Related papers: The isotropic correlation function of plane figure…
The Blume-Emery-Griffiths model on hypercubic lattices within the two-particle cluster approximation is investigated. The expressions for the pair correlation functions in $\bf{k}$-space are derived. On the basis of obtained results (at…
We study the possible positions of the Miquel point in the plane of a given triangle, which Miquel triangles are similar to the given one. We found out that these positions are eleven. We also study the possible positions of the Miquel…
We employ a procedure that enables us to calculate the excess free energies for a finite Ising cylinder with domain walls analytically. This procedure transparently covers all possible configurations of the domain walls under given boundary…
We construct an associative ring which is a deformation of the quantum cohomology ring of the projective plane. Just as the quantum cohomology encodes the incidence characteristic numbers of rational plane curves, the contact cohomology…
Two-dimensional Coulomb gases on an annulus at a special inverse temperature $\beta = 2$ are studied by using the orthogonal polynomial method borrowed from the theory of random matrices. The correlation functions among the Coulomb gas…
The absence of self averaging in mesoscopic systems is a consequence of long-range intensity correlation. Microwave measurements suggest and diagrammatic calculations confirm that the correlation function of the normalized intensity with…
A three parameter scaling relationship between isotopic distributions for elements with Z$\leq 8$ has been observed that allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling…
Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras additionally contains information with respect to rotational misalignment. It has been…
We provide a new formulation and proof of the triangle altitudes theorem in hyperbolic plane geometry, together with an easily computed discriminant to distinguish between different basic configurations of the altitudes of such a triangle.
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take…
In this paper, it is shown, using a geometrical approach, the isotropy of the velocity of light measured in a rotating frame in Minkowski space-time, and it is verified that this result is compatible with the Sagnac effect. Furthermore, we…
In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our result shows that if a geometric hexagonal triangulation of the…
A planar portrait of a manifold is the pair of the image and the critical values of the manifold through a stable map into the plane. It can be considerd a geometric representation of the manifold drawn in the plane. The cusped fan is its…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
Spatially-resolved photon counting of a twin beam performed by an iCCD camera allows for versatile tailoring the properties of the beams formed by parts of the original twin beam. Dividing the idler beam of the twin beam into three…
This article investigates the effect of using isotropic and anisotropic plastic response functions in the analysis of the elastic-plastic response of unidirectional fibre composites on the meso-scale. Three model problems that use a…
A natural analogue to angles and trigonometry is developed in taxicab geometry. This structure is then analyzed to see which, if any, congruent triangle relations hold. A nice application involving the use of parallax to determine the exact…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…