A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields

We give a complete list of normal forms for the 2-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.Comment: This is an extended version of the paper that will appear in Math. Annalen. Some typos were corrected, references were updated, title was changed (as in the journal version). 31 page

Interannual variability of thermal state of the cold subsurface layer in the Okhotsk Sea

Long-term variability of the cold subsurface water (CSW) in the Okhotsk Sea is analyzed on the base of all available oceanographic data collected in March through August of 1946-2015 (total 65,742 stations). The Integral Heat Content (IHC) is calculated for each station and average annual IHC anomalies of the cold subsurface water are determined by month and by 2-degree grid. The IHC anomaly series are analyzed using the EOF analysis. Cycles with period of approximately 30 years are revealed in the variations of the subsurface layer heat content. Thus, in the 1946-1950, its temperature decreased, but it grew since 2009-2010 to 2015. The warming of CSW was also observed in the 1951-1964 and 1978-1994, while the cooling was in the 1965-1977 and 1995-2008. Based on this criterion, the CSW thermal condition in certain years is classified as «extremely cold» in 2001, as «cold» in 1949, 1950, 1951, 1958, 1959, 1960, 1966, 1967, 1969, 1973, 1976, 1977, 1978, 1980, 1999, 2000, 2010, 2012, as «normal» in 1946, 1952, 1953, 1954, 1955, 1957, 1961, 1962, 1965, 1970, 1971, 1972, 1975, 1979, 1982, 1983, 1985, 1986, 1988, 1989, 1990, 1993, 1995, 1996, 1998, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2011, 2013, 2014, as «warm» in 1948, 1956, 1964, 1968, 1974, 1981, 1984, 1987, 1991, 1992, 1994, 1997, 2015, and as «extremely warm» in 1963. Statistically significant correlation is found between changes of the CSW thermal conditions and long-term variations of atmosphere and ocean climate indices, as well as local patterns of the atmosphere-ice-ocean interaction in the Okhotsk Sea and adjacent onshore and offshore areas of Asia and the Pacific Ocean

Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications

We extend the Gallot-Tanno Theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric $(0,2)-$tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed $(O(p+1,q),S^{p,q})$-manifold does not preserve any nondegenerate splitting of $\R^{p+1,q}$.Comment: minor correction

Quantitative Mapping of Strains and Young Modulus Based on Phase-Sensitive OCT

In this chapter we consider mapping of local strains and tissue elasticity in optical coherence tomography (OCT) based on analysis of phase-sensitive OCT scans. Conventional structural OCT scans correspond to spatially resolved mapping of the backscattering intensity of the probing optical beam. Deeper analysis of such sequentially acquired multiple OCT scans can be used to extract additional information about motion of scatterers in the examined region. Such detailed analysis of OCT scans has already resulted in creation of OCT-based visualization of blood microcirculation, which has been implemented in several commercially available devices, especially for ophthalmic applications. Another functional extension of OCT emerging in recent years is the OCT-based elastography, i.e., mapping of local strains and elastic properties in the imaged region. Here, we describe the main principles of local strain mapping in phase-sensitive OCT with a special focus on the recently proposed efficient vector method of estimation of interframe phase-variation gradients. The initially performed mapping of local strains is then used for realization of quantitative compressional elastography, i.e., mapping of the Young modulus and obtaining stress-strain dependences for the studied samples. The discussed principles are illustrated by simulated and experimental examples of elastographic OCT-based visualization. The presented elastographic principles are rather general and can be used in a wide area of biomedical and technical applications

Energy-Saving Vibration Impulse Coal Degradation at Finely Dispersed Coal-Water Slurry Preparation

Theoretical and experimental research results of processes of finely dispersed coal-water slurry preparation for further generation of energetic gas in direct flow and vortex gas generator plants have been presented. It has been stated that frequency parameters of parabolic vibration impulse mill influence degradation degree. Pressure influence on coal parameters in grinding cavity has been proven. Experimental researches have proven efficiency of vibration impulse mill with unbalanced mass vibrator generator development. Conditions of development on intergranular walls of coal cracks have been defined

Technical project of complex fast cycle heat treatment of hydrogenous coal preparation

Problems of heat-treated milled hydrogenous coal preparation site creation in leading fast cycle heat treatment complex were considered. Conditions for effective use of electrostatic methods of heat-treated milled hydrogenous coal preparation were set. Technical project of heat treatment of milled hydrogenous coal preparation site was developed including coupling of working equipment complex on fast heat treatment and experimental samples of equipment being designed for manufacturing. It was stated that methods of electrical separation are used for heat-treated milled hydrogenous coal preparation with effective ways of organic and mineral components separation. Laboratory test for determination of optimal separation size sent into separators of heat-treated milled hydrogenous coal were made