In a synchronized network of n nodes, each node will update its parameter based on the system state in a given iteration. It is well-known that the updates can converge to a fixed point if the maximum absolute eigenvalue (spectral radius) of the n × n iterative matrix F is less than one (i.e. ρ(F) < 1). However, if only a subset of the nodes update their parameter in an iteration (due to delays...

A dilation equation is a functional equation of the form f(t) = ∑N k=0 ck f(2t − k), and any nonzero solution of such an equation is called a scaling function. Dilation equations play an important role in several fields, including interpolating subdivision schemes and wavelet theory. This paper obtains sharp bounds for the Hölder exponent of continuity of any continuous, compactly supported sca...

homogeneity and uniformity of soil particles is a most potent factor which affects soil spectral signatures. geometric standard deviation of soil particles (?g) exhibits the homogeneity of soil components. this study presents the influence of ?g on spectral studying of soil geometric mean particle diameter as well as lime. the study was conducted in pol-e-dokhtar using the data set of lissiii-p...

The spectral radius of every d× d matrix A is bounded from below by c ‖A‖ ‖A‖, where c = c(d) > 0 is a constant and ‖·‖ is any operator norm. We prove an inequality that generalizes this elementary fact and involves an arbitrary number of matrices. In the proof we use geometric invariant theory. The generalized spectral radius theorem of Berger and Wang is an immediate consequence of our inequa...