Abstract:
A 3-$(n,4,1)$ packing design consists of an $n$-element set $X$ and a collection of $4$-element subsets of $X$, called {\it blocks}, such that every $3$-element subset of $X$ is contained in at most one block. The packing number of quadruples $d(3,4,n)$ denotes the number of blocks in a maximum $3$-$(n,4,1)$ packing design, which is also the maximum number $A(n,4,4)$ of codewords in a code of length $n$, constant weight $4$, and minimum Hamming distance 4. In this paper the undecided 21 packing numbers $A(n,4,4)$ are shown to be equal to Johnson bound $J(n,4,4)$ $( =\lfloor\frac{n}{4}\lfloor\frac{n-1}{3}\lfloor\frac{n-2}{2}\rfloor\rfloor\rfloor)$ where $n=6k+5$, $k\in \{m:\ m$ is odd, $3\leq m\leq 35,\ m\neq 17,21\}\cup \{45,47,75,77,79,159\}$.

Abstract:
Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In this paper, we present some new algebraic and combinatorial constructions for FHS sets, including an algebraic construction via the linear mapping, two direct constructions by using cyclotomic classes and recursive constructions based on cyclic difference matrices. By these constructions, a number of series of new FHS sets are then produced. These FHS sets are optimal with respect to the Peng-Fan bounds.

Abstract:
Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHSs and FHS sets with optimal partial Hamming correlation. We first establish a correspondence between FHS sets with optimal partial Hamming correlation and multiple partition-type balanced nested cyclic difference packings with a special property. By virtue of this correspondence, some FHSs and FHS sets with optimal partial Hamming correlation are constructed from various combinatorial structures such as cyclic difference packings, and cyclic relative difference families. We also describe a direct construction and two recursive constructions for FHS sets with optimal partial Hamming correlation. As a consequence, our constructions yield new FHSs and FHS sets with optimal partial Hamming correlation.

To conduct this study, the literatures,
questionnaires, interviews and other methods were used, the analysis of the
present situation and health status of the students’ physical education in universities “special group”, and the nature of the course and teaching modes of
thinking were also done in order to provide references to improve sports
education in colleges and universities.

Abstract:
In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form $f(X_n)$ with even degree $d$, if the polynomial is squarefreed after each iteration, the multivariate discriminant $\Delta(f)$ is a factor of the squarefreed iterated resultant. In fact, we find a factor $Hp(f,[x_1,\ldots,x_n])$ of the squarefreed iterated resultant, and prove that the multivariate discriminant $\Delta(f)$ is a factor of $Hp(f,[x_1,\ldots,x_n])$. Moreover, we conjecture that $Hp(f,[x_1,\ldots,x_n])=\Delta(f)$ holds for generic form $f$, and show that it is true for generic trivariate form $f(x,y,z)$.

Abstract:
Quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by the theory of complete discrimination systems, function \RealTriangularize in Maple15 and the so-called Criterions on Equality of Symmetric Inequalities method. The equivalent simple quantifier-free formula is proposed and is difficult to obtain automatically by previous methods or quantifier elimination tools.

Abstract:
Candida albicans (C. albicans) and Aspergillus fumigatus (A. fumigatus) are the two main pathogens
in the clinical setting to cause serious, sometimes, lethal fungal infections.
Immunocompromised patients fall victims to these fungi, with a mortality rate
rising drastically over the past decades. This is in correlation with the fact
that conventional antifungals are no longer capable of completely eradicating
the disease, or if so, high doses are usually required to do so, leading to eventual
resistance to those drugs and severe side effects. High drug resistance is in
association with the discovery that these opportunistic pathogens have the
ability to develop a multicellular complex, known as biofilm. Biofilms prevent
drugs from reaching the fungal cells by sequestering them in their
extracellular matrix. Other factors such as extracellular DNA, persister cells
or heat shock protein 90 (Hsp90) also play a role in biofilm and contribute to
drug recalcitrance. With the discovery of new antifungals lagging behind,
scientists focused on other more profitable ways to counteract this phenomenon.
Combination of two or more antifungals was found effective but came with
serious drawbacks. Natural plant extracts, such as traditional Chinese medicine
have also been demonstrated in vitro to possess antimicrobial actions. Great interest was directed towards their use
with conventional antifungal agents with a possibility of lowering the
necessary concentration required to inhibit the growth of fungi. This review
aims in understanding the different factors contributing to clinical drug
resistance and evaluating the effect of combination therapy and natural
products on those cases difficult to treat.

Abstract:
This paper is devoted to the stability and convergence analysis of the Additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of multidelay-integro-differential equations (MDIDEs). GDN-stability and D-convergence are introduced and proved. It is shown that strongly algebraically stability gives D-convergence, DA- DAS- and ASI-stability give GDN-stability. A numerical example is given to illustrate the theoretical results.

Abstract:
This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. Some examples are given in the end of this paper which confirms our results.

Abstract:
The recent advances in the photorefraction of doped lithium niobate crystals are reviewed. Materials have always been the main obstacle for commercial applications of photorefractive holographic storage. Though iron-doped LiNbO 3 is the mainstay of holographic data storage efforts, several shortcomings, especially the low response speed, impede it from becoming a commercial recording medium. This paper reviews the photorefractive characteristics of different dopants, especially tetravalent ions, doped and co-doped LiNbO 3 crystals, including Hf, Zr and Sn monodoped LiNbO 3, Hf and Fe, Zr and Fe doubly doped LiNbO 3, Zr, Fe and Mn, Zr, Cu and Ce triply doped LiNbO 3, Ru doped LiNbO 3, and V and Mo monodoped LiNbO 3. Among them, Zr, Fe and Mn triply doped LiNbO 3 shows excellent nonvolatile holographic storage properties, and V and Mo monodoped LiNbO 3 has fast response and multi-wavelength storage characteristics.