Results 31 to 40 of about 51,902 (192)
Journal of Function Spaces and Applications, 2011 I. Vekua’s integral representations of holomorphic functions, whose m-th derivative (m≥0) is Hӧlder-continuous in a closed domain bounded by the Lyapunov curve, are generalized for analytic functions whose m-th derivative is representable by a Cauchy ...
Vakhtang Kokilashvili +1 more
doaj +1 more source
Doubling measures, monotonicity, and quasiconformality [PDF]
, 2006 We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition.
Kovalev, Leonid V. +2 more
core +4 more sources
Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley +1 more source
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
wiley +1 more source
Convolutions with the Continuous Primitive Integral
Abstract and Applied Analysis, 2009 If F is a continuous function on the real line and f=F′ is its distributional derivative, then the continuous primitive integral of distribution f is ∫abf=F(b)−F(a).
Erik Talvila
doaj +1 more source
Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
wiley +1 more source
Multiple Lebesgue integration on time scales
Advances in Difference Equations, 2006 We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.
Guseinov Gusein Sh, Bohner Martin
doaj
Riemann Integral on Fractal Structures
MathematicsIn this work we start developing a Riemann-type integration theory on spaces which are equipped with a fractal structure. These topological structures have a recursive nature, which allows us to guarantee a good approximation to the true value of a ...
José Fulgencio Gálvez-Rodríguez +2 more
doaj +1 more source
A Short Journey Through the Riemann Integral [PDF]
, 2014 An introductory-level theory of integration was studied, focusing primarily on the well-known Riemann integral and ending with the Lebesgue integral. An examination of the Riemann integral\u27s basic properties and necessary conditions shows that this ...
Keyton, Jesse
core +1 more source
How to Integrate a Polynomial over a Simplex
, 2008 This paper settles the computational complexity of the problem of integrating a polynomial function f over a rational simplex. We prove that the problem is NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin and Straus.
Baldoni, Velleda +4 more
core +8 more sources