Results 81 to 90 of about 4,846 (246)
The Huang–Yang Formula for the Low‐Density Fermi Gas: Upper Bound
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1919-1972, August 2026.ABSTRACT We study the ground state energy of a gas of spin 1/2$1/2$ fermions with repulsive short‐range interactions. We derive an upper bound that agrees, at low density ϱ$\varrho$, with the Huang–Yang conjecture. The latter captures the first three terms in an asymptotic low‐density expansion, and in particular the Huang–Yang correction term of order
Emanuela L. Giacomelli +3 more
wiley +1 more source
Numerical Evaluation of Goursat’s Infinite Integral with an Unbounded Function
, 2009 The infinite integral R ∞ 0 xdx/(1+x^6 sin^2 x) converges but is hard to evaluate because the integrand f (x) = x/(1+x^6 sin^2 x) is a non-convergent and unbounded function, indeed f (kπ) = kπ →∞ (k →∞).
NINOMIYA, Ichizo +3 more
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Self‐Similar Blowup for the Cubic Schrödinger Equation
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1831-1918, August 2026.ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley +1 more source
On the Measurability of the Conjugate and the Subdifferential of a Normal Integrand
, 1995 Introduction The notion of normal integrand, introduced and studied extensively by R. T. Rockafellar in several papers (for example, [15--18]), is known to be well suited for dealing with minimization problems arising in many fields of applied ...
Christian Hess
core
Function-valued adaptive dynamics and optimal control theory
, 2012 In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function ...
Dieckmann, U., Parvinen, K., Heino, M.
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Regularity Results for Local Minimizers of Functionals with Discontinuous Coefficients
Bruno Pini Mathematical Analysis Seminar, 2016 We give an overview on recent regularity results of local vectorial minimizers of under two main features: the energy density is uniformly convex with respect to the gradient variable only at infinity and it depends on the spatial variable through a ...
Raffaella Giova +1 more
doaj +1 more source
Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.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
Numerical Integration of the Function with Twin Boundary Layers
Traditional numerical integration requires sufficient smoothness of the integrand to achieve high-order algebraic accuracy. If the function has a boundary layer with large gradient, the composite integration formula on the uniform mesh will produce very ...
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On the upper bound in Varadhan's Lemma
, 2015 In this paper, we generalize the upper bound in Varadhan’s Lemma. The standard formulation of Varadhan’s Lemma contains two important elements, namely an upper semicontinuous integrand and a rate function with compact sublevel sets. However, motivated by
Mandjes, Michel +8 more
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Master integrals for the four-loop Sudakov form factor
Nuclear Physics B, 2016 The light-like cusp anomalous dimension is a universal function in the analysis of infrared divergences. In maximally (N=4) supersymmetric Yang–Mills theory (SYM) in the planar limit, it is known, in principle, to all loop orders.
Rutger H. Boels +2 more
doaj +1 more source