Classroom note: Using the binomial series to prove the arithmetic mean–geometric mean inequality

In 1968, Leon Gerber compared (1 + x) ^a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented.     

The research on temperature measurement based on polarization dependent loss

This paper analyzes the properties of reflected polarization dependent loss of apodized fiber Bragg gratings with temperature effective. We simulates reflected spectrum and polarization dependent loss of the apodized fiber Bragg gratings. The reflected spectrum and polarization dependent loss are measured under different temperatures. The analysis results show that reflected polarization dependent loss presents two peaks which shift an equal proportion to long wavelength with temperature increasing and have very good stability so we propose an idea that use polarization dependent loss as temperature sensor measurement parameters. The results show that the accuracy of measurement can be increased almost by one order of magnitude.     

Advances in 1,8-Naphthyridines Chemistry

This review reports a broad overview of the synthetic procedures of 1,8-naphthyridines, dibenzo[b,g][1,8]naphthyridine, dibenzo[c,f][1,8]naphthyridine, 1,8-naphthyridine-3-carboxylic acid, 1,8-naphthyridine-3-carboxamide, and 1,8-naphthyridine-3-carbohydrazide compounds and their reactions. The physical properties, spectral data, and biological importance of naphthyridines are discussed.     

Designing and Characterization of Biodegradable Multiblock Poly(L-Lactic Acid)/Polybutadiene Elastomers

A series of poly(L-lactic acid)/polybutadiene (PLA/PB) biodegradable multiblock elastomers was synthesized and characterized. A two-step process to prepare PLA/PB multiblock elastomers was applied. Melt polymerization was used to prepare poly(L-lactic acid) (PLA) terminated with hydroxyl groups and, at the same time, hydroxyl-terminated polybutadiene (HTPB) and 1,6-hexamethylene diisocyanate (HDI) were employed to synthesize diisocyanate-terminated polybutadiene (ITPB). Then, PLA and ITPB were reacted with different PLA/PB weight ratios. Consequently, a series of PLA/PB biodegradable poly(ester-urethane)s with crosslinked chains was obtained. Swelling characteristics and crosslink density of the crosslinked elastomer were investigated. DMA was applied to characterize its thermal properties. The measurement of mechanical properties showed that a PLA/PB elastomer with adjustable mechanical properties was synthesized. Micromorphology, hydrophobicity, and degradability of the material were also characterized.     

On a family of highly regular graphs by Brouwer,Ivanov, and Klin

Highly regular graphs for which not all regularities are explainable by symmetries are fascinating creatures. Some of them like, e.g., the line graph of W. Kantor’s non-classical $GQ(5^2,5)$, are stumbling stones for existing implementations of graph isomorphism tests. They appear to be extremely rare and even once constructed it is difficult to prove their high regularity. Yet some of them, like the McLaughlin graph on 275 vertices and Ivanov’s graph on 256 vertices are of profound beauty. This alone makes it an attractive goal to strive for their complete classification or, failing this, at least to get a deep understanding of them. Recently, one of the authors discovered new methods for proving high regularity of graphs. Using these techniques, in this paper we study a classical family of strongly regular graphs, originally discovered by A.E. Brouwer, A.V. Ivanov, and M.H. Klin in the late 80s. We analyse their symmetries and show that they are $(3,5)$-regular but not 2-homogeneous. Thus we promote these graphs to the distinguished club of highly regular graphs with few symmetries.     

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action $\mathfrak{h}$, electric charge q, and magnetic flux ?. Also, $q\times ?=\text{action}$ and $q/?=1/\text{resistance}$ are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and ? (and also of $\mathfrak{h}$): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, ? appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.     

1stOpt软件在蔗糖水解实验教学中的应用

将1stOpt软件用于物理化学实验蔗糖水解反应速率常数的测定中，在无需严格记录反应开始时间和测定反应终了旋光度的情况下，通过非线性拟合无需编程及公式变换就可以简单方便准确地得到反应速率常数，避免了传统数据处理方法所带来的人为误差，可以补充和改进物理化学实验的教学。     

Isotactic poly(propylene‐co‐1‐pentene‐co‐1‐hexene) terpolymers: Synthesis,molecular characterization,and evidence of the trigonal polymorph

Terpolymers based on propylene with 1‐pentene and 1‐hexene as comonomeric units are satisfactorily synthesized using a metallocene catalyst. Thus, several terpolymers are prepared with distinct overall compositions in comonomers as well as three different 1‐pentene/1‐hexene ratios at a given composition to evaluate the influence on polymerization activity, intrinsic viscosity, and microstructural details. The new trigonal δ polymorph is observed in those quenched terpolymers with a global content in comonomers of about 14 mol %, independently of the ratio between both comonomers. However, preliminary results indicate a profound influence of that ratio on the crystallization rate. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3251–3259     

一类极限为1的未定式

对于一类00型或∞0型未定式，给出其极限为1的一个充分条件，并通过实例展示其应用。     

基于物理课堂有效教学的策略浅析

根据有效教学的理念提出了课堂有效教学的基本策略、动力策略和长效策略,并结合基础物理的教学,对这些教学策略的科学掌握和运用进行了探讨.