Search results for "Regular"
showing 10 items of 855 documents
Locally convex quasi $C^*$-normed algebras
2012
Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -normed algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-algebra over A 0 , but it is not necessarily a locally convex quasi ∗-algebra over the C ∗ -algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -normed algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.
Nonlinear Nonhomogeneous Elliptic Problems
2019
We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…
Maximal Operators with Respect to the Numerical Range
2018
Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $\mathfrak{n}$-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems
2017
We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…
Inflection points and topology of surfaces in 4-space
2000
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
Surface homeomorphisms with zero dimensional singular set
1998
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.
Multiresolution Analysis for Irregular Meshes
2003
International audience; The concept of multiresolution analysis applied to irregular meshes has become more and more important. Previous contributions proposed a variety of methods using simplification and/or subdivision algorithms to build a mesh pyramid. In this paper, we propose a multiresolution analysis framework for irregular meshes with attributes. Our framework is based on simplification and subdivision algorithms to build a mesh pyramid. We introduce a surface relaxation operator that allows to build a non-uniform subdivision for a low computational cost. Furthermore, we generalize the relaxationoperator to attributes such as color, texture, temperature, etc. The attribute analysis…
Phylogeny and origin of Jurassic irregular echinoids (Echinodermata: Echinoidea).
2006
27 pages; International audience; A phylogenetic analysis of Jurassic irregular echinoids is realized to explore the origin and early evolution of this important subset of echinoids. The phylogeny is based on 39 characters and considers data from apical system architecture, the corona including tuberculation and spines, Aristotle's lantern, and general test shape. Results corroborate the monophyly of Irregularia, and clarify the phylogenetic interrelationships existing between the main groups of irregular echinoids. Specializations of the Aristotle's lantern, spines, tubercles and phyllodes constitute the apomorphies for different taxa, as for the whole of Irregularia. The phylogenetic sign…
The diaptomid fauna of Israel (Copepoda, Calanoida, Diaptomidae), with notes on the systematics of Arctodiaptomus similis (Baird, 1859) and Arctodiap…
2014
Background: To date, only scarce information is available about the diaptomid copepods of the Middle East despite the ecological and biogeographical importance of the family Diaptomidae in the inland waters of the Holarctic region. Moreover, the taxonomic status of some of the taxa occurring in the area is in need of revision. We studied crustaceans collected from temporary and permanent lentic water bodies in Israel with the aim of providing an updated census of the diaptomid copepods occurring in the country. Furthermore, we morphologically and genetically analysed samples of Arctodiaptomus similis s.l. to shed light on its taxonomy. Results: Five diaptomid taxa were collected during this…
Analysis of spectral line shapes in low-temperature plasma by means of inverse ill-posed problem solution
2017
Promocijas darbs ir veltīts zemtemperatūras plazmas diagnostikas metodes attīstīšanai, augstfrekvences bezelektrodu lampām (ABL). Darbā tika izstrādāta jauna metode spektroskopisko datu apstrādei un reālo spektrāllīniju kontūru noteikšanai, risinot nekorekto apgriezto uzdevumu, kas balstās uz Tihonova regularizācijas algoritmu. Metode tika testēta aprēķinot patiesās profilu formas izmantojot eksperimentāli iegūtas Hg līnijās, emitētas no specialas formas mikro ABL. Tika pierādīts, ka aparatūras funkcijas neņemšana vērā zemtemperatūras plazmas gadījumā var ieviest lielu neprecizitāti, nosakot profilu formu un platumu un, sekojoši, ABL temperatūru. Tika analizēta arī atkarība no bufergāzes ve…