The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.

The (numerical) solution of Ordinary Differential Equations (ODEs) problems is of paramount relevance, ODEs system being an ubiquitous mathematical formulation of many physical phenomena (such as those involved in fluid dynamics, chemistry, biology, evolutionary-anthropology, ...): almost every dynamici phenomenon can be modeled by means of an ODEs system. The present paper is the first manifesto of FOODIE, a library aimed to numerically solve ODEs problems by means of a clear, concise and efficient abstract interface. FOODIE, meaning Fortran Object oriented Ordinary Differential Equations integration library, has manifolds aims: to provide a set to built-in numerical schemes that are accurate, robust, validated and efficient and to allow easy application of these schemes to (almost) all ODEs problems by means of an effective Abstract Calculus Pattern. The key idea is to allow the same solver-implementation to be applied to all ODEs problems thus avoiding the re-implementation of the ODEs solver for each different ODEs problem: code re-usability is consequently maximized, FOODIE being a general robust framework. Besides, the same framework also allows rapid development of new ODEs solvers due to the high abstraction level of the library itself. The present paper is the first announcement of FOODIE project: the current implementation is extensively discussed and its capabilities are proved by means of tests and examples.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

In a 2014 paper by C. Fulton, D. Pearson, and S. Pruess, a new characterization of the spectral density function is given for a Sturm-Liouville equation. These authors provide spectral theory showing that the Appell system, a companion linear system of ordinary differential equations, can be utilized to obtain a spectral density function. Though this new method is both elegant for its simplicity and fully viable (as is shown in this work), it has largely been ignored in the literature since its discovery with no citations yet logged in the MathSciNet database. To motivate greater attention towards this 2014 paper, the new spectral theory within it, and its potential applications, work is given here by this author demonstrating a nontrivial example of this new spectral method being applied towards the Bessel Equation in its Liouville-Normal (L-N) form. Validations of results obtained in this paper are also given, showing full agreement with the classical results obtained by E.C. Titchmarsh.

New class of conserved quantities is constructed. These quantities find direct application in mechanics of dissipative (generally non-conservative) dynamical systems. Approach demands formulation in the language of geometric mechanics, providing theoretical framework for situations with energy flow in and out of the system. As a by product, we suggest possibility of existence of Hamiltonian form for every autonomous ODE system, evolution of which is governed by non-potential generator of motion. Various examples are provided, ranging from physics and mathematics, to chemical kinetics and population dynamics in biology. Applications of these ideas in geometric integration techniques (GNI) of numerical analysis are discussed, and as an example of such, new discrete gradient-based numerical method is introduced.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

Summary: Studying biological systems generally relies on computational modeling and simulation, e.g., for model-driven discovery and hypothesis testing. Progress in standardization efforts led to the development of interrelated file formats to exchange and reuse models in systems biology, such as SBML, the Simulation Experiment Description Markup Language (SED-ML), or the Open Modeling EXchange format (OMEX). Conducting simulation experiments based on these formats requires efficient and reusable implementations to make them accessible to the broader scientific community and to ensure the reproducibility of the results. The Systems Biology Simulation Core Library (SBSCL) provides interpreters and solvers for these standards as a versatile open-source API in Java™. The library simulates even complex bio-models and supports deterministic Ordinary Differential Equations (ODEs); Stochastic Differential Equations (SDEs); constraint-based analyses; recent SBML and SED-ML versions; exchange of results, and visualization of in silico experiments; open modeling exchange formats (COMBINE archives); hierarchically structured models; and compatibility with standard testing systems, including the Systems Biology Test Suite and published models from the BioModels and BiGG databases. Availability and implementation: SBSCL is freely available at https://draeger-lab.github.io/SBSCL/.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the authors establish meaningfully and significantly two identities which simplify coefficients in a family of ordinary differential equations associated with higher order Bernoulli numbers of the second kind.

