Regularity of volume-minimizing flows on 3-manifolds

In Johnson and Smith (Indiana Univ Math J 44:45–85, 1995; Ann Global Anal Geometry 30:239–287, 2006; Proceedings of the VII International Colloquium on Differential Geometry, 1994, World Scientific, pp. 81–98), the authors characterized the singular set (discontinuities of the graph) of a volume-minimizing rectifiable section of a fiber bundle, showing that, except under certain circumstances, there exists a volume-minimizing rectifiable section with the singular set lying over a codimension-3 set in the base space. In particular, it was shown that for 2-sphere bundles over 3-manifolds, a minimizer exists with a discrete set of singular points. In this article, we show that for a 2-sphere bundle over a compact 3-manifold, such a singular point cannot exist. As a corollary, for any compact 3-manifold, there is a C ¹ volume-minimizing one-dimensional foliation. In addition, this same analysis is used to show that the examples, due to Pedersen (Trans Am Math Soc 336:69–78, 1993), of potentially volume-minimizing rectifiable sections (rectifiable foliations) of the unit tangent bundle to S ²ⁿ⁺¹ are not, in fact, volume minimizing.      

Visual screening for JAK2V617F mutation by a disposable dipstick

During the last 5 years, it was discovered that the JAK2V617F somatic mutation is present in virtually all patients with polycythemia vera and a large proportion of patients with essential thrombocythemia, primary myelofibrosis, and refractory anemia with ring sideroblasts and thrombocytosis. As a result, JAK2V617F was incorporated as a new clonal marker in the 2008 revision of the WHO diagnostic criteria. Current methods for JAK2 genotyping include direct sequencing, pyrosequencing, allele-specific PCR with electrophoresis, restriction fragment length polymorphism, real-time PCR, DNA-melting curve analysis, and denaturing HPLC. Some of these methods are labor intensive and time consuming, while the others require specialized costly equipment and reagents. We report a method for direct detection of the JAK2V617F allele by the naked eye using a dipstick test in a dry-reagent format. The method comprises a triprimer PCR combined with visual detection of the products within minutes by the dipstick test. Specialized instrumentation is not involved. The requirements for highly qualified technical personnel are minimized. Because the detection reagents exist in dry form on the dipstick, there is no need for multiple pipetting and incubation steps.     

Competing magnetic structures in the DySi FeB-type phase diagram

The temperature magnetic phase diagrams, of the dimorphic DySi compound, have been studied in terms of wave vectors in the range 1.5-45 K, by neutron diffraction. The polycrystalline sample consists of 26% of CrB-type (Cmcm no. 63, all atoms at 4c site: (0, y, 1/4)) and of 74% of FeB-type (Pnma no. 62, all atoms at 4c site: (x, 1/4, z)). The CrB-ordering is described by the wave vector: q₁=(0, 0, 1/2) over the entire magnetically ordered regime with a uniaxial magnetic structure along the shortest axis c. The FeB-type magnetic phase diagram reveals three distinct regions of magnetic ordering below T_N and one first order transition at T₂=23.5 K (on heating). The ordering is described by two symmetry independent magnetic vectors q₂=(0, 1/2, 1/6) and q₃=(0, q_3y, q_3z) with a temperature variable length. At 1.5 K q_3y≈1/2 and q_3z≈1/11. The two phases coexist in the form of domains. They differ in the moment orientation of the q₃ phase that deviates by ∼22° from the b-axis in the (0, 0, 1) plane. The low temperature range (LT) 1.5 K—T₂ subdivides into two regions: (i) LT-1, between 1.5 K—T₁ where the relative amount of the two phases remains unchanged and in (ii) LT-2: T₁-T₂ where the amount of the incommensurate q₃ phase increases at the cost of the commensurate q₂ amplitude modulated structure which remains unchanged but fully disappears at the first order transition at T₂=23.5 K. The q₃ phase undergoes minor changes until 22 K and gets destabilised at T₂ where the q_3z component jumps from the LT value q_3z≈1/11 to the HT value ≈1/7 and the q_3y component increases from 0.484(1) to 0.495(1). (iii) The high temperature (HT) range T₂-T_N (T_N=40±1 K) is described by a single wave vector q₃. The disproportionation of the HT magnetic phase q₃ below T₂ into two coexisting distinct phases q₂, q₃ down to 1.5 K is an unusual phenomenon, to our knowledge observed for the first time. Various mechanisms are discussed.     

Stereocontrolled synthesis of a d-amicetose functionalised tetrahydroxanthone related to kigamicin A

A glycosylated tetrahydroxanthone mimicking the ABC subunit of kigamicin A is synthesised in five steps by a sequence that exploits a Pd catalysed C–O bond forming reaction to construct the tetrahydroxanthone nucleus; chemo- and enantioselective Ru-catalysed transfer hydrogenation to establish the C-14 hydroxyl stereochemistry in the A-ring; and a trichloroacetimidate activated donor to introduce the β-linked d-amicetose unit in a stereoselective manner.     

