Monotone graph limits and quasimonotone graphs

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence satisfies a `quasi-monotonicity' property defined by a certain functional tending to zero. As a tool we prove an inequality relating the cut and $L^1$ norms of kernels of the form $W_1-W_2$ with $W_1$ and $W_2$ monotone that may be of interest in its own right; no such inequality holds for general kernels.Comment: 38 page

Reliability of a 2-Bout exercise test on a Wattbike cycle ergometer

Purpose: To determine the intraday and interday reliability of a 2 × 4-min performance test on a cycle ergometer (Wattbike) separated by 30 min of passive recovery (2 × 4MMP). Methods: Twelve highly trained cyclists (mean ± SD; age = 20 ± 2 y, predicted VO2max = 59.0 ± 3.6 mL · kg–1 · min–1) completed six 2 × 4MMP cycling tests on a Wattbike ergometer separated by 7 d. Mean power was measured to determine intraday (test 1 [T1] to test 2 [T2]) and interday reliability (weeks 1–6) over the repeated trials. Results: The mean intraday reliabilities of the 2 × 4MMP test, as expressed by the typical error of measurement (TEM, W) and coefficient of variation (CV, %) over the 6 wk, were 10.0 W (95% confidence limits [CL] 8.2–11.8), and 2.6% (95%CL 2.1–3.1), respectively. The mean interday reliability TEM and CV for T1 over the 6 wk were 10.4 W (95%CL 8.7–13.3) and 2.7% (95%CL 2.3–3.5), respectively, and 11.7 W (95%CL 9.8–15.1) and 3.0% (95%CL 2.5–3.9) for T2. Conclusion: The testing protocol performed on a Wattbike cycle ergometer in the current study is reproducible in highly trained cyclists. The high intraday and interday reliability make it a reliable method for monitoring cycling performance and for investigating factors that affect performance in cycling events

Ring-resonator-based wavelength filters

Microring resonators (MR) represent a class of filters with characteristics very similar to those of Fabry–Perot filters. However, they offer the advantage that the injected and reflected signals are separated in individual waveguides, and in addition, their design does not require any facets or gratings and is thus particularly simple. MRs evolved from the fields of fibre optic ring resonators and micron scale droplets. Their inherently small size (with typical diameters in the range between several to tens of micrometres), their filter characteristics and their potential for being used in complex and flexible configurations make these devices particularly attractive for integrated optics or VLSI photonics applications.\ud MRs for filter applications, delay lines, as add/drop multiplexers, and modulators will be covered in detail in this chapter, while other applications such as in optical sensing, in spectroscopy or for coherent light generation (MR lasers) are outside the scope of this chapter.\ud This chapter focuses primarily on 4-port microrings, while 2-port devices will play a minor role here and are covered in more detail in Chap. 9. The present chapter starts with design considerations, the functional behaviour, and key characteristics of a single microring resonator and continues with the design of cascaded MRs allowing the implementation of higher order filters. Finally, complex devices like add-drop filters, tuneable dispersion compensators, all-optical wavelength converters, and tuneable cross-connects are treated.\u

The analysis of passenger air transport development in Poland over the period 2010-2018

Purpose: The aim of the conducted research was analysis of data regarding aviation activities in the field of passenger transport at Polish airports over the period 2010-2018. Design/Methodology/Approach: The Analysis of the air travel segment referring passenger transport in Polish airports is based on available literature, analysis and statistical documentation of the air transport market for the years 2010-2018. Findings: The Polish market of air services continues to be in a state of flux. The pace at which changes occur results from a combination of external and internal factors, which precondition the behaviour of air carriers and customers, and the operation of airports. When analysing air transport development forecast, we can see a further upward trend in the number of activities of all market participants. That said, in the near future we should be expecting an expansion of connections, erection of state-of-the-art infrastructure, new air services, and above all a growth of importance of Poland on the aviation map of Europe. Practical Implications: Having regard to data included in the study, without a doubt the Polish aviation market should be considered a strongly developing one, having enormous potential ensuing not only from population mobility different EU standards, but also from demographic potential of Poland, gradual wealth gaining of the Polish society, and Poland’s geographic location. Originality/Value: A comparative analysis of the potential of selected air carriers and airports with respect to the volume of transported passengers and flights performed.peer-reviewe

Spontaneous Decay in the Presence of Absorbing Media

After giving a summary of the basic-theoretical concept of quantization of the electromagnetic field in the presence of dispersing and absorbing (macroscopic) bodies, their effect on spontaneous decay of an excited atom is studied. Various configurations such as bulk material, planar half space media, spherical cavities, and microspheres are considered. In particular, the influence of material absorption on the local-field correction, the decay rate, the line shift, and the emission pattern are examined. Further, the interplay between radiative losses and losses due to material absorption is analyzed. Finally, the possibility of generating entangled states of two atoms coupled by a microsphere-assisted field is discussed.Comment: 32 pages, 15 eps figures, contribution to Recent Research Developments in Optics, to be published by Research Signpos

Time Dependent Resonance Theory

An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g. the coupling of an atom or molecule to a photon-radiation field, and Auger states of the helium atom, as well as in spectral geometry and number theory. We present a dynamic (time-dependent) theory of such quantum resonances. The key hypotheses are (i) a resonance condition which holds generically (non-vanishing of the {\it Fermi golden rule}) and (ii) local decay estimates for the unperturbed dynamics with initial data consisting of continuum modes associated with an interval containing the embedded eigenvalue of the unperturbed Hamiltonian. No assumption of dilation analyticity of the potential is made. Our method explicitly demonstrates the flow of energy from the resonant discrete mode to continuum modes due to their coupling. The approach is also applicable to nonautonomous linear problems and to nonlinear problems. We derive the time behavior of the resonant states for intermediate and long times. Examples and applications are presented. Among them is a proof of the instability of an embedded eigenvalue at a threshold energy under suitable hypotheses.Comment: to appear in Geometrical and Functional Analysi