In the last years, new numerical methods have been applied to weather data for water budget es-timation. Geostatistics is one of the most powerful approaches, when it comes to studying spatially relevant natural phenomena, as it takes into account the spatial correlation among measurements over a specific study area and increases the reliability of the estimation by providing the associate uncertainty. In this study, we tested the feasibility of using a geostatistical method called Ordinary Kriging to provide a reliable estimation of the water budget of the Foro river basin (Periadriatic area, Central Italy), by comparing the obtained results with a more traditional yet robust approach based on the Thiessen polygon spatialization method, considered here as a reference. The spatial estimation with the selected geostatistical and traditional approaches was performed on the av-erage monthly rainfall and temperatures derived from 33-year-long time series measured at the weather station of the regional monitoring network. To transform the spatial variables quantities of both rainfall and air temperature into actual runoff estimates that ideally represent the river dis-charge, we used both the Turc and Thornthwaite methods, considering variable Potential Infiltra-tion Coefficients according to the hydrogeological complexes’ distribution. For the geostatistical method, the same procedure was applied to the 95% confidence interval limits, to quantitatively assess the possible impact of the spatial uncertainty on the estimation of the river discharge. The results obtained by both methods, subsequently converted into monthly discharges, were com-pared to the average monthly discharges related to 33-year-long time series measured at different locations along the Foro river. The results obtained with the geostatistical approach proved to be in line with the ones from the traditional method. Additionally, using the rainfall and temperature values obtained with the Ordinary Kriging and the corresponding confidence interval limits, it was possible to quantify the uncertainty associated with the discharge values, making the estimates more reliable than the ones obtained with the traditional approach. However, the yearly distribu-tion of river discharge obtained by both the geostatistical and traditional methods appeared to be dissimilar to the measured ones. In such anthropized and groundwater-dependent river basins, the surface water use as well as the regulatory effect of the alluvial aquifer regime may affect the river discharge variability over the year and then can account for similar discrepancies between the in-flow and outflow water volumes.

This work introduces the mathematical framework of the novel “First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (1st-CASAM-NODE)” which yields exact expressions for the first-order sensitivities of NODE decoder-responses to the NODE parameters, including encoder initial conditions, while enabling the most efficient computation of these sensitivities. The application of the 1st-CASAM-NODE is illustrated by using the Nordheim-Fuchs reactor dynamics/safety phenomenological model, which is representative of physical systems that would be modeled by NODE while admitting exact analytical solutions for all quantities of interest (hidden states, decoder outputs, sensitivities with respect to all parameters and initial conditions, etc.). This work also lays the foundation for the ongoing work on conceiving the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-CASAM-NODE)” which aims at yielding exact expressions for the second-order sensitivities of NODE decoder-responses to the NODE parameters and initial conditions while enabling the most efficient computation of these sensitivities.

This current study examines the economics of yam marketing in Bosso local government area of Niger State Nigeria, to this end, statistical tools such as descriptive statistics, marketing margin model, and regression analysis procedures was utilized as estimation techniques. The study relies on random sampling technique of selected 80 yam marketers. The motivation for this study, rest on the dominance of yam marketing operation in the study area as well as the need to chart a better and more efficient system of agricultural marketing for yam marketers in the sampled area. The empirical result reveals that an overwhelming majority (95.1%) of the marketers were 21-50 years of age with 6 years and above of marketing experience dominating (90%). However, most of the yam marketers started the business with capital base of N1,000- N20,000, it was also discovered was that majority (58.8%) of the marketers were female and within their active age with mean age of 35 years which goes to show that female can contribute to the responsibility of the family. The study also seeks to explore marketer’s preference for source of funding either from the formal institutions such as (Banks and Co-operatives) or the informal institutions (from friends or relatives) which is key in the effective and efficient in yam marketing. Finally, the study is set out to find out potential constraints to the attainment of the full gains of yam marketing in the study area and offer workable and visible remedy.

Moso bamboo is famous for fast growing and biomass accumulation, as well as high annual output for timber and bamboo shoots. These high outputs require high nutrient inputs to maintain and improve stand productivity. Soil nitrogen (N), phosphorus (P) and potassium (K) are important micronutrients for plant growth and productivity. Due to high variability of soils, analysing spatial patterns of soil N, P and K stocks is necessary for scientific nutrient management in Moso bamboo forests. In this study, soils were sampled from 138 locations across Yong’an City and ordinary kriging was applied for spatial interpolation of soil N, P and K stocks. Soil N stock showed a strong spatial dependence while soil N and P stocks presented a moderate spatial dependence, indicating soil N was mainly controlled by intrinsic factors while soil N and P stocks were controlled by both intrinsic and extrinsic factors. Different spatial patterns were observed for soil N, P and K stocks across the whole study area, indicating that fertilizations with different ratios of N:P:K should be applied for different sites to maintain and improve stand productivity. The total soil N, P and K stocks within 0-60 cm were 0.624, 0.020 and 0.583 Tg, respectively.

This case report investigates 5 real cases which followed legal channels and were judged by Mato Grosso Court in Brazil. Audio systems served as elements of key evidence on those lawsuits. The goal here is to analyze the cases by using a methodology based on the forensic speaker verification by using the Ordinary Least Squares (OLS) algorithm and to compare results with analyses obtained on real cases. The comparative analysis is assessed for time elapsed for obtaining results, as well as results quality. In Brazil, the lawsuit duration is very important, since the Penal Code foresees prescription after a given time, and it may lead to impunity. Results show that the analysis, by using OLS, generates immediate, effective results when compared to those obtained with traditional methodologies on the studied Brazilian lawsuits.

