On the Symmetry of Arithmetical Functions

Dual multiwavelet frames with symmetry from two-direction renable functions

Optimization of Conformal Mapping Functions used in Developing Closed-Form Solutions for Underground Structures with Conventional cross Sections

Elastic solutions applicable to single underground openings usually suffer from geometry related simplification. Most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. D-shape or horse-shoe shape tunnels and others with arched roof and floor are examples of the later category (one symmetry axis). In the present...

On the Symmetry of Arithmetical Functions in Almost All Short Intervals, Iv

Abstract. We study the arithmetic (real) function f = g ∗ 1, with g “essentially bounded” and supported over the integers of [1, Q]. In particular, we obtain non-trivial bounds, through f “correlations”, for the “Selberg integral” and the “symmetry integral” of f in almost all short intervals [x − h, x + h], N ≤ x ≤ 2N , beyond the “classical” level, up to a very high level of distribution (for...

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions

In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the qu...