We investigate the matrix equation X - AXB = C. For convenience, the matrix equation X - AXB = C is named as Kalman-Yakubovich-conjugate matrix equation. The explicit solution is constructed when the above matrix equation has unique solution. And this solution is stated as a polynomial of coefficient matrices of the matrix equation. Moreover, the explicit solution is also expressed by the symme...

A new spectral closure model of stably stratified turbulence is used to develop a K model suitable for applications to the atmospheric boundary layer. This K model utilizes vertical viscosity and diffusivity obtained from the spectral theory. In the equation, the Coriolis parameter-dependent formulation of the coefficient C1 suggested by Detering and Etling is generalized to include the depende...

Let u be a hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carathéodory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for F , zAF ′ = BF +CF +D and a distributional equation for u, D(Au) = B1u + C1u+H1L, where L is the Lebesgue functional, and the polynomials B1, C1,D1 are define...

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variab...

Abstract The aim of the study was to assess possibility using empirical formulas determine roughness coefficient in gravel-bed streams, bed slopes which range from 0.006 0.047. Another impact taking into account conditions non-uniform flow on application these and develop correlation relationships between water surface slope also friction order estimate n streams. studies were conducted eight m...

We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation (−∆)γ/2, 0 < γ ≤ 1). We show in this paper that if θ ∈ C((0, T ); C1−γ), or θ ∈ Lr((0, T ); Cα) with α = 1−γ+ γ r is a weak solution of the 2D quasi-geostrophic equation, then θ is a classical solution in (0, T ]× R2. This result improves our previous result in [18].

the variety of sprinkler devices available for the center pivot and linear irrigation systems has been increased dramatically in recent years. in the current study, via conducting some indoor experiments, one type of fixed pad spray sprinkler (d3000) and two types of moving pad spray sprinklers (r3000 and s3000) with various configurations (working pressure, nozzle size and type of deflector pa...