Integrability of Dirac reduced bi-Hamiltonian equations

First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.Comment: 15 pages. Corrected some typos and added missing equations in Section 5 for g=sl_n, n>

The challenge of balance (1996)

"3/96/3M.""Stress management. ""Information from Human Environmental Sciences Extension.

Positive discipline and child guidance (2007)

"Information from Human Environmental Sciences Extension.""Child development."New 10/98, Revised 4/07/Web

Spectrum of One-Dimensional Anharmonic Oscillators

We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high accuracy as the values recently obtained for the unbounded case by the inner-product quantization method. We also apply our method to the Morse potential. The eigenvalues obtained in this case are in excellent agreement with the exact values for the unbounded Morse potential.Comment: 11 pages, 5 figures, 4 tables; there are changes to match the version published in Can. J. Phy

Possible Index for Marine Pollution from of Scleractinean Corals in Northern Gulf of Aqaba, Jordan

The coral nubbins of Stylophora sp., Pocillopora sp., Acropora sp., Fungia sp., and Porites sp. were taken from shallow depths of about 5 m by SCUBS diving. Another set of coral samples were collected in front of the Marine Science Station for incubation experiments to study the resistance of corals to different concentrations of heavy metals ranged between 0.1 to 50 ppm. The skeleton and tissue layers of all coral samples were isolated for samples, digested (using a mixture of Nitric and Hydrochloric acids) and were analyzed to determine the concentrations of Cd, Cu, Pb, Cr, Zn, and Ni using Flame Atomic Absorption Spectroscopy (FAAS). However, the lowest concentrations were found along the marine park including the Marine Science Station, with lower contamination of ambient waters as heavy metals concentration in corals reflects the health of marine environment. The highest concentrations of all heavy metals (Cd, Cu, Pb, Zn, Cr, and Ni) in the coral skeletons were accumulated in Pocillopora species whereas the lowest concentrations were recorded in Porites species and the rest coral species could be arranged in the following ranking order (from high to low concentrations): Pocillopora sp.> Acropora sp.> Stylophora sp.> Fungia sp.> Porites sp. The incubation experiment showed that the toxicity of the individual metals increased in all coral species with increasing metal doze and time of exposure until total death was reached. The coral species resistance to death for all heavy metals (except for Nickel) can be arranged in the following ranking order (from low to high): Stylophora sp.< Acropora sp.< Pocillopora sp.< Fungia sp.< Porites sp. The coral species Porities was the most resistant species. Copper was found as the most toxic metal to all coral species compared with the toxicity of Pb, Cd or Zn. The toxicity of the studied heavy metals (except Ni) to all corals species can be arranged in the following order (from high to low): Cu>Pb>Cd>Zn. It is generally concluded that the pollutions levels of heavy metals along the Jordanian coast of the Gulf of Aqaba are still relatively low and the coral reef communities are healthy. Corals are suitable to be used as proxy tools to record environmental pollution (bio-indicators) from the Gulf of Aqaba and the Red Sea. Keywords: Heavy metals, Corals, Gulf of Aqaba, Red Sea

Possible Index for Marine Pollution from Scleractinean Corals in Northern Gulf of Aqaba, Jordan

The coral nubbins of Stylophora sp., Pocillopora sp., Acropora sp., Fungia sp., and Porites sp. were taken from shallow depths of about 5 m by SCUBS diving. Another set of coral samples were collected in front of the Marine Science Station for incubation experiments to study the resistance of corals to different concentrations of heavy metals ranged between 0.1 to 50 ppm. The skeleton and tissue layers of all coral samples were isolated for samples, digested (using a mixture of Nitric and Hydrochloric acids) and were analyzed to determine the concentrations of Cd, Cu, Pb, Cr, Zn, and Ni using Flame Atomic Absorption Spectroscopy (FAAS). However, the lowest concentrations were found along the marine park including the Marine Science Station, with lower contamination of ambient waters as heavy metals concentration in corals reflects the health of marine environment. The highest concentrations of all heavy metals (Cd, Cu, Pb, Zn, Cr, and Ni) in the coral skeletons were accumulated in Pocillopora species whereas the lowest concentrations were recorded in Porites species and the rest coral species could be arranged in the following ranking order (from high to low concentrations): Pocillopora sp.> Acropora sp.> Stylophora sp.> Fungia sp.> Porites sp. The incubation experiment showed that the toxicity of the individual metals increased in all coral species with increasing metal doze and time of exposure until total death was reached. The coral species resistance to death for all heavy metals (except for Nickel) can be arranged in the following ranking order (from low to high): Stylophora sp.< Acropora sp.< Pocillopora sp.< Fungia sp.< Porites sp. The coral species Porities was the most resistant species. Copper was found as the most toxic metal to all coral species compared with the toxicity of Pb, Cd or Zn. The toxicity of the studied heavy metals (except Ni) to all corals species can be arranged in the following order (from high to low): Cu>Pb>Cd>Zn. It is generally concluded that the pollutions levels of heavy metals along the Jordanian coast of the Gulf of Aqaba are still relatively low and the coral reef communities are healthy. Corals are suitable to be used as proxy tools to record environmental pollution (bio-indicators) from the Gulf of Aqaba and the Red Sea. Keywords: Heavy metals, Corals, Gulf of Aqaba, Red Sea.

