Harmonic sets and the harmonic prime number theorem

We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2

Toxicity of materials in fire situations: Laboratory data obtained at the University of San Francisco

Approximately 300 materials were evaluated using a specific set of test conditions. Materials tested included wood, fibers, fabrics and synthetic polymers. Data obtained using 10 different sets of test conditions are presented

Optimising sward structure and herbage yield for the performance of dairy cows at pasture.

End of Project ReportsThe basic unit of intake is the bite. The total daily intake of grazed grass is determined by the number of bites taken and the weight of the average bite. In this project the focus was on sward structure (architecture) and its effects on bite volume and weight. There were two objectives. The first was to determine the plant growth mechanism responsible for variations in sward structure. The investigation was carried out at The Queen’s University in Belfast and involved microscopic study of leaves from plants grown under controlled conditions. The second objective, to determine how bite volume and mass was affected by differences in sward structure was a field study using fistulated cows and was done at Moorepark.EU Structural Funds (EAGGF

Active Carbon and Oxygen Shell Burning Hydrodynamics

We have simulated 2.5$\times10^3$ s of the late evolution of a $23 \rm M_\odot$ star with full hydrodynamic behavior. We present the first simulations of a multiple-shell burning epoch, including the concurrent evolution and interaction of an oxygen and carbon burning shell. In addition, we have evolved a 3D model of the oxygen burning shell to sufficiently long times (300 s) to begin to assess the adequacy of the 2D approximation. We summarize striking new results: (1) strong interactions occur between active carbon and oxygen burning shells, (2) hydrodynamic wave motions in nonconvective regions, generated at the convective-radiative boundaries, are energetically important in both 2D and 3D with important consequences for compositional mixing, and (3) a spectrum of mixed p- and g-modes are unambiguously identified with corresponding adiabatic waves in these computational domains. We find that 2D convective motions are exaggerated relative to 3D because of vortex instability in 3D. We discuss the implications for supernova progenitor evolution and symmetry breaking in core collapse.Comment: 5 pages, 4 figures in emulateapj format. Accepted for publication in ApJ Letters. High resolution figure version available at http://spinach.as.arizona.ed

Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I

We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint operator whose commutator matches with a quantization of the classical Poisson bracket involving structure functions. Our quantization scheme is based on a geometric interpretation of the Hamiltonian constraint as a generator of phase space-dependent diffeomorphisms. The resulting Hamiltonian constraint at finite triangulation has a conceptual similarity with the "mu-bar"-scheme in loop quantum cosmology and highly intricate action on the spin-network states of the theory. We construct a subspace of non-normalizable states (distributions) on which the continuum Hamiltonian constraint is defined which leads to an anomaly-free representation of the Poisson bracket of two Hamiltonian constraints in loop quantized framework.Comment: 60 pages, 6 figure

Analysis of the kinetic mechanism of recombinant human isoprenylcysteine carboxylmethyltransferase (Icmt)

BACKGROUND: Isoprenylcysteine carboxyl methyltransferase (Icmt) is the third of three enzymes that posttranslationally modify proteins that contain C-terminal CaaX motifs. The processing of CaaX proteins through this so-called prenylation pathway via a route initiated by addition of an isoprenoid lipid is required for both membrane targeting and function of the proteins. The involvement of many CaaX proteins such as Ras GTPases in oncogenesis and other aberrant proliferative disorders has led to the targeting of the enzymes involved in their processing for therapeutic development, necessitating a detailed understanding of the mechanisms of the enzymes. RESULTS: In this study, we have investigated the kinetic mechanism of recombinant human Icmt. In the reaction catalyzed by Icmt, S-adenosyl-L-methionine (AdoMet) provides the methyl group that is transferred to the second substrate, the C-terminal isoprenylated cysteine residue of a CaaX protein, thereby generating a C-terminal prenylcysteine methyl ester on the protein. To facilitate the kinetic analysis of Icmt, we synthesized a new small molecule substrate of the enzyme, biotin-S-farnesyl-L-cysteine (BFC). Initial kinetic analysis of Icmt suggested a sequential mechanism for the enzyme that was further analyzed using a dead end competitive inhibitor, S-farnesylthioacetic acid (FTA). Inhibition by FTA was competitive with respect to BFC and uncompetitive with respect to AdoMet, indicating an ordered mechanism with SAM binding first. To investigate the order of product dissociation, product inhibition studies were undertaken with S-adenosyl-L-homocysteine (AdoHcy) and the N-acetyl-S-farnesyl-L-cysteine methylester (AFCME). This analysis indicated that AdoHcy is a competitive inhibitor with respect to AdoMet, while AFCME shows a noncompetitive inhibition with respect to BFC and a mixed-type inhibition with respect to AdoMet. These studies established that AdoHcy is the final product released, and that BFC and AFCME bind to different forms of the enzyme. CONCLUSIONS: These studies establish that catalysis by human Icmt proceeds through an ordered sequential mechanism and provide a kinetic framework for analysis of specific inhibitors of this key enzyme