Propagation Attenuation Maps Based on Parabolic Equation Method.

Modern wireless communication systems use various technological solutions to increase the efficiency of created radio networks. This efficiency also applies to radio resources. Currently, the utilization of a radio environment map (REM) is one of the directions allowing to improve radio resource management. The REM is increasingly used in emerging mobile ad-hoc networks (MANETs), in particular military tactical networks. In this case, the use of new technologies such as software-defined radio and network, cognitive radio, radio sensing, and building electromagnetic situational awareness made it possible to implement REM in tactical MANETs. Propagation attenuation maps (PAMs) are crucial REM elements that allow for determining the ranges of radio network nodes. In this paper, we present a novel algorithm for PAM based on a parabolic equation method (PEM). The PEM allows determining the signal attenuation along the assumed propagation direction. In this case, we consider terrain topography to obtain a more realistic analysis. Then, we average the adjacent attenuation profiles defined for the selected directions in places where attenuation has not been calculated. To this aim, linear regression is applied. Finally, we define several metrics that allow for the accuracy assessment of determining the PAM as a function of its dimensions.

Protein 3D Hydration: A Case of Bovine Pancreatic Trypsin Inhibitor.

Characterization of the hydrated state of a protein is crucial for understanding its structural stability and function. In the present study, we have investigated the 3D hydration structure of the protein BPTI (bovine pancreatic trypsin inhibitor) by molecular dynamics (MD) and the integral equation method in the three-dimensional reference interaction site model (3D-RISM) approach. Both methods have found a well-defined hydration layer around the protein and revealed the localization of BPTI buried water molecules corresponding to the X-ray crystallography data. Moreover, under 3D-RISM calculations, the obtained positions of waters bound firmly to the BPTI sites are in reasonable agreement with the experimental results mentioned above for the BPTI crystal form. The analysis of the 3D hydration structure (thickness of hydration shell and hydration numbers) was performed for the entire protein and its polar and non-polar parts using various cut-off distances taken from the literature as well as by a straightforward procedure proposed here for determining the thickness of the hydration layer. Using the thickness of the hydration shell from this procedure allows for calculating the total hydration number of biomolecules properly under both methods. Following this approach, we have obtained the thickness of the BPTI hydration layer of 3.6 Å with 369 water molecules in the case of MD simulation and 3.9 Å with 333 water molecules in the case of the 3D-RISM approach. The above procedure was also applied for a more detailed description of the BPTI hydration structure near the polar charged and uncharged radicals as well as non-polar radicals. The results presented for the BPTI as an example bring new knowledge to the understanding of protein hydration.

Simple Equations Method (SEsM): An Effective Algorithm for Obtaining Exact Solutions of Nonlinear Differential Equations.

Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method. The article begins with a short overview of the literature connected to the methodology for obtaining exact solutions of nonlinear differential equations. This overview includes research on nonlinear waves, research on the methodology of the Inverse Scattering Transform method, and the method of Hirota, as well as some of the nonlinear equations studied by these methods. The overview continues with articles devoted to the phenomena described by the exact solutions of the nonlinear differential equations and articles about mathematical results connected to the methodology for obtaining such exact solutions. Several articles devoted to the numerical study of nonlinear waves are mentioned. Then, the approach to the SEsM is described starting from the Hopf-Cole transformation, the research of Kudryashov on the Method of the Simplest Equation, the approach to the Modified Method of the Simplest Equation, and the development of this methodology towards the SEsM. The description of the algorithm of the SEsM begins with the transformations that convert the nonlinearity of the solved complicated equation into a treatable kind of nonlinearity. Next, we discuss the use of composite functions in the steps of the algorithms. Special attention is given to the role of the simple equation in the SEsM. The connection of the methodology with other methods for obtaining exact multisoliton solutions of nonlinear differential equations is discussed. These methods are the Inverse Scattering Transform method and the Hirota method. Numerous examples of the application of the SEsM for obtaining exact solutions of nonlinear differential equations are demonstrated. One of the examples is connected to the exact solution of an equation that occurs in the SIR model of epidemic spreading. The solution of this equation can be used for modeling epidemic waves, for example, COVID-19 epidemic waves. Other examples of the application of the SEsM methodology are connected to the use of the differential equation of Bernoulli and Riccati as simple equations for obtaining exact solutions of more complicated nonlinear differential equations. The SEsM leads to a definition of a specific special function through a simple equation containing polynomial nonlinearities. The special function contains specific cases of numerous well-known functions such as the trigonometric and hyperbolic functions and the elliptic functions of Jacobi, Weierstrass, etc. Among the examples are the solutions of the differential equations of Fisher, equation of Burgers-Huxley, generalized equation of Camassa-Holm, generalized equation of Swift-Hohenberg, generalized Rayleigh equation, etc. Finally, we discuss the connection between the SEsM and the other methods for obtaining exact solutions of nonintegrable nonlinear differential equations. We present a conjecture about the relationship of the SEsM with these methods.

