We provide geometrical interpretation of the Master Theorem to solve divide-and-conquer recurrences. We show how different cases of the recurrences correspond to different kinds of fractal images. Fractal dimension and Hausdorff measure are shown to be closely related to the solution of such recurrences.

In the last ten years, number of organ preservation surgeries for kidney cancer significantly increased. Per literature data, incidence recurrences after partial nephrectomy is between 2.9 and 11 %, mostly they are located in operated or contralateral kidney. Positive surgical margin, high stage histological subtype tumor, as well hereditary diseases, can serve predictors recurrences. renal rec...

for a constant c ∈ (1, 2). Using more clever backtracking, one can develop even more complex recurrences and a running time of O(1.27 · poly(n)). For the minimum vertex cover problem, we can therefore solve it on arbitrary graphs in time O∗(1.27n).1 In fact, one can get a slightly better running time for arbitrary graphs, via the following trick. Notice that if the vertex cover is of size at le...

Abstract Background Juvenile recurrent parotitis (JRP) is characterized by episodes of painful parotid swelling in children. The purpose this systematic review was to determine the diagnostic and therapeutic effectiveness sialendoscopy children affected JRP. Methods A literature search performed PubMed, EMBASE, Scopus Cochrane Library until April 2022, without language restrictions or specified...

X iv :0 80 9. 25 51 v1 [ m at h. C O ] 1 5 Se p 20 08 Spanning Trees in Grid Graphs Paul Raff July 25, 2008 Abstract A general method is obtained for finding recurrences involving the number of spanning trees of grid graphs, obtained by taking the graph product of an arbitrary graph and path or cycle. The results in this paper extend the work by Desjarlais and Molina and give concrete methods f...

There are many classical results in which orthogonal vectors stemming from Krylov subspaces are linked to short recurrence relations, e.g., three-terms recurrences for Hermitian and short rational recurrences for unitary matrices. These recurrence coefficients can be captured in a Hessenberg matrix, whose structure reflects the relation between the spectrum of the original matrix and the recurr...