In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...

The weak value of a variable O is a description of an effective interaction with that variable in the limit of weak coupling. For a pre-and post-selected system described at time t by the two-state vector Φ| |Ψ (see entry Two-State Vector Formalism), the weak value is [1]: O w ≡ Φ|O|Ψ Φ|Ψ. (1) Contrary to classical physics, variables in quantum mechanics might not have definite values at a give...

Starting from known necessary extremality conditions in terms of strict subdifferentials and normals the notion of weak stationarity is introduced. It is defined in terms of initial space elements. The necessary conditions become necessary and sufficient (for stationarity).

By incorporating reciprocity in an otherwise standard principalagent model, I investigate the relation between monetary gift-exchange and incentive pay, while allowing for worker heterogeneity. I assume that some, but not all, workers care more for their principal when they are convinced that the principal cares for them. The principal can be egoistic or altruistic. Absent worker heterogeneity,...

The strength with which a statement is made can have a significant impact on the audience. For example, international relations can be strained by how the media in one country describes an event in another; and papers can be rejected because they overstate or understate their findings. It is thus important to understand the effects of statement strength. A first step is to be able to distinguis...

There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and outlined for weak ncategories. The categorical aspects concern the development of descent theory in low dimensions in order to provide a template for a theory in...

We construct an equivalence between the categories of vertex operator algebras and vertex operator coalgebras. We then investigate to what degree weak modules, generalized modules and ordinary modules carry corresponding comodule structures, as well as when various comodules carry module structure.