Andreev states in a quasi-one-dimensional superconductor on the surface of a topological insulator

Theoretical and Mathematical Physics - We study bound states in an s-wave superconducting strip on the surface of a topological superconductor with the perpendicular Zeeman field. We prove...     

Collective vibrations in a three-band superconductor

Collective vibrations in a superconductor with three overlapping energy bands on the Fermi surface are investigated. It is shown that for certain relationships between the parameters of the theory there can, in addition to the acoustic branch, be two different branches of exciton type, which arise because of fluctuations of the phases of the order parameters.Institute of Applied Physics, Moldova Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 101–110, April, 1993.     

Nonlinear dynamics of a quasi-one-dimensional helicoidal structure

We analytically describe solitons and spin waves in the helicoidal structure of magnets without an inversion center using the ??dressing?? method in the framework of the sine-Gordon model. Analyzing the nonlinear dynamics of spin waves in the helicoidal-structure background reduces to solving linear integral equations on a Riemann surface generated by the superstructure. We obtain spectral expansions of integrals of motion with the soliton and spin-wave contributions separated.     

Interaction between Griffith cracks in a sandwiched orthotropic layer

A study is made of the interaction between three coplanar Griffith cracks which are located symmetrically in the midplane of an orthotropic layer of finite thickness 2h sandwiched between two identical orthotropic half planes. The Fourier transform technique is used to reduce the elastostatic problem to a set of integral equations which have been solved by using the finite Hilbert transform and Cooke's results. Analytical expressions for the stress intensity factors at the tips of cracks are obtained for large values of h. Numerical results concerning the interaction effects are presented with physical significance. It is shown that interaction effects are either shielding or amplification depending on the location of cracks, spacing of crack-tips, and the thickness of the layer. The stress magnification factors at the crack-tips are also calculated.     

Acceleration of a body in a channel in the quasi-one-dimensional magnetohydrodynamic approximation

Translated from Pryamye i Obratnye Zadachi Matematicheskoi Fiziki, pp. 248–258, 1991.     

刚性线夹杂与弹性圆夹杂的相互作用

本文将刚性线夹杂与弹性圆夹杂的相互作用，归为解一个标准的柯西型奇异积分方程，获得了刚性夹杂端点的应力强度因子及夹杂的界面应力．     

The Optimal Interaction between a Hedge Fund Manager and Investor

ABSTRACT

This study explores hedge funds from the perspective of investors and the motivation behind their investments. We model a typical hedge fund contract between an investor and a manager, which includes the manager’s special reward scheme, i.e., partial ownership, incentives and early closure conditions. We present a continuous stochastic control problem for the manager’s wealth on a hedge fund comprising one risky asset and one riskless bond as a basis to calculate the investors’ wealth. Then we derive partial differential equations (PDEs) for each agent and numerically obtain the unique viscosity solution for these problems. Our model shows that the manager’s incentives are very high and therefore investors are not receiving profit compared to a riskless investment. We investigate a new type of hedge fund contract where the investor has the option to deposit additional money to the fund at half maturity time. Results show that investors’ inflow increases proportionally with the expected rate of return of the risky asset, but even in low rates of return, investors inflow money to keep the fund open. Finally, comparing the contracts with and without the option, we spot that investors are sometimes better off without the option to inflow money, thus creating a negative value of the option.     

Interaction between cardiovascular system and respiration

A set of nonlinear dynamic models for the interactive respiration/cardiovascular mechanism is constructed and analyzed in this work. By employing equivalent electric circuits for heart/blood and lung/air systems, the dynamics of cardiovascular system and respiration cycle are established. In order to verify the validity of the dynamic models, numerical simulations and analysis on heart–lung interactions, including the valvular closure incompetence and pulmonary obstruction, are presented and compared with the empirical reports in literature. The derived dynamics of heart–lung interactions can be realized and examined in the biomechanical and medical engineering fields. In addition, the dynamic models can also be employed for the model-based controller synthesis in medical instrumentations, e.g., the Extracorporeal Membrane Oxygenation (ECMO), to retain the function of blood circulation and/or respiration by artificial intelligence.     

Interaction between data analysis and telecommunications

We consider interaction between data analysis and telecommunications from both sides, examining the contribution of each discipline to the other. The fast changes in telecommunications have some important consequences. First, the importance of statistics in the design of a network is growing, given the evolution of technology towards more digitalization and the resulting changes in dimensioning the network. Second, the technical tools of statistics are deeply modified, and there is concern about how to take this into account—particularly how to take advantage of the new economy of ‘value added services’ which uses the network as a ‘market place’.     

Critical temperature of soliton state stability in quasi-one-dimensional systems

The temperature effect on soliton state formation in quasi-one-dimensional systems is considered in the self-consistent field approximation. The critical temperature above which soliton states are nonstable is shown to exist. The crirical temperature dependence on nonlinearity parameter and system dimension is found. Soliton density at which the critical temperature is maximal is calculated.