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

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

Large Deviations for a Non-Centered Wishart Matrix

We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic potential theory, which in our case is a quadratic map involving the logarithmic energies, or Voiculescu's entropies, of two measures in the presence of an external field and an upper constraint. The proof is based on a two type particles Coulomb gas representation for the eigenvalue distribution, which gives a new insight on why such variational problems should describe the limiting spectral distribution. This representation is available because of a Nikishin structure satisfied by the weights of the multiple orthogonal polynomials hidden in the background.Comment: 40 page

Three-Beam Triangulating Sensor

© Published under licence by IOP Publishing Ltd. The new high precision triangulating sensor for measuring distance and/or inclination angle with high temperature stability for a wide range of technical and technological applications is proposed. The corresponding measurement algorithm is considered and hardware allowing its implementation is developed. The preferable embodiment of three beam triangulating sensor comprises three laser radiation sources, CCD- array based image sensor including optical system, and control electronic unit

Рифтовые системы шельфа Российской Восточной Арктики и арктического глубоководного бассейна: связь геологической истории и геодинамики

In our study, we have developed a new tectonic scheme of the Arctic Ocean, which is based mainly on seismic profiles obtained in the Arctic-2011, Arctic-2012 and Arctic-2014 Projects implemented in Russia. Having interpreted many seismic profiles, we propose a new seismic stratigraphy of the Arctic Ocean. Our main conclusions are drawn from the interpretation of the seismic profiles and the analysis of the regional geological data. The results of our study show that rift systems within the Laptev, the East Siberian and the Chukchi Seas were formed not earlier than Aptian. The geological structure of the Eurasian, Podvodnikov, Toll and Makarov Basins is described in this paper. Having synthesized all the available data on the study area, we propose the following model of the geological history of the Arctic Ocean: 1. The Canada Basin formed till the Aptian (probably, during Hauterivian-Barremian time). 2. During the Aptian-Albian, large-scale tectonic and magmatic events took place, including plume magmatism in the area of the De Long Islands, Mendeleev Ridge and other regions. Continental rifting started after the completion of the Verkhoyansk-Chukotka orogenу, and rifting occurred on the shelf of the Laptev, East Siberian, North Chukchi and South Chukchi basins, and the Chukchi Plateau; simultaneously, continental rifting started in the Podvodnikov and Toll basins. 3. Perhaps the Late Cretaceous rifting continued in the Podvodnikov and Toll basins. 4. At the end of the Late Cretaceous and Paleocene, the Makarov basin was formed by rifting, although local spreading of oceanic crust during its formation cannot be excluded. 5. The Eurasian Basin started to open in the Early Eocene. We, of course, accept that our model of the geological history of the Arctic Ocean, being preliminary and debatable, may need further refining. In this paper, we have shown a link between the continental rift systems on the shelf and the formation history of the Arctic Ocean.На основе российских сейсмических профилей, полученных в рамках проектов Арктика-2011, Арктика-2012 и Арктика-2014, составлена новая тектоническая схема Арктического океана. Приведены результаты интерпретации многих сейсмических профилей, представлена новая сейсмостратиграфия для Арктического океана. Основные выводы сделаны на основе интерпретации сейсмических профилей и на базе анализа региональных геологических данных. Показано, что рифтовые системы в пределах морей Лаптевых, Восточно-Сибирского и Чукотского были образованы не раньше аптского времени. Дано описание геологического строения бассейнов Евразийского, Подводников, Толля, Макарова и других. На основе синтеза всех данных получена следующая модель истории Арктического океана. 1. Канадский бассейн был образован до аптского времени (вероятно, в готериве-барреме). 2. В апте-альбе были крупномасштабные тектонические и магматические события: плюмовый магматизм был в районе поднятия Де-Лонга, на хребте Менделеева и в других областях. Континентальный рифтинг произошел сразу после окончания Верхоянско-Чукотской орогении и рифтинг был на шельфе морей Лаптевых, Восточно-Сибирского, Северо-Чукотского и Южно-Чукотского и на поднятии Чукотского плато; одновременно континентальный рифтинг начался в бассейнах Подводников и Толля. 3. В позднем мелу рифтинг, возможно, продолжился в бассейнах Подводников и Толля. 4. В конце позднего мела и в палеоцене в ходе рифтинга был образован бассейн Макарова; локальный спрединг океанической коры при формировании бассейна Макарова не исключен. 5. Евразийский бассейн начал образовываться в начале эоцена. Наша модель геологической истории Арктического океана является предварительной и дискуссионной. В целом, мы показали связь континентальных рифтовых систем на шельфах с историей раскрытия Арктического океана