Search results for "6b"
showing 10 items of 66 documents
Two-dimensional Banach spaces with polynomial numerical index zero
2009
We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.
Mehāniskās aktivācijas ietekme uz nātrija bismuta titanāta keramikas izgatavošanu.
2022
“Mehāniskās aktivācijas ietekme uz nātrija bismuta titanāta keramikas izgatavošanu” Atvars A., zinātniskie darba vadītāji vadošā pētniece Dr. phys. Dunce M. un asoc. prof. Dr. chem. Vaivars G. Bakalaura darbs. (46 lapas, 27 attēli, 49 literatūras avoti, 3 pielikumi). Latviešu valodā Bakalaura darba ietvaros tika veikta nātrija bismuta titanāta (Na0,5Bi0,5TiO3) un cietā šķīduma 0,975(0,94Na0,5Bi0,5TiO3-0,06BaTiO3)-0,025LiNbO3 iegūšana, izmantojot cietfāžu reakcijas metodi, veicot mehānisko aktivāciju vienā no posmiem. Nepieciešamie savienojumi tika iegūti, izmantojot nātrija karbonātu (Na¬2CO3), bismuta (III) oksīdu (Bi2O3), titāna dioksīdu (TiO2), litija karbonātu (Li2CO3), niobija (V) oksī…
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
CCDC 235065: Experimental Crystal Structure Determination
2005
Related Article: G.Stajer, F.Miklos, I.Kanizsai, F.Csende, R.Sillanpaa, P.Sohar|2004|Eur.J.Org.Chem.|2004|3701|doi:10.1002/ejoc.200400247
Space-filling vs. Luzin's condition (N)
2013
Let us assume that we are given two metric spaces, where the Hausdorff dimension of the first space is strictly smaller than the one of the second space. Suppose further that the first space has sigma-finite measure with respect to the Hausdorff measure of the corresponding dimension. We show for quite general metric spaces that for any measurable surjection from the first onto the second space, there is a set of measure zero that is mapped to a set of positive measure (both measures are the Hausdorff measures corresponding to the Hausdorff dimension of the first space). We also study more general situations where the measures on the two metric spaces are not necessarily the same and not ne…
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
2016
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.
On singular integral and martingale transforms
2007
Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued L^p-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.
Strong BV-extension and W1,1-extension domains
2021
We show that a bounded domain in a Euclidean space is a $W^{1,1}$-extension domain if and only if it is a strong $BV$-extension domain. In the planar case, bounded and strong $BV$-extension domains are shown to be exactly those $BV$-extension domains for which the set $\partial\Omega \setminus \bigcup_{i} \overline{\Omega}_i$ is purely $1$-unrectifiable, where $\Omega_i$ are the open connected components of $\mathbb{R}^2\setminus\overline{\Omega}$.
Differentiability in the Sobolev space W1,n-1
2014
Let Ω ⊂ Rn be a domain, n ≥ 2. We show that a continuous, open and discrete mapping f ∈ W1,n−1 loc (Ω, Rn ) with integrable inner distortion is differentiable almost everywhere on Ω. As a corollary we get that the branch set of such a mapping has measure zero. peerReviewed
Products of snowflaked Euclidean lines are not minimal for looking down
2017
We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.