The Lucas numbers, 2, 1, 3, 4, 7, 11, 18, 29, 47, . . . , named in honor of Edouard Lucas (1842-1891), are defined by L0 = 2, L1 = 1, and Ln = Ln−1 + Ln−2 for n ≥ 2. It is easy to show that, for n ≥ 1, Ln counts the ways to create a bracelet of length n using beads of length one or two, where bracelets that differ by a rotation or a reflection are still considered distinct. For example, there a...

We consider systems of unitary operators on the complex Hilbert space L(R) of the form U :=UDA , v1 ..., vn :=[DT l1 v1 } } } T ln vn : m, l1 , ..., ln # Z], where DA is the unitary operator corresponding to dilation by an n_n real invertible matrix A and Tv1 , ..., Tvn are the unitary operators corresponding to translations by the vectors in a basis [v1 , ..., vn] for R. Orthonormal wavelets a...

When a language theorist encounters a new operation on languages, his first impulse is to know whether this operation preserves rational languages. If the answer appears to be positive, he proceeds immediately to the construction of a more or less complicated automaton to solve the problem. However there are many operations on languages, many language theorists (see the references) and many dif...

A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications, including classification, denoising and signal separation, learn a dictionary from a given set of signals to be represented. Can we expect that the error in rep...

Previously, we reported that high-fat-diet (HFD)-induced obesity stimulates melanoma progression in the B16F10 allograft model. In this study, we examined whether oleuropein (OL), the most abundant phenolic compound in olives, inhibits HFD-induced melanoma progression. Four-week-old male C57BL/6N mice were fed a HFD-diet with or without OL. After 16 weeks of feeding, B16F10-luc cells were subcu...

objective(s)lupus nephritis (ln) is frequently associated with a poor long-term prognosis. renal biopsy is the diagnostic method of choice in this condition. urine biomarkers have been mentioned in the diagnosis of ln. the study,s purpose was to evaluate the performance of urinary monocyte chemoattractant protein 1(umcp-1) as a biomarker of renal involvement in systemic lupus erythematosus.mate...