The Planck constant, with its mathematical symbol h, is a fundamental constant in quantum mechanics that is associated with the quantization of light and matter. It is also of fundamental importance to metrology, such as the definition of ohm and volt and the latest definition of kilogram. One of the first measurements to determine the Planck constant is based on the photoelectric effect; however, the values thus obtained so far have exhibited a large uncertainty. The accepted value of the Planck constant, 6.626 070 15 × 10-34 J s, is obtained from one of the most precise methods, the Kibble balance, which involves the quantum Hall effect, the Josephson effect, and the use of the international prototype of the kilogram or its copies. Here, we present a precise determination of the Planck constant by modern photoemission spectroscopy technique. Through the direct use of Einstein's photoelectric equation, the Planck constant is determined by accurately measuring the energy position of the gold Fermi level using light sources with various photon wavelengths. AZD4573 in vivo The precision of the Planck constant as measured in this work, 6.626 10(13) × 10-34 J s, is improved by four to five orders of magnitude from the previous photoelectric effect measurements. We propose that this direct method of photoemission spectroscopy has potential to further increase its measurement precision of the Planck constant to be comparable to the most accurate methods available at present.We consider a large ring of nonlocally coupled phase oscillators and show that apart from stationary chimera states, this system also supports nonstationary coherence-incoherence patterns (CIPs). For identical oscillators, these CIPs behave as breathing chimera states and are found in a relatively small parameter region only. It turns out that the stability region of these states enlarges dramatically if a certain amount of spatially uniform heterogeneity (e.g., Lorentzian distribution of natural frequencies) is introduced in the system. In this case, nonstationary CIPs can be studied as stable quasiperiodic solutions of a corresponding mean-field equation, formally describing the infinite system limit. Carrying out direct numerical simulations of the mean-field equation, we find different types of nonstationary CIPs with pulsing and/or alternating chimera-like behavior. Moreover, we reveal a complex bifurcation scenario underlying the transformation of these CIPs into each other. These theoretical predictions are confirmed by numerical simulations of the original coupled oscillator system.The recurrence analysis of dynamic systems has been studied since Poincaré's seminal work. Since then, several approaches have been developed to study recurrence properties in nonlinear dynamical systems. In this work, we study the recently developed entropy of recurrence microstates. We propose a new quantifier, the maximum entropy (Smax). The new concept uses the diversity of microstates of the recurrence plot and is able to set automatically the optimum recurrence neighborhood (ϵ-vicinity), turning the analysis free of the vicinity parameter. In addition, ϵ turns out to be a novel quantifier of dynamical properties itself. We apply Smax and the optimum ϵ to deterministic and stochastic systems. The Smax quantifier has a higher correlation with the Lyapunov exponent and, since it is a parameter-free measure, a more useful recurrence quantifier of time series.Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a large variety of complex networks, in which some are deterministic and others are random. The goal of this paper is to generate a class of random scale-free networks. To achieve this, we introduce three types of operations, i.e., rectangle operation, diamond operation, and triangle operation, and provide the concrete process for generating random scale-free networks N(p,q,r,t), where probability parameters p,q,r hold on p+q+r=1 with 0≤p,q,r≤1. We then discuss their topological properties, such as average degree, degree distribution, diameter, and clustering coefficient. First, we calculate the average degree of each member and discover that each member is a sparse graph. Second, by computing the degree distribution of our network N(p,q,r,t), we find that degree distribution obeys the power-law distribution, which implies that each member is scale-free. Next, according to our analysis of the diameter of our network N(p,q,r,t), we reveal the fact that the diameter may abruptly transform from small to large. Afterward, we give the calculation process of the clustering coefficient and discover that its value is mainly determined by r.In this work, we analyze the growth of the cumulative number of confirmed infected cases by a novel coronavirus (COVID-19) until March 27, 2020, from countries of Asia, Europe, North America, and South America. Our results show that (i) power-law growth is observed in all countries; (ii) by using the distance correlation, the power-law curves between countries are statistically highly correlated, suggesting the universality of such curves around the world; and (iii) soft quarantine strategies are inefficient to flatten the growth curves. Furthermore, we present a model and strategies that allow the government to reach the flattening of the power-law curves. We found that besides the social distancing of individuals, of well known relevance, the strategy of identifying and isolating infected individuals in a large daily rate can help to flatten the power-laws. These are the essential strategies followed in the Republic of Korea. The high correlation between the power-law curves of different countries strongly indicates that the government containment measures can be applied with success around the whole world. These measures are scathing and to be applied as soon as possible.In this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo with the fractional parameter χ, where 0 less then χ≤1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top. The non-integer-order model suggested in the present study depicts the past behavior of the concentration of the solution on the basis of having information of the initial concentration present in the dye. Being nonlinear, it carries the possibility to have no exact solution. However, the Lipchitz condition shows the existence and uniqueness of the underlying model's solution in non-integer-order settings.