Trapezoidal Type Research Articles

A new extension of quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions

In this paper, we prove two identities involving quantum derivatives, quantum integrals, and certain parameters. Using the newly proved identities, we prove new inequalities of Simpson's and Newton's type for quantum differentiable convex functions under certain assumptions. Moreover, we discuss the special cases of our main results and obtain some new and existing Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities.

On Some New Inequalities of Hermite–Hadamard Midpoint and Trapezoid Type for Preinvex Functions in p,q-Calculus

In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

On Some New Trapezoidal Type Inequalities for Twice (p, q) Differentiable Convex Functions in Post-Quantum Calculus

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a p,q-integral identity involving the second p,q-derivative and then we used this result to prove some new trapezoidal type inequalities for twice p,q-differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

Some Parameterized Quantum Midpoint and Quantum Trapezoid Type Inequalities for Convex Functions with Applications.

Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and entropy, has various applications for quantum calculus. Inequalities and entropy functions have a strong association with convex functions. In this study, we prove quantum midpoint type inequalities, quantum trapezoidal type inequalities, and the quantum Simpson’s type inequality for differentiable convex functions using a new parameterized q-integral equality. The newly formed inequalities are also proven to be generalizations of previously existing inequities. Finally, using the newly established inequalities, we present some applications for quadrature formulas.

General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.

Performance evaluation of submerged breakwater using Multi-Domain Boundary Element Method

The gravity wave interaction with submerged breakwater of different structural configurations are investigated based on the small-amplitude wave theory. The boundary value problem is analysed in two-dimension using the linearized wave theory in water of finite depth. The submerged breakwater structural configuration such as (i) thin-walled type (impermeable), (ii) rectangular type (impermeable and permeable), (iii) triangular type (impermeable, permeable, perforated), (iv) trapezoidal type (impermeable, permeable, perforated) and (v) Tandem type (impermeable, permeable, perforated) are considered to analyse and performance of the breakwater. The numerical model is developed using the Multi-Domain Boundary Element Method (MDBEM) to analyse the hydrodynamic scattering coefficient (such as reflection, transmission and dissipation coefficient) for the change of physical parameters such as relative spacing between the breakwaters, relative water depth and structural dimensions. The convergence of the present numerical model is performed for the specific case of tandem breakwater and numerical computation is validated with the results available in the literature. The wave reflection and transmission coefficient along with wave force on the structure is analysed for different shapes, structural parameters and geometrical parameters of the breakwater to maximize the efficiency of breakwater. In the case of permeable breakwater, the submerged tandem breakwater is found to be more efficient in wave transformation as compared to rectangular, triangular and trapezoidal permeable submerged breakwaters. The comparative analysis performed on different configurations of the breakwater in the present study will be helpful in the effective design of the breakwater near the harbour regions.

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane mathbb{R} ^{2}. Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals

The present paper first establishes that an identity involving generalized fractional integrals is proved for differentiable functions by using two parameters. By utilizing this identity, we obtain several parameterized inequalities for the functions whose derivatives in absolute value are convex. Finally, we show that our main inequalities reduce to Ostrowski type inequalities, Simpson type inequalities and trapezoid type inequalities which are proved in earlier published papers.

Correlation between pleural tags on CT and visceral pleural invasion of peripheral lung cancer that does not appear touching the pleural surface.

