查询词典 dimensional analysis

In this paper, the existence of isometric mapping between the manifold in the high-dimensional data space and the parameter space is proved. By distinguishing the intrinsic dimensionality of high-dimensional data space from the manifold dimensionality, and it is proved that the intrinsic dimensionality is the upper bound of the manifold dimensionality in the high-dimensional space in which there is a toroidal manifold.

首先给出了高维数据的连续流形和低维参数空间之间的等距映射存在性证明，然后区分了嵌入空间维数、高维数据空间的固有维数和流形维数，并证明存在环状流形高维数据空间的参数空间维数小于嵌入空间维数。

In this paper, we have studied the dimensional effects, electronic state, the configurations of charge density and spin density for quasi-one-dimensional organic ferromagnets. First, considering interchain interaction, the itineracy of electrons, the electron-electron correlation, electron-phonon interaction and spin correlation in low dimensional system, we proposed an interchain coupling theoretical model for conjugated system and non-conjugated system of organic polymer ferromagnets, respectively. Based on the theoretical model, we studied the electronic property, spin structure, the configuration of dimerization and the stability of the ferromagnetic state with a self-consistent iterative method.

首先我们在考虑准一维有机铁磁体的链间相互作用、电子的巡游性、强的电子-电子关联、电子-声子耦合、自旋关联等因素的基础上，分别对两种类型的有机高聚物铁磁体各自提出一个包含链间耦合的理论模型，用自洽迭代的数值计算方法对其电子性质、自旋结构、二聚化特征及铁磁态的稳定性进行了研究。

By decomposing two-dimensional relation into separate one-dimensional relations, then applying one dimensional temporal interval logical concepts in constructing twodimensional interval logic, definitions of relations between twodimensional objects are given.

通过将二维空间关系分解成一维关系，然后借用一维时态区间逻辑关系的思想构建二维区间逻辑，给出了二维对象关系的定义。

Complex V shows a one-dimensional 'Z' chain which are linked into two-dimensional lamellar structures by weak π-π stackings. Complex VI shows one-dimensional chiral helical chains which are linked into molecular zipper. Both complexes show strong blue photoluminescent under R.T. Complexes VII and VIII are monometallic complexes of Fe.

由对苯二甲酸形成的化合物Ⅴ是由一维的'Z'型链组成的，链链之间通过π-π弱相互作用形成了二维结构；而由间苯二甲酸形成的化合物Ⅵ是由一维的手性螺旋链组成的，链链之间通过π-π相互作用形成拉链状的二维结构，Ⅴ和Ⅵ在室温下具有强荧光。

Early diagenesis has broad and bright prospects not only in theory but also in application, and three future trends are predicted. First, the area of early diagenesis study will be enlarged widely to lake, delta, soil. Then, the stable or nonstable one-dimensional, two-dimensional or three-dimensional multi-layer early diagenesis models will be established, and the methods and theoretical achievements of early diagenesis will be widely applied in environmental sedimentology to supervise and treat environment pollution.

早期成岩作用研究具有广阔的发展前景，未来可能在以下3方面快速取得突破：研究区域将进一步扩大，湖泊、三角洲及土壤中的相应研究将得以加强；多层的稳态或非稳态的一维、二维或三维的早期成岩数学模型将得以建立；其研究方法和理论成果将被广泛应用于环境沉积学及环境监测和治理等领域中。

Regarding (6) type, when tradition Time variable t is two spatial vectors (+ psi 1i) and (- psi 2j) Crossed products v also is not 0, it (x1, x2, x3) differs 90 compared to on speed with the three-dimensional space in the space by the pure imaginary number attribute, I=e^I pi, therefore it Number space has in the physical property with the dot product constitution the difference, because Crossed products psi 1i (X psi 2j extremely small visible it is equal to zero under the conventional speed, but is very big in the object movement speed time, Crossed products psi 1i (X psi 2j in the physical quantity and for the quantum mechanics in may not to the easy quantity, its space and the conventional space is different, the performance is intrinsic or the interior space If the definition vector (+ psi 1i) and (- psi 2j) the dot product constitutes the three-dimensional space (x1, x2, x3) is exterior space, but the three-dimensional space which (+ psi 1i) and (- psi 2j) Crossed products constitutes by the vector is the internal space, contrasts its component

对于⑥式，传统时间量t为两个空间矢量(+ψ1i)与(-ψ2j)的叉积比上速度v且不为0，其与三维空间(x1，x2，x3)在空间上相差90度以纯虚数表征，I=e^Iπ，故其与点积构成的实空间有物理性质上的不同，因为在常规速率下叉积ψ1i(Xψ2j非常小可视其等于零，而在物体运动速率很大时，叉积ψ1i(Xψ2j之中物理量与则为量子力学中的不可对易量，其空间与常规空间不同，表现为一个内在或内部性空间。若定义矢量(+ψ1i)与(-ψ2j)点积所构成的三维空间(x1，x2，x3)为外部空间，而由矢量(+ψ1i)与(-ψ2j)叉积而构成的三维空间为内部空间，对比其分量

A classical one dimensional sandpile model was researched in this paper, the model can not explain the self-organized criticality phenomena which appearing in one dimensional rice pile, so we did some mend on this model and make it including avalanche probability, with the new model we explained the SOC phenomena appearing in one dimensional grain pile.

本文考查了一个经典的一维BTW沙堆模型，发现它不能描述实验中已观察到的一维米粒堆的自组织临界现象，因此本文对经典一维BTW模型进行了改进，建立了一个含崩塌概率的一维沙堆模型，并用该模型解释一维米粒堆中出现的自组织临界现象。

SOC phenomena does not appears in classical one dimensional sandpile model, but for two or three dimensional model, it does. However, some people did some experiments with rice and find the SOC existing in one dimensional rice pile, it is not fit with the classical sandpile model. Nobody explained this phenomena.

在经典的一维沙堆模型中，沙堆崩塌时并没有出现自组织临界现象，只有在二维以上的沙堆模型中才出现自组织临界现象，然而，后来有人用米粒做实验，发现一维米粒堆中存在自组织临界现象，这与经典的一维沙堆模型相违背，但是却没能对这种现象作出一个较好的解释。

Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin).

大 约在一百年以前，庞加莱已经知道，二维球面本质上可由单连通性来刻画，他提出三维球面（四维空间中与原点有单位距离的点的全体）的对应问题。

In recovering a low dimensional parametrization of data lying on a low dimensional submanifold in high dimensional space, we need to understand and grasp the structure of image of the Laplacian Eigenmap.

在揭示建立在高维数空间中的一个低维子流形中的一个低维数的确定参数时，我们需要去了解并领会拉普拉斯特征映射的像的构造。

Then the author designs the preliminary questionnaire of adolescent psychosexual health, and forms the ...

本研究用正式的"青春期性心理健康问卷"对成都、重庆、深圳、上海、**五个城市的798名青少年进行的调查研究，并对青少年的性别、年龄阶段、民族等因素进行了分析，考察了青少年性心理健康的特点以及和心理健康之间的相关。

Gorman, Freda, and Pollack report the first successful prevention of maternal sensitization to the Rh factor by the administration of anti-Rho preparation following delivery.

戈尔曼，弗雷达和波拉克报道了第一项在分娩之后，通过Rho免疫球蛋白抗体预防的注射，成功完成母体对Rh因子致敏的预防。