块k-循环矩阵的Moore-Penrose逆和带W权的Drazin逆

文章定义了一种新的块k-循环矩阵,给出块k-循环矩阵被对角化的一种表示形式,利用Fourier变换和块k-循环矩阵的对角化形式,进一步研究了块k-循环矩阵的Moore-Penrose逆及带W权的Drazin逆;与此同时,还给出了块k-循环矩阵的Moore-Penrose逆及带W权的Drazin逆的计算公式.     

求解首尾差循环矩阵逆与广义逆的快速算法

提出首尾差循环矩阵的概念,利用多项式矩阵的初等变换理论给出了首尾差循环矩阵求逆阵及广义逆的一种快速算法。     

循环矩阵和分块循环矩阵的逆矩阵的简便求法

讨论了循环矩阵和分块循环矩阵的逆矩阵,给出了用初等变换求循环矩阵和分块循环矩阵的逆矩阵的简便方法.     

首尾和循环矩阵求逆的一种算法

利用多项式矩阵理论,对首尾和循环矩阵给出了一种算法,用来计算它的逆矩阵或群逆.     

特殊二元对称循环矩阵的逆矩阵

研究了二元对称循环矩阵的逆,并在已有结论的基础上进一步推导且给出了另一类二元对称循环矩阵逆矩阵的表达形式.     

特殊循环矩阵的逆矩阵

给出了一类特殊循环矩阵的逆矩阵的公式解.     

循环逆M-矩阵的性质

从逆M-矩阵A具有幂不变的零位模式、Ckn有向图的定义和基本性质出发,获得了循环逆M-矩阵的若干性质.     

对称循环矩阵的逆矩阵

介绍了求对称循环矩阵逆矩阵的简便方法,并用这种方法给出几类特殊对称循环矩阵的求逆公式。     

反循环矩阵的群逆

文［ｌ］给出了循环矩阵非奇异的充分必要条件．本文给出了反循环矩阵非奇异的充分必要条件和逆阵表达式．同时．对奇异反循环矩阵给出了奇异｛ｌ｝一逆，Ｍｏｏｒｅ－ｐｅｎｒｏｓｅ广义逆及群逆表达式．     

用合同变换求循环矩阵的逆及其行列式的值

对于循环矩阵的逆及循环行列式的计算,虽有不少讨论,但方法均显繁琐.本文利用合同变换给出了计算这类矩阵之逆及行列式值的简捷方法.     

块结构r-循环矩阵的性质及其算法研究

提出了一种新的块循环矩阵,称之为块首尾差r-循环矩阵(简记为bFLDCM_r)。首先,验证了其线性运算结果和矩阵乘积仍是bFLDCM_r;其次,给出了bFLDCM_r的判别法和非奇异性判定的充要条件,并讨论了bFLDCM_r的对角化;最后,利用Sherman-Morrison-Woodbury公式,给出了三对角块r-循环线性系统求解的直接算法。     

块为K4的cp-图的距离矩阵的行列式和逆

基于某些特殊图矩阵的求逆结果提出了一类新的图（块为K₄的cp-图）的逆矩阵求解问题,并将其与完全图求逆矩阵作对比,得出了适宜的求解方法,进而得出它的行列式与逆矩阵,均是与图中块数b相关的函数。通过初等行列式变换,求得距离矩阵的特征值和对应重数。     

Convergence in the<Emphasis Type="Italic">r</Emphasis>-th mean and the Marcinkiewicz type weak law of large numbers for weighted sums of<Emphasis Type="Italic">L</Emphasis><Subscript>q</Subscript>-mixingale arrays

L _r convergence and convergence in probability for weighted sums ofL _q-mixingale arrays have been discussed and the Marcinkiewicz type weak law of large numbers forL _q-mixingale arrays has been obtained. Foundation item: Supported by the National Natural Science Foundation of China (10071058) Biography: Gan Shi-xin (1939-), male, Professor, research direction; martingale theory, probability limiting theory and Banach space geometry theory.     

对偶L_q变换法则

在已有结果的基础上对对偶L_q Brunn-Minkowski理论做了一些推广,主要讨论了对偶L_q Brunn-Minkowski型不等式并得到部分结果.给出统一的处理对偶L_q Brunn-Minkowski型不等式的方法,称此方法为对偶L_q变换法则,通过运用此法则给出了关于对偶混合体积著名的对偶L_q Brunn-Minkowski型不等式的简化证明.     