Social inclusion as a perspective for the validation of the "DigCompEdu Check-In" questionnaire for teaching digital competence.

Making use of digital technologies and all the possibilities that benefit education is one of the objectives of the European Framework for the Digital Competence of Educators, as well as their potential for personal development and social inclusion, among other aspects. The aim of this study was to validate the «DigCompEdu Check-In¼ scale as an instrument for the self-reflection of educators regarding their digital competence from the perspective of social inclusion. This questionnaire provides a more accurate view of the digital competence framework and allows self-evaluating the strengths and weaknesses/needs of educators in digital learning. Exploratory and confirmatory factor analyses were performed, using structural equations. The study sample consisted of 2,262 faculty members from different public universities of Andalusia (Spain). The obtained results show the reliability and validity of the instrument and allow generating accurate scientific knowledge for the improvement of education quality and social inclusion, in both university and non-university institutions.

Simple Equations Method (SEsM): Algorithm, Connection with Hirota Method, Inverse Scattering Transform Method, and Several Other Methods.

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a "small" parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.

Sensitivity analysis of the Poisson Nernst-Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model.

Biological structures exhibiting electric potential fluctuations such as neuron and neural structures with complex geometries are modelled using an electrodiffusion or Poisson Nernst-Planck system of equations. These structures typically depend upon several parameters displaying a large degree of variation or that cannot be precisely inferred experimentally. It is crucial to understand how the mathematical model (and resulting simulations) depend on specific values of these parameters. Here we develop a rigorous approach based on the sensitivity equation for the electrodiffusion model. To illustrate the proposed methodology, we investigate the sensitivity of the electrical response of a node of Ranvier with respect to ionic diffusion coefficients and the membrane dielectric permittivity.

Proline hydration at low temperatures: its role in the protection of cell from freeze-induced stress.

The natural amino acid L-α-proline (Pro) is a compatible osmolyte which accumulates in the cell cytoplasm to protect structure and function of various proteins and enzymes under abiotic stress, like for instance, freezing. It is assumed that the interactions of Pro with intracellular water play an important role in the protection mechanism. However, until now the details of these interactions are far from being fully understood. We present results of a theoretical study of the hydration of Pro zwitterion (Pro-ZW) in water in the temperature range of 298-248 K. The data were obtained by the integral equation method in the framework of the 1D- and 3D-RISM approaches. The structural data were analyzed in terms of radial and spatial distribution functions. The observed features of Pro-ZW hydration are discussed from the position of the biological role of Pro as a cryoprotectant. In particular, it was found that under cooling conditions this protectant is able to bind a significant amount of water molecules and, thus, is helping to keep water inside the cell.

A comparison of the revised Delirium Rating Scale (DRS-R98) and the Memorial Delirium Assessment Scale (MDAS) in a palliative care cohort with DSM-IV delirium.

OBJECTIVE: Assessment of delirium is performed with a variety of instruments, making comparisons between studies difficult. A conversion rule between commonly used instruments would aid such comparisons. The present study aimed to compare the revised Delirium Rating Scale (DRS-R98) and Memorial Delirium Assessment Scale (MDAS) in a palliative care population and derive conversion rules between the two scales. METHOD: Both instruments were employed to assess 77 consecutive patients with DSM-IV delirium, and the measures were repeated at three-day intervals. Conversion rules were derived from the data at initial assessment and tested on subsequent data. RESULTS: There was substantial overall agreement between the two scales [concordance correlation coefficient (CCC) = 0.70 (CI 95 = 0.60-0.78)] and between most common items (weighted κ ranging from 0.63 to 0.86). Although the two scales overlap considerably, there were some subtle differences with only modest agreement between the attention (weighted κ = 0.42) and thought process (weighted κ = 0.61) items. The conversion rule from total MDAS score to DRS-R98 severity scores demonstrated an almost perfect level of agreement (r = 0.86, CCC = 0.86; CI 95 = 0.79-0.91), similar to the conversion rule from DRS-R98 to MDAS. SIGNIFICANCE OF RESULTS: Overall, the derived conversion rules demonstrated promising accuracy in this palliative care population, but further testing in other populations is certainly needed.

