Stickelberger elements for -extensions of function fields

We study Stickelberger elements associated to -extensions over global function fields of characteristic p>0 and show that they are in some sense generically irreducible in the Iwasawa algebras.     

Electrophoretically driven SDS removal and protein fractionation in the shotgun analysis of membrane proteomes

SDS is mostly used to enhance the solubilization and extraction of membrane proteins due to its strong detergency and low cost. Nevertheless, SDS interferes with the subsequent procedures and needs to be removed from the samples. In this work, a special gradient gel electrophoresis (GGE) system was developed to remove SDS from the SDS-solubilized protein samples. As a proof-of-principle experiment, the GGE system was designed to be composed of an agarose loading layer, six polyacrylamide fractionation layers with different concentrations and a high-concentration polyacrylamide sealing layer. The advantages of the GGE system are that it not only can electrophoretically remove SDS efficiently so that the protein loss resulted from the repeated gel washing after electrophoresis was avoided, but also can reduce the complexity of the sample, prevent the precipitation of proteins after loading and avoid the loss of proteins with low molecular weight during the electrophoresis. Using GGE system, about 85% of SDS in the sample and gel was electrophoretically removed and the proteins were fractionated. Compared with the two representative gel-based sample cleanup methods reported in literature, GGE-based strategy significantly improved the identification efficiency of proteins in terms of the number and coverage of the identified proteins.     

Cryptanalysis of a Matrix-based MOR System

We cryptanalyze a recently proposed matrix-based MOR cryptosystem. The security of the system depends on the difficulty of solving the following discrete logarithm problem: given an inner automorphism φ of SL(d, 𝔽 _q ) and φ ^a (each given in terms of their images on generators of SL(d, 𝔽 _q )), find a. We show that this problem can be reduced to a small number of similar problems in quotients of polynomial rings and solved in subexponential-time.     

纳米TiO2∶Zn薄膜电极紫外光电特性研究

采用sol-gel法制备了Zn2+掺杂的锐钛矿相纳米TiO2薄膜电极.通过光电流作用谱和电流-电位（I-U）曲线研〖WTBZ〗究了掺杂不同浓度Zn2+的TiO2薄膜电极的光电特性.由光电流作用谱可知，Zn2+的掺杂可显著影响薄膜电极的光电流大小，且掺杂的最佳浓度与薄膜晶粒尺度有关.在320nm单色光照射下，掺杂浓度（摩尔浓度）为0.1％的薄膜电极光电流最大，与未掺杂的本征薄膜电极相比增幅达40％.I-U曲线表明，光照下，随电极电位由正到负逐渐降低，不同掺杂浓度的TiO2薄膜电极中均出现了阳极电流向阴极电流转换的现象，且Zn2+掺杂浓度可影响电极阳极电流的初始电位.另外，无光照的暗态下，各薄膜在负电位区域观察到了相似的随电位降低而迅速增大的阴极暗电流.     

What do teachers need? Math and special education teacher educators’ perceptions of essential teacher knowledge and experience

Special education and mathematics education are becoming increasingly intertwined in inclusive classrooms. However, research and practice in these two fields are not always aligned. We discuss, in the context of extant research on pedagogical theory, concepts of access, and the findings of an exploratory study, how these two education sub-fields view teacher expertise. Teacher educators (from math and special education) were asked to rank the importance of different types of expertise for effectively posing purposeful mathematical questions. The groups differed significantly in their rankings of the importance of knowing individual students and general teaching experience. There were also notable differences between the groups’ rankings of the importance of knowing the needs of students with disabilities and mathematical content knowledge. The possible reasons for this are discussed, along with suggestions for improving professional collaboration.     

Preface: Special issue in honor of Claude-Michel Brauner

This special issue of the Journal of Applied Analysis and Computation is dedicated to Claude-Michel Brauner on the occasion of his 70th birthday. Claude-Michel Brauner is Emeritus Professor at the university of Bordeaux (IMB) and was Professor at the School of Mathematical Sciences of Xiamen University for eight years. Furthermore, he is corresponding member of the SMAI (french SIAM) for China and has played a significant role in Sino-French cooperation in applied mathematics. In June 9-12, 2017 the Sino-French Conference on Modeling, Mathematical Analysis and Computation was held in Xiamen University to celebrate his 70th birthday. This volume gathers carefully selected contributions from invited speakers and participants of the conference; it reflects the large variety of the themes addressed during this event.     

SIM(2)-invariant modifications of electrodynamic theory

In the Cohen–Glashow Very Special Relativity we exhibit possible modifications to the Maxwell theory and to the quantum electrodynamics Lagrangian in some generality, and discuss characteristic features depending on the modifications. Modified gauge transformations in SIM(2)-invariant theories are introduced and the related gauge fields, with two polarization states, can have nonzero mass. Also considered are SIM(2)-covariant modifications to the Proca-type field equations for a massive spin-1 particle.     

On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)

The derivative of the associated Legendre function of the first kind of integer degree with respect to its order, , is studied. After deriving and investigating general formulas for μ arbitrary complex, a detailed discussion of , where m is a non-negative integer, is carried out. The results are applied to obtain several explicit expressions for the associated Legendre function of the second kind of integer degree and order, . In particular, we arrive at formulas which generalize to the case of (0 ≤ m ≤ n) the well-known Christoffel’s representation of the Legendre function of the second kind, Q _n (z). The derivatives and , all with m > n, are also evaluated.