Integer division by constants: optimal bounds
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DOI: 10.1016/j.heliyon.2021.e07442
Abstract: The integer division of a numerator n by a divisor d gives a quotient q and a remainder r. Optimizing compilers accelerate software by replacing the division of n by d with the division of… read more here.
Keywords: constants optimal; integer division; optimal bounds; division ... See more keywords
Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means
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DOI: 10.1186/s13660-017-1516-7
Abstract: In the article, we prove that the double inequality αL(a,b)+(1−α)T(a,b)0$ with a≠b$a\ne b $ if and only if α≥1/4$\alpha\ge1/4$ and β≤1−π/[4log(1+2)]$\beta\le1-\pi/[4\log(1+\sqrt{2})]$, where NS(a,b)$\mathit{NS}(a,b)$, L(a,b)$L(a,b)$ and T(a,b)$T(a,b)$ denote the Neuman-Sándor, logarithmic and second Seiffert means of… read more here.
Keywords: seiffert means; optimal bounds; second seiffert; logarithmic second ... See more keywords
Optimal bounds for the generalized Euler–Mascheroni constant
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DOI: 10.1186/s13660-018-1711-1
Abstract: We provide several sharp upper and lower bounds for the generalized Euler–Mascheroni constant. As consequences, some previous bounds for the Euler–Mascheroni constant are improved. read more here.
Keywords: bounds generalized; optimal bounds; mascheroni constant; euler mascheroni ... See more keywords
Optimal bounds for Toader mean in terms of general means
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DOI: 10.1186/s13660-020-02384-y
Abstract: In this paper, we present the best possible parameters α ( r ) $\alpha (r)$ , β ( r ) $\beta (r)$ such that the double inequality [ α ( r ) M r (… read more here.
Keywords: mean terms; optimal bounds; bounds toader; terms general ... See more keywords
Optimal bounds for the Sándor mean in terms of the combination of geometric and arithmetic means
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Inequalities"
DOI: 10.7153/jmi-2021-15-48
Abstract: In this paper, we prove that λ = 1/2− √ 1− e−2/p/2 and μ = 1/2−√6p/(6p) are the best possible parameters on the interval (0,1/2) such that the double inequalities G [λa+(1−λ)b,λb+(1−λ )a]A1−p (a,b) <… read more here.
Keywords: terms combination; combination geometric; bounds ndor; optimal bounds ... See more keywords