Regularity of the Fractional Maximal Function

The purpose of this work is to show that the fractional maximaloperator has somewhat unexpected regularity properties. Themain result shows that the fractional maximal operator mapsL^p-spaces boundedly into certain first-order Sobolev spaces.It is also proved that the fractional maximal operator preservesfirst-order Sobolev spaces. This extends known results for theHardy-Littlewood maximal operator. 2000 Mathematics SubjectClassification 42B25, 46E35.     

Invariant and angular variables for five particle processes

Angles and rapidity variables which are simply related to the invariants of a five-particle process are derived and the connecting equations established. Classification of the different forms of the phase space integral, obtained by successive use of these equations, is given. The symmetric treatment clarifies the meaning of several (commonly used or here introduced) sets of variables.     

Kinetics of reactions between methyl and acetyl radicals in gas phase produced by flash photolysis of acetic anhydride

The reaction products of photolysis of acetic anhydride in gas phase at 25°C, where He or CO₂ was present as buffer gas, were analyzed by gas chromatography. The extent of photodissociation was 52% ± 5% and the extent of intramolecular hydrogen transfer reaction producing acetic acid and ketene was 48% ± 5%. The rate constants of the hydrogen exchange and radical combination reactions between methyl and acetyl radicals were calculated from the amounts of products. The value of the ratio of the rate constants of hydrogen exchange and radical combination reactions between methyl and acetyl radicals, ??₇/??₆ = 0.15, indicates that acetyl radical is a relatively poor hydrogen donor. The corresponding ratio of rate constants for the reactions between two acetyl radicals, ??₉/??_s = 0.42, indicates that acetyl radical is a better hydrogen acceptor than methyl radical.     

Molecular Engineering of Fracture Energy Dissipating Sacrificial Bonds Into Cellulose Nanocrystal Nanocomposites

Even though nanocomposites have provided a plethora of routes to increase stiffness and strength, achieving increased toughness with suppressed catastrophic crack growth has remained more challenging. Inspired by the concepts of mechanically excellent natural nanomaterials, one‐component nanocomposites were fabricated involving reinforcing colloidal nanorod cores with polymeric grafts containing supramolecular binding units. The concept is based on mechanically strong native cellulose nanocrystals (CNC) grafted with glassy polymethacrylate polymers, with side chains that contain 2‐ureido‐4[1H]‐pyrimidone (UPy) pendant groups. The interdigitation of the grafts and the ensuing UPy hydrogen bonds bind the nanocomposite network together. Under stress, UPy groups act as sacrificial bonds: simultaneously providing adhesion between the CNCs while allowing them to first orient and then gradually slide past each other, thus dissipating fracture energy. We propose that this architecture involving supramolecular binding units within side chains of polymer grafts attached to colloidal reinforcements opens generic approaches for tough nanocomposites.     

All-cellulose multilayers: long nanofibrils assembled with short nanocrystals

Self-organized multilayer films were formed by sequential addition of oppositely charged cellulose I nanoparticles. The all-cellulosic multilayers were prepared via adsorption of cationicially modified cellulose nanofibrils (cat NFC) and anionic short crystalline cellulose (CNC) at pH 4.5 and pH 8.3. The properties and build-up behavior of layer-by-layer-constructed films were studied with microgravimetry (QCM-D) and the direct surface forces in these systems were explored with colloidal probe microscopy to gain information about the fundamental interplay between cat NFC and anionic CNC. The importance of the first layer on the adsorption of the consecutive layers was demonstrated by comparing pure in situ adsorption in the QCM-D with multilayer films made by spin coating the first cationic NFC layer and then subsequently adsorbing the following layers in situ in the QCM-D chamber. Differences in adsorbed amount and viscoelastic behavior were observed between those two systems. In addition, a significant pH dependence of cat NFC charge was found for both direct surface interactions and layer properties. Moreover the underlying cellulose layer in multilayer film was established to influence the surface forces especially at lower pH, where the cat NFC chains extensions were facilitated and overall charge was affected by the cationic counterpart within the layers. This enhanced understanding the effect of charge and structure on the interaction between these renewable nanoparticles is valuable when designing novel materials based on nanocellulose.     

On compactness of the difference of composition operators

Let φ and ψ be analytic self-maps of the unit disc, and denote by C_φ and C_ψ the induced composition operators. The compactness and weak compactness of the difference T=C_φ−C_ψ are studied on H^p spaces of the unit disc and L^p spaces of the unit circle. It is shown that the compactness of T on H^p is independent of p∈[1,∞). The compactness of T on L¹ and M (the space of complex measures) is characterized, and examples of φ and ψ are constructed such that T is compact on H¹ but non-compact on L¹. Other given results deal with L^∞, weakly compact counterparts of the previous results, and a conjecture of J.E. Shapiro.     

Degradation and Crystallization of Cellulose in Hydrogen Chloride Vapor for High‐Yield Isolation of Cellulose Nanocrystals

Despite the structural, load‐bearing role of cellulose in the plant kingdom, countless efforts have been devoted to degrading this recalcitrant polysaccharide, particularly in the context of biofuels and renewable nanomaterials. Herein, we show how the exposure of plant‐based fibers to HCl vapor results in rapid degradation with simultaneous crystallization. Because of the unchanged sample texture and the lack of mass transfer out of the substrate in the gas/solid system, the changes in the crystallinity could be reliably monitored. Furthermore, we describe the preparation of cellulose nanocrystals in high yields and with minimal water consumption. The study serves as a starting point for the solid‐state tuning of the supramolecular properties of morphologically heterogeneous biological materials.     

Copper(I) Bromide: An Alternative Emitter for Blue‐Colored Flame Pyrotechnics

Copper(I) bromide was evaluated as an alternative emitter for blue flame pyrotechnic compositions. CuBr and CuCl emission spectra were recorded from a butane torch flame and compared. Cu(BrO₃)₂ was synthesized and used in pyrotechnic compositions as an oxidizer and the source for the generation of CuBr species. Pyrotechnic compositions, which contained copper and potassium bromates as oxidizers, were optimized for the generation of blue flames. The experimental data, including emission spectra of the flames, chromaticity coordinates, burning rates, luminous intensities, and sensitivity tests, were analyzed and compared.