Abstract: In this work, we give a characterization of the control for ill-posed problems. We propose the regularization method which consists in improving the data in order to obtain a well-posed problems. As the problem is nonlinear, we will use the adapted low-regret control method in order to be able to respectively determine the charaterization of the low-regret and no-regret control of the problem. PubDate: Tue, 29 Nov 2022 17:11:51 +000

Abstract: The Collatz conjecture (or Syracuse conjecture) states: all Syracuse sequences converge to 1. We present a Syracuse sequence, and we prove that the conjecture is true, first by using the fact that all convergent integer sequences are eventually constant. We then prove wrong 2 hypotheses: the case where the sequence tends to infinity, and the case where the sequence has no limit and is eventually periodic. We conclude by elimination, afterward. PubDate: Tue, 29 Nov 2022 16:12:34 +000

Abstract: The well-known Broken Spaghetti Problem is a geometric problem which can be stated as: A stick of spaghetti breaks into three parts and all points of the stick have the same probability to be a breaking point. What is the probability that the three sticks, putting together, form a triangle'In this note, we describe a hidden geometric pattern behind the symmetric version of this problem, namely a fractal that parametrizes the sample space of this problem. Using that fractal, we address the question about the probability to obtain a δ-equilateral triangle. PubDate: Mon, 28 Nov 2022 16:18:44 +000

Abstract: We suggest a new approach to the Some Blaise Abbo (SBA) method for solving systems of nonlinear fractional partial differential equations and we have tested it with two examples. PubDate: Mon, 28 Nov 2022 15:48:59 +000

Abstract: An original definition of the generalized Euler-Mascheroni constants allowed us to prove that their infinite sum converges to the number (1-Ln2) . By considering this number is the Lebesgue measure of a set defined as the difference between the area of the square unit and the area under the curve y=1/x 1≤x≤2 ; we introduced a partition of this set such that each Lebesgue measure of the subsets can be related to values of Riemann zeta function at integers. From this relationship, we proved that the Lambert W function can produce all ζ(s) values whatever is the parity of s . Finally, by considering that ζ(s) values allow calculation of the probability, for s integers chosen in an interval [1,n] n∈N , to be coprime; we proved that Lambert W function can describe prime numbers distribution. PubDate: Mon, 28 Nov 2022 15:11:17 +000