猜想

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

But they have no knowledge therein. They follow nothing but conjecture; and conjecture avails nothing against Truth.

他们对于那种称呼，绝无任何知识，他们只凭猜想；而猜想对于真理，确是毫无裨益的。

The proposed model is applied to finding complex eigenpairs and zeros of cmplex polynomials. 5. We study Baldi and Hornik's conjecture on Oja PCA neural algorithm, and give an energy function for one-unit Oja rule.

研究了Baldi和Hornik关于Oja主分量神经网络算法的一个猜想，给出了一个单元的Oja算法的能量函数，从而部分解决了这一猜想。

Secondly, a conjecture about the stability for these systems is proposed based on the sufficient and necessary condition of the isolated transfer function being positive real. When the zeros and poles of the transfer functions lie in the imaginary axis, a known conclusion is derived from the conjecture; while the zeros and poles are on the real axis, a new result is obtained and is proved in this note. Finally, according to the conjecture, an example with poles existing on the complex plane is presented, which is not only interesting but also challenging.

然后， 基于所有孤立部分传递函数都正实的充分必要条件给出了上述系统为稳定的一个猜想，当传递函数的零极点都位于虚轴上时，由这一猜想得到了一个已知的结论；当传递函数的零极点都位于实轴上时，由这一猜想得到了一个新的结论，本文证明该结论是正确的；最后，根据这一猜想，给出了传递函数极点位于复平面的一个例子，它涉及到一类系数矩阵为时变正定矩阵的振动方程的稳定性问题，值得去深入研究。

It is true,……What I guess'd when I loaf'd on the grass,What I guess'd while I lay alone in my bed, And again as I walk'd the beach under the paling stars of themorning.

他说：当我在草地上闲游时所猜想的事，当我独自一人躺在床上所猜想的事，还有我在凌晨愈来愈暗淡的星光下在海滩上散步时所猜想的事，都是真实的事。

The major technique to get the information of structure of those free groups is to sudy the action of automorphisms on them. In this paper we show that every normal automorphism of a nontrivial free product of groups is inner as well. Traub[16] made a purely algebraic conjecture and showed that it implied Poincare"s Conjecture. He also showed that Poincare"s Conjecture implied this algebraic conjecture modulo another topological hypothesis.

在本文中我们给出任意两个非平凡群的自由积的每个正规自同构也是内自同构的；在文献[16]中，Traub给出了一个纯代数的猜想并证明了这个猜想蕴含着着庞加莱猜想的成立，并且作者也证明了在一个拓扑假设的前提下庞加莱猜想也同时蕴涵着猜想1是成立的，后来这个拓扑假设被Waldhausen([7])证明是成立的。

Afterward Waldhausen ([7]) showed that this topological hypothesis was true. Besides, Stallings ([11]) gave another conjecture that was equivalent to Poincare"s Conjecture. Thus we know both conjectures made respec- tively by Traub and Stallings are equivalent to Poincare"s Conjecture.

另外Stallings([11])又提出了另一个代数的猜想并同时证明也证明了这个猜想与庞加莱猜想是等价的，由此可知Traub所给的猜想与Stallings的猜想都与庞加莱猜想是等价的，从而这两个代数的猜想也是等价的。

Second, we think about the Conjecture(Conjecture8.7,Conjecture8.23;[2]Conjec-ture2.3) and prove that some particular ideals have the same graded Betti numbers via shifting operations,that s,.if is a simpcial complex and I is a monomial ideal generated in one degree,we have that...

后一部分的主要结论是：针对J.Herzog提出的猜想([1]猜想8.7，猜想8.23；[2]猜想2.3)，证明了当I_Δ为同一次数生成元生成的稳定理想时，对i，j，有β_=β_。当I_Δ为无平方分量线性理想，特别地当I_Δ是弱稳定理想时，对i，j，有β_=β_=β_。

Second, we think about the Conjecture(Conjecture8.7,Conjecture8.23;[2]Conjec-ture2.3) and prove that some particular ideals have the same graded Betti numbers via shifting operations,thats,.if is a simpcial complex and I is a monomial ideal generated in one degree,we have that ij = ij, for i.j.

后一部分的主要结论是：针对J.Herzog提出的猜想([1]猜想8.7，猜想8.23；[2]猜想2.3)，证明了当I_Δ为同一次数生成元生成的稳定理想时，对i，j，有β_=β_。

S.O.S Jonas Brothers lyrics By Larry Cheng I told you I made dinner plans for you and and me and no one else that don't include your crazy friends well I'm done with awkward situations empty conversations oooh, this is an S.O.

先说翻译：我告诉你我有了晚餐的计划只有你和我不包括你那些疯狂的朋友好了，我已经做好了准备面对这尴尬而空洞的对话 oooh ，这是一个求救信号不要再去猜想这是底线这是真的我将一切给你可现在，我的心脏碎成了两半而我无法找到另一半我就像走在碎玻璃上我相信在流血这将是一个我永远也不会接的电话因此，这个故事将在此完结对于这次失败的交流我放弃了 oooh ，这是一个求救信号不要再去猜想这是底线这是真的我将一切给你可现在，我的心脏碎成了两半而我无法找到另一半我就像走在碎玻璃上我相信在流血这将是一个我永远也不会接的电话当我再次见到你我不能再和你紧紧相拥因为那再也不可能了这只是奢望 oooh ，这是一个求救信号不要再去猜想这是底线这是真的我将一切给你可现在，我的心脏碎成了两半是啊！

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。