•Concept of polynomials in logistic function is introduced.•Nonlinear differential equations with exact solutions in the form of polynomials in logistic function are found.•It is shown there are ...solitary waves with many maximum and minimum.•Algorithm for finding of exact solutions by means of polynomial in logistic function is given.
Properties of polynomials in logistic function are studied. It is demonstrated that these polynomials can be used for construction of exact solutions to nonlinear differential equations. Nonlinear differential equations with exact solutions in the form of polynomials in logistic function are found. It is shown there are solitary waves of nonlinear differential equations described by polynomial in logistic function with many maximum and minimum.
A method for finding solitary wave solutions to nonlinear differential equations is presented. A generalization for the logistic function to obtain a solitary wave solution is introduced. Properties ...of this basic function are discussed. An algorithm for finding exact solutions in the form of a solitary wave for nonlinear differential equations is formulated. The method has significant advantages over other approaches of this type. Its advantage is due to the fact that in the calculations we do not use the form of a specific function. Our approach is particularly effective in finding exact solutions to high-order nonlinear differential equations used in describing the propagation of pulses in an optical fiber. The application of the exact solutions search method for finding highly dispersed solitons of nonlinear differential equations is shown.
The task of projecting the number of inhabitants is based on rigorous calculations, on prior knowledge about the behavior of demographic variables that imply population entries or exits. The ...objective of this article was to present a statistical method for estimating demographic projections, showing its methodological and technical aspects, so that non-demographers have the necessary elements for their estimation. The above was achieved through the use of the Logistics Function, taking the reader step by step in order to make the procedure to follow clear; Subsequently, for this purpose, a projection exercise is carried out using data for the young population (15 to 29 years old) in the Metropolitan Zone of the Valley of Mexico (ZMVM) as an example. The results show that in 2050 the number of young people in the ZMVM will reach 5.2 million, which corresponds to a decrease of 0.76%. This indicates that, within approximately 30 years, the number of young people in the ZMVM will still be high (22.27% of the total population of said area). It is concluded that by using the logistic function an acceptable estimate can be obtained in population projections, in general and by large age groups.
•Annual start of season estimates from combined Landsat and Sentinel-2 time series.•Choice of vegetation index more important than choice of model.•Results indicate higher suitability of EVI for ...estimating start of season than NDVI.•Combination of sensors improved estimates compared to single-sensor time series.•Decreasing observation frequency diminished start of season estimates.
Vegetation phenology has a great impact on land-atmosphere interactions like carbon cycling, albedo, and water and energy exchanges. To understand and predict these critical land-atmosphere feedbacks, it is crucial to measure and quantify phenological responses to climate variability, and ultimately climate change. Coarse-resolution sensors such as MODIS and AVHRR have been useful to study vegetation phenology from regional to global scales. These sensors are, however, not capable of discerning phenological variation at moderate spatial scales. By offering increased observation density and higher spatial resolution, the combination of Landsat and Sentinel-2 time series might provide the opportunity to overcome this limitation.
In this study, we analyzed the potential of combined Sentinel-2 and Landsat time series for estimating start of season (SOS) of broadleaf forests across Germany for the year 2018. We tested two common statistical modeling approaches (logistic and generalized additive models using thin plate splines) and the two most commonly used vegetation indices, the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI).
We found strong agreement between SOS estimates from logistic and spline models (rEVI = 0.86; rNDVI = 0.65), whereas agreement was higher for EVI than for NDVI (RMSDEVI = 3.07, RMSDNDVI = 5.26 days). The choice of vegetation index thus had a higher impact on the results than the fitting method. The EVI-based SOS also showed higher correlation with ground observations compared to NDVI (rEVI = 0.51, rNDVI = 0.42). Data density played an important role in estimating land surface phenology. Models combining Sentinel-2A/B, with an average cloud-free observation frequency of 12 days, were largely consistent with the combined Landsat and Sentinel-2 models, suggesting that Sentinel-2A/B may be sufficient to capture SOS for most areas in Germany in 2018. However, in non-overlapping swath areas and mountain areas, observation frequency was significantly lower, underlining the need to combine Landsat and Sentinel-2 for consistent SOS estimates over large areas. Our study demonstrates that estimating SOS of temperate broadleaf forests at medium spatial resolution has become feasible with combined Landsat and Sentinel-2 time series.
In this note the Hausdorff approximation of the Heaviside step function by several sigmoid functions (log–logistic, transmuted log–logistic and generalized logistic functions) is considered and ...precise upper and lower bounds for the Hausdorff distance are obtained. Numerical examples, that illustrate our results are given, too.
Dispatching unmanned aerial vehicles (UAVs) to harvest sensing-data from distributed sensors is expected to significantly improve the data collection efficiency in conventional wireless sensor ...networks (WSNs). In this paper, we consider a UAV-enabled WSN, where a flying UAV is employed to collect data from multiple sensor nodes (SNs). Our objective is to maximize the minimum average data collection rate from all SNs subject to a prescribed reliability constraint for each SN by jointly optimizing the UAV communication scheduling and three-dimensional (3D) trajectory. Different from the existing works that assume the simplified line-of-sight (LoS) UAV-ground channels, we consider the more practically accurate angle-dependent Rician fading channels between the UAV and SNs with the Rician factors determined by the corresponding UAV-SN elevation angles. However, the formulated optimization problem is intractable due to the lack of a closed-form expression for a key parameter termed effective fading power that characterizes the achievable rate given the reliability requirement in terms of outage probability. To tackle this difficulty, we first approximate the parameter by a logistic ("S" shape) function with respect to the 3D UAV trajectory by using the data regression method. Then, the original problem is reformulated to an approximate form, which, however, is still challenging to solve due to its non-convexity. As such, we further propose an efficient algorithm to derive its suboptimal solution by using the block coordinate descent technique, which iteratively optimizes the communication scheduling, the UAV's horizontal trajectory, and its vertical trajectory. The latter two subproblems are shown to be non-convex, while locally optimal solutions are obtained for them by using the successive convex approximation technique. Finally, extensive numerical results are provided to evaluate the performance of the proposed algorithm and draw new insights on the 3D UAV trajectory under the Rician fading as compared to conventional LoS channel models.
