We prove that the evolutionary Navier-Stokes equation in n-D torus with initial data in a wide class of distributions has a unique solution that is analytic in all variables. We also estimate the Fourier coefficients of this solution

Let be a connected compact oriented surface and be either ℝ or . Let () be the space of Morse mappings → with compact-open topology. The classification of path-components of () was independently obtained by S. V. Matveev and V. V. Sharko for the case = ℝ, and by the author for = . In this...

The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form = 1/2+λ. Hilbert-Polya argued that if a Hermitian operator exists whose eigenvalues are the imaginary parts of the zeta zeros, λ's, then the RH is true. In this paper a fractal...

Significant compositional biases in bacterial chromosomes have been explained by replication- and transcription-coupled repair mechanisms, the latter causing GC skew to indicate the direction of replication when gene polarity is correspondingly entrained. Correlations between indicators of...

To a finite Hopf-Galois extension A|B we associate dual bialgebroids := End and over the centralizer using the depth two theory in [18, Kadison-Szlachányi]. First we extend results on the equivalence of certain properties of Hopf-Galois extensions with corresponding properties of the coacting...

A simple one-parameter analytical extension of Benford™s law for first digits of numerical data is constructed. Based on the maximum likelihood method, the fitting capabilities of the new distribution is illustrated at some interesting and important integer sequences including the numeri...

Some sharp inequalities of Grüss type for sequences of vectors in real or complex inner product spaces are obtained. Applications for Jensen's inequality for convex functions defined on such spaces are also provided

Transformations that preserve circles or spheres are similarities.Dans cet article, nous nous intéressons aux applications d'un espace euclidien vers lui—meme qui transforment quatre points cocycliques quelconques en quatre points cocycliques, c'est—à— dire qui transforment tout cercie...

We prove that the evolutionary Navier-Stokes equation in n-D torus with initial data in a wide class of distributions has a unique solution that is analytic in all variables. We also estimate the Fourier coefficients of this solution