean (or Lagrangean) contact structure $E\oplus F \subset TM$, we give an elementary construction of invariant partial connection on the quotient bundle $TM/F$. This permits us to develop naïve version relative tractor calculus and construct second order differential operator, which turns out be first BGG operator induced by connection.

where the second order differential operator F is of Hamilton-Jacobi-Bellman (HJB) type, that is, F is a supremum of linear elliptic operators, f is sublinear in u at infinity, and Ω ⊂ R is a regular bounded domain. HJB operators have been the object of intensive study during the last thirty years – for a general review of their theory and applications we refer to [26], [33], [43], [14]. Well-k...

In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for practical calculations on finite lattices. In this second paper I show how the small (order 1/N) errors introduced by truncating the operators to a finite lattice m...

Abstract In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying contractive conditions are obtained, without appealing to completeness of X or normality cone. continuity mapping relaxed. Furthermore, we prove that necessary if has a . These results greatly generalize several well-known comparable liter...

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...

The rank of a bimatrix game (A,B) is the rank of the matrix A + B. We give a construction of rank-1 games with exponentially many equilibria, which answers an open problem by Kannan and Theobald (2010).

We show that the scattering operator for defocusing energy critical semilinear wave equations \square u+f(u)=0, with f C-infinity and ~ u^5, in three space dimensions, determines f.

We establish a Wiman–Valiron theory of polynomial series based on the Askey–Wilson operator $${\mathcal {D}}_q$$ , where $$q\in (0,1)$$ . For an entire function f log-order smaller than 2, this includes (i) estimate which shows that behaves locally like consisting terms near maximal term its expansion, and (ii) {D}}_q^n f$$ compared to f. then apply in studying growth solutions difference eq...