Let p be prime, N be a positive integer prime to p, and k be an integer. Let Pk(t) be the characteristic series for Atkin’s U operator as an endomorphism of p-adic overconvergent modular forms of tame level N and weight k. Motivated by conjectures of Gouvêa and Mazur, we strengthen a congruence in [W] between coefficients of Pk and Pk′ for k ′ p-adically close to k. For p − 1 | 12, N = 1, k = 0...

A laboratory incubation experiment was conducted during December, 2017 to March, 2018 in Department of Soil Science and Agricultural Chemistry, College Agriculture, Raichur, Karnataka, India study the fractionation phosphorus (P) black soil amended with different phosphatic fertilizers under submerged condition. The were kept subemerged condition for 90 days phophatic such as single super phosp...

Serre in the 1970s was the first to formalize such a question on the way to constructing p-adic L-functions, by way of developing the notion of a p-adic modular form to be the p-adic limit of some compatible family of q-expansions of classical modular forms. Katz came along fairly soon afterwards and generalized the theory to a much more geometric context, and showed that Serre’s p-adic forms e...

Using the differential-geometric control theory, we present in this note a necessary and sufficient condition under which an affine system is locally feedback equivalent to, via a change of coordinates and restricted smooth state feedback, a generalized normal form called —normal form, which includes Brunovsky canonical form and feedback linearizable systems in a lower-triangular form as its sp...

Spiking neural P system is a computing device recently introduced as a bridge between spiking neural nets and membrane computing. In this paper we focus on normal forms of these systems while preserving their computational power. We show that certain combinations of existing normal forms are possible without loss of computational power, thus answering partially open problems stated in [3,8]. We...

Complex dynamical systems on the Riemann sphere do not possess " invariant forms ". However there exist non-trivial examples of dynamical systems, defined over number fields, satisfying the property that their reduction modulo ℘ possesses " invariant forms " for all but finitely many places ℘. The paper completely characterizes those dynamical systems possessing the latter property. 1. Motivati...

1 Department of Computer Science University of California Santa Barbara, CA 93106, USA [email protected], [email protected] 2 Department of Computer Science, Louisiana Tech University, Ruston PO Box 10348, Louisiana, LA-71272 USA [email protected] 3 Universidad Politécnica de Madrid UPM, Faculdad de Informática Campus de Montegancedo s/n, Boadilla del Monte, 28660 Madrid, Spain [email protected]...

Phosphorus (P) is a key indicator of the aquatic organism growth and eutrophication in lakes. The distribution and speciation of P and its release characteristics from sediments were investigated by analyzing sediment and water samples collected during high flow and low flow periods. Results showed that the average concentrations (ranges) of total phosphorus (TP) in the surface and deep water w...

We describe the inorganic polymer K(4)P(8)Te(4) which is soluble, giving solutions that exhibit white emission upon 355 nm laser irradiation. An indirect band gap semiconductor (E(g) approximately 1.4 eV), K(4)P(8)Te(4) crystallizes in the space group P2(1)/m, with a = 6.946(1) A, b = 6.555(1) A, c = 9.955(2) A, and beta = 90.420(3) degrees at 173(2) K. The compound features infinite chains of ...