Dynamical property of interaction solutions to the Chafee-Infante equation via NMSE method.

In this work, we study the Chafee-Infante model with conformable fractional derivative. This model describes the energy balance between equator and pole of solar system, which transmit energy via heat diffusion. To explore the multi soliton solutions and their interaction, we implemented the new modified simple equation (NMSE) scheme. Under some conditions, the obtained solutions are trigonometric, hyperbolic, exponential and their combine form. Only the proposed technique can be provided the solution in terms of trigonometric and hyperbolic form together directly. The periodic, solitary wave and novel interaction of such solitary and sinusoidal solutions has also been established and discussed analytically. For the special values of the existing free parameter, some novel waveforms are existed for the proposed model including, periodic solution, double periodic wave solution, multi-kink solution. The behavior of the obtained solutions is presented in 3-D plot, density plot and counter plot with the help of computational software Maple 18.

An improved technology for monitoring groundwater flow velocity and direction in fractured rock system based on colloidal particles motion.

The colloidal borescope, using colloidal particle motion, is used to monitor the flow velocities and directions of groundwater. It integrates advanced techniques such as microscopy, high-speed photography, and big data computing and enjoys high sensitivity at the micron level. However, In the same well, the groundwater flow velocity monitored by colloidal hole mirror is varies greatly from that obtained by conventional hydrogeological monitoring, such as pumping test. In order to solve this problem, the stability catcher and stratified packer are designed to control the interference of the vertical flow in drilling, and to monitor the flow velocity and direction of groundwater velocity at the target aquifer and target fracture. Five wells with different aquifers and different groundwater types were selected for monitoring in south-central China. The instantaneous velocity and direction are converted into east-west component and north-south component, the average velocity and direction is calculated according to the time of 10 min, and the particle trajectory diagram is established. Based on these results, it proposed a concept of cumulative flow velocity. Using curve-fitting equations, the limits of cumulative flow velocities as the monitoring time tends to infinity were then calculated as the actual flow velocities of the groundwater. The permeability coefficient of aquifer is calculated by using the fissure ratio of aquifer, hydraulic slope and flow velocity, and compared with the permeability coefficient obtained by pumping test. The results are as follows: (1) The variation coefficient of the instantaneous flow velocity measured at the same depth in the same well at different times is greater than that of the time average flow velocity and greater than that of the cumulative flow velocity. The variation coefficient of the actual velocity is the smallest, indicating that the risk of using the actual flow velocity is lower. (2) The variation coefficient of the flow rate monitored at different depths in the same well is mainly controlled by the properties of the aquifer. The more uniform water storage space in the aquifer, the smaller the variation coefficient. (3) The comparison between the permeability coefficient obtained by monitoring and the permeability coefficient obtained by pumping test shows that the flow of structural fissure water controlled by planar fissure is more surface flow, and the results are consistent. When the groundwater flow is controlled by pores and solution gaps, the flow channel is complicated, which is easy to produce turbulent flow, and the result consistency is poor. (4) According to different research accuracy requirements, different monitoring and calculation methods can be selected for different aquifers and groundwater types. Researches show that, the permeability coefficient calculated for the actual flow velocity in well DR01 is the same as that calculated for the pumping test. The aquifer characteristics reflected by the coefficient of variation of the actual flow velocity in the same aquifer are more realistic. The pumping test method obtains the comprehensive parameters of a certain aquifer, and this method can be used to monitor a certain fissure. In this paper, the new technology developed for monitoring, and the new algorithm established for data processing, can accurately obtain the flow velocity and direction of groundwater, using capsule hole mirror monitoring method. The key parameters of hydrogeology can be obtained by using one well, which can reduce the time and cost input and improve the work efficiency.

Soliton solutions of nonlinear coupled Davey-Stewartson Fokas system using modified auxiliary equation method and extended ( G ' / G 2 ) -expansion method.

The captivating realm of the nonlinear coupled Davey-Stewartson Fokas system is explored in this research paper. As a powerful tool, the proposed system is utilized for the realistic representation of various non-linear dynamical mechanisms in different fields of sciences and engineering including non-linear optical fibers, plasma physics and water waves theory. Two distinct exact methods, namely the modified auxiliary equation method and the extended ( G ' / G 2 ) -expansion method, are utilized to acquire the exact soliton solutions of the non-linear coupled Davey-Stewartson Fokas system. A plethora of novel soliton solutions containing anti-kink, kink, bright, dark, dark-bright, bright-dark and some other singular soliton solutions, have been obtained using the employed exact methods. The significance of proposed manuscript lies in the novelty of obtained solutions. Kink, dark and bright solitons have wide applications in optical fiber communications, plasma physics and water waves dynamics. The acquired nontrivial exact solutions contain exponential, trigonometric, rational and hyperbolic functions. Some obtained solutions are visually represented through graphical simulations of 3D, 2D-contour and 2D-line plots, providing a comprehensive visualization of the soliton dynamics.The modulation instability of the proposed nonlinear system has been investigated, which ensures the stability of the system.