Secular variations in geomagnetic Field caused by the fluctuations in the fluid flow in the outer-core

The theoretical spatial power spectrum of a dipole located at ( r0, θ60, φ0) can be fitted by a straight line in logarithmic scale when n is larger than 2. Based on the spherical harmonic coefficients of geomagnetic field during 1900-1995, the depth( r0) of source-layer of every 5a is calculated. The results show that r0 decreased from 1900 to 1960; abruptly changed from 1945 to 1950 related to some kind of disturbance; decreased again from 1960 to 1975; increased from 1975 to 1985; and kept stable after 1985. Then the mean energy density (MED) of each year is induced to its corresponding r0. We find that MED of dipole field kept nearly unchanged from 1900 to 1960. While, MED of non-dipole field increased. The change of r0 coinciding with the geomagnetic secular variation, impulse and length-of-day happened around 1970, suggesting that the change of r0 may be related to the impulse. The variation in the fluid flow in the outer-core caused by the core-mantle coupling is a plausible candidate in explaining the changes in geomagnetic Jerk, length-of-day, and r0.     

完全图Kn的{P5,C5}分解

图分解问题已在很多邻域中得到了广泛的应用。用P₅表示5个顶点的路，C₅表示5个顶点的圈，本研究讨论了完全图K_n分解成5个顶点的路P₅和圈C₅的存在性，给出完全图K_n存在{P₅,C₅}-强制分解的充分必要条件是n≥7(n≠8)，以及完全图K_n存在{P₅,C₅}-分解的充分必要条件是n≥5(n≠6)。     

分裂四元数矩阵方程AX+XB=C的反Hermite解

针对分裂四元数矩阵A,B和C,研究矩阵方程AX+XB=C的反Hermite解存在的充分必要条件以及有解时的通解表达式。本文利用Kronecker积,矩阵列拉直算子以及Moore-Penrose广义逆和分裂四元数矩阵的复表示。     

Chemical states of the atoms in magnetic multilayers Ta/NiO x /Ni81Fe19/Ta and Co/AlO x /Co

Ta/NiO _x /Ni₈₁Fe₁₉/Ta and Co/AlO _x /Co multilayers were prepared by rf reactive and dc magnetron sputtering. The exchange coupling field (H _ex) and the coercivity (H _c) of NiO _x /Ni₈₁Fe₁₉ as a function of the ratio of Ar to O₂ during the deposition process were studied. The composition and chemical states at the interface region of NiO _x /NiFe were also investigated using the X-ray photoelectron spectroscopy (XPS) and peak decomposition technique. The results show that when the ratio of Ar to O₂ is equal to 7 and the argon sputtering pressure is 0.57 Pa, the x value is approximately 1 and the valence of nickel is +2. At this point, NiO _x is antiferromagnetic NiO and the corresponding H_ex is the largest. As the ratio of Ar/O₂ deviates from 7, the H _ex will decrease due to the presence of magnetic impurities such as Ni⁺³ or metallic Ni at the interface region of NiO _x /NiFe, while the H _c will increase due to the metallic Ni. Al layers in Co/AlO _x /Co multilayers were also studied by angle-resolved XPS. Our finding is that the bottom Co could be completely covered by depositing an Al layer about 1.8 nm. The thickness of AlO _x was 1.2 nm.     

小球藻(Chlorella vulgaris)抗铵品系的紫外诱变选育

【目的】获得耐受高铵浓度的优良养殖小球藻(Chlorella vulgaris)品系,可以有效防止其在养殖过程中被轮虫,纤毛虫等污染生物吞食。【方法】首先对小球藻进行紫外线诱变,然后用高浓度NH_4HCO_3作为筛选压力对其进行筛选。【结果】筛选到具有生长优势的小球藻突变株B4和C6,培养12d,在NH_4HCO_3浓度为800mg/L、1 000mg/L、1 200mg/L条件下,B4和C6的生物量比出发藻株分别提高41.18%和9.54%,32.64%和29.41%,37.74%和22.85%;对比出发藻株,B4和C6的最大光能转化效率有显著提高。【结论】突变株B4和C6在高铵培养条件下更能显示生长优势,且它们的生长优势可能来自光合效率的提高。     

基于谣言攻击的产品需求波动CISRaRd模型研究

与产品相关的谣言影响个体对于产品的判断及购买欲望,进而波及整个供应链中产品的市场需求.考虑个体的情绪和个体对谣言的判断,将经典谣言传播模型中的免疫者R细分成为蒙蔽者R_a和清醒者R_d,两种状态的个体都知道但不传播谣言,不同的是R_a受谣言蒙蔽相信谣言不购买产品,R_d作为清醒者不相信谣言,且继续购买产品.基于系统动力学构建CISR_aR_d谣言传播模型,对模型进行稳定性证明,探讨谣言攻击对产品需求的遏制情况,并在此基础上进行了数值模拟.研究表明,与产品相关的谣言严重制约产品的市场需求,商家在应对谣言攻击时所作出的正面宣传对于产品需求的恢复有其积极意义.