Zobrazeno 1 - 10
of 241
pro vyhledávání: '"Altschuler, Eric Lewin"'
Given $N$ cities and $R < N^2 - N$ directed (unidirectional/one way) roads does there exist a tour of all $N$ cities stopping at each city exactly once using the given roads (a Hamiltonian cycle)? This Hamiltonian cycle problem (HCP) is an NP-complet
Externí odkaz:
http://arxiv.org/abs/1701.03136
Almost all public secure communication relies on the inability to factor large numbers. There is no known analytic or classical numeric method to rapidly factor large numbers. Shor[1] has shown that a quantum computer can factor numbers in polynomial
Externí odkaz:
http://arxiv.org/abs/1402.1201
How many unit $n-$dimensional spheres can simultaneously touch or kiss a central $n-$dimensional unit sphere? Beyond mathematics this question has implications for fields such as cryptography and the structure of biologic and chemical macromolecules.
Externí odkaz:
http://arxiv.org/abs/1301.4884
Recent high resolution structures for viral capsids with 12, 32 and 72 subunits ($T1$, $T3$ and $T7$ viruses) have confirmed theoretical predictions of an icosadeltahedral structure with 12 subunits having five nearest neighbors (pentamers) and $(10T
Externí odkaz:
http://arxiv.org/abs/0902.3566
We use the Hopf fibrillation to give simple and intuitive geometric constructions of the 24-cell, $E_8$ and $\Lambda_{16}$ lattices.
Comment: 2 figures
Comment: 2 figures
Externí odkaz:
http://arxiv.org/abs/math/0612728
Inspired by, and using methods of optimization derived from classical three dimensional electrostatics, we note a novel beautiful symmetric four dimensional polytope we have found with 80 vertices. We also describe how the method used to find this sy
Externí odkaz:
http://arxiv.org/abs/physics/0601139
Publikováno v:
Phys. Rev. E, 73, 036108 (2006)
Given $N$ unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy $\sum_{i>j=1}^N 1/r_{ij}$? Due to an exponential rise in good local minima, finding global minima for this problem,
Externí odkaz:
http://arxiv.org/abs/cond-mat/0509501
Using numerical arguments we find that for $N$ = 306 a tetrahedral configuration ($T_h$) and for N=542 a dihedral configuration ($D_5$) are likely the global energy minimum for Thomson's problem of minimizing the energy of $N$ unit charges on the sur
Externí odkaz:
http://arxiv.org/abs/cond-mat/0408355
The oldest (c. 4000 BC) undeciphered language is the Old European Script known from approximately 940 inscribed objects (82% of inscriptions on pottery) found in excavations in the Vinca-Tordos region Transylvania. Also, it is not known for what the
Externí odkaz:
http://arxiv.org/abs/math/0309157
We note that the first unambiguous description of the Milk Way as being composed of a large number of discrete stars is in Sonnet 31 of Thomas Watson's (d 1592) Hekatompathia (1582), nearly 30 years before Galileo's description. We discuss implicatio
Externí odkaz:
http://arxiv.org/abs/physics/0305010