Given an arbitrary n, we consider anisotropic quadratic forms of dimension n over all fields of characteristic = 2 and prove that the height of an n-dimensional excellent form (depending on n only) is the (precise) lower bound of the heights of all forms of dimension n.

a trial study was carried out to assess the influence of the plant residue management in conjuction with application of different nitrogen sources on wheat yield and components, at the agricultural faculty of shahidchamran university of ahvaz during 2011-2012.the experimental design was splitplot at randomized completed block design arrangement. the main plot were different wheat residue manage...

Let R be the ring of integers in a finite extension K of Qp, let k be its residue field and let χ : π1(X) → R× = GL1(R) be a ”geometric” rank one representation of the arithmetic fundamental group of a smooth affine k-scheme X. We show that the locally Kanalytic characters κ : R× → Cp are the Cp-valued points of a K-rigid space W and that L(κ ◦ χ, T ) = ∏ x∈X 1 1− (κ ◦ χ)(Frobx)T deg(x) , viewe...

In the crystal structure of the title salt, C(8)H(12)N(+)·C(2)F(3)O(2) (-), all of the ammonium H atoms serve as donors for hydrogen bonds to carboxyl-ate O atoms, forming an R(4) (3)(10) ring motif based on two cations and two anions. Since both cations and anions act as inter-ion bridging groups, R(10) rings aggregate in a one-dimensional supra-molecular network by sharing the strongest N-H⋯O...

The title compound, C(2)H(8)NO(3)P, crystallizes in its zwitterionic form H(3)N(+)CH(CH(3))PO(O(-))(OH). In the crystal, the molecules are linked by N-H⋯O and O-H⋯O hydrogen bonds.

The title compound, C(3)H(10)NO(3)P, crystallizes in its zwitterionic form, H(3)N(+)CH(C(2)H(5))PO(O(-))(OH), with the asymmetric unit being composed by two of such entities (Z' = 2). The crystal packing leads to a sequence of hydro-phobic and hydro-philic layers. While the hydro-phobic layer comprises the aliphatic substituent groups, the hydro-philic one is held together by a series of strong...