SummaryWe employ the stochastic abacus to compute winning probabilities at each level of game “Pass Buck” on a complete binary tree with starting vertex being root tree. The derivation is also generalized play l-ary trees.

Let R be a 2-torsion free prime ring with center Z, right Utumi quotient ring U , generalized derivation F associated with a nonzero derivation d of R and L a Lie ideal of R. If F (uv)n = F (u)mF (v)l or F (uv)n = F (v)lF (u)m for all u, v ∈ L, where m,n, l are fixed positive integers, then L ⊆ Z. We also examine the case where R is 312 Ahmad N. Alkenani et al. a semiprime ring. Finally, as an ...

Within the ?! model of coupled nucleon-meson systems, a generalized rel-ativistic Lennard{Balescu{equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium eeects as well as uctuation eeects. It contains all possible pr...

This article provides further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M ; we show that kernel of a certain Dirac operator defined over S, which we called submanifold Dirac operator, gives the data of the immersion. In the derivation, we use a relation between the generalized Weierstrass relations and the Frobenious reciprocity of Cl...

The purpose of the present paper is to classify generalized derivations satisfying more specific algebraic identities in a prime ring with
 involution second kind. Some well-known results
 characterizing commutativity rings by have
 been using derivation.

This paper considers the global synchronization of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbors states. For such networks we derive a generalized Riccati solution that quantifies and incorporates uncertainty of the ...