How Many Bits have to be Changed to Decrease the Linear Complexity?

The k-error linear complexity of periodic binary sequences is defined to be the smallest linear complexity that can be obtained by changing k or fewer bits of the sequence per period. For the period length p ⁿ, where p is an odd prime and 2 is a primitive root modulo p ², we show a relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. Moreover, we describe an algorithm to determine the k-error linear complexity of a given p ⁿ-periodic binary sequence.     

Nuclear charge radius of 11Li

We have determined the nuclear charge radius of ¹¹Li by high-precision laser spectroscopy. The experiment was performed at the TRIUMF-ISAC facility where the ⁷Li-¹¹Li isotope shift (IS) was measured in the 2s→3s electronic transition using Doppler-free two-photon spectroscopy with a relative accuracy better than 10⁻⁵. The accuracy for the IS of the other lithium isotopes was also improved. IS’s are mainly caused by differences in nuclear mass, but changes in proton distribution also give small contributions. Comparing experimentally measured IS with advanced atomic calculation of purely mass-based shifts, including QED and relativistic effects, allows derivation of the nuclear charge radii. The radii are found to decrease monotonically from ⁶Li to ⁹Li, and then increase with ¹¹Li about 11% larger than ⁹Li. These results are a benchmark for the open question as to whether nuclear core excitation by halo neutrons is necessary to explain the large nuclear matter radius of ¹¹Li; thus, the results are compared with a number of nuclear structure models.     

Chemical Constituents of Two Liverworts Metacalypogeia Alternifolia and Chandonanthus Hirtellus

A novel linear dihydrodichromene derivative, metacalypogin, was identified from the Taiwanese liverwort Metacalypogeia alternifolia. Together with data from M. cordifolia, the chemical marker of the genus Metacalypogeia is obvious chroman derivatives, which is far different from that of Calypogeia, the other genus in the same family. In addition, two isomeric diterpenoids of cembrane‐type were identified from the Chinese liverwort Chandonanthus hirtellus. The relative stereostructures of the latter two isomers were proved by X‐ray crystallography. Both compounds were unstable in chloroform solution and further oxidized to the corresponding peroxy hemiacetal derivatives.     

Structure and properties of Ce<Subscript>3</Subscript>Pd<Subscript>3</Subscript>Bi<Subscript>4</Subscript>, CePdBi,and CePd<Subscript>2</Subscript>Zn<Subscript>3</Subscript>

The intermetallic cerium compounds Ce₃-Pd₃Bi₄, CePdBi, and CePd₂Zn₃ were synthesized from the elements in sealed tantalum ampoules in an induction furnace. The compounds were characterized by X-ray powder and single crystal diffraction: CeCo₃B₂ type (ordered version of CaCu₅), P6/mmm, a = 538.4(4), c = 427.7(4) pm, wR2 = 0.0540, 115 F ² values, 9 variables for CePd₂Zn₃ and Y₃Au₃Sb₄ type, I \({\bar 4}\)3d, a = 1005.2(2) pm, w R2 = 0.0402, 264 F ² values, 9 variables for Ce₃Pd₃Bi₄, and MgAgAs type, a = 681.8(1) pm for CePdBi. The bismuthide structures are build up from three-dimensional networks of corner-sharing PdBi₄ tetrahedra with Pd–Bi distances of 281 (Ce₃Pd₃Bi₄) and 296?pm (CePdBi), respectively. The cerium atoms are located in larger voids of coordination number 12 (Ce₃Pd₃Bi₄) and 10 (CePdBi). In CePd₂Zn₃ the cerium atoms fill larger channels within the three-dimensional [Pd₂Zn₃] network with 18 (6 Pd + 12 Zn) nearest neighbors. The three compounds contain stable trivalent cerium with experimental magnetic moments of μ_eff = 2.70(2), 2.48(1), and 2.49(1) μ_B/Ce atom for CePd₂Zn₃, Ce₃Pd₃Bi₄, and CePdBi, respectively. Susceptibility and specific heat data gave no hint for magnetic ordering down to 2.1?K.     

Remarks on the <Emphasis Type="Italic">k</Emphasis>-error linear complexity of <Emphasis Type="Italic">p</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>-periodic sequences

Recently the first author presented exact formulas for the number of 2 ⁿ -periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k ≥ 2, of a random 2 ⁿ -periodic binary sequence. A crucial role for the analysis played the Chan–Games algorithm. We use a more sophisticated generalization of the Chan–Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for p ⁿ -periodic sequences over prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p ⁿ -periodic sequences over .      

Thorium under strong compression—a test case for the evaluation of EOS data by different forms and procedures

Abstract

X-ray diffraction on Thorium under pressures to 300 GPa at ambient temperature provides new EOS data for both the (low pressure) fcc phase as well as for the (high pressure) bct phase. A detailed evaluation of these data and a comparison with previous results shows systematic differences in the fitted parameters resulting from the use of different EOS forms and from the correlations in the parameters used in all these fitting procedures. The absolute uncertainties in these parameters are elucidated and special attention is given to the compatibility of different EOS forms for phases which are related by second order transitions.     

Recent developments in collinear laser spectroscopy at COLLAPS/ISOLDE

Collinear laser spectroscopy (CLS) provides fast, sensitive and accurate means for the determination of nuclear ground state properties via optical isotope shift and hyperfine structure measurements. Recent developments at COLLAPS, the CLS setup at ISOLDE, are summarized. This includes the use of the ISCOOL cooler and buncher for studies on gallium and copper isotopes and frequency-comb-based CLS with quasi-simultaneous collinear and anticollinear measurements on beryllium isotopes.     

Local Algorithms for the Prime Factorization of Strong Product Graphs

The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant “approximate” prime factorization, is the development of local approaches that cover the graph by factorizable patches and then use this information to derive global factors. We present here a local, quasi-linear algorithm for the prime factorization of “locally unrefined” graphs with respect to the strong product. To this end we introduce the backbone \mathbbB (G)\mathbb{B} (G) for a given graph G and show that the neighborhoods of the backbone vertices provide enough information to determine the global prime factors.