Integro-local and integral theorems for sums of random variables with semiexponential distributions

We obtain some integro-local and integral limit theorems for the sums S(n) = ξ(1) + ? + ξ(n) of independent random variables with general semiexponential distribution (i.e., a distribution whose right tail has the form $P(\xi \ge t) = e^{ - t^\beta L(t)} $ , where β ∈ (0, 1) and L(t) is a slowly varying function with some smoothness properties). These theorems describe the asymptotic behavior as x → ∞ of the probabilities P(S(n) ∈ [x, x + Δ)) and P(S(n) ≥ x) in the zone of normal deviations and all zones of large deviations of x: in the Cramér and intermediate zones, and also in the “extreme” zone where the distribution of S(n) is approximated by that of the maximal summand.     

Properties of a functional of trajectories which arises in studying the probabilities of large deviations of random walks

The deviation functional (or integral) describes the logarithmic asymptotics of the probabilities of large deviations of trajectories of the random walks generated by the sums of random variables (vectors) (see [1, 2] for instance). In this article we define it on a broader function space than previously and under weaker assumptions on the distributions of jumps of the random walk. The deviation integral turns out the Darboux integral ∫ F(t, u) of a semiadditive interval function F(t, u) of a particular form. We study the properties of the deviation integral and use the results elsewhere in [3] to prove some generalizations of the large deviation principle established previously under rather restrictive assumptions.     

Large deviation principles in boundary problems for compound renewal processes

We find explicit logarithmic asymptotics for the probability of events related to the intersection (or nonintersection) of arbitrary remote boundaries by the trajectory of a compound renewal process.     

Computing Arithmetic Functions Using Immobilised Enzymatic Reaction Networks

Living systems use enzymatic reaction networks to process biochemical information and make decisions in response to external or internal stimuli. Herein, we present a modular and reusable platform for molecular information processing using enzymes immobilised in hydrogel beads and compartmentalised in a continuous stirred tank reactor. We demonstrate how this setup allows us to perform simple arithmetic operations, such as addition, subtraction and multiplication, using various concentrations of substrates or inhibitors as inputs and the production of a fluorescent molecule as the readout.     

Local convergence of tensor methods

Mathematical Programming - In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear...     

Fundamental Aspects of Xanthene Dye Aggregation on the Surfaces of Nanocluster Polyoxometalates: H- to J-Aggregate Switching

The induced aggregation of the xanthene dye rhodamine B (RhB) on metal oxide centers belonging to the highly symmetric surfaces of precise nanoscale templates with Keplerate (Mo₁₃₂) or toroidal (Mo₁₃₈) structures has been studied. With the joint use of the Langmuir isotherm and full Stern–Volmer models, the thermodynamic reasons for dye adsorption on the nanocluster surface, such as a mixture of monomer, H-aggregate (H-dimer), and J-aggregate forms (which can coexist or switch one into another under the exact conditions), were established: this was shown through UV/Vis and fluorescence spectroscopies. By using the framework of the exciton model, it is shown that the angle (α) between the transition dipole moments of RhB is very sensitive to surface strain inside the dye sub-monolayer. As a result, it is possible to switch from H- to J-aggregates by the post-functionalization of polyoxometalate (POM)-RhB associates by the surfactant bilayer shell, which allows the surface strain to grow. Recommendations are provided for managing the appearance of H- or J-aggregates on metal oxide (or polyelectrolyte) surfaces during photovoltaic or bioimaging applications.     

Study of the Electron Density in an Inductively Coupled Plasma of Fluorine-Hydrogen-Argon Gas Mixture

Plasma Chemistry and Plasma Processing - In this paper, we present the results of non-contact measurements of electron density in an inductively coupled chemically active plasma at a pressure of...     

Polymer‐anchored mononuclear and binuclear CuII Schiff‐base complexes: Impact of heterogenization on liquid phase catalytic oxidation of a series of alkenes

Liquid phase catalytic oxidation of a number of alkenes, for example, cyclohexene, cis‐cyclooctene, styrene, 1‐methyl cyclohexene and 1‐hexene, was performed using polymer‐anchored copper (II) complexes PS‐[Cu (sal‐sch)Cl] ( 5 ), PS‐[Cu (sal‐tch)Cl] ( 6 ), PS‐[CH₂{Cu (sal‐sch)Cl}₂] ( 7 ) and PS‐[CH₂{Cu (sal‐tch)Cl}₂] ( 8 ). Neat complexes [Cu (sal‐sch)Cl] ( 1 ), [Cu (sal‐tch)Cl] ( 2 ), [CH₂{Cu (sal‐sch)Cl}₂] ( 3 ) and [CH₂{Cu (sal‐tch)Cl}₂] ( 4 ) were isolated by reacting CuCl₂·2H₂O with [Hsal‐sch] ( I ), [Hsal‐tch] ( II ), [H₂bissal‐sch] ( III ) and [H₂bissal‐tch] ( IV ), respectively, in refluxing methanol. Complexes 1–4 have been covalently anchored in Merrifield resin through the amine nitrogen of the semicarbazide or thiosemicarbazide moiety. A number of analytical, spectroscopic and thermal techniques, such as CHNS analysis, Fourier transform‐infrared, UV–Vis, PMR, ¹³C‐NMR, electron paramagnetic resonance, scanning electron microscopy, energy‐dispersive X‐ray analysis, thermogravimetric analysis, atomic force microscopy, atomic absorption spectroscopy, and electrospray ionization‐mass spectrometry, were used to analyze and establish the molecular structure of the ligands ( I )–( IV ) and complexes ( 1 )–( 8 ) in solid state as well as in solution state. Grafted complexes 5 – 8 were employed as active catalysts for the oxidation of a series of alkenes in the presence of hydrogen peroxide. Copper hydroperoxo species ([Cu^III (sal‐sch)‐O‐O‐H]), which is believed to be the active intermediate, generated during the catalytic oxidation of alkenes, are identified. It was found that supported catalysts are very economical, green and efficient in contrast to their neat complexes as well as most of the recently reported heterogeneous catalysts.     

Hyperpolarizing Concentrated Metronidazole 15NO2 Group over Six Chemical Bonds with More than 15 % Polarization and a 20 Minute Lifetime

The NMR hyperpolarization of uniformly ¹⁵N-labeled [¹⁵N₃]metronidazole is demonstrated by using SABRE-SHEATH. In this antibiotic, the ¹⁵NO₂ group is hyperpolarized through spin relays created by ¹⁵N spins in [¹⁵N₃]metronidazole, and the polarization is transferred from parahydrogen-derived hydrides over six chemical bonds. In less than a minute of parahydrogen bubbling at approximately 0.4 μT, a high level of nuclear spin polarization (P_15N) of around 16 % is achieved on all three ¹⁵N sites. This product of ¹⁵N polarization and concentration of ¹⁵N spins is around six-fold better than any previous value determined for ¹⁵N SABRE-derived hyperpolarization. At 1.4 T, the hyperpolarized state persists for tens of minutes (relaxation time, T₁≈10 min). A novel synthesis of uniformly ¹⁵N-enriched metronidazole is reported with a yield of 15 %. This approach can potentially be used for synthesis of a wide variety of in vivo metabolic probes with potential uses ranging from hypoxia sensing to theranostic imaging.