Some Formulae of Products of the Apostol-Bernoulli and Apostol-Euler Polynomials by Yuan He, Chunping Wang

“…Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials are established by applying the generating function methods and some summation transform techniques, and various known results are derived as special cases.…”
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Research on Parameter Sensitivity of Reasoning Formula Based on Error Principle by ZHOU Bin

“…The relative error propagation equation of the first-order algebraic precision of eachoriginal parameter can be obtained by expanding the basic equation of reasoning formula with thefirst-order Taylor formula of multivariate function. …”
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CFT and Logarithmic Corrections to the Black Hole Entropy Product Formula by Parthapratim Pradhan

“…These results have been explicitly checked by giving several examples.…”
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A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry by S. B. Rutkevich

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A Prebiotic Formula Improves the Gastrointestinal Bacterial Flora in Toddlers by Ya-Ling Chen, Fang-Hsuean Liao, Shyh-Hsiang Lin, Yi-Wen Chien

“…Our results revealed that the consumption of 3-prebiotic formula three times per day giving total intake of 1.8 g prebiotic ingredients significantly showed the increased number of probiotic Bifidobacterium spp. colonies and the reduced populations of both C. perfringens and total anaerobic bacteria on the fecal bacterial flora in toddlers at 18~36 months. …”
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Analytic Formula for the Vibration and Sound Radiation of a Nonlinear Duct by Yiu-Yin Lee

“…The main advantage of the analytic formula is that no nonlinear equation solver is required during the solution procedure. …”
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A Formula Adaptive Pixel Pair Matching Steganography Algorithm by Min Long, Fenfang Li

“…This will allow users to embed secret message directly without storing and searching the look-up table. Experimental results and analysis show that the proposed method could embed secret data directly without searching the neighborhood sets by using a formula and it still maintains flexibility in the selection of notional system, high image quality, and strong anti-steganalysis ability.…”
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RESEARCH ON ADAPTABILITY AND RELIABILITY OF DESIGN FORMULAS IN PRESSURE EQUIPMENT PRESSURE by LIU Cen, WU SengLin, YANG Fan, HONG Kai, ZHANG Shu, LIU XiaoNing

“…The researching results show that:（ 1） When the confidence of both sides was 99%,4 formulas corresponding random variables statistical samples are effective and homogeneous; if the significance was 0. 05,the 3 random variables are basically accorded with normal distribution,when the confidence of both sides was 98%,the value interval of distribution parameters are obtained.（ 2） Of the three random variables that basically fit the normal distribution,there is no significant difference in the distribution parameters of two random variables,but there is significant difference with the distribution parameters of the other one.…”
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16-Channel Hybrid WDM-PDM-MDM (de) Multiplexer for Multi-Band Large-Capacity Optical Transmission System Based on Thick Si<inline-formula><tex-math notation="LaTeX">$_{3}$</tex-mat... by Deyue Ma, Xiwen He, Chen Zhou, Mingyue Xiao, Jiqiao Liu, Weibiao Chen, Zhiping Zhou

“…We propose a novel design of hybrid multi-band wavelength/polarization/mode (de)multiplexer based on 800 nm thick Si<inline-formula><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula>N<inline-formula><tex-math notation="LaTeX">$_{4}$</tex-math></inline-formula> platform. …”
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Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions by D. Baleanu, P. Agarwal, S. D. Purohit

“…Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.…”
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Contribution for the Summation Formulas for the Generalized Hypergeometric Series F65−1 by Prathima Jayarama, Dongkyu Lim, Arjun Kumar Rathie

“…For this, we have established eight theorems containing general results. This is achieved by means of applying generalized Watson’s and Dixon’s summation formulas obtained earlier by Lavoie et al. into a known transformation formula available in the literature. …”
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Numerical analysis of application limits of Vyalov’s formula for an ice-soil thickness by Maxim Zhelnin, Anastasiia Kostina, Oleg Plekhov, Ivan Panteleev, Lev Levin

“…In order to conform results given by Vyalov’s formula and the numerical simulation, two modifications of the formula have been proposed.…”
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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. …”
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Lightweight Design of Formula Racing Sprocket based on Topology Optimization Method by Jixiong Li, Jianliang Tan, Guojie Mai

“…The physical experiments are carried out on the racing car. The results show that the sprocket optimized meets the working requirements.…”
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Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups by Dakun Zhang, Yonggang Lin, Guozhi Song

“…It includes the reflection and rotation conversion, which derived six common formulae on cycle decomposition expressions of group; it designed the generation algorithm on the cycle decomposition expressions of group, which is based on the method of replacement conversion and the classification formula; algorithm analysis and the results of the process show that the generation algorithm which is based on the classification formula is outperformed by the general algorithm which is based on replacement conversion; it has great significance to solve the enumeration of the necklace combinational scheme, especially the structural problems of combinational scheme, by using group theory and computer.…”
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Unified Compact Formulas of Output Characteristics for External Hydraulic Gear-motors by Liu Ping, Li Yulong, Hou Xinyu, Zhang Lihua

“…It is concluded that the obtaining method of output characteristics is simpler, the principle is clearer, the form is more concise, and the results are more reliable.…”
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Infant Exposure to Metals through Consumption of Formula Feeding in Mekelle, Ethiopia by Tadele Eticha, Melat Afrasa, Getu Kahsay, Hailekiros Gebretsadik

“…This study aimed at determination of heavy metals (cadmium, lead, and zinc) in milk-based infant formulas collected from Mekelle, Ethiopia, and their associated health risks to the infants through consumption of these products. …”
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Calculation of Mobility on Combined Mechanisms Based on the Modified G-K's Formula by Xu Zhaotang

“…Using the modified Grübler-Kutzbach's formula of mechanism mobility, the calculation of the mobility of combined mechanism may produce wrong results. …”
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Proposal of an objective formula-based model for equitable ranking of veterinary colleges by Robert M. Gogal, Steven David Holladay

“…This formula is designed to be readily modified within and beyond the veterinary profession.ResultsThe new ranking system works from calculations that are straightforward and transparent with little room for subjective interpretation. …”
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Accuracy of Intraocular Lens Power Calculation Formulas for Highly Myopic Eyes by Yichi Zhang, Xiao Ying Liang, Shu Liu, Jacky W. Y. Lee, Srinivasan Bhaskar, Dennis S. C. Lam

“…Results. One hundred seventy-one eyes were enrolled. …”
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