Composition Formulae for the k-Fractional Calculus Operator with the S-Function by Hagos Tadesse, Haile Habenom, Anita Alaria, Biniyam Shimelis

“…In this study, the S-function is applied to Saigo’s k-fractional order integral and derivative operators involving the k-hypergeometric function in the kernel; outcomes are described in terms of the k-Wright function, which is used to represent image formulas of integral transformations such as the beta transform. …”
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A formula to calculate the spectral radius of a compact linear operator by Fernando Garibay Bonales, Rigoberto Vera Mendoza

“…There is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. …”
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Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials by Maryam Salem Alatawi

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UNCERTAINTY PRINCIPLES AND CALDER ´ON’S FORMULAS FOR THE DEFORMED HANKEL 𝐿^2_𝛼-MULTIPLIER OPERATORS by A. Chana, A. Akhlidj

“…The main purpose of this paper is to introduce the deformed Hankel 𝐿^2_𝛼-multiplier operators and to give some new results related to these operators as Plancherel’s, Calderon’s reproducing formulas and Heisenberg’s, Donoho-Stark’s uncertainty principles. …”
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On approximation of two-dimensional potential and singular operators by Charyyar Ashyralyyev, Sedanur Efe

“…The purpose of this paper is the construction of second-order of accuracy quadrature formulas for the numerical calculation of the Vekua types two-dimensional potential and singular integral operators in the unit disk of complex plane. …”
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Nutritional safety and suitability of a specific protein hydrolysate manufactured by Fonterra Co‐operative Group Ltd derived from a whey protein concentrate and used in infant formula and follow‐on formula by EFSA Panel on Nutrition, Novel Foods and Food Allergens (NDA), Torsten Bohn, Montaña Cámara, Jacqueline Castenmiller, Stefaan de Henauw, Karen‐Ildico Hirsch‐Ernst, Angeles Jos, Alexandre Maciuk, Inge Mangelsdorf, Breige McNulty, Androniki Naska, Kristina Pentieva, Alfonso Siani, Frank Thies, Laurence Castle, Mary Fewtrell, Hildegard Przyrembel, Ariane Titz, Dominique Turck

“…Abstract The European Commission asked EFSA to deliver an opinion on the nutritional safety and suitability for use in infant and follow‐on formula of a specific protein hydrolysate from whey protein concentrate manufactured by Fonterra Co‐operative Group Ltd. …”
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Tauberian-Cardy formula with spin by Sridip Pal, Zhengdi Sun

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Quadrupole formulae with cosmological constant: comparison by Denis Dobkowski-Ryłko, Jerzy Lewandowski

“…All of them lead to generalizations of the quadrupole formula, however, due to different gauge conditions and choices of the hypersurfaces, across which the energy flux is computed, it is nontrivial to see that they all coincide, as one would expect from the symplectic theory. …”
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Low Temperature Expansion in the Lifshitz Formula by M. Bordag

“…The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. …”
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Explicit Formulas Involving -Euler Numbers and Polynomials by Serkan Araci, Mehmet Acikgoz, Jong Jin Seo

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Kreĭn's trace formula and the spectral shift function by Khristo N. Boyadzhiev

“…Let A,B be two selfadjoint operators whose difference B−A is trace class. Kreĭn proved the existence of a certain function ξ∈L1(ℝ) such that tr[f(B)−f(A)]=∫ℝf′(x)ξ(x)dx for a large set of functions f. …”
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Best approximation of Hartley-Bessel multiplier operators on weighted Sobolev spaces by Ahmed Chana, Abdellatif Akhlidj

“… The main goal of this paper is to introduce the Hartley-Bessel \(L^2_\alpha\)-multiplier operators and to give for them some new results as Plancherel’s, Calderon’s reproducing formulas and Heisenberg’s, Donoho-Stark’s uncertainty principles. …”
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Asymptotic Formulae via a Korovkin-Type Result by Daniel Cárdenas-Morales, Pedro Garrancho, Ioan Raşa

“…We present a sort of Korovkin-type result that provides a tool to obtain asymptotic formulae for sequences of linear positive operators.…”
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New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions by Jarunee Soontharanon, Muhammad Ali, Shahram Rezapour, Muhammad Toseef, Thanin Sitthiwirattham

Subjects: “…open newton-cotes formulas…”
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A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry by S. B. Rutkevich

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Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation by Gusein Sh. Guseinov

“…Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. …”
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On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems by Ahmed Fadili, Hamid Bounit

“…We first present results on the validity of the inverse formula of the Laplace transform for the resolvent families associated with scalar Volterra integral equations of convolution type in Banach spaces, which extends and improves the results in Hille and Philllips (1957) and Cioranescu and Lizama (2003, Lemma 5), respectively, including the stronger version for a class of scalar Volterra integrodifferential equations of convolution type on unconditional martingale differences UMD spaces, provided that the leading operator generates a C0-semigroup. …”
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Density Formula in Malliavin Calculus by Using Stein’s Method and Diffusions by Hyun-Suk Park

“…In this paper, unlike previous studies, we will use the Stein’s method for invariant measures of diffusions to obtain the density formula of <i>G</i>. By comparing the density function obtained in this paper with that of the diffusion invariant measure, we find that the diffusion coefficient of an Itô diffusion with an invariant measure having a density can be expressed as in terms of operators in Malliavin calculus.…”
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The Efficacy and Safety of the Chinese Herbal Formula, JTTZ, for the Treatment of Type 2 Diabetes with Obesity and Hyperlipidemia: A Multicenter Randomized, Positive-Controlled, Open-Label Clinical Trial by Xiaotong Yu, Lipeng Xu, Qiang Zhou, Shengping Wu, Jiaxing Tian, Chunli Piao, Hailong Guo, Jun Zhang, Liping Li, Shentao Wu, Meizhen Guo, Yuzhi Hong, Weirong Pu, Xiyan Zhao, Yang Liu, Bing Pang, Zhiping Peng, Song Wang, Fengmei Lian, Xiaolin Tong

“…A total of 450 participants with T2D (HbA1c ≥ 7.0%; waist circumference ≥ 90 cm and 80 cm in males and females, resp.; and triglycerides (TG) ≥ 1.7 mmol/L) were randomly assigned, in equal proportions, to two groups in this multicenter randomized, positive-controlled, open-label trial. One group received JTTZ formula, and the other received metformin (MET) for 12 consecutive weeks. …”
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Gradient formulae for probability functions depending on a heterogenous family of constraints by van Ackooij, Wim, Pérez-Aros, Pedro

“…These constraints have become a very popular modelling tool and are indeed intuitively easy to understand. …”
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