On strong convergence in real Banach spaces obtained by dropping the Lipshitz condition

We consider an implicit iterative process for two finite families of mappings in a real Banach space and prove strong convergence results without using the Lipschitz condition on mappings. Our results mainly improve and extend the recent results of Chang et al. (2001, 2009, 2007) [1], [2], [3], Cho et al. (2005) [4], Gu (2008) [14], Ofoedu (2006) [9], Schu (1991) [13], Zeng (2003, 2005) [20], [21], and Qin et al. (2008) [11], [12].     

Convergence to common fixed points by a modified iteration process

We modify an iteration process of Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61–79, 2007) to the case of two mappings and prove some weak and strong convergence theorems for two asymptotically nonexpansive mappings. We also point out that this process cannot be used for three mappings in its existing form even for nonexpansive mappings. We have to impose an extra condition to get convergence. We give an example to show that there do exist two nonexpansive mappings satisfying that condition.     

Deterministic and random coincidence point results for f-nonexpansive maps

Some deterministic and random coincidence theorems for f-nonexpansive maps are obtained. As applications, invariant approximation theorems are derived. Our results unify, extend and complement various known results existing in the literature.     

Electrical anisotropy in the hot-forged CaBi4Ti4O15 ceramics

Textured CaBi₄Ti₄O₁₅ (CBT) ceramics have been fabricated via a hot-forging technique. The effect of grain orientation on the dielectric and electrical properties is studied by impedance (Z¹) and modulus (M¹) spectroscopy. The degree of orientation (F) calculated from X-ray diffraction pattern is found to be 89.4% along the c-axis of the crystal structure. The permittivity was measured along both perpendicular and parallel directions of the forging axis. The ratio of permittivity along perpendicular to parallel direction is found to be ～3 at the Curie temperature of 797 °C. The non-superimposition of the normalized Z″ and M″ vs. frequency plot revealed the conduction in the material is localized and deviate from ideal Debye behavior. The power law exponent n of the material has been explained on the basis of jump relaxation model and revealed the conduction through grain boundary. Activation energy (E_a) is obtained from Arrhenius plots of the dc conductivity for both the ceramics and it is found to be 0.89 eV and 0.78 eV for CBT (∥) and CBT (⊥), respectively.     

On certain analytic functions associated with Ruscheweyh derivatives and bounded Mocanu variation

Using Ruscheweyh derivative and convolution operator, we introduce a new subclass of analytic functions defined in the unit disc. Some inclusion results, a radius problem and some other interesting properties of this class are investigated.     

Common fixed points for Banach operator pairs with applications

The existence of common fixed point results for a Banach operator pair under certain generalized contractions is established. The invariant best approximation results are proved as applications and the existence of solutions of variational inequalities is obtained. We also study the solution of functional equations arising from dynamic programming.     

One-pot dichlorinative deamidation of primary β-ketoamides

An approach to the dichlorinative deamidation of primary β-ketoamides through ketonic cleavage is described, and a series of α,α-dichloroketones were furnished mostly in the presence of TEMPO. Based on control experiments, a mechanism involving tandem dichlorination and deamidation is proposed to interpret the observed reactivity.     

Fabrication of superhydrophobic filter paper and foam for oil–water separation based on silica nanoparticles from sodium silicate

Journal of Sol-Gel Science and Technology - We demonstrate the synthesis of hydrophobic silica nanoparticles from sodium silicate and their application in separation of the oil–water mixture....     

Thermal management of microelectronic devices using micro-hole cellular structure and nanofluids

Journal of Thermal Analysis and Calorimetry - We investigated the thermal performance of micro-hole cellular structure using Al2O3–H2O and CuO–H2O nanofluids with 0.67% and 0.4%,...     

Energy Conditions and Conservation Laws in LRS Bianchi Type Ⅰ Spacetimes via Noether Symmetries

In this paper, we have completely classified the locally rotationally symmetric(LRS) Bianchi Type Ⅰ spacetimes via Noether symmetries(NS). The usual Lagrangian corresponding to LRS Bianchi Type Ⅰ metric is used to find the set of determining equations. To achieve a complete classification, these determining equations are generally integrated to find the components of NS vector field and the metric coefficients. During this procedure, several cases arise which give different Noether algebras of dimension 5,..., 9, 11, and 17. A comparison is established between the obtained NS and the Killing and homothetic vectors. Corresponding to all NS generators, the conservation laws are stated by using Noether's theorem. The metrics which we have obtained as a result of our classification are shown to be anisotropic or perfect fluids which satisfy certain energy conditions.