Integrable four-dimensional symplectic maps of standard type

We search for rational, four-dimensional maps of standard type (x_{n+1} - 2x_n + x_{n-1} = eps f(x,eps)) possessing one or two polynomial integrals. There are no non-trivial maps corresponding to cubic oscillators, but we find a four-parameter family of such maps corresponding to quartic oscillators. This seems to be the only such example.Comment: 5 pages, compile with plain TEX. No figures. To appear in Physics Letters

PENGARUH KEPEMIMPINAN KEPALA SEKOLAH, BUDAYA SEKOLAH DAN KOMITMEN KERJA TERHADAP DISIPLIN GURU DI SMAN KABUPATEN KENDAL

Abstrak Rumusan masalah penelitian ini adalah: (1) Adakah pengaruh kepemimpinan kepala sekolah terhadap disiplin guru di SMA Negeri Kabupaten Kendal?, (2) Adakah pengaruh budaya sekolah terhadap disiplin guru di SMA Negeri Kabupaten Kendal?, (3) Adakah pengaruh komitmen kerja guru terhadap disiplin guru di SMA Negeri Kabupaten Kendal?, (4) Adakah pengaruh secara bersama sama antara kepemimpinan kepala sekolah, budaya sekolah dan komitmen kerja terhadap disiplin guru di SMA Negeri Kabupaten Kendal? Populasi penelitian ini 573 guru di Sekolah Menengah Atas Negeri Kabupaten Kendal. Sampel 236 guru diambil secara proporsionale random sampling. Pengumpulan data menggunakan kuesioner. Pengolahan data untuk uji validitas, uji reliebilitas, uji persyaratan dan uji hipotesis menggunakan program SPSS for Windows 21. Hasil penelitian menunjukkan bahwa: (1) Ada pengaruh kepemimpnan kepala sekolah terhadap disiplin guru sebesar 57,2% dengan kontribusi tertinggi dari dimensi disiplin peraturan organisasi dan kontribusinya paling rendah adalah pada dimensi disiplin peraturan kerja. (2) Ada pengaruh budaya sekolah terhadap disiplin guru sebesar 37,1% dengan kontribusi tertinggi dari dimensi supervisi dan kontribusinya paling rendah adalah pada dimensi manajerial. (3) Ada pengaruh komitmen kerja terhadap disiplin guru sebesar 27,2% dengan kontribusi tertinggi dari kontribusi adalah dimensi komitmen berkelanjutan dan kontribusinya paling rendah yaitu komitmen efektif. (4) Ada pengaruh kepemimpinan kepala sekolah, budaya sekolah, dan komitmen kerja secara bersama-sama terhadap disiplin guru sebesar 65,8%, dengan kontribusi tertinggi dari variabel kepemimpinan kepala sekolah dan kontribusi terendah dari variabel komitmen kerja guru. Berdasarkan hasil penelitian maka direkomendasikan, (1) Guru agar memiliki komitmen terhadap tanggungjawab tugasnya secara disiplin. (2) Kepala sekolah agar melibatkan guru dalam menyusun perencanaan kegiatan sekolah. (3) Dinas Pendidikan untuk memberikan arahan kepada kepala sekolah agar memberikan bimbingan kepada semua guru untuk mentaati peraturan jam kerja ASN.Kata kunci: kepemimpinan kepala sekolah, budaya sekolah, komitmen kerja, disiplin guru

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

Integrable systems without the Painlev\'e property

We examine whether the Painlev\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlev\'e continuous linearisable systems. We find that while these discrete systems are themselves linearisable, they possess nonconfined singularities

Extension of the Adler-Bobenko-Suris classification of integrable lattice equations

The classification of lattice equations that are integrable in the sense of higher-dimensional consistency is extended by allowing directed edges. We find two cases that are not transformable via the 'admissible transformations' to the lattice equations in the existing classification.Comment: 14 pages, 2 figure

The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.Comment: 13 pages, 2 figure

Special solutions for Ricci flow equation in 2D using the linearization approach

The 2D Ricci flow equation in the conformal gauge is studied using the linearization approach. Using a non-linear substitution of logarithmic type, the emergent quadratic equation is split in various ways. New special solutions involving arbitrary functions are presented. Some special reductions are also discussed.Comment: 8 pages, latex, no figure

Aleuritic Acid

Aleuritic Aci

Linearisable Mappings and the Low-Growth Criterion

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more stringent criterion of nonexponential growth of the degrees of the iterates. We show that the linearisable mappings are characterised by a very special degree growth. The ones linearisable by reduction to projective systems exhibit zero growth, i.e. they behave like linear systems, while the remaining ones (derivatives of Riccati, Gambier mapping) lead to linear growth. This feature may well serve as a detector of integrability through linearisation.Comment: 9 pages, no figur

On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian

A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.Comment: 12 pages, 3 figures, NATO ARW, 15-19 september 2002, Elb