A diagonal quasi-Newton updating method for unconstrained optimization

Numerical Algorithms - A diagonal quasi-Newton updating algorithm is presented. The elements of the diagonal matrix approximating the Hessian are determined by minimizing both the size of the...     

p-Adic Analogue of the Wave Equation

In this paper, a p-adic analogue of the wave equation with Lipschitz source is considered. Since it is hard to arrive the solution of the problem, we propose a regularized method to solve the problem from a modified p-adic integral equation. Moreover, we give an iterative scheme for numerical computation of the regularlized solution.

     

Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures. Part I: model description and validation

Nonlinear Dynamics - This paper is first of the two papers dealing with the nonlinear modelling and investigation of coupled cross-flow and in-line vortex-induced vibrations (VIVs) of flexible...     

Nano‐Ruby: A Promising Fluorescent Probe for Background‐Free Cellular Imaging

Bioprobes based on fluorescent ruby nanoparticles, which are suitable for ultrasensitive imaging, are reported. A stable aqueous/buffer colloid, permitting facile conjugation to proteins, is produced by femtosecond laser ablation of ruby and the nanoparticles (mean size 17 nm) are photostable, with long lifetime (1–4 ms) 694 nm emission. With time‐gating complete (>20 dB) suppression of cell autofluorescence and suppression of exogenous fluorophores is observed. Nanoparticles are imaged in as‐grown cells and those immunolabeled with quantum dots. Immunoassay binding to target biomolecules is also demonstrated.     

Highly Efficient Trityl-Nitroxide Biradicals for Biomolecular High-Field Dynamic Nuclear Polarization

Dynamic nuclear polarization (DNP) is a powerful method to enhance the sensitivity of solid-state magnetic nuclear resonance (ssNMR) spectroscopy. However, its biomolecular applications at high magnetic fields (preferably>14 T) have so far been limited by the intrinsically low efficiency of polarizing agents and sample preparation aspects. Herein, we report a new class of trityl-nitroxide biradicals, dubbed SNAPols that combine high DNP efficiency with greatly enhanced hydrophilicity. SNAPol-1, the best compound in the series, shows DNP enhancement factors at 18.8 T of more than 100 in small molecules and globular proteins and also exhibits strong DNP enhancements in membrane proteins and cellular preparations. By integrating optimal sensitivity and high resolution, we expect widespread applications of this new polarizing agent in high-field DNP/ssNMR spectroscopy, especially for complex biomolecules.     

The Effect of Calcium-Silicate Cements on Reparative Dentinogenesis Following Direct Pulp Capping on Animal Models

Dental pulp vitality is a desideratum for preserving the health and functionality of the tooth. In certain clinical situations that lead to pulp exposure, bioactive agents are used in direct pulp-capping procedures to stimulate the dentin-pulp complex and activate reparative dentinogenesis. Hydraulic calcium-silicate cements, derived from Portland cement, can induce the formation of a new dentin bridge at the interface between the biomaterial and the dental pulp. Odontoblasts are molecularly activated, and, if necessary, undifferentiated stem cells in the dental pulp can differentiate into odontoblasts. An extensive review of literature was conducted on MedLine/PubMed database to evaluate the histological outcomes of direct pulp capping with hydraulic calcium-silicate cements performed on animal models. Overall, irrespective of their physico-chemical properties and the molecular mechanisms involved in pulp healing, the effects of cements on tertiary dentin formation and pulp vitality preservation were positive. Histological examinations showed different degrees of dental pulp inflammatory response and complete/incomplete dentin bridge formation during the pulp healing process at different follow-up periods. Calcium silicate materials have the ability to induce reparative dentinogenesis when applied over exposed pulps, with different behaviors, as related to the animal model used, pulpal inflammatory responses, and quality of dentin bridges.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

Variable Dimensionality of Europium(III) and Terbium(III) Coordination Compounds with a Flexible Hexacarboxylate Ligand

A reaction between 4,4′,4″-(benzene-1,3,5-triyltris(oxy))triphthalic acid (H₆L) and lanthanide(III) nitrates (Ln = Eu³⁺, Tb³⁺) in water under the same conditions gave a molecular coordination compound [Tb(H_4.5L)₂(H₂O)₅]∙6H₂O in the case of terbium(III) and a one-dimensional linear coordination polymer {[Eu₂(H₃L)₂(H₂O)₆]∙8H₂O}_n in the case of europium(III). The crystal structures of both compounds were established by single-crystal X-ray diffraction, and they were further characterized by powder X-ray diffraction, thermogravimetric analysis and infrared spectroscopy. The compounds demonstrated characteristic lanthanide-centered photoluminescence. The lanthanide-dependent dimensionality of the synthesized compounds, which are the first examples of the coordination compounds of hexacarboxylic acid H₆L demonstrates its potential as a linker for new coordination polymers.     

Structural Diversity and Carbon Dioxide Sorption Selectivity of Zinc(II) Metal-Organic Frameworks Based on Bis(1,2,4-triazol-1-yl)methane and Terephthalic Acid

A three-component reaction between the 1,4-benzenedicarboxylic (terephthalic) acid (H₂bdc), bis(1,2,4-triazol-1-yl)methane (btrm) and zinc nitrate was studied, and three new coordination polymers were isolated by a careful selection of the reaction conditions. Coordination polymers {[Zn₃(DMF)(btrm)(bdc)₃]·nDMF}_∞ and {[Zn₃(btrm)(bdc)₃]·nDMF}_∞ containing trinuclear {Zn₃(bdc)₃} secondary building units are joined by btrm auxiliary linkers into three-dimensional metal–organic frameworks. The coordination polymer {[Zn(bdc)(btrm)]∙nDMF}_∞ consists of Zn²⁺ cations joined by bdc²⁻ and btrm linkers into a two-fold interpenetrated network. Upon activation, MOF [Zn₃(btrm)(bdc)₃]_∞ demonstrated CO₂/N₂ adsorption selectivity with an ideal adsorbed solution theory (IAST) factor of 21. All three MOF demonstrated photoluminescence with a maximum near 435–440 nm upon excitation at 330 nm.     

Simple vertices of maximal minor polytopes

Themaximal minor polytope Π _{m, n} is the Newton polytope of the product of all maximal minors of anm×n matrix of indeterminates. The family of polytopes {Π _{m, n} } interpolates between the symmetric transportation polytope (form=n−1) and the permutohedron (form=2). Both transportation polytope and the permutohedron aresimple polytopes but in general Π _{m, n} is not simple. The main result of this paper is an explicit construction of a class of simple vertices of Π _{m, n} for generalm andn. We call themvertices of diagonal type. For every such vertexv we explicitly describe all the edges and facets of Π _{m, n} which containv. Simple vertices of Π _{m, n} have an interesting algebro-geometric application: they correspond tononsingular extreme toric degenerations of the determinantal variety ofm×n matrices not of full rank. Andrei Zelevinsky was partially supported by the NSF under Grant DMS-9104867.