Abstract:
By extending Lv-Xin-Zhou's first layer formulas of the $q$-Dyson product, we prove Kadell's conjecture for the Dyson product and show the error of his $q$-analogous conjecture. With the extended formulas we establish a $q$-analog of Kadell's conjecture for the Dyson product.

Abstract:
We present an example of two isotopic but not strongly isotopic commutative semifields. This example shows that a recent result of Coulter and Henderson on semifield of order p^n, n odd, can not be generalized to the case n even.

Abstract:
We show that every $(2^n,2^n,2^n,1)$-relative difference set $D$ in $\Z_4^n$ relative to $\Z_2^n$ can be represented by a polynomial $f(x)\in \F_{2^n}[x]$, where $f(x+a)+f(x)+xa$ is a permutation for each nonzero $a$. We call such an $f$ a planar function on $\F_{2^n}$. The projective plane $\Pi$ obtained from $D$ in the way of Ganley and Spence \cite{ganley_relative_1975} is coordinatized, and we obtain necessary and sufficient conditions of $\Pi$ to be a presemifield plane. We also prove that a function $f$ on $\F_{2^n}$ with exactly two elements in its image set and $f(0)=0$ is planar, if and only if, $f(x+y)=f(x)+f(y)$ for any $x,y\in\F_{2^n}$.

Abstract:
By taking the leading and the second leading coefficients of the Morris identity, we get new polynomial coefficients. These coefficients lead to new results in the sumsets with polynomial restrictions by the polynomial method of N. Alon.

Pattern search algorithms is one of
most frequently used methods which were designed to solve the derivative-free optimization
problems. Such methods get growing need with the development of science,
engineering, economy and so on. Inspired by the idea of Hooke and Jeeves, we
introduced an integer m in the algorithm which controls the number of steps
of iteration update. We mean along the descent direction to allow the algorithm to go ahead m steps at most to explore whether we can get
better solution further. The experiment proved the strategy’s efficiency.

Biochemical factors can play an important role in regulating gene expression in human umbilical vein endothelial cells (HUVECs), yet the role of biophysical factors during this process is unknown. Here, we show that physical cues, in the form of parallel microgrooves on the surface of cell adhesive substrates, can change the morphology of HUVECs as well as specific microRNA expression. Cells cultured on microgrooved poly (dimethyl siloxane) (PDMS) surface exhibited a more elongated morphology relative to those cultured on flat surfaces, and favored outgrowth along the axis of groove alignment. The level of microRNAs in the cell was screened by miRNA microchip and verified by qRT-PCR. The result showed that around 26 microRNAs have been modified significantly, among which miR-21 level was dramatically elevated. Western-blotting analysis demonstrated that PTEN, a target of miR- 21, was up-regulated in HUVECs with elongated morphology. Cell apoptosis level was significantly decreased, with was associated with the increasing of miR-21 level. These results suggested that biophysical factors can directly modify HUVECs morphology, thus induce miR-21 expression in HUVECs and its downstream biological functions such as decreasing apoptosis. This study provided evidence that surface microtopology should also be considered in designing biomaterials in tissue engineering application.

Abstract:
In this paper, a subspace method is proposed for blind channel estimation in orthogonalfrequency-division multiplexing (OFDM) systems over time-dispersive channel. The proposedmethod does not require a cyclic prefix (CP) and thus leading to higher spectral efficiency. Byexploiting the block Toeplitz structure of the channel matrix, the proposed blind estimationmethod performs satisfactorily with very few received OFDM blocks. Numerical simulationsdemonstrate the superior performance of the proposed algorithm over methods reported earlier inthe literature.

Abstract:
We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.

Abstract:
A new family of commutative semifields with two parameters is presented. Its left and middle nucleus are both determined. Furthermore, we prove that for any different pairs of parameters, these semifields are not isotopic. It is also shown that, for some special parameters, one semifield in this family can lead to two inequivalent planar functions. Finally, using similar construction, new APN functions are given.

Abstract:
Zero-difference balanced (ZDB) functions can be employed in many applications, e.g., optimal constant composition codes, optimal and perfect difference systems of sets, optimal frequency hopping sequences, etc. In this paper, two results are summarized to characterize ZDB functions, among which a lower bound is used to achieve optimality in applications and determine the size of preimage sets of ZDB functions. As the main contribution, a generic construction of ZDB functions is presented, and many new classes of ZDB functions can be generated. This construction is then extended to construct a set of ZDB functions, in which any two ZDB functions are related uniformly. Furthermore, some applications of such sets of ZDB functions are also introduced.