Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths

The problem of counting plane trees with $n$ edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity was also obtained by Bonin, Shapiro and Simion in their study of Schr\"oder paths, and it was recently derived by Coker using the Lagrange inversion formula. An equivalent problem for partitions was independently studied by Klazar. We present three parity reversing involutions, one for unlabelled plane trees, the other for labelled plane trees and one for 2-Motzkin paths which are in one-to-one correspondence with Dyck paths.Comment: 8 pages, 4 figure

Causal sites as quantum geometry

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle of a smooth manifold. Examples with reasonable finiteness conditions have an intrinsic geometry, which can approximate classical solutions to general relativity. We propose an approach to quantization of causal sites as well.Comment: 21 pages, 3 eps figures; v2: added references; to appear in JM

Fluctuation Bounds For Interface Free Energies in Spin Glasses

We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.Comment: 19 pages, 0 figure

Proses Penuntutan Bagi Para Pelaku Tindak Pidana Hak Cipta Sesuai Dengan Hukum Acara Pidana

Seseorang menciptakan sesuatu yang merupakan hasil karya ciptaannya pada umumnya selain digunakan untuk diri sendiri, juga kemudian diperbanyak untuk dapat dimanfaatkan kepada orang lain.Sebagaimana diketahui bahwa menciptakan sesuatu karya cipta bukan sesuatu hal mudah dilakukan seseorang. Oleh karena itu, orang lain diwajibkan menghormatinya dan hal ini merupakan sebuah kebutuhan yang tidak boleh dilalaikan begitu saja.Secara garis besar Hak Cipta bersama-sama dengan Hak Kekayaan Industri menjadi bagian dari Hak atas Kekayaan Intelektual yang disingkat HAKI. Berdasarkan uraian tersebut di atas, yang melatarbelakangi permasalahan dalam penulisan ini ialahbagaimana proses penuntutan perkara pidana hak cipta serta apa sajakah yang menjadi penyebab seseorang melanggar hak cipta. Metode penulisan yang digunakan adalah metode penelitian yuridis normatif dengan menggunakan data kepustakaan yang diperoleh dengan meneliti peraturan yang terkait dengan permasalahan yang diteliti. Dalam penelitian ini bahan pustaka merupakan data dasar penelitian yang digolongkan sebagai data sekunder. Hasil penelitian menunjukkan bahwa proses penuntutan perkara pidana di bidang hak cipta; setelah perkara pidana di bidang hak cipta selesai dilakukan penyidikan maka selanjutnya penyidik PNS (penyidik khusus di bidang hak cipta) melimpahkan berkas tersebut kepada penuntut umum melalui penyidik Polri. Penyidik Polri harus mengetahui dan berperan dalam pelimpahan perkara pidana ke kejaksaan negeri, karena sebagai koordinator dan pengawas penyidik PNS tidak dapat dilewati begitu saja. Berkas yang sudah sampai di kejaksaan negeri kemudian dilakukan penuntutan. Selanjutnya penyebab-penyebab timbulnya pelanggaran hak cipta yaitu: masyarakat memandang hak cipta sebagai milik bersama; barang bajakan lebih murah dari barang orisinil; kemajuan teknologi mempermudah terjadinya pelanggaran hak cipta; UU Hak Cipta masih kurang memasyarakat; proses penuntutan perkara pidana hak cipta ialah hasil pelimpahan berkas dari penyidik PNS di bidang hak cipta melalui penyidik Polri kepada penuntut umum. Dari hasil penelitian dapat ditarik kesimpulan bahwa masalah penyebab masyarakat melakukan pelanggaran hak cipta dapat disimpulkan bahwa masyarakat melakukan pelanggaran karena menganggap hak cipta itu milik bersama, ingin memiliki suatu karya cipta orang lain dengan harga yang murah, kemajuan teknologi yang mempermudah melakukan pelanggaran hak cipta dan Undang-Undang yang kurang memasyarakat

A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces

Let $G/K$ be a simply connected spin compact inner irreducible symmetric space, endowed with the metric induced by the Killing form of $G$ sign-changed. We give a formula for the square of the first eigenvalue of the Dirac operator in terms of a root system of $G$. As an example of application, we give the list of the first eigenvalues for the spin compact irreducible symmetric spaces endowed with a quaternion-K\"{a}hler structure

An Investigation of the Large-scale Variability of the Apparently Single Wolf-Rayet Star WR 1

In recent years, much studies have focused on determining the origin of the large-scale line-profile and/or photometric patterns of variability displayed by some apparently single Wolf-Rayet stars, with the existence of an unseen (collapsed?) companion or of spatially extended wind structures as potential candidates. We present observations of WR 1 which highlight the unusual character of the variations in this object. Our narrowband photometric observations reveal a gradual increase of the stellar continuum flux amounting to Delta v = 0.09 mag followed by a decline on about the same timescale (3-4 days). Only marginal evidence for variability is found during the 11 following nights. Strong, daily line-profile variations are also observed but they cannot be easily linked to the photometric variations. Similarly to the continuum flux variations, coherent time-dependent changes are observed in 1996 in the centroid, equivalent width, and skewness of He II 4686. Despite the generally coherent nature of the variations, we do not find evidence in our data for the periods claimed in previous studies. While the issue of a cyclical pattern of variability in WR 1 is still controversial, it is clear that this object might constitute in the future a cornerstone for our understanding of the mechanisms leading to the formation of largely anisotropic outflows in Wolf-Rayet stars.Comment: 11 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Solving Potential Scattering Equations without Partial Wave Decomposition

Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a partial-wave expansion. We illustrate this procedure for the Bethe-Salpeter equation for pion-nucleon scattering and give explicit details for the one-nucleon-exchange term in the potential. Finally, we show how this method can be applied to pion photoproduction from the nucleon with $\pi N$ rescattering being treated so as to maintain unitarity to first order in the electromagnetic coupling. The procedure for removing the azimuthal angle dependence becomes increasingly complex as the spin of the particles involved increases.Comment: 15 pages, 4 figure

Consumer Choice and Information: New Experimental Evidence

This paper reports on a series of experiments designed to explore the so-called "information overload" hypothesis. We generally find that our subjects do quite well at screening out irrelevant information. Further, we find that a key element determining the quality of choices made by our subjects is the number of "salient" attributes, not just the number of attributes for which information is provided. Weak evidence is found which suggests a form of overload might occur when the number of salient dimensions is high and information is given on all of them. Finally, we discuss the implications of these results on the disclosure controversy

Optimal and Nonoptimal Satisficing I: A Model of 'Satisfactory' Choice

In this paper the authors report the results of a series of individual choice experiments designed to test the usefulness of a particular theory of satisficing and of conjunctive choice models. Several authors have argued that modeling complicated choice problems by using a conjunctive approach can provide useful simplifications. In fact optimal behavior with these models can involve implementation of extremely complicated strategies. The experiments reported deal with multidimensional search problems structured so that the conjunctive model is appropriate. Four groups of subjects performed the same tasks with similar results. In general, subjects' behavior conforms well to predictions based on optimization and where there is systematic deviation they are consistent with a specific theory of satisficing