It is well known [4] that the non-Archimedean residue class fields K of the ring of continuous real valued functions on a space are realclosed and 7/i-sets. It does not appear to be known that the exponential function in the reals induces an exponential function in K (definitions to follow) ; thus K is exponentially closed. The property of being exponentially closed is a new invariant which wil...

We now consider generic algorithms for the discrete logarithm problem. We shall assume throughout that N = |α| is known. This is a reasonable assumption, since there is a generic algorithm to compute N using o( √ N) group operations [9], which is strictly less than the complexity of any generic algorithm for this problem (we will prove an Ω( √ N) lower bound). The cyclic group 〈α〉 is isomorphic...

We discuss how renormalisation group equations can be consistently formulated using the algebraic framework, in context of a dimensionally-renormalised chiral field theory BMHV scheme, where BRST symmetry, originally broken at quantum level, is restored via finite counterterms. compare it with more standard multiplicative approach, which application would cumbersome this setting. Both procedure...

Many formulations of proof nets and sequent calculi for Classical Linear Logic (CLL) [7, 8] take it for granted that a type A is identical to its double negation A⊥⊥. On the other hand, since Seely [13], it has been assumed that ∗-autonomous categories [1, 2] are the appropriate semantic models of (the multiplicative fragment of) CLL. However, in general, in a ∗-autonomous category an object A ...

$D$ if $D^{j}$ is a g-cyclic A-cover of $D$ for some $g\in A$ . In the case that $A$ is abelian, . then $D_{g}(\alpha)$ is simply called a cyclic abelian cover. Let $\alpha$ and $\beta$ be two alternating functions $homA(D)$ into $A$ , and let $\Gamma$ be a subgroup of the automorphism group Aut $D$ of $D$ , denoted $\Gamma\leq$ Aut $D$ . Let $g,$ $h\in A$ . Then two cyclic A-covers $D_{g}(\alp...

Background: For psychiatric disorders, comorbidity is a rule rather than exception. Thus it is particularly important to study additive and multiplicative effects of multiple mental disorders on suicidal behaviors. Objectives: The aim of this study was to investigate the ethnic differences in multiplicative effects of mental disorders on suicidal ideation among Black adults in the United States...

todeschini et al. have recently suggested to consider multiplicative variants of additive graphinvariants, which applied to the zagreb indices would lead to the multiplicative zagrebindices of a graph g, denoted by ( ) 1  g and ( ) 2  g , under the name first and secondmultiplicative zagreb index, respectively. these are define as  ( )21 ( ) ( )v v gg g d vand ( ) ( ) ( )( )2 g d v d v gu...

Let G and G' be multiplicative systems. A half-homomorphism of G into G' will mean a mapping a—>a' of G into C such that for all a, bEG, (ab)'=a'V or b'a'. An anti-homomorphism is a mapping such that always (ab)' = b'a'. The terms half-isomorphism, etc., are defined similarly. It will be shown that any half-homomorphism of a group G into a group G' is either a homomorphism or an anti-homomorphi...