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.

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 $frac{2r}{3}$

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.

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.

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 $k$.

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).

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.

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.

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.

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.