Search results for "continuity"

Extremal length and Hölder continuity of conformal mappings

1986

Persistence of temperature and precipitation: from local to global anomalies

2021

Using detrended fluctuation analysis (DFA) we find that all continents are persistent in temperature. The scaling exponents of the southern hemisphere (SH) continents, i.e., South America (0.77) and Oceania (0.72) are somewhat higher than scaling exponents of Europe (0.70), Asia (0.69) and North America (0.64), but the scaling of Africa is by far the highest (0.86). The reason for this is the location of Africa near the equator. The scaling exponents of the precipitation are much smaller, i.e. between 0.55 (Europe) and 0.68 (North America). The scaling exponent of Europe is near that of the random noise (0.5), while the other continents are slightly persistent in precipitation. We also show…

COMPLEX ANALYSIS OF COMPANY BANKRUPTCY FORECASTING: THEORETICAL INSIGHT

2018

In modern conditions for dynamic and competitive businesses, more and more companies face financial problems and eventually go bankrupt. A noteworthy trend: not only new companies that have not yet managed to establish themselves in the market go bankrupt but also large companies operating for years and maintaining good traditions. Bankruptcies of companies cause many problems not only for the companies themselves but also for the state and many members of society. Thus, it is crucial to evaluate the financial state of a company and its activity results as accurately and early as possible when forecasting the possibility of a bankruptcy. The paper recommends a complex analysis methodology f…

Poincaré inequalities and Steiner symmetrization

1996

A complete geometric characterization for a general Steiner symmetric domain Ω ⊂ Rn to satisfy the Poincare inequality with exponent p > n−1 is obtained and it is shown that this range of exponents is best possible. In the case where the Steiner symmetric domain is determined by revolving the graph of a Lipschitz continuous function, it is shown that the preceding characterization works for all p > 1 and furthermore for such domains a geometric characterization for a more general Sobolev–Poincare inequality to hold is given. Although the operation of Steiner symmetrization need not always preserve a Poincare inequality, a general class of domains is given for which Poincare inequalities are…

Texture advection on discontinuous flows

2015

Texture advection techniques, which transport textures using a velocity field, are used to visualize the dynamics of a flow on a triangle mesh. Some flow phenomena lead to velocity fields with discontinuities that cause the deformation of the texture which is not properly controlled by these techniques. We propose a method to detect and visualize discontinuities on a flow, keeping consistent texture advection at both sides of the discontinuity. The method handles the possibility that the discontinuity travels across the domain of the flow with arbitrary velocity, estimating its speed with least-squares approximation. The technique is tested with different sample scenarios and with two avala…

On the relativistic heat equation in one space dimension

2012

We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows for analysing further properties of their qualitative behaviour. J.A.C. acknowledges partial support by MINECO project, reference MTM2011-27739-C04-02, by GRC 2009 SGR 345 by the Generalitat de Catalunya, and by the Engineering and Physical Sciences Research Council grant number EP/K008404/1. J.A.C. also acknowledges support from the Royal Society through a Wolfson Research Merit Award. V.C. acknowledges partial support by MINECO project, refere…

Generalized Alomari functionals

2015

We consider a generalized form of certain integral inequalities given by Guessab, Schmeisser and Alomari. The trapezoidal, mid point, Simpson, Newton-Simpson rules are obtained as special cases. Also, inequalities for the generalized Alomari functional in terms of the $n$-th order modulus, $n=\overline{1,4}$, are given and applied to some known quadrature rules.

Plenty of big projections imply big pieces of Lipschitz graphs

2020

I prove that a closed $n$-regular set $E \subset \mathbb{R}^{d}$ with plenty of big projections has big pieces of Lipschitz graphs. This answers a question of David and Semmes.

Mappings of finite distortion: Sharp Orlicz-conditions

2003

We establish continuity, openness and discreteness, and the condition $(N)$ for mappings of finite distortion under minimal integrability assumptions on the distortion.

A note on mappings of finite distortion: The sharp modulus of continuity

2005