Inter-ELM power decay length for JET and ASDEX upgrade: measurement and comparison with heuristic drift-based model

Experimental measurements of the SOL power decay length (λ(q)) estimated from analysis of fully attached divertor heat load profiles from two tokamaks, JET and ASDEX Upgrade, are presented. Data was measured by means of infrared thermography. An empirical scaling reveals parametric dependency λ(q) in mm = 0.73B(T)(-0.78)q(cyl)(1.2)P(SOL)(0.1)R(geo)(0), where B(T)(T) describes the toroidal magnetic field, q(cyl) the cylindrical safety factor, P(SOL)(MW) the power crossing the separatrix and R(geo)(m) the major radius of the device. A comparison of these measurements to a heuristic particle drift-based model shows satisfactory agreement in both absolute magnitude and scaling. Extrapolation to ITER gives λ(q) ? 1 mm.     

Primes in tuples II

We prove that

$ \mathop{ \lim \inf}\limits_{n \rightarrow \infty} \frac{p_{n+1}-p_{n}}{\sqrt{\log p_{n}} \left(\log \log p_{n}\right)^{2}}< \infty, $

where p _n denotes the nth prime. Since on average p _n+1?p _n is asymptotically log _n , this shows that we can always find pairs of primes much closer together than the average. We actually prove a more general result concerning the set of values taken on by the differences p?p′ between primes which includes the small gap result above.

     

On the $$L^1$$ L 1 norm of an exponential sum involving the divisor function

Archiv der Mathematik - In this paper, we obtain bounds on the $$L^1$$ -norm of the sum $$\sum _{n\le x}\tau (n)e(\alpha n)$$ where $$\tau (n)$$ is the divisor function.     

A reagentless electrochemical biosensor based on a protein scaffold

Apo-myoglobin, labeled with the environmentally sensitive redox probe RuII(NH3)4(1,10-phenanthroline-5-maleimide)2+, was immobilized onto gold electrodes modified with 11-mercaptoundecanoic acid and subsequently labeled with biotin; avidin binding to the immobilized biotin was specifically and quantitatively detected by a change in cyclic voltammetry of the co-immobilized probe.     

A note on S(t) and the zeros of the Riemann zeta-function

Let S(t) denote the argument of the Riemann zeta-function atthe point 1/2 + it. Assuming the Riemann hypothesis, we sharpenthe constant in the best currently known bounds for S(t) andfor the change of S(t) in intervals. We then deduce estimatesfor the largest multiplicity of a zero of the zeta-function,and for the largest gap between the zeros.     

A model recognition switch. Electrochemical control and transduction of imidazole binding by electrode-immobilized microperoxidase-11

Electrode-immobilized microperoxidase-11 exhibited a titratable potentiometric response to imidazole, demonstrating both molecular recognition and the capability for "switchable" changes in the affinity of an immobilized redox-receptor for a target ligand.     

On the Pair Correlation of Zeros of the Riemann Zeta-Function

To study the distribution of pairs of zeros of the Riemann zeta-function,Montgomery introduced the function where is real and T 2, and ' denote the imaginary parts ofzeros of the Riemann zeta-function, and w(u) = 4/(4 + u²). Assumingthe Riemann Hypothesis, Montgomery proved an asymptotic formulafor F() when || 1, and made the conjecture that F() = 1 + o(1)as T for any bounded with || 1. In this paper we use anapproximation for the prime indicator function together witha new mean value theorem for long Dirichlet polynomials andtails of Dirichlet series to prove that, assuming the GeneralizedRiemann Hypothesis for all Dirichlet L-functions, then for any > 0 we have uniformlyfor and all T T₀(). 1991Mathematics Subject Classification: primary 11M26; secondary11P32.     

Higher correlations of divisor sums related to primes II: variations of the error term in the prime number theorem

We calculate the triple correlations for the truncated divisorsum _R(n). The _R(n) behave over certain averages just as theprime counting von Mangoldt function (n) does or is conjecturedto do. We also calculate the mixed (with a factor of (n)) correlations.The results for the moments up to the third degree, and thereforethe implications for the distribution of primes in short intervals,are the same as those we obtained (in the first paper with thistitle) by using the simpler approximation _R(n). However, when_R(n) is used, the error in the singular series approximationis often much smaller than what _R(n) allows. Assuming the GeneralizedRiemann Hypothesis (GRH) for Dirichlet L-functions, we obtainan _±-result for the variation of the error term in theprime number theorem. Formerly, our knowledge under GRH wasrestricted to -results for the absolute value of this variation.An important ingredient in the last part of this work is a recentresult due to Montgomery and Soundararajan which makes it possiblefor us to dispense with a large error term in the evaluationof a certain singular series average. We believe that our resultson the sums _R(n) and _R(n) can be employed in diverse problemsconcerning primes.