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 y2=x5−xy^2=x^5-x

Main objects of uniformization of the curve $y^2=x^5-x$ 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 $q$-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