On the eve of the Brexit process, in the context of a rising Euroscepticism that fuels the modest confidence of European citizens in their national and European institutions, the article assesses the efficiency and effectiveness of the European Parliament within the framework of the ordinary legislative procedure (co-decision). After defining and formulating the main indicators, the paper analyses the micro- and macro-performance of the European Parliament within the decision-making process from a quantitative-qualitative and a qualitative-quantitative perspective, highlighting the relativizing factors and the responsiveness of the European decision-making process to the Europeans’ needs.

In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.

We enhance Frobenius' method for solving linear ordinary differential equations about regular singular points. Key to Frobenius' approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-zero integer. We demonstrate the method on Bessel's equation and derive previously unknown tandem recurrence relations for coefficients of solutions of the second kind, for Bessel equations of all integer and half-integer order.

In this paper, closed and semi-closed form solutions are presented for the self - and mutual inductance of ordinary and Better disk coils which lie concentrically in a plane. The solutions are given as the combination of the elliptic integral of the first kind and a simple integral or only as the second elliptic integral of the second kind. All formulas or obtained in remarkably simple form and give extremely accurate results with significantly neglectable computational time. All cases either regular or singular (disks in contact or overlap) are covered. The formulas for the mutual inductances can be directly used to calculating the self-inductance of the ordinary disk coil or the Bitter disk coil, respectively. Many presented examples show the excellent numerical agreement with previous publish methods.

Presented is semivariogram and the Ordinary Kriging analyses of porosity data from the Sava Depression (Northern Croatia), as part of the Croatian part of the Pannonian Basin System. Data are taken from hydrocarbon reservoirs of the Lower Pontian (Upper Miocene) age, which belongs to the Kloštar-Ivanić Formation. Original datasets had been jack-knifed with purpose to “artificially” increased data and calculate the more reliable semivariograms. The results showed that such improvements can assist in the interpolation of more reliable maps. The both sets, made by original and jack-knifed data, need to be compared using geological recognition of non-allowed shapes (“bull-eyes”, “butterfly effects”) as well as cross-validation results. That comparison made possible to select the most appropriate porosity interpolation.

Infection of liver flukes (Opisthorchis viverrini) is partly due to their suitability for habitats in sub-basin areas, which causes the intermediate host to remain in the watershed system in all seasons. Spatial monitoring of fluke infection at the small basin analysis scale is important because this can enable analysis at the level of the spatial factors involved and influencing infections. The spatial mathematical model was weighted by the nine spatial factors by dividing the analysis into two levels. 1) sub-basin boundary level analyzed with ordinary least square (OLS) model used to analyze spatial factors of liver fluke aimed at analyzing spatial factors related to human liver fluke infection according to sub-basin boundaries, and 2) infection risk positional analysis level with machine learning-based forest classification and regression (FCR) and displaying predictive results of infection risk locations along stream lines. The analysis results show 4 prototype models that import different independent variable factors. The results show that Model-1 and Model-2 give the most AUC = 0.964 and the variables that influence infection risk the most were distance to stream lines, and distance to water bodies, NDMI and NDVI factors rarely affect accuracy. This FCR machine learning application approach can be applied to the analysis of infection risk areas at the sub-basin level, but independent variables must be screened with a preliminary mathematical model weighted to the spatial units in order to obtain the most accurate predictions.

