Variational wave equations of two fermions interacting via scalar,pseudoscalar, vector,pseudovector and tensor fields

We consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.     

Noise generation by vacuum cleaner suction units: Part II. Effect of vaned diffuser on noise characteristics

Noise emitted by a vacuum cleaner suction unit has aerodynamic, mechanical and electromagnetic noise origins. The aerodynamically generated noise within the blower mostly prevails in the total emitted noise at design and off-design operations. The vaned diffuser built into the blower has an important effect on the aerodynamically generated noise and its spectra. Therefore, in this part of the paper, the effects of the vaned diffuser on the performance and noise characteristics have been measured and analysed at the design and off-design operation. Analysis of measurement results have shown that the built-in vaned diffuser has numerous disadvantages, including: increase in the rotational noise, increase in the non-rotational turbulent noise, especially at off-design operation, increase in production costs and reduction of the flow rate. Therefore, and due to variable operating conditions of the suction units built into a vacuum cleaner, it could be omitted or replaced by a vaneless one.     

Combinatorial solution-phase synthesis of alkyl (1S*,2S*,3R*,5R*,6R*)-1-alkyl-3-aryl-6-benzoylamino-1-hydroxy-7- oxo-5-phenylhexahydropyrazolo[1,2-a]pyrazole-2-carboxylates

Combinatorial solution-phase cycloadditions of (1Z,4R*,5R*)-4-benzoylamino-5-phenylpyrazolidin-3-on-1-azomethine imines 3 to beta-keto esters 4 afforded a library of 26 bicyclic pyrazolidinones 5 in 6-89% yields and in 14-100% de. All products were isolated in >90% purity according to 1H NMR, and 25 of them were analytically pure. The structures of cycloadducts were confirmed by NMR and X-ray diffraction. Most of the products were isolated as mixtures of the major (1S*,2S*,3R*,5R*,6R*)-epimers 5 and the minor (1R*,2S*,3R*,5R*,6R*)-epimers 6. Epimerization of cycloadducts 5/6 at the anomeric position 1 in solution was confirmed by 1H NMR.     

Universal scaling of the conductivity at the superfluid-insulator phase transition

The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from omega k scaling of the conductivity towards omega k/T scaling at low Matsubara frequencies omega k. By careful analytic continuation using Padé approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with omega/T at small frequencies and low temperatures. We estimate the universal dc conductivity to be sigma* = 0.45(5)Q2/h, distinct from previous estimates in the T = 0, omega/T > 1 limit.     

New heterometallic copper zinc alkoxides: synthesis, structure properties and pyrolysis to Cu/ZnO composites

The copper compound [(THF)KCu(O^tBu)₃]_∞ 1 was obtained by interaction of a 1:1 mixture of ZnCl₂/CuCl₂ with KO^tBu. Bi- and trifunctional aminoalcohols were used to synthesize the intramolecularly donor stabilized Cu(II) alkoxides Cu(OCH(R)CH₂NMe₂)₂ (3: R=Me, 4: =CH₂NMe₂) where 4 was structurally characterized. Lewis acid–base adduct formation with (Me₃Si)₃CZnCl gave the heterodinuclear compounds (Me₃Si)₃CZnCl · Cu(OCH(R)CH₂NMe₂)₂ (5: R=Me, 6: R=CH₂NMe₂), which were characterized by X-ray single-crystal structure analysis. The two metal centers Cu and Zn of 5 and 6 are bridged by two oxygen atoms to form a Cu–O–Zn core. Pyrolysis of compounds 5 and 6 in dry argon or a H₂/N₂ mixture at atmospheric pressure forms metallic copper and zinc oxide, whereas pyrolysis under O₂/Ar forms additionally oxidized copper species. Elemental analysis of the pyrolysis products showed carbon and nitrogen contamination. Scanning electron microscopy and energy dispersive X-ray analysis were performed to get information on the morphology and the chemical composition of the pyrolysis products.     