Possible Index for Marine Pollution from of Scleractinean Corals in Northern Gulf of Aqaba, Jordan

The coral nubbins of Stylophora sp., Pocillopora sp., Acropora sp., Fungia sp., and Porites sp. were taken from shallow depths of about 5 m by SCUBS diving. Another set of coral samples were collected in front of the Marine Science Station for incubation experiments to study the resistance of corals to different concentrations of heavy metals ranged between 0.1 to 50 ppm. The skeleton and tissue layers of all coral samples were isolated for samples, digested (using a mixture of Nitric and Hydrochloric acids) and were analyzed to determine the concentrations of Cd, Cu, Pb, Cr, Zn, and Ni using Flame Atomic Absorption Spectroscopy (FAAS). However, the lowest concentrations were found along the marine park including the Marine Science Station, with lower contamination of ambient waters as heavy metals concentration in corals reflects the health of marine environment. The highest concentrations of all heavy metals (Cd, Cu, Pb, Zn, Cr, and Ni) in the coral skeletons were accumulated in Pocillopora species whereas the lowest concentrations were recorded in Porites species and the rest coral species could be arranged in the following ranking order (from high to low concentrations): Pocillopora sp.> Acropora sp.> Stylophora sp.> Fungia sp.> Porites sp. The incubation experiment showed that the toxicity of the individual metals increased in all coral species with increasing metal doze and time of exposure until total death was reached. The coral species resistance to death for all heavy metals (except for Nickel) can be arranged in the following ranking order (from low to high): Stylophora sp.< Acropora sp.< Pocillopora sp.< Fungia sp.< Porites sp. The coral species Porities was the most resistant species. Copper was found as the most toxic metal to all coral species compared with the toxicity of Pb, Cd or Zn. The toxicity of the studied heavy metals (except Ni) to all corals species can be arranged in the following order (from high to low): Cu>Pb>Cd>Zn. It is generally concluded that the pollutions levels of heavy metals along the Jordanian coast of the Gulf of Aqaba are still relatively low and the coral reef communities are healthy. Corals are suitable to be used as proxy tools to record environmental pollution (bio-indicators) from the Gulf of Aqaba and the Red Sea. Keywords: Heavy metals, Corals, Gulf of Aqaba, Red Sea

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has a polynomial solution of degree at most n. We show that the classical differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this criterion. Further, we find the polynomial solutions for the generalized Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page

Precision hard turning of ti6al4v using polycrystalline diamond inserts: Surface quality, cutting temperature and productivity in conventional and high-speed machining

This article presents the results of an experimental investigation into the machinability of Ti6Al4V alloy during hard turning, including both conventional and high-speed machining, using polycrystalline diamond (PCD) inserts. A central composite design of experiment procedure was followed to examine the efects of variable process parameters; feed rate, cutting speed and depth of cut (each at five levels) and their interaction efects on surface roughness and cutting temperature as process responses. The results revealed that cutting temperature increased with increasing cutting speed and decreasing feed rate in both conventional and high-speed machining. It was found that high speed machining showed an average increase in cutting temperature of 65% compared with conventional machining. Nevertheless, high speed machining showed better performance in terms of lower surface roughness despite using higher feed rates compared to conventional machining. High-speed machining of Ti6Al4V showed an improvement in surface roughness of 11% compared with conventional machining, with a 207% increase in metal removal rate (MRR) which offered the opportunity to increase productivity. Finally, an inverse relationship was verified between generated cutting temperature and surface roughness. This was attributed mainly to the high cutting temperature generated, softening, and decreasing strength of the material in the vicinity of the cutting zone which in turn enabled smoother machining and reduced surface roughness

Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method

Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in excellent agreement with the ones obtained before. Without any loss of generality, other states and molecules could be treated in a similar way