Mathematics

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17 pages, 4724 KiB

Open AccessArticle

Nonlinear Mixed Convective Flow over a Moving Yawed Cylinder Driven by Buoyancy

by Prabhugouda M. Patil, Hadapad F. Shankar and Mikhail A. Sheremet

Mathematics 2021, 9(11), 1275; https://doi.org/10.3390/math9111275 - 01 Jun 2021

Cited by 16 | Viewed by 2349

The fluid flow over a yawed cylinder is useful in understanding practical significance for undersea applications, for example, managing transference and/or separation of the boundary layer above submerged blocks and in suppressing recirculating bubbles. The present analysis examines nonlinear mixed convection flow past [...] Read more.

The fluid flow over a yawed cylinder is useful in understanding practical significance for undersea applications, for example, managing transference and/or separation of the boundary layer above submerged blocks and in suppressing recirculating bubbles. The present analysis examines nonlinear mixed convection flow past a moving yawed cylinder with diffusion of liquid hydrogen. The coupled nonlinear control relations and the border restrictions pertinent to the present flow problem are nondimensionalized by using nonsimilar reduction. Further, implicit finite difference schemes and Quasilinearization methods are employed to solve the nondimensional governing equations. Impact of several nondimensional parameters of the analysis on the dimensionless velocity, temperature and species concentration patterns and also on Nusselt number, Sherwood number and friction parameter defined at the cylinder shell is analyzed through numerical results presented in various graphs. Velocity profiles can be enhanced, and the coefficients of friction at the surface can be reduced, for increasing values of velocity ratio parameters along chordwise as well as spanwise directions. Species concentration profile is reduced, while the Sherwood number is enhanced, for growth of the Schmidt number and yaw angles. Furthermore, for an increasing value of yaw angle, skin-friction coefficient in chordwise direction diminishes in opposing buoyancy flow case, whereas the results exhibit the opposite trend in assisting buoyancy flow case. Moreover, very importantly, for increasing magnitude of nonlinear convection characteristic, the liquid velocity and surface friction enhance in spanwise direction. Further, for increasing magnitude of combined convection characteristics, velocity profiles and coefficient of friction at the surface enhance in both spanwise and chordwise directions. Moreover, we have observed that there is no deviation for zero yaw angle in Nusselt number and Sherwood number. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

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10 pages, 247 KiB

Open AccessArticle

A New Algebraic Inequality and Some Applications in Submanifold Theory

by Ion Mihai and Radu-Ioan Mihai

Mathematics 2021, 9(11), 1175; https://doi.org/10.3390/math9111175 - 23 May 2021

Cited by 2 | Viewed by 1237

Abstract

We give a simple proof of the Chen inequality involving the Chen invariant

δ (k)

of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

18 pages, 381 KiB

Open AccessArticle

Inequalities for Information Potentials and Entropies

by Ana Maria Acu, Alexandra Măduţa, Diana Otrocol and Ioan Raşa

Mathematics 2020, 8(11), 2056; https://doi.org/10.3390/math8112056 - 18 Nov 2020

Cited by 2 | Viewed by 1425

Abstract

We consider a probability distribution

(p_{0} (x), p_{1} (x), \dots)

depending on a real parameter x. The associated information potential is [...] Read more.

We consider a probability distribution

(p_{0} (x), p_{1} (x), \dots)

depending on a real parameter x. The associated information potential is

S (x) : = \sum_{k} p_{k}^{2} (x)

. The Rényi entropy and the Tsallis entropy of order 2 can be expressed as

R (x) = - log S (x)

and

T (x) = 1 - S (x)

. We establish recurrence relations, inequalities and bounds for

S (x)

, which lead immediately to similar relations, inequalities and bounds for the two entropies. We show that some sequences

{(R_{n} (x))}_{n \geq 0}

and

{(T_{n} (x))}_{n \geq 0}

, associated with sequences of classical positive linear operators, are concave and increasing. Two conjectures are formulated involving the information potentials associated with the Durrmeyer density of probability, respectively the Bleimann–Butzer–Hahn probability distribution. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

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11 pages, 320 KiB

Open AccessArticle

On an Inequality for Legendre Polynomials

by Florin Sofonea and Ioan Ţincu

Mathematics 2020, 8(11), 2044; https://doi.org/10.3390/math8112044 - 17 Nov 2020

Cited by 2 | Viewed by 1883

Abstract

This paper is concerned with the orthogonal polynomials. Upper and lower bounds of Legendre polynomials are obtained. Furthermore, entropies associated with discrete probability distributions is a topic considered in this paper. Bounds of the entropies which improve some previously known results are obtained [...] Read more.

