Electron paramagnetic resonance of NH 3 + radical in potassium sulphate

Room temperature EPR spectra of (NH₄)₂SO₄ doped K₂SO₄ monocrystals irradiated with x-rays show the presence of NH₃ ⁺ radicals. The EPR parameters areg ‖=2.0037 andg ⊥ = 2.0068;¹⁴NA _XX=13.75;A _YY=24.5;A _ZZ=25.5 gauss;¹HA _XX=A _YY=22 andA _ZZ=25 gauss. From the¹⁴N and¹H coupling constants it has been inferred that at room temperature the planar NH₃ ⁺ radical undergoes rotation about theC ₃ axis which corroborates with the equivalence of the protons, but the radical itself is in an asymmetric crystal field environment. The 77K spectra indicate a considerable reduction in the motion of the radical with the free motion almost completely stopped. Part of Ph.D. work of the second author     

Temperature dependence of the photoelastic behaviour of crystals—Part I

A modified form of Filon’s spectrometer method is used to study the variation of the stress-optical constants (q ₁₁-q ₁₂) andq ₄₄ of KCl, KBr, KI, LiF, MgO and NaCl in the temperature range 30° C. to 400° C. It is found that (q ₁₁-q ₁₂) andq ₄₄ generally increase numerically with the increase of temperature except those of NaCl which show a decrease. In KBr and KI,q ₄₄ first increases and then decreases numerically. The potassium halides show an interesting gradation of variation of these constants. In all the crystals studied, which are of NaCl type, the variation in (q ₁₁-q ₁₂) is greater than that inq ₄₄. Mueller’s ultrasonic method is used for measuring the ratio of strain-optical constantsp ₁₂/p ₁₁, in the temperature range 30°C. to 250°C. Combining the results obtained by these two methods, the absolute strain-optical constantsp ₁₁ andp ₁₂ have been evaluated at different temperatures. Curves are given showing the variation ofp ₁₁ andp ₁₂ with temperature. The variation ofp ₁₁ andp ₁₂ with temperature is discussed in terms of the contributions of the various factors considered by Mueller in his theory of photoelastic effect in cubic crystals.     

A problem of Chowla revisited

In 1964, S. Chowla asked if there is a non-zero integer-valued function f with prime period p such that f(p)=0 and

     

Oligosaccharide Analogues of Polysaccharides,Part 21 , Towards New Cellulose I Mimics: Synthesis of Dialkynyl C‐glucosides of peri‐Substituted Anthraquinone

The bis‐C‐glucoside 2 has been synthesised as the first representative of a series of templated glucosides and cellooligosaccharides that mimick part of the unit cell of cellulose I. As expected, there are, at best, weakly persistent H‐bonds between the two glucosyl residues in (D₆)DMSO and (D₇)DMF solution. The acetylated oct‐1‐ynitol 7 and deca‐1,3‐diynitol 12 were prepared from the gluconolactone 5 (Scheme 1). Coupling of 12 to PhI and 2‐iodothiophene yielded 13 and 14 , respectively, while dimerisation of the benzylated and acetylated deca‐1,3‐diynitols 10 and 12 afforded the bis‐C‐glucosyloctatetrayne 15 and the less stable 16 , respectively. The 2‐glucosylthiophene 17 was obtained by treating the C‐silylated deca‐1,3‐diynitol 9 with Na₂S. Cross‐coupling of (trimethylsilyl)acetylene (TMSA) with 1,8‐bis(triflyloxy)‐9,10‐anthraquinone ( 20 ) at elevated temperature gave the dialkynylated 21 ; its structure was established by X‐ray analysis (Scheme 2). Sequential coupling of 6 or 7 and TMSA to 20 gave the symmetric dialkyne 21 , the mixed dialkynes 23 (from 6 ) and 25 (from 7 ), and the symmetric diglucoside 36 (from 7 ) in modest yields; a stepwise coupling to the acetylated monotriflate 28 proved advantageous. It led to the oct‐1‐ynitol 29 and the deca‐1,3‐diynitol 33 that were transformed into the triflates 30 and 34 , respectively. Coupling of the triflate 34 to the oct‐1‐ynitol 7 gave the unsymmetric bis‐C‐glucoside 35 ; this was obtained in higher yields by coupling the triflate 30 to the deca‐1,3‐diynitol 12 . Coupling of the bistriflate 20 with either 7 or 12 afforded the symmetric bis‐C‐glucosides 36 and 37 , respectively. Deacetylation (KCN in MeOH) of 35 – 37 provided the unsymmetric bis‐C‐glucoside 2 and the symmetric analogues 3 and 4 .     

Efficient algorithms for Koblitz curves over fields of characteristic three

The nonadjacent form method of Koblitz [Advances in Cryptology (CRYPTO'98), in: Lecture Notes in Comput. Sci., vol. 1462, 1998, pp. 327–337] is an efficient algorithm for point multiplication on a family of supersingular curves over a finite field of characteristic 3. In this paper, a further discussion of the method is given. A window nonadjacent form method is proposed and its validity is proved. Efficient reduction and pre-computations are given. Analysis shows that more than 30% of saving can be achieved.     

Application of FPE based AR model for signal detection and digital data compression

Two applications of Autoregressive model of time series obtained by the Final Prediction Error (FPE) criterion introduced by Akaike are discussed: one, in detection of weak transient signals embedded in noise and two, in digital data compression. Typical results of a few case studies are presented.