There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Climate change vulnerability, adaptation and risk perceptions at farm level in Punjab, Pakistan.

In the article, we present an elegant double inequality for the ratio of the zero-balanced hypergeometric functions, which improve and refine some previously known results and also give a positive answer the question by proposed by Ismail.

On some refinements for inequalities involving zero-balanced hypergeometric function

https://doi.org/10.1016/j.eij.2022.03.003

Smart cities: Fusion-based intelligent traffic congestion control system for vehicular networks using machine learning techniques

Abstract As early as 1917, Einstein had predicted that momentum is transferred in the absorption and emission of light, but it was not until the 1980's that such optical momentum transfer was used to cool and trap neutral atoms. By properly tuning laser light close to atomic transitions, atomic samples can be cooled to extremely low temperatures, the brightness of atomic beams can be enhanced to unprecedented values, and atoms can be manipulated with extraordinary precision. In this review several of the techniques for laser cooling and trapping of neutral atoms are described.

Cooling and trapping of neutral atoms

Revealing and elucidating chemical speciation mechanisms for lead and nickel adsorption on zeolite in aqueous solutions

In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called - polynomial preinvex functions. We use the - polynomial preinvex functions to develop - analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for - differentiable function. However, the problem has been proven to utilize the obtained identity, we give - analogues of the Ostrowski-type integrals inequalities which are connected with the - polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.

/pdf/new-estimates-of-q1q2-ostrowski-type-inequalities-within-a-2k467qdk5r.pdf

New Estimates of q1q2-Ostrowski-Type Inequalities within a Class of n-Polynomial Prevexity of Functions

By using the contemporary theory of inequalities, this study is devoted to proposing a number of refinements inequalities for the Hermite-Hadamard’s type inequality and conclude explicit bounds for two new definitions of ( p 1 p 2 , q 1 q 2 ) -differentiable function and ( p 1 p 2 , q 1 q 2 ) -integral for two variables mappings over finite rectangles by using pre-invex set. We have derived a new auxiliary result for ( p 1 p 2 , q 1 q 2 ) -integral. Meanwhile, by using the symmetry of an auxiliary result, it is shown that novel variants of the the Hermite-Hadamard type for ( p 1 p 2 , q 1 q 2 ) -differentiable utilizing new definitions of generalized higher-order strongly pre-invex and quasi-pre-invex mappings. It is to be acknowledged that this research study would develop new possibilities in pre-invex theory, quantum mechanics and special relativity frameworks of varying nature for thorough investigation.

Post Quantum Integral Inequalities of Hermite-Hadamard-Type Associated with Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre-Invex Mappings

We study and examine the Goos–Hanchen shifts of a propagating probe light field in a four-level tripodtype cold and hot atomic medium. The behavior of Goos–Hanchen shifts is studied in reflection and transmission beams in the presence of the coherent Kerr effect and the Doppler broadening effect. We observe that these shifts can be controlled by the relative propagation direction of the control field to that of the probe field.

Goos–Hänchen Shift from Cold and Hot Atomic Media Using Kerr Nonlinearity

In this paper, we present a new definition of higher-order generalized strongly preinvex functions. Moreover, it is observed that the new class of higher-order generalized strongly preinvex functions characterize various new classes as special cases. We acquire a new q 1 q 2 -integral identity, then employing this identity, we establish several two-variable q 1 q 2 -integral inequalities of Simpson-type within a class of higher-order generalized strongly preinvex and quasi-preinvex functions. Finally, the utilities of our numerical approximations have concrete applications.

https://www.mdpi.com/2073-8994/12/1/51/pdf

Muhammad Idrees

Papers

Revealing and elucidating chemical speciation mechanisms for lead and nickel adsorption on zeolite in aqueous solutions

New Estimates of q1q2-Ostrowski-Type Inequalities within a Class of n-Polynomial Prevexity of Functions

Post Quantum Integral Inequalities of Hermite-Hadamard-Type Associated with Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre-Invex Mappings

Goos–Hänchen Shift from Cold and Hot Atomic Media Using Kerr Nonlinearity

Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions