Abstract:
The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties of $p$-mappings and restrictable hom-Lie algebras. Finally, the cohomology of restricted hom-Lie algebras is researched.

Abstract:
The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in [6]. Second, we obtain some properties of $p$-mappings and restrictable Leibniz algebras, and discuss restricted Leibniz algebras with semisimple elements. Finally, Cartan decomposition and the uniqueness of decomposition for restricted Leibniz algebras are determined.

Abstract:
In this paper, we introduce the relevant concepts of $n$-ary multiplicative Hom-Nambu-Lie superalgebras and construct three classes of $n$-ary multiplicative Hom-Nambu-Lie superalgebras. As a generalization of the notion of derivations for $n$-ary multiplicative Hom-Nambu-Lie algebras, we discuss the derivations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras. In addition, the theory of one parameter formal deformation of $n$-ary multiplicative Hom-Nambu-Lie superalgebras is developed by choosing a suitable cohomology.

Abstract:
The paper studies nilpotent $n$-Lie superalgebras. More specifically speaking, we first prove Engel's theorem for $n$-Lie superalgebras. Second, we research some properties of nilpotent $n$-Lie superalgebras, Finally, we give several sufficient conditions that an $n$-Lie superalgebra is nilpotent.

Abstract:
In this paper, we discuss the representations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras as a generalization of the notion of representations for $n$-ary multiplicative Hom-Nambu-Lie algebras. We also give the cohomology of an $n$-ary multiplicative Hom-Nambu-Lie superalgebra and obtain a relation between extensions of an $n$-ary multiplicative Hom-Nambu-Lie superalgebra $\mathfrak{b}$ by an abelian one $\mathfrak{a}$ and $Z^1(\mathfrak{b}, \mathfrak{a})_{\bar{0}}$. We also introduce the notion of $T^*$-extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras and prove that every finite-dimensional nilpotent metric $n$-ary multiplicative Hom-Nambu-Lie superalgebra $(\g,[\cdot,\cdots,\cdot]_{\g},\alpha,\langle ,\rangle_{\g})$ over an algebraically closed field of characteristic not 2 in the case $\alpha$ is a surjection is isometric to a suitable $T^*$-extension.

Abstract:
Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Some results in the literature are improved.

Realizing digital signal demodulation on
the general computer is an important research direction in the field of signal
processing in recent years. In this paper, the algorithm of BPSK signal demodulation
which has high real-time requirements is researched on the general computer.
According to the characteristics of “CPU + GPU” heterogeneous computing, the
parallel computation model of digital communication is put forward, and BPSK
signal demodulation is realized on CUDA platform. Test results show that the
computing time ratio of 1:1.7, when ？the bit error rate can
be achieved 10^{?5}.

Abstract:
LTE heterogeneous networks (HetNets) is becoming a popular topic since it was first developed in 3GPP Release 10. HetNets has the advantage to assemble various cell networks and enhance users’ Quality of Service (QoS) within the system. However, its development is still constrained by two main issues: 1) Load imbalance caused by different transmission powers for various tiers, and 2) The unbalanced transmission power may also increase unnecessary handover rate. In order to solve the first issue, Cell range expansion (CRE) can be applied in the system, which will benefit lower-tier cell during user association phase; CRE, Hysteresis Margin (HM) and Time-to-Trigger (TTT) will be utilized to bound UE within lower tier network of HetNets and therefore solve the second issue. On the other hand, the relationship of these parameters may be complicated and even reduce QoS if they are chosen incorrectly. This paper will evaluate the advantage and disadvantage of all three parameters and propose a Markov Chain Process (MCP) based method to find optimal HM, CRE and TTT values. And then, the simulation is taken and the optimal combination for our scenario is obtained to be 1 dB, 6 dB and 60 ms respectively. First contribution of this paper is to map the HetNets handover process into MCP and all the phases of handover can be calculated and analysed in probability way, so that further prediction and simulation can be realised. Second contribution is to establish a mathematical method to model the relationship of HM, CRE and TTT in HetNets, therefore the coordination of these three important parameters is achieved to obtain system optimization.

Abstract:
Error Analysis is one of the most common methods in statistics. According to Corder S. P (1967) error is significant to learners. This paper applies it to the teaching of Chinese-English translation. Taking a whole class as a research unit and by analyzing the common errors made by students in their homework, the researcher records the error types, numbers of each type of error as well as the corresponding frequencies separately. Then the researcher lists out the top six errors and calculates the total frequency of them (total percentage of the six errors occupied in the class). After the analysis, the teacher feedbacks the results to the students as well as explains the methods of error identification and correction. This paper compares two non-English major classes with 60 freshmen; one has adopted “Error Analysis” in the teaching of Chinese-English Translation, while the other has not. Finally after one semester, the class which has applied “Error Analysis” makes greater progress than the class not. From some aspects, the research does show that “Error Analysis Teaching Method” could promote the Chinese-English translating skills of non-English major freshmen. Though this research has its limitations, it is valuable in improving the traditional translation teaching strategies.

Abstract:
Let $\mathcal{W}$ and $\mathcal{S}$ denote the even parts of the general Witt superalgebra $W$ and the special superalgebra $S$ over a field of characteristic $ p>3,$ respectively. In this note, using the method of reduction on $\mathbb{Z}$-gradations, we determine the derivation space $\mathrm{Der}(\mathcal{W}, W_{\bar{1}})$ from $\mathcal{W}$ into $W_{\bar{1}} $ and the derivation space $\mathrm{Der}(\mathcal{S}, W_{\bar{1}})$ from $\mathcal{S}$ into $W_{\bar{1}}. $ In particular, the derivation space $\mathrm{Der}(\mathcal{S}, S_{\bar{1}})$ is determined.