Search results for "Infinitesimal"
showing 10 items of 67 documents
Modulus of continuity with respect to semigroups of analytic functions and applications
2016
Abstract Given a complex Banach space E , a semigroup of analytic functions ( φ t ) and an analytic function F : D → E we introduce the modulus w φ ( F , t ) = sup | z | 1 ‖ F ( φ t ( z ) ) − F ( z ) ‖ . We show that if 0 α ≤ 1 and F belongs to the vector-valued disc algebra A ( D , E ) , the Lipschitz condition M ∞ ( F ′ , r ) = O ( ( 1 − r ) 1 − α ) as r → 1 is equivalent to w φ ( F , t ) = O ( t α ) as t → 0 for any semigroup of analytic functions ( φ t ) , with φ t ( 0 ) = 0 and infinitesimal generator G , satisfying that φ t ′ and G belong to H ∞ ( D ) with sup 0 ≤ t ≤ 1 ‖ φ ′ ‖ ∞ ∞ , and in particular is equivalent to the condition ‖ F − F r ‖ A ( D , E ) = O ( ( 1 − r ) α ) as r …
Cores for parabolic operators with unbounded coefficients
2009
Abstract Let A = ∑ i , j = 1 N q i j ( s , x ) D i j + ∑ i = 1 N b i ( s , x ) D i be a family of elliptic differential operators with unbounded coefficients defined in R N + 1 . In [M. Kunze, L. Lorenzi, A. Lunardi, Nonautonomous Kolmogorov parabolic equations with unbounded coefficients, Trans. Amer. Math. Soc., in press], under suitable assumptions, it has been proved that the operator G : = A − D s generates a semigroup of positive contractions ( T p ( t ) ) in L p ( R N + 1 , ν ) for every 1 ⩽ p + ∞ , where ν is an infinitesimally invariant measure of ( T p ( t ) ) . Here, under some additional conditions on the growth of the coefficients of A , which cover also some growths with an ex…
Boundary/Field Variational Principles for the Elastic Plastic Rate Problem
1991
An elastic-plastic continuous solid body under quasi-statically variable external actions is herein addressed in the hypoteses of rate-independent material model with dual internal variables and of infinitesimal displacements and strains. The related analysis problem for assigned rate actions is first formulated through a boundary/field integral equation approach, then is shown to be characterized by two variational principles, one of which is a stationarity theorem, the other a min-max one.
Metric Lie groups admitting dilations
2019
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $ d(\delta_\lambda x,\delta_\lambda y) = \lambda d(x,y)$, for all $x,y\in G$ and all $\lambda>0$. First, we show that all such distances are admissible, that is, they induce the manifold topology. Second, we characterize multiplicative one-parameter groups of Lie automorphisms that are dilations for some left-invariant distance in terms of algebraic properties of their infinitesimal generator. Third, we show that an admissible left-invariant distance on a Lie …
Topics on n-ary algebras
2011
We describe the basic properties of two n-ary algebras, the Generalized Lie Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology relevant for the central extensions and infinitesimal deformations of FAs. It is seen that semisimple FAs do not admit central extensions and, moreover, that they are rigid. This extends the familiar Whitehead's lemma to all $n\geq 2$ FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is no longer required to be fully skewsymmetric one is led to the n-Leibniz (or…
Quantum groups and deformed special relativity
1994
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its covariance properties as described by appropriate reflection equations. Some isomorphisms among the space-time and derivative algebras are demonstrated, and their representations are described briefly. Finally, some physical consequences and open problems are discussed.
Václav Hlavatý on intuition in Riemannian space
2019
Abstract We present a historical commentary together with an English translation of a mathematical-philosophical paper by the Czech differential geometer and later proponent of a geometrized unified field theory Vaclav Hlavatý (1894–1969). The paper was published in 1924 at the height of interpretational debates about recent advancements in differential geometry triggered by the advent of Einstein's general theory of relativity. In the paper he argued against a naive generalization of analogical reasoning valid for curves and surfaces in three-dimensional Euclidean space to the case of higher-dimensional curved Riemannian spaces. Instead, he claimed, the only secure ground to arrive at resu…
Generalized Camassa-Holm Equations: Symmetry, Conservation Laws and Regular Pulse and Front Solutions
2021
In this paper, we consider a member of an integrable family of generalized Camassa–Holm (GCH) equations. We make an analysis of the point Lie symmetries of these equations by using the Lie method of infinitesimals. We derive nonclassical symmetries and we find new symmetries via the nonclassical method, which cannot be obtained by Lie symmetry method. We employ the multiplier method to construct conservation laws for this family of GCH equations. Using the conservation laws of the underlying equation, double reduction is also constructed. Finally, we investigate traveling waves of the GCH equations. We derive convergent series solutions both for the homoclinic and heteroclinic orbits of the…
About Leibniz cohomology and deformations of Lie algebras
2011
We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones by a very elementary approach. The comparison gives some conditions, which are easy to verify for a given Lie algebra, for deciding whether it has more Leibniz deformations than just the Lie ones. We also give the complete description of a Leibniz (and Lie) versal deformation of the 4-dimensional diamond Lie algebra, and study the case of its 5-dimensional analogue.
Functional Differential and Difference Equations with Applications
2012
and Applied Analysis 3 solutions to a class of nonlocal boundary value problems for linear homogeneous secondorder functional differential equations with piecewise constant arguments are obtained. The last but not the least, this issue features a number of publications that report recent progress in the analysis of problems arising in various applications. In particular, dynamics of delayed neural network models consisting of two neurons with inertial coupling were studied, properties of a stochastic delay logistic model under regime switching were explored, and analysis of the permanence and extinction of a single species with contraception and feedback controls was conducted. Other applie…