Second-order hyperbolic s.p.d.e.'s driven by homogeneous Gaussian noise on a hyperplane

We study a class of hyperbolic stochastic partial differential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions differ. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.

     

Weakly dependent chains with infinite memory

We prove the existence of a weakly dependent strictly stationary solution of the equation _Xt=F(_Xt−1,_Xt−2,_Xt−3,…;_ξt)$X_t=F(X_{t-1},X_{t-2},X_{t-3},\dots ;{\xi }_t)$ called a chain with infinite memory. Here the innovations  _ξt${\xi }_t$ constitute an independent and identically distributed sequence of random variables. The function F$F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F$F$ and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle.     

Uniqueness results for nonlocal Hamilton-Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.     

Incorporation of nanogels within calcite single crystals for the storage,protection and controlled release of active compounds

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds. However, current formulations often employ open structures that achieve efficient loading of active agents, but that suffer undesired leakage and instability of the payloads over time. Here, a straightforward strategy that overcomes these issues is presented, in which protein nanogels are encapsulated within single crystals of calcite (CaCO₃). Demonstrating our approach with bovine serum albumin (BSA) nanogels loaded with (bio)active compounds, including doxorubicin (a chemotherapeutic drug) and lysozyme (an antibacterial enzyme), we show that these nanogels can be occluded within calcite host crystals at levels of up to 45 vol%. Encapsulated within the dense mineral, the active compounds are stable against harsh conditions such as high temperature and pH, and controlled release can be triggered by a simple reduction of the pH. Comparisons with analogous systems – amorphous calcium carbonate, mesoporous vaterite (CaCO₃) polycrystals, and calcite crystals containing polymer vesicles – demonstrate the superior encapsulation performance of the nanogel/calcite system. This opens the door to encapsulating a broad range of existing nanocarrier systems within single crystal hosts for the efficient storage, transport and controlled release of various active guest species.

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds.     

Building Giant Carbocycles by Reversible C−C Bond Formation

We describe a simple way to build giant macrocyclic hydrocarbons by the reversible formation of carbon–carbon bonds. Specifically, extended spirobifluorene‐substituted derivatives of Wittig's hydrocarbon were synthesized and found to undergo oligomerization, giving the largest hydrocarbon that has been crystallized and characterized by X‐ray diffraction to date.     

Relative quantification of long chain branching in essentially linear polyethylenes

The aim of this work is to describe a method whereby low levels of long chain branching, LCB, can be quantified on a relative basis for whole, unfractionated, and essentially linear ethylene/α-olefin copolymers. The method is based on a well established, relatively fast and robust experiment, namely the measurement of the linear viscoelastic properties by a single, isothermal, small amplitude oscillatory shear experiment. The analysis of the data is predicated on the use of the so-called van Gurp-Palmen plots (the phase angle, δ (=tan⁻¹(G″/G′)), plotted against the absolute value of the dynamic complex modulus, |G∗| = (G′²+G″²)^1/2). From this plot, the value of δ at |G∗| = 10 kPa is recorded, and it is demonstrated that the amount of LCB inversely correlates with such value of the phase angle, δ. Depending on the desired frequency range, the experiment duration varies between 15 and 60 min rendering this technique well suited for high throughput parallel testing. Its applicability is critically examined with a wide variety of commercial ethylene/α-olefin copolymers. Moreover, we have improved on the long chain branching index (LCBI) proposed by Shroff and Mavridis [Shroff RN, Mavridis H. Long-chain-branching index for essentially linear polyethylenes. Macromolecules 1999;32:8454-64] by basing it on data of truly linear polyethylenes (hydrogenated anionically synthesized polybutadienes) instead of apparently linear commercial polyethylenes.     

Using chemical probes to investigate the sub-inhibitory effects of azithromycin

The antibacterial drug azithromycin has clinically beneficial effects at sub-inhibitory concentrations for the treatment of conditions characterized by chronic Pseudomonas aeruginosa infection, such as cystic fibrosis. These effects are, in part, the result of inhibition of bacterial biofilm formation. Herein, the efficient synthesis of azithromycin in 4 steps from erythromycin and validation of the drug's ability to inhibit biofilm formation at sub-MIC (minimum inhibitory concentration) values are reported. Furthermore, the synthesis of immobilized and biotin-tagged azithromycin analogues is described. These chemical probes were used in pull-down assays in an effort to identify azithromycin's binding partners in vivo. Results from these assays revealed, as expected, mainly ribosomal-related protein binding partners, suggesting that this is the primary target of the drug. This was further confirmed by studies using a P. aeruginosa strain containing plasmid-encoded ermC, which expresses a protein that modifies 23S rRNA and so blocks macrolide entry to the ribosome. In this strain, no biofilm inhibition was observed. This work supports the hypothesis that the sub-inhibitory effects of azithromycin are mediated through the ribosome. Moreover, the synthesis of these chemical probes, and proof of their utility, is of value in global target identification in P. aeruginosa and other species.     

Formation of negative oxidation states of platinum and gold in redox ionic liquid: Electrochemical evidence

The electrochemical reduction of noble metal electrodes in the presence of redox ionic liquid, 1-ferrocenylethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [FcEMIM][TFSI], was investigated by cyclic voltammetry. Our experiments suggest the formation of metal with negative oxidation states, in the cases of platinum and gold electrodes [M_n⁻, FcEMIM⁺]. By analogy with the previous work, the formation of these phases is concomitant with the insertion of the supporting electrolyte; which correspond in our experimental condition to the redox cation of the ionic liquid. As an exciting result, the electrochemical investigations of the reduced electrode in electrolytic solution, containing solvent and supporting electrolyte, evidence the presence of the ferrocene groups at the electrode surface. Moreover, the reduced electrode exhibits the presence of the ferrocene even after, contact with air, after ultrasound, and after physical polishing, highlighting the large stability of this organo-metallic phases formed in this media. The AFM investigations demonstrate the morphological change of the platinum surface after the reduction process. Finally, our works bring a formal electrochemical proof of the presence of the ionic liquid cation inside the electrode material after the cathodic treatment in this media.     

Gadolinium chelate coated gold nanoparticles as contrast agents for both X-ray computed tomography and magnetic resonance imaging

Functionalized gold nanoparticles were applied as contrast agents for both in vivo X-ray and magnetic resonance imaging. These particles were obtained by encapsulating gold cores within a multilayered organic shell which is composed of gadolinium chelates bound to each other through disulfide bonds. The contrast enhancement in MRI stems from the presence of gadolinium ions which are entrapped in the organic shell, whereas the gold core provides a strong X-ray absorption. This study revealed that these particles suited for dual modality imaging freely circulate in the blood vessels without undesirable accumulation in the lungs, spleen, and liver.