On the Number of Unbordered Factors

We illustrate a general technique for enumerating factors of k-automatic sequences by proving a conjecture on the number f(n) of unbordered factors of the Thue-Morse sequence. We show that f(n) = 4 and that f(n) = n infinitely often. We also give examples of automatic sequences having exactly 2 unbordered factors of every length

Detecting Determinacy in Prolog Programs: 22nd International Conference, ICLP 2006, Seattle, WA, USA, August 17-20, 2006. Proceedings

In program development it is useful to know that a call to a Prolog program will not inadvertently leave a choice-point on the stack. Determinacy inference has been proposed for solving this problem yet the analysis was found to be wanting in that it could not infer determinacy conditions for programs that contained cuts or applied certain tests to select a clause. This paper shows how to remedy these serious deficiencies. It also addresses the problem of identifying those predicates which can be rewritten in a more deterministic fashion. To this end, a radically new form of determinacy inference is introduced, which is founded on ideas in ccp, that is capable of reasoning about the way bindings imposed by a rightmost goal can make a leftmost goal deterministic

Fractal Holography: a geometric re-interpretation of cosmological large scale structure

The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit representation of information content, and also the value itself is a geometric signature of area. It is proposed that the fractal distribution of galaxies may thus be interpreted as a signature of holography (``fractal holography''), providing more support for current theories of holographic cosmologies. Implications for entropy bounds are addressed. In particular, because of spatial scale invariance in the matter distribution, it is shown that violations of the spherical entropy bound can be removed. This holographic condition instead becomes a rigid constraint on the nature of the matter density and distribution in the Universe. Inclusion of a dark matter distribution is also discussed, based on theoretical considerations of possible universal CDM density profiles.Comment: 13 pp, LaTeX. Revised version; to appear in JCA

The Mineralogy and Petrology of Anomalous Eucrite Emmaville

It has long been known that certain basaltic achondrites share similarities with eucrites. These eucrite-like achondrites have distinct isotopic compositions and petrologic characteristics indicative of formation on a separate parent body from the howardite-eucrite-diogenite (HED) clan (e.g., Ibitira, Northwest Africa (NWA) 011). Others show smaller isotopic variations but are otherwise petrologically and compositionally indistinguishable from basaltic eucrites (e.g., Pasamonte, Pecora Escarpment (PCA) 91007). The Emmaville eucrite has a delta O-17 value of -0.137 plus or minus 0.024 per mille (1 sigma), which is substantially different from the eucrite mean of -0.246 plus or minus 0.014 per mille (2 sigma), but similar to those of A-881394 and Bunburra Rockhole (BR). Currently little data exist for Emmaville in terms of petrology or bulk composition. Studying anomalous eucrites allows us to more completely understand the numbers of asteroids represented by eucrite- like basalts and thus constrain the heterogeneity of the HED suite. In this study, we present our preliminary petrological and mineral composition results for Emmaville

Carbon Nanotubes Band Assignation, Topology, Bloch States and Selection Rules

Various properties of the energy band structures (electronic, phonon, etc.), including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the single-wall carbon nanotubes are established. The complete set of quantum numbers consists of quasi momenta (angular and linear or helical) and parities with respect to the z-reversal symmetries and, for achiral tubes, the vertical plane. The assignation of the electronic bands is performed, and the generalized Bloch symmetry adapted eigen functions are derived. The most important physical tensors are characterized by the same set of quantum numbers. All this enables application of the presented exhaustive selection rules. The results are discussed by some examples, e.g. allowed interband transitions, conductivity, Raman tensor, etc.Comment: 11 pages, 2 figures, 2 tables; pdf available from: http://www.ff.bg.ac.yu/qmf/qsg_e.ht

Persistent currents in carbon nanotubes based rings

Persistent currents in rings constructed from carbon nanotubes are investigated theoretically. After studying the contribution of finite temperature or quenched disorder on covalent rings, the complexity due to the bundle packing is addressed. The case of interacting nanotori and self-interacting coiled nanotubes are analyzed in details in relation with experiments.Comment: 7 sections, 9 figure

Suppression of electron-electron repulsion and superconductivity in Ultra Small Carbon Nanotubes

Recently, ultra-small-diameter Single Wall Nano Tubes with diameter of $\sim 0.4 nm$ have been produced and many unusual properties were observed, such as superconductivity, leading to a transition temperature $T_c\sim 15^oK$, much larger than that observed in the bundles of larger diameter tubes. By a comparison between two different approaches, we discuss the issue whether a superconducting behavior in these carbon nanotubes can arise by a purely electronic mechanism. The first approach is based on the Luttinger Model while the second one, which emphasizes the role of the lattice and short range interaction, is developed starting from the Hubbard Hamiltonian. By using the latter model we predict a transition temperature of the same order of magnitude as the measured one.Comment: 7 pages, 3 figures, to appear in J. Phys.-Cond. Ma

Band structures of periodic carbon nanotube junctions and their symmetries analyzed by the effective mass approximation

The band structures of the periodic nanotube junctions are investigated by the effective mass theory and the tight binding model. The periodic junctions are constructed by introducing pairs of a pentagonal defect and a heptagonal defect periodically in the carbon nanotube. We treat the periodic junctions whose unit cell is composed by two kinds of metallic nanotubes with almost same radii, the ratio of which is between 0.7 and 1 . The discussed energy region is near the undoped Fermi level where the channel number is kept to two, so there are two bands. The energy bands are expressed with closed analytical forms by the effective mass theory with some assumptions, and they coincide well with the numerical results by the tight binding model. Differences between the two methods are also discussed. Origin of correspondence between the band structures and the phason pattern discussed in Phys. Rev. B {\bf 53}, 2114, is clarified. The width of the gap and the band are in inverse proportion to the length of the unit cell, which is the sum of the lengths measured along the tube axis in each tube part and along 'radial' direction in the junction part. The degeneracy and repulsion between the two bands are determined only from symmetries.Comment: RevTeX, gif fil

Magneto-optical Selection Rules in Bilayer Bernal Graphene

The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with four most important interlayer interactions taken into account. Since the main features of the wave functions are well depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions

Analysis of quantum conductance of carbon nanotube junctions by the effective mass approximation

The electron transport through the nanotube junctions which connect the different metallic nanotubes by a pair of a pentagonal defect and a heptagonal defect is investigated by Landauer's formula and the effective mass approximation. From our previous calculations based on the tight binding model, it has been known that the conductance is determined almost only by two parameters,i.e., the energy in the unit of the onset energy of more than two channels and the ratio of the radii of the two nanotubes. The conductance is calculated again by the effective mass theory in this paper and a simple analytical form of the conductance is obtained considering a special boundary conditions of the envelop wavefunctions. The two scaling parameters appear naturally in this treatment. The results by this formula coincide fairly well with those of the tight binding model. The physical origin of the scaling law is clarified by this approach.Comment: RevTe