Influence of surface tension on damping of the oscillations of a viscous incompressible fluid in a cylindrical channel

A numerical calculation is made of small oscillations of a viscous incompressible fluid that fills half of a horizontal cylindrical channel. The calculation is made with and without allowance for surface tension. The results of the calculation show that allowance for surface tension increases the damping of the oscillations. The general properties of problems of the normal oscillations of a heavy and capillary viscous incompressible fluid were studied in [1–3], in which the possibility of applying the Bubnov-Galerkin method to these problems was pointed out. A method for calculating the oscillations of a viscous incompressible fluid that partly fills an arbitrary vessel at large Reynolds numbers was developed in [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–132, May–June, 1980.     

Development of a microfluidic platform for single-cell secretion analysis using a direct photoactive cell-attaching method

A precise understanding of individual cellular processes is essential to meet the expectations of most advanced cell biology. Therefore single-cell analysis is considered to be one of possible approach to overcome any misleading of cell characteristics by averaging large groups of cells in bulk conditions. In the present work, we modified a newly designed microchip for single-cell analysis and regulated the cell-adhesive area inside a cell-chamber of the microfluidic system. By using surface-modification techniques involving a silanization compound, a photo-labile linker and the 2-methacryloyloxyethyl phosphorylcholine (MPC) polymer were covalently bonded on the surface of a microchannel. The MPC polymer was utilized as a non-biofouling compound for inhibiting non-specific binding of the biological samples inside the microchannel, and was selectively removed by a photochemical reaction that controlled the cell attachment. To achieve the desired single-macrophage patterning and culture in the cell-chamber of the microchannel, the cell density and flow rate of the culture medium were optimized. We found that a cell density of 2.0 × 10(6) cells/ml was the appropriate condition to introduce a single cell in each cell chamber. Furthermore, the macrophage was cultured in a small size of the cell chamber in a safe way for 5 h at a flow rate of 0.2 μl/min under the medium condition. This strategy can be a powerful tool for broadening new possibilities in studies of individual cellular processes in a dynamic microfluidic device.     

One-dimensional uranium-organic coordination polymers: crystal and electronic structures of uranyl-diacetohydroxamate

The structure of the uranyl-diacetohydroxamate compound, UO(2)(C(2)NO(2)H(4))(2), was elucidated using a combination of single crystal X-ray diffraction measurements and all-electron scalar relativistic density functional calculations. This polymeric compound crystallizes in the C2/c space group (IT No. 15; a = 12.8386(13) ?, b = 7.5661(7) ?, c = 8.9299(9) ?, β = 103.185(2) °; Z = 4), with main-chain repeating units featuring a bidentate structure analogous to that frequently found for d-block as well as lanthanide metal ions. Density functional analysis reveals that this compound is a semiconductor, with a direct band gap of 1.1 eV.     

On the elucidation of the mechanism of Vinca alkaloid fluorination in superacidic medium

Detailed investigations on one of the key steps of the superacidic fluorination of Vinca alkaloids that is the origin of C20' activation are reported. While two different pathways can be envisioned for the emergence of the transient secondary carbocationic intermediate, isotopic labeling experiments unambiguously revealed the involvement of a 1,2-hydride shift mechanism.     

An improvement of the Nevanlinna-Gundersen theorem

A well-known result of Nevanlinna states that for two nonconstant meromorphic functions f and g on the complex plane C and for four distinct values aj∈C∪{∞}, if νf−aj=νg−aj for all 1?j?4, then g is a Möbius transformation of f. In 1983, Gundersen generalized the result of Nevanlinna to the case where the above condition is replaced by: min{νf−aj,1}=min{νg−aj,1} for j=1,2 and νf−aj=νg−aj for j=3,4. In this paper, we prove that the theorem of Gundersen remains valid to the case where min{νf−aj,1}=min{νg−aj,1} for j=1,2, and min{νf−aj,2}=min{νg−aj,2} for j=3,4. Furthermore, we work on the case where {aj} are small functions.     

Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.     

Solid state structure of thorium(IV) complexes with common aminopolycarboxylate ligands

The crystal structures of the complexes formed by reaction of thorium(IV) nitrate with iminodiacetic acid (H(2)IDA), nitrilotriacetic acid (H(3)NTA), and ethylenediaminetetraacetic acid (H(4)EDTA) under hydrothermal conditions are reported. In [Th(HIDA)(2)(C(2)O(4))]·H(2)O (1), the metal atom is chelated by two carboxylate groups from two HIDA(-) anions and by two oxalate ligands formed in situ; two additional oxygen atoms from two more HIDA(-) anions complete the ten-coordinate environment of bicapped square antiprismatic geometry. The uncoordinated nitrogen atom is protonated and involved in hydrogen bonding. Two different ligands are present in [Th(NTA)(H(2)NTA)(H(2)O)]·H(2)O (2), one of them being a O(3),N-chelating trianion which acts also as a bridge toward two neighboring metal ions, and the other being a bis-monodentate bridging species with an uncoordinated carboxylic arm and a central ammonium group. An aqua ligand completes the nine-coordinated, capped square antiprismatic metal environment. The EDTA(4-) anion in [Th(EDTA)(H(2)O)]·2H(2)O (3) is chelating through one oxygen atom from each carboxylate group and the two nitrogen atoms, as in a previously reported molecular complex. Two carboxylate groups are bridging, which, with the addition of an aqua ligand, gives a capped square antiprismatic coordination polyhedron. Aminopolycarboxylate ligands have been much investigated in relation with actinide decorporation and nuclear wastes management studies, and the present results add to the structural information available on their complexes with thorium(IV), which has mainly been obtained up to now by extended X-ray absorption fine structure (EXAFS) spectroscopy. In particular, the bridging (non-chelating) coordination mode of H(2)NTA(-) is a novel feature in this context. All three complexes crystallize as two-dimensional assemblies and are thus novel examples of thorium-organic coordination polymers.     

L-Cysteine as a chiral linker in lanthanide-cucurbit[6]uril one-dimensional assemblies

The reaction of neodymium, europium, or terbium nitrate with cucurbit[6]uril (CB6) in the presence of the α-amino acid L-cysteine (L-cys) gives the complexes [Nd(L-cys)(CB6)(NO(3))(H(2)O)(4)]·2NO(3)·10H(2)O (1) and {[Ln(L-cys)(CB6)(H(2)O)(5)][Ln(L-cys)(CB6)(NO(3))(H(2)O)(4)]}·5NO(3)·22H(2)O with Ln = Eu (2) or Tb (3). 2 and 3 only differ from 1 by the presence of two independent metal ions in slightly different environments. In all cases, each metal atom is bound to the bidentate CB6 and the monodentate L-cys molecules, with the latter being in its zwitterionic form. The ammonium group of L-cys is directed away from CB6 and is involved in ion-dipole and hydrogen bonding interactions with the uncomplexed portal of the neighboring molecule, which gives rise to the formation of chiral one-dimensional assemblies of columnar shape.     

Cohen–Macaulayness of monomial ideals and symbolic powers of Stanley–Reisner ideals

We present criteria for the Cohen–Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen–Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen–Macaulayness of the second symbolic power or of all symbolic powers of a Stanley–Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen–Macaulay. In particular, all symbolic powers are Cohen–Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen–Macaulayness can pass from a symbolic power to another symbolic powers in different ways.