On Dickson Polynomials and Difference Sets

In 1998, Maschietti constructed several cyclic difference sets from monomial hyperovals. R. Evans, H.D.L. Holloman, C. Krattnthaler and Qing Xiang gave an algebraic proof of the two autocorrelation property of the related binary sequence. In this paper, we show that hyperovals are very closely related to two-to-one maps, and then we proceed to generalize Maschietti＇s result.

Simultaneous determination of five phenylethanoid glycosides in Cistanches Herba using quantitative analysis of multi-components by single marker

In the present study, a method for the quantitative analysis of multi-components by single marker(QAMS) has been developed and validated for the simultaneous determination of echinacoside(ECH), tubuloside A, acteoside, isoacteoside, and2’-acetylacteoside in Cistanches Herba. ECH was used as the internal standard(IS) to obtain the relative correction factors(RCFs) of the other four phenylethanoid glycosides(PhGs);meanwhile, various influencing factors on RCFs were investigated under different conditions. The content of each component was calculated with RCF. The results were compared with those obtained by the external standard method(ESM) to verify the feasibility and accuracy of the established QAMS method. No significant difference was found in the quantitative results of 10 batches of Cistanches Herba between QAMS and ESM. The proposed QAMS method for simultaneous determination of PhGs in Cistanches Herba is accurate and feasible, providing an efficient and economical approach for the quality control of Cistanches Herba.

Exact Polynomial Solutions of Schrdinger Equation with Various Hyperbolic Potentials

The Schrodinger equation with hyperbolic potential V （ x ）=- Vosinh 2q （ x / d） / cosh 6 （ x / d） （q= 0, 1, 2, 3） is studied by transforming it into the confluent Heun equation. We obtain genera/symmetric and antisymmetric polynomial solutions of the SchrSdinger equation in a unified form via the Functional Bethe ansatz method. Furthermore, we discuss the characteristic of wavefunction of bound state with varying potential strengths. Particularly, the number of wavefunction＇s nodes decreases with the increase of potentiaJ strengths, and the particle tends to the bottom of the potential well correspondingly.

Polymorphic Pb_(14)O_(8)I_(12) and Pb_(7)O_(4)I_(6) oxyhalides featuring unprecedented[O_(8)Pb_(14)]clusters with broad IR transparency

Wide transmittance range is an essential factor for the design of infrared optical materials.Traditionally,the designs of mid-far infrared crystals have focused on oxygenfree systems of chalcogenides and pnictides.Nevertheless,the introduction of elements with large atomic numbers,such as the lone-pair cation Pb^(2+) and halogen anion I^(-),based on the oxyhalides,can broaden the infrared transmittance range.Thus,two new polymorphs of Pb(Ⅱ)-containing oxyhalides,Pb_(14)O_(8)I_(12)(α-POI)and Pb_(7)O_(4)I_(6)(β-POI),are successfully synthesized via the high-temperature solution method.Interestingly,they crystallize in the same space group,P1,and present unprecedented[O_(8)Pb_(14)]clusters from the perspective of oxocentered[OPb_(4)]basic units.Remarkably,POI exhibits a quite wide transparent range(0.47-16.0μm),which enlightens the oxyhalides with prominent infrared optical properties.Additionally,the first principles calculations show that they have large birefringence(0.139 and 0.108 for α-and β-POI at 1064 nm,respectively),which makes POI promising infrared optical materials.