A Quantum-Gravity Perspective on Semiclassical vs. Strong-Quantum Duality

It has been argued that, underlying M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this letter we prove that the above semiclassical vs. strong-quantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.Comment: 10 page

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Production Technology and Competitiveness In the Hungarian Manufacturing Industry

Following the big transformations of the 1990s, enterprise structure and technological level seem to have become stabilised in Hungary. Under these circumstances it is especially interesting to identify the elements responsible for competitiveness in general, and the role technology plays in development in particular, according to managers experienced in production and marketing. This empirical study – based on in-depth interviews and field research – summarises characteristics of the technological level in the sectors examined, role of technology and labour in production, effects of foreign direct investment, relations between competition and firm-level factors determining competitiveness, and concludes by summing up those most frequently mentioned proposals that should be incorporated into economic policy according to managers. Main findings indicate that more qualified, more intensive and cheaper labour can be substituted for high technology. The competitiveness of an enterprise is not determined by technology alone, but rather by a combination of technology, the parameters of available labour and the costs of investment increasing productivity. The insufficiency of inter-company relations, together with a shortage of available assets necessary for investment constitute the major threat undermining the competitiveness of enterprises in present-day Hungary

An explicit solution to the weak Schottky problem

We give an explicit weak solution to the Schottky problem, in the spirit of Riemann and Schottky. For any genus g, we write down a collection of polynomials in genus g theta constants such that their common zero locus contains the locus of Jacobians of genus g curves as an irreducible component. These polynomials arise by applying a specific Schottky-Jung proportionality to an explicit collection of quartic identities for genus g - 1 theta constants

Technical note: Lithium isotopes in dolostone as a palaeo-environmental proxy - an experimental approach

Lithium (Li) isotopes in marine carbonates have considerable potential as a proxy to constrain past changes in silicate weathering fluxes and improve our understanding of Earth\u27s climate. To date the majority of Li isotope studies on marine carbonates have focussed on calcium carbonates. The determination of the Li isotope fractionation between dolomite and a dolomitizing fluid would allow us to extend investigations to deep times (i.e. Precambrian) when dolostones were the most abundant marine carbonate archives. Dolostones often contain a significant proportion of detrital silicate material, which dominates the Li budget; thus, pretreatment needs to be designed so that only the isotope composition of the carbonate-associated Li is measured. This study aims to serve two main goals: (1) to determine the Li isotope fractionation between Ca-Mg carbonates and solution, and (2) to develop a method for leaching the carbonate-associated Li out of dolostone while not affecting the Li contained within the detrital portion of the rock. We synthesized Ca-Mg carbonates at high temperatures (150 to 220 ∘C) and measured the Li isotope composition (δ7Li) of the precipitated solids and their respective reactive solutions. The relationship of the Li isotope fractionation factor with temperature was obtained ..

On the uniqueness of (p,h)(p,h)-gonal automorphisms of Riemann surfaces

Let $X$ be a compact Riemann surface of genus $g\geq 2$. A cyclic subgroup of prime order $p$ of $Aut(X)$ is called properly $(p,h)$-gonal if it has a fixed point and the quotient surface has genus $h$. We show that if $p>6h+6$, then a properly $(p,h)$-gonal subgroup of $Aut(X)$ is unique. We also discuss some related results.Comment: final version, 9 pages, minor improvements, added 2 reference

Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

We test classical nucleation theory (CNT) in the case of simulations of deeply supercooled, high density liquid silica, as modelled by the BKS potential. We find that at density $\rho=4.38$~g/cm$^3$, spontaneous nucleation of crystalline stishovite occurs in conventional molecular dynamics simulations at temperature T=3000 K, and we evaluate the nucleation rate J directly at this T via "brute force" sampling of nucleation events. We then use parallel, constrained Monte Carlo simulations to evaluate $\Delta G(n)$, the free energy to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200 and 3300 K. We find that the prediction of CNT for the n-dependence of $\Delta G(n)$ fits reasonably well to the data at all T studied, and at 3300 K yields a chemical potential difference between liquid and stishovite that matches independent calculation. We find that $n^*$, the size of the critical nucleus, is approximately 10 silicon atoms at T=3300 K. At 3000 K, $n^*$ decreases to approximately 3, and at such small sizes methodological challenges arise in the evaluation of $\Delta G(n)$ when using standard techniques; indeed even the thermodynamic stability of the supercooled liquid comes into question under these conditions. We therefore present a modified approach that permits an estimation of $\Delta G(n)$ at 3000 K. Finally, we directly evaluate at T=3000 K the kinetic prefactors in the CNT expression for J, and find physically reasonable values; e.g. the diffusion length that Si atoms must travel in order to move from the liquid to the crystal embryo is approximately 0.2 nm. We are thereby able to compare the results for J at 3000 K obtained both directly and based on CNT, and find that they agree within an order of magnitude.Comment: corrected calculation, new figure, accepted in JC

DNA uptake into nuclei: Numerical and analytical results

The dynamics of polymer translocation through a pore has been the subject of recent theoretical and experimental works. We have considered theoretical estimates and performed computer simulations to understand the mechanism of DNA uptake into the cell nucleus, a phenomenon experimentally investigated by attaching a small bead to the free end of the double helix and pulling this bead with the help of an optical trap. The experiments show that the uptake is monotonous and slows down when the remaining DNA segment becomes very short. Numerical and analytical studies of the entropic repulsion between the DNA filament and the membrane wall suggest a new interpretation of the experimental observations. Our results indicate that the repulsion monotonically decreases as the uptake progresses. Thus, the DNA is pulled in (i) either by a small force of unknown origin, and then the slowing down can be interpreted only statistically; (ii) or by a strong but slow ratchet mechanism, which would naturally explain the observed monotonicity, but then the slowing down requires additional explanations. Only further experiments can unambiguously distinguish between these two mechanisms.Comment: 12 pages, 6 figures, submitted to J. Phys. Cond. Ma

Zassenhaus conjecture for central extensions of S5

We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature, settles the conjugacy question for units of prime-power order in the integral group ring of a finite Frobenius group

Two-photon double ionization of neon using an intense attosecond pulse train

We present the first demonstration of two-photon double ionization of neon using an intense extreme ultraviolet (XUV) attosecond pulse train (APT) in a photon energy regime where both direct and sequential mechanisms are allowed. For an APT generated through high-order harmonic generation (HHG) in argon we achieve a total pulse energy close to 1 $\mu$J, a central energy of 35 eV and a total bandwidth of $\sim30$ eV. The APT is focused by broadband optics in a neon gas target to an intensity of $3\cdot10^{12}$W$\cdot$cm$^{-2}$. By tuning the photon energy across the threshold for the sequential process the double ionization signal can be turned on and off, indicating that the two-photon double ionization predominantly occurs through a sequential process. The demonstrated performance opens up possibilities for future XUV-XUV pump-probe experiments with attosecond temporal resolution in a photon energy range where it is possible to unravel the dynamics behind direct vs. sequential double ionization and the associated electron correlation effects