Flocking in noisy environments

In recent years, a number of articles proposed mathematical models for emergent phenomena. This is the case, for instance for the flocking of birds or the schooling of fish. In particular, in [F. Cucker, S. Smale, Emergent behavior in flocks, IEEE Trans. on Autom. Control 52 (2007) 852–862], a model was proposed for flocking and it was proved that under certain conditions on the initial positions and velocities of the birds, flocking occurs. In this paper we modify this model by adding random noise to it. We prove that, under conditions similar to those just mentioned, (nearly) flocking occurs in finite time with a certain confidence.     

Inequalities for the Extended Best Polynomial Approximation Operator in Orlicz Spaces

In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m~p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.     

Controlled Synthesis of Oligomers Containing Main-Chain B(sp2)-B(sp2) Bonds

A number of novel alkynyl-functionalized diarylbis(dimethylamino)diboranes(4) are prepared by salt metathesis, and the appended alkynyl groups are subjected to hydroboration. Their reactions with monohydroboranes lead to discrete boryl-appended diborane(4) species, while dihydroboranes induce their catenation to oligomeric species, the first known examples of well-characterized macromolecular species with B−B bonds. The oligomeric species were found to comprise up to ten repeat units and are soluble in common organic solvents. Some of the oligomeric species have good air stability and all were characterized by NMR and vibrational spectroscopy and size-exclusion chromatography techniques.     

An HPLC method for the determination of adenosine diphosphate: An important marker of hexokinase activity in metabolic diseases

Hexokinases play a critical role in the cellular uptake and utilization of glucose. As such, they are of fundamental importance to all cells. By catalyzing glucose to produce glucose‐6‐phosphate, hexokinases control the first irreversible step of glucose metabolism and initiate all major pathways of glucose consumption. Our objective was to develop and validate highly sensitive and selective high‐performance liquid chromatography with photodiode array detector (HPLC‐PDA) assays allowing the determination of adenosine diphosphate, which was used for the determination of hexokinase activity. Samples were analyzed by HPLC‐PDA using a C₁₈ analytical column (250 × 4.6 mm) for chromatographic separation. Optimal detection was achieved based on isocratic elution with a mobile phase consisting of a mixture of sodium phosphate monobasic buffer and methanol. This method met all of the requirements of specificity, sensitivity, linearity, precision, accuracy and stability generally accepted in bioanalytical chemistry and was successfully applied to a study of hexokinase activity in an alloxan‐induced diabetic rat model. Determination of hexokinase activity will permit characterization of cellular metabolic state in many diseases, such as cancer and diabetes.     

Boranediyl- and Diborane(4)-1,2-diyl-Bridged Platinum A-Frame Complexes

Diplatinum A-frame complexes with a bridging (di)boron unit in the apex position were synthesized in a single step by the double oxidative addition of dihalo(di)borane precursors at a bis(diphosphine)-bridged Pt⁰₂ complex. While structurally analogous to well-known μ-borylene complexes, in which delocalized dative three-center-two-electron M-B-M bonding prevails, theoretical investigations into the nature of Pt−B bonding in these A-frame complexes show them to be rare dimetalla(di)boranes displaying two electron-sharing Pt−B σ-bonds. This is experimentally reflected in the low kinetic stability of these compounds, which are prone to loss of the (di)boron bridgehead unit.     

Facile Formation of Redox‐Active Totally Organic Nanoparticles in Water by In Situ Reduction of Organic Precursors Stabilized through Aromatic–Aromatic Interactions by Aromatic Polyelectrolytes

The formation of redox‐active, totally organic nanoparticles in water is achieved following a strategy similar to that used to form metal nanoparticles. It is based on two fundamental concepts: i) complexation through aromatic–aromatic interactions of a water‐soluble precursor aromatic molecule with polyelectrolytes bearing complementary charged aromatic rings, and ii) reduction of the precursor molecule to achieve stabilized nanoparticles. Thus, formazan nanoparticles are synthesized by reduction of a tetrazolium salt with ascorbic acid using polyelectrolytes bearing benzene sulfonate residues of high linear aromatic density, but cannot be formed in the presence of nonaromatic polyelectrolytes. The red colored nanoparticles are efficiently encapsulated in calcium alginate beads, showing macroscopic homogeneity. Bleaching kinetics with chlorine show linear rates on the order of tenths of milli­meters per minute. A linear behavior of the dependence of the rate of bleaching on the chlorine concentration is found, showing the potential of the nanoparticles for chlorine sensing.

     

Simulation of Single-Phase Multicomponent Flow Problems in Gas Reservoirs by Eulerian–Lagrangian Techniques

Over the past two decades most discussions of the simulation of miscible displacement in porous media were related to incompressible flow problems; recently, however, attention has shifted to compressible problems. The first goal of this paper is the derivation of the governing equations (mathematical models) for a hierarchy of miscible isothermal displacements in porous media, starting from a very general single-phase, multicomponent, compressible flow problem; these models are then compared with previously proposed models. Next, we formulate an extension of the modified method of characteristics with adjusted advection to treat the transport and dispersion of the components of the miscible fluid; the fluid displacement must be coupled in a two-stage operator-splitting procedure with a pressure equation to define the Darcy velocity field required for transport and dispersion, with the outer stage incorporating an implicit solution of the nonlinear parabolic pressure equation and an inner stage for transport and diffussion in which the mass fraction equations are solved sequentially by first applying a globally conservative Eulerian–Lagrangian scheme to solve for transport, followed by a standard implicit procedure for including the diffusive effects. The third objective is a careful investigation of the underlying physics in compressible displacements in porous media through several high resolution numerical experiments. We consider real binary gas mixtures, with realistic thermodynamic correlations, in homogeneous and heterogeneous formations.