GRASSET B., Pascal, Paris, Ellipses, 2017, 224 p.

Symmetric Pascal matrices modulo p

T =  1 1 1 1 2 1 1 3 3 1 .. . . .  = exp  0 1 0 0 2 0 0 3 0 . . .  with coefficients ti,j = (i j ) . This shows that det(P (n)) = 1 and that P (n) is positive definite for all n ∈ N. It implies furthermore that the characteristic polynomial det(tI(n)−P (n)) = ∑ k=0 αkt k (where I(n) denotes the identity matrix of order n) of P (n) has only positive real roots. The in...

P-224: Chlropromazine-Induced Hyperprolactinemia on Rat

P-224: Mechanisms That Reduce Endometrial Receptivity in Endometriosis

Background: Several studies indicate clear relationship between infertility and endometriosis. However, the etiology of this association is uncertain. Endometrial dysfunction is a possible cause of infertility in women with endometriosis, which could explain the high rates of implantation failure and miscarriages in these women. Delay in endometrial maturation and intrauterine biochemical abnor...

DECOMPOSITION OF PASCAL ’ S KERNELS MOD p s Richard

For a prime p we define Pascal’s Kernel K(p, s) = [k(p, s)ij] ∞ i,j=0 as the infinite matrix satisfying k(p, s)ij = 1 ps ( i+j j ) mod p if ( i+j j ) is divisible by p and k(p, s)ij = 0 otherwise. While the individual entries of Pascal’s Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula to explain the global geo...

THE INVERSE OF THE PASCAL LOWER TRIANGULAR MATRIX MODULO p

Let L(n)p be the Pascal lower triangular matrix with coefficients `i j ́ (mod p), 0 ≤ i, j < n. In this paper, we found the inverse of L(n)p modulo p. In fact, we generalize a result due to David Callan [4].