一种求非负不可约三对角矩阵最大特征值的方法

就非负不可约三对角矩阵,给出了一种求最大特征值的方法,关键是求迭代因子g的新方法,且证明了此迭代因子大于文献[2]中的迭代因子(r+3d)/(r+2d),从而减少了迭代次数,节约了运算时间.     

非线性比式和问题的全局优化算法

In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Nume...     

Zur Tiefendosis- und Vernetzungsgradverteilung bei Bestrahlung von Polymeren mit energiereichen Elektronen

Aus experimentell ermittelten Tiefendosisverteilungen von energiereichen Elektronen wurde eine Formel zur mathematischen Beschreibung des Tiefendosisverlaufs im Energiebereich 0,5–3 MeV entwickelt, die als Grundlage zur Berechung von Dosis- und Vernetzungsgradverteilungen im bestrahlten Material dienen kann.

Als Beispiel werden einige Verteilungen diskutiert, die sich bei Mehrseitenbestrahlung von zylindrischen Absorbern mit energiereichen Elektronen ergeben.     

Self-pure-generators over Dedekind domains

We prove that all pure submodules of a finite rank torsion-free module A over a Dedekind domain are A-generated (i.e. A is a self-pure-generator) if and only if A has a rank 1 direct summand B such that $\mathbf{type}(B)$ is the inner type of A. This result is applied to describe the direct products of torsion-free groups of finite rank which are self-pure-generators.     

An Ore-type condition for large k-factor and disjoint perfect matchings

Win conjectured that a graph $G$ on $n$ vertices contains $k$ disjoint perfect matchings, if the degree sum of any two nonadjacent vertices is at least $n+k-2$, where $n$ is even and $n\ge k+2$. In this paper, we prove that Win's conjecture is true for $k\ge n∕2$, where $n$ is sufficiently large. To show this result, we prove a theorem on $k$-factor in a graph under some Ore-type condition. Our main tools include Tutte's $k$-factor theorem, the Karush-Kuhn-Tucker theorem on convex optimization and the solution to the long-standing 1-factor decomposition conjecture.     

The spectrum for self-converse large set of pure Mendelsohn triple systems

An $LPMTS(v,\lambda )$ is a collection of $\frac{v-2}{\lambda }$ disjoint pure Mendelsohn triple system $PMTS(v,\lambda )s$ on the same set of v elements. An $LPMT{S}^{⁎}(v)$ is a special $LPMTS(v,1)$ which contains exactly $\frac{v-2}{2}$ converse pairs of $PMTS(v)s$. In this paper, we mainly discuss the existence of an $LPMT{S}^{⁎}(v)$ for $v\equiv 6,10\mathrm{mod 12}$ and get the following conclusions: (1) there exists an $LPMT{S}^{⁎}(v)$ if and only if $v\equiv 0,4\mathrm{mod 6},v\ge 4$ and $v\ne 6$. (2) There exists an $LPMTS(v,\lambda )$ with index $\lambda \equiv 2,4\mathrm{mod 6}$ if and only if $v\equiv 0,4\mathrm{mod 6},v\ge 2\lambda +2,v\equiv 2\mathrm{mod}\mathit{\lambda }$.     

Constructions of several classes of linear codes with a few weights

Recently, linear codes with a few weights have been constructed and extensively studied due to their applications in secret sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, we construct several classes of linear codes with a few weights over ${\mathbb{F}}_p$, where $p$ is an odd prime. The weight distributions of these constructed codes are also settled by applications of the theory of quadratic forms and Gauss sums over finite fields. Some of the linear codes obtained are optimal or almost optimal. The parameters of these linear codes are new in most cases. Moreover, two classes of MDS codes are obtained.     

Evaluation of important fatty acid ratios in poultry feed lipids by ATR FTIR spectroscopy

A rapid, simple and reproducible single bounce attenuated total reflectance (SB-ATR) Fourier transform infrared (FTIR) spectroscopic method was developed for determination of the n − 6, n − 3 and ratio of n − 6:n − 3 polyunsaturated fatty acids (PUFAs) in poultry feed lipids using partial least squares (PLS) regression. Data for n − 6, n − 3 and ratio of n − 6:n − 3 was acquired by gas chromatography (GC) and used as a standard values for FTIR calibration. The best regression results were achieved using first derivatives of the 1475–650 cm⁻¹ spectral region for n − 6, n − 3 and ratio of n − 6:n − 3 with high regression coefficients (R²) of 0.999, 0.994 and 0.998, respectively and low RMSEP values of 1, 0.06 and 0.83, respectively. The results of the present study revealed that FTIR could be used for rapid and accurate determination of n − 6, n − 3 and ratio of n − 6:n − 3 PUFAs present in poultry feed lipids.     

Six ways to look at linear interpolation

Linear interpolation has been explained from different perspectives that are likely to be easily understood by students. Some methods seem to be more interesting in some situations. Apart from its suitability in classrooms, it has also a mnemonic value often expected by many readers.