Nested Artin strong approximation property

We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.     

Low power capacitively coupled plasma microtorch for simultaneous multielemental determination by atomic emission using microspectrometers

A new, low power capacitively coupled plasma microtorch (30 W, 13.56 MHz, 0.5 L min^?1 Ar) was investigated in conjunction with commercially available microspectrometers for the simultaneous multielemental analysis by atomic emission spectrometry of liquid samples without desolvation. Emission spectrum is simpler than in ICP-AES, the resonance lines are the most intense, so that a microspectrometer with FWHM of at least 1.5 nm is satisfactory for the record. The deviation from the Boltzmann distribution for Fe I has demonstrated the departure from the LTE in plasma. The non-spectral matrix effects of Li, Na, K, Ca and Mg on analytes emission are depressive and depend on matrix volatility, ionization potential of the interferent and analyte excitation energy. The detection limits (μg mL^?1) are in the range 0.003 (Li) and 1.5 (Mn). The use of the standard additions method allowed the simultaneous determination of elements in environmental certified reference materials with overall recovery of 95 ± 10% and relative standard deviation of 1.7–8.2%. Compared to the traditional ICP, the microtorch has a simple construction, runs at low argon flow and can be integrated in a portable system suitable for in-situ simultaneous determination of elements.     

The developing heat transfer and fluid flow in micro-channel heat sink with viscous heating effect

The numerical modeling of the conjugate heat transfer and fluid flow through the micro-heat sink was presented in the paper, considering the viscous dissipation effect. Three different fluids with temperature dependent fluid viscosity are considered: water, dielectric fluid HFE-7600 and isopropanol. The square shape of the cross-section is considered with D _h  = 50 μm with a channel length L = 50 mm. As most of the reported researches dealt with fully developed fluid flow and constant fluid properties in this paper the thermal and hydro-dynamic developing laminar fluid flow is analyzed. Two different heat transfer conditions are considered: heating and cooling at various Br. The influence of the viscous heating on local Nu and Po is analyzed. It was shown that for a given geometry the local Po and Nu numbers are strongly affected by the viscous heating. Moreover the Po number attains the fully developed value as the external heating is equal with the internal viscous heating.     

The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization

We consider the Steklov problem for the linear biharmonic equation. We survey existing results for the positivity preserving property to hold. These are connected with the first Steklov eigenvalue. We address the problem of minimizing this eigenvalue among suitable classes of domains. We prove the existence of an optimal convex domain of fixed measure.     

A monomial cycle basis on Koszul homology modules

We give a class of p-Borel principal ideals of a polynomial algebra over a field K for which the graded Betti numbers do not depend on the characteristic of K and the Koszul homology modules have a monomial cyclic basis.