This paper analyzes a Monte Carlo algorithm for solving Smoluchowski’s coagulation equation. A finite number of particles approximates the initial mass distribution. Time is discretized and random numbers are used to move the particles according to the coagulation dynamics. Convergence is proved when quasi-random numbers are utilized and if the particles are relabeled according to mass in every...

Given α1, . . . , αm ∈ (0, 1), we characterize all integrable functions f : [0, 1] → C satisfying ∫ A1×···×Am f = 0 for any collection of disjoint measurable sets A1, . . . , Am ⊆ [0, 1] of respective measures α1, . . . , αm. We use this characterization to settle some of the conjectures in [S. Janson and V. Sós, More on quasi-random graphs, subgraph counts and graph limits, European J. Combin....

Department of Gene Expression, Institute of Molecular Biology and Biotechnology, Adam Mickiewicz University, Poznan, Poland, Department of Molecular and Cellular Biology, Institute of Molecular Biology and Biotechnology, Adam Mickiewicz University, Poznan, Poland, Max Planck Institute for Plant Breading Research, 50829, Germany, Biomathematics and Statistics Scotland (BioSS), James Hutton Insti...

We introduce and study the notions of a strongly completable and of a strongly complete quasi-uniform space. A quasi-uniform space (X,U) is said to be strongly complete if every Cauchy filter (in the sense of Sieber and Pervin) clusters in the uniform space (X,U ∨ U−1). An interesting motivation for the study of this notion of completeness is the fact, proved here, that the quasi-uniformity ind...

incredible diversity of explanatory systems (some heuristic, others theoretic) dauntingly facing the young medical thinker or natural philosopher in the mid-eighteenth century. Thus Hutton opted for belief in five chemical principles (for Hutton principles were ad hoc labellings rather than ultimate constituents of Nature): salt, water, sulfur, earth, and air. It was as good a classification as...

In this paper, sufficient conditions have been obtained so that all oscillatory solutions of the n-th order differential equations with quasi derivatives tend to zero as t tends to infinity.