Particular Integrability and (Quasi)-exact-solvability

A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland Hamiltonians for all roots are found. In the classical case some special trajectories for which the corresponding particular constants of motion appear are indicated.Comment: 13 pages, typos correcte

Flavor Delta(54) in SU(5) SUSY Model

We design a supersymmetric SU (5) GUT model using \Delta (54), a finite non-abelian subgroup of SU (3)f . Heavy right handed neutrinos are introduced which transform as three-dimensional repre-sentation of our chosen family group. The model successfully reproduces the mass hierarchical mass structures of the Standard Model, and the CKM mixing matrix. It then provides predictions for the light neutrino with a normal hierarchy and masses such that m{\nu},1 \approx 5\times10-3 eV, m{\nu}, 2 \approx 1\times 10-2 eV, and m{\nu},3 \approx 5 \times 10-2 eV. We also provide predictions for masses of the heavy neutrinos, and correc- tions to the tri-bimaximal matrix that fit within experimental limits, e.g. a reactor angle of -7.31o. A simple modification to our model is introduced at the end and is shown to also produce predictions that fall well within those limits.Comment: 22 page

Inelastic and elastic collision rates for triplet states of ultracold strontium

We report measurement of the inelastic and elastic collision rates for ^{88}Sr atoms in the (5s5p)^3P_0 state in a crossed-beam optical dipole trap. This is the first measurement of ultracold collision properties of a ^3P_0 level in an alkaline-earth atom or atom with similar electronic structure. Since the (5s5p)^3P_0 state is the lowest level of the triplet manifold, large loss rates indicate the importance of principle-quantum-number-changing collisions at short range. We also provide an estimate of the collisional loss rates for the (5s5p){^3P_2} state.Comment: 4 pages 5 figure

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

Composite Cutting with Abrasive Water Jet

Abrasive Water Jet (AWJ) technology has demonstrated to be an interesting manufacturing process for space, aircraft, boat and automotive sectors due to its specific advantages when machining composite materials. However, AWJ cutting of composite laminates possesses several challenges. It is necessary to develop a methodology to adapt the process parameters for each type of FRP & CFRP material which will allow AWJ trimming operations to be easily carried out on composite materials, since machine manufacturers still do not provide good databases for composite cutting. The presented work aims at studying the behaviour of a machinability model in composite materials. The machinability index for various composite materials with different thicknesses was found experimentally, which showed very different results for different materials. A study of the effect of the abrasive waterjet process parameters on the quality of cut (taper and surface roughness) was carried out

Repumping and spectroscopy of laser-cooled Sr atoms using the (5s5p)3P2 - (5s4d)3D2 transition

We describe repumping and spectroscopy of laser-cooled strontium (Sr) atoms using the (5s5p)3P2 - (5s4d)3D2 transition. Atom number in a magneto-optical trap is enhanced by driving this transition because Sr atoms that have decayed into the (5s5p)3P2 dark state are repumped back into the (5s2)1S0 ground state. Spectroscopy of 84Sr, 86Sr, 87Sr, and 88Sr improves the value of the (5s5p)3P2 - (5s4d)3D2 transition frequency for 88Sr and determines the isotope shifts for the transition.Comment: 4 pages, 5 figure

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

Plasmid DNA recovery from fermentation broths by a combined process of micro- and ultrafiltration : modeling and application

Microfiltration and ultrafiltration operations were used in tandem to isolate and purify a 6050 bp plasmid DNA (pDNA). To achieve primary isolation of the plasmid from fermentation broths, immediately after cell lysis, a 0.2 μm microfiltration membrane was selected for solid/liquid separation, which was performed in a diafiltration mode, as an alternative to centrifugation. Then to attain plasmid concentration and purification, an ultrafiltration membrane with a pore radius of 4.1 nm was selected. Permeation of pDNA and RNA in the two membrane steps was modeled using recently published mass transfer models applicable to the permeation of closed segmented chains and freely-jointed chains, respectively. The permeation of proteins and genomic DNA (gDNA) was also studied in these operations. The microfiltration operation allowed high plasmid and RNA permeation, as expected. It was observed that significant amounts of gDNA, previously precipitated during the cell lysis step, reappear in solution during the diafiltration step. The effect of the ionic strength on this apparent re-solubilization was investigated, by testing the addition of two different salts to the diafiltration buffer: CH3COOK and CaCl2. The results show that these salts can be used to control gDNA apparent re-solubilization. During the ultrafiltration operation high plasmid retention with low adsorption was obtained under low ionic strength conditions. The results also show that a significant removal proteins and the re-solubilized gDNA is achieved, as well as some purification in respect to low molecular weight RNA, since all these components permeate through the ultrafiltration membrane