2,880 research outputs found
Jacobi multipliers, non-local symmetries and nonlinear oscillators
Constants of motion, Lagrangians and Hamiltonians admitted by a family of
relevant nonlinear oscillators are derived using a geometric formalism. The
theory of the Jacobi last multiplier allows us to find Lagrangian descriptions
and constants of the motion. An application of the jet bundle formulation of
symmetries of differential equations is presented in the second part of the
paper. After a short review of the general formalism, the particular case of
non-local symmetries is studied in detail by making use of an extended
formalism. The theory is related to some results previously obtained by
Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local
symmetries for such two nonlinear oscillators is proved.Comment: 20 page
On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain
A generalization of Jacobi's elliptic functions is introduced as inversions
of hyperelliptic integrals. We discuss the special properties of these
functions, present addition theorems and give a list of indefinite integrals.
As a physical application we show that periodic kink solutions (kink chains) of
the double sine-Gordon model can be described in a canonical form in terms of
generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table
Quasi-doubly periodic solutions to a generalized Lame equation
We consider the algebraic form of a generalized Lame equation with five free
parameters. By introducing a generalization of Jacobi's elliptic functions we
transform this equation to a 1-dim time-independent Schroedinger equation with
(quasi-doubly) periodic potential. We show that only for a finite set of
integral values for the five parameters quasi-doubly periodic eigenfunctions
expressible in terms of generalized Jacobi functions exist. For this purpose we
also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics
From Lagrangian to Quantum Mechanics with Symmetries
We present an old and regretfully forgotten method by Jacobi which allows one
to find many Lagrangians of simple classical models and also of nonconservative
systems. We underline that the knowledge of Lie symmetries generates Jacobi
last multipliers and each of the latter yields a Lagrangian. Then it is shown
that Noether's theorem can identify among those Lagrangians the physical
Lagrangian(s) that will successfully lead to quantization. The preservation of
the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger
equation is the key that takes classical mechanics into quantum mechanics.
Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of
Physics: Conference Series, (2012
Poisson Structures for Aristotelian Model of Three Body Motion
We present explicitly Poisson structures, for both time-dependent and
time-independent Hamiltonians, of a dynamical system with three degrees of
freedom introduced and studied by Calogero et al [2005]. For the
time-independent case, new constant of motion includes all parameters of the
system. This extends the result of Calogero et al [2009] for semi-symmetrical
motion. We also discuss the case of three bodies two of which are not
interacting with each other but are coupled with the interaction of third one
Radar observations of geomagnetic disturbance effects on midlatitude mesosphere/lower thermosphere dynamics
Zeitreihen von Monatsmittelwerten des Windes in der Mesosphäre/unteren Thermosphäre über Collm werden auf mögliche Korrelationen mit der Nordatlantischen Oszillation (NAO) und der Südlichen Oszillation (SO) hin untersucht. Während eine positive Korrelation bis in die 1990er Jahre existiert, schwächt sich diese in der Folge ab und kehrt sich teilweise um. Da NAO und SO gekoppelt sind, erfolgen diese Änderungen etwa zur selben Zeit. Die Änderung der Kopplung steht wahrscheinlich in Verbindung mit einer generellen Änderung der Dynamik der mittleren Atmosphäre
On uniformization of Burnside's curve
Main objects of uniformization of the curve are studied: its
Burnside's parametrization, corresponding Schwarz's equation, and accessory
parameters. As a result we obtain the first examples of solvable Fuchsian
equations on torus and exhibit number-theoretic integer -series for
uniformizing functions, relevant modular forms, and analytic series for
holomorphic Abelian integrals. A conjecture of Whittaker for hyperelliptic
curves and its hypergeometric reducibility are discussed. We also consider the
conversion between Burnside's and Whittaker's uniformizations.Comment: Final version. LaTeX, 23 pages, 1 figure. The handbook for elliptic
functions has been moved to arXiv:0808.348
Prejudice Toward Fat People: The development and Validation of the Antifat Attitudes Test
Although the stigma of obesity in our society is well documented, the measurement of antifat attitudes has been a difficult undertaking, Two studies were conducted to construct and validate the Antifat Attitudes Test (AFAT), In study 1, college students (110 men and 175 women) completed the preliminary 54-item AFAT and specific indices of body image and weight-related concerns, Psychometric and factor analysis revealed a 47-item composite scale and three internally consistent factors that were uncorrelated with social desirability: Social/Character Disparagement, Physical/Romantic Unattractiveness, and Weight Control/Blame. Several body image correlates of antifat prejudice were identified, and men expressed more negative attitudes than women, Study 2 experimentally examined the effects of information about the controllability of weight on the antifat attitudes of 120 participants, Exposure to information on behavioral vs. biogenetic control led to greater blame of persons who are fat for their body size, The implications of the findings and the potential utility of the AFAT are discussed
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