On Atkin and Swinnerton-Dyer Congruence Relations (2)

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the $p$-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale

Thermal acclimation of leaf and root respiration: an investigation comparing inherently fast- and slow-growing plant species

We investigated the extent to which leaf and root respiration W differ in their response to short- and long-term changes in temperature in several contrasting plant species (herbs, grasses, shrubs and trees) that differ in inherent relative growth rate (RGR, increase in mass per unit starting mass and time). Two experiments were conducted using hydroponically grown plants. In the long-term (LT) acclimation experiment, 16 species were grown at constant 18,23 and 28degreesC. In the short-term (ST) acclimation experiment, 9 of those species were grown at 25/20degreesC (day/night) and then shifted to a 15/10degreesC for 7 days. Short-term Q(10) values (proportional change in R per 10degreesC) and the degree of acclimation to. longer-term changes in temperature were compared. The effect of growth temperature on root and leaf soluble sugar and nitrogen concentrations was examined. Light-saturated photosynthesis (A(sat)) was also measured in the LT acclimation experiment. Our results show that Q(10) values and the degree of acclimation are highly variable amongst species and that roots exhibit lower Q(10) values than leaves over the 15-25degreesC measurement temperature range. Differences in RGR or concentrations of soluble sugars/nitrogen could not account for the inter-specific differences in the Q(10) or degree of acclimation. There were no systematic differences in the ability of roots and leaves to acclimate when plants developed under contrasting temperatures (LT acclimation). However, acclimation was greater in both leaves and roots that developed at the growth temperature (LT acclimation) than in pre-existing leaves and roots shifted from one temperature to another (ST acclimation). The balance between leaf R and A(sat) was maintained in plants grown at different temperatures, regardless of their inherent relative growth rate. We conclude that there is tight coupling between the respiratory acclimation and the temperature under which leaves and roots developed and that acclimation plays an important role in determining the relationship between respiration and photosynthesis

Growth of uniform infinite causal triangulations

We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to estimate the geodesic distance of a given triangle to the rooted boundary in terms of the time of the growth process and to determine from this the fractal dimension. Furthermore, convergence of the boundary process to a diffusion process is shown leading to an interesting duality relation between the growth process and a corresponding branching process.Comment: 27 pages, 6 figures, small changes, as publishe

Two-divisibility of the coefficients of certain weakly holomorphic modular forms

We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly divisible by 2.Comment: Corrected typos. To appear in the Ramanujan Journa

DESIGN AND ANALYSIS OF 2.56 GBPS CML CMOS TRANSCEIVER WITH SPECIFIC LOAD FOR PHYSICAL INSTRUMENTATION APPLICATIONS

In the work we describe the process of designing 2.56 Gbps CML receiver and 1.28 Gbps CML transmitter with specific transmission line properties. The blocks have been designed for the specific need of high speed data transmission in the radiation environment. Signal integrity is also analyzed

Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

Continuum Random Combs and Scale Dependent Spectral Dimension

Numerical computations have suggested that in causal dynamical triangulation models of quantum gravity the effective dimension of spacetime in the UV is lower than in the IR. In this paper we develop a simple model based on previous work on random combs, which share some of the properties of CDT, in which this effect can be shown to occur analytically. We construct a definition for short and long distance spectral dimensions and show that the random comb models exhibit scale dependent spectral dimension defined in this way. We also observe that a hierarchy of apparent spectral dimensions may be obtained in the cross-over region between UV and IR regimes for suitable choices of the continuum variables. Our main result is valid for a wide class of tooth length distributions thereby extending previous work on random combs by Durhuus et al.Comment: 27 pages, 2 figures. Typos and references corrected, new figure