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.     

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.     

Inertial contributions to the pressure in the truncated-cone-and-plate apparatus with application to dilute polymer solutions

New measurements of the pressure distribution generated by two Newtonian liquids in the Truncated Cone-and-Plate Apparatus are presented, in order to evaluate the exact form of the inertial contribution for a range of Reynolds numbers (Re) fromRe = 140 toRe = 36,000;Re = R ² /, where and are the liquid density and viscosity respectively,R is the plate radius, and is the angular velocity of the cone. The Walters equation for lowRe, p ^w = 0.15 ² (r² – R²), is shown to be in excellent agreement with the measurements up toRe = 1000, provided an appropriate correction for the Newtonian hole pressure is made. Up toRe = 1000, the measured slope is within 1% of the theoretical value of 0.15 given by the Walters equation; as the Reynolds number increases above 1000, the data become increasingly nonlinear inr ². Other theoretical predictions made especially for largeRe begin to disagree with the data even belowRe = 1000. The application of the experimentally determined additive inertial contribution to measurements of pressure distribution in four dilute polymer solutions is found to reproduce adequately the expected form of the viscoelastic pressure distribution, even at highRe where the Walters equation is not valid. Measurements of a combination of normal-stress differencesN ₁ + 2N ₂ for polymer solutions involving specific polymer/solvent interaction sites show a difference of 45% with change of solvent, while no difference is observed in solutions of polymers without the interaction sites. The normal-stress ratio —N ₂/N ₁ for a 5% solution of cis-polybutadiene is 0.24 at a shear rate of 100 s^–1, and it appears to approach the zero shear limit of 2/7 given by the Doi-Edwards theory. The Higashitani-Pritchard-Baird-Lodge equation relating the elastic hole pressure to the normal-stress differenceN ₁ –N ₂ gives a qualitative agreement betweenN ₁ –N ₂ from the TCP Apparatus and the hole pressure from the Stressmeter; the percent difference is 0 at shear stress < 25 Pa, 35% at = 45 Pa, and 18% at the highest = 63 Pa.