To evaluate the association between a sign and visceral pleural invasion (VPI) of peripheral non-small-cell lung cancer (NSCLC) that does not appear touching the pleural surface. A total of 221 consecutive patients with NSCLC that did not appear touching the pleural surface, ≤ 3 cm in solid tumor diameter, and was surgically resected between January 2009 and December 2015 were included. We focused on the flat distortion of the tumor caused by an arch-shaped linear tag between the tumor and the pleura on CT and named it a bridge tag sign. We evaluated the associations between the clinicopathological features of the tumor, including the bridge tag sign, and VPI. We also evaluated the associations between histopathological findings and the bridge tag sign. The utility of the bridge tag sign in the diagnosis of VPI was statistically assessed. The bridge tag sign was observed in 48 (20.8%) patients. VPI was positive in 9 (4.1%) patients; among these, the bridge tag sign was positive in 8 patients. In multivariate analysis, a bridge tag sign was significantly associated with VPI. The bridge tag sign was associated with longer contact length of the pleura with the tumor and trapezoid type pleural retraction. The sensitivity, specificity, accuracy, positive predictive value, and negative predictive value of the bridge tag sign in the diagnosis of VPI were 88.9%, 83.5%, 83.7%, 18.6%, and 99.4%, respectively. A bridge tag sign on CT might improve the accuracy of the prediction of VPI. • We present the bridge tag sign which is defined as a flat distortion of an NSCLC tumor by an arch-shaped linear tag between the tumor and chest wall or interlobar fissure. • The bridge tag sign was an independent predictive factor for visceral pleural invasion. • The sensitivity, specificity, accuracy, positive predictive value, and negative predictive value of the bridge tag sign in the diagnosis of visceral pleural invasion were 88.9%, 83.5%, 83.7%, 18.6%, and 99.4%, respectively.

A PERFORMANCE EVALUATION OF TRAPEZOIDAL VARIANTS FOR NUMERICAL CUBATURE

In this work, double integration cubature schemes of Trapezoid type have been focused. Recently, some derivative-based Trapezoid-type schemes have been proposed in literature incorporating derivatives at means of the limits of integration. We carry out the exhaustive performance evaluation of the existing closed Newton-Cotes Trapezoidal (CNCT) double integral scheme with its derivative-based variants in recent literature. The derivative-free and derivative-based rules are discussed in basic forms with local error terms and composite forms with global error terms. The performance of the rules on some double integrals in the form of observed order of accuracy, computational costs and error drops demonstrates the encouraging performance of the derivative-based trapezoidal variants over the derivative-free scheme performing numerical experiments.

Some Inequalities for a New Class of Convex Functions with Applications via Local Fractional Integral

The understanding of inequalities in convexity is crucial for studying local fractional calculus efficiency in many applied sciences. In the present work, we propose a new class of harmonically convex functions, namely, generalized harmonically ψ - s -convex functions based on fractal set technique for establishing inequalities of Hermite-Hadamard type and certain related variants with respect to the Raina’s function. With the aid of an auxiliary identity correlated with Raina’s function, by generalized Hölder inequality and generalized power mean, generalized midpoint type, Ostrowski type, and trapezoid type inequalities via local fractional integral for generalized harmonically ψ - s -convex functions are apprehended. The proposed technique provides the results by giving some special values for the parameters or imposing restrictive assumptions and is completely feasible for recapturing the existing results in the relative literature. To determine the computational efficiency of offered scheme, some numerical applications are discussed. The results of the scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.

Aerodynamic performance of several passive vortex generator configurations on an Ahmed body subjected to yaw angles

We evaluate the aerodynamic performance of several passive vortex generators (VGs) placed on a standard Ahmed body, with a slant angle (α = 35º), subjected to different yawing angles (β) using RANS-based models. Rigorous validation of the numerical results is performed with previously published experimental data for (β ≤ 8º) for the Ahmed body. Our model results depict a good overall agreement with several experimental data sets. An array of different vortex generators such as the delta-winglet (DVGs), the cylindrical (CVGs) and trapezoidal (TVGs) types are introduced on to the validated model. The introduction of CVGs and DVGs tends to have a beneficial aerodynamic performance for (β = 0º). In contrast, the TVGs tend to impair the performance by producing massive flow separation over the slant for (β = 0º). Conversely, for (β > 0º), a swift transition happens with TVGs wherein the high-energy streamwise vortices that are produced tend to improve the pressure footprint, thereby reducing the overall drag. A deterioration in the performance of DVGs is predicted during (β > 4º), wherein the ‘c’-pillar vortex on the leeward side interferes with the streamwise vortical structure, which adversely influences the flow over the roof-slant edge. Overall, a maximum of ~ 8.5% and ~ 7.7% drag reduction appears to be possible with the designed CVGs and TVGs at smaller vehicle yawing conditions.

Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk

Some sharp trapezoid and midpoint type inequalities for Lipschitzian bifunctions defined on a closed disk in Euclidean sense are obtained by the use of polar coordinates. Also, bifunctions whose partial derivative is Lipschitzian are considered. A new presentation of Hermite-Hadamard inequality for convex function defined on a closed disk and its reverse are given. Furthermore, two mappings H t and h t are considered to give some generalized Hermite-Hadamard type inequalities in the case that considered functions are Lipschitzian in Euclidean sense on a disk.

Dynamical significance of generalized fractional integral inequalities via convexity

<abstract> The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type inequalities. Moreover, we establish new mid-point type and trapezoid type integral inequalities for $ (\eta_{1}, \eta_{2}) $-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for $ (\eta_{1}, \eta_{2}) $-convex function related to Fejér type. The results discussed in this paper are a generalized version of many inequalities in literature. </abstract>

On generalizations of quantum Simpson's and quantum Newton's inequalities with some parameters

&lt;abstract&gt;&lt;p&gt;In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson's and Newton's type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities.&lt;/p&gt;&lt;/abstract&gt;

Generalized integral inequalities for ABK-fractional integral operators

<abstract> In this paper, we employ new version of the Atangana-Baleanu integral operator namely $ ABK $-fractional integrals to obtain two general integral identities complying second-order derivatives for a given function. Thus allowing us to derive new generalized Hermite-Hadamard type inequalities via $ ABK $- fractional integrals. Moreover we give several new versions of Mid-point and Trapezoid type inequalities by employing Hölder, Young and Jensen inequalities. </abstract>

Certain m-Convexity Inequalities Related to Fractional Integrals with Exponential Kernels

In this paper, we establish some mid-point type and trapezoid type inequalities via a new class of fractional integral operators which is introduced by Ahmad et al. We derive a new fractional-type integral identity to obtain Dragomir-Agarwal inequality for m-convex mappings. Moreover, some inequalities of Hermite-Hadamard type for m-convex mappings are given related to fractional integrals with exponential kernels. The results presented provide extensions of those given in earlier works.

Numerical Analysis of Labyrinth Seal Performance for the Impeller Backface Cavity of a Supercritical CO2 Radial Inflow Turbine

For a radial inflow turbine (RIT), leakage flow in impeller backface cavity has critical impacts on aerodynamic performance of the RIT and axial force acting on the RIT impeller. In order to control this leakage flow, different types of labyrinth seals are numerically studied in this paper based on a supercritical carbon dioxide (S-CO2) RIT. The effects of seal clearance and cavity outlet pressure are first analyzed, and the impacts of seal design parameters, including height, number and shape of seal teeth, are evaluated. Results indicate that adding labyrinth seal can improve cavity pressure and hence adequately inhibits leakage flow. Decreasing the seal clearance and increasing the height of seal teeth are beneficial to improve sealing performance, and the same effect can be obtained by increasing the number of seal teeth. Meanwhile, employing seals can reduce leakage loss and improve RIT efficiency under a specific range of cavity outlet pressure. Finally, the influences of seal types on the flow field in seal cavity are numerically analyzed, and results demonstrate that isosceles trapezoidal type of seal cavity has better sealing performance than triangular, rectangular and right-angled trapezoidal seal cavities.

New generalized trapezoid type inequalities for complex functions defined on unit circle and applications

UDC 517.5 We establish new generalized trapezoid type inequalities for complex functions defined on unit circle via the function of bounded variation and the functions satisfying H¨older type condition. Using these results, quadrature rule formula is also provided.

New generalized trapezoidal type integral inequalities with applications

Abstract Trapezoidal inequalities for functions of diverse nature are useful in numerical computations. The authors have proved an identity for a generalized integral operator via a differentiable function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in the recent decades. Various special cases have been identified. Some applications of presented results have been analyzed.