不相容方程

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖，其中‖·‖为Frobenius范数，S分别表示矩阵方程 AXB=D，AXA~T+BYB~T=D，AXB+CYD=E和矩阵方程组=，=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

The theory of incompatible equations and least square are used to build an equation about the pressure of gas and the site of coal, according to the original statistical data of gas pressure .

应用不相容方程组和最小二乘理论，根据已有的瓦斯压力原始统计资料，建立了煤层瓦斯压力和煤层地理位置关系的方程，并进行了相关性分析。

E=mc2 is Wrong - Einstein's Special Relativity Fundamentally Flawed by MStrauss Is Albert Einstein's Special Relativity incompatible with the very equations upon which science's greatest theory is built?

电子=MC2不妥-爱因斯坦狭义相对论mstrauss基本上是错误的，是爱因斯坦的狭义相对论不相容十分方程科学依据的理论是建立最大？

The conventional matrix decomposition methods have been used to find the least-squares solutions of the abovementioned inconsistent matrix equations over given matrix set in many references, and the general expressions of these solutions were obtained. But it is difficult to determine the solution of Problem I by utilizing these expressions due to the fact that the orthogonal invariance of Frobenius norm does no hold for the general nonsingular matrices.

对于求上述不相容矩阵方程在给定矩阵集合上的最小二乘解，很多文献中利用传统的矩阵分解方法得到了其通解表达式，但是利用该表达式很难得到问题Ⅰ的解，这是因为一般的非奇异矩阵并不满足Frobenius范数的正交不变性。

Moreover, Problem I can be transformed equivalently into a problem that finding the minimum norm least-squares solution of a new inconsistent matrix equation.

而问题Ⅰ可等价转化为求一个新的不相容矩阵方程的最小范数最小二乘解的问题。

Kinetic equations of multibody systems with scleronomic constraint s are projected along the feasible and unfeasible directons of the constiaints respectively,and generalized accelerations of the systems are decomposed along the two directons using the bases of constraint matrix and its orthocomplement.

通过约束矩阵及其正交补的两组基，将定常约束多体系统的动力学方程沿与约束相容和不相容的两个方向上投影，并将系统的广义加速度沿这两个方向进行分解，得到描述系统运动的纯微分方程和求约束力的公式，同时提出了违约修正的一种方法。

It also pointed out that thesolution set of the equation is inconsistent.

3首次提出了逻辑方程的概念，给出了逻辑方程的解的存在性定理，并详细分析了逻辑方程解的性质，指出对于一般的逻辑方程而言，其解集合是不相容的。

The solutions of ProblemⅠ,ⅡandⅢare discussed by using the generalized conjugate gradient method. When the equation is consistent, the solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found; When the equation is inconsistent, the least-squares solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are also found successfully. The generalized conjugate gradient method has the following traits:(1) It can judge automatically the information of solutions.

利用广义共轭梯度法，讨论了问题Ⅰ、Ⅱ和Ⅲ解的情况：当方程相容时，研究了方程的一般解、对称解、中心对称解、自反矩阵解、双对称解、对称次反对称解及其最佳逼近等问题；当方程不相容时，研究了方程的最小二乘一般解、最小二乘对称解、最小二乘中心对称解、最小二乘自反矩阵解、最小二乘双对称解、最小二乘对称次反对称解及其最佳逼近等问题。

Week 15 Wave function, Schrodingger equation, infinite deep potential well in one dimension. Spin of electron, forth quantum number, description of hydrogen atom with quantum mechanics, Pauli exclusion principle, shell distribution of electrons out of atomic nucleus.

第15周波函数；薛定谔方程；一维无限深势阱；氢原子的定态薛定谔方程和求解的主要步骤；解的物理意义；电子的自旋-第四个量子数；氢原子的量子力学描述；泡利不相容原理；元素原子核外电子的壳层分布。

First, we deduce a formula for vacuum polarization pressure as f ＝ G m M （ r ∕ r ＋ v ∕ c ）∕ r 2 , based on the isotropy of distribution of neutrinos ν0 in the lowest energy state in the physical vacuum, requested by the Pauli exclusion principle. Then, we deduced the metric equation of the general relativity and the equivalence principle according to this formula. Further, we demonstrate that this vacuum polarization pressure is the gravitation in general meaning.

首先从泡利不相容原理要求的在物理真空中最低能态中微子ν0分布的均匀各向同性出发，推导出真空极化压力公式 f ＝ G m M （ r ∕ r ＋ v ∕ c ）∕ r 2 ，然后由此公式推导出广义相对论的度规方程和等效原理，并论证此弱作用力的真空极化压力就是通常意义下的引力。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。