Topics in differential geometry.

Based on lectures given in the spring of 1949; a few of the latest results of work done since that time have been included.

Definition of the requirements in plane geometry, solid geometry, plane and solid geometry, major requirement, plane and solid geometry minor requirement /

Wm. F. Osgood, chairman.

Selected topics in algebraic geometry; report of the Committee on rational transformations:

Bibliography at end of each chapter.

Selected topics in algebraic geometry

Cover-title.

Brickwork, a practical treatise embodying the general and higher principles of bricklaying, cutting and setting ... and a series of problems in applied geometry,

Mode of access: Internet.

Historical development of some ideas in analytic geometry of space.

Thesis (A.M.)--Cornell Univ., June 1913.

First lessons in plane geometry : together with an application of them to the solution of problems ... /

Cooper 1704.

First lessons in practical geometry : containing such problems as are essentially necessary in exercising most of the industrious professions ; intended for the use of students in elementary schools /

Shoemaker

First lessons in observational geometry,

Mode of access: Internet.

Distributed temperature change sensor, based on Rayleigh backscattering in an optical fibre

A frequency-modulated continuous-wave technique is used to detect the presence of frequency shifts in the Rayleigh-backscattered light in a single-mode optical fiber as a result of a changing temperature. The system is able to detect a rate of temperature change of 0.014 K/s, when a 20-cm length of fiber is heated. The system is also able to demonstrate a spatial resolution of better than 15 cm.

Distributed temperature change sensor, based on Rayleigh backscattering in an optical fibre

A frequency-modulated continuous-wave technique is used to detect the presence of frequency shifts in the Rayleigh-backscattered light in a single-mode optical fiber as a result of a changing temperature. The system is able to detect a rate of temperature change of 0.014 K/s, when a 20-cm length of fiber is heated. The system is also able to demonstrate a spatial resolution of better than 15 cm.

Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials.

X-ray-diffraction study of quasipseudomorphic ErSi1.7 layers formed by channeled ion-beam synthesis

ErSi1.7 layers with high crystalline quality (chi(min) of Er is 1.5%) have been formed by 90 keV Er ion implantation to a dose of 1.6X10(17)/cm(2) at 450 degrees C using channeled implantation. The perpendicular and parallel elastic strain e(perpendicular to)=-0.94%+/-0.02% and e(parallel to)=1.24%+/-0.08% of the heteroepitaxial erbium silicide layers have been measured with symmetric and asymmetric x-ray reflections using a double-crystal x-ray diffractometer. The deduced tetragonal distortion e(T(XRD))=e(parallel to)-e(perpendicular to)=2.18%+/-0.10%, which is consistent with the value e(T(RBS))2.14+/-0.17% deduced from the Rutherford backscattering and channeling measurements. The quasipseudomorphic growth of the epilayer and the stiffness along a and c axes of the epilayer deduced from the x-ray diffraction are discussed.

Interfaces in heterostructures of AlInGaN/GaN/Al2O3

Rutherford backscattering/channeling (RBS/C) and X-ray diffraction (XRD) are used to comprehensively characterize a heterostructure of AlInGaN/GaN/Al2O3(0001). The AlInGaN quaternary layer was revealed to process a high crystalline quality with a minimum yield of 1.4% from RBS/C measurements. The channeling spectrum of (1 (2) under bar 13) exhibits higher dechanneling than that of (0001) at the interface of AlInGaN/GaN. XRD measurements prove a coherent growth of AlInGaN on the GaN template layer. Combining RBS/C and XRD measurements, we found that the interface of GaN/Al2O3 is a nucleation layer, composed of a large amount of disorders and cubic GaN slabs, while the interface of AlInGaN/GaN is free of extra disordering (i.e. compare with the GaN layer). The conclusion is further evidenced by transmission electron microscopy (TEM). (c) 2005 Elsevier Ltd. All rights reserved.