On the decomposition of n!n! into primes

In this note, we approximate the average of prime powers in the decomposition of $n!$ into prime numbers.Comment: 9 page

On the irreducible action of psl(2, r) on the 3-dimensional einstein universe

We describe the orbits of the irreducible action of PSL(2, R) on the 3-dimensional Einstein universe Ein 1,2. This work completes the study in [2], and is one element of the classification of cohomo-geneity one actions on Ein 1,2 ([5])

A Generalization of Multiplication Table

In this note, we generalize the concept of multiplication table by connecting with lattice points. Then we introduce and proof a generalization of Erdös multiplication table theorem

Counting and Computing by ee

In this paper we count the number of paths and cycles in complete graphs by using the number $e$. Also, we compute the number of derangements in same way. Connection by $e$ yields some nice formulas for the number of derangements, such as $D_n=\lfloor\frac{n!+1}{e}\rfloor$ and $D_n=\lfloor(e+e^{-1})n!\rfloor-\lfloor en!\rfloor$, and using these relations allow us to compute some incomplete gamma functions and hypergeometric summations; these connections are hidden in the heart of a nice polynomial that we call it derangement function and a simple ordinary differential equation concerning it.Comment: 12 pages, no figure, review of my works about the number of derangement

Singular Spectrum Analysis: Methodology and Comparison

In recent years Singular Spectrum Analysis (SSA), used as a powerful technique in time series analysis, has been developed and applied to many practical problems. In this paper, the performance of the SSA technique has been considered by applying it to a well-known time series data set, namely, monthly accidental deaths in the USA. The results are compared with those obtained using Box-Jenkins SARIMA models, the ARAR algorithm and the Holt-Winter algorithm (as described in Brockwell and Davis (2002)). The results show that the SSA technique gives a much more accurate forecast than the other methods indicated above.ARAR algorithm; Box-Jenkins SARIMA models; Holt-Winter algorithm; singular spectrum analysis (SSA); USA monthly accidental deaths series

A Note on Short Intervals Containing Primes

In 1999, P. Dusart showed that for x ≥ 3275, there exists at least a prime number in the interval (x, x(1 + 1/(2ln²x))] and in 2003, O. Ramaré and Y. Saouter showed that for x ≥ 10726905041 there exists at least a prime number in the interval (x(1 − ∆⁻¹), x], in which ∆ = 28314000. In this note, we show that for x ≥ 1.17×10¹⁶³⁴, we can yield Ramaré-Saouter’s result from Dusart’s result