Correlated adiabatic and isocurvature cosmic microwave background fluctuations in the wake of the results from the wilkinson microwave anisotropy probe

In general correlated models, in addition to the usual adiabatic component with a spectral index n(ad1) there is another adiabatic component with a spectral index n(ad2) generated by entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature cosmic microwave background fluctuations of the Wilkinson Microwave Anisotropy Probe (WMAP) group, who set the two adiabatic spectral indices equal. Allowing n(ad1) and n(ad2) to vary independently we find that the WMAP data favor models where the two adiabatic components have opposite spectral tilts. Using the WMAP data only, the 2sigma upper bound for the isocurvature fraction f(iso) of the initial power spectrum at k(0)=0.05 Mpc(-1) increases somewhat, e.g., from 0.76 of n(ad2)=n(ad1) models to 0.84 with a prior n(iso)<1.84 for the isocurvature spectral index.     

Solid-State Reactions between Cu(Ni) Alloys and Sn

Solid-state interfacial reactions between Sn and Cu(Ni) alloys have been investigated at the temperature of 125°C. The following results were obtained. Firstly, the addition of 0.1 at.% Ni to Cu decreased the total thickness of the intermetallic compound (IMC) layer to about half of that observed in the␣binary Cu/Sn diffusion couple; the Ni addition decreased especially the thickness of Cu₃Sn. Secondly, the addition of 1 to 2.5 at.% Ni to Cu further decreased the thickness of Cu₃Sn, increased that of Cu₆Sn₅ (compared to that in the binary Cu/Sn couple) and produced significant amount of voids at the Cu/Cu₃Sn interface. Thirdly, the addition of 5 at.% Ni to Cu increased the total thickness of the IMC layer to about two times that observed in the binary Cu/Sn diffusion couple and made the Cu₃Sn disappear. Fourthly, in contrast to the previous case, the addition of 10 at.% Ni to Cu decreased the total IMC (Cu₆Sn₅) thickness again close to that of the Cu/Sn couple. With this Ni content no voids were detected. The results are rationalized with the help of␣the thermodynamics of the Sn-Cu-Ni system as well as with kinetic considerations.     

Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality

We provide a sharp quantitative version of the Gaussian concentration inequality: for every \(r>0\), the difference between the measure of the r-enlargement of a given set and the r-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space. We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set. This is equivalent to the stability of the Brunn–Minkowski inequality for the Minkowski sum between a convex set and a generic one.     

Analysis and modeling of piano sustain-pedal effects

This paper describes the main features of the sustain-pedal effect in the piano through signal analysis and presents an algorithm for simulating the effect. The sustain pedal is found to increase the decay time of partials in the middle range of the keyboard, but this effect is not observed in the case of the bass and treble tones. The amplitude beating characteristics of piano tones are measured with and without the sustain pedal engaged, and amplitude envelopes of partial overtone decay are estimated and displayed. It is found that the usage of the sustain pedal introduces interesting distortions of the two-stage decay. The string register response was investigated by removing partials from recorded tones; it was observed that as the string register is free to vibrate, the amount of sympathetic vibrations is increased. The synthesis algorithm, which simulates the string register, is based on 12 string models that correspond to the lowest tones of the piano. The algorithm has been tested with recorded piano tones without the sustain pedal. The objective and subjective results show that the algorithm is able to approximately reproduce the main features of the sustain-pedal effect.     

Hydrolysis products of water treatment chemical aluminium sulfate octadecahydrate by electrospray ionization mass spectrometry

Hydrolysis and speciation of aluminium sulfate octadecahydrate Al₂(SO₄₎₃·18H₂O${\text{Al}}_2({\text{SO}}_4{)}_3·18{\text{H}}_2\text{O}$ was studied by electrospray time of flight mass spectrometry (ESI TOF MS). Several novel polymeric species were determined. Highly charged polymers, characterized by other methods, such as the Keggin cation [Al₁₃O₄(OH)₂₄(H₂O)₁₂]⁷⁺ and the octameric aluminium hydroxide cluster [Al₈(OH)₁₄(H₂O)₁₈](SO₄)₅ 16H₂O, were found using ESI-MS as the anions [Al₁₃O₄(OH)₂₅(SO₄)₄]²⁻ and [Al₈O(OH)₁₄(SO₄)₅(H₂O)₄]²⁻. All the main species identified contained sulfate or hydrogen sulfate. The compositions of the determined ions mimicked those of several stable mineral forms.     

An ab initio study of van der Waals potential energy parameters for silver clusters

We employ ab initio calculations of van der Waals complexes to study the potential energy parameters (C(6) coefficients) of van der Waals interactions for modeling of the adsorption of silver clusters on the graphite surface. Electronic structure calculations of the (Ag(2))(2), Ag(2)-H(2), and Ag(2)-C(6)H(6) complexes are performed using a coupled-cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)), M?ller-Plesset second-order perturbation theory (MP2), and spin-component-scaled MP2 (SCS-MP2) methods. Using the atom pair approximation, the C(6) coefficients for silver-silver, silver-hydrogen, and silver-carbon atom systems are obtained after subtracting the energies of quadrupole-quadrupole interactions from the total electronic energy.     

Convexity Criteria and Uniqueness of Absolutely Minimizing Functions

We show that an absolutely minimizing function with respect to a convex Hamiltonian \({H : \mathbb{R}^{n} \rightarrow \mathbb{R}}\) is uniquely determined by its boundary values under minimal assumptions on H. Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in L^∞.     

On Markov's Undecidability Theorem for Integer Matrices

We study a problem considered originally by A. Markov in 1947: Given two finitely generated matrix semigroups, determine whether or not they contain a common element. This problem was proved undecidable by Markov for 4 x 4 matrices, even in a very restrict form, and for 3 x 3 matrices by Krom in 1981. Here we give a new proof in the 3 x 3 case which gives undecidability in an almost as restricted form as the result of Markov.     

Phase Evolution in the AuCu/Sn System by Solid-State Reactive Diffusion

The interfacial reactions between several Au(Cu) alloys and pure Sn were studied experimentally at 200°C. Amounts of Cu in the AuSn₄ and AuSn₂ phases were as low as 1 at.%. On the basis of these experimental results there is no continuous solid solution between (Au,Cu)Sn and (Cu,Au)₆Sn₅. The copper content of (Au,Cu)Sn was determined to be approximately 7–8 at.%. Substantial amounts of Au were present in the (Cu,Au)₆Sn₅ and (Cu,Au)₃Sn phases. Two ternary compounds were formed, one with stoichiometry varying from (Au_40.5Cu₃₉)Sn_20.5 to (Au_20.2Cu_59.3)Sn_20.5 (ternary “B”), the other with the composition Au₃₄Cu₃₃Sn₃₃ (ternary “C”). The measured phase boundary compositions of the product phases are plotted on the available Au–Cu–Sn isotherm and the phase equilibria are discussed. The complexity and average thickness of the diffusion zone decreases with increasing Cu content except for the Au(40 at.%Cu) couple.