We call φ the root function of Φ. The continuity of Φ implies that (1.2) φ(γ) → |γ| as |γ| → ∞. Moreover the converse is true, if φ is continuous and satisfies this asymptotic formula, then the function Φ formed as in (1.1) is a multiplicative distance function. Theorem 1.1. A continuous function φ : C → [0,∞) is the root function of a multiplicative distance function iff it satisfies (1.2). Ar...

In the present paper we provide a general algorithm to compute multiplicative cohomological operations on algebraic oriented cohomology of projective homogeneous G-varieties, where G is split reductive group over field k characteristic 0. More precisely, extend such respective T-equivariant (T maximal torus G) theories, and then them using equivariant Schubert calculus techniques. This generali...

The event calculus [45, 66, 74, 98, 100] is a formalism for reasoning about action and change. Like the situation calculus, the event calculus has actions, which are called events, and time-varying properties or fluents. In the situation calculus, performing an action in a situation gives rise to a successor situation. Situation calculus actions are hypothetical, and time is tree-like. In the e...

We apply the well-known Banach-Nečas-Babuška inf-sup theory in a stochastic setting to introduce a weak space-time formulation of the linear stochastic heat equation with additive noise. We give sufficient conditions on the the data and on the covariance operator associated to the driving Wiener process, in order to have existence and uniqueness of the solution. We show the relation of the obta...

The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by...

Nonnormal characteristics of geophysical time series are important determinants of extreme events and may provide insight into the underlying dynamics of a system. The structure of nonnormality in winter temperature is examined through the use of linear filtering of radiosonde temperature time series. Filtering either low or high frequencies generally suppresses what is otherwise statistically ...

In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y = N + A, where the measure dA is carried by the set of zeros of Y. In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, thes...

In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y = N +A, where the measure dA is carried by the set of zeros of Y . In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, thes...