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Search Results: 1 - 10 of 88040 matches for " Yin Chen "
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On the Putnam-Fuglede theorem
Yin Chen
International Journal of Mathematics and Mathematical Sciences , 2004, DOI: 10.1155/s0161171204311312
Abstract: We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.
Multi-dimensional Hadamard's inequalities
Yin Chen
Tamkang Journal of Mathematics , 2012, DOI: 10.5556/j.tkjm.43.2012.1-10
Abstract: In this paper, Hadamard's inequalities are extended to a convex function on a convex set in $R^2$ or $R^3$. In particular, it is proved that the average of convex function on a ball of radius $r$ is between the average of the function on the circle of radius r and that on the circle of $frac{2r}{3}$
Hadamard's inequality on a triangle and on a polygon
Yin Chen
Tamkang Journal of Mathematics , 2004, DOI: 10.5556/j.tkjm.35.2004.247-254
Abstract: In this paper, some inequalities of Hadamard's type for a convex function of double variable defined on a triangle and on a regular polygon are proved. As a consequence, Hadamard's inequality on a disk is also given.
On Modular Invariants of A Vector and A Covector
Yin Chen
Mathematics , 2012,
Abstract: Let $SL_{2}(F_{q})$ be the special linear group over a finite field $F_{q}$, $V$ be the 2-dimensional natural representation of $SL_{2}(F_{q})$ and $V^{\ast}$ be the dual representation. We denote by $F_{q}[V\oplus V^{\ast}]^{SL_{2}(F_{q})}$ the corresponding invariant ring of a vector and a covector for $SL_{2}(F_{q})$. In this paper, we construct a free module basis over some homogeneous system of parameters of $F_{q}[V\oplus V^{\ast}]^{SL_{2}(F_{q})}$. We calculate the Hilbert series of $F_{q}[V\oplus V^{\ast}]^{SL_{2}(F_{q})}$, and prove that it is a Gorenstein algebra. As an application, we confirm a special case of the recent conjecture of Bonnafe and Kemper in 2011.
Noether's problem for p-groups with three generators
Yin Chen
Mathematics , 2013,
Abstract: Let $p$ be an odd prime and $G$ be a nonabelian group of order $p^{n}$ with the presentation $$<\alpha,\beta,\gamma\mid \alpha^{p^{a}}=\beta^{p^{b}}=\gamma^{p^{c}}=1, [\alpha,\gamma]=1,[\gamma,\beta]=\alpha^{p^{r}},[\alpha,\beta]=\gamma^{p^{e}}>,$$ where $n>a\geq b\geq c\geq 1$. Let $k$ be a field containing a primitive $p^{a}$-th root of unity and $G$ act on the rational function field $k(x_{h}:h\in G)$ by $g\cdot x_{h}=x_{gh}$ for all $g,h\in G$. In this note, we prove that the fixed field $k(G)=k(x_{h}:h\in G)^{G}$ is rational over $k$. As a corollary, we prove that if $k$ contains a primitive $p^{4}$-th root of unity and $G$ is a nonabelian group of order $p^{5}$ generated by three elements, then $k(G)$ is rational over $k$.
Noether's problem for p-groups of order p^{5}
Yin Chen
Mathematics , 2013,
Abstract: Let $k$ be any field, $p>3$ be any prime number and $G$ be a nonabelian $p$-group of order $p^{5}$. Consider the action of $G$ on the rational function field $k(x_{h}:h\in G)$ by $g\cdot x_{h}=x_{gh}$ for all $g,h\in G$. Let $e$ be the exponent of $G$. Noether's problem asks whether the fixed field $k(G)=k(x_{h}:h\in G)^{G}$ is rational (i.e., purely transcendental) over $k$. In this paper, we will prove that if $G$ does not belong to the isoclinic family $\Phi_{10}$ in James's classification \cite{Jam1980} and $k$ contains a primitive $e$th root of unity, then $k(G)$ is rational over $k$. As a corollary, if $k=\textbf{C}$ is the field of complex numbers, then $\textbf{C}(G)$ is rational over $\textbf{C}$ if and only if $G$ is not in the family $\Phi_{10}$. This refines a recent result of Hoshi, Kang and Kunyavskii (\cite{HKK2012}, Theorem 1.12).
