Growth of the degrees of polynomial bases and approximation of trigonometric projectors

The dependence of the growth rate of MOCVD-grown GaAs and AlAs on the growth temperature and the V/III ratio was investigated. It was found that (1) the growth rate suddenly began to decrease above a critical temperature Tc, (2) the uniformity in the layer thickness deteriorated above Tc, and (3) the growth rate of GaAs began to depend on the V/III ratio above Tc while that of AlAs did not. A new growth mechanism including Ga atoms and Ga-complexes as the active species contributing to the growth is proposed, and it is shown that the most plausible Ga-complex consists of [GaAs]n molecules.

https://iopscience.iop.org/article/10.1143/JJAP.23.709/pdf

Mechanism of MOCVD Growth for GaAs and AlAs

Growth of degrees of polynomial bases

We obtain conditions for the convergence in the spaces L
 p
 [0, 1], 1 ≤ p < ∞, of biorthogonal series of the form $$
f = \sum\limits_{n = 0}^\infty {(f,\psi _n )\phi _n } 
$$
 in the system {ϕ
 n
 }
 n≥0 of contractions and translations of a function ϕ. The proposed conditions are stated with regard to the fact that the functions belong to the space $$
\mathfrak{L}^p 
$$
 of absolutely bundleconvergent Fourier-Haar series with norm $$
\left\| f \right\|_p^ * = \left| {f,\chi _0 } \right| + \sum\limits_{k = 0}^\infty {2^{k({1 \mathord{\left/
 {\vphantom {1 2}} \right.
 \kern-\nulldelimiterspace} 2} - {1 \mathord{\left/
 {\vphantom {1 p}} \right.
 \kern-\nulldelimiterspace} p})} } \left( {\sum\limits_{n = 2^k }^{2^{k + 1} - 1} {\left| {f,\chi _n } \right|^p } } \right)^{{1 \mathord{\left/
 {\vphantom {1 p}} \right.
 \kern-\nulldelimiterspace} p}} ,
$$
 where (f,χ
 n
 ), n = 0, 1, ..., are the Fourier coefficients of a function f ∊ L
 p
 [0, 1] in the Haar system {χ
 n
 }
 n≥0. In particular, we present conditions for the system {ϕ
 n
 }
 n≥0 of contractions and translations of a function ϕ to be a basis for the spaces L
 p
 [0, 1] and $$
\mathfrak{L}^p 
$$
 .

Convergence of biorthogonal series in the system of contractions and translations of functions in the spaces L p [0, 1]

On caracterise deux familles de bases deC[0,1] et l'on etudie les formules de quadrature associees On montre en particulier que les formules de quadrature de Romberg proviennent d'une suite de bases engendrees par des polynomes

We characterize two families of bases ofC[0,1] and we study the associated quadrature formulae In particular, we prove that the Romberg quadrature formulae come from a sequence of bases generated by polynomials

Bases de type schauder deC[0,1] et formules de quadrature associées

In this paper, new bases for the space of continuous functions are constructed, similar to the Schauder basis but having better differentiability properties. The bases constructed are applied to the problem of the order of growth of the degrees of a polynomial basis of the space . It is proved that for any nondecreasing sequence of natural numbers satisfying the condition it is possible to construct a polynomial basis with order of growth , .Bibliography: 16 items.

Z A Čanturija

Papers

Bases of the Space of Continuous Functions