Perfect State Transfer on Weighted Abelian Cayley Graphs*

Recently, there are extensive studies on perfect state transfer (PST for short) on graphs due to their significant applications in quantum information processing and quantum computations. However, there is not any general characterization of graphs that have PST in literature. In this paper, the authors present a depiction on weighted abelian Cayley graphs having PST. They give a unified approach to describe the periodicity and the existence of PST on some specific graphs.     

Cyclotomic construction of strong external difference families in finite fields

Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group G are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906, 2016) and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in G. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes. Particularly, we present an \((n,m,k,\lambda )=(243,11,22,20)\)-SEDF in \((\mathbb {F}_q,+)\ (q=3^5=243)\) by using the cyclotomic classes of order 11 in \(\mathbb {F}_q\) which answers an open problem raised in Paterson and Stinson (2016).     

Raman spectroscopy of synthetic CaHPO4·2H2O– and in comparison with the cave mineral brushite

The mineral brushite has been synthesised by mixing calcium ions and hydrogen phosphate anions to mimic the reactions in caves. The vibrational spectra of the synthesised brushite were compared with that of the natural cave mineral. Bands attributable to the PO₄^3– and HPO₄^2– anions are observed. Brushite, both synthetic and natural, is characterised by an intense sharp band at 985 cm⁻¹ with a shoulder at 1000 cm⁻¹. Characteristic bending modes are observed in the 300 to 600 cm⁻¹ region. The spectra of the synthesised brushite matches very well the spectrum of brushite from the Moorba Cave, Western Australia. Copyright © 2011 John Wiley & Sons, Ltd.     

Construction of cyclotomic codebooks nearly meeting the Welch bound

Ding and Feng (IEEE Trans Inform Theory 52(9):4229–4235, 2006, IEEE Trans Inform Theory 53(11):4245–4250, 2007) constructed series of (N, K) codebooks which meet or nearly meet the Welch bound \({\sqrt{\frac{N-K}{(N-1)K}}}\) by using difference set (DS) or almost difference set (ADS) in certain finite abelian group respectively. In this paper, we generalize the cyclotomic constructions considered in (IEEE Trans Inform Theory 52(9):4229–4235, 2006, IEEE Trans Inform Theory 53(11):4245–4250, 2007) and (IEEE Trans Inform Theory 52(5), 2052–2061, 2006) to present more series of codebooks which nearly meet the Welch bound under looser conditions than ones required by DS and ADS.     

Vibrational spectroscopy of synthetic stercorite H(NH4)Na(PO4)·4H2O--a comparison with the natural cave mineral

In order to mimic the chemical reactions in cave systems, the analogue of the mineral stercorite H(NH(4))Na(PO(4))·4H(2)O has been synthesised. X-ray diffraction of the stercorite analogue matches the stercorite reference pattern. A comparison is made with the vibrational spectra of synthetic stercorite analogue and the natural Cave mineral. The mineral in nature is formed by the reaction of bat guano chemicals on calcite substrates. A single Raman band at 920 cm(-1) (Cave) and 922 cm(-1) (synthesised) defines the presence of hydrogen phosphate in the mineral. In the synthetic stercorite analogue, additional bands are observed and are attributed to the dihydrogen and phosphate anions. The vibrational spectra of synthetic stercorite only partly match that of the natural stercorite. It is suggested that natural stercorite is more pure than that of synthesised stercorite. Antisymmetric stretching bands are observed in the infrared spectrum at 1052, 1097, 1135 and 1173 cm(-1). Raman spectroscopy shows the stercorite mineral is based upon the hydrogen phosphate anion and not the phosphate anion. Raman and infrared bands are found and assigned to PO(4)(3-), H(2)O, OH and NH stretching vibrations. Raman spectroscopy shows the synthetic analogue is similar to the natural mineral. A mechanism for the formation of stercorite is provided.     

纸飞机

<正>用一张纸叠成的纸飞机常常会引起许多成年人愉快童年的回忆,著名力学家张维院士生前在回忆与钱学森先生幼时同窗时讲到:"记得当时小学生中盛行一种游戏是扔纸镖,看谁扔得远.纸镖是用一张方纸,依对角线折成一个长而尖、     

A reassignment of the EPR spectra previously attributed to Cu@C60

EPR spectra attributed to the endohedral metallofullerene Cu@C60 are better explained by the previously characterized Cu(II) dithiocarbamate family of compounds.     

Maximal values of generalized algebraic immunity

The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions and/or over arbitrary finite fields and reasonable upper bounds for such generalized algebraic immunities has been proved in Armknecht and Krause (Proceedings of ICALP 2006, LNCS, vol. 4052, pp 180–191, 2006), Ars and Faugere (Algebraic immunity of functions over finite fields, INRIA, No report 5532, 2005) and Batten (Canteaut, Viswanathan (eds.) Progress in Cryptology—INDOCRYPT 2004, LNCS, vol. 3348, pp 84–91, 2004). In this paper we show that the upper bounds can be reached as the maximal values of algebraic immunities for most of generalizations by using properties of Reed–Muller codes.