Exact Solutions for the Wick-Type Stochastic Schamel-Korteweg-de Vries Equation by Xueqin Wang, Yadong Shang, Huahui Di

“…With the aid of symbolic computation and Hermite transformation, by employing the (G′/G,1/G)-expansion method, we derive the new exact travelling wave solutions, which include hyperbolic and trigonometric solutions for the considered equations.…”
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A Transference Result of the Lp-Continuity of the Jacobi Littlewood-Paley g-Function to the Gaussian and Laguerre Littlewood-Paley g-Function by Eduard Navas, Wilfredo O. Urbina

“…We develop a transference method to obtain the Lp-continuity of the Gaussian-Littlewood-Paley g-function and the Lp-continuity of the Laguerre-Littlewood-Paley g-function from the Lp-continuity of the Jacobi-Littlewood-Paley g-function, in dimension one, using the well-known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials.…”
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On a More Accurate Half-Discrete Mulholland-Type Inequality Involving One Multiple Upper Limit Function by Xianyong Huang, Bicheng Yang

“…By the use of the weight functions, the symmetry property, and Hermite-Hadamard’s inequality, a more accurate half-discrete Mulholland-type inequality involving one multiple upper limit function is given. …”
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Operator (p, η)-Convexity and Some Classical Inequalities by Chuanjun Zhang, Muhammad Shoaib Saleem, Waqas Nazeer, Naqash Shoukat, Yongsheng Rao

“…Furthermore, we develop famous Hermite–Hadamard, Jensen type, Schur type, and Fejér’s type inequalities for this generalized function.…”
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Ostrowski Type Inequalities for s-Convex Functions via q-Integrals by Khuram Ali Khan, Allah Ditta, Ammara Nosheen, Khalid Mahmood Awan, Rostin Matendo Mabela

“…The new outcomes of the present paper are q-analogues (q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s-convex mappings. …”
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Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials by Maryam Salem Alatawi

“…The corresponding results for Hermite–Lambda polynomials are also obtained. In addition, a conclusion is given.…”
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Some Inequalities Related to Interval-Valued ηh-Convex Functions by Lei Chen, Muhammad Shoaib Saleem, Muhammad Sajid Zahoor, Rahat Bano

“…In this paper, we introduced interval-valued generalized ηh convex function and proved Hermite–Hadamard-, Jensen-, and Ostrowski-type inequalities in this generalization. …”
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A Refinement of the Integral Jensen Inequality Pertaining Certain Functions with Applications by Zaid Mohammed Mohammed Mahdi Sayed, Muhammad Adil Khan, Shahid Khan, Josip Pečarić

“…We utilize the refinement to obtain some new refinements of the Hermite-Hadamard and Hölder’s inequalities as well. …”
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Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion ⊆ Relation by Zareen A. Khan, Waqar Afzal, Mujahid Abbas, Kwara Nantomah

“…As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér-type inequalities under inclusion order relations. …”
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A generalization of Phillips operators by using the Appell polynomials of class A ( 2 ) $A^{(2)}$ by Melek Sofyalıoğlu Aksoy

“…Then we establish a quantitative Voronovskaya-type asymptotic result. We also introduce Hermite polynomials and Gould–Hopper polynomials, which are more specific examples of Appell polynomials.…”
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Proposal of a quantum version of active particles via a nonunitary quantum walk by Manami Yamagishi, Naomichi Hatano, Hideaki Obuse

“…For our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a nontrivial manner as we increase the non-Hermiticity parameter $${g}$$ ( g ) , which is similar to the classical active Brownian particle. …”
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Enhanced sensitivity via non-Hermitian topology by Midya Parto, Christian Leefmans, James Williams, Robert M. Gray, Alireza Marandi

“…We show that this peculiar response arises due to the combined synergy between non-Hermiticity and topology, something that is absent in Hermitian topological lattices. …”
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Trapezoidal Type Fejér Inequalities Related to Harmonically Convex Functions and Application by Sercan Turhan

“…Some authors introduced the concepts of the harmonically arithmetic convex functions and establish some integral inequalities of Hermite Hadamard Fejér type related to the harmonically arithmetic convex functions. …”
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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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