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261 articles for “S-Numbers”
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Research ArticleOpen accessEvery word in the titleA Simple and Accurate Relation Between the Logarithm Integral Li(x) and the Primes Counting Function π(x) is Derived Making use of the O.E.I.S. Prime Numbers “Sequences”Paolo AscarelliToday the prime numbers π(x) contained under the number x appears to be somewhat overestimated by the logarithm integral function Li(x) and underestimated by the function x/ln(x), both originally proposed by Gauss around 1792-1796. However, a simple and accurate expression, relating Li(x) and π(x), may be derived using the data reported on the O.E.I.S. “Sequences”. This relation can also suggest … …Journal of Mathematics and Statistics, Vol. 17, Issue 1 · 30 Sep 2021 · 7,739 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleS-Numbers of Weighted Shift Operators on P-Summable Formal Entire Functions of M-VariablesNashat Faried, Z.A. Hassanain, H. Abd El Ghaffar, A. LokmanThe idea of multiplying a formal Taylor power series by z to make a right shift operator on the space of all square summable sequences of real numbers was due to A.L. Shield. In this work, we consider Taylor power series in m-variables and we give upper and lower estimations of s-numbers for multiplication of m- right weighted shift operators. … …Journal of Mathematics and Statistics, Vol. 15, Issue 1 · 3 May 2019 · 6,922 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleEXTENDED MASS RELATION FOR SEVEN FUNDAMENTAL MASSES AND NEW EVIDENCE OF LARGE NUMBERS HYPOTHESISCurtis J. Forsythe, Dimitar T. ValevA previously derived mass relation has been extended to seven equidistant fundamental masses covering an extremely large mass range from ~10-69 to ~1053 kg. Six of these masses are successfully identified as mass of the observable universe, Eddington mass limit of the most massive stars, mass of hypothetical quantum “Gravity Atom” whose gravitational potential is equal to electrostatic potential e2/S, … …Physics International, Vol. 5, Issue 2 · 16 Jul 2014 · 8,271 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleTHE COMPLEX STATISTICS PARADIGM AND THE LAW OF LARGE NUMBERSAbdo Abou JaoudeThe five basic axioms of Kolmogorov define the probability in the real set R and do not take into consideration the imaginary part which takes place in the complex set C, a problem that we are facing in applied mathematics. Whatever the probability distribution of the random variable in R is, the corresponding probability in the whole set C equals … …Journal of Mathematics and Statistics, Vol. 9, Issue 4 · 9 Oct 2013 · 8,199 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleTesting Randomness: Poker Test with Hands of Three NumbersWael Mohamed Fawaz Abdel-Rehim, Ismail Amr Ismail, Ehab MorsyProblem statement: The problem of testing randomness is motivated by the need to evaluate of the quality of different random number generators used by many practical applications including computer simulations, cryptography and communications industry. In particular, the quality of the randomness of the generated numbers affects the quality of such applications. In this study we focus on one of the … …Journal of Computer Science, Vol. 8, Issue 8 · 30 Jul 2012 · 9,752 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleThe Importance of Numbers and the Need to Study Primes: The Prime QuestionsMatthew Curtis, Gurudeo A. TularamProblem statement: The study of prime numbers is important today as it was in ancient times. The level of interest in any form of mathematics of students in Australian high schools is decreasing and furthermore the level of interest in number theory is also less that it was before; prime numbers is not being considered as an area of interest … …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 14 Sep 2011 · 9,656 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleTwo New Formulas for Generating Infinite Sets of Integer Numbers as a Sum of Two and Three Signed Cubic NumbersRand Alfaris, Hailiza KamarulhailiProblem statement: Two new families are introduced for generating infinite sets of integers by the summation of two and three signed cubic numbers. Approach: These two families have reduced the number of representation of finite sets of integer as a sum of cubic numbers from four cubes to two and three signed cubes. Results: It is also shown that not … …Journal of Mathematics and Statistics, Vol. 6, Issue 4 · 31 Dec 2010 · 7,069 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleRounding Theorem the Possibility of Applying the Cryptosystems on the Decimal NumbersRand Alfaris, Muhamad Rezal Kamel Ariffin, Mohamed Rushdan Md SaidThe possibility of using the decimal numbers in cryptography as the base of the encryption and decryption is proposed by introducing the "Rounding Theorem". Until now, cryptosystems are used the integer numbers to avoid the fractions of the decimal numbers. That is to avoid losing the original plaintext after the decryption. This theorem is proved that there is no lost … …Journal of Mathematics and Statistics, Vol. 4, Issue 1 · 31 Mar 2008 · 7,204 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleComputer Arithmetic Algorithms for Mega-Digit Floating Point Numbers' PrecisionMusbah J. Aqel, Mohammed H. SalehIEEE standard 754 floating point is the most common representation used for floating point numbers, and many computer arithmetic algorithms are developed for basic operations on this standard. In this study, new computer algorithms are proposed to increase the precision range and to solve some problems that are available while using these algorithms. However, these algorithms provide an optional range … …Journal of Computer Science, Vol. 3, Issue 2 · 28 Feb 2007 · 6,649 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn the Optimum Numbers of Stages in Vapour Compression Refrigeration SystemsDurriye Bilge, Galip TemirIn this study, cases of single-stage and multi-stage compression have been compared and contrasted through various angles while concentrating on refrigeration systems with 600 kW cooling capacity and working with ammonia. For five different numbers of stages, power consumption, costs of investment, operation and maintenance (O and M), COP and 2nd law efficiencies have been calculated. As the amount of … …American Journal of Applied Sciences, Vol. 1, Issue 2 · 30 Jun 2004 · 6,688 accessesView PDFCite