A Humanoid Robot Gait Planning and Its Stability Validation  [PDF]
Jian Zeng, Haibo Chen, Yan Yin, Yan Yin
Journal of Computer and Communications (JCC) , 2014, DOI: 10.4236/jcc.2014.211009
Abstract:

Gait planning based on linear inverted pendulum (LIPM) on structured road surface can be quickly generated because of the simple model and definite physical meaning. However, over-simplifi- cation of the model and discontents of zero velocity and acceleration boundary conditions when robot starts and stops walking lead to obvious difference between the model and the real robot. In this paper, parameterized gait is planned and trajectories’ smoothness of each joint angle and centroid are ensured using the 3-D LIPM theory. Static walking method is used to satisfy zero velocity and acceleration boundary conditions. Besides, a multi-link model is built to validate the stability. Simulation experiments show that: despite of some deviation from the theoretical solution, the actual zero-moment point (ZMP) is still within the support polygon, and the robot walks steadily. In consequence, the rationality and validity of model simplification of LIPM is demonstrated.

Dynamic Spatial Discrimination Maps of Discriminative Activation between Different Tasks Based on Support Vector Machines  [PDF]
Guangxin Huang, Huafu Chen, Feng Yin
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.21010
Abstract: As a set of supervised pattern recognition methods, support vector machines (SVMs) have been successfully applied to functional magnetic resonance imaging (fMRI) field, but few studies have focused on visualizing discriminative regions of whole brain between different cognitive tasks dynamically. This paper presents a SVM-based method for visualizing dynamically discriminative activation of whole-brain voxels between two kinds of tasks without any contrast. Our method provides a series of dynamic spatial discrimination maps (DSDMs), representing the temporal evolution of discriminative brain activation during a duty cycle and describing how the discriminating information changes over the duty cycle. The proposed method was applied to investigate discriminative brain functional activations of whole brain voxels dynamically based on a hand-motor task experiment. A set of DSDMs between left hand movement and right hand movement were reached. Our results demonstrated not only where but also when the discriminative activations of whole brain voxels occurred between left hand movement and right hand movement during one duty cycle.
An Improved 6S Code for Atmospheric Correction Based on Water Vapor Content  [PDF]
Yin Zhang, Xiaoqin Wang, Yunzhi Chen
Advances in Remote Sensing (ARS) , 2012, DOI: 10.4236/ars.2012.11002
Abstract: Water vapor content in the atmosphere is very significant for atmospheric correction of optical remote sensing data. Nowadays, the common atmospheric correction models use a single value of the average water vapor content of the study area to perform atmospheric correction. As the distribution of water vapor content varies greatly with time and space, it is obviously inaccurate to represent the total water vapor conditions of the whole area by just reading the average water vapor content. In this study, we altered the 6S sources so that it could read the water vapor content image which was retrieved from MODIS 1 km data. Atmospheric correction was implemented for the band 1 of MODIS 500 m data pixel-by-pixel using the improved 6S model. In comparison with the traditional 6S model, this improved 6S model is more reasonable in atmospheric correction, for it considers the spatial distribution of the water vapor content retrieved from MODIS data in the near infrared to define the atmospheric conditions for simulating the atmospheric radiative transfer. The results corrected by the improved 6S model showed more reasonable in pixel spatial distribution and closer histogram with the original image than those by traditional 6S model.
Investigating the English Proficiency of Learners: A Corpus-Based Study of Contrastive Discourse Markers in China  [PDF]
Guo-Ping Yang, Yin Chen
Open Journal of Modern Linguistics (OJML) , 2015, DOI: 10.4236/ojml.2015.53025
Abstract: Discourse markers signal the relationship between the neighboring sentences. The present comparative study investigates the use of Contrastive Discourse Markers between Chinese English learners and native speakers based on corpus data. Special attention is allocated to but and however, since these two small words are the most popular discourse markers in Chinese English Learners and Native Speakers. Quantitative and qualitative analyses indicate that both groups prefer to employ discourse markers like but, although, (even) though, however, etc. when signaling a contrastive relationship between S1 and S2, though they have different priorities in different contextual situation; besides, but is overused significantly by Chinese English Learners to signal a contrastive relationship rather than add further information in context; lastly, Chinese English Learner usually employs however at the beginning of the sentence, while native speakers put it both at the beginning or middle of the sentences, which both signal the relationship between topics and messages. The findings also suggest that more detailed instructions should be delivered on the procedural meanings and syntactical positions of Contrastive Discourse Markers used in context.
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