Fluid model and discrete-packet model are two approaches to model TCP, where different loss processes are used in different models. In this paper, we present both a discrete SMP model and a fluid model to model the TCP window evolution process. Loss process is I.I.D. in the SMP model, and is a poisson process with window size dependent arrival rate in the fluid model. Analysis shows that the di...

Let (Xn)n∈ω be a sequence of uniform spaces such that each space Xn is a closed subspace in Xn+1. We give an explicit description of the topology and uniformity of the direct limit u-lim −→ Xn of the sequence (Xn) in the category of uniform spaces. This description implies that a function f : u-lim −→ Xn → Y to a uniform space Y is continuous if for every n ∈ N the restriction f |Xn is continuo...

Actinin-associated LIM protein (ALP) and Enigma are two subfamilies of Postsynaptic density 95, discs large and zonula occludens-1 (PDZ)-Lin-11, Isl1 and Mec-3 (LIM) domain containing proteins. ALP family members have one PDZ and one LIM domain, whereas Enigma proteins contain one PDZ and three LIM domains. Four ALP and three Enigma proteins have been identified in mammals, each having multiple...

We wish to characterize when a Lévy process Xt crosses boundaries like t�, �>0, in a oneor two-sided sense, for small times t; thus, we inquire when lim sup t↓0|Xt|/t�, lim sup t↓0Xt/t� and/or lim inf t↓0Xt/t� are almost surely (a.s.) finite or infinite. Necessary and sufficient conditions are given for these possibilities for all values of �>0. This completes and extends a line of research goi...