We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin S = 1/2 Ising-like model and a (logistic) Fermi–Dirac-like function to describe ...the spread of Covid-19. Our analysis show that: (i) in many cases the epidemic curve can be described by a Gaussian-type function; (ii) the temporal evolution of the accumulative number of infections and fatalities follow a logistic function; (iii) the key role played by the quarantine to block the spread of Covid-19 in terms of an interacting parameter between people. In the frame of elementary percolation theory, we show that: (i) the percolation probability can be associated with the probability of a person being infected with Covid-19; (ii) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing. Yet, we make a connection between epidemiological concepts and well-established concepts in condensed matter Physics.
The κ-exponential function, representing a generalization of the exponential function, has been firstly introduced in physics, and, then, it has been considered in a noteworthy number of fields ...because of its ability to take rare events into account. Among the possible applications of this function, one of particular interest is in economics in which rare events may consist in natural disasters, such as earthquakes that reduce the supply of capital, or epidemics or other external shocks influencing the supply of intermediate inputs, human or physical capital. Starting from the κ-exponential function, the κ-logistic function, which is a generalization of the sigmoidal function, can be obtained and used to describe production functions in a unique setting to take into account (1) several shapes usually considered in economics (i.e. concave and non-concave production functions), (2) economies at different development levels, and, (3) the possible occurrence of rare events. In this paper, we investigate the economic growth model as proposed by Böhm and Kaas (2000), wherein the production function utilizes the κ-logistic function. We provide theoretical results confirmed by extensive computational experiments and in line with economic literature showing that a poverty trap may emerge together with fluctuations, multistability and complex dynamics.
•The κ-logistic production function is a generalization of the sigmoidal production function.•Economic growth is considered across various levels of development.•Non-concave production functions can lead to the occurrence of multistability and complex dynamics.•The poverty trap can be exhibited.
The Accelerator Driven Advanced Nuclear Energy System (ADANES) is currently undergoing research and development (R&D), presenting challenges in cost estimation due to significant uncertainties. ...Traditional nuclear power cost assessment methods, tailored for mature technologies, lack relevance for advanced systems like ADANES. To address this gap, our study proposes a unique cost analysis approach, dividing ADANES into two stages: the experimental research and development (ERD) stage and the industrial demonstration (ID) stage. Specificlly, in the ERD stage, this study employs a Logistic function-based evaluation method that considers factors such as construction period extension, the proportion of fixed costs, and the upper limit of cost estimated by experts to address potential cost overruns. For the ID stage, this study utilizes a stochastic differential equation (SDE) to account for uncertainties. Monte Carlo simulation is employed to analyze the impact of parameter changes, including construction period extension and acceptable upper limits of cost and duration. Results reveal a substantial increase in expected cost during the ERD stage, ranging from 100% to 140% of the original budget when extending the experimental research duration by 10% to 50%. The ID stage demonstrates an even more significant impact, with a 50% construction period extension resulting in an expected cost of 182% of the original budget. The study suggests that judiciously extending acceptable cost and duration caps can enhance the project's success rate. This innovative cost analysis approach provides valuable insights for navigating the uncertainties associated with ADANES development.
•A cost analysis approach is introduced for the disruptive ADANES nuclear energy system.•It employs a logistic function-based evaluation method and stochastic differential equation to account for uncertainties.•A case study validates the method, revealing the numerical relationship between time extension and cost overrun of ADANES.
In central-western Argentina, an Early Paleozoic belt including mafic-ultramafic bodies and marine metasedimentary rocks occurs along the western margin of the Precordillera and in the eastern ...Frontal Cordillera. In this paper, we present the analysis of aeromagnetic data and its processing focused on mapping geological limits, structures and the relation at depth of the southern Precordillera. With this main objective were applied filtering algorithms, reduction to the pole, tilt derivative, analytic signal, and particularly, the use of Improved Logistic Function (IL) as a new method of edge detection, in combination with the inversion map obtained from the Magnetization Vector Inversion (MVI) method. The results allow us to describe at depth the main trend of the Southern Precordillera Mafic Ultramafic Belt as two separated bocks, one in Peñasco and another in Cerro (Co.) Cortaderas, passing through Cerro (Co.) Pozos with a possible NNE-SSW direction. The combination of this techniques also can be used as prospecting guide to Pb–Zn–Ag vein deposits and High sulfidation Au-Epitermal deposits.
•Determination of the Precordillera Mafic-Ultramafic Belt.•Linkage of maximum susceptibility, IL filter, outcrops of Mafic Ultramafic rocks and structural lineaments.•Magnetic Susceptibility 3D Model.
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