The author is grateful for support from a PhD grant from the Engineering and Physical Sciences Research council of the UK and post-doctoral fellowship number SFRH/BPD/40762/2007 from the Fundação para a Ciéncia e a Tec-nologia of Portugal. This paper contains some work included in the authors PhD thesis ([5]). Abstract We introduce notions of compactness and weak compactness for multi-linear ma...

We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider linear maps T : A → B between Banach algebras that are “close to multiplicative” in the following senses: the failure of multiplicativity, defined by ST (a, b) = T (a)T (b) − T (ab) (a, b ∈ A), is co...

Consider a set of single-input, single-output nonlinear systems whose input–output maps are described only in terms convergent Chen–Fliess series without any assumption that finite dimensional state space models available. It is shown additive or multiplicative interconnection such always has representation can be computed explicitly iterated formal Lie derivatives.

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

‎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...

We investigate properties of a multivariate function E(m1,m2, . . . ,mr), called orbicyclic, that arises in enumerative combinatorics in counting non-isomorphic maps on orientable surfaces. E(m1,m2, . . . ,mr) proves to be multiplicative, and a simple formula for its calculation is provided. It is shown that the necessary and sufficient conditions for this function to vanish are equivalent to f...

CNN architectures have terrific recognition performance but rely on spatial pooling which makes it difficult to adapt them to tasks that require dense, pixel-accurate labeling. This paper makes two contributions: (1) We demonstrate that while the apparent spatial resolution of convolutional feature maps is low, the high-dimensional feature representation contains significant sub-pixel localizat...

We construct three di erent spectra, and hence three generalized cohomology theories, associated to an algebraic variety X: the morphic spectrum ZX an E1-ring spectrum related to intersection theory when X is smooth; the multiplicative morphic spectrum MX and the holomorphic K-theory spectrum KX . The constructions use holomorphic maps from X into appropriate moduli spaces, and are functorial o...