Products of resolvents and multivalued hybrid mappings in CAT(0) spaces

In this article, we introduce and investigate the concept of multivalued hybrid mappings in CAT(0) spaces by using the concept of quasilinearization. Also, we present a new iterative algorithm involving products of Moreau-Yosida resolvents for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in CAT(0) spaces.     

Biomimetic Epxidation of Alkenes by Phenyliodonium Diacetate [PhI(OAc)_2] in the Presence of Mn(Ⅲ) Complex of meso-Tetrakis(4-methoxyphenylporphyrin) Acetate Mn[(T4-OCH_3P)P]OAc

We have reported that phenyliodonium diacetate[PhI(OAc)2] can serve as an eco-friendly mild oxidant for the epoxidation of alkenes in the presence of Mn(III) complex of meso-tetrakis(4-methoxyphenylporphyrin) acetate Mn[(T4-OCH3P)P]OAc and imidazole in CH2Cl2.The amounts of the products(%) and selectivities are very dependent upon the electronic and steric properties of the starting alkenes.To evaluate the validity of this catalytic system for C H activation,cyclohexane and ethylbenzene were oxidized under ...     

Ionic liquid-based dispersive liquid–liquid microextraction for determination of trace amounts of iron in water, rock and human blood serum samples

A green and sensitive dispersive liquid-phase microextraction procedure based on room-temperature ionic liquid (1-hexyl-3-methylimidazolium hexafluorophosphate) for preconcentration and determination of total iron in real samples prior to flame atomic absorption spectrometry was developed. 2-Mercaptopyridine-N-oxide (pyrithione) and ethanol were used as complexing agent and dispersive solvent in the proposed method, respectively. The factors influencing the extraction were optimized. Under optimum conditions, the enhancement factor of 15 was obtained from only 11.35 mL of aqueous phase. The linear dynamic range and the detection limit were 10.0–700 and 2.4 μg L^?1, respectively. The relative standard deviation (RSD) for ten replicate measurements of 500 μg L^?1 of iron is 3.1 %. The developed method has been successfully applied for the determination of iron in water samples, human blood serum and rock certified reference material with high efficiency.     

A shift‐adaptive meshfree method for solving a class of initial‐boundary value problems with moving boundaries in one‐dimensional domain

A new shift‐adaptive meshfree method for solving a class of time‐dependent partial differential equations (PDEs) in a bounded domain (one‐dimensional domain) with moving boundaries and nonhomogeneous boundary conditions is introduced. The radial basis function (RBF) collocation method is combined with the finite difference scheme, because, unlike with Kansa's method, nonlinear PDEs can be converted to a system of linear equations. The grid‐free property of the RBF method is exploited, and a new adaptive algorithm is used to choose the location of the collocation points in the first time step only. In fact, instead of applying the adaptive algorithm on the entire domain of the problem (like with other existing adaptive algorithms), the new adaptive algorithm can be applied only on time steps. Furthermore, because of the radial property of the RBFs, the new adaptive strategy is applied only on the first time step; in the other time steps, the adaptive nodes (obtained in the first time step) are shifted. Thus, only one small system of linear equations must be solved (by LU decomposition method) rather than a large linear or nonlinear system of equations as in Kansa's method (adaptive strategy applied to entire domain), or a large number of small linear systems of equations in the adaptive strategy on each time step. This saves a lot in time and memory usage. Also, Stability analysis is obtained for our scheme, using Von Neumann stability analysis method. Results show that the new method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution, and the adaptive grading scheme is effective in localizing oscillations due to sharp gradients or discontinuities in the solution. The efficiency and effectiveness of the proposed procedure is examined by adaptively solving two difficult benchmark problems, including a regularized long‐wave equation and a Korteweg‐de Vries problem. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1622–1646, 2016     

Coupled Criticality Analysis of Inflation and Unemployment

In this paper, we focus on the critical periods in the economy that are characterized by unusual and large fluctuations in macroeconomic indicators, like those measuring inflation and unemployment. We analyze U.S. data for 70 years from 1948 until 2018. To capture their fluctuation essence, we concentrate on the non-Gaussianity of their distributions. We investigate how the non-Gaussianity of these variables affects the coupling structure of them. We distinguish “regular” from “rare” events, in calculating the correlation coefficient, emphasizing that both cases might lead to a different response of the economy. Through the “multifractal random wall” model, one can see that the non-Gaussianity depends on time scales. The non-Gaussianity of unemployment is noticeable only for periods shorter than one year; for longer periods, the fluctuation distribution tends to a Gaussian behavior. In contrast, the non-Gaussianities of inflation fluctuations persist for all time scales. We observe through the “bivariate multifractal random walk” that despite the inflation features, the non-Gaussianity of the coupled structure is finite for scales less than one year, drops for periods larger than one year, and becomes small for scales greater than two years. This means that the footprint of the monetary policies intentionally influencing the inflation and unemployment couple is observed only for time horizons smaller than two years. Finally, to improve some understanding of the effect of rare events, we calculate high moments of the variables’ increments for various q orders and various time scales. The results show that coupling with high moments sharply increases during crises.