scholarly journals Expansion of Generalized Hukuhara Differentiable Interval Valued Function

2019 ◽  
Vol 15 (03) ◽  
pp. 553-570
Author(s):  
Priyanka Roy ◽  
Geetanjali Panda
Keyword(s):  
Higher Dimension ◽  
Interval Valued Function ◽  
Generalized Hukuhara Differentiability ◽  
Monotonic Property ◽  
Theoretical Results ◽  
Interval Valued ◽  
Theoretical Developments

In this paper, the concept of [Formula: see text]-monotonic property of interval valued function in higher dimension is introduced. Expansion of interval valued function in higher dimension is developed using this property. Generalized Hukuhara differentiability is used to derive the theoretical results. Several examples are provided to justify the theoretical developments.

scholarly journals Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nidhi Sharma ◽  
Sanjeev Kumar Singh ◽  
Shashi Kant Mishra ◽  
Abdelouahed Hamdi
Keyword(s):  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Interval Valued Function ◽  
Preinvex Functions ◽  
Theoretical Results ◽  
Interval Valued

AbstractIn this paper, we introduce $(h_{1},h_{2})$ ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.

scholarly journals Some Inequalities for LR-$$\left({h}_{1}, {h}_{2}\right)$$-Convex Interval-Valued Functions by Means of Pseudo Order Relation

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Kottakkaran Sooppy Nisar ◽  
Khadiga Ahmed Ismail ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Critical Role ◽  
Order Relation ◽  
Strong Relationship ◽  
New Class ◽  
Starting Point ◽  
Interval Valued Function ◽  
Fejér Inequality ◽  
Definition Of ◽  
Interval Valued

AbstractIn both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of the definition of convexity, both concepts convexity and integral inequality depend on each other. Therefore, the relationship between convexity and symmetry is strong. Whichever one we work on, we introduced the new class of generalized convex function is known as LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued function (LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -IVF) by means of pseudo order relation. Then, we established its strong relationship between Hermite–Hadamard inequality (HH-inequality)) and their variant forms. Besides, we derive the Hermite–Hadamard–Fejér inequality (HH–Fejér inequality)) for LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued functions. Several exceptional cases are also obtained which can be viewed as its applications of this new concept of convexity. Useful examples are given that verify the validity of the theory established in this research. This paper’s concepts and techniques may be the starting point for further research in this field.

scholarly journals Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches

2020 ◽  
Vol 26 (13-14) ◽  
pp. 1119-1132 ◽  
Author(s):  
Vinciane Guillot ◽  
Arthur Givois ◽  
Mathieu Colin ◽  
Olivier Thomas ◽  
Alireza Ture Savadkoohi ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Internal Resonance ◽  
Harmonic Balance Method ◽  
Mode Shapes ◽  
Governing Equations ◽  
Internal Resonances ◽  
Thin Beam ◽  
Beam Focusing ◽  
Theoretical Results ◽  
Theoretical Developments

Experimental and theoretical results on the nonlinear dynamics of a homogeneous thin beam equipped with piezoelectric patches, presenting internal resonances, are provided. Two configurations are considered: a unimorph configuration composed of a beam with a single piezoelectric patch and a bimorph configuration with two collocated piezoelectric patches symmetrically glued on the two faces of the beam. The natural frequencies and mode shapes are measured and compared with those obtained by theoretical developments. Ratios of frequencies highlight the realization of 1:2 and 1:3 internal resonances, for both configurations, depending on the position of the piezoelectric patches on the length of the beam. Focusing on the 1:3 internal resonance, the governing equations are solved via a numerical harmonic balance method to find the periodic solutions of the system under harmonic forcing. A homodyne detection method is used experimentally to extract the harmonics of the measured vibration signals, on both configurations, and exchanges of energy between the modes in the 1:3 internal resonance are observed. A qualitative agreement is obtained with the model.

scholarly journals On Properties of the Choquet Integral of Interval-Valued Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Lee-Chae Jang
Keyword(s):  
Convergence Theorem ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Interval Valued Function ◽  
Interval Valued

Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of interval-valued functions. We also discuss convergence in the(C)mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem for the Choquet integral of measurable interval-valued functions.

