We prove that Hadwiger’s conjecture holds for line graphs. Equivalently, we show that for every loopless graph G (possibly with parallel edges) and every integer k ≥ 0, either G is k-edge-colourable, or there are k + 1 connected subgraphs A1, ..., Ak+1 of G, each with at least one edge, such that E(Ai ∩ Aj) = ∅ and V (Ai ∩ Aj) 6= ∅ for 1 ≤ i < j ≤ k.

Let Qn(x) = ∑n i=0 Aix i be a random algebraic polynomial where the coefficients A0, A1, · · · form a sequence of centered Gaussian random variables. Moreover, assume that the increments ∆j = Aj − Aj−1, j = 0, 1, 2, · · · are independent, A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We study the asymptotic behaviour of the expected number of lo...

In this paper, we investigate the relations between the small functions and the solutions, first, second derivatives, and differential polynomial of the solutions to the differential equation f ′′ +A1e P f ′ +A0e f = 0, where P (z) = anz + · · · + a0, Q(z) = bnz + · · · + b0 are polynomials with degree n (n ≥ 1), ai, bi (i = 0, 1, . . . , n), anbn 6= 0 are complex constants, Aj(z) 6≡ 0 (j = 0, ...

Background: Numerous studies have indicated that there is a possible relationship between GBA variants and Parkinson's disease (PD), however, most of them focused on a few variants such as L444P, N370S. We performed a comprehensive pooled analysis to clarify the relationship between variations of GBA and the risk of PD in different racial groups. Methods: Standard meta-analysis was conducted, i...

Abstract An analysis is presented of the submesoscale tidally-induced anticyclonic eddies formed at eastern mouth Strait Gibraltar and their role in explaining mesoscale features Atlantic Jet – Western Alboran Gyre (AJ-WAG) system. These have been identified for first time using an observational approach based on High Frequency Radar (HFR) derived surface currents which has complemented with Se...

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times Tj, areas Aj and winding angles θj (j = 1, . . . , n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P ({Tj}), ...

Let rj , j = 0, 1, . . . be the Rademacher functions on [0, 1]. We prove that for every measurable subset E of [0, 1] with |E| > 0 and for each λ > 1 there exists a positive integer N such that for all real-valued sequences {aj} there exists a subset J of [0, 1] such that ∑∞ j=N |aj | ≤ λ |J| ∫ J∩E ∣∣∣∑∞j=0 ajrj(t)∣∣∣2 dt.

monary inflammation in healthy human volunteers. Am J Respir Crit Care Med 2000; 162:981–988. 35. Pekkanen J, Brunner EJ, Anderson HR, Tiittanen P, Atkinson RW. Daily concentrations of air pollution and plasma fibrinogen in London. Occup Environ Med 2000;57:818–822. 36. Mutlu GM, Green D, Bellmeyer A, Baker CM, Burgess Z, Rajamannan N, Christman JW, Foiles N, Kamp DW, Ghio AJ, Chandel NS, Dean ...

We study the problem of non-preemptive scheduling to minimize energy consumption for devices that allow dynamic voltage scaling. Specifically, consider a device that can process jobs in a non-preemptive manner. The input consists of (i) the set R of available speeds of the device, (ii) a set J of jobs, and (iii) a precedence constraint Π among J . Each job j in J , defined by its arrival time a...

This review especially describes the dangerous pathogens research program in Azerbaijan (AJ) funded by the US Defense Threat Reduction Agency under the Cooperative Biological Engagement Program (CBEP) from 2011 through 2015. The objectives of the CBEP are to prevent the proliferation of biological weapons; to consolidate and secure collections of dangerous pathogens in central repositories; to ...