Accurate knowledge of the rain amount is an crucial driver in several hydro-meteorological applications. This is especially true in complex orography territories, which are typically impervious, thus leaving ungauged most of the mountain areas. Thanks to their spatial and temporal coverage, weather radars can potentially overcome such an issue. However, weather radar, if not accurately processed, can suffer from several limitations (e.g., beam blocking, altitude of the observation, path attenuation, indirectness of the measurement) that can hamper the reliability of the rain estimates performed. In this study, a comparison between rain gauge and weather radar retrievals is performed in the target area of the Abruzzo region in Italy, which is characterized by a heterogeneous orography ranging from the sea side to Apennine ridge. Consequently, the Abruzzo region has an inhomogeneous distribution of the rain gauges, with station density decreasing with the altitude reaching up to approximately 1500 m a.s.l. Notwithstanding, pluviometric inflow spatial distribution shows a sub-regional dependency as a function of four climatic and altimetric factors: coastal, hilly, mountain, and inner plain areas (i.e., Marsica). Such areas are used in this analysis to characterize the radar retrieval vs. rain gauge amounts in each of those zones. Compared to previous studies on the topic, the analysis presented an attention to the importance of an accurate selection of the climatic and altimetric sub-regional areas where undertake the radar vs. rain gauge comparison. This aspect is not only of great importance to correct biases in radar retrievals in a more selective way, but it also paves the way for more accurate hydro-meteorological applications (e.g., hydrological model initialization, quantify the aquifers recharge etc.) which, in general, require the accurate knowledge of rain amounts upstream of a basin. To fill the gap caused by the uneven rain gauge distribution, Ordinary Kriging has been applied on a regional scale to obtain 2D maps of rainfall data, which are cumulated on a monthly and yearly base. Weather radar data from the Italian mosaic are considered as well, in terms of rain rate retrievals and cumulations performed on the same time frame used for rain gauges. The period considered for the analysis is two continuous years: 2017 and 2018. The output of the elaborations are raster maps for both radar and interpolated rain gauges, where every pixel contains a rainfall quantity. Although the results show a general underestimation in the weather radar data especially in mountain and Marsica areas, even though within the 95% confidence interval of the OK estimation. Our analysis highlights that the average bias between radar and rain gauges, in terms of precipitation amounts, is a function of altitude and is almost constant in each of the selected areas. This achievement suggests that after a proper selection of homogeneous target areas, the radar retrievals can be corrected using the denser network of rain gauges typically distributed at lower altitudes and extend such correction at higher altitudes without loss of generality.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*>0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

Estimating the parameters of statistical distributions generally involves solving a system of nonlinear equations or a nonlinear equation, being a technical difficulty in their usual application in hydrology. This article presents improved approximations and, in some cases, new approximations for the estimation with the method of ordinary moments and the method of linear moments, which are useful for the direct calculation of the parameters, because the errors in the approximate estimation are similar to the use of iterative numerical methods. Thirteen statistical distributions of two and three parameters frequently used in hydrology are presented, for which parameter estimation was laborious. Thus, the approximate estimation of the parameters by the two methods is simple but also precise and easily applicable by hydrology researchers. The approximate forms characterized by very small errors are the result of the research conducted within the Faculty of Hydrotechnics to update the romanian normative standards in the hydrotechnical field.

In this work, we have developed a non-ordinary state-based peridynamic model for multiple crack initiation and propagation due to compression-compression fatigue load. In each loading cycle, the fatigue loading is redistributed among the peridynamic solid body, leading to the progressive fatigue damage initiation and propagation in an autonomous fashion. The proposed fatigue model parameters are firstly validated by 3D numerical benchmark tests, and then it is applied to simulate widespread fatigue damage evolution of the aircraft wing corner box. The modified constitutive damage model has been implemented into the peridynamics framework at finite strain. Furthermore, the criterion algorithm from multiple initiation to propagation is discussed. It is shown that the numerical results obtained from peridynamics simulations are in general agreement with those from the experiment data. The comparison of experimental and numerical results indicates that the proposed non-ordinary state-based peridynamics fatigue model has the ability to capture the multiple crack initiation and propagation and other features of the aluminium alloy material.

This research paper is divided into two aspects: first part describes the modelling techniques which are referred for handling infectious diseases in public health domain, second part describes the modelling techniques which are referred for building epidemiology cases in public health domain. To illustrate further, first part helps in understanding various modeling ordinary differential equations have been defined to develop the definition, described to know the terminologies involved in developing the equations and henceforth established to understand the end-to-end process. Second part helps in understanding various aspects of epidemiology in public health domain and how they help in addressing the public health domain policy-making.

This work aimed to assess and characterize the air quality in what concerns particulate pollution in urban-industrial environments. The main objectives were to study the spatial variability of the deposition flux of particulate pollution identifying areas with higher deposition, associate the variability with climatological variables and with possible surrounding emitting sources. The method for collecting the deposited particles was based on the standard NF X 43-007. Sampling for particulate pollution took place between April 2015 and February 2016, through seven sampling campaigns. Maps of the spatial dispersion for the particulate pollution were obtained through statistics and geostatistics techniques. Elemental identification by scanning electron microscopy (SEM) was also used but only in two sampling campaigns. The results show that the sampling campaigns that took place during hot and dry periods, 2nd and 3rd, present higher deposition flux: 2.04 g/(m2 x month) and 1.72 g/(m2 x month), respectively. Lower deposition fluxes were registered in the 6th and 7th campaigns: 0.23 g/(m2 x month) and 0.24 g/(m2 x month), respectively. It was also observed a recurrent high deposition at specific sampling points which may be due to both the nearby road traffic and the presence of chimneys. SEM analysis allowed to associate repetitive element deposition, at the same sampling point, to the same emitting source.