Oxidative ring-opening of rel-(2R,3R,5S)-5-aryl-2-benzoylamino-6,7-bis(methoxycarbonyl)-2,3-dihydro-1-oxo-3-phenyl-1H,5H-pyrazolo[1,2-a]-pyrazoles. Synthesis of rel-(2R,3R)-3-phenyl-3-[5-aryl-3,4-bis(methoxycarbonyl)pyrazolyl-1]alanine esters

rel-(2R,3R)-N-Benzoylamino-6,7-bis(methoxycarbonyl)-2,3-dihydro-1-oxo-1H,5H-pyrazolot[1,2-a]-pyrazoles 5 , accesible by cycloaddition of dimethyl acetylenedicarboxylate ( 3 ) to (1Z)-rel-(4R,5R)-1-aryl-methylidene-4-benzoylamino-5-phenyl-3-pyrazolidinone-1-azomethine imines 4 , undergo oxidative ring cleavage with methanolic bromine giving rel-(2R,3R)-N-benzoyl-3-phenyl-3-[5-aryl-3,4-bis(methoxy-carbonyl)pyrazolyl-1]alanine methyl esters 6 as products.     

Coordination Chemistry of Aluminum,Gallium, and Indium at Transition Metals

The current upswing in the interest in organoelement chemistry of Group 13 metals is attributed not least to the establishment of the coordination chemistry of R_aE fragments (E=Al, Ga, In; a=1, 2) at d-block metals (M). Recently the availability of low-valent organoelement compounds as building blocks for synthesis has substantially enriched the structure chemistry of this class of compounds. The M–E bonding conditions and the question of the significance of M(d_π)-E(p_π) backbonding as well as potential applications in materials science, for example, as single-source precursors for the deposition of thin intermetallic films by chemical vapor deposition, are discussed.     

Noncommutative Polynomials Describing Convex Sets

Foundations of Computational Mathematics - The free closed semialgebraic set $${\mathcal {D}}_f$$ determined by a hermitian noncommutative polynomial $$f\in {\text {M}}_{{\delta }}({\mathbb...     

Detection of cavitation in operation of kinetic pumps. Use of discrete frequency tone in audible spectra

Safe operation of kinetic pumps, as liquid movers, can be threatened by cavitation phenomenon in, amongst others. Cavitation is the Achilles’ heel of kinetic pumps. It can cause deterioration of the hydraulic performance, damage of the pump by pitting and material erosion, and structure vibration and noise. Cavitation can appear within the entire range of operating conditions, therefore it must by all means be prevented. To prevent cavitation in a pump we have to know the beginning and development of the cavitation in the pump. For this purpose, the emitted noise in the audible range can be used, amongst other possibilities. Experiments have shown that there is a discrete frequency tone within the audible noise spectra, which is in strong correlation with development of the cavitation process in the pump. Therefore, the discrete frequency tone can be separated from the noise spectra of a cavitating pump and used to detect the incipient of cavitation and its development as well as to prevent the onset of the cavitation process in the pump, by means of initiating an alarm, shutdown, or control signal via an electrical control system.     

Internalization of (bis)phosphonate-modified cellulose nanocrystals by human osteoblast cells

Covalent conjugation of (bis)phosphonate group-containing molecules, sodium Alendronate (Aln) and 3-AminoropylPhosphoric Acid (ApA), to Cellulose nanocrystals (CNCs) was performed via oxidation/Shiff-base reaction. Further fluorescent labelling with Rhodamine B Iso ThioCyanate (RBITC) was performed to follow CNCs interaction and potential internalization with/in human osteoblasts by confocal microscopy. Complementary analyses were applied to identify the conjugation (Atenuated Total Reflectance–Fourier Transform Infrared and UV–VIS spectroscopies), physico-chemical (Dynamic Light Scattering and Nanoparticle Tracking Analysis) and morphological (Transmission Electron Microscopy) features of native and ApA/Aln-modified CNCs in physiologically relevant environments (Phosphate Buffer Saline, Advanced Dulbecco’s Modified Eagle Medium). While conjugation did not affect the CNCs` size, the RBITC-labelling promotes their aggregation. Faster (1 h vs. 2 h) uptake by osteoblasts of RBITC-CNCoxAln, compared to RBITC-CNCoxApA, and no-internalization (in 24 h) of native RBITTC-CNC, indicate a higher affinity of Aln-modified CNCs to the cells, while all CNCs (in 0.25–0.06 wt%) promote the cell growth. Aln/Apa-modified CNCs shows high potential in drug-delivery for bone therapies, and theranostics.