Physical properties of SrSn(4) single crystals

We present detailed thermodynamic and transport measurements on single crystals of the recently discovered binary intermetallic superconductor, SrSn(4). We find this material to be a slightly anisotropic three-dimensional, strongly coupled, possibly multiband, superconductor. Hydrostatic pressure causes a decrease in the superconducting transition temperature at the rate of ≈?-?0.068?K?kbar(-1). Band structure calculations are consistent with experimental data on the Sommerfeld coefficient and upper superconducting critical field anisotropy, and suggest a complex, multi-sheet Fermi surface formed by four bands.     

Sigmoids as precursors of solar eruptions

Coronal mass ejections (CMEs) appear to originate preferentially in regions of the Sun's corona that are sigmoidal, i.e., have sinuous S or reverse-S shapes. Yohkoh solar X-ray images have been studied before and after a modest number of Earth-directed (halo) CMEs. These images tend to show sigmoidal shapes before the eruptions and arcades, cusps, and transient coronal holes after. Using such structures as proxies, it has been shown that there is a relationship between sigmoidal shape and tendency to erupt. Regions in the Sun's corona appear sigmoidal because their magnetic fields are twisted. Some of this twist may originate deep inside the Sun. However, it is significantly modulated by the Coriolis force and turbulent convection as this flux buoys up through the Sun's convection zone. As the result of these phenomena, and perhaps subsequent magnetic reconnection, magnetic flux ropes form. These flux ropes manifest themselves as sigmoids in the corona. Although there are fundamental reasons to expect such flux ropes to be unstable, the physics is not as simple as might first appear, and there exist various explanations for instability. Many gaps need to be filled in before the relationship between sigmoids and CMEs is well enough understood to be a useful predictive tool     

μSR studies of borocarbides

The muon‐spin‐relaxation technique has been utilized to characterize the magnetic properties of the borocarbide compounds RNi₂B₂C ( R=\,Tm, Er, Ho and Dy), which exhibit coexistence of superconductivity and magnetism. Some general features of their magnetic ground‐state and unusual results obtained in the Ho, Tm and Dy systems are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A sequential sorting network analogous to the batcher merge

We present a network of delay log₂N, whose comparators have only log₂N different lengths with maximum length N/2. This network is log-sequential in that it will sort N data items when they are passed through it log₂Ntimes. The design, which is related to the Batcher odd-even merge, is distinctly different from the first known example of a log-delay log-sequential network, due to Dowd, Perl, Rudolf, and Saks. It is quite probably the best possible sorting network.     

The two basic linear time Planarity algorithms: Are they the same?

We compare the two most widely known planarity testing algorithms, the one due to Hoperoft and Tarjan, and the other to Lempel. Even, and Cederbaum. These two algorithms are generally viewed as very different approaches to the problems of planarity testing and graph embedding. In this paper, however, by utilizing previously unnoticed freedoms of choice in the order in which the operations of the Hoperoft-Tarjan algorithm can be performed, we create a variation of this algorithm which, in terms of the order in which vertices are processed, is indistinguishable on all planar graph inputs from the Lempel -Even-Cederbaum algorithm. This allows one to create hybridized algorithms which, when interpreted as embedding algorithms, combine all of the features of both procedures.     

Specific heat and anisotropic superconducting and normal-state magnetization of HoNi2B2C

The magnetization of single-crystal HoNi₂B₂C has been measured as a function of applied field (H) and temperature in order to probe the interplay between superconductivity and magnetism in this complex layered system. The normal-state magnetic susceptibility of HoNi₂B₂C is highly anisotropic with a Curie-Weiss-like temperature dependence for H applied perpendicular to the c-axis and with a much weaker temperature dependence for H applied parallel to the c-axis, indicating that the Ho⁺³ magnetic moments lie predominately in the tetragonal a−b plane below 20 K. High-field magnetization (2000 Oe), low-field magnetization (20 Oe) and zero-field specific heat all give an antiferromagnetic ordering temperature of T_N=5.0 K. Remarkably, in 20 Oe applied field both superconductivity (T_c=8.0 K) and antiferromagnetism (T_N=5.0 K) clearly make themselves manifest in the magnetization data. From these magnetization data a phase diagram in the H−T plane was constructed for both directions of applied field. This phase diagram shows a non-monotonic temperature dependence of H_c2 with a deep minimum at T_N=5 K. The high-field magnetization data for H applied perpendicular to the c-axis also reveal a cascade of three phase transitions for T < 5 K and H < 15 000 Oe, contributing to the rich H versus T phase diagram for HoNi₂B₂C at low temperatures.     

On a problem of Oppenheim concerning “factorisatio numerorum”

Let f(n) denote the number of factorizations of the natural number n into factors larger than 1 where the order of the factors does not count. We say n is “highly factorable” if f(m)<f(n) for all m < n. We prove that f(n)=n·L(n)^?1+0(1) for n highly factorable, where $\text{L(n)=}\text{exp}\text{{}\text{log}\text{n}\text{logloglog}\text{n}\text{loglog}\text{n}\text{}}$. This result corrects the 1926 paper of Oppenheim where it is asserted that f(n)=n·L(n)^?2+0(1). Some results on the multiplicative structure of highly factorable numbers are proved and a table of them up to 10⁹ is provided. Of independent interest, a new lower bound is established for the function Ψ(x, y), the number of n≤x free of prime factors exceeding y.     

Relation between the Superconducting Transition Temperature and the Axial Ratio in R Ni 2 B 2 C ( R =Y,Ho, Er,Tm, Lu) Under High Pressure

The effect of pressure on the lattice parameters of R Ni 2 B 2 C ( R = Y, Ho, Er, Tm, Lu) has been measured in order to investigate the relation of T C to axial ratio c/a in the tetragonal lattice or the cohesive properties of these materials. The large anisotropies are observed in the lattice compression curves especially for R =Ho and Tm; the c -axis is more compressible than the a -axis. On the other hand, the anisotropy in the lattice compression is found to be relatively small for R =Y and Lu. The close relation between T C and c/a is pointed out particularly for R =Ho.