This paper is concerned with the orthogonal polynomials. Upper and lower bounds of Legendre polynomials are obtained. Furthermore, entropies associated with discrete probability distributions is a topic considered in this paper. Bounds of the entropies which improve some previously known results are obtained in terms of inequalities. In order to illustrate the results obtained in this paper and to compare them with other results from the literature some graphs are provided. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

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21 pages, 1901 KiB

Open AccessArticle

Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains

by Daniele Mortari and David Arnas

Mathematics 2020, 8(9), 1593; https://doi.org/10.3390/math8091593 - 16 Sep 2020

Cited by 7 | Viewed by 2711

Abstract

This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) complex mapping, (b) the projection mapping, and (c) polynomial mapping. In that respect, [...] Read more.

This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) complex mapping, (b) the projection mapping, and (c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings with no closed-form inverse. Advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace boundary constraints expressed in terms of a piece-wise sequence of functions with a single function, which is compatible and required by the Theory of Functional Connections already developed for rectangular domains. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

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10 pages, 220 KiB

Open AccessArticle

Simpson’s Rule and Hermite–Hadamard Inequality for Non-Convex Functions

by Slavko Simić and Bandar Bin-Mohsin

Mathematics 2020, 8(8), 1248; https://doi.org/10.3390/math8081248 - 31 Jul 2020

Cited by 3 | Viewed by 1532

Abstract

In this article we give a variant of the Hermite–Hadamard integral inequality for twice differentiable functions. It represents an improvement of this inequality in the case of convex/concave functions. Sharp two-sided inequalities for Simpson’s rule are also proven along with several extensions. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

9 pages, 251 KiB

Open AccessArticle

Some Properties of Extended Euler’s Function and Extended Dedekind’s Function

by Nicuşor Minculete and Diana Savin

Mathematics 2020, 8(8), 1222; https://doi.org/10.3390/math8081222 - 25 Jul 2020

Cited by 2 | Viewed by 1842

Abstract

In this paper, we find some properties of Euler’s function and Dedekind’s function. We also generalize these results, from an algebraic point of view, for extended Euler’s function and extended Dedekind’s function, in algebraic number fields. Additionally, some known inequalities involving Euler’s function [...] Read more.

In this paper, we find some properties of Euler’s function and Dedekind’s function. We also generalize these results, from an algebraic point of view, for extended Euler’s function and extended Dedekind’s function, in algebraic number fields. Additionally, some known inequalities involving Euler’s function and Dedekind’s function, we generalize them for extended Euler’s function and extended Dedekind’s function, working in a ring of integers of algebraic number fields. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

14 pages, 255 KiB

Open AccessArticle

A New Extension of Hardy-Hilbert’s Inequality Containing Kernel of Double Power Functions

by Bicheng Yang, Shanhe Wu and Qiang Chen

Mathematics 2020, 8(6), 894; https://doi.org/10.3390/math8060894 - 02 Jun 2020

Cited by 14 | Viewed by 1432

Abstract

In this paper, we provide a new extension of Hardy-Hilbert’s inequality with the kernel consisting of double power functions and derive its equivalent forms. The obtained inequalities are then further discussed regarding the equivalent statements of the best possible constant factor related to [...] Read more.

In this paper, we provide a new extension of Hardy-Hilbert’s inequality with the kernel consisting of double power functions and derive its equivalent forms. The obtained inequalities are then further discussed regarding the equivalent statements of the best possible constant factor related to several parameters. The operator expressions of the extended Hardy-Hilbert’s inequality are also considered. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

12 pages, 268 KiB

Open AccessFeature PaperArticle

Convergence of Generalized Lupaş-Durrmeyer Operators

by Mohd Qasim, Mohammad Mursaleen, Asif Khan and Zaheer Abbas

Mathematics 2020, 8(5), 852; https://doi.org/10.3390/math8050852 - 24 May 2020

Cited by 1 | Viewed by 2379

Abstract

The main aim of this paper is to establish summation-integral type generalized Lupaş operators with weights of Beta basis functions which depends on

μ

having some properties. Primarily, for these new operators, we calculate moments and central moments, weighted approximation is discussed. Further, [...] Read more.

