Oceanic structures of the Earth and the North Depression of Mars: A comparison of the formation mechanisms

The system of contemporary oceans on Earth and the North Depression of Mars are quasi-symmetrical in reference to the centers of of the hemispheres. Both systems had been formed over the common megacycle of evolution of planets and their origin is likely to have similar features. The formation of the Earth's oceanic system within the South Hemisphere seems to have proceeded in three stages: (1) the formation of a network of passive rifts at the center of the Gondwana; (2) the formation of the system of active rifts at the zones of forthcoming spreading; and (3) the spreading of the oceanic crust. The formation of the Mar's North Depression seems to have proceeded in two stages: (1) a formation of a dense network of grabens and faults at the center of the North Hemisphere over the upper mantle zone characterized by an anomalous warm-up and a density decrease; and (2) a collapse of the ancient crust and it's overflowing by basalts. The first stage of the ocean formation on Earth and Mars is similar. But there seems to have been a thinner lithosphere on Mars. The dense areal rifting was immediately followed by a total collapse

On the differences in continental rifting at the Earth, Mars and Venus

During the process of continental rifting on Earth, the lower ductile crust stretches, forming a neck, while the upper brittle crust is broken in blocks by faults, and the blocks sink down the thinned lower crust; if the stretching continues, the neck may break and a newly originated oceanic crust is formed at this place. The rift system structure depends on the depth of the boundary surface between the brittle crust and the ductile crust, the litospheric thickness, the tension value, etc.. The rigid brittle rifting when narrow necks form in the lower crust is characteristic of the contemporary Earth; on Mars the brittle rifting with large subsidence was characteristic of the Tharsis upland formation epoch. The ductile rifting is typical of the Venus. The differences in rheologic features of the lithospheres of different planets causes the variation in types of rifting

A family of Nikishin systems with periodic recurrence coefficients

Suppose we have a Nikishin system of $p$ measures with the $k$th generating measure of the Nikishin system supported on an interval \Delta_k\subset\er with $\Delta_k\cap\Delta_{k+1}=\emptyset$ for all $k$. It is well known that the corresponding staircase sequence of multiple orthogonal polynomials satisfies a $(p+2)$-term recurrence relation whose recurrence coefficients, under appropriate assumptions on the generating measures, have periodic limits of period $p$. (The limit values depend only on the positions of the intervals $\Delta_k$.) Taking these periodic limit values as the coefficients of a new $(p+2)$-term recurrence relation, we construct a canonical sequence of monic polynomials $\{P_{n}\}_{n=0}^{\infty}$, the so-called \emph{Chebyshev-Nikishin polynomials}. We show that the polynomials $P_{n}$ themselves form a sequence of multiple orthogonal polynomials with respect to some Nikishin system of measures, with the $k$th generating measure being absolutely continuous on $\Delta_{k}$. In this way we generalize a result of the third author and Rocha \cite{LopRoc} for the case $p=2$. The proof uses the connection with block Toeplitz matrices, and with a certain Riemann surface of genus zero. We also obtain strong asymptotics and an exact Widom-type formula for the second kind functions of the Nikishin system for $\{P_{n}\}_{n=0}^{\infty}$.Comment: 30 pages, minor change

Different types of small volcanos on Venus

One of the studies of volcanic activity on Venus is the comparison of that with the analogous volcanic activity on Earth. The preliminary report of such a comparison and description of a small cluster of small venusian volcanos is represented in detail in this paper

Eliminating the Hubble Tension in the Presence of the Interconnection between Dark Energy and Matter in the Modern Universe

It is accepted in modern cosmology that the scalar field responsible for the inflationary stage of the early Universe is completely transformed into matter. It is assumed that the accelerated expansion is currently driven by dark energy (DE), which is likely determined by Einstein's cosmological constant. We consider a cosmological model where DE can have two components, one of which is Einstein's constant ($\Lambda$) and the other, smaller variable component DEV ($\Lambda_V$), is associated with the remnant of the scalar field that caused inflation after the main part of the scalar field has turned into matter. It is assumed that such a transformation continues at the present time and is accompanied by the reverse process of the DM transformation into a scalar field. The interconnection between DM and DEV, which leads to a linear relationship between the energy densities of these components after recombination $\rho_{DM}=\alpha\;\rho_{DEV}$, is considered. Variants with a dependence of the coefficient $\alpha(z)$ on the redshift are also considered. One of the problems that have arisen in modern cosmology, called Hubble Tension (HT), is the discrepancy between the present values of the Hubble constant measured from observations at small redshifts $z\lesssim1$ and the values found from fluctuations of the cosmic microwave background at large redshifts $z\approx1100$. In the considered model, this discrepancy can be explained by the deviation of the real cosmological model from the conventional cold dark matter (CDM) model of the Universe by action of the additional DE component at the stages after recombination. Within this extended model, we consider various $\alpha(z)$ functions that can eliminate the HT. To maintain the ratio of DEV and DM energy densities close to constant over the interval $0\le z\le1100$, we assume the existence of a wide spectrum of DM particle masses

Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials

In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, generalized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type lattic

An Algebraic Model for the Multiple Meixner Polynomials of the First Kind

An interpretation of the multiple Meixner polynomials of the first kind is provided through an infinite Lie algebra realized in terms of the creation and annihilation operators of a set of independent oscillators. The model is used to derive properties of these orthogonal polynomials

Critical behavior in Angelesco ensembles

We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where we let the number of particles of the ensemble tend to infinity while the parameter a tends to -1 at a rate of order n^{-1/2}. The correlation kernel converges, in this regime, to a new kind of universal kernel, the Angelesco kernel K^{Ang}. The result follows from the Deift/Zhou steepest descent analysis, applied to the Riemann-Hilbert problem for multiple orthogonal polynomials.Comment: 32 pages, 9 figure

METHODS FOR MANAGING INTANGIBLE ASSETS AND ECOMMERCE RESOURCES: SYSTEMATIC REVIEW

Objective: The study aims at classifying and supplementing general and special methods for managing intangible assets and eCommerce resources. The present stage of management science is characterized by an insufficient number and incomplete nature of the existing studies on the structure of methods for managing intangible assets and eCommerce resources, which is mainly due to the relative novelty of the Internet environment and its management. The challenge of solving this issue is the intangibility of the management object under study (intangible assets and resources) and the intangibility of the management environment (Internet environment), which makes management in such conditions more difficult. Methods: When preparing this article, we used qualitative research methods, including grouping sets of homogeneous management methods, systematizing such methods according to homogeneous features, comparing different methods with each other, and generalizing the obtained groups of methods to draw conclusions and recommendations. When grouping methods for managing intangible assets and eCommerce resources, we took the classification according to a functional attribute as the basis. Results: As a result of the study, the authors have revealed that the management of intangible assets and eCommerce resources requires the full range of general management methods (planning, organizational, evaluation, accounting, analytical, motivational, control, and coordination methods), special methods for managing intangible assets and resources (identification, visualization, and security methods), as well as specific methods for managing intangible assets and resources in the Internet environment (online methods). Conclusion: Based on the study results, it has been concluded that online management methods are most actively developing in the modern market, and in the near future the importance of these methods will increase. The novelty of the study is to determine the presence and composition of previously unexplored groups of management methods applied to intangible assets and eCommerce resources