A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media by Tongjun Sun, Keying Ma

“…Under the regularity assumption for the pressure, cubic Hermite finite element method is used for the pressure equation, which ensures the approximation of the velocity smooth enough. …”
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Uniform Treatment of Jensen’s Inequality by Montgomery Identity by Tahir Rasheed, Saad Ihsan Butt, Đilda Pečarić, Josip Pečarić, Ahmet Ocak Akdemir

“…As an application, we give generalized variants of Hermite–Hadamard inequality. Montgomery identity has a great importance as many inequalities can be obtained from Montgomery identity in q−calculus and fractional integrals. …”
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Existence and Uniqueness of Weak Solutions for a New Class of Convex Optimization Problems Related to Image Analysis by Anas Tiarimti Alaoui, Mostafa Jourhmane

“…Initially, a family of new diffusion functions based on cubic Hermite spline is provided for optimal image denoising. …”
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Differential representations of dynamical oscillator symmetries in discrete Hilbert space by Andreas Ruffing

“…., a discrete Hilbert space structure. Generalized q-Hermite functions and systems of creation and annihilation operators are derived. …”
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Some Improvements of Jensen’s Inequality via 4-Convexity and Applications by Hidayat Ullah, Muhammad Adil Khan, Tareq Saeed, Zaid Mohammed Mohammed Mahdi Sayed

“…We acquire new improvements of the Hölder and Hermite–Hadamard inequalities with the help of the main results. …”
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Trapezium-Type Inequalities for k-Fractional Integral via New Exponential-Type Convexity and Their Applications by Artion Kashuri, Sajid Iqbal, Saad Ihsan Butt, Jamshed Nasir, Kottakkaran Sooppy Nisar, Thabet Abdeljawad

“…New generalizations of Hermite–Hadamard-type inequality for the s,m-exponential-type convex function ψ and for the products of two s,m-exponential-type convex functions ψ and ϕ are proved. …”
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Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators by K. Zhukovsky

“…We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. …”
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Beam Shaping by Mode Superposition With Coefficient Optimization by Guowen Zhang, Hang Sun, Ziyang Chen, Yanli Zhang, Jixiong Pu, Jianqiang Zhu

“…One conventional approach for beam shaping is using the superposition of eigenmodes, such as the Hermite-Gaussian (HG) modes. However, despite the generation of a flat-top beam by HG modes with identical coefficients, it is challenging to achieve other specific intensity distributions by this method. …”
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The Computational Solution of Generalized Inverse Eigenvalue Problem for Pseudo-Jacobi Matrix by Fuxia Yi, Enhua Li

“…This paper is concerned with two generalized inverse eigenvalue problems for a kind of pseudo-Jacobi matrix. From a non-Hermite matrix, an r×r Jacobi matrix, two distinct real eigenvalues, and part of the corresponding eigenvectors, an n×n pseudo-Jacobi matrix is constructed. …”
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Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption by O. D. Makinde

“…The steady-state problem is solved using a perturbation technique together with a special type of the Hermite-Padé approximants. Graphical results are presented and discussed quantitatively with respect to various embedded parameters controlling the systems. …”
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A new class of generalized polynomials associated with Milne-Thomson-based poly-Bernoulli polynomials by Waseem Ahmad Khan, Divesh Srivastava, Kottakkaran Sooppy Nisar

“…As obvious special cases of the newly introduced polynomials, we also called power sum-Laguerre-Hermite polynomials and generalized Laguerre and poly-Bernoulli polynomials and present some of their involved identities and formulas. …”
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Dynamical Techniques for Analyzing Iterative Schemes with Memory by Neha Choubey, A. Cordero, J. P. Jaiswal, J. R. Torregrosa

“…The parameters have been defined by Hermite interpolating polynomial that allows the accelerating effect. …”
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Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application by Yuanpeng Zhu, Xuli Han, Shengjun Liu

“…The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape parameters. …”
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Circular thin plates buckling analysis with HRPIM method by Baid Sokayna, Hilali Youssef, Mesmoudi Saïd, Bourihane Oussama

“…The algorithm integrates high-order continuation (HOC) solver and the Hermite-type radial point interpolation method (HRPIM). …”
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On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira by L. M. B. C. Campos

“…As an application, these generalized series can be used to generate special functions with complex parameters (Campos 1986), e.g., the Hermite and Bessel types.…”
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Connectivity, Information Jumps, and Market Stability: An Agent-Based Approach by Khaldoun Khashanah, Talal Alsulaiman

“…Three experiments examine the role of hubs, normal agents, and hermits in the network when intermediate combinations of agent types have information awareness. …”
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Generating Solar Sail Trajectories in the Earth-Moon System Using Augmented Finite-Difference Methods by Geoffrey G. Wawrzyniak, Kathleen C. Howell

“…Two augmented finite-difference methods (FDMs) are developed and compared to a Hermite-Simpson collocation scheme. With 101 evenly spaced nodes, solutions from the FDM are locally accurate to within 1740 km. …”
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Linear Bending Wave Propagation in Laminar and Turbulent Disks by Callum W. Fairbairn

“…We clearly elucidate the theory from first principles, wherein the general Fourier–Hermite formalism can be simplified to a reduced framework which extends previous results toward locally isothermal disks. …”
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Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation by Waqar Afzal, Khurram Shabbir, Mubashar Arshad, Joshua Kiddy K. Asamoah, Ahmed M. Galal

“…Our first step was to establish the Hermite−Hadamard H.H inequality and then to establish Jensen inequality using these notions. …”
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Bayesian Approach for Sequential Probabilistic Back Analysis of Uncertain Geomechanical Parameters and Reliability Updating of Tunneling-Induced Ground Settlements by Cong Li, Shui-Hua Jiang, Jinhui Li, Jinsong Huang

“…Within the framework of the proposed approach, a complex Bayesian back analysis problem is transformed into an equivalent structural reliability problem based on subset simulation. Hermite polynomial chaos expansion-based surrogate models are constructed to improve the computational efficiency of probabilistic back analysis. …”
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