Another independent self-dual basis for the trivial variety

We give a new independent self-dual 3-basis for the trivial variety with two binary operations. Received October 24, 2006; accepted in final form January 25, 2007.     

Stagnation flow on a cylinder with partial slip--an exact solution of the Navier-Stokes equations

The stagnation slip flow on an axially moving cylinder is studied.The Navier–Stokes and energy equations reduce to nonlinearordinary differential equations under a similarity transform.For large slip, the flow field decays exponentially into potentialflow. The heat transfer can be expressed as an incomplete gammafunction. In general, the heat transfer increases with slip,Prandtl number and Reynolds number.     

The essential Lagrangian-Grassmannian and the homotopy type of the Fredholm Lagrangian-Grassmannian

Let H be a separable infinite dimensional Hilbert space endowed with a symplectic structure and let L₀⊂H be a Lagrangian subspace. Using the results of [A. Abbondandolo, P. Majer, Infinite dimensional Grassmannians, math.AT/0307192], we show that the Fredholm Lagrangian-Grassmannian FL₀(Λ) has the homotopy type of Gc(L₀), the Grassmannian of all Lagrangian subspaces of H that are compact perturbations of L₀. It is well known that the latter has the homotopy type of the quotient U(∞)/O(∞). As a corollary, we recover a result by B. Booss-Bavnbek and K. Furutani (see [B. Booss-Bavnbek, K. Furutani, Symplectic functional analysis and spectral invariants, Contemp. Math. 242 (1999) 53-83; K. Furutani, Fredholm-Lagrangian-Grassmannian and the Maslov index, J. Geom. Phys. 51 (2004) 269-331]) that the L₀-Maslov index is an isomorphism between the fundamental group of FL₀(Λ) and the integers.     

Magnetic,structural and electrical properties of ordered and disordered Co50Fe50 films

Co₅₀Fe₅₀ films with thickness varying from 100 to 500 Å were deposited on a glass substrate by sputtering process, respectively. Two kinds of CoFe films were studied: one was the as-deposited film, and the other the annealed film. The annealing procedure was to keep the films at 400 °C for 5 h in a vacuum of 5×10⁻⁶ mbar. From the X-ray study, we find that the as-deposited film prefers the CoFe(1 1 0) orientation. Moreover, the body-centered cubic (bcc) CoFe(1 1 0) line is split into two peaks: one corresponding to the ordered body-centered tetragonal (bct) phase, and the other, the disordered bcc phase. After annealing, the peak intensity of the ordered bct phase becomes much stronger, while that of the disordered bcc phase disappears. The annealing has also caused the ordered CoFe(2 0 0) line to appear. When the amount of the ordered bct phase in Co₅₀Fe₅₀ is increased, the saturation magnetization (M_s) and coercivity (H_c) become larger, but the electrical resistivity (ρ) decreases. From the temperature coefficient of resistance (TCR) measurement, we learn that the bct grains in the CoFe film start to grow at temperature 82 °C.     

The Nature of Electronic Charge

Advances in gauge theories and unified theories have not thrown light on the meaning of electron. The problem of the origin of electronic charge is made precise, new insights gained from Weyl space are summarized, and the origin of charge in terms of fractional spin is suggested. A new perspective on the abelian Chern-Simons theory is presented to explain charge.     

Analysis of some medicinal plants in South-western Nigeria using PIXE

Summary Analysis of thirteen medicinal plants of various biological activities commonly used in South-western Nigeria was carried out using PIXE technique. Nine of these plants are anti-cancer while four are antimicrobial. PIXE measurements were carried out using collimated proton beams delivered by the 2. 5 MV AN 2000 Van de Graaff accelerator at the Istituto Nazionale di Fisica Nucleare (INFN), (LNL) Legnaro, (Padova), Italy. The results showed the presence of twenty three different elements in the plants and none of them contains any toxic heavy metals. Only Chenopodium ambrosioides showed detectable levels of selenium which is considered important in cancer prevention.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Anionic polymerization of star-shaped nylon 6 with a trifunctional initiator

The anionic polymerization of ?-caprolactam (CLM) has been shown to proceed at high reaction rate when catalyzed by metallic lactamates and initiated by acyllactams. The role of initiator and catalyst concentration on the process of ?-caprolactam anionic polymerization has been explored, with the aim of selecting the most suitable experimental conditions for reaction injection molding (RIM). The overall polymerization rates and physical properties for reaction injection molding of star-shaped nylon 6 homopolymer have been studied by the quasi-adiabatic process. In order to model the actual rapid molding conditions, time vs. temperature reaction profiles were measured, and the relative rates of polymerization subsequently determined from these data.     

Superstring motivated gauge models based on a rank six subgroup ofE 6

We discuss gauge models based on a superstring motivated rank six subgroup ofE ₆. Lepton number is an accidental unbroken symmetry of the models which leads to an essentially stable proton. One of the neutral gauge bosons couples toB-L and may have mass below a TeV.     

Fourier Analysis of Semistable Distributions

We consider the generalized convolution powers G _α ^*u (x) of an arbitrary semistable distribution function G _α (x) of exponent α∈(0,2), and prove that for all j, k∈{0,1,2,…} and u>0 the derivatives G _α ^(k,j)(x;u)=∂ ^k+j G _α ^*u (x)/∂ x ^k ∂ u ^j , x∈ℝ, are of bounded variation on the whole real line ℝ. The proof, along with an integral recursion in j, is new even in the special case of stable laws, and the result provides a framework for possible asymptotic expansions in merge theorems from the domain of geometric partial attraction of semistable laws. An erratum to this article can be found at