Hamiltonian models of interacting fermion fields in quantum field theory

We consider Hamiltonian models representing an arbitrary number of spin 1 / 2 fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction form factors are supposed to satisfy some regularity conditions in both position and momentum space. Without any restriction on the strength of the interaction, we prove that the Hamiltonian identifies to a self-adjoint operator on a tensor product of antisymmetric Fock spaces and we establish the existence of a ground state. Our results rely on new interpolated \(N_\tau \) estimates. They apply to models arising from the Fermi theory of weak interactions, with ultraviolet and spatial cutoffs.

     

Coordinating Ability of Anions,Solvents, Amino Acids,and Gases towards Alkaline and Alkaline-Earth Elements,Transition Metals,and Lanthanides

After briefly reviewing the applications of the coordination ability indices proposed earlier for anions and solvents toward transition metals and lanthanides, a new analysis of crystal structures is applied now to a much larger number of coordinating species: anions (including those that are present in ionic solvents), solvents, amino acids, gases, and a sample of neutral ligands. The coordinating ability towards s-block elements is now also considered. The effect of several factors on the coordinating ability will be discussed: (a) the charge of an anion, (b) the chelating nature of anions and solvents, (c) the degree of protonation of oxo-anions, carboxylates and amino carboxylates, and (d) the substitution of hydrogen atoms by methyl groups in NH₃, ethylenediamine, benzene, ethylene, pyridine and aldehydes. Hit parades of solvents and anions most commonly used in the areas of transition metal, s-block and lanthanide chemistry are deduced from the statistics of their presence in crystal structures.     

(ω,c)-asymptotically periodic functions,first-order Cauchy problem,and Lasota-Wazewska model with unbounded oscillating production of red cells

In this paper, we study a new class of functions, which we call (ω,c)-asymptotically periodic functions. This collection includes asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch-periodic, and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we prove the existence and uniqueness of (ω,c)-asymptotically periodic mild solutions to the first-order abstract Cauchy problem on the real line. Also, we establish some sufficient conditions for the existence of positive (ω,c)-asymptotically periodic solutions to the Lasota-Wazewska equation with unbounded oscillating production of red cells.     

Environmental implications for online retailing

Recent press has highlighted the environmental benefits associated with online shopping, such as emissions savings from individual drivers, economies of scale in package delivery, and decreased inventories. We formulate a dual channel model for a retailer who has access to both online and traditional market outlets to analyze the impact of customer environmental sensitivity on its supply. In particular, we analyze stocking decisions for each channel incorporating price dependent demand, customer preference/utility for online channels, and channel related costs. We compare and contrast results from both deterministic and stochastic models, and utilize numerical examples to illustrate the implications of industry specific factors on these decisions. Finally, we compare and contrast the findings for disparate industries, such as electronics, books and groceries.     

Void‐Assisted Ion‐Paired Proton Transfer at Water–Ionic Liquid Interfaces

At the water–trihexyl(tetradecyl)phosphonium tris(pentafluoroethyl)trifluorophosphate ([P_14,6,6,6][FAP]) ionic liquid interface, the unusual electrochemical transfer behavior of protons (H⁺) and deuterium ions (D⁺) was identified. Alkali metal cations (such as Li⁺, Na⁺, K⁺) did not undergo this transfer. H⁺/D⁺ transfers were assisted by the hydrophobic counter anion of the ionic liquid, [FAP]^?, resulting in the formation of a mixed capacitive layer from the filling of the latent voids within the anisotropic ionic liquid structure. This phenomenon could impact areas such as proton‐coupled electron transfers, fuel cells, and hydrogen storage where ionic liquids are used as aprotic solvents.     

Adsorption of the anionic surfactant sodium dodecyl sulfate on a C18 column under micellar and high submicellar conditions in reversed‐phase liquid chromatography

Micellar liquid chromatography makes use of aqueous solutions or aqueous‐organic solutions containing a surfactant, at a concentration above its critical micelle concentration. In the mobile phase, the surfactant monomers aggregate to form micelles, whereas on the surface of the nonpolar alkyl‐bonded stationary phases they are significantly adsorbed. If the mobile phase contains a high concentration of organic solvent, micelles break down, and the amount of surfactant adsorbed on the stationary phase is reduced, giving rise to another chromatographic mode named high submicellar liquid chromatography. The presence of a thinner coating of surfactant enhances the selectivity and peak shape, especially for basic compounds. However, the risk of full desorption of surfactant is the main limitation in the high submicellar mode. This study examines the adsorption of the anionic surfactant sodium dodecyl sulfate under micellar and high submicellar conditions on a C₁₈ column, applying two methods. One of them uses a refractive index detector to obtain direct measurements of the adsorbed amount of sodium dodecyl sulfate, whereas the second method is based on the retention and peak shape for a set of cationic basic compounds that indirectly reveal the presence of adsorbed monomers of surfactant on the stationary phase.     

Highly Recyclable and Tough Elastic Vitrimers from a Defined Polydimethylsiloxane Network

Despite intensive research on sustainable elastomers, achieving elastic vitrimers with significantly improved mechanical properties and recyclability remains a scientific challenge. Herein, inspired by the classical elasticity theory, we present a design principle for ultra-tough and highly recyclable elastic vitrimers with a defined network constructed by chemically crosslinking the pre-synthesized disulfide-containing polydimethylsiloxane (PDMS) chains with tetra-arm polyethylene glycol (PEG). The defined network is achieved by the reduced dangling short chains and the relatively uniform molecular weight of network strands. Such elastic vitrimers with the defined network, i.e., PDMS-disulfide-D, exhibit significantly improved mechanical performance than random analogous, previously reported PDMS vitrimers, and even commercial silicone-based thermosets. Moreover, unlike the vitrimers with random network that show obvious loss in mechanical properties after recycling, those with the defined network enable excellent thermal recyclability. The PDMS-disulfide-D also deliver comparable electrochemical signals if utilized as substrates for electromyography sensors after the recycling. The multiple relaxation processes are revealed via a unique physical approach. Multiple techniques are also applied to unravel the microscopic mechanism of the excellent mechanical performance and recyclability of such defined network.