The general solutions of some nonlinear second and third order PDEs with constant and nonconstant parameters

Selection of 25 examples from extensive nontrivial families for different types of nonlinear PDEs and their formal general solutions are given. The main goal here is to show on examples the types of solvable PDEs and what their general solutions look like.Comment: 15 page

Star complexes and starburst clumps in spiral galaxies

Star complexes are the highest level groupings in the hierarchy of the embedded young stars, clusters and associations, which obey the size - age relation. Starburst clumps, superassociations, supergiant HII regions are different titles for the groupings of the same size as complexes but with active star formation over all the grouping. The coherent star formation in the regions of violent star formation was probably triggered by external pressure. The issue of gravitational boundness of complexes and superassociations is briefly discussedComment: Contribution to the Transactions of the conference "Gamov-100", Odessa, August 200

Lie type algebras with an automorphism of finite order

An algebra $L$ over a field $\Bbb F$, in which product is denoted by $[\,,\,]$, is said to be \textit{ Lie type algebra} if for all elements $a,b,c\in L$ there exist $\alpha, \beta\in \Bbb F$ such that $\alpha\neq 0$ and $[[a,b],c]=\alpha [a,[b,c]]+\beta[[a,c],b]$. Examples of Lie type algebras are associative algebras, Lie algebras, Leibniz algebras, etc. It is proved that if a Lie type algebra $L$ admits an automorphism of finite order $n$ with finite-dimensional fixed-point subalgebra of dimension $m$, then $L$ has a soluble ideal of finite codimension bounded in terms of $n$ and $m$ and of derived length bounded in terms of $n$

Constraints on strongly coupled chameleon fields from the experimental test of the weak equivalence principle for the neutron

The chameleon scalar field is considered as a possible cause of accelerated expansion of the Universe. The chameleon field induces an interaction potential between a particle and a massive body. Previous experiments with falling cold neutrons intended to measure the neutron coherent scattering lengths and verification of the weak equivalence principle for the neutron are used to constrain the parameters characterizing the strength of the scalar chameleon fields.Comment: 4 p. + 1 fi

Reply to 'Comment for "Limits on a nucleon-nucleon monopole-dipole (axionlike) P,T-noninvariant interaction from spin relaxation of polarized He-3" [arXiv:0912.4963], by A.P. Serebrov'

It is shown, that criticism, presented in [arXiv:0912.4963], is based on an elementary error in the calculation of the collision frequency of an atom in a gas with walls of a container and misunderstanding of the method used in [arXiv:0902.1682v2] for obtaining constraints on new short-range spin-dependent interactions.Comment: 3

Gravitational waves from primordial black holes collisions in binary systems

It was shown by (Nakamura et al. 1997), (Ioka et al. 1998), and (Sasaki et al. 2016) that primordial black holes (PBHs) binaries can form effectively at the cosmological stage of radiation dominance, and the merge of the PBHs in pairs can explain the gravitational wave burst GW150914. In this paper, the model is re-examined by considering the effect of inflationary dark matter density perturbations which produce additional tidal forces. As a result, the merge rate of PBHs binaries and the corresponding rate of the gravitational bursts are suppressed by the factor $\sim1.5-2$ in comparison with previous calculations. This rate matches the LIGO data if the PBHs constitute the $f\sim5\times10^{-4}-5\times10^{-3}$ fraction of dark matter.Comment: 6 pages, 2 figures, Presented at the Conference on Physical Interpretation of Relativity Theory (PIRT-2017), Moscow, Russi

The introduction to the operator method for solving differential equations.First-order DE

We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of the equations and then to transform them to more convenient form with help of developed family of operator identities. On example of non-linear first-order DEs we analyse analytical and algorithmical possibilities for solutions obtaining. Different forms of solutions for first-order DEs are given, including for some integro-differential equations and equations with variational derivatives. We describe new algorithms for direct computing the solutions with help of computer algebra system (CAS). We also discuss recipe for finding new solvability conditions, which allow to enlarge DE solving abilities of existent CAS.Comment: 18 page

The Chronological Operator Algebra and Formal Solutions of Differential Equations

The aim of this paper is twofold. First, we obtain the explicit exact formal solutions of differential equations of different types in the form with Dyson chronological operator exponents. This allows us to deal directly with the solutions to the equations rather than the equations themselves. Second, we consider in detail the algebraic properties of chronological operators, yielding an extensive family of operator identities. The main advantage of the approach is to handle the formal solutions at least as well as ordinary functions. We examine from a general standpoint linear and non-linear ODEs of any order, systems of ODEs, linear operator ODEs, linear PDEs and systems of linear PDEs for one unknown function. The methods and techniques involved are demonstrated on examples from important differential equations of mathematical physics.Comment: 36 page

Dirac points, spinons and spin liquid in twisted bilayer graphene

Twisted bilayer graphene is an excellent example of highly correlated system demonstrating a nearly flat electron band, the Mott transition and probably a spin liquid state. Besides the one-electron picture, analysis of Dirac points is performed in terms of spinon Fermi surface in the limit of strong correlations. Application of gauge field theory to describe deconfined spin liquid phase is treated. Topological quantum transitions, including those from small to large Fermi surface in the presence of van Hove singularities, are discussed.Comment: 4 pages, JETP Letters, accepte

Scaling behaviour of exclusive reactions with the deuteron and 3He at high p_T in the Gev region

The scaling behaviour s^{-11} of the cross section of the reaction \gamma d-> pn observed at SLAC and Jlab at energies E_{\gamma}=1-4 GeV and large p_T most likely displays quark degrees of freedom in the deuteron. We show that the cross sections of the dd->3Hp and pd-> 3Hen reactions measured at SATURNE follow the scaling regime s{-22} at T_d= 0.5 -1.2 GeV and $\theta_{cm}=50^\circ-60^\circ$. A necessity to get new data on this and other exclusive reactions is argued.Comment: 6 pages, 4 figures; talk at XVIII International Baldin Seminar "Relativistic Nuclear Physics and QCD", September 25-30,2006, Dubn