Search results for "functional analysis"

Eberlein–Šmulian theorem and some of its applications

2014

Masteroppgave i matematikkdidaktikk – Universitetet i Agder 2014 The thesis is about Eberlein-Šmulian and some its applications. The goal is to investigate and explain different proofs of the Eberlein-Šmulian theorem. First we introduce the general theory of weak and weak* topology defined on a normed space X. Next we present the definition of a basis and a Schauder basis of a given Banach space. We give some examples and prove the main theorems which are needed to enjoy the proof of the Eberlein-Šmulian theorem given by Pelchynski in 1964. Also we present the proof given by Whitley in 1967. Next there is described the connection between the weak topology and the topology and the topology o…

Schauder bases and locally complemented subspaces of Banach spaces

2014

Masteroppgave i matematikkdidaktikk – Universitetet i Agder 2014 The thesis is about Schauder basis in infinite-dimensional Banach spaces and locally complemented subspaces. It starts with the notion of bases and it proves that it is equivalent with that of Schauder basis. It follows with some general theory about bases, and gives the notion of basic sequences and equivalence of bases. It proves that every Banach space has a basic sequence. Next it gives some general theory about unconditional basis. To give an other version of the definition of complemented subspaces, we present adjoint operators and projections. We prove that c0 is not complemented in l∞. The Principle of Local Reflexivit…

New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions

2015

Abstract This paper proposes an input–output (IO) approach to the delay-dependent stability analysis and H ∞ controller synthesis for a class of continuous-time Markovian jump linear systems (MJLSs). The concerned systems are with a time-varying delay in the state and deficient mode information in the Markov stochastic process, which simultaneously involves the exactly known, partially unknown and uncertain transition rates. It is first shown that the original system with time-varying delay can be reformulated by a new IO model through a process of two-term approximation and the stability problem of the original system can be transformed into the scaled small gain (SSG) problem of the IO mo…

Probability Measures on Product Spaces

2020

In order to model a random time evolution, the canonical procedure is to construct probability measures on product spaces. Roughly speaking, the first step is to take a probability measure that models the initial distribution. In the second step, on a different probability space, the distribution after one time step is modeled. Then in each subsequent step, on a further probability space, the random state in the next time step given the full history is modeled. On a formal level, we consider products of probability spaces and Markov kernels between such spaces. Finally, the Ionescu-Tulcea theorem shows that the whole procedure can be realized on a single infinite product space. Furthermore,…

The Dirichlet-Bohr radius

2015

[EN] Denote by Ω(n) the number of prime divisors of n ∈ N (counted with multiplicities). For x ∈ N define the Dirichlet-Bohr radius P L(x) to be the best r > 0 such that for every finite Dirichlet polynomial n≤x ann −s we have X n≤x |an|r Ω(n) ≤ sup t∈R X n≤x ann −it . We prove that the asymptotically correct order of L(x) is (log x) 1/4x −1/8 . Following Bohr’s vision our proof links the estimation of L(x) with classical Bohr radii for holomorphic functions in several variables. Moreover, we suggest a general setting which allows to translate various results on Bohr radii in a systematic way into results on Dirichlet-Bohr radii, and vice versa

L-fuzzy valued measure and integral

2012

Promocijas darbā mēra un integrāļa koncepcijas ir attīstītas L-kopu teori- jas kontekstā, kur L ir pilns, pilnīgi distributīvs režģis ar minimuma t-normu. Darba mērķis ir ieviest mēra un integrāļa jēdzienus gadījumā, kad ne tikai kopas, bet arī mēra un integrāļa vērtības ir L-nestriktas. Darbā ir izstrādā- tā vispārīgā shēma parasto kopu mēra turpinājumam līdz L-kopu mēram ar vērtībām L-nestriktajā reālajā taisnē. Ir definēts L-nestrikti vērtīgs integrālis pa mērojamu L-kopu pēc L-nestrikti vērtīga mēra, ir izpētītas tā īpašības un aprakstītas integrēšanas metodes. Izmantojot integrāli, ir uzdota L-nestrikti vērtīga norma, kura raksturo integrējamas funkcijas L-kopās. Ir aprakstīti daži L-n…

Matemātika

2005

Description of Relaxor State in Na1/2Bi1/2TiO3-SrTiO3-PbTiO3 System of Solid Solutions

2011

Vogel-Fulcher law, traditionally applied to describe dispersion of dielectric permittivity in relaxor ferroelectrics, requires introduction of two different relaxation mechanisms above and below freezing temperature correspondingly. Extending distribution function of relaxation times, previously known for low-temperature region, allows creating common description of relaxation in all range, where distribution function of relaxation times can be regarded as wide, without freezing at certain temperature.

Phase separation of binary mixtures in thin films: Effects of an initial concentration gradient across the film.

2012

We study the kinetics of phase separation of a binary (A,B) mixture confined in a thin film of thickness $D$ by numerical simulations of the corresponding Cahn-Hilliard-Cook (CHC) model. The initial state consisted of 50$%$ A:50$%$ B with a concentration gradient across the film, i.e., the average order parameter profile is ${\ensuremath{\Psi}}_{\mathrm{av}}(z,t=0)=(2z/D\ensuremath{-}1){\ensuremath{\Psi}}_{g},\phantom{\rule{0.28em}{0ex}}0\ensuremath{\leqslant}z\ensuremath{\leqslant}D$, for various choices of ${\ensuremath{\Psi}}_{g}$ and $D$. The equilibrium state (for time $t\ensuremath{\rightarrow}\ensuremath{\infty}$) consists of coexisting A-rich and B-rich domains separated by interfac…

Excited state absorption spectra of dissolved and aggregated distyrylbenzene: A TD-DFT state and vibronic analysis

2017

Made available in DSpace on 2018-12-11T17:33:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-07-21 Federación Española de Enfermedades Raras Ministerio de Economía y Competitividad A time-dependent density functional theory study is performed to reveal the excited state absorption (ESA) features of distyrylbenzene (DSB), a prototype π-conjugated organic oligomer. Starting with a didactic insight to ESA based on simple molecular orbital and configuration considerations, the performance of various density functional theory functionals is tested to reveal the full vibronic ESA features of DSB at short and long probe delay times. UNESP-Universidade Estadual Paulista POSMAT-Graduate Pr…