Chouikha, Abd Raouf

Thanks to representation of the Jacobi theta functions \\ $\theta_j(v,\tau) = f_j(v,\tau) f_j(v+1,\tau)$ \ we deduce a trigonometric expression of the Weierstrass function \ $\wp(z,\tau)$\ with primitive periods \ $(2, 2\tau)$.\\ It allows us to find again more directly many known identities. In particular we derive the following identity$$4\wp(2z,...

Maatouk, Hassan Rullière, Didier Bay, Xavier

Generating multivariate normal distributions is widely used in many fields (such as engineering). In this paper, simulating large multivariate normal distributions truncated on the intersection of a set of hyperplanes is investigated. The proposed methodology focuses on Gaussian vectors extracted from a Gaussian process (GP) in one dimension. It is...

Lascabettes, Paul Agon, Carlos Andreatta, Moreno Bloch, Isabelle

This paper deals with the computational analysis of musical structures by focusing on the use of morphological filters. We first propose to generalize the notion of melodic contour to a chord sequence with the chord contour, representing some formal intervallic relations between two given chords. By defining a semi-metric, we compute the self-dista...

Pham, Ngoc-Sang

In a market economy, the aggregate production level depends not only on the aggregate variables but also on the distribution of individual characteristics (e.g., productivity, credit limit, ...). We point out that, due to financial frictions the equilibrium aggregate production may be non-monotonic in both individual productivity and credit limit. ...

Bagayoko, Vincent van der Hoeven, Joris

Ech-chatbi, Charaf

We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.

Ech-chatbi, Charaf

We present a proof of the Generalized Riemann hypothesis (GRH) based on asymptotic expansions and operations on series. The advantage of our method is that it only uses undergraduate maths which makes it accessible to a wider audience.

Dumitrescu, Cristian Wolf, M

Applying Littlewood's lemma in connection to Riemann's Hypothesis and exploiting the symmetry of Riemann's xi function we show that almost all nontrivial Riemann's Zeta zeros are on the critical line.

Chornomaz, Bogdan

We discuss a conjecture that a finite lattice satisfies Sauer-Shelah-Perles inequality (is SSP) iff it is relatively complemented (RC). It is straightforward to prove that SSP implies RC and it is the other direction that is problematic. Our main advance in this direction is that a subset in an RC lattice, whose order-ideal of non-shattered element...

Oukil, W

We prove that $\frac{\zeta(s)}{s}\neq \frac{\zeta(1-s)}{1-s}$ for every $\Re(s)\in(0,\frac{1}{2})$ and $\Im(s)\in\mathbb{R}^*$, where $\zeta$ is the Riemann Zeta function. In the end of the paper, we give a discussion about the Riemann hypothesis.