Related papers: The Representation of Line Dirac Delta Function Al…
This paper introduces the expanded real numbers as an ordered subring of the hyperreal number field that does not contain any infinitesimals, and defines the set of all integrable functions from the real numbers to the expanded real…
In practical purposes for some geometrical problems in computer science we have as information the coordinates of some finite points in surface instead of the whole body of a surface. The problem arised here is: "How to define a distance…
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries,…
Hilbert's two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that…
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…
While the concept of straight-line length is well understood in taxicab geometry, little research has been done into the length of curves or the nature of area and volume in this geometry. This paper sets forth a comprehensive view of the…
In this study, we define a new type of direction curves in the Euclidean 3-space such as osculating-direction curve. We give the characterizations for these curves. Moreover, we obtain the relationships between osculating direction curves…
We have shown that in some region where the Euler integral of the first kind diverges, the Euler formula defines a generalized function. The connected of this generalized function with the Dirac delta function is found.
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.
We write the Dirac equation in curved 4-dimensional Lorentzian spacetime using concepts from the analysis of partial differential equations as opposed to geometric concepts.
The transmission poles of $N$ number of identical Dirac delta potentials placed periodically in one-dimension are examined in the complex-energy plane. The numerical results show that the imaginary part of the poles scales with 1/N. An…
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and…
The article presents, in an elementary way, but with mathematical precision and without harm to the intuition, the path from the integral representation to the Dirac delta, starting with Schwartz's functional approach. Next, the considered…
This thesis presents three results in geometric analysis. We first analyze the curve-shortening flow on figure eight curves in the plane. Afterwards, we examine the point-wise curvature preserving flow on space curves. Lastly, we present an…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while well-defined, is not continuous. Space-filling…
In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…