Let M be a finite module and let I be an arbitrary ideal over a Noetherian local ring. We define the generalized Hilbert function of I on M using the 0th local cohomology functor. We show that our definition re-conciliates with that of Ciupercă. By generalizing Singh’s formula (which holds in the case of λ(M/IM)<∞), we prove that the generalized Hilbert coefficients j0, . . . , jd−2 are preserv...

Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring OP,X at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if OP,X is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré se...

Tris paper, through analy3is to the specific power of the compressor, indicates that to reduce the power loss caused by friction is an important way to reduce the specific power of the compressor, investigates the realizability employing a single piston ring or a piston ring with small elasticity in the high speed double acting compressor, and raises a standpoint for a high speed double acting ...

5 Hopf Rings 11 5.1 What is a Hopf ring? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2 DS as a co-Hopf ring spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.3 Rational Morava E-theory of DS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 EDS is a formal power series ring under ? 12 6.1 Determining...

Sufficient conditions on a space are given which guarantee that the K-theory ring is an invariant of the adic genus. An immediate consequence of this result about adic genus is that for any positive integer n, the power series ring Z[[x1, . . . , xn]] admits uncountably many pairwise non-isomorphic λ-ring structures.

We study how reliably generalized synchronization can be detected and characterized from time-series analysis. To that end, we analyze synchronization in a generalized sense of delay-coupled chaotic oscillators in unidirectional ring configurations. The generalized synchronization condition can be verified via the auxiliary system approach; however, in practice, this might not always be possibl...

We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions. We consider the set R ⊂ C[[z 1 , z 2 ]], z 1 , z 2 ∈ C k × C m of formal power series of the form f (z) = f (z 1 , z 2) = n P n (z 2)z n 1 where P n is a polynomial in m variables of total degree d 0 P n ≤ C 0 + C...