Related papers: Less Singular Terms and Small x Evolution in a Sol…
The small-$x$ quark helicity evolution equations at double-logarithmic order, with the kernel $\sim\alpha_s\ln^2(1/x)$, have been derived previously. In this work, we derive the single-logarithmic corrections to the equations, to order…
We study models of quintessence consisting of a number of scalar fields coupled to several dark matter components. In the case of exponential potentials the scaling solutions can be described in terms of a single field. The corresponding…
We study the large-x behaviour of the physical evolution kernels for flavour non-singlet observables in deep-inelastic scattering, where x is the Bjorken variable, semi-inclusive e^+ e^- annihilation and Drell-Yan lepton-pair production.…
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
A class of generalized non-minimal coupling theories is investigated, in search of scaling attractors able to provide an accelerated expansion at the present time. Solutions are found in the strong coupling regime and when the coupling…
Hamilton et al. have suggested an invaluable scaling formula which describes how the power spectra of density fluctuations evolve into the nonlinear regime of hierarchical clustering. This paper presents an extension of their method to…
We consider a system of evolution equations for quark and gluon structure functions satisfying the leading-logarithmic behaviour due to both QCD collinear $ \left(LLQ^2 \right) $ and infrared $ (LL1/x) $ singularities. We show that these…
For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the…
In this work, we study the existence and regularity results of anisotropic elliptic equations with a singular lower order term that grows naturally with respect to the gradient and unbounded coefficients. We take up the following model…
We study the De Giorgi type conjecture, that is, one dimensional symmetry problem for entire solutions of an two components elliptic system in $\mathbb{R}^n$, for all $n\geq 2$. We prove that, if a solution $(u,v)$ has a linear growth at…
A famous theorem of Bers and Finn states that isolated singularities of solutions to the non-parametric minimal surface equation are removable. We show that this result remains valid, if the area functional is replaced by a general…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
A survey is given of recent developments on the resummed small-$x$ evolution, in a framework based on the renormalization group equation, of non--singlet and singlet structure functions in both unpolarized and polarized deep--inelastic…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
The accelerated expansion of the universe is a rather established fact in cosmology and many different models have been proposed as a viable explanation. Many of these models are based on the standard general relativistic framework of…
By introducing a new classification of the growth rate of exponential functions, singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities are constructed. The strategy is to introduce a model…
We present a Monte Carlo study of the one-component $\phi^4$ model on the cubic lattice in three dimensions. Leading order scaling corrections are studied using the finite size scaling method. We compute the corrections to scaling exponent…
The evolution of sub-spaces in the framework of gravity with higher derivatives is studied. Numerical solutions to exact differential equations are found. It is shown that the initial conditions play crucial role in the space dynamic.…