Motion planning problems can be simplified by admissible projections of the configuration space to sequences lower-dimensional quotient-spaces, called sequential simplifications. To exploit simplifications, we present Quotient-space Rapidly-exploring Random Trees (QRRT) algorithm. QRRT takes as input a start and goal configuration, sequence quotient-spaces. The algorithm grows trees on quotient...

the main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. we develop the theory of t-bestsimultaneous approximation in quotient spaces. then, we discuss the relationshipin t-proximinality and t-chebyshevity of a given space and its quotientspace.

A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every /7-map on X with separated range is a proximity quotient map. Introduction. In 1959 Katetov [3] introduced proximity quotient maps. They have since been...

The prime and primitive spectra of Oq(k), the multiparameter quantized coordinate ring of affine n-space over an algebraically closed field k, are shown to be topological quotients of the corresponding classical spectra, specO(kn) and maxO(kn) ≈ kn, provided the multiplicative group generated by the entries of q avoids −1.

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

We consider a version of the AdSd+1/CFTd correspondence, in which the bulk space is taken to be the quotient manifold AdSd+1/Γ with a fairly generic discrete group Γ acting isometrically on AdSd+1. We address some geometrical issues concerning the holographic principle and the UV/IR relations. It is shown that certain singular structures on the quotient boundary S/Γ can affect the underlying ph...

We prove that a space is quotient π-image of a locally separable metric space if and only if it has a πand double cs∗cover. We also investigate quotient π-s-images of locally separable metric spaces.

This paper investigates the S -transform on the space of tempered Boehmians. Inversion and properties are also discussed.

We extend a geometric framework for the interpretation of search operators to encompass the genotype-phenotype mapping derived from an equivalence relation defined by an isometry group. We show that this mapping can be naturally interpreted using the concept of quotient space, in which the original space corresponds to the genotype space and the quotient space corresponds to the phenotype space...

A natural problem in algebraic geometry is the formation of quotients. This is particularly important in the theory of moduli, where many moduli spaces are naturally constructed as quotients of parameter spaces by linear algebraic groups. Examples of quotient moduli spaces include moduli spaces of curves, stable maps and stable vector bundles (with fixed determinant). Unfortunately, the quotien...