Vorlesungen über differentialgeometrie,

Available on demand as hard copy or computer file from Cornell University Library.

An elementary treatise on curves, functions, and forces.

Available on demand as hard copy or computer file from Cornell University Library.

Traité d'analyse,

Available on demand as hard copy or computer file from Cornell University Library.

Analyse appliquée a la géometrie des trois dimensions : comprenant les surfaces du second ordre, avec la théorie générale des surfaces courbes et des lignes à double courbure /

Mode of access: Internet.

Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal,

1. ptie. Généralités. Coordonnées curvilignes. Surfaces minima. 1887.--2. ptie. Les congruences et les équations linéaires aux dérivées partielles. Des lignes tracées sur les surfaces. 1889.--3. ptie. Lignes géodésiques et courbure géodésique. Paramètres différentiels. Déformation des surfaces. 1894.--4. ptie. Déformation infiniment petite et représentation sphérique. Notes et additions: I. Sur les méthodes d'approximations successives dans la théorie des équations différentielles, par É. Picard. II. Sur les géodésiques à intégrales quadratiques, par G. Koenigs. III. Sur la théorie des équations aux dérivées partielles du second ordre, par E. Cosserat. IV-XI. Par l'auteur. 1896.

A course in mathematical analysis,

Vol. II translated by Earle Raymond Hedrick and Otto Dunkel, published in 2 parts.

Electrochemical deposition of cupric ions for the determination of mass transfer rates to a stepped rotating cylinder electrode

The stepped rotating cylinder electrode (SRCE) geometry has been developed as a simple aid to the practical study of the flow-enhanced corrosion and applied electrochemistry problems commonly observed under conditions of disturbed, turbulent flow. The electrodeposition of cupric ions from an acid sulphate plating bath has been used to characterise differential rates of mass transfer to the SRCE. The variation in thickness of electrodeposited copperfilms has allowed the mapping of local rates of mass transfer over the active surface of this geometry. Both optical and scanning electron microscopy were used for the examination of metallographic sections to provide a high resolution evaluation of the distribution of mass transfer coefficient. Results are also discussed using the convective-diffusion model in combination with the existing direct numerical flow simulation (DNS) data for this geometry.

A geometric approach to quantum circuit lower bounds

What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2(n)). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call Pauli geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Structure-function analysis of amino acid 74 of human RAMP1 and RAMP3 and its role in peptide interactions with adrenomedullin and calcitonin gene-related peptide receptors

The receptors for calcitonin gene-related peptide (CGRP) and adrenomedullin (AM) are complexes of the calcitonin receptor-like receptor (CLR) and receptor activity-modifying proteins (RAMP). The CGRP receptor is a CLR/RAMP1 pairing whereas CLR/RAMP2 and CLR/RAMP3 constitute two subtypes of AM receptor: AM(1) and AM(2), respectively. Previous studies identified Glu74 in RAMP3 to be important for AM binding and potency. To further understand the importance of this residue and its equivalent in RAMP1 (Trp74) we substituted the native amino acids with several others. In RAMP3, these were Trp, Phe, Tyr, Ala, Ser, Thr, Arg and Asn; in RAMP1, Glu, Phe, Tyr, Ala and Asn substitutions were made. The mutant RAMPs were co-expressed with CLR in Cos7 cells; receptor function in response to AM, AM(2)/intermedin and CGRP was measured in a cAMP assay and cell surface expression was determined by ELISA. Phe reduced AM potency in RAMP3 but had no effect in RAMP1. In contrast, Tyr had no effect in RAMP3 but enhanced AM potency in RAMP1. Most other substitutions had a small effect on AM potency in both receptors whereas there was little impact on CGRP or AM(2) potency. Overall, these data suggest that the geometry and charge of the residue at position 74 contribute to how AM interacts with the AM(2) and CGRP receptors and confirms the role of this position in dictating differential AM pharmacology at the AM(2) and CGRP receptors.

Micro-fabrication of advanced photonic devices by means of direct point-by-point femtosecond inscription in silica

We present recent results on experimental micro-fabrication and numerical modeling of advanced photonic devices by means of direct writing by femtosecond laser. Transverse inscription geometry was routinely used to inscribe and modify photonic devices based on waveguiding structures. Typically, standard commercially available fibers were used as a template with a pre-fabricated waveguide. Using a direct, point-by-point inscription by infrared femtosecond laser, a range of fiber-based photonic devices was fabricated including Fiber Bragg Gratings (FBG) and Long Period Gratings (LPG). Waveguides with a core of a couple of microns, periodic structures, and couplers have been also fabricated in planar geometry using the same method.

Micro-fabrication of advanced photonic devices by means of direct point-by-point femtosecond inscription in silica

We present recent results on experimental micro-fabrication and numerical modeling of advanced photonic devices by means of direct writing by femtosecond laser. Transverse inscription geometry was routinely used to inscribe and modify photonic devices based on waveguiding structures. Typically, standard commercially available fibers were used as a template with a pre-fabricated waveguide. Using a direct, point-by-point inscription by infrared femtosecond laser, a range of fiber-based photonic devices was fabricated including Fiber Bragg Gratings (FBG) and Long Period Gratings (LPG). Waveguides with a core of a couple of microns, periodic structures, and couplers have been also fabricated in planar geometry using the same method.

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

The Nonexistence of [132, 6, 86]3 Codes and [135, 6, 88]3 Codes

We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.

Използване на системата MATLAB в техническите университети

Mihail Konstantinov, Vladimir Todorov, Galina Pelova, Juliana Boneva - We consider some aspect of the mathematical education in technical universities using MATLAB. Special attention is paid to the subjects Analytical Geometry and Differential Equations.