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This article is devoted to the properties of the planar triangulations. The conjugated planar triangulation will be introduced and on the base of the properties, which were achieved by the other authors there will be proved some theorems,…
The radiation pressure due to reflected chameleons is suggested for their detection. Sensitive photon radiation pressure or force measuring techniques could become the new antennas for chameleons or other particles with similar properties,…
The flag f-vectors of three-colored complexes are characterized. This also characterizes the flag h-vectors of balanced Cohen-Macaulay complexes of dimension two, as well as the flag h-vectors of balanced shellable complexes of dimension…
Steffen's polyhedron was believed to have the least number of vertices among polyhedra that can flex without self-intersections. Maksimov clarified that the pentagonal bipyramid with one face subdivided into three is the only polyhedron…
This article evaluates the determinants of two classes of special matrices, which are both from a number theory problem. Applications of the evaluated determinants can be found in [arXiv:math.NT/0509523]. Note that the two determinants are…
A method to investigate possible loosely bound dibaryon states is suggested. The momentum dependence of a two-pion correlation function is shown to depend on the (non)existence of a bound state.
There are fifteen edge-to-edge tilings of the sphere by congruent pentagons with the edge combination $a^3b^2$: five one-parameter families of pentagonal subdivision tilings, and ten flip modifications of three special cases of two…
It is shown that the Heisenberg double has a canonical element, satisfying the pentagon relation. From a given invertible constant solution to the pentagon relation one can restore the structure of the underlying algebras. Drinfeld double…
The microscopic structure of the high-index Si$(331)-(12\times1)$ surface is investigated combining scanning tunneling microscopy with ab initio calculations. We present a structural model of the Si(331) surface, employing a reconstruction…
The goal of this research is to determine and study a physical system that will enable a fast and intrinsically two-photon detector, which would be of interest for quantum information and metrology applications. We consider two types of…
We define biquandle structures on a given quandle, and show that any biquandle is given by some biquandle structure on its underlying quandle. By determining when two biquandle structures yield isomorphic biquandles, we obtain a…
By using of a special reduction way of density matrices, in this Letter we find the entanglement between two bunches of particles, its measure can be represented by the entanglement of formation.
One of the most important problems in Geometric Tomography is to establish properties of a given convex body if we know some properties over its sections or its projections. There are many interesting and deep results that provide…
A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…
We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…
The band structure of a novel type of photonic crystal with superconducting constituent elements is calculated numerically via a plane wave expansion. The density of states and the dependence of the width of the photonic gap on the filling…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated…
We give an introduction to Gaussian states and operations. A discussion of the entanglement properties of bipartite Gaussian states in terms of its covariance matrix follows. It is explained how entanglement can be witnessed using feasible…
Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex pentagons of the same area and the same perimeter.
The correlated two-particle problem is solved analytically in the presence of a finite cavity. The method is demonstrated here in terms of exactly solvable models for both the cavity as well as the two-particle correlation where the…