The main aim of this paper is to establish summation-integral type generalized Lupaş operators with weights of Beta basis functions which depends on

μ

having some properties. Primarily, for these new operators, we calculate moments and central moments, weighted approximation is discussed. Further, Voronovskaya type asymptotic theorem is proved. Finally, quantitative estimates for the local approximation is taken into consideration. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

12 pages, 282 KiB

Open AccessArticle

Estimates for the Differences of Certain Positive Linear Operators

by Ana Maria Acu, Sever Hodiş and Ioan Rașa

Mathematics 2020, 8(5), 798; https://doi.org/10.3390/math8050798 - 14 May 2020

Cited by 9 | Viewed by 1682

Abstract

The present paper deals with estimates for differences of certain positive linear operators defined on bounded or unbounded intervals. Our approach involves Baskakov type operators, the kth order Kantorovich modification of the Baskakov operators, the discrete operators associated with Baskakov operators, Meyer–König [...] Read more.

The present paper deals with estimates for differences of certain positive linear operators defined on bounded or unbounded intervals. Our approach involves Baskakov type operators, the kth order Kantorovich modification of the Baskakov operators, the discrete operators associated with Baskakov operators, Meyer–König and Zeller operators and Bleimann–Butzer–Hahn operators. Furthermore, the estimates in quantitative form of the differences of Baskakov operators and their derivatives in terms of first modulus of continuity are obtained. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

7 pages, 248 KiB

Open AccessCommunication

Absolute Continuity of Fuzzy Measures and Convergence of Sequence of Measurable Functions

by Jun Li

Mathematics 2020, 8(5), 726; https://doi.org/10.3390/math8050726 - 05 May 2020

Viewed by 1629

Abstract

In this note, the convergence of the sum of two convergent sequences of measurable functions is studied by means of two types of absolute continuity of fuzzy measures, i.e., strong absolute continuity of Type I, and Type VI. The discussions of convergence a.e. [...] Read more.

In this note, the convergence of the sum of two convergent sequences of measurable functions is studied by means of two types of absolute continuity of fuzzy measures, i.e., strong absolute continuity of Type I, and Type VI. The discussions of convergence a.e. and convergence in measure are done in the general framework relating to a pair of monotone measures, and general results are shown. The previous related results are generalized. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

13 pages, 322 KiB

Open AccessArticle

Inertial Krasnoselskii–Mann Method in Banach Spaces

by Yekini Shehu and Aviv Gibali

Mathematics 2020, 8(4), 638; https://doi.org/10.3390/math8040638 - 21 Apr 2020

Cited by 6 | Viewed by 2437

Abstract

In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q-uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong [...] Read more.

In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q-uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

12 pages, 267 KiB

Open AccessArticle

About Aczél Inequality and Some Bounds for Several Statistical Indicators

by Augusta Raţiu and Nicuşor Minculete

Mathematics 2020, 8(4), 574; https://doi.org/10.3390/math8040574 - 13 Apr 2020

Cited by 1 | Viewed by 1708

Abstract

In this paper, we will study a refinement of the Cauchy–Buniakowski–Schwarz inequality and a refinement of the Aczél inequality by the technique of the monotony of a sequence. In the final part, we present some properties of bounds of several statistical indicators of [...] Read more.

In this paper, we will study a refinement of the Cauchy–Buniakowski–Schwarz inequality and a refinement of the Aczél inequality by the technique of the monotony of a sequence. In the final part, we present some properties of bounds of several statistical indicators of variation. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

17 pages, 320 KiB

Open AccessArticle

Generalized Integral Transforms via the Series Expressions

by Hyun Soo Chung

Mathematics 2020, 8(4), 539; https://doi.org/10.3390/math8040539 - 06 Apr 2020

Cited by 7 | Viewed by 1632

Abstract

From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, [...] Read more.

From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

14 pages, 286 KiB

Open AccessArticle

Short Remarks on Complete Monotonicity of Some Functions

by Ladislav Matejíčka

Mathematics 2020, 8(4), 537; https://doi.org/10.3390/math8040537 - 05 Apr 2020

Cited by 2 | Viewed by 2181

Abstract

In this paper, we show that the functions

x^{m} | β^{(m)} (x) |

are not completely monotonic on

(0, \infty)

for all

m \in N,

where

β (x)

is the Nielsen’s [...] Read more.

In this paper, we show that the functions

x^{m} | β^{(m)} (x) |

are not completely monotonic on

(0, \infty)

for all

m \in N,

where

β (x)

is the Nielsen’s

β

-function and we prove the functions

x^{m - 1} | β^{(m)} (x) |

and

x^{m - 1} | ψ^{(m)} (x) |

are completely monotonic on

(0, \infty)

for all

m \in N,

m > 2,

where

ψ (x)

denotes the logarithmic derivative of Euler’s gamma function. Full article

(This article belongs to the Special Issue Applications of Inequalities and Functional Analysis)

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