Related papers: Analytic theories around the simplest screw
We investigate the screw line corresponding to the screw function associated with the Riemann zeta-function under the Riemann hypothesis and derive three necessary and sufficient conditions for the Riemann hypothesis as applications. One of…
We introduce a screw function corresponding to the Riemann zeta-function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them…
We give a completely elementary study for averages of short correlations of so-called sieve functions (a pretty general class of arithmetic functions).
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
Some notes and observations on analytic functions defined on an annulus
The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.
Flow forming involves complicated tooling/workpiece interactions. Purely analytical models of the tool contact area are difficult to formulate, resulting in numerical approaches that are case-specific. Provided are the details of an…
A telegraphic survey of some of the standard results and conjectures about the set $C({\bf Q})$ of rational points on a smooth projective absolutely connected curve $C$ over ${\bf Q}$.
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Perhaps, it is not too far from the truth to say that, among the great concepts (as compactness, completeness, order, convexity) on which functional analysis is based, connectedness is relatively less popular, though this does not mean that…
Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…
We present a generic solution to the fundamental problem of how to connect two points in a plane by a smooth curve that goes through these points with a given slope. The smoothness of any curve depends both on its curvature and its length.…
Analytic approximations of functions of Cayley-Dickson variables are investigated. The case of functions of complexified Cayley-Dickson variables is also encompassed. Moreover, extensions of functions of Cayley-Dickson variables are…
In these notes we generalize the theory of graphical functions from scalar theories to theories with spin.
The theory of screws clarifies many analogies between apparently unrelated notions in mechanics, including the duality between forces and angular velocities. It is known that the real 6-dimensional space of screws can be endowed with an…
In this note, we offer some relations and congruences for an interesting $spt$-type function.
Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based…