Operator maps of Jensen-type

Let \(\mathbb {B}_J({\mathcal {H}})\) denote the set of self-adjoint operators acting on a Hilbert space \(\mathcal {H}\) with spectra contained in an open interval J. A map \(\Phi :\mathbb {B}_J({\mathcal {H}})\rightarrow {{\mathbb {B}}}({\mathcal {H}})_\text {sa} \) is said to be of Jensen-type if

$$\begin{aligned} \Phi (C^*AC+D^*BD)\le C^*\Phi (A)C+D^*\Phi (B)D \end{aligned}$$

for all \( A, B \in \mathbb {B}_J({\mathcal {H}})\) and bounded linear operators C, D acting on \( \mathcal {H} \) with \( C^*C+D^*D=I\), where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form \(\Phi (A)=f(A)\) for some operator convex function f defined in J.

     

Sinc-Galerkin method for numerical solution of the Bratu’s problems

Study of the performance of the Galerkin method using sinc basis functions for solving Bratu’s problem is presented. Error analysis of the presented method is given. The method is applied to two test examples. By considering the maximum absolute errors in the solutions at the sinc grid points are tabulated in tables for different choices of step size. We conclude that the Sinc-Galerkin method converges to the exact solution rapidly, with order, $O(\exp{(-c \sqrt{n}}))$ accuracy, where c is independent of n.     

A simple route for the synthesis of novel N-alkyl-2-(alkylthio)-1H-imidazole derivatives

Novel $N$ -alkyl-2-(alkylthio)-1 $H$ -imidazole derivatives were synthesized in a single step by an efficient and simple method in high yields. Readily available starting materials, mild reaction conditions, operational simplicity and novelty are the key advantages of this method. Besides their novel structures, these compounds may have important biological activities and industrial applications.     

A note on “A new method for solving fully fuzzy linear programming problems”

This note shows that solving fully fuzzy linear programming (FFLP) model presented by Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 35 (2011) 817–823] needs some corrections to make the model well in general. A new version is provided in this note. A simple example is also presented to demonstrate the new form.     

DFT study of SiO2 nanoparticles as a drug delivery system: structural and mechanistic aspects

Structural Chemistry - Adsorption and reaction mechanisms for the noncovalent and covalent functionalization of SiO2 nanoparticle (SiNP) with gemcitabine (GEM) anticancer drug have been...     

Multi-objective optimization on the machining parameters for bio-inspired nanocoolant

Journal of Thermal Analysis and Calorimetry - The emphasis of this paper is to evaluate the thermophysical properties of crystalline nanocellulose (CNC)-based nanofluid and the optimized machining...     

State of the art on flow and heat transfer performance of compact fin-and-tube heat exchangers

Journal of Thermal Analysis and Calorimetry - The need for better thermal–hydraulic performance of heat exchangers remains the primary reason for further improving the design of heat...     

A Novel Bacterial Route to Synthesize Cu Nanoparticles and Their Antibacterial Activity

Journal of Cluster Science - This report focuses on a facile and one-pot way to synthesize stable Cu nanoparticles (NPs) through a bacterial approach using an inexpensive and non-toxic copper salt...