3,948 research outputs found
A Group Theoretical Identification of Integrable Equations in the Li\'enard Type Equation : Part II: Equations having Maximal Lie Point Symmetries
In this second of the set of two papers on Lie symmetry analysis of a class
of Li\'enard type equation of the form ,
where over dot denotes differentiation with respect to time and and
are smooth functions of their variables, we isolate the equations which
possess maximal Lie point symmetries. It is well known that any second order
nonlinear ordinary differential equation which admits eight parameter Lie point
symmetries is linearizable to free particle equation through point
transformation. As a consequence all the identified equations turn out to be
linearizable. We also show that one can get maximal Lie point symmetries for
the above Li\'enard equation only when (subscript denotes
differentiation). In addition, we discuss the linearising transformations and
solutions for all the nonlinear equations identified in this paper.Comment: Accepted for publication in Journal of Mathematical Physic
Elasticity analysis of unemployed people quantity in relation to gross domestic product of Russia
The article estimates parameters of interrelation between accession rate of unemployed people quantity and gross domestic product volume in Russia on the grounds of quarterly data for 1995-2013. For estimation of model parameters the authors use the method of instrumental variable. Analysis of mutual influence of unemployed people quantity and gross domestic product increase is performed on the grounds of elasticity notion. © IDOSI Publications, 2014
Approximate nonlinear self-adjointness and approximate conservation laws
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is
introduced and its properties are studied. Consequently, approximate
conservation laws which cannot be obtained by the approximate Noether theorem
are constructed by means of the method. As an application, a class of perturbed
nonlinear wave equations is considered to illustrate the effectiveness.Comment: 13 pages, 2 table
Integrability of Lie systems through Riccati equations
Integrability conditions for Lie systems are related to reduction or
transformation processes. We here analyse a geometric method to construct
integrability conditions for Riccati equations following these approaches. This
approach provides us with a unified geometrical viewpoint that allows us to
analyse some previous works on the topic and explain new properties. Moreover,
this new approach can be straightforwardly generalised to describe
integrability conditions for any Lie system. Finally, we show the usefulness of
our treatment in order to study the problem of the linearisability of Riccati
equations.Comment: Corrected typo
On the hierarchy of partially invariant submodels of differential equations
It is noticed, that partially invariant solution (PIS) of differential
equations in many cases can be represented as an invariant reduction of some
PIS of the higher rank. This introduce a hierarchic structure in the set of all
PISs of a given system of differential equations. By using this structure one
can significantly decrease an amount of calculations required in enumeration of
all PISs for a given system of partially differential equations. An equivalence
of the two-step and the direct ways of construction of PISs is proved. In this
framework the complete classification of regular partially invariant solutions
of ideal MHD equations is given
Invariants of differential equations defined by vector fields
We determine the most general group of equivalence transformations for a
family of differential equations defined by an arbitrary vector field on a
manifold. We also find all invariants and differential invariants for this
group up to the second order. A result on the characterization of classes of
these equations by the invariant functions is also given.Comment: 13 page
Exponential and moment inequalities for U-statistics
A Bernstein-type exponential inequality for (generalized) canonical
U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen
inequalities for sums of independent random variables are extended to
(generalized) U-statistics of any order whose kernels are either nonnegative or
canonicalComment: 22 page
Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
We investigate the main features of the flat
Friedmann-Lema{\i}tre-Robertson-Walker cosmological models in the f(T)
teleparallel gravity. In particular, a general approach to find out exact
cosmological solutions in f (T) gravity is discussed. Instead of taking into
account phenomenological models, we consider as a selection criterion, the
existence of Noether symmetries in the cosmological f(T) point-like Lagrangian.
We find that only power-law models admit extra Noether symmetries. A complete
analysis of such cosmological models is developed.Comment: 16 pages, 1 figure, to be published in Phys. Rev.
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