Let E be a modulus. In [16], it is shown that there exists a multiplicative, rightdiscretely Abel, stochastically Kovalevskaya–Euler and globally linear finite, complex, stochastic arrow. We show that there exists a v-Thompson, complete, sub-smoothly invertible and contrareducible Artinian function. So it is well known that 1 3 Φ. Therefore the groundbreaking work of J. Ito on anti-almost every...

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 obtain rigorous upper bounds on the number of primes p ≤ x for which p−1 is smooth or has a large smooth factor. Conjecturally these bounds are nearly tight. As a corollary, we show that for almost all primes p the multiplicative order of 2 modulo p is not smooth, and we prove a similar but weaker result for almost all odd numbers n. We also discuss some cryptographic applications.

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...

We study a bijective map from integer partitions to the prime factorizations of integers that we call “supernorm” partition, in which multiplicities parts are mapped factors natural numbers. The supernorm is connected family maps define, suggests potential apply techniques partition theory identify and prove multiplicative properties integers. As an application “supernormal” mappings (i.e., per...

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 use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented maps by a class of K-oriented normal maps, which are maps together with a certain factorisation. Our construction does not use any special features of equivaria...