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.

We consider maximizing a monotone submodular function under cardinality constraint or knapsack in the streaming setting. In particular, elements arrive sequentially and at any point of time, algorithm has access to only small fraction data stored primary memory. propose following algorithms taking O(ε− 1) passes: (1) (1 − e− 1 ε)-approximation for cardinality-constrained problem, (2) (0.5 knaps...

We investigate the convergence rate of optimal entropic cost $$v_\varepsilon $$ to transport as noise parameter $$\varepsilon \downarrow 0$$ . show that for a large class functions c on $${\mathbb {R}}^d\times {\mathbb {R}}^d$$ (for which plans are not necessarily unique or induced by map) and compactly supported $$L^{\infty }$$ marginals, one has -v_0= \frac{d}{2} \varepsilon \log (1/\varepsil...

This paper concerns an approximation of the expectation values position and momentum solution to semiclassical Schrödinger equation with a Gaussian as initial condition. Of particular interest is obtained by our symplectic/Hamiltonian formulation wave packet dynamics that introduces correction term conventional using classical Hamiltonian system Hagedorn others. The main result proof gives high...

The response of a semi-infinite ocean to slowly travelling atmospheric perturbation crossing the coast provides simple example breakdown nearly geostrophic balance induced by boundary. We examine this in linear shallow-water model at small Rossby number $\varepsilon \ll 1$. Using matched asymptotics we show that long Kelvin wave, with $O(\varepsilon^{-1})$ length scale and $O(\varepsilon)$ ampl...

Abstract Let $\mathrm{AP}_k=\{a,a+d,\ldots,a+(k-1)d\}$ be an arithmetic progression. For $\varepsilon>0$ we call a set $\mathrm{AP}_k(\varepsilon)=\{x_0,\ldots,x_{k-1}\}$ $\varepsilon$ -approximate progression if for some and d , $|x_i-(a+id)|<\varepsilon d$ holds all $i\in\{0,1\ldots,k-1\}$ . Complementing earlier results of Dumitrescu (2011, J. Comput. Geom. 2 (1) 16–29), in this paper ...

We study algorithms for the sliding-window model, an important variant of data-stream in which goal is to compute some function a fixed-length suffix stream. extend smooth-histogram framework Braverman and Ostrovsky (FOCS 2007) almost-smooth functions, includes all subadditive functions. Specifically, we show that if can be \(\left( 1+{{\varepsilon }}\right) \)-approximated insertion-only strea...