In the framework of analytic approach to QCD, which has been recently intensively developed, the dependence of nonperturbative contributions in a running coupling of strong interaction on initial perturbative approximation to 3-loop order is studied. The nonperturbative contributions are obtained in an explicit form. In the ultraviolet region they are shown to be represented in the form of the ...

There are several statements equivalent to the famous Riemann hypothesis. In 2011, Solé and Planat stated that hypothesis is true if only inequality \(\zeta(2) \cdot \prod_{q\leq q_{n}} (1+\frac{1}{q}) > e^{\gamma} \log \theta(q_{n})\) holds for all prime numbers \(q_{n}> 3\), where \(\theta(x)\) Chebyshev function, \(\gamma \approx 0.57721\) Euler-Mascheroni constant, \(\zeta(x)\) zeta f...

Let Tn,k(X) be the characteristic polynomial of the nth Hecke operator acting on the space of cusp forms of weight k for the full modular group. We record a simple criterion which can be used to check the irreducibility of the polynomials Tn,k(X). Using this criterion with some machine computation, we show that if there exists n ≥ 2 such that Tn,k(X) is irreducible and has the full symmetric gr...

desertification is specific phenomenon of arid, semi-arid, dry sub humid regions. this phenomenon has a high rate in developing countries such as iran. the main objective of this research was calibration of imdpa model in abuzeidabad (kashan) region with emphasis on land criteria. imdpa model, introduced by iranian researchers to assess desertification intensity in iran. before application, the...

INTRODUCTION Systemic lupus erythematosus (SLE or lupus) is a chronic autoimmune disease, and kidney involvement with SLE, a.k.a. lupus nephritis (LN), is a frequent and severe complication of SLE that increases patient morbidity and mortality. About 50% of patients with SLE encounter renal abnormalities which, if left untreated, can lead to end-stage renal disease. Kidney biopsy is considered ...

Let K be a field of characteristic p > 0. It is proved that the group Autord(D(Ln)) of order preserving automorphisms of the ring D(Ln) of differential operators on a Laurent polynomial algebra Ln := K[x ±1 1 , . . . , x n ] is isomorphic to a skew direct product of groups Z n p⋊AutK(Ln) where Zp is the ring of p-adic integers. Moreover, the group Autord(D(Ln)) is found explicitly. Similarly, A...

ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...

This paper proposes a cumulant (higher-order statistics) based mean-square-error (MSE) criterion for the design of Wiener filters when both the given wide-sense stationary random signal x(n) and the desired signal d(n) are non-Gaussian and contaminated by Gaussian noise sources. It is theoretically shown that the designed Wiener filter associated with the proposed criterion is identical to the ...

in this paper, first, a new criterion, titled “surplus percent of the customers” is defined for static transmission expansion planning in restructured power systems. then by a simple example, the new criterion is compared with some already presented market-based criteria and it is shown that the new criterion can realistically evaluate the transmission network expansion from the market view. in...

This is the appendix to the paper Temporal Analysis of Static Priority Preemptive Scheduled Cyclic Streaming Applications using CSDF Models [1]. The temporal analysis approach presented in [1] makes use of an iterative algorithm that computes so-called maximum busy periods over multiple task phases. The algorithm contains a stop criterion indicating after which iteration of the algorithm subseq...