This paper groups together some results that share a theme (orbits of automorphism groups on elements of a field) and some proof ideas (constructing an additive or multiplicative “trace/norm map”). Namely, we prove that a field whose automorphism group acts with finitely many orbits must be finite (Theorem 1.1), we discuss a stronger conjecture, and we show that the automorphisms of a Mal’cev-N...

We show that the dynamics of transmission control protocol (TCP) may often be chaotic via a quasiperiodic route consisting of more than two independent frequencies, by employing a commonly used ns-2 network simulator. To capture the essence of the additive increase and multiplicative decrease mechanism of TCP congestion control, and to qualitatively describe why and when chaos may occur in TCP ...

We construct a map ζ from K0(P) to (Z[x]/xd+1)× × Z, where (Z[x]/xd+1)× is a multiplicative Abelian group with identity 1, and show that ζ induces an isomorphism between K0(P) and its image. This is inspired by a correspondence between Chern and Hilbert polynomials stated in Eisenbud [1, Exercise 19.18]. The equivalence of these two polynomials over Pd is discussed in this paper.

Cohn’s problem on character sums (see [6], p. 202) asks whether a multiplicative character on a finite field can be characterized by a kind of two level autocorrelation property. Let f be a map from a finite field F to the complex plane such that f(0) = 0, f(1) = 1, and | f(α) |= 1 for all α 6= 0. In this paper we show that if for all a, b ∈ F ∗, we have (q − 1) ∑ α∈F f(bα)f(α+ a) = − ∑

In this paper, at first the elemantary and basic concepts of multiplicative discrete and continous differentian and integration introduced. Then for these kinds of differentiation invariant functions the general solution of discrete and continous multiplicative differential equations will be given. Finaly a vast class of difference equations with variable coefficients and nonlinear difference e...

We present the following reflexivity-like result concerning the automorphism group of the C∗-algebra B(H), H being a separable Hilbert space. Let φ : B(H) → B(H) be a multiplicative map (no linearity or continuity is assumed) which can be approximated at every point by automorphisms of B(H) (these automorphisms may, of course, depend on the point) in the operator norm. Then φ is an automorphism...

Multiplicative Binary Moment Diagram (*BMD) is a new representation that inherits from BDD. *BMDs map Boolean variables to integer values and so they are well-suited to handle a hierarchical veri-cation methodology. In this paper we experiment this representation to verify sequential arithmetic circuits. We extend *BMDs and provide an algebra that includes main operators commonly used at the bi...

(using the restricted product topology ensures that a 7→ a−1 is continuous, which is not true of the subspace topology). As a topological group, IK is locally compact and Hausdorff. The multiplicative group K× is canonically embedded as a discrete subgroup of IK via the diagonal map x 7→ (x, x, x, . . .), and the idele class group is the quotient CK := IK/K, which is locally compact but not com...

‎Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The first, second and third Zagreb indices of G are respectivly defined by: $M_1(G)=sum_{uin V} d(u)^2, hspace {.1 cm} M_2(G)=sum_{uvin E} d(u).d(v)$ and $ M_3(G)=sum_{uvin E}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in G and uv is an edge of G connecting the vertices u and v. Recently, the first and second m...