Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both dissipative and conservative controllers are considered. We show that the shear flow structure of the undriven system causes a Takens-Bogdanov birfurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrodinger equation.Comment: 25 pages, 11 figures, resubmitted to Physical Review E March 2004 (originally submitted June 2003), added content and reference

Pengaruh Kebutuhan Memiliki Npwp, Kemudahan dalam Perpajakan, dan Pemahaman Wajib Pajak terhadap Kepemilikan Nomor Pokok Wajib Pajak (Npwp) (Studi Empiris pada Pengusaha UMKM di Kota Pekanbaru)

This study aimed to examine the effect caused by the need to have a TIN , convenience in taxation , taxpayers understanding to the ownership TIN. This study used a simple technique accidental sampling with a sample of 100 people who have been determined based on those results slovin formula . Data collection techniques in this study is a questionnaire , the data is processed using Logistic Regression with SPSS version 20 .The results of the testing that has been done , that factor does not affect the need to have a TIN to ownership variables NPWP . While the convenience in taxation factor and tax payers understanding factors affect the ownership TIN variables.Keywords : Needs to have a TIN , convenience in taxation , and understanding taxpayars, ownership taxpayer identification number (TIN

Can music be figurative? Exploring the possibility of crossmodal similarities between music and visual arts

According to both experimental research and common sense, classical music is a better fit for figurative art than jazz. We hypothesize that similar fits may reflect underlying crossmodal structural similarities between music and painting genres. We present two preliminary studies aimed at addressing our hypothesis. Experiment 1 tested the goodness of the fit between two music genres (classical and jazz) and two painting genres (figurative and abstract). Participants were presented with twenty sets of six paintings (three figurative, three abstract) viewed in combination with three sound conditions: 1) silence, 2) classical music, or 3) jazz. While figurative paintings scored higher aesthetic appreciation than abstract ones, a gender effect was also found: the aesthetic appreciation of paintings in male participants was modulated by music genre, whilst music genre did not affect the aesthetic appreciation in female participants. Our results support only in part the notion that classical music enhances the aesthetic appreciation of figurative art. Experiment 2 aimed at testing whether the conceptual categories ‘figurative’ and ‘abstract’ can be extended also to music. In session 1, participants were first asked to classify 30 paintings (10 abstract, 10 figurative, 10 ambiguous that could fit either category) as abstract or figurative and the to rate them for pleasantness; in session 2 participants were asked to classify 40 excerpts of music (20 classical, 20 jazz) as abstract or figurative and to rate them for pleasantness. Paintings which were clearly abstract or figurative were all classified accordingly, while the majority of ambiguous paintings were classified as abstract. Results also show a gender effect for painting’s pleasantness: female participants rated higher ambiguous and abstract paintings. More interestingly, results show an effect of music genre on classification, showing that it is possible to classify music as figurative or abstract, thus supporting the hypothesis of cross-modal similarities between the two sensory-different artistic expressions

On the realization of Symmetries in Quantum Mechanics

The aim of this paper is to give a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that the relevance of Wigner's theorem is not fully appreciated in general. It is Wigner's theorem which allows the use of linear realizations of symmetries and therefore guarantees that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical point of view in order to prove this theorem. It becomes apparent that Wigner's theorem is nothing else but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics.Comment: 8 page

Electrophysiological Signatures of Spatial Boundaries in the Human Subiculum.

Environmental boundaries play a crucial role in spatial navigation and memory across a wide range of distantly related species. In rodents, boundary representations have been identified at the single-cell level in the subiculum and entorhinal cortex of the hippocampal formation. Although studies of hippocampal function and spatial behavior suggest that similar representations might exist in humans, boundary-related neural activity has not been identified electrophysiologically in humans until now. To address this gap in the literature, we analyzed intracranial recordings from the hippocampal formation of surgical epilepsy patients (of both sexes) while they performed a virtual spatial navigation task and compared the power in three frequency bands (1-4, 4-10, and 30-90 Hz) for target locations near and far from the environmental boundaries. Our results suggest that encoding locations near boundaries elicited stronger theta oscillations than for target locations near the center of the environment and that this difference cannot be explained by variables such as trial length, speed, movement, or performance. These findings provide direct evidence of boundary-dependent neural activity localized in humans to the subiculum, the homolog of the hippocampal subregion in which most boundary cells are found in rodents, and indicate that this system can represent attended locations that rather than the position of one\u27s own body

Solitary waves of nonlinear nonintegrable equations

Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first class, which includes the well known so-called truncation methods, one \textit{a priori} assumes a given class of expressions (polynomials, etc) for the unknown solution; the involved work can easily be done by hand but all solutions outside the given class are surely missed. In the second class, instead of searching an expression for the solution, one builds an intermediate, equivalent information, namely the \textit{first order} autonomous ODE satisfied by the solitary wave; in principle, no solution can be missed, but the involved work requires computer algebra. We present the application to the cubic and quintic complex one-dimensional Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation.Comment: 28 pages, chapter in book "Dissipative solitons", ed. Akhmediev, to appea

Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation

I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered regimes encountered. The nature of the transition lines separating these phases is discussed, and preliminary results are presented which aim at evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to amoco.saclay.cea.fr in directory pub/chate, or by requesting them to [email protected]

An instability criterion for nonlinear standing waves on nonzero backgrounds

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a finite interval. Localized standing wave solutions on a non-zero background, e.g., dark solitons trapped by the inhomogeneity, are identified and studied. A novel instability criterion for such states is established through a topological argument. This allows instability to be determined quickly in many cases by considering simple geometric properties of the standing waves as viewed in the composite phase plane. Numerical calculations accompany the analytical results.Comment: 20 pages, 11 figure

Remarks on the Configuration Space Approach to Spin-Statistics

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.Comment: 18 page