Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system with third order ladders operators and found a family of superintegrable systems with higher order integrals of motion. We obtain also the polynomial algebra generated by these integrals. We calculate numerically the trajectories and show that all bounded trajectories are closed.Comment: 10 pages, 4 figures, to appear in j.math.phys

On convergence towards a self-similar solution for a nonlinear wave equation - a case study

We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In the first step we determine the spectrum of linearized perturbations about the attractor using a method of continued fractions. In the second step we demonstrate numerically that the resulting eigensystem provides an accurate description of the dynamics of convergence towards the attractor.Comment: 9 pages, 5 figure

Transformations of Heun's equation and its integral relations

We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erd\'elyi-type). Such kernels, by a limiting process, also afford new kernels for the confluent Heun equation.Comment: This version was published in J. Phys. A: Math. Theor. 44 (2011) 07520

A Bilinear Approach to Discrete Miura Transformations

We present a systematic approach to the construction of Miura transformations for discrete Painlev\'e equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of $\tau$-functions. Elimination of $\tau$-functions from the resulting system leads to another nonlinear equation, which is a ``modified'' version of the original equation. The procedure therefore yields Miura transformations. In this letter, we illustrate this approach by reproducing previously known Miura transformations and constructing new ones.Comment: 7 pages in TeX, to appear in Phys. Letts.

Inovasi Produk Sanseviera sebagai Pengharum dan Penyerap Asap

Pencemaran udara merupakan salah satu akibat dari aktivitas Perubahan manusia sehingga udara seringkali menurun kualitasnya. Perubahan kualitas ini dapat berupa Perubahan sifat-sifat fisis maupun sifat-sifat kimiawi. Keanekaragaman hayati di Indonesia dapat menjadi solusi dari permasalahan pencemaran udara yang semakin memperihatinkan. Terdapat banyak jenis tumbuhan yang berpotensi dalam menyerap polusi udara diantaranya tanaman lidah mertua (Sanseviera). Sansevieria mampu menyerap 107 jenis polutan di daerah padat lalu lintas dan ruangan yang penuh asap rokok,Tanaman sansevieria mampu mengurangi pencemaran udara baik di luar maupun di dalam ruangan terutama pencemaran yang disebabkan oleh CO dari asap rokok dan menurut penelitian NASA bekerja sama dengan ALCA telah menemukan bukti bahwa tanaman ini secara alami mampu menyerap bahan beracun, seperti karbondioksida, benzene, formaldehyde, trichloroethylene, Sehingga dapat mengurangi polusi dari bahan beracun tersebut. (Lestari, 2013). Adapun tujuan penelitian ini adalah untuk mengetahui kemampuan dan perbandingan yang lebih baik dalam menyerap polusi udara antara yang menggunakan sanseviera yang hidup dengan sanseviera yang kering. Penelitian ini dilakukan sebanyak 3 tahap. Tahap pertama persiapan sanseviera yakni sanseviera dipotong-potong kemudian di keringkan dan penentuan jenis sanseviera. Tahap kedua adalah proses pemasukan dalam toples yaitu sanseviera kering dikontakkan dengan asap rokok dan bauh tidak sedap dengan dosis 10, 20 dan 30. Tahap ketiga merupakan tahap melihat hasil penelitian dengan dengan dosis 10, 20 dan 30 setelah kontak dengan asap rokok dan bauh tidak sedap. Adapun Variabel proses dalam toples sanseviera meliputi dosis dan waktu menyerap sanseviera. Dari hasil percobaan diperoleh perbandingan dan penyerapan sanseviera adalah 30 gr sedangkan waktu terbaik selama proses penyerapan adalah 24 jam selama 1 minggu

Comparison of electron injection and recombination on TiO2 nanoparticles and ZnO nanorods photosensitized by phthalocyanine

Titanium dioxide (TiO2) and zinc oxide (ZnO) semiconductors have similar band gap positions but TiO2performs better as an anode material in dye-sensitized solar cell applications. We compared two electrodes made of TiO2nanoparticles and ZnO nanorods sensitized by an aggregation-protected phthalocyanine derivative using ultrafast transient absorption spectroscopy. In agreement with previous studies, the primary electron injection is two times faster on TiO2, but contrary to the previous results the charge recombination is slower on ZnO. The latter could be due to morphology differences and the ability of the injected electrons to travel much further from the sensitizer cation in ZnO nanorodsSpanish MINECO (CTQ2017-85393-P) and the Comunidad de Madrid (FOTOCARBON, S2013/MIT-2841) are highly acknowledged. K.V. acknowledges the Doctoral Programme of Tampere University of Technology for the financial support

Sentinel Lymph Node Biopsy in Pure DCIS: Is It Necessary?

Introduction. Sentinel lymph node biopsy (SLNB) in patients with pure ductal carcinoma in situ (DCIS) has been a matter of debate due to very low rate of axillary metastases. We therefore aimed to identify factors in a single institutional series to select patients who may benefit from SLNB. Material and Methods. Patients, diagnosed with pure DCIS (n = 63) between July 2000 and March 2011, were reviewed. All the sentinel lymph nodes were examined by serial sectioning (50 μm) of the entire lymph node and H&E staining, and by cytokeratin immunostaining in suspicious cases. Results. Median age was 51 (range, 30–79). Of 63 patients, 40 cases (63.5%) with pure DCIS underwent SLN, and 2 of them had a positive SLN (5%). In both 2 cases with SLN metastases, only one sentinel lymph node was involved with tumor cells. Patients who underwent SLNB were more likely to have a tumor size >30 mm or DCIS with intermediate and high nuclear grade or a mastectomy in univariate and multivariate analyses. Conclusion. In our series, we found a slightly higher rate of SLNB positivity in patients with pure DCIS than the large series reported elsewhere. This may either be due to the meticulous examination of SLNs by serial sectioning technique or due to our patient selection criteria or both

Volume calculation of the cattle (Bos taurus L.) and the water buffalo (Bos bubalis L.) metapodia with stereologic method

In this study, stereological volume estimations using 26 cattle metapodia (26 metacarpal and 26 metatarsal bones) and 8 water buffalo metapodia (8 metacarpal and 8 metatarsal bones) were made. For this purpose metapodia were parallel sectioned at 1 cm intervals according to Cavalieri principle. Grids with 0.4 cm probe intervals were superimposed on top of these sections and the matching points were counted. All of the bone structures and medullar cavity volumes were calculated with the data obtained from a formulation (V = t × a(p) × ΣP) as a spreadsheet using Microsoft Excel® Windows XP. In addition, percent ratio of this volume to whole bone volume was calculated. The mean ratio of bone marrow space to whole bone structure volume equals 15% in all of the cattle and buffalos. The difference between whole bone volumes of cattle and water buffalo was significant (p < 0.05) while the difference in volume of medullary cavity (cavum medullare) was not significantly different between the two investigated species. The aim of current study is to present a new method that can be used for the volumes calculation of whole bones and medullary cavity in metapodial bones and their percentages.