scholarly journals Noncommutative Blackwell–Ross martingale inequality

2018 ◽  
Vol 21 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Ali Talebi ◽  
Mohammad Sal Moslehian ◽  
Ghadir Sadeghi
Keyword(s):  
Type Inequality ◽  
Suitable Condition ◽  
Martingale Inequality ◽  
Noncommutative Setting

We establish a noncommutative Blackwell–Ross inequality for supermartingales under a suitable condition which generalizes Khan’s work to the noncommutative setting. We then employ it to deduce an Azuma-type inequality.

On the equicontinuity of families of inverse mappings of Riemannian manifolds

2019 ◽  
Vol 16 (4) ◽  
pp. 557-566
Author(s):  
Denis Ilyutko ◽  
Evgenii Sevost'yanov
Keyword(s):  
Riemannian Manifolds ◽  
Type Inequality ◽  
The Given ◽  
Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

Green Synthesis and Spectroscopic Studies of Ag-rGO Nanocomposites for Highly Selective Mercury (II) Sensing

2018 ◽  
Vol 9 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Shubhangi J. Mane-Gavade ◽  
Sandip R. Sabale ◽  
Xiao-Ying Yu ◽  
Gurunath H. Nikam ◽  
Bhaskar V. Tamhankar
Keyword(s):  
Green Synthesis ◽  
Color Change ◽  
Limit Of Detection ◽  
Aqueous Media ◽  
Suitable Condition ◽  
Cost Effective ◽  
Spectroscopic Studies ◽  
Calibration Plot ◽  
First Time

Introduction: Herein we report the green synthesis and characterization of silverreduced graphene oxide nanocomposites (Ag-rGO) using Acacia nilotica gum for the first time. Experimental: We demonstrate the Hg2+ ions sensing ability of the Ag-rGO nanocomposites form aqueous medium. The developed colorimetric sensor method is simple, fast and selective for the detection of Hg2+ ions in aqueous media in presence of other associated ions. A significant color change was noticed with naked eye upon Hg2+ addition. The color change was not observed for cations including Sr2+, Ni2+, Cd2+, Pb2+, Mg2+, Ca2+, Fe2+, Ba2+ and Mn2+indicating that only Hg2+ shows a strong interaction with Ag-rGO nanocomposites. Under the most suitable condition, the calibration plot (A0-A) against concentration of Hg2+ was linear in the range of 0.1-1.0 ppm with a correlation coefficient (R2) value 0.9998. Results & Conclusion The concentration of Hg2+ was quantitatively determined with the Limit of Detection (LOD) of 0.85 ppm. Also, this method shows excellent selectivity towards Hg2+ over nine other cations tested. Moreover, the method offers a new cost effective, rapid and simple approach for the detection of Hg2+ in water samples.

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

DETERMINATION OF A SUITABLE CONDITION OF GRAFT COPOLYMERIZATION OF VINYLTRIETHOXYSILANE ONTO NR TO FORM NANOMATRIX STRUCTURE

2018 ◽  
Vol 91 (4) ◽  
pp. 767-775 ◽  
Author(s):  
Yuanbing Zhou ◽  
Yoshimasa Yamamoto ◽  
Seiichi Kawahara
Keyword(s):  
Silica Nanoparticles ◽  
Graft Copolymerization ◽  
Monomer Concentration ◽  
Minor Component ◽  
Suitable Condition ◽  
Average Diameter ◽  
Silica Matrix ◽  
Rubber Particles ◽  
Hydrolysis And Condensation ◽  
Nanomatrix Structure

ABSTRACT Graft copolymerization of vinyltriethoxysilane (VTES) onto NR particles in the latex stage is a unique reaction, since it occurs together with hydrolysis and condensation of the triethoxysilane group of VTES to form a colloidal silica linking to the rubber particles. These reactions may contribute to the formation of a silica nanomatrix structure that consists of a dispersoid of rubber particles as the major component and a silica matrix as the minor component. Here, the graft copolymerization of VTES followed by hydrolysis and condensation is investigated to determine a suitable condition to prepare NR with a silica nanomatrix structure. The mechanical properties of the resulting graft copolymer are discussed in relation to the morphology, silica content, and gel content of the rubber. Based on morphological observations, NR particles with an average diameter of approximately 1 μm are well dispersed in a nanomatrix consisting of silica nanoparticles. The thickness of the silica nanomatrix increases as the monomer concentration increases, and a long incubation time generates large silica nanoparticles. The tensile strength and viscoelastic properties are significantly improved by forming the silica nanomatrix structure, with its continuous structure that prevents the NR particles from merging.

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

scholarly journals Mixing rates for potentials of non-summable variations

2021 ◽  
pp. 1-18
Author(s):  
CHRISTOPHE GALLESCO ◽  
DANIEL Y. TAKAHASHI
Keyword(s):  
Invariance Principle ◽  
Type Inequality ◽  
Upper Bounds ◽  
Decay Of Correlations ◽  
Relaxation Rates ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
Coupling Inequality ◽  
Mixing Rates

Abstract Mixing rates, relaxation rates, and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. This paper exhibits upper bounds for these quantities for dynamics defined by potentials with square-summable variations. We obtain these bounds as corollaries of a new block coupling inequality between pairs of dynamics starting with different histories. As applications of our results, we prove a new weak invariance principle and a Hoeffding-type inequality.

scholarly journals A note on generalized convex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Generalized Convex Functions

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.

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