We relate weak limit preservation properties of coalgebraic type functors F to structure theoretic properties of the class of all F -coalgebras.

In this paper we prove the existence of weak solutions for the thin film equation with prescribed non zero contact angle and for a large class of mobility coefficients, in dimension 1. The existence of weak solutions for this degenerate parabolic fourth order free boundary problem was proved by F. Otto in [35] when the mobility coefficient is given by f(u) = u, using a particular gradient flow ...

Two dimensional (2D) numerical simulation of low-frequency (1/f) noise is carried out in N-channel polysilicon thin film transistors biased from weak to strong inversion. Noise is simulated by Generation-Recombination processes. Simulation is based on the impedance field method of Shockley. A 2D analysis of the local noise level shows that contribution at grain boundaries dominates from weak to...

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)− hL(y)| ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x)− hW (y)| ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing w...

In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset subject to forbidden r+ s configurations, where r+s = 4. Generalizing previous work on weak discrepancy in [5, 12, 13], the notion of fractional weak discrepancy wdF (P ) of a poset P = (V,≺) was introduced in [7] as the minimum nonnegative k for which there exists a function f : V → R ...

We show that the extent of a Tychonoff space of countable weak extent can be arbitrary big. The extent of X is e(X) = sup{|F | : F ⊂ X is closed and discrete} while we(X) = min{τ : for every open cover U of X there is A ⊂ X such that |A| ≤ τ and St(A,U) = X} is the weak extent of X (also called the star-Lindelöf number of X). Also we show that the extent of a normal space with countable weak ex...

Let $${{\mathcal {F}}}_n$$ be the Farey series of order $$n\ge 1$$ . We obtain sharp effective estimates sums $$\begin{aligned} F_n(f)= \sum _{\frac{{\kappa }}{{\lambda }}\in {{\mathcal {F}}}_n} f\Big (\frac{{\kappa }}\Big ),{\qquad }F_{n,{\sigma }}(f)= \frac{1}{{\kappa }^{\sigma }{\lambda }}f\Big }0< {\sigma }\le 1, \end{aligned}$$ for 1-periodic functions f satisfying weak local regularity as...

When moving to a Type Theory without proof-irrelevance the notion of a setoid has to be generalized to the notion of a weak ω-groupoid. As a first step in this direction we study the formalisation of weak ω-groupoids in Type Theory. This is motivated by Voevodsky’s proposal of univalent type theory which is incompatible with proof-irrelevance and the results by Lumsdaine and Garner/van de Berg ...