Linear codes from vectorial Boolean power functions

In this paper, three classes of binary linear codes with few weights are proposed from vectorial Boolean power functions, and their weight distributions are completely determined by solving certain equations over finite fields. In particular, a class of simplex codes and a class of first-order Reed-Muller codes can be obtained from our construction by taking the identity map, whose dual codes are Hamming codes and extended Hamming codes, respectively.     

On a reverse Hardy-Littlewood-Polya's inequality

By the use of the weight coefficients, the idea of introduced parameters and Euler-Maclaurin summation formula, a reverse Hardy-Littlewood-Polya''s inequality with parameters as well as the equivalent forms are provided. The equivalent statements of the best possible constant factor related to a few parameters and some particular cases are given.     

Promoting symmetric weight selection in data envelopment analysis: A penalty function approach

Traditionally, data envelopment analysis models assume total flexibility in weight selection, though this assumption can lead to several variables being ignored in determining the efficiency score. Existing methods constrain weight selection to a predefined range, thus removing possible feasible solutions. As such, in this paper we propose the symmetric weight assignment technique (SWAT) that does not affect feasibility and rewards decision making units (DMUs) that make a symmetric selection of weights. This allows for a method of weight restrictions that does not require preference constraints on the variables. Moreover, we show that the SWAT method may be used to differentiate among efficient DMUs.     

基于卟啉化合物的异质结有机太阳能电池

采用混合溶剂制备了四苯基卟啉(TPP)及其铜配合物(TPPCu)和氯化对甲氧基四苯基铁卟啉(TMPPFeCl),将三种卟啉化合物和富勒烯的衍生物(PCBM)分别共混,制备异质结太阳能电池。器件结构是ITO/porphyrin∶PCBM/Al,研究此类电池的性能。结果显示基于TPP∶PCBM的器件性能最优,其短路电流密度(JSC)是0.98mA.cm-2,开路电压(VOC)是0.52V,填充因子(FF)为30.1%。TPP是三种卟啉化合物中最佳的给体材料。进而考察了TPP∶PCBM的不同浓度配比对器件性能的影响。TPP∶PCBM的最佳浓度配比为1∶1,增加或减少TPP的量都会使器件的短路电流和开路电压降低,对填充因子的影响不大。     

Mori Dream Spaces and blow-ups of weighted projective spaces

For every $n\ge 3$, we find a sufficient condition for the blow-up of a weighted projective space $\mathbb{P}(a,b,c,d_1,?,d_{n?2})$ at the identity point not to be a Mori Dream Space. We exhibit several infinite sequences of weights satisfying this condition in all dimensions $n\ge 3$.     

A class of binary cyclic codes with generalized Niho exponents

In this paper, a class of binary cyclic codes with three generalized Niho-type nonzeros is introduced. Based on some techniques in solving certain equations over finite fields, the proposed cyclic codes are shown to have six nonzero weights and the weight distribution is also completely determined.     

Irradiation effects of 12 eV oxygen ions on polyimide and fluorinated ethylene propylene

Polyimide (PI) and Fluorinated Ethylene Propylene (FEP) samples (15 mm×15 mm×50 μm ) were exposed to atomic oxygen ions of average energy ～12 eV and flux ～5×10¹³ ions cm ^?2 s ^?1, produced in the Electron Cyclotron Resonance (ECR) plasma. The energy and the flux of the oxygen ions at different positions in the plasma were measured by a retarding field analyzer. The fluence of the oxygen ions was varied from sample to sample in the range of ～5×10¹⁶ to 2×10¹⁷ ions cm ^?2 by changing the irradiation period. The pre- and the post-irradiated samples were characterized by the weight loss, Scanning Electron Microscopy (SEM), X-ray Photoelectron Spectroscopy (XPS), and Fourier Transform Infrared (FTIR) techniques. The weight of the PI and FEP samples decreased with increasing the ion fluence. However, the erosion yield for the PI is found to be higher, by almost a factor five, when compared with that of FEP. On the surface region of irradiated samples, the concentrations of the carbon, fluorine, and oxygen and their corresponding chemical bonds have changed appreciably. Moreover, blisters and nanoglobules were also observed even at a fluence of ～10¹⁷ ions cm ^?2. This oxygen ion fluence is almost two orders of magnitude lower than that of the 5 eV atomic oxygen, which a satellite encounters in the space, at the low Earth orbit, during its mission period of about 7 years.     

Refined weight of edges in normal plane maps

The weight $w\left(e\right)$ of an edge $e$ in a normal plane map (NPM) is the degree-sum of its end-vertices. An edge $e=uv$ is of type $(i,j)$ if $d\left(u\right)\le i$ and $d\left(v\right)\le j$. In 1940, Lebesgue proved that every NPM has an edge of one of the types $(3,11)$, $(4,7)$, or $(5,6)$, where 7 and 6 are best possible. In 1955, Kotzig proved that every 3-connected planar graph has an edge $e$ with $w\left(e\right)\le 13$, which bound is sharp. Borodin (1989), answering Erd?s’ question, proved that every NPM has either a $(3,10)$-edge, or $(4,7)$-edge, or $(5,6)$-edge.A vertex is simplicial if it is completely surrounded by 3-faces. In 2010, Ferencová and Madaras conjectured (in different terms) that every 3-polytope without simplicial 3-vertices has an edge $e$ with $w\left(e\right)\le 12$. Recently, we confirmed this conjecture by proving that every NPM has either a simplicial 3-vertex adjacent to a vertex of degree at most 10, or an edge of types $(3,9)$, $(4,7)$, or $(5,6)$.By a $k^{\left(?\right)}$-vertex we mean a $k$-vertex incident with precisely $?$ triangular faces. The purpose of our paper is to prove that every NPM has an edge of one of the following types: $(3^{\left(3\right)},10)$, $(3^{\left(2\right)},9)$, $(3^{\left(1\right)},7)$, $(4^{\left(4\right)},7)$, $(4^{\left(3\right)},6)$, $(5^{\left(5\right)},6)$, or $(5,5)$, where all bounds are best possible. In particular, this implies that the bounds in $(3,10)$, $(4,7)$, and $(5,6)$ can be attained only at NPMs having a simplicial 3-, 4-, or 5-vertex, respectively.     

Complete weight enumerators of a class of linear codes with two or three weights

We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they have at most three weights and they are suitable for applications in secret sharing schemes. This is an extension of the results raised by Wang et al. (2017).