Cuts for two-body decays at colliders

Fixed-order perturbative calculations of fiducial cross sections for two-body decay processes at colliders show disturbing sensitivity to unphysically low momentum scales and, in the case of H → γγ in gluon fusion, poor convergence. Such problems have their origins in an interplay between the behaviour of standard experimental cuts at small transverse momenta (pt) and logarithmic perturbative contributions. We illustrate how this interplay leads to a factorially divergent structure in the perturbative series that sets in already from the first orders. We propose simple modifications of fiducial cuts to eliminate their key incriminating characteristic, a linear dependence of the acceptance on the Higgs or Z-boson pt, replacing it with quadratic dependence. This brings major improvements in the behaviour of the perturbative expansion. More elaborate cuts can achieve an acceptance that is independent of the Higgs pt at low pt, with a variety of consequent advantages.

Effects of Temporal Expectations on the Perception of Motion Gestalts

Gestalt psychology has traditionally ignored the role of attention in perception, leading to the view that autonomous processes create perceptual configurations that are then attended. More recent research, however, has shown that spatial attention influences a form of Gestalt perception: the coherence of random-dot kinematograms (RDKs). Using ERPs, we investigated whether temporal expectations exert analogous attentional effects on the perception of coherence level in RDKs. Participants were presented fixed-length sequences of RDKs and reported the coherence level of a target RDK. The target was indicated immediately after its appearance by a postcue. Target expectancy increased as the sequence progressed until target presentation; afterward, remaining RDKs were perceived without target expectancy. Expectancy influenced the amplitudes of ERP components P1 and N2. Crucially, expectancy interacted with coherence level at N2, but not at P1. Specifically, P1 amplitudes decreased linearly as a function of RDK coherence irrespective of expectancy, whereas N2 exhibited a quadratic dependence on coherence: larger amplitudes for RDKs with intermediate coherence levels, and only when they were expected. These results suggest that expectancy at early processing stages is an unspecific, general readiness for perception. At later stages, expectancy becomes stimulus specific and nonlinearly related to Gestalt coherence.

High-Temperature Evolution of the Magnetization of Aluminum Reduction Cell Steel

The magnetic properties of steel of a structural element of an aluminum reduction cell have been investigated in the temperature range of 300–900 K. The analysis of the temperature dependence of the saturation magnetization MS(T) showed (i) the applicability of the Bloch’s 3=2 law and a reason- able value of the Bloch’s constant for steel and (ii) the quadratic dependence MS(T) (1 - T2) in the temperature range of 380–700 K.

Why quadratic log-log dependence is ubiquitous and what next

Purpose In many real-life situations ranging from financial to volcanic data, growth is described either by a power law – which is linear in log-log scale or by a quadratic dependence in the log-log scale. The purpose of this paper is to explain this empirical fact. Design/methodology/approach The authors use natural scale invariance requirements. Findings In this paper, the authors used natural scale invariance requirement to explain the ubiquity of quadratic log-log dependencies. The authors also explain what to do if quadratic log-log models turn out to be insufficiently accurate. In this case, scale-invariance requirements lead to dependencies which in the log-log scale take cubic, 4th order, etc. form. Originality/value To the best of authors’ knowledge, this is the first theoretical explanation of the empirical quadratic log-log dependence.

Рост ограненных пор в кристалле по механизму Бартона--Кабреры--Франка

The growth of a faceted pore in a crystal via Burton-Cabrera-Frank mechanism under tensile load is considered. The growth is due to diffusion of vacancies containing in the crystal, towards terraces and steps on the pore surface. Expressions for the rate of advance of a single step and a group of parallel steps are found as well as the expression for the dependence of the normal growth rate of a pore by a spiral mechanism on the applied tensile load. It is shown that in a certain range of small tensile loads, the pore growth rate may have a quadratic dependence on the load, whereas for large loads this dependence is linear.

Simulation of the optimal diameter and wall thickness of hollow Fe3O4 microspheres in magnetorheological fluids

The shear stress exhibited a quadratic dependence on the dimensionless wall thickness under a certain particle diameter.

GDP AS A FACTOR INFLUENCING THE SOCIAL INDICATORS OF UKRAINE'S LIVELIHOOD: MODELLING

In the period 1996-2017, the dynamics of the subsistence minimum, the minimum wage, the consumer price index and the gross domestic product of Ukraine are analysed. These indicators have a growing trend. The necessity to use the mathematical modelling to study social and economic indicators of living standards of the population is emphasised. The trend of the dynamics of the minimum wage in the UAH is given. It has a tendency to increase. This tendency is described by quadratic dependence. The following periods are distinguished: 1996-2010 – the smooth growth of wages in quadratic dependence; 2010-2016 years – their slowed down growth by linear dependence. From 2017, when average wage has increased two times, the period of significant wages growing begins. Minimum wage retardation from the subsistence minimum until 2017 is shown. The dynamics of the subsistence minimum, which has the same periods and regularities as the salary, is analysed. Its trend is presented. The dynamics of the consumer price index is analysed. It has been broken down into the following intervals: I (1996-2010) – steady inflation growth; II (2010-2013) – price stability; III (2014 – until now) – rapid growth of prices or inflation. The inflation forecasting for 2018 is given. It is shown that economic growth (GDP) and social standards are cyclical. The main tendencies of the influence of the gross domestic product on the minimum wage, the consumer price index, the subsistence minimum are summarized. The dependence of the minimum wage on the volume of GDP is given. Econometric models of the dependence of the minimum wage on GDP in UAH and the level of inflation from the minimum wage are presented. It is shown that GDP growth is accompanied by the minimum wage increase. It is emphasized that growth of social payments negatively affects the growth of the consumer price index. It is noted that the rate of growth of the economy is not sufficient to ensure the growth of social benefits. The recommendations for economic growth are given.