Re-entrant ferrimagnetism in TbMn6Ge6

The magnetic ordering of the hexagonal compound TbMn₆Ge₆ has been studied by neutron diffraction at various temperatures between 1.8 and 500 K. In almost the whole magnetically ordered regime the magnetic structures are incommensurate with the crystal lattice. The corresponding wave vector q₁ = (0,0,q_z) is strongly temperature dependent and decreases from q_z = 0.1307 r.l.u. at 1.8 K to q_z = 0.091 r.l.u. at 410 K. The low-temperature range (T < 85 K) is characterised by a triple ferrimagnetic spiral structure with net moment along the c-direction. At T_t = 85 K the net moment disappears and the magnetic ordering changes into a flat spiral structure that probably persists up to the magnetic ordering temperature, T_N = 450 K. Before reaching the magnetic ordering temperature, however, an additional ferrimagnetic component perpendicular to the c-direction develops, marking the onset of re-entrant ferrimagnetism. The resulting structure described by two propagation vectors corresponds to a distorted spiral. Various models are discussed. The observed re-entrant ferrimagnetism is in agreement with results of previously reported magnetic measurements.     

The antiferromagnetic structures of TbCu2Ge2 and HoCu2Ge2 by neutron diffraction

The magnetic structures of TbCu₂Ge₂ and HoCu₂Ge₂ were studied by neutron diffraction. At 293 K the chemical structure is tetragonal body centered, space group I 4/mmm. The magnetic cell at 4.2 K is four times larger than the chemical one with a wave vector $\text{k =}\text{1}\text{2}\text{0}\text{1}\text{2}$. The magnetic space group is triclinic P_a$\text{1}$(Sh₂⁷) for both compounds. The moment values and directions are μ_Tb = 8.48(6) [μ_B] along [110] tetr. and μ_HO = 6.5(1)[μ_B] making an angle of 81.4(°) with c and 80(°) with a₁. The structure consists of ferromagnetic (101) layers stacked antiferromagnetically.     

Rewritable Optical Storage with a Spiropyran Doped Liquid Crystal Polymer Film

Rewritable optical storage has been obtained in a spiropyran doped liquid crystal polymer films. Pictures can be recorded on films upon irradiation with UV light passing through a grayscale mask and they can be rapidly erased using visible light. Films present improved photosensitivity and optical contrast, good resistance to photofatigue, and high spatial resolution. These photochromic films work as a multifunctional, dynamic photosensitive material with a real‐time image recording feature.

     

Molecular motion of a nickel-bis(dithiolato) complex in solution

The molecular motion of the planar bis(maleonitriledithiolato)nickel anion, Ni(mnt)(2)(-), has been studied as a function of temperature using electron spin resonance (ESR) in several polar solvents; they are ethyl alcohol, eugenol, dimethyl phthalate, tri-n-butyl phosphate, tris(2-ethyl-hexyl)phosphate, diglyme, and a dimethylformamide-chloroform mixed solvent. Calculated spectra in agreement with the experimental X-band spectra are obtained using axially symmetric reorientation when the long in-plane axis is the unique (parallel) axis of the rotational diffusion tensor with D parallel/D perpendicular = 3.0-4.0; D parallel and D perpendicular are the diffusion constants for reorientation about the parallel and perpendicular axes, respectively. The reorientational model required for the simulations is either in or close to the Brownian rotational diffusion limit. In the slow motional (low temperature) region, the spectra can be simulated using the glassy g values. As the temperature increases, however, agreement is obtained only if the intermediate g factor, g(y), for the non-axially symmetric Zeeman interaction increases while g(x), g(z), and the motional model remain unchanged; this scheme and others for which gx and g(z) are possibly temperature-dependent are discussed. The values of D perpendicular from the simulations are in general agreement with those from earlier analyses of the width of the central spectral feature. The simulations and width analyses indicate (as do electrochemical, conductivity, and vapor-phase osmometry data) that the paramagnetic species reorienting in solution has a shape similar to that of the Ni(mnt)(2)(-) ion.     

Genotyping of single nucleotide polymorphisms by primer extension reaction and a dual-analyte bio/chemiluminometric assay

Primer extension reaction (PEXT) is the most widely used approach to genotyping of single nucleotide polymorphisms (SNP). It is based on the high accuracy of nucleotide incorporation by the DNA polymerase. We propose a dual-analyte bio/chemiluminometric method for the simultaneous detection of the PEXT reaction products of the normal and mutant allele in a high sample-throughput format. PCR-amplified DNA fragments that span the SNP of interest are subjected to two PEXT reactions using normal and mutant primers in the presence of digoxigenin-dUTP and biotin-dUTP. Both primers contain a d(A)₃₀ segment at the 5′-end but differ in the final nucleotide at the 3′-end. Under optimized conditions only the primer that is perfectly complementary with the interrogated DNA will be extended by DNA polymerase and lead to a digoxigenin- or biotin-labeled product. The products of the PEXT reactions are mixed, denatured, and captured in microtiter wells through hybridization with immobilized oligo(dT) strands. Detection is performed by adding a mixture of antidigoxigenin–alkaline phosphatase (ALP) conjugate and a streptavidin–aequorin conjugate. The flash-type bioluminescent reaction of aequorin is triggered by the addition of Ca²⁺. ALP is then measured by adding the appropriate chemiluminogenic substrate. The method was evaluated by genotyping two SNPs of the human mannose-binding lectin gene (MBL2) and one SNP of the cytochrome P450 gene CYP2D6. Patient genotypes showed 100% concordance with direct DNA sequencing data.