Prescribing the Jacobian in critical spaces

We consider the Sobolev space $X = W^{s,p} \left( {\mathbb{S}^m ;\mathbb{S}^{k - 1} } \right)$ . We prove the existence of a robust distributional Jacobian Ju for u ∈ X, provided sp ≥ k ? 1; this generalizes a result of Bourgain, Brezis, and the second author [10] dealing with the case m = k. We identify the image of the map X ? u ? Ju in the critical case sp = k ? 1. This extends a result of Alberti, Baldo, and Orlandi [2] for s = 1 and p = k ? 1. We also present a new, analytical, dipole construction method.     

Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains

Let Ω   be a smooth bounded simply connected domain in R²${\mathbb{R}}^2$. We investigate the existence of critical points of the energy _Eε(u)=1/2_∫Ω|∇u|²+1/(4ε²)_∫Ω(1−|u|²)²$E_{\epsilon }(u)=1/2{\int }_{\Omega }{|\mathrm{\nabla }u|}^2+1/(4{\epsilon }^2){\int }_{\Omega }{(1-{|u|}^2)}^2$, where the complex map u has modulus one and prescribed degree d on the boundary. Under suitable nondegeneracy assumptions on Ω, we prove existence of critical points for small ε. More can be said when the prescribed degree equals one. First, we obtain existence of critical points in domains close to a disk. Next, we prove that critical points exist in “most” of the domains.     

A novel design of a temperature-controlled FT-ICR cell for low-temperature black-body infrared radiative dissociation (BIRD) studies of hydrated ions

A novel design for a temperature-controlled ICR cell is described for use in black-body infrared radiative dissociation (BIRD) studies of weakly bound systems like water clusters. Due to several improved design features, it provides a very uniform black-body radiation environment, and at the same time maintains efficient pumping for a low collision rate on the order of 10^?2 s^?1. At the lowest temperatures reached, nominally 89 K cell plate temperature, water evaporation effectively ceases, while intracluster reactions in V⁺(H₂O)_n with a small activation energy are still observed. BIRD rate constants for Ag⁺(H₂O)_n, n = 4–6, are shown in the temperature range T = 160–320 K. For n = 6, a linear Arrhenius plot with R² = 0.9943 is obtained without any calibration, confirming the suitability of the cell for quantitative BIRD studies.     

Multivalued fractals in <Emphasis Type="Italic">b</Emphasis>-metric spaces

Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.     

Short‐term UV‐B Dose Stimulates Production of Protective Metabolites in Matricaria chamomilla Leaves

Physiological response of two cultivars of Matricaria chamomilla plants on UV irradiation was studied. The impact of used short‐time UV dose was evaluated in three time points; 2, 24 and 48 h after irradiation. Used UV irradiation immediately resulted in changes in plant oxidative status monitored as increased concentration of H₂O₂. Decrease in chlorophyll a and b indicated the impact on photosynthetic apparatus. For phenolic secondary metabolites, an increase in total soluble phenols and AlCl₃‐reactive flavonols was observed. The activity of main phenolic enzyme, phenylalanine ammonia‐lyase, increased with time after irradiation. Significant changes, mainly decreasing trends, in the content of free coumarins and their glycosidic precursors were observed. Enhanced accumulation in chlorogenic and 1,5‐dicaffeoylquinic acid and in (Z)‐isoform of dicycloethers was detected. From these results, the redirecting precursors of coumarin biosynthesis to biosynthesis of substances with higher antioxidative potential can be assumed. Different reactions in diploid and tetraploid plants were recorded, too.     

Influence of mechanical activation time,annealing, and Fe/O ratio on Fe3O4/Fe composites formation from Fe2O3 and Fe powders mixture

Commercially, iron (α-Fe) and hematite (α-Fe₂O₃) powders were used for the synthesis of composite powders of Fe₂O₃/Fe type by mechanical milling. Several ratios of Fe₂O₃/Fe were chosen for the composite synthesis; the atomic percent of oxygen in the starting mixtures ranged from 21 to 46 %. The Fe₂O₃/Fe composite samples with various Fe/O ratios were milled for different milling times. The milled composite samples were subjected to the heat treatments in argon up to 900 °C. During the heat treatment at temperatures that do not exceed 550 °C, Fe₃O₄/Fe composite particles are formed by the reaction between the Fe₂O₃ and Fe. Further increase of the heat treatment up to 700 °C leads to the reaction of the Fe₃O₄/Fe composite component phases, resulting thus in the formation of FeO/Fe composite. The heat treatment up to 900 °C of the Fe₂O₃/Fe leads to the formation of a composite of FeO/Fe₃O₄/Fe independent of the milling time and Fe₂O₃/Fe ratios. The onset temperatures of the Fe₃O₄ and FeO formations decrease upon increasing the milling time. Another important aspect is that, in the case of the same milling time but with a large amount of iron into the composite powder the formations temperatures of Fe₃O₄ and FeO are also decreasing. The influence of the mechanical activation time, heat treatment temperature, and Fe/O ratio on the formation of the (Fe₃O₄, FeO)/Fe composite from Fe₂O₃+Fe precursor mixtures was studied by differential scanning calorimetry and X-ray diffraction techniques.     

Recent developments in the field of Thermal Analysis and Calorimetry in Romania and Republic of Moldova

Journal of Thermal Analysis and Calorimetry -     

Behaviour of the Primary Nitro Group Under Denitration Conditions

ABSTRACT

Treatment of per-O-acetylated or acetalated glycosylnitromethanes derived from the common hexoses and pentoses with tributyltin hydride and a catalytic amount of a radical initiator [1,1′-azobis(cyclohexanecarbonitrile)] in refluxing benzene easily afforded the corresponding glycosylmethanal oximes in 84-97% yields. Per-O-acetylated C-β-glycopyranosylmethanal oximes were employed for synthesis of versatile C-β-glycopyranosyl cyanides of the β-D-gluco, β-D-manno, β-D-galacto, β-D-xylo, and β-L-rhamno configurations.     

Embeddings, Operator Ranges, and Dirac Operators

We present a generalized operator range construction associated to an indefinite unbounded selfadjoint operator that yields closed embeddings of Kreĭn spaces. As an application we obtain an energy space representation, in the sense of Friedrichs, of a general free Dirac operator.