Search results for " Classical"

Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

2015

We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed.

Traces of weighted function spaces: dyadic norms and Whitney extensions

2017

The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.

Dynamics of the scenery flow and geometry of measures

2015

We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a n…

Matrix Computations for the Dynamics of Fermionic Systems

2013

In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and lowering operators play a relevant role in this analysis. The technical problem of our approach stands in the difficulty of solving the equations of motion, which are, first of all, {\em operator-valued} and, secondly, quite often nonlinear. In this paper we construct a general procedure which significantly simplifies the treatment for those systems which can be described in terms of fermionic operators. The proposed procedure allows to get an analytic solut…

Quantum dynamics for classical systems

2012

Nonlinear multivalued Duffing systems

2018

We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita-Kowalski (JMAA, https://doi.org/10.1016/j.jmaa. 2018.01.067).

Rapid and Standardized Quantitation of Hemolytic Activity of the Fourth Component of Human Complement

1990

Based on a method that uses the fourth component of complement (C4)-deficient guinea pig serum to quantify the hemolytic activity of C4, we developed an assay that allows the processing of a large number of individual samples with high reproducibility. In contrast to the conventional procedure using titration curves of each sample to be determined, we can show that a single appropriate dilution of the sample allows accurate quantitation of hemolytic activity. The reliability of the procedure is demonstrated using either C4A- or C4B- deficient and normal individual samples.

Riesz transform and vertical oscillation in the Heisenberg group

2023

We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, and Young, we first introduce new scale and translation invariant coefficients $\operatorname{osc}_{\Omega}(B(q,r))$. These coefficients quantify the vertical oscillation of a domain $\Omega \subset \mathbb{H}$ around a point $q \in \partial \Omega$, at scale $r > 0$. We then proceed to show that if $\Omega$ is a domain bounded by an intrinsic Lipschitz graph $\Gamma$, and $$\int_{0}^{\infty} \operatorname{osc}_{\Omega}(B(q,r)) \, \frac{dr}{…

Nonsymmetric conical upper density and $k$-porosity

2017

We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in R n \mathbb {R}^n . As an application, we find an upper bound close to n − k n-k for the Hausdorff dimension of sets with large k k -porosity. With k k -porous sets we mean sets which have holes in k k different directions on every small scale.

Estudio comparativo de dos metodologías aplicadas para la comprensión de la música contemporánea en la educación secundaria obligatoria

2016

In this paper we try to discover which methodology is more appropriate for the comprehension of the contemporary music in the Secondary Education. For that purpose by a quasi-experiment, mixed, qualitative and quantitative, the preserved results through the application of two different methodologies have been compared: a traditional one base on the masterly class and another based in different kinds of audition. The obtained results after the didactical application on the quantitative level weren´t significant, however, on the qualitative level we could also observe that the pupils who subjected to that methodology had more advantageous results regarding to the comprehension of the contempo…