Recursive formulation of Madelung continuity equation leads to propagation equation

We apply a recursive approach to the continuity equation of the Madelung fluid resulting in a propagation equation for particle probability densities. This propagation equation can be used to propagate particle distributions in the presence of a Madelung pressure field. We show that the derived propagation equation goes over into the guidance equation of the de Broglie-Bohm theory in the limit of well located single particles. As an example, we propagate particles that enter the lower slit of a double-slit experiment, while the Madelung fluid enters both slits.Comment: Article replaced because: Reformulated from a mathematical point of vie

Polynominals related to powers of the Dedekind eta function

The vanishing properties of Fourier coefficients of integral powers of the Dedekind eta function correspond to the existence of integral roots of integer-valued polynomials Pn(x) introduced by M. Newman. In this paper we study the derivatives of these polynomials. We obtain non-vanishing results at integral points. As an application we prove that integral roots are simple if the index n of the polynomial is equal to a prime power pm or to pm + 1. We obtain a formula for the derivative of Pn(x) involving the polynomials of lower degree

Special Propeller Protractor

A special protractor was designed and built with a view towards supplying a simple, inexpensive, practical, portable instrument for making measurements to detect propeller warpage under practically all conditions, without the use of auxiliary equipment, and without having to remove the propeller from the airplane. A detailed description is given of the protractor. Techniques for measuring are described. Directions are given on how to use the protractor to set detachable blade-type propellers on an airplane

NNLL resummation for s-channel single top quark production

I present the next-to-next-to-leading-logarithm (NNLL) resummation of soft and collinear gluon corrections to single top quark production in the s channel. Attaining NNLL accuracy involves the calculation of the two-loop soft anomalous dimension for the partonic subprocesses. Finite-order expansions of the resummed cross section are calculated through next-to-next-to-leading order (NNLO). Numerical results are presented for s-channel single top quark production at the Tevatron and the LHC, including the dependence of the cross sections on the top quark mass and the uncertainties in the theoretical prediction. The higher-order corrections are significant for energies at both colliders and they decrease the theoretical uncertainty.Comment: 17 pages, 12 figures; added figures and discussio

Effects of electron transfer on the stability of hydrogen bonds.

The measurement of the dimerization constants of hydrogen-bonded ruthenium complexes (12, 22, 32) linked by a self-complementary pair of 4-pyridylcarboxylic acid ligands in different redox states is reported. Using a combination of FTIR and UV/vis/NIR spectroscopies, the dimerization constants (KD) of the isovalent, neutral states, 12, 22, 32, were found to range from 75 to 130 M-1 (ΔG0 = -2.56 to -2.88 kcal mol-1), while the dimerization constants (K2-) of the isovalent, doubly-reduced states, (12)2-, (22)2-, (32)2-, were found to range from 2000 to 2500 M-1 (ΔG0 = -4.5 to -4.63 kcal mol-1). From the aforementioned values and the comproportionation constant for the mixed-valent dimers, the dimerization constants (KMV) of the mixed-valent, hydrogen-bonded dimers, (12)-, (22)-, (32)-, were found to range from 0.5 × 106 to 1.2 × 106 M-1 (ΔG0 = -7.78 to -8.31 kcal mol-1). On average, the hydrogen-bonded, mixed-valent states are stabilized by -5.27 (0.04) kcal mol-1 relative to the isovalent, neutral, hydrogen-bonded dimers and -3.47 (0.06) kcal mol-1 relative to the isovalent, dianionic hydrogen bonded dimers. Electron exchange in the mixed valence states imparts significant stability to hydrogen bonding. This is the first quantitative measurement of the strength of hydrogen bonds in the presence and absence of electronic exchange