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Soc-$\oplus$-Supplemented Modules
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This paper presents numerical solution of elliptic partial differential equations (Poisson’s equation) using direct and indirect radial basis function networks. These methods use multiquadric radial basis function approximation scheme. Also, a comparison is made between these methods with Adomian double decomposition method.
In this paper we prove existence of common fixed point of two closed bounded multi-valued mappings defined on a complete epsilon chainable metric space.
We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b). Copyright Blackwell Publishers Inc. 1997.
In this report I offer an exploration of the insights that may be provided by a situated perspective on learning. Through an extension of my previous analysis of students learning mathematics in 2 schools (Boaler, 1998), I consider the ways in which a focus on the classroom community and the behaviors and practices implicit within such communities may increase one's understanding of students' mathematical knowledge production and use. The implications of such a focus for classroom pedagogy and assessment as well as for research in mathematics education are considered.
We consider control problems for systems driven by linear backward stochastic differential equations (BSDEs). We prove the existence of strict optimal controls under the convexity of the control domain as well as the cost functional. Our approach is based on strong convergence techniques for the associated linear BSDEs. Moreover, we establish necessary as well as sufficient conditions of optimality, satisfied by an optimal strict control. The proof of this result is based on the convex optimization principle.
If $\mathcal{X}$ is a class of groups, then a group $G$ is said to be minimal non $\mathcal{X}$-group if all its proper subgroups are in the class $\mathcal{X}$, but $G$ itself is not an $\mathcal{X}$-group. The main result of this note is that if $c>0$ is an integer and if $G$ is a minimal non $\mathcal{(LF)N}$ (respectively, $\mathcal{(LF)N}_{c}$)-group, then $G$ is a finitely generated perfect group which has no non-trivial finite factor and such that $G/Frat(G)$ is an infinite simple group; where $\mathcal{N}$ (respectively, $\mathcal{N}_{c}$, $\mathcal{LF}$) denotes the class of nilpotent (respectively, nilpotent of class at most $c$, locally finite) groups and $Frat(G)$ stands for the Frattini subgroup of $G$.
A module M is called UC-module if every submodule has a unique closure (i.e., maximal essential extension) in M. The paper establishes a large number of conditions equivalent to this property.