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## Параметризация характеристик наката одиночных волн в бухте параболического сечения

It is shown characteristic parameters of wave run-up for different pulses normalized by their height and wave length (duration), have close values and can be parameterized. The details of the form of the individual symmetric bell-shape pulse does not influence much run-up characteristics and can be neglected.

Instrumental data of the long-term observation of abnormally large waves (freak waves) on the shelf of Sakhalin Island near the village Vsmorie, cape Ostriy, orifi ce of the Izmenchivae Lake, cape Svobodniy and cape Aniwa since 2007 are adduced. These measurements were made with using bottom stations, measuring variations in bottom pressure, induced by surface waves. These sensors do not interfere with navigation and do not affect the ecology of the area. The important problem of the translation variations of bottom pressure in the vertical oscillations of the sea surface is discussed. The linear theory of water waves used here as a fi rst approximation. About 1,400 waves that are abnormal, and their height twice the height of the background waves (amplitude criterion killer waves) are allocated from the total number of individual waves (several million). About 20 waves have a height greater than the height of the background by 2.7 times. The wave group, which was fi xed for the term «three sisters» is typical form of abnormal waves. On average, two or three abnormal waves are recorded per day

short review of the potential tsunamis of cosmic origin is given

Non reflected waves in the strongly inhomogeneous atmosphere are discussed. The application to the geophysical and astrophysical problems is done

The 2011 Tohoku earthquake triggered extremely destructive tsunami waves which propagated over the Pacific Ocean, Atlantic Ocean through Drake Passage and Indian Ocean respectively. A total of 10 tide-gauge records collected from the UNESCO/IOC site were analyzed through a band-pass digital filtering device to examine the observed tsunami characteristics. The ray tracing method and finite-difference model with GEBCO 30 arc second bathymetry were also applied to compare the travel times of the Tohoku-originated tsunami, particularly at Rodrigues in the Indian Ocean and King Edward Point in the Atlantic Ocean with observation-based estimates. At both locations the finite-difference model produced the shortest arrival times, while the ray method produced the longest arrival times. Values of the travel time difference however appear to be within tolerable ranges, considering the propagation distance of the tsunami waves. The observed tsunami at Rodrigues, Mauritius in the west of the Madagascar was found to take a clockwise travel path around Australia and New Zealand, while the observed tsunami at King Edward Point in the southern Atlantic Ocean was found to traverse the Pacific Ocean and then passed into the Atlantic Ocean through the Drake Strait. The formation of icebergs captured by satellite images in Sulzberger in the Antarctica also supports the long-range propagation of the Tohoku-originated tsunami

Nonlinear waves in the coastal zone can be dangered for coastal infrastructure, tourism and waterways. Given books deals with dynamics of nonlinear long waves taking into account the breaking effects. Developed theory is applied for interpretation of the natural and laboratory data including freak wave phenomenon.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.