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

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 443 ◽  
Author(s):  
Humaira Kalsoom ◽  
Saima Rashid ◽  
Muhammad Idrees ◽  
Farhat Safdar ◽  
Saima Akram ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Research Study ◽  
Type Inequality ◽  
Higher Order ◽  
Auxiliary Result ◽  
Contemporary Theory ◽  
Invex Set ◽  
Quantum Integral ◽  
Novel Variants ◽  
Explicit Bounds

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.

scholarly journals New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating ℏ-Convex Functions in Hilbert Space

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 222 ◽  
Author(s):  
Saima Rashid ◽  
Humaira Kalsoom ◽  
Zakia Hammouch ◽  
Rehana Ashraf ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Convex Function ◽  
Convex Functions ◽  
Higher Order ◽  
Quasiconvex Functions ◽  
Auxiliary Result ◽  
Data Segmentation ◽  
Special Cases ◽  
Novel Variants ◽  
Convexity Theory

In Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating ℏ-convex function and predominating quasiconvex function, with respect to η , are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of η -convex functions, η -quasiconvex functions, strongly ℏ-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of κ -fractional integral operator to generate novel variants related to the Hermite–Hadamard type for p t h -order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature.

Weighted higher order exponential type inequalities in metric spaces and applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huiju Wang ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Sobolev Spaces ◽  
Exponential Type ◽  
Metric Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Geodesic Space ◽  
Stratified Lie Groups ◽  
Weighted Case

AbstractIn this paper, we establish weighted higher order exponential type inequalities in the geodesic space {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

scholarly journals Interesting Examples of Violation of the Classical Equivalence Principle but Not of the Weak One

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Antonio Accioly ◽  
Wallace Herdy
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Experimental Test ◽  
Equivalence Principle ◽  
Free Fall ◽  
Higher Order ◽  
Tree Level ◽  
Quantum Particles ◽  
Bohr Atom

The equivalence principle (EP) and Schiff’s conjecture are discussed en passant, and the connection between the EP and quantum mechanics is then briefly analyzed. Two semiclassical violations of the classical equivalence principle (CEP) but not of the weak one (WEP), i.e., Greenberger gravitational Bohr atom and the tree-level scattering of different quantum particles by an external weak higher-order gravitational field, are thoroughly investigated afterwards. Next, two quantum examples of systems that agree with the WEP but not with the CEP, namely, COW experiment and free fall in a constant gravitational field of a massive object described by its wave-function Ψ, are discussed in detail. Keeping in mind that, among the four examples focused on in this work only COW experiment is based on an experimental test, some important details related to it are presented as well.

scholarly journals Experimental test of local observer independence

2019 ◽  
Vol 5 (9) ◽  
pp. eaaw9832 ◽  
Author(s):  
Massimiliano Proietti ◽  
Alexander Pickston ◽  
Francesco Graffitti ◽  
Peter Barrow ◽  
Dmytro Kundys ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Scientific Method ◽  
Free Choice ◽  
Empirical Investigation ◽  
State Of The Art ◽  
Thought Experiment ◽  
Type Inequality ◽  
Repeated Measurements ◽  
Wigner’S Friend ◽  
Local Observer

The scientific method relies on facts, established through repeated measurements and agreed upon universally, independently of who observed them. In quantum mechanics the objectivity of observations is not so clear, most markedly exposed in Wigner’s eponymous thought experiment where two observers can experience seemingly different realities. The question whether the observers’ narratives can be reconciled has only recently been made accessible to empirical investigation, through recent no-go theorems that construct an extended Wigner’s friend scenario with four observers. In a state-of-the-art six-photon experiment, we realize this extended Wigner’s friend scenario, experimentally violating the associated Bell-type inequality by five standard deviations. If one holds fast to the assumptions of locality and free choice, this result implies that quantum theory should be interpreted in an observer-dependent way.

Some new fractional integral inequalities for generalized relative semi-m-(r; h1, h2)-preinvex mappings via generalized Mittag-Leffler function

2019 ◽  
Vol 26 (1/2) ◽  
pp. 41-55 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

scholarly journals Integrable and Superintegrable Systems with Higher Order Integrals of Motion: Master Function Formalism

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Z. Alizadeh ◽  
H. Panahi
Keyword(s):  
Quantum Mechanics ◽  
Higher Order ◽  
Supersymmetric Quantum Mechanics ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Function Formalism ◽  
Superintegrable Systems ◽  
Master Function

We construct two-dimensional integrable and superintegrable systems in terms of the master function formalism and relate them to Mielnik’s and Marquette’s construction in supersymmetric quantum mechanics. For two different cases of the master functions, we obtain two different two-dimensional superintegrable systems with higher order integrals of motion.

scholarly journals HIGHER ORDER MEASURES, GENERALIZED QUANTUM MECHANICS AND HOPF ALGEBRAS

2004 ◽  
Vol 19 (03) ◽  
pp. 197-212 ◽  
Author(s):  
C. CHRYSSOMALAKOS ◽  
MICHO ĐURĐEVICH
Keyword(s):  
Quantum Mechanics ◽  
Hopf Algebras ◽  
Higher Order ◽  
Complex Conjugate ◽  
Quantum Amplitude ◽  
Additive Measures

We study Sorkin's proposal of a generalization of quantum mechanics and find that the theories proposed derive their probabilities from k th order polynomials in additive measures, in the same way that quantum mechanics uses a probability bilinear in the quantum amplitude and its complex conjugate. Two complementary approaches are presented, a C* and a Hopf-algebraic one, illuminating both algebraic and geometric aspects of the problem.

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