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

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...

We count algebraic points of bounded height and degree on the graphs certain functions analytic unit disk, obtaining a bound which is polynomial in logarithm multiplicative height. combine this work with $p$-adic methods to obtain, for each positive $\varepsilon$, an upper form $cD^{3n/4 + \varepsilon n}$ number irreducible factors $P^{\circ n}(X)-P^{\circ n}(\alpha)$ over $K$, where $K$ field,...

An expander code is a binary linear whose parity-check matrix the bi-adjacency of bipartite graph. We provide new formula for minimum distance such codes. also proof result that $2(1-\varepsilon) \gamma n$ lower bound given by an $(m,n,d,\gamma,1-\varepsilon)$

Milne-like spacetimes are a class of hyperbolic FLRW which admit continuous spacetime extensions through the big bang, $\tau = 0$. The existence extension follows from writing metric in conformal Minkowskian coordinates and assuming that scale factor satisfies $a(\tau) \tau + o(\tau^{1+\varepsilon})$ as \to 0$ for some $\varepsilon > This asymptotic assumption implies o(\tau)$. In this paper, w...

Abstract We prove that analogues of the Hardy–Littlewood generalised twin prime conjecture for almost primes hold on average. Our main theorem establishes an asymptotic formula number integers $n=p_1p_2 \leq X$ such $n+h$ is a product exactly two which holds all $|h|\leq H$ with $\log^{19+\varepsilon}X\leq H\leq X^{1-\varepsilon}$ , under restriction size one factors n and . Additionally, we co...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...