Evaluation of siltation of rivers with intensive economic development of watersheds

In regions with a high degree of agricultural development with an active development of erosion processes and the critical level of degradation of the river network to which the Middle-Russian Upland belongs, the evaluation of sedimentation for various combinations of natural and economic conditions becomes an immediate proble

Functioning of back-to-back high voltage direct current link model in Tomsk electric power system

In this article the research results of steady-state and dynamic performance of asynchronous back-to-back HVDC link in Tomsk electric power system are presented. It is proposed to use the back-to-back HVDC link to provide an asynchronous link for parallel operation of the North and South parts of Tomsk electric power system. The steady-state stability limit and maximum allowed power flow were defined. Based on this the more effective location and power of back-to-back HVDC link were determined. Therefore, it is shown the application of back-to-back HVDC link decreases the level of short-circuit current, power fluctuations and increases the stability of load operation, especially of motor load at substation

On the water-bag model of dispersionless KP hierarchy

We investigate the bi-Hamiltonian structure of the waterbag model of dKP for two component case. One can establish the third-order and first-order Hamiltonian operator associated with the waterbag model. Also, the dispersive corrections are discussed.Comment: 19 page

Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems

Reciprocal transformations of Hamiltonian operators of hydrodynamic type are investigated. The transformed operators are generally nonlocal, possessing a number of remarkable algebraic and differential-geometric properties. We apply our results to linearly degenerate semi-Hamiltonian systems in Riemann invariants. Since all such systems are linearizable by appropriate (generalized) reciprocal transformations, our formulae provide an infinity of mutually compatible nonlocal Hamiltonian structures, explicitly parametrized by arbitrary functions of one variable.Comment: 26 page

Pharmacological sequestration of mitochondrial calcium uptake protects against dementia and β-amyloid neurotoxicity

All forms of dementia including Alzheimer's disease are currently incurable. Mitochondrial dysfunction and calcium alterations are shown to be involved in the mechanism of neurodegeneration in Alzheimer's disease. Previously we have described the ability of compound Tg-2112x to protect neurons via sequestration of mitochondrial calcium uptake and we suggest that it can also be protective against neurodegeneration and development of dementia. Using primary co-culture neurons and astrocytes we studied the effect of Tg-2112x and its derivative Tg-2113x on β-amyloid-induced changes in calcium signal, mitochondrial membrane potential, mitochondrial calcium, and cell death. We have found that both compounds had no effect on β-amyloid or acetylcholine-induced calcium changes in the cytosol although Tg2113x, but not Tg2112x reduced glutamate-induced calcium signal. Both compounds were able to reduce mitochondrial calcium uptake and protected cells against β-amyloid-induced mitochondrial depolarization and cell death. Behavioral effects of Tg-2113x on learning and memory in fear conditioning were also studied in 3 mouse models of neurodegeneration: aged (16-month-old) C57Bl/6j mice, scopolamine-induced amnesia (3-month-old mice), and 9-month-old 5xFAD mice. It was found that Tg-2113x prevented age-, scopolamine- and cerebral amyloidosis-induced decrease in fear conditioning. In addition, Tg-2113x restored fear extinction of aged mice. Thus, reduction of the mitochondrial calcium uptake protects neurons and astrocytes against β-amyloid-induced cell death and contributes to protection against dementia of different ethology. These compounds could be used as background for the developing of a novel generation of disease-modifying neuroprotective agents

Representations of sl(2,?) in category O and master symmetries

We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin-Ono-type equation, a new integrable Davey-Stewartson-type equation, and two different versions of (2+1)-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries

Reciprocal transformations and local Hamiltonian structures of hydrodynamic type systems

We start from a hyperbolic DN hydrodynamic type system of dimension $n$ which possesses Riemann invariants and we settle the necessary conditions on the conservation laws in the reciprocal transformation so that, after such a transformation of the independent variables, one of the metrics associated to the initial system be flat. We prove the following statement: let $n\ge 3$ in the case of reciprocal transformations of a single independent variable or $n\ge 5$ in the case of transformations of both the independent variable; then the reciprocal metric may be flat only if the conservation laws in the transformation are linear combinations of the canonical densities of conservation laws, {\it i.e} the Casimirs, the momentum and the Hamiltonian densities associated to the Hamiltonian operator for the initial metric. Then, we restrict ourselves to the case in which the initial metric is either flat or of constant curvature and we classify the reciprocal transformations of one or both the independent variables so that the reciprocal metric is flat. Such characterization has an interesting geometric interpretation: the hypersurfaces of two diagonalizable DN systems of dimension $n\ge 5$ are Lie equivalent if and only if the corresponding local hamiltonian structures are related by a canonical reciprocal transformation.Comment: 23 pages; corrected typos, added counterexample in Remark 3.

Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a generic gl(n)-spin chain possessing on each site an arbitrary gl(n)-representation. For open spin chains, we use the classification of the reflection matrices to treat all the diagonal boundary cases. As a result, we obtain the Bethe equations in their full generality for closed and open spin chains. The classifications of finite dimensional irreducible representations for the Yangian (closed spin chains) and for the reflection algebras (open spin chains) are directly linked to the calculation of the transfer matrix eigenvalues. As examples, we recover the usual closed and open spin chains, we treat the alternating spin chains and the closed spin chain with impurity