In this note we give an algebraic proof of “deformation quantization” by making use of the theory of Unital Gröbner bases over a valuation ring. MSC: 16Z05,13P10 In this note we give an algebraic proof of deformation quantization (c.f. [7]). We do this be developing in (Sec. 1) the theory of unital Gröbner bases over a valuation ring. We then in (Sec. 2) obtain, almost immediately, our desired ...

We find a characterization of those Polish ultrametric spaces on which each Baire one function is first return recoverable. The notion of pseudo-convergence originating in the theory of valuation fields plays a crucial role in the characterization.

Ring NTPases are a class of ubiquitous molecular motors involved in basic biological partitioning processes. dsDNA viruses encode ring ATPases that translocate their genomes to near-crystalline densities within pre-assembled viral capsids. Here, X-ray crystallography, cryoEM, and biochemical analyses of the dsDNA packaging motor in bacteriophage phi29 show how individual subunits are arranged i...

We give a de nition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp((t)), which works uniformly for all p and all nite eld extensions of these elds, and in many other Henselian valued elds as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modi cation of the language of Macintyre. Furthermore, we show the negative result th...

Scan and ring schemes of the pseudo-ring memory selftesting are investigated. Both schemes are based on emulation of the linear or nonlinear feedback shift register by memory itself. Peculiarities of the pseudo-ring schemes implementation for multi-port and embedded memories, and for register file are described. It is shown that only small additional logic is required and allows microcontroller...

In this paper, scan and ring schemes of the pseudo-ring memory self-testing are investigated. Both schemes are based on emulation of the linear or nonlinear feedback shift register by memory itself. Peculiarities of the pseudo-ring schemes implementation for multi-port and embedded memories, and for register file are described. It is shown that only small additional logic is required and allows...

In this paper we study rank one discrete valuations of the field k((X1, . . . ,Xn)) whose center in k[X1, . . . ,Xn] is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field o...