JASPER: a software for quantum chromodynamics Dyson-Schwinger equation numerical calculation

The JASPER program is the first part of the high-performance computing information system for estimate some elementary particle properties, developing at Petersburg Nuclear Physics Institute. The JASPER is an implementation of the Dyson-Schwinger equation numerical solution for simple dressed quark propagator calculation in rainbow approximation. The Dyson-Schwinger equation solution with the Marice-Tandy Ansatz is one of several phenomenological approaches to obtain quantitative results in quantum chromodynamics (QCD) within strong coupling regime. The JASPER program is programmed in the C++ language and uses the numerical algorithms from the GNU Scientific Library (GSL). The numerical results for dynamical quark mass in complex Euclidean space were obtained. This result will be employed to study the hadron spectrum with the Bethe-Salpeter equation approach.

NONLINEAR CONTACT DYNAMICS AND ANTI-SYMMETRY OF CORPUSCULAR-VORTEX-WAVE FORMS OF ELECTROMAGNETIC AND GRAVITATIONAL FIELDS IN THE BACKGROUND MEDIUM OF A COMPLEX EUCLIDEAN SPACE. SPECTRA OF HEATON RADIATION

Based on the hydrodynamic-wave calibration of potentials in Maxwell’s equations and their analogues for the gravitational field, nonlinear equations with respect to the vector potentials of these fields in the background medium of a complex Euclidean space are obtained. The nonlinear contact dynamics of corpuscular-vortex-wave forms of fields and violation of antisymmetry, which leads to the formation of matter and generation of electromagnetic, gravitational, hydrodynamic , acoustic waves separately in real and imaginary half-spaces of complex Euclidean space, are considered. Analytical expressions for the spectra of heaton radiation in a complex Euclidean space are obtained. It is shown that these expressions describe, in particular, the spectrum of solar radiation, collider resonance spectra, the spectrum of microwave background radiation generated by the Oort Cloud, and other spectra in technical, space and geodynamic systems. The fundamental technical failures in the field of controlled thermonuclear fusion and the known catastrophes in nuclear energy and hydropower related to the disregard of corpuscular-wave dualism in macrosystems and the limitations of a purely real part of the complex Euclidean space are analyzed.

Toward Classification of 2nd Order Superintegrable Systems in 3-Dimensional Conformally Flat Spaces with Functionally Linearly Dependent Symmetry Operators

We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD) symmetry generators, with special emphasis on complex Euclidean space. The symmetries for these systems are linearly dependent only when the coefficients are allowed to depend on the spatial coordinates. The Calogero-Moser system with 3 bodies on a line and 2-parameter rational potential is the best known example of an FLD superintegrable system. We work out the structure theory for these FLD systems on 3D conformally flat space and show, for example, that they always admit a 1st order symmetry. A partial classification of FLD systems on complex 3D Euclidean space is given. This is part of a project to classify all 3D 2nd order superintegrable systems on conformally flat spaces.

Quasi-Einstein Hypersurfaces of Complex Space Forms

Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura.

A Frobenius–Nirenberg theorem with parameter

The Newlander–Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the complex structure in the complex Euclidean space. We will show two results about the Newlander–Nirenberg theorem with parameter. The first extends the Newlander–Nirenberg theorem to a parametric version, and its proof yields a sharp regularity result as Webster’s proof for the Newlander–Nirenberg theorem. The second concerns a version of Nirenberg’s complex Frobenius theorem and its proof yields a result with a mild loss of regularity.

Regularity of CR mappings of abstract CR structures

We study the [Formula: see text] regularity problem for CR maps from an abstract CR manifold [Formula: see text] into some complex Euclidean space [Formula: see text]. We show that if [Formula: see text] satisfies a certain condition called the microlocal extension property, then any [Formula: see text]-smooth CR map [Formula: see text], for some integer [Formula: see text], which is nowhere [Formula: see text]-smooth on some open subset [Formula: see text] of [Formula: see text], has the following property: for a generic point [Formula: see text] of [Formula: see text], there must exist a formal complex subvariety through [Formula: see text], tangent to [Formula: see text] to infinite order, and depending in a [Formula: see text] and CR manner on [Formula: see text]. As a consequence, we obtain several [Formula: see text] regularity results generalizing earlier ones by Berhanu–Xiao and the authors (in the embedded case).