Revisiting Gouy phase

The aim of this paper is to highlight the added value of the generalized Gouy phase shift introduced by Siegman. Although suited for optical systems study, including those more complex than free space, we note that it did not meet the use that it deserves so far. The analysis of the whole of the ideas and analytical approaches associated to the important concept of the Gouy phase proves its effectiveness.

Usually, the resonance condition is systematically built on the basis of the equivalent empty cavity. Unfortunately, this approach does not cover some of the useful parameters of the real resonator. By means of the generalized Gouy phase and the self-consistent complex parameter q, we derive here a new approach for the calculation of the resonance condition for the real cavity. Moreover, the use of the generalized Gouy phase clearly simplifies the study of resonators, while making it possible to avoid the use of the Huygens’ Fresnel integral.     

Growth and study of single crystals of (Na,K)NbO<Subscript>3</Subscript> solid solutions

(Na, K)NbO₃ crystals with a perovskite structure and a KNbO₃ content up to 40 mol % were grown from flux with the use of the solvent NaBO₂. The dielectric measurements of the crystals grown revealed phase transitions that had never been observed before in ceramic samples.     

Enhancing the Success of African-American Students in the Sciences: Freshman Year Outcomes

The Meyerhoff Program is an intensive, multicomponent program focused on enhancing the success of talented African-American students in science and engineering at a predominantly white, medium-sized university. The program components, taken together, address the four primary factors emphasized in the research literature as limiting minority student performance and persistence in science: knowledge and skills, motivation and support, monitoring and advising, and academic and social integration. Outcome analyses indicated that the first three cohorts of Meyerhoff students (total N=69) achieved an overall GPA (mean=3.5) significantly greater than that of an African-American historical comparison sample (mean=2.8) of comparably talented science students at the university. This difference was even greater for first year science GPA (means of 3.4 and 2.4, respectively), and in specific science and mathematics courses. Observational and questionnaire data indicated that the Meyerhoff program study groups, peerbased community, financial scholarships, summer bridge program and staff appear to be especially important contributors to student success. Implications of the findings for enhancing the success of African-American and other underrepresented populations in science are discussed.     

Inconsistency of a metatheory of Nudel''man

A metatheory of Nudel'man outlined in [1] is proved inconsistent. The groundwork for the proof is the method of arithmetization of metamathematics.Translated fromAlgebra i Logika, Vol. 34, No. 1, pp. 41–43, January–February, 1995.     

A local search approach to a circle cutting problem arising in the motor cycle industry

This paper is concerned with the development of a customized circle packing algorithm for a manufacturer of sprockets for the motor cycle industry. Practical constraints mean that the problem differs somewhat from those tackled elsewhere in the literature. In particular, the layouts need to conform to a given structure. This is achieved by using a local search algorithm with an appropriate starting solution and a series of neighbourhoods designed to preserve the layout structure. Empirical evidence based on real data shows that the quality of the resulting solutions closely matches that of cutting patterns currently produced by human experts. Computation times average around 20–30?s per order as compared to several hours for an equivalent manual solution.     

VECTOR FIELDS IN R2 WITH MAXIMAL INDEX

We consider the method of Poincaré to investigate thelocal index of vector fields in the plane. If m is the degreeof the first non-zero jet, X_m, of the vector field X at an isolatedzero, we explore the geometry of the pencil generated by thecoordinate functions of X_m when the absolute value of the indexof X, |ind (X)|, is m. We also find necessary and sufficientconditions for |ind (X)| to be m.     

The double exponential map and covariant derivation

We study the double exponential map which is a composition of a special form of two exponential maps on a manifold with connection. We relate this map and the composition of covariant derivations as well as the composition of pseudodifferential operators on these manifolds.     

Discovery of a new long-lived isomeric state in 125Ce

A new long-lived isomeric state in the near proton dripline nucleus ¹²⁵Ce has been identified with Schottky mass spectrometry at GSI. The excitation energy E ^* = 103(12)keV and the decay time of 193(1)s have been obtained from a single stored fully ionized ^125m Ce⁵⁸⁺ ion. The data implies an E3 transition and a 1/2⁺ assignment for the spin of the isomer.