Helicopter Ground Resonance Phenomenon With Blade Stiffness Dissimilarities: Experimental and Theoretical Developments

2012 ◽  
Author(s):  
Leonardo Sanches ◽  
Guilhem Michon ◽  
Alain Berlioz ◽  
Daniel Alazard
Keyword(s):  
Equations Of Motion ◽  
Resonance Phenomenon ◽  
Aging Effects ◽  
Ground Resonance ◽  
Different Types ◽  
Stability Chart ◽  
Instability Regions ◽  
The Stability ◽  
Theoretical Results ◽  
Theoretical Developments

Recent works study the ground resonance in helicopters under the aging effects. Indeed, the blades lead-lag stiffness may vary randomly with time and be different from each other (i.e.: anisotropic rotor). The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon is determined through numerical investigations on the periodical equations of motion, treated by using Floquet’s theory. Stability chart highlights the appearance of new instability zones as function of the perturbation introduced on the lead-lag stiffness of one blade. In order to validate the theoretical results, a new experimental setup is designed and developed. The ground resonance instabilities are investigated for different types of rotor configurations (i.e.: isotropic and anisotropic rotors) and the boundaries of stability are determined. A good correlation between both theoretical and experimental results is obtained and the new instability zones, found in asymmetric rotors, are verified experimentally. The temporal responses of the measured signals highlight the exponential divergence at the instability regions.

scholarly journals Effective Weak Non-Ieptonic Hamiltonians for Flavour Changing Processes

1982 ◽  
Vol 35 (3) ◽  
pp. 235 ◽  
Author(s):  
Robert DC Miller ◽  
Bruce HJ McKellar
Keyword(s):  
Numerical Analysis ◽  
Effective Theory ◽  
Complete Analysis ◽  
Matrix Formalism ◽  
Minimal Subtraction ◽  
The Standard Model ◽  
Ms Scheme ◽  
Detailed Application ◽  
Theoretical Results ◽  
Theoretical Developments

We present a complete analysis of the W mediated effective weak non-leptonic theory for s, c, b and t flavour changing processes. Calculations are based upon the standard model with n generations. The theory is developed using a matrix formalism which leads to compact theoretical results and a simpler numerical analysis. In our analysis we take account of scheme and effective theory dependence of the QCD parameters. Explicit numerical calculations are performed for effective weak non-leptonic Hamiltonians describing s, c, band t decay, in both the penguin free and penguin generating sectors of the theory, for the modified minimal subtraction (ms) scheme and IX = 0 gauge. Our approach is to display the calculations as a detailed application of the Appelquist-Carazzone decoupling theorem incorporating some of the latest theoretical developments in this area.

scholarly journals Some Hadamard–Fejér Type Inequalities for LR-Convex Interval-Valued Functions

2021 ◽  
Vol 6 (1) ◽  
pp. 6
Author(s):  
Muhammad Bilal Khan ◽  
Savin Treanțǎ ◽  
Mohamed S. Soliman ◽  
Kamsing Nonlaopon ◽  
Hatim Ghazi Zaini
Keyword(s):  
Order Relation ◽  
Inclusion Relation ◽  
Hadamard Inequality ◽  
New Class ◽  
Starting Point ◽  
Interval Valued Function ◽  
Fejér Inequality ◽  
Interval Space ◽  
Interval Valued

The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation ( ≤p ). This order relation is defined on interval space. We have proved that if the interval-valued function is LR-convex then the inclusion relation “ ⊆ ” coincident to pseudo-order relation “ ≤p ” under some suitable conditions. Moreover, the interval Hermite–Hadamard–Fejér inequality is also derived for LR-convex interval-valued functions. These inequalities also generalize some new and known results. Useful examples that verify the applicability of the theory developed in this study are presented. The concepts and techniques of this paper may be a starting point for further research in this area.

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