This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvatu...

For the first time since the establishment of TCP and UDP, the Internet transport layer is subject to a major change by the introduction of QUIC. Initiated by Google in 2012, QUIC provides a reliable, connection-oriented low-latency and fully encrypted transport. In this paper, we provide the first broad assessment of QUIC usage in the wild. We monitor the entire IPv4 address space since August...

in this paper, we study fuzzy substructures in connection withhv-structures. the original idea comes from geometry, especially from thetwo dimensional euclidean vector space. using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. we connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as hv-groups...

the general relatively isotropic mean landsberg metrics contain the general relativelyisotropic landsberg metrics. a class of finsler metrics is given, in which the mentioned two conceptsare equivalent. in this paper, an interpretation of general relatively isotropic mean landsberg metrics isfound by using c-conformal transformations. some necessary conditions for a general relativelyisotropic ...