ON THE NEUTRINO MASS,THE ABUNDANCE OF RIGHT-HANDED NEUTRINO AND THE CLOSENESS OF THE UNIVERSE

We point out that although the neutrino mass is finite,the left-handed neutrino density still dominates over the righthanded one in the universe unless there exists one or more elementary fernions (quark or lepton) whose mass is larger than 10⁶ GeV. or M_WR/M_WL≤10². (M_WLand M_WR are the left and right handed intermediate boson respectively.If there exists neutrino the mass of which is about 34 ev. as indicated in some experiments, then one can conclude that the total neutrino mass of the universe s,bvld contribute abput 99%. to the whole masses and lead to the closeness of the universe.This conclusion can be brought to the agreement of all observation datd which have been-obtained so far. A mass limit of all species of neutrinos obtained by reexamining all data is ≤ 200 eV.     

NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE FLOW BY A NEW FORMULATION

A new mathematical formulation, called the pseudovorticity–velocity formulation, of the three-dimensional incompressible Navier–Stokes equations is presented as an alternative to the vorticity–velocity approach. For the model lid-driven cavity flow problem in two and three dimensions, combined with an explicit mixed spectral /finite different numerical scheme the proposed formulation is found to be efficient and very accurate as compared with the results available in the literature. In particular, the simulation results demonstrate an attractive feature of the present formulation compared with the vorticity–velocity approach, namely that the divergence-free condition of the velocity field can always be achieved on a non-staggered mesh.     

Realization of Tip Tilting By 8-Step Line Tilting

By direct calculation of rotation matrices of SO（3）, we show how certain specific sequence of eight consecutive rotations of digital angles can yield a tilting of a facet mirror. We also design a detailed program specifically to tilt an array of mirrors from planar orientation to the required focusing orientation. We describe how to use the 8-step to realize the focusing of the mirror array. We have found, in our designed program, an important feature of row-sharing during the rotations for the columns and similarly the column-sharing during the rotations for the row. This feature can save a lot of operating time during the actual realization of the mechanical movements.     

Tuning the potentials of "extra" electrons in colloidal n-type ZnO nanocrystals via Mg2+ substitution

Colloidal reduced ZnO nanocrystals are potent reductants for one-electron or multielectron redox chemistry, with reduction potentials tunable via the quantum confinement effect. Other methods for tuning the redox potentials of these unusual reagents are desired. Here, we describe synthesis and characterization of a series of colloidal Zn(1-x)Mg(x)O and Zn(0.98-x)Mg(x)Mn(0.02)O nanocrystals in which Mg(2+) substitution is used to tune the nanocrystal reduction potential. The effect of Mg(2+) doping on the band-edge potentials of ZnO was investigated using electronic absorption, photoluminescence, and magnetic circular dichroism spectroscopies. Mg(2+) incorporation widens the ZnO gap by raising the conduction-band potential and lowering the valence-band potential at a ratio of 0.68:0.32. Mg(2+) substitution is far more effective than Zn(2+) removal in raising the conduction-band potential and allows better reductants to be prepared from Zn(1-x)Mg(x)O nanocrystals than can be achieved via quantum confinement of ZnO nanocrystals. The increased conduction-band potentials of Zn(1-x)Mg(x)O nanocrystals compared to ZnO nanocrystals are confirmed by demonstration of spontaneous electron transfer from n-type Zn(1-x)Mg(x)O nanocrystals to smaller (more strongly quantum confined) ZnO nanocrystals.     

Giant Nernst effect and bipolarity in the quasi-one-dimensional metal Li0.9Mo6O17

The Nernst coefficient for the quasi-one-dimensional metal, Li{0.9}Mo{6}O{17}, is found to be among the largest known for metals (ν?500 μV/KT at T～20 K), and is enhanced in a broad range of temperature by orders of magnitude over the value expected from Boltzmann theory for carrier diffusion. A comparatively small Seebeck coefficient implies that Li{0.9}Mo{6}O{17} is bipolar with large, partial Seebeck coefficients of opposite sign. A very large thermomagnetic figure of merit, ZT～0.5, is found at high field in the range T≈35-50 K.     

Ω＋Ω→（ΩΩ）Jπ=0＋＋X Cross section Calculation

The cross sections of Ω+Ω→(ΩΩ)_J^π=0⁺+X are studied by using an effective Hamiltonian method. The results are σ_{Ω+Ω→(ΩΩ)0⁺+γ}=0.03～0.16×10^-29 cm² for p_Ω=100～400 MeV, and the cross sections of η production are about 10^-28 cm² for p_Ω > 880 MeV.     

α-Carbonyl Radical Cyclizatio n in Organic Synthesis

Intramolecular radical cyclization reactions are now used routinely to synthesize carbocyclic and heterocyclic structures. We have reported that α-carbonyl radicals 1, generated from the corresponding iodo ketones or enones, underwent intramolecular radical cyclization smoothly to afford products 2.1, 2,3     

Nathan Jacobson (1910-1999)

Nathan Jacobson, who died on 5 December 1999, was an outstandingalgebraist, whose work on almost all aspects of algebra wasof fundamental importance, and whose writings will exercisea lasting influence. He had been an honorary member of the Societysince 1972. Nathan Jacobson (later known as ‘Jake’ to his friends)was born in Warsaw (in what he describes as the ‘Jewishghetto’) on 5 October 1910 (through an error some documentshave the date 8 September); he was the second son of CharlesJacobson (as he would be known later) and his wife Pauline,née Rosenberg. His family emigrated to the USA duringthe First World War, first to Nashville, Tennessee, where hisfather owned a small grocery store, but they then settled inBirmingham, Alabama, where Nathan received most of his schooling.Later the family moved to Columbus, Mississippi, but the youngNathan entered the University of Alabama in 1926 and graduatedin 1930. His initial aim was to follow an uncle and obtain adegree in law, but at the same time he took all the (not verynumerous) mathematics courses, in which he did so well thathe was offered a teaching assistantship in mathematics in hisjunior (3rd) year. This marked a turning point; he now decidedto major in mathematics and pursue this study beyond College.During his final year at Alabama he applied for admission andfinancial aid to three top graduate schools in the country:Princeton, Harvard and Chicago. He was awarded a research assistantshipat Princeton; after the first year he was appointed a part-timeinstructor for two years, and during his fourth year he wasappointed a Procter Fellow. The stipend was enough to enablehim to make a grand tour of Europe by car in 1935, in the companyof two Princeton fellow-students at the time: H. F. Bohnenblustand Robert J. Walker.     

On the Group of Symplectic Matrices Over a Free Associative Algebra

Symplectic groups are well known as the groups of isometriesof a vector space with a non-singular bilinear alternating form.These notions can be extended by replacing the vector spaceby a module over a ring R, but if R is non-commutative, it willalso have to have an involution. We shall here be concernedwith symplectic groups over free associative algebras (witha suitably defined involution). It is known that the generallinear group GL_n over the free algebra is generated by the setof all elementary and diagonal matrices (see [1, Proposition2.8.2, p. 124]). Our object here is to prove that the symplecticgroup over the free algebra is generated by the set of all elementarysymplectic matrices. For the lowest order this result was obtainedin [4]; the general case is rather more involved. It makes useof the notion of transduction (see [1, 2.4, p. 105]). When thereis only a single variable over a field, the free algebra reducesto the polynomial ring and the weak algorithm becomes the familiardivision algorithm. In that case the result has been provedin [3, Anhang 5].