Generalized inverses on normed vector spaces

We extend the concepts, introduced by C.R. Rao for Euclidean norms, of minimum g-inverses and least square g-inverses, using arbitrary norms. We give a characterization of such generalized inverses and an application to the case in which the norm is l_∞. As a result of this application we obtain that when $\text{A?}\text{C}{}^{\mathrm{(n+1)\times n}}$ has rank n, there exists a generalized inverse of A, which serves the same purpose as the Moore-Penrose inverse, when the norm is l_∞.     

Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for the least 2-norm solution of linear programs

Given an arbitrary point (x, u) inR ⁿ × R ₊ ^m , we give bounds on the Euclidean distance betweenx and the unique solution to a strongly convex program in terms of the violations of the Karush-Kuhn-Tucker conditions by the arbitrary point (x, u). These bounds are then used to derive linearly and superlinearly convergent iterative schemes for obtaining the unique least 2-norm solution of a linear program. These schemes can be used effectively in conjunction with the successive overrelaxation (SOR) methods for solving very large sparse linear programs.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. This material is based on research sponsored by National Science Foundation Grant No. DCR-8420963 and Air Force Office of Scientific Research Grant No. AFOSR-ISSA-85-00080.On leave from CRAI, via Bernini 5, Rende, Cosenza, Italy.     

Modeling of InGaAsP–InP 1.55 μm lasers with integrated mode expanders using fiber-matched leaky waveguides

A new concept for InGaAsP–InP 1.55 μm lasers integrated with spot size converters using leaky waveguides is presented. The large fundamental mode size and the high discrimination of the higher order modes make ARROWs (Antiresonant Reflecting Optical Waveguides) and antiguided waveguides useful for fiber coupling functions. Three-dimensional (3-D) beam propagation method (BPM) results show that the devices have transformation losses lower than 0.22 dB. Fiber-coupling efficiencies of 60% are possible with standard cleaved single-mode fibers (SMF). The horizontal and vertical FWHM can be efficiently reduced to 9.70° (horizontal) and 17.80° (vertical). The fabrication of such devices avoids the growth of thick layers of quaternary material with a low Ga and As fraction, and simplifies the fabrication to one planar epitaxial growth step and one non-critical conventional etch. Received: 16 May 2001 / Published online: 30 October 2001     

On ascending and subnormal subgroups of infinite factorized groups

We consider an almost hyper-Abellan group G of a finite Abelian sectional rank that is the product of two subgroups A and B. We prove that every subgroup H that belongs to the intersection A ∩ B and is ascending both in A and B is also an ascending subgroup in the group G. We also show that, in the general case, this statement is not true. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 842–848, June, 1997.     

推出-拉回图上的覆盖性同态

In a pushout-pullback diagram,which consists of four morphisms f : A → B,g : A → C,α : C → D and β : B → D,we give some relations among the covers of these four modules.If kerf ∈ I(L ),then g : A → C is L -covering if and only if β : B → D is L -covering.If every module has an L -precover and kerf ∈ I(L ),then A and C have isomorphic L -precovers if and only if B and D have isomorphic L -precovers.     

Electron traps in GaS

Measurements performed on n-GaS by means of the space-charge limited current method indicate the presence of a deep trap for electrons, at 0.57 eV from the conduction band and with a density of about 2.3 × 10¹³cm^?3. Another deeper trap at 0.63 eV and with a density of 6 × 10¹²cm^?3 is probably also present. The results seem to confirm the validity of a new direct method of analysis. Traps are tentatively attributed to compensated sulphur vacancies.     

Oxygen adsorption on Cu(110): Determination of atom positions with low energy ion scattering

The position of adsorbed oxygen on Cu($\text{1}$10) surfaces was determined with Low Energy Ion Scattering (LEIS). The experiments were performed by bombarding the copper surface at small angles of incidence with low energy Ne⁺ ions (3–5 keV). Measurements of the Ne⁺ ions scattered by adsorbed oxygen showed regular peaks in the azimuthal distribution of the scattered ions due to a shadowing effect. From the symmetry of the azimuthal distributions it follows that the centre of an adsorbed oxygen atom on the Cu(1̄10) surface lies about 0.6 Å below the midpoint between two neighbouring Cu atoms in a 〈001〉 row. A comparison of the azimuthal distributions of Ne⁺ ions scattered from clean Cu surfaces and oxygen-covered Cu surfaces showed that hardly any surface reconstruction had occurred in the oxygen-covered surfaces. The applied method seems to be an appropriate one for locating adsorbed atoms because it uses only simple qualitative considerations about azimuthal distributions of scattered ions.     

Interferometric focal length measurement of power-distributed lenses

An interferometric method for measuring the focal length of power-distributed lenses is described. The test lens is illuminated by a regular pitch interferometric pattern produced by a reflective diffraction grating interferometer. In order to measure the focal length, a CCD camera digitizes the image of the pattern magnified by the lens, and fast Fourier transformed to reconstruct the phase modulo 2π along each row. The change in spatial frequency is determined by unwrapping the phase along each row of the digitized imaged pattern. The technique is used for measuring the focal length distribution inside the progression corridor of both positive and negative progressive lenses.     

A new characterization of projections of quadrics in finite projective spaces of even characteristic

We will classify, up to linear representations, all geometries fully embedded in an affine space with the property that for every antiflag {p,L} of the geometry there are either 0, α, or q lines through p intersecting L. An example of such a geometry with α=2 is the following well known geometry . Let Q_n+1 be a nonsingular quadric in a finite projective space , n≥3, q even. We project Q_n+1 from a point r∉Q_n+1, distinct from its nucleus if n+1 is even, on a hyperplane not through r. This yields a partial linear space whose points are the points p of , such that the line 〈p,r〉 is a secant to Q_n+1, and whose lines are the lines of which contain q such points. This geometry is fully embedded in an affine subspace of and satisfies the antiflag property mentioned. As a result of our classification theorem we will give a new characterization theorem of this geometry.     

137-01137-01137-01-deformed extended Galilei algebra

We apply the pseudoextension mechanism, which in the undeformed case gives the centrally extended Galilei group {ie137-02} as a contraction of a trivial extensionP×U(1) of the Poincaré group, to the case of the-Poincaré algebra. As a result, the four-dimensional {ie137-03}-deformed extended Galilei algebra is obtained.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.