Let L be a real (Hausdorff) topological vector space. The space %[L] of nonempty compact subsets of L forms a (Hausdorff) topological semivector space with singleton origin when 3C[L] is given the uniform (equivalently, the finite) hyperspace topology determined by L. Then %[L] is locally compact iff L is so. Furthermore, 90.[Z,], the set of nonempty compact convex subsets of L, is the largest ...

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...

in this paper, we investigate the general fuzzy linear system of equations.  the  main aim of this paper is based on the embedding approach. we find the necessary and sufficient conditions for the existence of fuzzy solution of the mentioned systems.  finally, numerical examples are presented to more illustration of the proposed model.

We initiate the study of metric embedding problems from an approximation point of view. Metric embedding is a map from a guest metric to a host metric. The quality of the embedding is defined in terms of distortion, the ratio by which pairwise distances get skewed in the host metric. While metric embeddings in general have received quite a lot of attention in theory community, most of the resul...

We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the intended semantics of iFOL and mFOL. Our proof is intuitionistic and provides an effective procedure Prf that converts uniform minimal evidence into a formal fi...

The solution space of a constant coefficient ODE gives rise to a natural real analytic curve in Euclidean space. We give necessary and sufficient conditions on the ODE to ensure that this curve is a proper embedding of infinite length or has finite total first curvature. If all the roots of the associated characteristic polynomial are simple, we give a uniform upper bound for the total first cu...

The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J. Folkman, J. Lawrence, Oriented matroids, J. Combin. Theory Ser. B 25 (1978) 199–236]. In this paper we exhibit a characterization of such graphs (for the uniform case) via their natural embedding into Qn—the 1-skeleto...

A new method for identification of an optimal set of time lags based on non-uniform attractor embedding from the observed non-linear time series is proposed in this paper. Simple deterministic method for the determination of non-uniform time lags comprises the pre-processing stage of the time series forecasting algorithm which is implemented in the form of a fuzzy inference system. optimization...

We study the transmission coefficient of a plane wave through a 1D finite quasi-periodic system – the Frenkel-Kontorova (FK) model – embedding in an infinite uniform harmonic chain. By varying the mass of atoms in the infinite uniform chain, we obtain the transmission coefficients for all eigenfrequencies. The phonon localization of the incommensurated FK chain is also studied in terms of the t...

This study describes a non-invasive method for mapping interstitial fluid pressure within hydrogel-based microscale tissues. The method is based on embedding (or forming) a tissue within a silicone (PDMS) microfluidic device, and measuring the extremely slight displacement (<1 μm) of the PDMS optically when the device is pressurized under static and flow conditions. The displacement field under...