An adaptive parameter approach for an approximate solution of optimal control problems

In this paper, we consider a class of nonlinear optimal control problems (Bolza-problems) with constraints of the control vector, initial and boundary conditions of the state vectors. The time interval is fixed. Our approach to parametrize both the state functions and the control functions is described by general piecewise polynomials with unknown coefficients (parameters), where a fixed partition of the time interval is used. Here each of these functions in a suitable way individually will be approximated by such polynomials. The optimal control problem thus is reduced to a mathematical programming problem for these parameters. The existence of an optimal solution is assumed. Convergence properties of this method are not considered in this paper.     

Existence of time periodic solutions for the 3-D viscous primitive equations of large-scale dry atmosphere

In this paper, we consider the existence of time periodic solutions of the 3-D viscous primitive equations of large-scale dry atmosphere. We used the Galerkin method. Firstly, by Leray-Schauder fixed point theorem, we prove the existence of approximate solutions of the primitive equations, then we show the convergence of the approximate solutions, and we also get the uniqueness to the primitive equations.     

Primitive complete normal bases: Existence in certain 2-power extensions and lower bounds

The present paper is a continuation of the author’s work (Hachenberger (2001) [3]) on primitivity and complete normality. For certain 2-power extensions E over a Galois field F_q, we are going to establish the existence of a primitive element which simultaneously generates a normal basis over every intermediate field of E/F_q. The main result is as follows: Letq≡3mod4and letm(q)≥3be the largest integer such that2^m(q)dividesq²−1; ifE=F_q^2l, wherel≥m(q)+3, then there exists a primitive element inEthat is completely normal overF_q.Our method not only shows existence but also gives a fairly large lower bound on the number of primitive completely normal elements. In the above case this number is at least 4⋅(q−1)^2l−2. We are further going to discuss lower bounds on the number of such elements in r-power extensions, where r=2 and q≡1mod4, or where r is an odd prime, or where r is equal to the characteristic of the underlying field.     

On Korn’s Inequality

Two models based on the hydrostatic primitive equations are proposed. The first model is the primitive equations with partial viscosity only, and is oriented towards large-scale wave structures in the ocean and atmosphere. The second model is the viscous primitive equations with spectral eddy viscosity, and is oriented towards turbulent geophysical flows. For both models, the existence and uniqueness of global strong solutions are established. For the second model, the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established.     

On the global well-posedness of the 3D viscous primitive equations

Here we consider the global well-posedness of the 3D viscous primitive equations of the large-scale ocean. Inspired by the methods in Cao etc\cite{CT3} and Guo etc\cite{GH2}, we prove the global well-posedness and the long-time dynamics for the primitive equations.     

On the density of primitive sets

Classical results by Behrend, Erdös, Pillai, Szemerédi, the authors, and others are improved and extended to other concepts of densities in two directions, based on smooth and multiplicative weightings.     

POINTED REPRESENTATIONS OFINFINITE DIMENSIONAL LIE ALGEBRAS

ＰＯＩＮＴＥＤＲＥＰＲＥＳＥＮＴＡＴＩＯＮＳＯＦＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＬＩＥＡＬＧＥＢＲＡＳ￥ＸＵＸＩＡＮＧＡｂｓｔｒａｃｔ：ＡｃｏｎｔｒａｖａｒｉｅｄｂｉｌｉｎｅａｒｐａｉｒｉｎｇＸｏｎｅｖｅｒｙＭ（ρ）×Ｍ（ρθ）ｉｓｄｅｔｅｒｍ...     

关于可约布尔矩阵幂敛指数的一个Brualdi─Ross型上界

本文证明了可约布尔矩阵幂敛指数的一个Ｂｒｕａｌｄｉ－Ｒｏｓｓ型上界，并给出了幂敛指数达到此上界的矩阵的完全刻划．     

对称本原矩阵广义上指数的极矩阵

本文以伴随图的形早了对称本原矩阵和迹零对称本原矩阵的广义上指数的极矩阵。     

Optimisation of flow-injection-hydride generation inductively coupled plasma spectrometric determination of selenium in electrolytic manganese

Flow-injection-hydride generation procedure for Se in electrolytic manganese was optimized by means of the experimental design approach. Instrumental variables like power supplied (P), sample (F) and argon (G) flow rates together with chemical variables like NaBH₄ and HCl concentrations were studied. In case of the chemical variables, it was concluded that sodium tetrahydridoborate concentrations higher than 1.0% extinguished the plasma while HCl concentration should always be higher than 0.6 mol dm⁻³. The analysis of effects suggested that all the instrumental variables are significant factors, and the optimum conditions were P = 1550 W, F = 4.75 mL min⁻¹ and G = 0.6 mL min⁻¹. The influence of Mn was specially studied and it was concluded that the interferences were negligible if Mn is below 2.0 g L⁻¹. In the same sense, the interferences of antimony(III), arsenic(V) and mercury(II) were also considered negligible. Finally, a detection limit of 0.0005% (w/w) was obtained (a repeatability R.S.D. <2.0% for all Se concentrations tried). Some manganese samples were also spiked with different concentrations of Se(IV) and the results demonstrated to be in good statistical agreement with expected values.