We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number of points growing polynomially in the degree, these polynomials provide nearly optimal approximant...

The general rationale of analytic number theory is to derive statistical information about a sequence {an} from the analytic behaviour of an appropriate generating function, such as a power series ∑ anz or a Dirichlet series ∑ ann−s . The type of generating function employed depends on the problem being investigated. There are no rigid rules governing the kind of generating function that is app...

In this paper, we characterise the analytic functions φ mapping the open unit disk ∆ into itself whose induced composition operator Cφ : f 7→ f ◦ φ is an isometry on the Bloch space. We show that such functions are either rotations of the identity function or have a factorisation φ = gB where g is a non-vanishing analytic function from ∆ into the closure of ∆, and B is an infinite Blaschke prod...

Using the theory of o-minimality we show that the p-adic method of Skolem-Mahler-Lech-Chabauty may be adapted to prove instances of the dynamical Mordell-Lang conjecture for some real analytic dynamical systems. For example, we show that if f1, . . . , fn is a finite sequence of real analytic functions fi : (−1, 1)→ (−1, 1) for which fi(0) = 0 and | f ′ i (0)| ≤ 1 (possibly zero), a = (a1, . . ...

We give an example of an affinoid curve without analytic continuation. We use this to produce an example of an affinoid morphism that cannot be flattened by a finite sequence of local blow-ups. Thus the global rigid analogue, [7], Theorem 2.3, of Hironaka’s complex analytic flattening theorem is not true. Since this is a key step in the proof of the affinoid elimination theorem, [7], Theorem 3....

Let f be a piecewise analytic (but not analytic) function in @[a, b], k > 0, and let p,* be the sequence of polynomials of best uniform approximation to f on [a, b]. It is well known that every point of [a, b] is a limit point of the zeros of the p,*. Let x E [a, b], and suppose that f is analytic at x and f(x) # 0. The main purpose of this paper is to show that there exists a constant y (which...

paris polyphylla smith var. yunnanensis (liliaceae) is an important traditional medicinal plant of the yunnan province in china. however, the genomic information regarding this plant is limited. to further understand its molecular background, we conducted illumina hiseq 2000 second-generation sequencing of this plant species. approximately 30,198,679 reads with an average length of 202 bases we...

bioinformatics, through the sequencing of the full genomes for many species, is increasingly relying on efficient global alignment tools exhibiting both high sensitivity and specificity. many computational algorithms have been applied for solving the sequence alignment problem. dynamic programming, statistical methods, approximation and heuristic algorithms are the most common methods applied t...

Visualization of temporal event data is increasingly important for the analysis of a broad range of data including electronic health records, web logs, and financial data. In many analytic tasks, users need the capability to manipulate the data to reveal patterns and make insights. To support this analytic need, we introduce a novel temporal search and replace tool (TSR) implemented in our exis...

We introduce the sequence of generalized Gončarov polynomials, which is a basis for the solutions to the Gončarov interpolation problem with respect to a delta operator. Explicitly, a generalized Gončarov basis is a sequence (tn(x))n≥0 of polynomials defined by the biorthogonality relation εzi(d (tn(x))) = n!δi,n for all i, n ∈ N, where d is a delta operator, Z = (zi)i≥0 a sequence of scalars, ...