Time-dependent gradient perturbations of fractional Laplacian

We construct a fundamental solution of the equation {partial_t - Delta^{alpha/2} - b(cdot, cdot) cdotnabla_{x} = 0} for TeX{alpha in (1, 2)} and b satisfying a certain integral space-time condition. We also show it has α-stable upper and lower bounds

Shape-changing Collisions of Coupled Bright Solitons in Birefringent Optical Fibers

Wecritically review the recent progress in understanding soliton propagation in birefringent optical fibers.By constructing the most general bright two-soliton solution of the integrable coupled nonlinear Schroedinger equation (Manakov model) we point out that solitons in birefringent fibers can in general change their shape after interaction due to a change in the intensity distribution among the modes even though the total energy is conserved. However, the standard shape-preserving collision (elastic collision) property of the (1+1)-dimensional solitons is recovered when restrictions are imposed on some of the soliton parameters. As a consequence the following further properties can be deduced using this shape-changing collision. (i) The exciting possibility of switching of solitons between orthogonally polarized modes of the birefringent fiber exists. (ii) When additional effects due to periodic rotation of birefringence axes are considered, the shape changing collision can be used as a switch to suppress or to enhance the periodic intensity exchange between the orthogonally polarized modes. (iii) For ultra short optical soliton pulse propagation in non-Kerr media, from the governing equation an integrable system of coupled nonlinear Schroedinger equation with cubic-quintic terms is identified. It admits a nonlocal Poisson bracket structure. (iv) If we take the higher-order terms in the coupled nonlinear Schroedinger equation into account then their effect on the shape-changing collision of solitons, during optical pulse propagation, can be studied by using a direct perturbational approach.Comment: 14 pages, ROMP31, 4 EPS figure

Asymptotics of the solutions of the stochastic lattice wave equation

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic

Micro–Raman Spectroscopy of Diamonds from JaH 054 and Sahara 98505 Ureilites, Statistic Research

In this paper Raman spectra of diamonds from two different ureilites, JaH 054 and Sahara 98505, were measured. Obtained results for both ureilites showed the Raman shift ranged between 1321 cm -1 and 1336 cm -1 for JaH 054 and between 1329 cm -1 and 1336 cm -1 for Sahara 98505. FWHM parameter (full width at half maximum) varied also in wide range especially for Sahara 98505. Raman imaging was done for JaH 054 sample and diamonds of different Raman shifts (1321 cm-1, 1328 cm-1, 1330 cm-1) were found in few tens (im sized area of carbon vein. Raman peaks of ureilitic diamonds were compared with literature data of laboratory diamonds produced under high pressure, under low pressure with MW PACVD method and with other ureilites. Presented research showed that even in highly shocked ureilites Raman shift versus FWHM parameter plots are similar with CVD diamonds for ureilites. However, the origin of diamonds in ureilites is not explained based on the obtained results, close coexistence of different diamonds in investigated ureilites suggests that the mechanism of diamond creation in meteorites was very complex and could be multi-step process

PERANAN SISTEM FULL DAY SCHOOL DALAM MENUMBUHKAN SEMANGAT BELAJAR PESERTA DIDIK PADA PEMBELAJARAN PPKn (Studi Deskriptif di SMA Negeri 1 Gantar Kec. Gantar Kab. Indramayu)

Sebelum diterapkannya sistem full day school di dunia pendidikan yang peserta didiknya diharuskan untuk berada di sekolah selama 9 jam masih banyak siswa yang mengeluh atau malas untuk belajar, apalagi dengan diterapkannya sistem full day school yang siswanya diharuskan belajar di sekolah selama 11 jam dengan rentang waktu dari pukul 07.00-16.00 WIB. Untuk mengatasi adanya gesekan yang mungkin akan menimbulkan perpecahan, maka setiap sekolah menerapkan beberapa sanksi untuk memperbaiki sikap dan moral para peserta didikya, salah satu cara yang dilakukan adalah dengan adanya penerapan sanksi-sanksi bagi siapapun yang melanggar peraturan sekolah. Adapun tujuan dalam penelitian ini yaitu: 1) Mengetahui keadaan di sekolah dalam menumbuhkan semangat belajar peserta didik pada pembelajaran PPKn di SMA Negeri 1 Gantar. 2) Mengetahui pelaksanaan sistem full day school dalam menumbuhkan semangat belajar peserta didik pada pembelajaran PPKn di SMA Negeri 1 Gantar. 3) Mengetahui peranan sistem full day school dalam menumbuhkan semangat belajar peserta didik pada pembelajaran PPKn di SMA Negeri 1 Gantar. 4) Mengetahui hambatan yang muncul dan upaya yang dilakukan dalam menumbuhkan semangat belajar peserta didik pada pembelajaran PPKn di SMA Negeri 1 Gantar. Penelitian ini menggunakan studi deskriptif dengan pendakatan kualitatif, dalam penelitian ini yang menjadi subjek adalah Guru mata pelajaran PPKn dan peserta didik kelas XI MIPA 1 dan XII IPS SMA Negeri 1 Gantar. Pengumpulan data dan Instrumen penelitian dalam metode kualitatif yaitu observasi, wawancara, angket, studi dokumentasi. Hasil dari penelitian ini sebagai berikut: Melalui wawancara, peranan sistem full day school dalam menumbuhkan semangat belajar peserta sangat berperan dan membantu peserta didik dalam belajar. Dan untuk meningkatkan prestasi peserta didik dengan cara model pembelajaran yang menarik serta sarana dan prasarana yang memadai. Hasil angket yang penulis deskripsikan, keadaan di sekolah dalam menumbuhkan semangat belajar peserta didik di SMA Negeri 1 Gantar dapat di lihat di atas dalam diagram 4.2 menyatakan 56,60% peserta didik menyetujui bahwa peserta didik menyukai suasana belajar yang menyenangkan, adapun 44% lainnya menjawab setuju. Dan untuk meningkatkan semangat belajar peserta didik dapat meningkatkan prestasi belajar dapat di lihat di dalam diagram 4.5 menyatakan 0% ragu bahwa prestasi belajar tidak di pengaruhi oleh semangat belajar peserta didik adapun 20,75% sangat setuju, 24,53% setuju, dan 37,74% tidak setuju. Kata Kunci: Sistem Full Day School, Semangat Belajar Peserta Didi