Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Generalized distance-squared mappings of the plane into the plane
2016
Abstract We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
Correlation functions for a strongly coupled boson system and plane partitions.
2011
A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q -boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.
Strictly convex corners scatter
2017
We prove the absence of non-scattering energies for potentials in the plane having a corner of angle smaller than $\pi$. This extends the earlier result of Bl{\aa}sten, P\"aiv\"arinta and Sylvester who considered rectangular corners. In three dimensions, we prove a similar result for any potential with a circular conic corner whose opening angle is outside a countable subset of $(0,\pi)$.
On complete metric spaces containing the Sierpinski curve
1998
It is proved that a complete metric space topologically contains the Sierpiński universal plane curve if and only if it has a subset with so-called bypass property, i.e. it has a subset K K containing an arc such that for each a ∈ K a\in K and for each open arc A ⊂ K A\subset K with a ∈ A a\in A , there exists an arbitrary small arc in K ∖ { a } K\setminus \{a\} joining the two components of A ∖ { a } A\setminus \{a\} .
X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks
2019
The analysis of large amplitude vibrations of cracked plates is considered in this study. The problem is addressed via a Ritz approach based on the first-order shear deformation theory and von Karman’s geometric nonlinearity assumptions. The trial functions are built as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour (which motivates why the method is dubbed as eXtended Ritz); boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions along the plate edges. Convergence and accuracy are assessed to validate the approach and show its efficiency and potential. Original results are then…
Multiplicity results for fourth order two-point boundary value problems with asymmetric nonlinearities
1998
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
2016
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…
Regularity properties for quasiminimizers of a $(p,q)$-Dirichlet integral
2021
Using a variational approach we study interior regularity for quasiminimizers of a $(p,q)$-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and supporting a Poincar\'{e} inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally H\"{o}lder continuous and they satisfy Harnack inequality, the strong maximum principle, and Liouville's Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for H\"older continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we cons…
Weighted pointwise Hardy inequalities
2009
We introduce the concept of a visual boundary of a domain �¶ �¼ Rn and show that the weighted Hardy inequality �¶ |u|pd�¶ �A.p C �¶ |�Þu|pd�¶ �A, where d�¶(x) = dist(x, �Ý�¶), holds for all u �¸ C �� 0 (�¶) with exponents �A < �A0 when the visual boundary of �¶ is sufficiently large. Here �A0 = �A0(p, n, �¶) is explicit, essentially sharp, and may even be greater than p . 1, which is the known bound for smooth domains. For instance, in the case of the usual von Koch snowflake domain the sharp bound is shown to be �A0 = p . 2 + �E, with �E = log 4/ log 3. These results are based on new pointwise Hardy inequalities.
Finite element approximation of vector fields given by curl and divergence
1981
In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.