Related papers: Evolution equations in QCD and QED
A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a…
We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence groupoid of a class of…
In this paper we give classification of two-dimensional real evolution algebras. For several chains of evolution algebras we study their classification dynamics.
The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation.…
It is shown that twist-3 fragmentation functions in the large-$N_c$ limit of QCD obey the DGLAP evolution equations. The anomalous dimensions are found explicitly. The Gribov-Lipatov reciprocity is violated at the twist-3 level in the…
In order to recognize environmental effects on the evolution of dwarf galaxies in clusters of galaxies, it is first necessary to quantify the properties of objects which have evolved in relative isolation. With oxygen abundance as the gauge…
The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…
The discovery of equations with knowledge of the process origin is a tempting prospect. However, most equation discovery tools rely on gradient methods, which offer limited control over parameters. An alternative approach is the…
In the present paper we study some algebraic properties of evolution algebras. Moreover, we reduce the study of evolution algebras of permutations to two special types of evolution algebras, idempotents and absolute nilpotent elements of…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
We discuss skewed parton distributions in the coordinate space. Solution of the corresponding LO evolution equation is constructed in terms of eigenfunctions of the evolution kernel and its relation to the conformal symmetry is explained.
Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to current 3D black codes that simulate…
This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed.…
I review the subject of the cosmological evolution of galaxies, including different aspects of growth in disk galaxies, by focussing on the angular momentum problem, mergers, and their by-products. I discuss the alternative to merger-driven…
I discuss the evolution of computer architectures with a focus on QCD and with reference to the interplay between architecture, engineering, data motion and algorithms. New architectures are discussed and recent performance results are…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
We examine the parametrization of the QCD coupling in the Evolution Equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k^2_{\perp}/\beta or just k^2_{\perp}, stands only…
We consider the higher-order resummation of Sudakov double logarithms in the presence of multiple coupled gauge interactions. The associated evolution equations depend on the coupled $\beta$ functions of two (or more) coupling constants…
Evolutionary PDEs for geometric order parameters that admit propagating singular solutions are introduced and discussed. These singular solutions arise as a result of the competition between nonlinear and nonlocal processes in various…