Long time behaviour and self-similarity in an addition model with slow Input of monomers

We consider a coagulation equation with constant coefficients and a time dependent power law input of monomers. We discuss the asymptotic behaviour of solutions as $t \to \infty$, and we prove solutions converge to a similarity profile along the non-characteristic direction

The masses of vector supermultiplet and of the Higgs supertriplet in supersymmetric SU(5) model

The masses of vector supermultiplet and of the Higgs supertriplet in standard supersymmetric SU(5) model are calculated. Taking into account uncertainties related with the initial coupling constants and threshold corrections we find that in supersymmetric SU(5) model the scale of the supersymmetry breaking could be up to 50 Tev. We find that in the extensions of the standard SU(5) supersymmetric model it is possible to increase the supersymmetry breaking scale up to $O(10^{12})$ Gev. In standard supersymmetric SU(5) model it is possible to increase the GUT scale up to $5 \cdot 10^{17}$ Gev provided that the masses of chiral superoctets and supertriplets are $m_{3,8} \sim O(10^{13}) Gev$. We also propose SU(5) supersymmetric model with 6 light superdoublets and superoctet with a mass $O(10^{9})$ Gev.Comment: 11 pages, latex, no figure

The signed loop approach to the Ising model: foundations and critical point

The signed loop method is a beautiful way to rigorously study the two-dimensional Ising model with no external field. In this paper, we explore the foundations of the method, including details that have so far been neglected or overlooked in the literature. We demonstrate how the method can be applied to the Ising model on the square lattice to derive explicit formal expressions for the free energy density and two-point functions in terms of sums over loops, valid all the way up to the self-dual point. As a corollary, it follows that the self-dual point is critical both for the behaviour of the free energy density, and for the decay of the two-point functions.Comment: 38 pages, 7 figures, with an improved Introduction. The final publication is available at link.springer.co

Outcome from balloon induced coronary artery dissection after intracoronary beta radiation

OBJECTIVE: To evaluate the healing of balloon induced coronary artery dissection in individuals who have received beta radiation treatment and to propose a new intravascular ultrasound (IVUS) dissection score to facilitate the comparison of dissection through time. DESIGN: Retrospective study. SETTING: Tertiary referral centre. PATIENTS: 31 patients with stable angina pectoris, enrolled in the beta energy restenosis trial (BERT-1.5), were included. After excluding those who underwent stent implantation, the evaluable population was 22 patients. INTERVENTIONS: Balloon angioplasty and intracoronary radiation followed by quantitative coronary angiography (QCA) and IVUS. Repeat QCA and IVUS were performed at six month follow up. MAIN OUTCOME MEASURES: QCA and IVUS evidence of healing of dissection. Dissection classification for angiography was by the National Heart Lung Blood Institute scale. IVUS proven dissection was defined as partial or complete. The following IVUS defined characteristics of dissection were described in the affected coronary segments: length, depth, arc circumference, presence of flap, and dissection score. Dissection was defined as healed when all features of dissection had resolved. The calculated dose of radiation received by the dissected area in those with healed versus non-healed dissection was also compared. RESULTS: Angiography (type A = 5, B = 7, C = 4) and IVUS proven (partial = 12, complete = 4) dissections were seen in 16 patients following intervention. At six month follow up, six and eight unhealed dissections were seen by angiography (A = 2, B = 4) and IVUS (partial = 7, complete = 1), respectively. The mean IVUS dissection score was 5.2 (range 3-8) following the procedure, and 4.6 (range 3-7) at follow up. No correlation was found between the dose prescribed in the treated area and the presence of unhealed disse

Spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron at low values of x and Q^2

We present a precise measurement of the deuteron longitudinal spin asymmetry A_1^d and of the deuteron spin-dependent structure function g_1^d at Q^2 < 1 GeV^2 and 4*10^-5 < x < 2.5*10^-2 based on the data collected by the COMPASS experiment at CERN during the years 2002 and 2003. The statistical precision is tenfold better than that of the previous measurement in this region. The measured A_1^d and g_1^d are found to be consistent with zero in the whole range of x.Comment: 17 pages, 10 figure

Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs

We present a determination of the gluon polarization Delta G/G in the nucleon, based on the helicity asymmetry of quasi-real photoproduction events, Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarized muon beam scattered on a polarized 6-LiD target. The helicity asymmetry for the selected events is = 0.002 +- 0.019(stat.) +- 0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3 (GeV}/c)^2.Comment: 10 pages, 3 figure

Measurement of the Spin Structure of the Deuteron in the DIS Region

We present a new measurement of the longitudinal spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron in the range 1 GeV^2 < Q^2 < 100 GeV^2 and 0.004< x <0.7. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarised muon beam and a large polarised 6-LiD target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region 0.004 < x < 0.03.Comment: 10 pages, 6 figures, subm. to PLB, revised: author list, Fig. 4, details adde