The use of triethanolamine in a buffer for the determination of fluoride in calcium and transition metal orthophosphates, using a fluoride-selective el

A method is described for the determination of fluoride in inorganic orthophosphates. Interference by complex-forming metal ions is avoided by the use of a citric acid-triethanolamine buffer, pH < 7.5.     

Diffusion Collisionnelle Induite Pour Les Bandes Rayleigh Et ν1 Raman Du Liquide Isotopique CCl4

We have studied the depolarized component of the ν₁ Raman band of the isotopic liquid C³⁵Cl₄ at 296 K. We compare the experimental Rayleigh and Raman depolarized scattering with theoretical spectra calculated using dipole induced dipole approximation.     

The bromination,debromination and debromosilylation of silylstyrenes and other vinylsilanes

The bromination of some vinylsilanes, and the debrominations and debromosilylations of their dibromides are stereospecific. Based on the crystal structure of the dibromide derived form trans-triphenylsilylstyrene, it is shown that bromination and debromination of silylstyrenes occur with syn stereochemistry, and that debromosilylation occurs with anti stereochemistry in polar solvents. Different stereochemistries may prevail with other vinylsilanes. Other elimination and substitution reactions are also described.     

On the significance of perihelion shift calculations

In this paper an attempt is made to resolve a confusion which exists in the literature over whether the perihelion precession of planetary orbits is a linear or non-linear effect. The problem is both one of physics and semantics.     

Quantum gravity in 2 + ε dimensions

We examine quantum gravity in 2 + ε dimensions, where the theory is formally renormalizable. Paying due attention to surface integrals (which prove crucial), we calculate the one-loop counterterms and establish a criterion for asymptotic freedom. We find, incidentally, that the β function vanishes to one-loop order for all models which are supersymmetric in two dimensions.     

Flat space as a gravitational instanton

Gravitational instantons may influence elementary particle phenomena, even when space-time is flat. To illustrate this point, we employ instanton techniques to rederive a result first obtained by totally different methods; an observer accelerating uniformly in flat Minkowski space experiences a heat bath whose temperature is proportional to his acceleration.     

A Class of Incomplete Orthogonal Factorization Methods. I: Methods and Theories

We present a class of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: Incomplete Givens Orthogonalization (IGO-method) and its generalisation (GIGO-method), which drop entries from the incomplete orthogonal and upper triangular factors by position; Threshold Incomplete Givens Orthogonalization (TIGO()-method), which drops entries dynamically by their magnitudes; and its generalisation (GTIGO(,p)-method), which drops entries dynamically by both their magnitudes and positions. Theoretical analyses show that these methods can produce a nonsingular sparse incomplete upper triangular factor and either a complete orthogonal factor or a sparse nonsingular incomplete orthogonal factor for a general nonsingular matrix. Therefore, these methods can potentially generate efficient preconditioners for Krylov subspace methods for solving large sparse systems of linear equations. Moreover, the upper triangular factor is an incomplete Cholesky factorization preconditioner for the normal equations matrix from least-squares problems.     

Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems

We determine explicit orbit representatives of reducible Jordan algebras and their corresponding Freudenthal triple systems. This work has direct application to the classification of extremal black hole solutions of ${\mathcal{N}=2}$ , 4 locally supersymmetric theories of gravity coupled to an arbitrary number of Abelian vector multiplets in D = 4, 5 space-time dimensions.