An Epiperimetric Inequality for the Regularity of Some Free Boundary Problems: The 2-Dimensional Case

Using a direct approach, we prove a two-dimensional epiperimetric inequality for the one-phase problem in the scalar and vectorial cases and for the double-phase problem. From this we deduce, in dimension 2, the C^1,α regularity of the free boundary in the scalar one-phase and double-phase problems, and of the reduced free boundary in the vectorial case, without any restriction on the sign of the component functions. Furthermore, we show that in the vectorial case each connected component of might have cusps, but they must be a finite number. © 2018 Wiley Periodicals, Inc.     

Inductively coupled plasma atomic emission spectrometry — Optimization of the operating conditions in the determination of trace of elements in line-rich emission matrices

Radial viewing 40.68 MHz inductively coupled plasma atomic emission spectrometer was used in the determination of Y, Sc and rare earth elements in Eu₂O₃ or Lu₂O₃ as pure rare earth matrices. The Mg II 280.270 nm/Mg I 285.213 nm line intensity ratio was measured to evaluate the robustness of the operating conditions. The operating conditions were affected by varying the incident power and sheathing gas flow rate. The carrier gas flow rate remained a constant value. The relationship between the Mg II 280.270 nm/Mg I 285.213 nm ratio and the excitation temperature was obtained. A dependence of the magnesium ratio in the pure solvent and the corresponding values in the presence of the above matrices was established.     

Problems,possibilities and limitations of inductively coupled plasma atomic emission spectrometry in the determination of platinum,palladium and rhodium in samples with different matrix composition

The economic and geological importance of platinum group of elements has led to the development of analytical methods to quantify them in different types of samples. In the present paper the quantitative information for spectral interference in radial viewing 40.68 MHz inductively coupled plasma atomic emission spectrometry in the determination of Pt, Pd and Rh in the presence of complex matrix, containing Al, Ca, Fe, Mg, Mn, P and Ti as matrix constituents was obtained. The database was used for optimum line selections. By using the selected analysis lines the following detection limits in ng g^− 1 were obtained: Pt 1700, Pd-1440, Rh-900. The reached detection limits determine the possibilities and limitation of the direct ICP-AES method in the determination of Pt, Pd and Rh in geological and environmental materials. The database for spectral interferences in the presence of aluminum can be used for the determination of platinum group of elements in car catalysts.     

Nuclear <Superscript>111</Superscript>Cd probes detect a hidden symmetry change at the γ → α transition in cerium considered isostructural for 60 years

We use the time-differential perturbed angular correlation technique to study nuclear electric quadupole hyperfine interactions of probe ¹¹¹Cd nuclei in cerium lattice sites at room temperature under pressures up to 8 GPa. We have found that the well known γ → α phase transition in cerium is not isostructural. In α-Ce, the probe ¹¹¹Cd nuclei reveal a quadrupole electron charge density component that is absent in γ-Ce. The hidden spacial structure of electronic quadrupoles in α-Ce is triple-q antiferroquadrupolar, as was suggested in [14]. We relate our findings to the current understanding of the γ → α phase transition and also report on nuclear quadrupole interactions in other high-pressure phases of cerium: α″ (C2/m space symmetry) and α′ (α-U structure).     

Investigation of hyperfine quadrupole interactions in UGe<Subscript>2</Subscript> and UAl<Subscript>2</Subscript> compounds on <Superscript>111</Superscript>Cd probe nuclei by the perturbed angular correlation method

The parameters of nuclear quadrupole hyperfine interaction in intermetallic UGe₂ and UAl₂ compounds have been measured in a temperature range of 100–300 K using the perturbed angular γγ correlation method on ¹¹¹Cd probe nuclei. The results obtained for UGe₂ indicate a pronounced anisotropic character in the distribution of f electrons in agreement with the calculation of the electronic structure of this compound. The hybridization degree between f electrons of U and p electrons of Al in UAl₂ is lower than the hybridization degree between f electrons of U and p electrons of Ge in UGe₂.     

Some examples on the use of atomic emission spectral analysis in analytical control of the preparation of oxide single crystals

The application of atomic emission spectrometric methods (AES) to the different stages of preparation of white sapphire and neodymium doped yttrium-aluminium garnet (Y₃Al₅O₁₂ : Nd³⁺) single crystals is discussed. Optimum conditions for d.c. arc analysis of NH₄Al(SO₄)₂·12H₂O and Al₂O₃ were established and the detection limits for impurities were determined. The applicability of laser spectral microanalysis for monitoring the distribution of neodymium in the single crystals is shown.     

The TDPAC study of the hyperfine interactions at Cd nuclei in RAl3 compounds synthesized under high pressure

The time-differential perturbed angular correlations technique (TDPAC) has been employed for measuring the parameters of hyperfine interactions in earlier known RAl₃ compounds, synthesized at high pressure (8 GPa) and high temperature, where R = La, Ce, Sm, Gd, Tb, Dy, Ho, Er, Yb and Lu. The ¹¹¹Cd(¹¹¹In) radioactive atom was used as a probe nucleus. The X-ray method has revealed that with the increase in the atomic number of a rare-earth element R, the obtained RAl₃ high-pressure phases crystallize, respectively, into orthorhombic, hexagonal and cubic structures. It has been found that in the compounds containing R=La, Ce, Sm and Gd, a deviation from earlier known structural types and the formation of new ones is observed, which is associated with the change of the stoichiometric composition of the said compounds. The results of the PAC measurements have confirmed the deviation from the predetermined stoichiometric composition 1R:3Al for the compounds LaAl₃, CeAl₃, SmAl₃ and GdAl₃ and have verified the RAl₃ stoichiometric structure for the other high-pressure phases obtained in this work.     

Optimal Potentials for Problems with Changing Sign Data

The main purpose of this paper is to study the duality and penalty method for a constrained nonconvex vector optimization problem. Following along with the image space analysis, a Lagrange-type duality for a constrained nonconvex vector optimization problem is proposed by virtue of the class of vector-valued regular weak separation functions in the image space. Simultaneously, some equivalent characterizations to the zero duality gap property are established including the Lagrange multiplier, the Lagrange saddle point and the regular separation. Moreover, an exact penalization is also obtained by means of a local image regularity condition and a class of particular regular weak separation functions in the image space.