Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

The site of ionization in the acetylation of aliphatic esters by [(CH3CO)3]+

A series of esters RCOOR′ (where R, R′ = CH₃, CH₃CH₂, (CH₃)₂CH, (CH₃)₃C) were reacted with the [(CH₃CO)₃]⁺ ion from biacetyl in an ion cyclotron resonance spectrometer. A steric effect influences the rate of formation of stable products [RCOOR′·CH₃CO]⁺ and is used to determine that either oxygen of the ester may be initially acylated by [(CH₃CO)₃]⁺.     

The formation of metal—carbon bonds via insertion reactions in gaseous negative ion/molecule reactions

The negative ion mass spectra under chemical ionization conditions for a series of copper(II), nickel(II), and cobalt(II) Schiff base complexes have been measured. Reagent gases employed include methane, isobutane, and methane-d₄. For all complexes, molecular negative ions were produced with all three reagent gases via secondary electron capture processes. Ion/molecule reactions between the molecular negative ion and the neutral reactant gas appear to be the dominant processes for the formation of secondary ions. The secondary reactions lead to the incorporation of the CH₂ moiety into the nickel(II) complexes and the CH₃ group into the cobalt(II) compounds.     

Synthesis of Iron Oxide Nanoparticles Used as MRI Contrast Agents: A Parametric Study

Colloidal iron oxides play an important role as magnetic resonance imaging (MRI) contrast agents. The superparamagnetic particles actually used are constituted by solid cores (diameter of 5-15 nm), generally coated by a thick polysaccharidic layer (hydrodynamic radii of 30-100 nm), and formulated by direct coprecipitation of iron salts in the presence of polymeric material. To better control the synthesis, we attempted to formulate new stable uncoated superparamagnetic nanoparticles. Colloids were generated by coprecipitation of an aqueous solution of iron salts and tetramethylammonium hydroxide (TMAOH) solution. The influence of parameters such as media composition, iron media, injection fluxes, Fe and TMAOH concentrations, temperature, and oxygen on size, magnetic and magnetic resonance relaxometric properties, and colloidal stability of particles were evaluated. We have determined the relative importance of these parameters as well as the optimal conditions for obtaining uncoated stable particles with an average size of 5 nm and interesting relaxivities. The interpretation of the observed limits takes into account diffusibilities of reactants and product, feeding rates of reactants, and surface properties of nanoparticles. A model of synthesis, related to spontaneous emulsification of suspensions, is proposed. Copyright 1999 Academic Press.     

The effect of transverse normal strain in contact of an orthotropic beam pressed against a circular surface

The contact problem of a straight orthotropic beam pressed onto a rigid circular surface is considered using beam theories that account for transverse shear and transverse normal deformations. The circular nature of the rigid surface emphasizes the difference between Euler Bernoulli theory behavior, where point loads develop at the edge of contact, and the higher order theories that predict non-singular pressure distributions. While Timoshenko beam theory is the simplest theory that addresses this behavior, the prediction of a maximum value of pressure at the edge of contact contradicts the elasticity theory result that contact pressure must drop to zero. Transverse normal strain is therefore introduced, both to study this fundamental discrepancy and to include an important effect in many contact problems. To investigate this effect, higher order beam theories that account for both constant and linear transverse normal strain through the beam thickness are derived using the principle of virtual work. The resulting orthotropic beam theories depend on the bending stiffness (EI), shear stiffness (GA), axial stiffness (EA₁) and transverse normal stiffness (EA₂), which are independent stiffness parameters that can differ by orders of magnitude. The above mentioned contact problem is then solved analytically for these theories, along with the Timoshenko beam model which assumes zero transverse normal strain. The results for different orthotropic materials show that inclusion of transverse normal deformation has a significant effect on the contact pressure solution. Furthermore, the solution using higher order beam theories encompasses the two extremes of a Hertz-like contact pressure when the half contact length is smaller than the thickness of the beam, and the Timoshenko beam theory case when the half contact length is much larger than the thickness. Concerning the behavior of the pressure at the edge of contact, adherence to the boundary conditions required by the principle of virtual work, shows that while the pressure does tend to zero, it does not become zero unless artificially enforced. In this regard the solution for the case of linear strain is better than that for constant strain. All beam solutions are validated with plane elasticity solutions obtained using the commercial finite element software ABAQUS.