Search results for " Mathematica"
showing 10 items of 689 documents
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 the Almost Everywhere Convergence of Multiple Fourier-Haar Series
2019
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set $$W\subset\mathbb{R}_+^n$$ containing the intersection of some neighborhood of the origin with $$\mathbb{R}_+^n$$ . It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
Electronic structure and optical properties of III-N nanowires
2011
The term III-N nanowire (NW) will refer throughout this work to the free-standing nanowires made of group-III-nitrides semiconductors, namely InN, GaN and AlN. These nanostructures have a large length/diameter ratio, of the order of 100 (sev- eral micrometers versus tenths of nanometers). The term free-standing highlights the fact that the NWs are not embedded in another material. The improvement of the epitaxial techniques, and in particular, those based on III-N semiconductors, has lead an important part of the Solid State Physics community to concentrate the attention in the last years towards a better understanding of the physical properties of those NWs. Nanowires present several di er…
Quantization of Poisson Lie Groups and Applications
1996
LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.
Description of hard-sphere crystals and crystal-fluid interfaces: a comparison between density functional approaches and a phase-field crystal model.
2012
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three--dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a …
Analitiskā ģeometrija telpā: lekcijas lasītas Latvijas Universitātes Inženierzinātņu un mehanikas fakultātēs
1931
Analītiskā ģeometrija: 2. daļa, Analītiskā ģeometrija plāksnē
1941
Lekcijas lasītas Fizikas-matematikas fakultātes studentiem 1940./41.g.
Schul-Stereometrie
1883
Vektoru rēķini
1942
Modernās elementārās algebras un ģeometrijas elementi matemātikas skolotājiem
2020
Grāmata paredzēta studiju kursa “Modernās elementārās algebras un ģeometrijas elementi” (4 kredītpunkti) apguvei integrētās profesionālās bakalaura studiju programmas “Skolotājs” studentiem. Tajā iekļauts teorijas materiāls, uzdevumu piemēri un uzdevumi ar atrisinājumiem patstāvīgajam darbam. Materiālu var izmantot arī matemātikas skolotāji mācību procesā, gatavojot vidusskolēnus matemātikas olimpiādēm.