Lp Microlocal Properties for Multi-Quasi-Elliptic Pseudodifferential Operators

2010 Mathematics Subject Classification: Primary 35S05; Secondary 35A17.

On the Holomorphic Extension of Solutions of Elliptic Pseudodifferential Equations

2010 Mathematics Subject Classification: 35B65, 35S05, 35A20.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

Existence Theorems for Non-Cooperative Elliptic Systems

2010 Mathematics Subject Classification: 35J65, 35K60, 35B05, 35R05.

Radio-frequency spectrum coding in ultra-long fibre laser based cryptography

We propose a new approach for secret key exchange involving the variation of the cavity length of an ultra-long fibre laser. The scheme is based on the realisation that the free spectral range of the laser cavity can be used as an information carrier. We present a proof-of-principle demonstration of this new concept using a 50-km-long fibre laser to link two users, both of whom can randomly add an extra 1-km-long fibre segment.

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50

Probabilistic Models in Cryptography, Coding Theory and Tests for PRNG

2000 Mathematics Subject Classification: 94A29, 94B70

Corrigendum for "Weierstrass Points with first Non-Gap four on a Double Covering of a Hyperelliptic Curve"

In the proof of Lemma 3.1 in [1] we need to show that we may take the two points p and q with p ≠ q such that p+q+(b-2)g21(C′)∼2(q1+… +qb-1) where q1,…,qb-1 are points of C′, but in the paper [1] we did not show that p ≠ q. Moreover, we hadn't been able to prove this using the method of our paper [1]. So we must add some more assumption to Lemma 3.1 and rewrite the statements of our paper after Lemma 3.1. The following is the correct version of Lemma 3.1 in [1] with its proof.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14J26.

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Luoghi geometrici e curve celebri

Scopo di questo elaborato è affrontare lo studio di luoghi geometrici piani partendo dagli esempi più semplici che gli studenti incontrano nel loro percorso scolastico, per poi passare a studiare alcune curve celebri che sono definite come luoghi geometrici. Le curve nell'elaborato vengono disegnate con l'ausilio di Geogebra, con il quale sono state preparate delle animazioni da mostrare agli studenti. Di alcuni luoghi si forniscono dapprima le equazioni parametriche e successivamente, attraverso il teorema di eliminazione e il software Singular, viene ricavata l'equazione cartesiana.

Homogenization of elliptic problems in thin domains with oscillatory boundaries

Los dominios finos, es decir, dominios sustancialmente más pequeños en alguna o varias de sus direcciones que en el resto, aparecen en muchos campos de la ciencia. Por ejemplo, dinámica de fluídos (lubricación, conducción de fluídos en tubos delgados, dinámica de oceanos...), mecánica de sólidos (barras delgadas, placas o cáscaras) o incluso en fisiología (circulación de la sangre). Así, el amplio número de posibles aplicaciones a situaciones reales ha hecho que la investigación de modelos de ecuaciones en derivadas parciales en dominios finos se convierta en un tema muy estudiado en los últimos años. Desde un punto de vista matemático, el estudio de las soluciones de una EDP en un dominio fino es un caso particular de la cuestión general relativa a cómo la variación de los dominios afecta al comportamiento de las soluciones de la EDP. En este marco, obtener la ecuación límite del modelo considerado, comparar la solución de la ecuación límite y las soluciones del problema en el dominio fino, analizar los coeficientes de la ecuación límite y comprender cómo la geometría del dominio afecta a la ecuación límite son algunos de los objetivos que deberían ser alcanzados. De hecho, es importante señalar que este tipo de cuestiones no sólo proporcionan importantes resultados teóricos sino que son muy relevantes desde el punto de vista de las aplicaciones. Por ejemplo, ser capaz de reducir el problema original a un problema mucho más sencillo, problema límite, que refleje las principales características del problema de partida puede ser muy útil para ingenieros y físicos...