Numerical values of the real-number factorial in the equation of elution adsorption dynamics

2011 ◽  
Vol 84 (6) ◽  
pp. 1263-1266 ◽  
Author(s):  
A. V. Larin
Keyword(s):  
Real Number ◽  
Adsorption Dynamics ◽  
The Real ◽  
Elution Adsorption Dynamics

scholarly journals An algebraic proof of the real number PCP theorem

2017 ◽  
Vol 40 ◽  
pp. 34-77 ◽  
Author(s):  
Martijn Baartse ◽  
Klaus Meer
Keyword(s):  
Real Number ◽  
Algebraic Proof ◽  
The Real ◽  
Pcp Theorem

scholarly journals II. On the Number of the Lost Books of Tacitus. By the Lord Mahon

Archaeologia ◽  
1838 ◽  
Vol 27 ◽  
pp. 15-17
Author(s):  
Mahon
Keyword(s):  
Real Number ◽  
The Real

The historical works of Tacitus which remain to us are, as is well known, besides the Life of Agricola, the four first books of the Annals, part of the fifth, the sixth, the eleventh, twelfth, thirteenth, fourteenth, fifteenth, and part of the sixteenth, the four first books of the History, and part of the fifth. It is asserted by Brotier, in his excellent edition, that the total number of books must have been sixteen of Annals and fourteen of History, and this assertion has never yet, so far as I know, been doubted or called in question. I think, however, that there are strong grounds for presuming that the real number of books was eighteen of Annals and twelve of History; and, though the point be of small importance, it may perhaps not be without some interest to the admirers of the greatest of Historians.

scholarly journals A Stochastic Simulation Model for the Optimization of the Taxi Management System

2019 ◽  
Vol 11 (14) ◽  
pp. 3838
Author(s):  
Aleksander Król ◽  
Małgorzata Król
Keyword(s):  
Simulation Model ◽  
Real Number ◽  
Service Level ◽  
Critical Number ◽  
System Behavior ◽  
Taxi Drivers ◽  
The Real ◽  
Incomplete Knowledge ◽  
Stochastic Simulation Model ◽  
Queue Theory

The paper presents a simplified simulation model of the operation of a taxi system. The model retains the main features of a real taxi transportation system and despite its simplicity examines the system behavior in different conditions. It was shown that for every request generation rate a critical number of taxis in disposal could be determined. If the real number of taxis is lower than the critical number, the queue of pending requests grows in an unlimited way. On the other hand, if the real number of taxis is significantly higher, the service level is clearly not better and leads to the waste of taxi drivers’ time and fuel. The presented model can be regarded as a queue system; therefore, the well-known queue theory is used to describe its nature. However, this approach has some practical limitations coming from incomplete knowledge on real transportation demands, which additionally undergo significant fluctuations. A method, which optimizes the assignment of vacant taxis to the pending requests was also introduced. It was proven that this method mitigated the influence of the above-mentioned limitations.

scholarly journals An estimate for trigonometrical sums over square-free integers with a constant number of prime factors

1967 ◽  
Vol 15 (4) ◽  
pp. 249-255
Author(s):  
Sean Mc Donagh
Keyword(s):  
Positive Integer ◽  
Real Number ◽  
Prime Number ◽  
Rational Number ◽  
Large Integer ◽  
Constant Number ◽  
The Real ◽  
Prime Factors ◽  
Squarefree Number ◽  
Image Position

1. In deriving an expression for the number of representations of a sufficiently large integer N in the formwhere k: is a positive integer, s(k) a suitably large function of k and pi is a prime number, i = 1, 2, …, s(k), by Vinogradov's method it is necessary to obtain estimates for trigonometrical sums of the typewhere ω = l/k and the real number a satisfies 0 ≦ α ≦ 1 and is “near” a rational number a/q, (a, q) = 1, with “large” denominator q. See Estermann (1), Chapter 3, for the case k = 1 or Hua (2), for the general case. The meaning of “near” and “arge” is made clear below—Lemma 4—as it is necessary for us to quote Hua's estimate. In this paper, in Theorem 1, an estimate is obtained for the trigonometrical sumwhere α satisfies the same conditions as above and where π denotes a squarefree number with r prime factors. This estimate enables one to derive expressions for the number of representations of a sufficiently large integer N in the formwhere s(k) has the same meaning as above and where πri, i = 1, 2, …, s(k), denotes a square-free integer with ri prime factors.

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