In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

We study phases and fractal structures of three-dimensional simplicial quantum gravity by the Monte-Carlo method. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution (LLD) in two-dimensional quantum gravity, we classify the fractal structures into three types: (i) in the hot (strong coupling) phase, strong gravity makes the s...

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infectionwave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the tem...

Service Level Objectives (SLOs) describe the desired behavior of a service. They present agreed-upon target behaviors (e.g. capacity, performance, availability, cost) that the clients of a service can expect, and that the service provider can manage against. Both clients and service providers need a way to monitor how a service is doing against its SLOs, and display the result of that monitorin...

abstract introduction: impression making is one of the most important steps in fixed prosthodontics. due to contra-dictory opinions on the issue of the accuracy of silicone impression material as a function of technique, this study was carried out to assess the dimensional accuracy of master casts made by rapid silicone material as a function of three impression techniques: with 2mm space, with...

Holography is a new concept of the superstring theory based on the duality between gauge and supergravity theories, proposed by Maldacena in 1997.1 The superstring theory with conformal and Lorentz invariance has ten-dimensional space-time to avoid anomalies. Its elemental degrees of freedom are one-dimensional open or closed strings. The fluctuation modes of these strings are expected to give ...

A packing of congruent balls of unit radius in three-dimensional Euclidean space is determined by and is identified with the set Λ of centers of the balls. A packing Λ determines a region called the Voronoi cell around each ball. The Voronoi cell Ω(Λ, v) around a ball at v ∈ Λ consists of points of space that are closer to v than to any other w ∈ Λ. The Voronoi cell is a convex polyhedron conta...

The present study considers of the water and air flow and Micro-Bubble production inside the venturi tube, by the use of dimensional analysis. Numerical analysis of Micro-Bubble creation in venturi tube requires fast computers and large amounts of storage space. Up to now, there has been no numerical analysis concerning Micro-Bubble creation and all other existing studies are experimental. To s...