Generalizations of some Hardy-Littlewood-Pólya type inequalities and related results
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In this paper, we use an identity of Fink and present some interesting identities and inequalities for real valued functions and r-convex functions respectively. We also obtain generalizations of some Hardy-Littlewood-P?lya type inequalities. In addition, we use the Cebysev functional and the Gr?ss type inequalities and find the bounds for the remainder in the obtained identities. Finally, we present an interesting result related to the Ostrowski type inequalities.Cite
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Chinese remainder theorem
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A new method is introduced about the remainder estimation of infinite alternating series constructed by the reciprocal of odd natural numbers.The inequality of remainder estimation range is given with the remainder of the first term to any the nth partial sum of the series and it is proved.Estimation formula is extremely simple.It is shown by calculation that relative error of the remainder estimation is smaller than 1℅ when n=5 and smaller than 1‰ when n=16.
Reciprocal
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We prove two separate lower bounds -- one for nondegenerate convex domains and the other for nondegenerate $\mathbb{C}$-convex (but not necessarily convex) domains -- for the squeezing function that hold true for all domains in $\mathbb{C}^n$, for a fixed $n\geq 2$, of the stated class. We provide explicit expressions in terms of $n$ for these estimates.
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Maxima
Chinese remainder theorem
Maxima and minima
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Remainder theorems are very popular for finding the remainder in various types of problems. In this paper, we have proposed a simplified approach of finding the remainder using basic mathematics. This method is very effective in solving certain types of problems which involve exponentiation of dividend by some positive integer and those which have common factors in their dividend and divisor. Here, we have discussed how the individual factors of the dividend can be used to find the remainder. This method is easy to understand and leads to faster remainder computation, using simple calculations and works very effectively for big dividends as well. The proof of this method is given along with an example to explain its working for both types of problems. The concept of negative remainder and repetitive application of the simplified method are also discussed. References
Chinese remainder theorem
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Sequence (biology)
Chinese remainder theorem
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Abstract The remainder equations were introduced by S. O. Hansson. In this paper, we will give an exhaustive characterization of the set of solutions for remainder equations. Moreover, solutions to some unsolved problems proposed by Hansson are reported.
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Abstract The remainder set A ⟂ B of a set of sentences A modulo a set of sentences B is the set of all maximal subsets of A not implying any element of B. A remainder equation is an expression containing remainder sets, such as { A } = B ⟂ X , in which at least one set is unknown. Solutions to some classes of remainder equations are reported, and some unsolved problems are listed.
Chinese remainder theorem
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In this paper, we study supnorm and modified H\"{o}lder estimates for the integral solution of the di-bar-equation on a class of convex domains of general type in $\C^2$ that includes many infinite type examples.
Bar (unit)
Hölder condition
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