Comparison of the mathematical equation and trapezoidal approach for 24 h area under the plasma concentration-time curve calculation in patients who received intravenous vancomycin in an acute care setting.

The current recommendation for therapeutic monitoring of vancomycin has recently suggested AUC-guided dosing in patients with serious methicillin-resistant Staphylococcus aureus infections. The study objective was to evaluate mathematical equations and trapezoidal methods for calculating the 24 h area under the plasma vancomycin concentration-time curve (AUC24). The analysis of plasma vancomycin concentrations was performed in 20 adult patients treated with intravenous vancomycin. For each patient, AUC24 was estimated using two methods including, equation and trapezoidal calculation. The AUC24 from two methods was analyzed for correlation. The correlation between the equation and trapezoidal methods was strong. The coefficient of determination (R2 ) values was greater than .99. The two plasma vancomycin concentrations to achieve the highest correlation were concentration at 2.5 to 3 h after starting the infusion and concentration at 1 h before the next dose. Moreover, the AUC24 calculation from trapezoidal and equation methods showed that 19 out of 20 patients (95%) had AUC24 of more than 400 mg·h/L, and more than 50% in this group had AUC24/MIC greater than 600. Of those patients with AUC-trapezoidal >600, 15.38% of patients had trough under 15 mg/L, 15.38% of patients had trough in the range 15 to 20 mg/L and 69.23% of patients had trough more than 20 mg/L. The results of AUC-equation were similar to those of the AUC-trapezoidal method. Our study confirmed that the AUC monitoring is more appropriate than the trough vancomycin concentration. Given these considerations, the AUC-equation method is better and more practical to use in part of a point-of-care treatment, especially in the part of the Bayesian program is not available. The best sampling time point of the peak concentration was 0.5-1 h after 2-h infusion.

Traveling wave solutions of a coupled Schrödinger-Korteweg-de Vries equation by the generalized coupled trial equation method.

The coupled Schrödinger-Korteweg-de Vries equation is a critical system of in nonlinear evolution equations. It describes various processes in dusty plasma, such as Langmuir waves, dust-acoustic waves, and electromagnetic waves. This paper uses the generalized coupled trial equation method to solve the equation. By the complete discrimination system for polynomial, a series of exact traveling wave solutions are obtained, including discontinuous periodic solutions, solitary wave solutions, and Jacobian elliptical function solutions. In addition, to determine the existence of the solutions and understand their properties, we draw three-dimensional images of the modules of the solutions with Mathematica. We obtain more comprehensive and accurate solutions than previous studies, and the results give the system more profound physical significance.

Dynamical interaction of solitary, periodic, rogue type wave solutions and multi-soliton solutions of the nonlinear models.

This study presents a modification form of modified simple equation method, namely new modified simple equation method. Multiple waves and interaction of soliton solutions of the Phi-4 and Klein-Gordon models are investigated via the scheme. Consequently, we derive various novels and more general interaction, and multiple wave solutions in term of exponential, hyperbolic, and trigonometric, rational function solutions combining with some free parameters. Taking special values of the free parameters, interaction of two dark bells, interaction of two bright bells, two kinks, two periodic waves, kink and soliton, kink-rogue wave solutions are obtained which is the key significance of this method. Properties of the achieved solutions have many useful descriptions of physical behavior, correlated to the solutions are attained in this work through plentiful 3D figures, density plot and 2D contour plots. The results derived may increase the prospect of performing significant experimentations and carry out probable applications.

Association between different obesity phenotypes and hypothyroidism: a study based on a longitudinal health management cohort.

