‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

We report the results of experimental studies of the short-time-long-wavelength behavior of collective particle displacements in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) colloid suspensions. Our results are reported via the q → 0 behavior of the hydrodynamic function H(q) that relates the effective collective diffusion coefficient D(e)(q), with the static structure factor S(q...

the internal structure of dna-ctab and dna-ddab is investigated by a small angel x- ray scattering(saxs) instrument. hexagonal packing of dna was observed for dna complex with ctab, and for ddabcomplex is observed lamellar structure. variations in the internal spacing and degree of long-range ordering aredependent on both surfactant type and concentrations of added salt. when we increased the a...

Let p be a prime e be a positive integer, q = p, and let Fq denote the finite field of q elements. Let m, n, 1 ≤ m, n ≤ q − 1, be integers. The monomial digraph D = D(q; m, n) is defined as follows: the vertex set of D is Fq, and ((x1, x2), (y1, y2)) is an arc in D if x2 + y2 = x1 y 1 . In this note we study the question of isomorphism of monomial digraphs D(q; m1, n1) and D(q; m2, n2). In part...

The second weight of the Generalized Reed-Muller code of order d over the finite field with q elements is now known for d < q and d > (n − 1)(q − 1). In this paper, we determine the second weight for the other values of d which are not multiple of q − 1 plus 1. For d = a(q − 1) + 1 we only give an estimate.

Canonical quantization (CQ) is built around [Q, P] = ih1l , while affine (AQ) [Q,D] ihQ, where D ≡ (PQ +QP) / 2 . The basic CQ operators must fit -∞ P, Q P ≠ 0 < ∞ AQ can also be the key to quantum gravity, as our simple outline demonstrates.

For a smooth surface X in P of degree d, defined over a finite field Fq with q elements, q prime, we prove that X has at most d(d+q−1)(d+2q−2)/6+d(11d−24)(q+1) points with coordinates in Fq.

1. Notation and notions We repeat some definitions and facts, we need in our exposition but for special case. Let Q be an open set belonging to Rn. By D(Q) we denote the space {φ ∈ C∞(Q); suppφ ⊂ Kφ}, Kφ is a compact set in Q which depends on φ. D′(Q) is the space of continuous linear functionals on D(Q) the space of distributions. Every f ∈ Lloc(Q) defines a distribution, called regular distri...