An asymptotic version of the Gowers dichotomy and a new proof of Wagner theorem

We present an asymptotic version of the Gowers dichotomy and a new proof of a generalized version of Wagner’s theorem. They both concern weaker forms of unconditionality in the context of the asymptotic theory of Banach spaces.     

Sharp weighted logarithmic bound for maximal operators

The paper contains the study of sharp weighted logarithmic estimates for maximal operators on probability spaces equipped with a tree-like structure. These inequalities can be regarded as LlogL versions of the classical estimates of Fefferman and Stein. The proof exploits the existence of a certain special function, enjoying appropriate majorization and concavity conditions.     

Strong-coupling superconductivity induced by calcium intercalation in bilayer transition-metal dichalcogenides

We theoretically investigate the possibility of achieving a superconducting state in transition-metal dichalcogenide bilayers through intercalation, a process previously and widely used to achieve metallization and superconducting states in novel superconductors. For the Ca-intercalated bilayers MoS₂ and WS₂, we find that the superconducting state is characterized by an electron–phonon coupling constant larger than 1.0 and a superconducting critical temperature of 13.3 and 9.3 K, respectively. These results are superior to other predicted or experimentally observed two-dimensional conventional superconductors and suggest that the investigated materials may be good candidates for nanoscale superconductors. More interestingly, we proved that the obtained thermodynamic properties go beyond the predictions of the mean-field Bardeen–Cooper–Schrieffer approximation and that the calculations conducted within the framework of the strong-coupling Eliashberg theory should be treated as those that yield quantitative results.     

A new synthetic approach to 5-dethia-4-methyl-5-oxacephems

Starting from (l)-ethyl lactate and 4-vinyloxy-azetidin-2-one the diastereomeric (4S,6R)- and (4S,6S)-4-methyl-5-oxa-3-methylene and 3-oxo-cephams were obtained. The formation of the cepham skeleton proceeds with a diastereomeric excess up to 80%, depending on catalyst and reaction conditions. For comparison, the corresponding racemic cephams lacking a methyl at C-4 or with a gem-dimethyl group at C-4 were synthesized.     

On relations between gradient and classical equivariant homotopy groups of spheres

We investigate relations between stable equivariant homotopy groups of spheres in classical and gradient categories. To this end, the auxiliary category of orthogonal equivariant maps, a natural enlargement of the category of gradient maps, is used. Our result allows for describing stable equivariant homotopy groups of spheres in the category of orthogonal maps in terms of classical stable equivariant groups of spheres with shifted stems. We conjecture that stable equivariant homotopy groups of spheres for orthogonal maps and for gradient maps are isomorphic.     

A Way To Discover Maxwell's Equations Theoretically

The Coulomb force, established in the rest frame of a source-charge Q, when transformed to a new frame moving with a velocity V has a form F = q E + q v × B, where E = E′_∥ + γE′_⊥ and B = (1/c ²)v × E and E′ is the electric field in the rest frame of the source. The quantities E and B are then manifestly interdependent. We prove that they are determined by Maxwell's equations, so they represent the electric and magnetic fields in the new frame and the force F is the well known from experiments Lorentz force. In this way Maxwell's equations may be discovered theoretically for this particular situation of uniformly moving sources. The general solutions of the discovered Maxwell's equations lead us to fields produced by accelerating sources.     

HF-HCl: stationary points on the scf energy hypersurface and thermodynamics of formation

Three stationary points on the SCF 4-31G energy hypersurface of HF-HCl were examined. Two of them are real minima corresponding to HF?HCl and HCl?HF quasilinear structures. The third one, a cyclic structure, is a saddle point. The role of the basis-set superposition error and of dispersion energy is discussed for all stationary points. The process leading to the formation of the stable isomer HF?HCl is entropy controlled.     

Analysis of melanosomes from cattle eyes by pyrolysis—gas chromatography

The application of Curie-point pyrolysis—gas chromatography—mass spectrometry to the differentiation of melanosomes isolated from the retinal pigment epithelium, ciliary body and iris of cattle eyes, with special attention to the preparation and the characterization of their melanin part, was investigated. Computer data analysis and evaluation of the pyrograms obtained was used to display variations between the pyrograms of melanosomes and their components represented by sets of peak heights for comparative studies.The mechanisms of formation of the pyrolytic products and the usefulness of the proposed procedure based on pattern recognition in view of biochemical processes in melanosomes are discussed.