We present an algorithm for aggregating states in solving large MDPs (represented as factored MDPs) using search by successive re nement in the space of nonhomogeneous partitions. Homogeneity is de ned in terms of stochastic bisimulation and reward equivalence within blocks of a partition. Since homogeneous partitions that de ne equivalent reduced-state-space MDPs can have a large number of blo...

For k ≥ 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on that of an indecomposible symmetric space. All the local scalar Weyl curvature invariants of these manifolds vanish. Dedicated to Professor Sekigawa on his 60th bir...

*Correspondence: [email protected] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China Abstract The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integralMβ ,ρ ,q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the a...

An inflammatory pseudotumor (IPT) is a rare benign lesion, characterized by nonneoplastic proliferation of inflammatory cells and presence of intermingling collagen fibers. IPT commonly occurs in the lungs and orbita, while an intraspinal IPT is extremely rare. IPT can mimic both clinically and radiologically malignant processes, and making a definitive preoperative diagnosis is often difficult...

Abstract Let $M \subset X$ be a submanifold of rational homogeneous space $X$ such that the normal sequence splits. We prove $M$ is also homogeneous.

We consider the stabilization problem for three dimensional homogeneous polynomial systems, and derive an intrinsic suucient condition for stablizability. We show that this condition is satissed by an open set in the space of homogeneous systems of a xed degree.

In this paper we study supremal representations positively homogeneous of degree one and symmetric positively homogeneous of degree two functions deened on a reeexive Banach space the Urysohn peak.

A homogeneous space X = G/H of a connected Lie group G is called a symmetric homogeneous space if there exists an involution σ of G such that H lies between the fixed point group G and its identity component Go . Example 0. For a connected Lie group G′, put G = G′×G′, σ(g1, g2) ) = (g2, g1) and H = G. Then the homogeneous space X = G/H is naturally isomorphic to G′ by the map (g1, g2) 7→ g1g−1 ...

The purpose of this paper is to analysis the viscoelastic models under dynamic loading. A five-parameter model is chosen for study exhibits elastic, viscous, and retarded elastic response to shearing stress. The viscoelastic specimen is chosen which closely approximates the actual behavior of a polymer. The module of elasticity and viscosity coefficients are assumed to be space dependent i.e. f...