Search results for "Functional analysis"

Matemātika

1997

Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals

2021

The paper deals with the identification of material parameters characterizing components in heterogeneous geocomposites provided that the interfaces separating different materials are known. We use the optimal control approach with flux type cost functionals. Since solutions to the respective state problems are not regular, in general, the original cost functionals are expressed in terms of integrals over the computational domain using the Green formula. We prove the existence of solutions to the optimal control problem and establish convergence results for appropriately defined discretizations. The rest of the paper is devoted to computational aspects, in particular how to handle high sens…

Fundamental isomorphism theorems for quantum groups

2017

The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in this class would be the Noether isomorphism theorems, Zassenhaus' butterfly lemma, the Schreier refinement theorem for subnormal series of subgroups, the Dedekind modularity law, and last but not least the Jordan-H\"older theorem. We discuss analogues of the above-mentioned results in the context of locally compact quantum groups and linearly reductive quantum groups. The nature of the two cases is different: the former is operator algebraic and the latt…

Removable singularities for div v=f in weighted Lebesgue spaces

2018

International audience; Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1<p<+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.

Generalized Riesz systems and quasi bases in Hilbert space

2019

The purpose of this article is twofold. First of all, the notion of $(D, E)$-quasi basis is introduced for a pair $(D, E)$ of dense subspaces of Hilbert spaces. This consists of two biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n \}$ such that $\sum_{n=0}^\infty \ip{x}{\varphi_n}\ip{\psi_n}{y}=\ip{x}{y}$ for all $x \in D$ and $y \in E$. Secondly, it is shown that if biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n \}$ form a $(D ,E)$-quasi basis, then they are generalized Riesz systems. The latter play an interesting role for the construction of non-self-adjoint Hamiltonians and other physically relevant operators.

State Neutrality and Psychopharmacological Enhancement

2010

Functional analysis of 12 ORFs fromSaccharomyces cerevisiae chromosome II

1999

Twelve different ORFs have been deleted from the right arm of Saccharomyces cerevisiae chromosome II; namely YBR193c, YBR194w, YBR197c, YBR198c, YBR201w, YBR203w, YBR207w, YBR209w, YBR210w, YBR211c, YBR217w and YBR228w. Tetrad analysis of heterozygous deletant strains revealed that YBR193c, YBR198c and YBR211c are essential genes for vegetative growth. No effects were detected in any of the haploid deletion mutants for the rest of the ORFs with respect to growth, gross morphology or mating.

Functional analysis of yeast gene families involved in metabolism of vitamins B1and B6

2002

In order to clarify their physiological functions, we have undertaken a characterization of the three-membered gene families SNZ1-3 and SNO1-3. In media lacking vitamin B(6), SNZ1 and SNO1 were both required for growth in certain conditions, but neither SNZ2, SNZ3, SNO2 nor SNO3 were required. Copies 2 and 3 of the gene products have, in spite of their extremely close sequence similarity, slightly different functions in the cell. We have also found that copies 2 and 3 are activated by the lack of thiamine and that the Snz proteins physically interact with the thiamine biosynthesis Thi5 protein family. Whereas copy 1 is required for conditions in which B(6) is essential for growth, copies 2 …

Deperturbation treatment of theAΣ+1–bΠ3complex of NaRb and prospects for ultracold molecule formation inXΣ+1(v=0;J=0)

2007

High resolution Fourier transform spectra (FTS) of laser induced fluorescence (LIF) of $C\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+};D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ transitions in ${\mathrm{Na}}^{85}\mathrm{Rb}$ and ${\mathrm{Na}}^{87}\mathrm{Rb}$ were obtained. An analysis of the direct LIF spectra together with the rotational relaxation satellite…

The probability that $x$ and $y$ commute in a compact group

2010

We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs $(x,y)$ in $G \times G$ for which $[x,y] = 1$; this, formally, is the probability that two randomly picked elements commute. We prove that $d(G)$ is always rational and that it is positive if and only if $G$ is an extension of an FC-group by a finite group. This entails that $G$ is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and re…