Calcineurin is a Ca2+/calmodulin-dependent phosphatase that dephosphorylates numerous substrates in different neuronal compartments. Genetic and pharmacological studies have provided insight into its involvement in the brain. Cyclosporin A (CsA) is used as a specific calcineurin inhibitor in many pharmacological experiments. However, the calcineurin activity of CsA-treated brain has not been reported. To examine the relationship between calcineurin activity and brain function, we injected CsA into the left lateral ventricle of the mouse brain and assayed calcineurin activity. CsA reduced calcineurin activity in a dose-dependent manner, without affecting the amount of calcineurin protein. Assays of the effect of protein phosphatase inhibitors on CsA-injected mouse brain extracts and kinetic analysis revealed that CsA inhibited calcineurin activity in a non-competitive manner in vivo, in agreement with in vitro results. Injection of CsA led to enhanced phosphorylation of tau at Ser-262 (12E8 site), Ser-198, Ser-199, and/or Ser-202 (Tau-1 site) and Ser-396 and/or Ser-404 (PHF-1 site), as well as to impaired spatial memory, which are two characteristic features of Alzheimer's disease. We propose that inhibition of calcineurin may play an important role in Alzheimer's disease.
Korteweg–de Vries (KdV)-type equations are used as approximate models governing weakly nonlinear long waves in fluids, where the first-order nonlinear and dispersive terms are retained and in balance. The retained second-order terms can result in the extended fifth-order KdV equation. Through the Darboux transformation (DT), multi-soliton solutions for the extended fifth-order KdV equation with coefficient constraints are constructed. Soliton propagation properties and interactions are studied: except for the velocity, the amplitude and width of the soliton are not influenced by the coefficient of the original equation; the amplitude, velocity, and wave shape of each soltion remain unchanged after the interaction. By virtue of the generalised DT and Taylor expansion of the solutions for the corresponding Lax pair, the first- and second-order rational solutions of the equation are obtained.
Under investigation in this article is a (2+1)-dimensional generalised variable-coefficient shallow water wave equation, which describes the interaction of the Riemann wave propagating along the y axis with a long-wave propagating along the x axis in a fluid, where x and y are the scaled space coordinates. Bilinear forms, Bäcklund transformation, Lax pair, and infinitely many conservation law are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota method. Propagation and interaction of the solitons are illustrated graphically: (i) variable coefficients affect the shape of the multi-soliton interaction in the scaled space and time coordinates. (ii) Positions of the solitons depend on the sign of wave numbers after each interaction. (iii) Interaction of the solitons is elastic, i.e. the amplitude, velocity, and shape of each soliton remain invariant after each interaction except for a phase shift.
The nonlinear Schrödinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration.Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i. e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.
The Boiti–Leon–Manna–Pempinelli (BLMP) equation is seen as a model for the incompressible fluid. In this article, a (3+1)-dimensional BLMP equation is investigated. With the aid of the Bell polynomials, bilinear form of such an equation is obtained. By virtue of the bilinear form, two kinds of soliton solutions with different nonlinear dispersion relations and another kind of analytic solutions are derived. Lax pairs and Bäcklund transformations are also constructed. Soliton propagation and interaction are analysed: (i) solitions with different nonlinear dispersion relations have different velocities and backgrounds; (ii) for another kind of analytic solutions with different nonlinear dispersion relations, the periodic property is displayed.
In this paper, a generalized variable-coefficient Calogero-Bogoyavlenskii-Schiff equation is investigated. Based on the Bell polynomials and an auxiliary variable, bilinear forms of such an equation are obtained. One-, two-, and three-soliton solutions are given through the Hirota method and symbolic computation. N-soliton solutions are also constructed. Multi-soliton interaction and propagation are investigated and illustrated: (i) properties of the multi-soliton interaction on different planes in space depend on the forms of the only variable coefficient; (ii) positions of the solitons change when the wave numbers have the reverse signs.
Thermal choke is commonly employed in a fixed geometry RBCC combustor to eliminate the need for physically variable exit geometry. This paper proposed detailed numerical studies based on a two-dimensional integration model to characterize thermal choke behaviors driven by various embedded rocket operations in an RBCC engine at Mach 4 in ramjet mode. The influences of different embedded rocket operations as well as the corresponding secondary fuel injection adjustment on thermal choke generation process, the related thermal throat feature, and the engine performance are analyzed. Operations of embedded rocket bring significant effects on the thermal choke behaviors: (1) the thermal throat feature becomes much more irregular influenced by the rocket plume; (2) the occupancy range in the combustor is significantly lengthened; (3) the asynchrony of the flow in different regions accelerating to sonic speed becomes much more significant; (4) as the rocket throttling ratio decreases, the thermal choke position constantly moves upstream integrally, and the heated flow in the top region that is directly affected by the rocket plume reaches sonic speed more rapidly. Finally, we can conclude that appropriate secondary fuel injection adjustment can provide a higher integration thrust for the RBCC engine with the embedded rocket operating, while the thermal choke is stably controlled, and the increased heat release and combustion pressure are well balanced by the variations of pre-combustion shocks in the inlet isolator.