Invariability of Trivial Extensions of Tilted Algebras Under Stable Equivalences

As a sequel to [8], we investigate here the behaviour of thetrivial extensions of tilted algebras under stable equivalence.It will be shown that if a finite-dimensional symmetric algebra is stably equivalent to the trivial extension of a tilted algebraB, then is the trivial extension of some tilted algebra A whichhas the same type as B.     

Luikov equations applicable to sublimation-drying

Present paper presents a derivation of Luikov equations applicable to sublimation-drying. The physical situation and transfer mechanism are elucidated clearly. The coefficients appearing in Luikov equations are given in a more explicit way. Some formulation mistakes in recent publications are indicated.

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Anwendung der Luikov-Gleichungen auf die Sublimationstrocknung

Zusammenfassung Die Untersuchung bezieht sich auf eine Ableitung der Luikov-Gleichungen, mittels deren sich der Vorgang der Sublimationstrocknung analysieren läßt. Physikalische Anfangssituation und Austauschmechanismen werden klar herausgestellt und die in den Luikov-Gleichungen auftretenden Koeffizienten in expliziter Weise angegeben. Ferner erfolgt Hinweis auf Formulierungsfehler in jüngeren Veröffentlichungen.

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Nomenclature C M _v/V _f, concentration of vapor, kg/m³ - c _pv specific heat of vapor at constant pressure, J/kg K - c _pw specific heat of adsorbed water at constant pressure, J/kg K - c _s specific heat of solid skeleton, J/kg K - C _s M _s/V _f, concentration of solid skeleton, kg/m³ - C _w M _w/V _f, concentration of adsorbed water, kg/m³ - f V _w/V _f, volumetric fraction of adsorbed water - j _F mass flux of vapor by diffusion (Fick) transfer, kg/m² s - j _D mass flux of vapor by filtration (Darcy) transfer, kg/m² s - j _v total mass flux of vapor, kg/m² s - k permeability, m² - M _s mass of solid skeleton, kg - M _v mass of vapor in pores, kg - M _w mass of adsorbed water, kg - P pressure, Pa - q heat flux, W/m² - R gas constant, J/kg K - T temperature, K - V _f volume of the framework of porous medium, m³ - V _v volume of vapor in porous medium, m³ - V _w volume of the absorbed water, m³ Greek symbols /(c _p), effective thermal diffusivity, m²/s - _m effective vapor diffusivity in porous medium, m²/s - _p R T /, Luikov pressure diffusivity, m²/s - +f, porosity of the porous medium - effective thermal conductivity of porous body, W/m K - dynamic viscosity of vapor, kg/m s - kinematic viscosity, m²/s - Ck/=k/, Luikov filtration motion coefficient, s - V _v/V _f, volumetric fraction of vapor - density of absorbed water, kg/m³ - (c _p) M _v c _pv+M _s c _s+M _w c _pw /V _f=Cc _pv+C _s c _s+fc _pw, effective product of density and specific heat of humid porous body, J/m³K     

Mechanism transition of self-pumped phase conjugation in KTa1 −xNbxO3:Fe crystals

Mechanism transitions of Self-Pumped Phase Conjugation (SPPC) with wavelength and doping concentration are observed in KTN:Fe (KTa_{1 –x} Nb _x O₃:Fe with _x = 0.48) crystals. The SPPC mechanism in KTN: Fe (0.4 wt. %) crystal transforms from Stimulated Photorefractive Backscattering and Four-Wave Mixing (SPB-FWM) to cat (or total internal reflection) as the wavelength increases from 514.5 nm to 620 nm. SPPC at 514.5 nm is formed with the cat mechanism in a 0.2 wt. % doped KTN:Fe crystal, while with the SPB-FWM mechanism in a 0.4 wt. % doped one. These mechanism transitions are discussed with respect to the dependence of the backscattering gain coefficient of the crystals on wavelength and doping concentration.