Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

On computing joint invariants of vector fields

A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko, Patera and Popoyvich \cite{BPP}

d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge

Pengurangan Kadar H2s Dari Biogas Limbah Cair Rumah Sakit Dengan Metode Adsorpsi

Biogas sebelum digunakan harus dimurnikan terlebih dahulu dari kandungan asam sulfida (H2S) yang meskipun jumlahnya kecil namun menimbulkan kerugian karena menimbulkan korosi pada logam atau apabila dibakar akan membentuk SO2 atau SO3 yang dikenal dengan SOx yang menyebabkan terjadinya hujan asam. Tujuan dari penelitian ini adalah mencari waktu jenuh adsorben dalam menjerap H2S, mengetahui kemampuan adsorben karbon aktif dalam menyerap dan mencari konstanta persamaan adsorpsi isotherm Freundlich pada variasi ukuran karbon aktif yang digunakan dalam menghitung waktu tinggal adsorpsi. Bahan yang digunakan adalah sludge dari hasil pengolahan limbah cair rumah sakit. Metode yang dilakukan dalam penelitian ini yaitu mengukur kandungan H2S dalam biogas sebelum melalui adsorber disusun secara seri ukuran tinggi kolom 70 cm, diameter ½ inch, tinggi isian 64 cm bahan isian karbon aktif dengan ukuran 4, 7, 10, 12, 14 mesh kecepatan biogas 0.5 liter/menit diperoleh hasil karbon aktif paling cepat mengalami kejenuhan ukuran 4 mesh yaitu 60 menit, H2S yang terjerap 202.42 unit dari effisiensi kejenuhan 9.76% sedangkan waktu jenuh paling lama 90 menit ukuran karbon aktif 14 mesh H2S yang terjerap 368.65 unit effisiensi kejenuhan 9.79%. Karbon aktif yang optimal digunakan yaitu 12 mesh waktu jenuh 80 menit, effisiensi kejenuhan 9.82% dengan waktu tinggal 127.927 detik sedangkan waktu tinggal paling singkat terjadi pada ukuran adsorben 4 mesh, yaitu waktu tinggal 73.855 detik. Keywords: limbah, biogas, adsorpsi, asam sulfida, karbon aktif Biogas is purified before being used in from the acid content of sulfide (H2S), although the numbers are small, but the resulting loss due to corrode metal or when burned to form SO2 or SO3, known as SOx that cause acid rain. The purpose of this study to find time in the saturated adsorbent adsorb H2S, the ability of the activated carbon adsorbent adsorb adsorption equation and find the constants in the Freundlich isotherm variations in the size of activated carbon for in calculating the residence time of adsorption. The materials used are the sludge from the hospital wastewater treatment. The method was performed in this study for measure the content of H2S in the biogas before passed through to the third adsorber column 70 cm height, ½ inch diameter, 64 cm high filling packing material of activated carbon with a size of 4, 7, 10, 12, 14 mesh velocity biogas 0 , 5 litre. / min obtained results most rapidly activated carbon burnout mesh size of 4 is 60 minutes, H2S is adsorption 202.42 mg of 9.76% while the efficiency of saturation saturation time exceeding 90 minutes 14 mesh size activated carbon is adsorption H2S 368.65 mg 9.79% saturation efficiency. Optimal use of activated carbon which is 12 mesh saturated 80-minute time, efficiency saturated 9.82% with a residence time of 127.927 seconds while the shortest residence time occurs on the mesh size of adsorbent 4, the residence time of 73.855 seconds

Future Community-Based Ecotourism (CBET) development

Ecotourism is an alternative form of tourism and is usually confused with natural and cultural tourism.CBET is fast becoming a popular biodiversity conservation tool that develops and benefits the local community. Based on the context of conservation theory and practice, Community-Based Ecotourism (CBET) is a form of community-based natural resource management. However, a sustainable CBET development through Community Capacity Building (CCB)programs is not something that it easily achievable. Local community’s capacity varies from one culture to another. It takes a high level of community participation, in order for it to come to a level where the community members themselves are motivated to participate and contribute to the development of the program. This fully qualitative research involved 15 respondents from the community of Kg. Selai, Bekok in Johor, Malaysia. The result show there are five factors that sustained the ecotourism development based for Orang Asli Community in Kg. Selai, namely, existing CBET development, past CBET development, local community participation in planning stage of tourism, local participation in implementation stage of tourism and participation in nature conservation

Bound - states for truncated Coulomb potentials

The pseudoperturbative shifted - $l$ expansion technique PSLET is generalized for states with arbitrary number of nodal zeros. Bound- states energy eigenvalues for two truncated coulombic potentials are calculated using PSLET. In contrast with shifted large-N expansion technique, PSLET results compare excellently with those from direct numerical integration.Comment: TEX file, 22 pages. To appear in J. Phys. A: Math. & Ge

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Can Van Hove singularities be observed in relativistic heavy-ion collisions ?

Based on general arguments the in-medium quark propagator in a quark-gluon plasma leads to a quark dispersion relation consisting of two branches, of which one exhibits a minimum at some finite momentum. This results in a vanishing group velocity for collective quark modes. Important quantities such as the production rate of low mass lepton pairs and mesonic correlators depend inversely on this group velocity. Therefore these quantities, which follow from self energy diagrams containing a quark loop, are strongly affected by Van Hove singularities (peaks and gaps). If these sharp structures could be observed in relativistic heavy-ion collisions it would reveal the physical picture of the QGP as a gas of quasiparticles.Comment: 12 pages including nine figures and style files, invited talk given at the ICPAQGP-2001, November 26-30, 2001, Jaipur, Indi

Thermodynamics of the PNJL model with nonzero baryon and isospin chemical potentials

We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavours to include the isospin chemical potential ($\mu_I$). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential ($\mu_0$) and isospin chemical potential upto sixth order have been extracted at $\mu_0 = \mu_I = 0$. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavour diagonal and off-diagonal susceptibilities are also presented. Comparison to Lattice QCD (LQCD) data of some of these susceptibilities for which LQCD data are available, show similar temperature dependence, though there are some quantitative deviations above the crossover temperature. We have also looked at the effects of instanton induced flavour-mixing coming from the $U_A(1)$ chiral symmetry breaking 't Hooft determinant like term in the NJL part of the model. The diagonal quark number and isospin susceptibilities are completely unaffected. The off-diagonal susceptibilities show significant dependence near the crossover. Finally we present the chemical potential dependence of specific heat and speed of sound within the limits of chemical potentials where neither diquarks nor pions can condense.Comment: 15 pages, 7 figures, Added discussions and references, version to appear in Phys. Rev.