Rigidity Theorems for Einstein–Thorpe Metrics Dedicated to my parents

We will prove that every Einstein–Thorpe metric on T ⁸ must be flat and that on compact oriented hyperbolic manifolds of dimension 8, every Einstein–Thorpe metric is a hyperbolic metric up to rescalings and diffeomorphisms.     

Compressible Navier–Stokes system with hard sphere pressure law and general inflow–outflow boundary conditions

We prove the existence of a weak solution to the compressible Navier–Stokes system with hard sphere possibly non-monotone pressure law involving, in particular, the Carnahan–Starling model [2] largely employed in various physical and industrial applications. We take into account large velocities prescribed at the boundary of a bounded piecewise $C^2$ domain and large densities prescribed at the inflow boundary without any restriction neither on the shape of the inflow/outflow boundaries nor on the shape of the domain.     

Effect of an inhomogeneous interphase zone on the bulk modulus and conductivity of a particulate composite

A model is presented of a particulate composite containing spherical inclusions, each of which are surrounded by a localized region in which the elastic moduli vary smoothly with radius. This region may represent an interphase zone in a composite, or the transition zone around an aggregate particle in concrete, for example. An exact solution is derived for the displacements and stresses around a single inclusion in an infinite matrix, subjected to a far-field hydrostatic compression, and is then used to derive an approximate expression for the effective bulk modulus of a material containing a random dispersion of these inclusions. The analogous conductivity (thermal, electrical, etc.) problem is then discussed, and it is shown that the expression for the normalized effective conductivity corresponds exactly to that for the normalized effective bulk modulus, if the Poisson ratios of both phases are set to zero.     

Noise reduction using three-step gain factor and iterative-directional-median filter

Musical residual noise is a major problem for a speech enhancement system. This noise is very annoying to the human ear and can significantly deteriorate the perception quality of enhanced speech. In this study, we aim at reducing the quantity of musical residual noise by a two-stage speech enhancement approach. In the first stage a preprocessor enhances noisy speech using an algorithm which combines the two-step-decision-directed and the Virag methods. In the second stage the enhanced speech signal is post-processed by an iterative-directional-median filter to significantly reduce the quantity of residual noise, while maintaining the harmonic spectra. Experimental results show that the proposed approach can significantly improve the performance of a speech enhancement system by reducing the quantity of residual noise.     

A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion

In this paper, we consider a path-dependent option in finance under the constant elasticity of variance diffusion. We use a perturbation argument and the probabilistic representation (the Feynman–Kac theorem) of a partial differential equation to obtain a complete asymptotic expansion of the option price in a recursive manner based on the Black–Scholes formula and prove rigorously the existence of the expansion with a convergence error.     

A $$\mathrm {GL}_3$$ GL 3 analog of Selberg’s result on S(t)

The Ramanujan Journal - We are concerned with counting self-conjugate $$(s,s+1,s+2)$$ -core partitions. A Motzkin path of length n is a path from (0, 0) to (n, 0) which stays...     

Quasi-synchronization of delayed chaotic systems with parameters mismatch and stochastic perturbation

This paper studies synchronization behavior of coupled time-delay chaotic systems for the case that parameter mismatch and stochastic perturbation occur in the response system. We establish quasi-synchronization criterion by analyzing stochastic stability of synchronization error system. A numerical example is also presented to show the effectiveness of theoretical results.     

Functional Limit Theorems for d-dimensional FBM in HSlder Norm

In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.