With reference to Planck scale, increasing support for large scale cosmic anisotropy and preferred directions and by considering an increasing ratio of Hubble parameter to angular velocity, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the baby universe in all directions). We would like suggest that, from the beginning of Planck scale, 1) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies. 2) Cosmic angular velocity decreases with square of the decreasing cosmic temperature. 3) Increasing ratio of Hubble parameter to angular velocity plays a crucial role in estimating increasing cosmic expansion velocity and decreasing density ratios of dark matter and ordinary matter. 4) There is no need to consider dark energy for understanding cosmic acceleration.

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework's capabilities. Calibration and verification demonstrate the models' effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory's neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

With reference to Planck scale, Mach’s relation, increasing support for large scale cosmic anisotropy and preferred directions and by introducing two new parameters Gamma and Beta, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the baby universe in all directions). We would like suggest that, from the beginning of Planck scale, 1) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies. 2) Cosmic angular velocity is directly proportional to squared cosmic temperature. 3) Ratio of critical temperature to actual temperature plays a heuristic role in understanding ordinary and dark matter density ratios. 4) Cosmic expansion velocity increases with decreasing total matter density ratio. 5) There is no need to consider dark energy for understanding cosmic acceleration.

With reference to Planck scale, Mach's relation and by introducing two new parameters Gamma and Beta, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the Planck mass in all directions). In analogy with currently believed cosmic acceleration, with a decreasing trend of total matter density ratio, cosmic expansion velocity can be shown to be increasing. By considering $H_0\cong 70$ km/sec/Mpc, estimated current cosmic mass, radius, total matter density, expansion velocity, temperature and age are: $4.3352\times {10}^{53}\mathrm{kg},$ $3.207\times {10}^{26}\mathrm{m},$ $3.138\times {10}^{-27}\mathrm{kg}{.\mathrm{m}}^{-3},$ $2.43c,$ $2.721\mathrm{K}$ and $19.78\mathrm{Billion}\mathrm{years}$ respectively. Point to be noted is that, with reference to Planck scale, cosmic temperature seems to be redshifted by a factor ${\left(Z_T\right)}_t\cong \sqrt{1+\ln \left(H_{pl}/H_t\right)}-1$ where $\left(H_{pl},H_t\right)$ represent Planck scale and time dependent Hubble parameters respectively. As a peculiar case, considering the equality of current Hubble parameter and current angular velocity, current cosmic rotational kinetic energy can be estimated to be 0.667 times the current critical energy. It needs further study.

This article analyzes 6 probability distributions from the Generalized Pareto family, with 3, 4 and 5 parameters, with main purpose to identify other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distributions use are presented like, the probability density functions, the complementary cumulative distribution functions, the quantile functions, the exact and approximate relations for estimating parameters, for both methods of parameters estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor river, to numerically present the analyzed distributions. The performance of this distributions is evaluated using relative mean error, relative absolute error and linear moments diagram.

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.

The thymus hosts the development of a specific type of adaptive immune cells called T cells. T cells orchestrate the adaptive immune response through recognition of antigen by the highly variable T-cell receptor (TCR). T-cell development is a tightly coordinated process comprising lineage commitment, somatic recombination of Tcr gene loci and selection for functional, but non-self-reactive TCRs, all interspersed with massive proliferation and cell death. Thus, the thymus produces a pool of T cells throughout life capable of responding to virtually any exogenous attack while preserving the body through self-tolerance. The thymus has been of considerable interest to both immunologists and theoretical biologists due to its multiscale quantitative properties, bridging molecular binding, population dynamics and polyclonal repertoire specificity. Here, we review mathematical modelling strategies that were reported to help understand the flexible dynamics of the highly dividing and dying thymic cell populations. Furthermore, we summarize the current challenges to estimating in vivo cellular dynamics and to reaching a next-generation multiscale picture of T-cell development.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

This article presents six probability distributions from the Gamma family with three parameters, for the flood frequency analysis in hydrology. The choice of the Gamma family of statistical dis-tributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the im-provement of the estimation of maximum flows and including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected pa-rameters was researched, being an element of novelty. The linear moments method is better than MOM because it avoids the choice of skewness depending on the origin of the flows, practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed, using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented like, quantile functions, the exact and ap-proximate relations for estimating parameters and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river, to verify the proposed methodology. The per-formance of this distributions is evaluated using Kiling-Gupta and Nash-Sutcliff coefficients.