PURPOSE: Obese individuals have an increased risk of hypothyroidism. This study investigated the sex-specific association between obesity phenotypes and the development of hypothyroidism. METHODS: The study population was derived from a health management cohort in Shandong Provincial Hospital from 2012 to 2016. In total, 9011 baseline euthyroid adults were included and classified into four groups according to obesity phenotype: metabolically healthy nonobese (MHNO), metabolically healthy obese (MHO), metabolically unhealthy nonobese (MUNO), and metabolically unhealthy obese (MUO). The median follow-up time was 1.92 (1.00-2.17) years. Incidence density was evaluated and a generalized estimation equation method was used to investigate the associations between obesity phenotypes and the development of hypothyroidism. RESULTS: The incidence densities of hypothyroidism in males with a consistent obesity phenotype were 12.19 (8.62-16.76), 15.87 (11.39-21.56), 14.52 (6.74-27.57), and 19.88 (14.06-27.34) per 1000 person-years in the MHNO, MHO, MUNO, and MUO groups, respectively. After adjusting for confounding factors, compared with the MHNO phenotype, the MHO, MUNO, and MUO phenotypes were independent risk factors for developing hypothyroidism in males. In the subgroup analysis, the MHO and MUO phenotypes were independent risk factors for developing hypothyroidism in males under 55 years, while the MUNO phenotype was an independent risk factor in males over 55 years. The MHO, MUNO, and MUO phenotypes were not independent risk factors for hypothyroidism in females. CONCLUSION: Both obesity and metabolic abnormities are associated with a higher risk of hypothyroidism in males. The underlying mechanism of the sex and age differences in this association needs further investigation.

Analytical method for the out-of-plane buckling of the telescopic boom with guy cables.

The guy cables can effectively improve the bearing capacity for the telescopic boom of the crane, while the introduction of tensioned cables makes the buckling analysis complicated. The primary objective of this study was to propose an analytical method for the out-of-plane buckling of the telescopic boom with the spatial symmetric guy cables. To analyze the influence of the guy cables on the out-of-plane buckling property of the telescopic boom, the deflection differential equation of the multi-stepped telescopic boom with guy cables was established based on the theory of elastic beam, then the buckling characteristic equation to determine the critical load of the telescopic boom was derived. Comparison of results with that given by the finite element method showed the high accuracy of the proposed method. In the end, with this equation, the influences of the structural geometric parameters on the critical load were investigated. The results indicated that, in the engineering application, the critical load of the telescopic boom can be increased by decreasing the length ratio a/L or increasing the angle φ between the two cables. The influence of angle θ on the out-of-plane buckling analysis of the telescopic boom can be neglected. With the proposed method, the buckling behavior of the telescopic boom with guy cables can be solved accurately. The present work is significant to structural design and safety analysis of the telescopic boom, and it can be utilized to provide technical support for the structural design of telescopic boom.

Leaf water status monitoring by scattering effects at terahertz frequencies.

The applications of terahertz (THz) radiation for plant water status monitoring require systematic studies on interaction of THz wave and plants. Here, we present theoretical investigations on scattering behavior of THz waves reflected by and transmitting through a plant leaf under different water content. A theoretical model combining integral equation and radiative transfer theory is presented to fit the measured data. Good agreement confirms the availability of the model for water status evaluation when variation of leaf thickness and surface roughness is considered. We investigate the applicability of THz waves for water status monitoring in reflection and transmission geometries under different temperatures, salinities and polarizations.

Volume Integral Equation Method Solution for Spheroidal Inclusion Problem.

In this paper, the volume integral equation method (VIEM) is introduced for the numerical analysis of an infinite isotropic solid containing a variety of single isotropic/anisotropic spheroidal inclusions. In order to introduce the VIEM as a versatile numerical method for the three-dimensional elastostatic inclusion problem, VIEM results are first presented for a range of single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under uniform remote tensile loading. We next considered single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under remote shear loading. The authors hope that the results using the VIEM cited in this paper will be established as reference values for verifying the results of similar research using other analytical and numerical methods.

Inverse estimation of finite-duration source release mass in river pollution accidents based on adjoint equation method.

Obtaining the pollutant release mass at a timely manner is crucial in emergency response for river pollution accidents. However, compared to the instantaneous source, release mass estimation of finite-duration source has been rarely studied. In addition, few studies involve the influence of partial observation data and observation data with different levels of noise on inversion results. Based on the adjoint equation method (AEM), this study developed a new release mass estimation model to make up the above deficiencies. In this model, one-dimensional physical transport advection-dispersion equation was used as governing equation to describe pollutant transport and the finite-duration sources and instantaneous sources were both considered. Two synthetic experiments and two field experiments were used to evaluate this model. In synthetic experiments, detailed analysis of the influence of observation errors and incomplete concentration data due to equipment failure was conducted. Results indicate that the effect of observation errors on the inverse estimation results was within the relative error of 12%; the incomplete concentration data could also be used to obtain inverse estimation results. The two field experiments gave confidence to the application of this model in release mass estimation in actual pollution accidents with a relative error within 10%. These findings will assist in the decision-making for dealing with actual river pollution accidents.