In this paper we show how ideas from spline theory can be used to construct a local basis for the space of translates general iterated Brownian Bridge kernel $k_{\beta,\varepsilon}$ $\beta\in\mathbb{N}$, $\varepsilon\geq 0$. simple case $\beta=1$, derive an explicit formula corresponding Lagrange basis, which allows us solve interpolation problems without inverting any linear system. We use pro...

We evaluate asymptotically the variance of number squarefree integers up to $x$ in short intervals length $H < x^{6/11 - \varepsilon}$ and arithmetic progressions modulo $q$ with $q > x^{5/11 + \varepsilon}$. On assumption respectively Lindel\"of Hypothesis Generalized we show that these ranges can be improved x^{2/3 x^{1/3 Furthermore obtaining a bound sharp factors $H^{\varepsilon}$ full rang...

Abstract We show that for any $\varepsilon&amp;gt;0$, $\alpha \in [0,\frac {1}{2})$, as $g\to \infty $ a generic finite-area genus $g$ hyperbolic surface with $n=O\left (g^{\alpha }\right )$ cusps, sampled probability arising from the Weil–Petersson metric on moduli space, has no non-zero eigenvalue of Laplacian below $\frac {1}{4}-\left (\frac {2\alpha +1}{4}\right )^{2}-\varepsilon $. For =0$...

Abstract In this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. particular, under some proper assumptions, prove that attractor $\{A_{\varepsilon }(t)\}_{t\in \mathbb{R}}$ { A ? <mml:m...

Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's in semi-classical regime. Here solutions exhibit strong multiple-scale behavior due to a small parameter $\hbar$, sense that dynamics of states and induced observables can occur on different spatial temporal scales. Such finds many applications, including Born-O...

Penalizing incompressibility in the Stokes problem leads, under mildassumptions, to matrices with condition numbers $\kappa =\mathcal{O}(\varepsilon ^{-1}h^{-2})$, $\varepsilon =$ penalty parameter $\ll1$ and$h= $ meshwidth $<1$. Although =\mathcal{O}(\varepsilon^{-1}h^{-2}) is large, practical tests seldom report difficulty solvingthese systems. In SPD case, using conjugate gradient method, th...

Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional $1$-injective Banach space contains a hyperplane is $(2+\varepsilon )$-injective for $\varepsilon \gt 0$, yet not $2$-injective, rem

a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...

The different variants of two-stage random sequential adsorption (RSA) models for packing disks and discorectangles on a two-dimensional (2D) surface were investigated. In the SD (sticks+disks) model, first deposited then added. DS (disks+sticks) At stage particles up to selected concentration at final (second) saturated (jamming) state. main parameters stage, aspect ratio $\ensuremath{\varepsi...

Coordinate descent methods have considerable impact in global optimization because (or, at least, almost global) minimization is affordable for low-dimensional problems. with high-order regularized models smooth nonconvex box-constrained are introduced this work. High-order stationarity asymptotic convergence and first-order worst-case evaluation complexity bounds established. The computer work...