Search results for "LYN"
showing 10 items of 910 documents
New coordination polymer based on a triply bridged dicarboxylate ligand: Synthesis, structure, and magnetic properties of the adipato complex [Cu4(bp…
2007
International audience; One-pot reaction of copper(II) chloride dihydrate CuCl2 · 2H2O with 2,2′-bipyridyl (bpy = C10H8N2) in the presence of sodium adipate Na2adip (adip2− = [O2C(CH2)4CO2]2−) and potassium 1,1,3,3-tetracyano-2-ethoxypropenide (tcnoet− = [(NC)2CC(OEt)C(CN)2]−) gives the new compound [Cu4(bpy)4(adip)3](tcnoet)2 · 2H2O (1), which was characterized by single crystal X-ray diffraction analysis. The Cu(II) metal ion presents an elongated square pyramidal CuN2O3 environment, with an oxygen atom in apical position and a base plane involving almost equivalent bond lengths. The structure can be described as a pseudo dinuclear species in which two Cu(bpy) units are triply bridged by …
Indefinite integrals involving Jacobi polynomials from integrating factors
2020
A method was presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many special f...
Analytical solution for multisingular vortex Gaussian beams: The mathematical theory of scattering modes
2016
We present a novel procedure to solve the Schr\"odinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use the scattering modes, which are solutions of the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore permit to solve the problem. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role than Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations need…
Accommodation in human eye models: a comparison between the optical designs of Navarro, Arizona and Liou-Brennan.
2017
Aim To simulate and compare accommodation in accommodative and non-accommodative human eye models. Methods Ray tracing and optical design program was used. Three eye models were designed and studied: the Navarro, the Arizona and the Liou-Brennan. In order to make the Navarro and Liou-Brennan models to accommodate, specific geometric parameters of the models were altered with values that were chosen from the literature. For the Arizona model, its' mathematical functions for accommodation were used for the same accommodative demands. The simulation included four distances of accommodation for each model: at infinity, 3, 1 and 0.5 m.The results were diffraction images of a "letter F" for graph…
Long-Lasting Cranial Nerve III Palsy as a Presenting Feature of Chronic Inflammatory Demyelinating Polyneuropathy
2015
We describe a patient with chronic inflammatory demyelinating polyneuropathy (CIDP) in which an adduction deficit and ptosis in the left eye presented several years before the polyneuropathy. A 52-year-old man presented with a 14-year history of unremitting diplopia, adduction deficit, and ptosis in the left eye. At the age of 45 a mild bilateral foot drop and impaired sensation in the four limbs appeared, with these symptoms showing a progressive course. The diagnostic workup included EMG/ENG which demonstrated reduced conduction velocity with bilateral and symmetrical sensory and motor involvement. Cerebrospinal fluid studies revealed a cytoalbuminologic dissociation. A prolonged treatmen…
On complete set of solutions for polynomial matrix equations
1990
Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.
An elementary proof of Hilbertʼs theorem on ternary quartics
2012
Abstract In 1888, Hilbert proved that every nonnegative quartic form f = f ( x , y , z ) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry. Up to now, no elementary proof is known. Here we present a completely new approach. Although our proof is not easy, it uses only elementary techniques. As a by-product, it gives information on the number of representations f = p 1 2 + p 2 2 + p 3 2 of f up to orthogonal equivalence. We show that this number is 8 for generically chosen f, and that it is 4 when f is chosen generically with a real zero. Although these facts were known, there wa…
Computational Aspects in Spaces of Bivariate Polynomial of w-Degree n
2005
Multivariate ideal interpolation schemes are deeply connected with H-bases. Both the definition of a H-basis and of an ideal interpolation space depend of the notion of degree used in the grading decomposition of the polynomial spaces. We studied, in the case of bivariate polynomials, a generalized degree, introduced by T. Sauer and named w-degree. This article give some theoretical results that allow us to construct algorithms for calculus of the dimension of the homogeneous spaces of bivariate polynomials of w – degree n. We implemented these algorithms in C++ language. The analysis of the results obtained, leads us to another theoretical conjecture which we proved in the end.
An approximate Rolle's theorem for polynomials of degree four in a Hilbert space
2005
We show that the fourth degree polynomials that satisfy Rolle’s Theorem in the unit ball of a real Hilbert space are dense in the space of polynomials that vanish in the unit sphere. As a consequence, we obtain a sort of approximate Rolle’s Theorem for those polynomials.
Symmetric identities in graded algebras
1997
Let P k be the symmetric polynomial of degree k i.e., the full linearization of the polynomial x k . Let G be a cancellation semigroup with 1 and R a G-graded ring with finite support of order n. We prove that if R 1 satisfies $ P_k \equiv 0 $ then R satisfies $ P_{kn} \equiv 0 $ .