In this work we introduce a novel approach to generate lower and upper L2 estimates for solution derivatives of arbitrary order to a general class of dissipative systems in the case that such estimates are available for the solutions themselves. Our method also works in reverse order: from the L2 estimates of solution derivatives of some (arbitrary) order we can derive lower and upper L2 estimates for the solutions and then to their derivatives of any order. This procedure is based on very simple monotonicity properties combined with standard energy estimates in physical space, following previous ideas of Kreiss, Hagstrom, Lorenz and Zingano. For simplicity, it is applied here in the context of algebraic rates, but the method can be used in other contexts as well (exponential, logarithm, and so forth).

QPEs (Quantitative Precipitation Estimates) obtained from remote sensing or ground-based radars could complement or even be an alternative to rain gauge readings. However, to be used in operational applications, a validation process has to be carried out, usually by comparing their estimates with those of a rain gauges network. In this paper, the accuracy of two QPEs are evaluated for three extreme precipitation events in the last decade in the southeast of the Iberian Peninsula. The first QPE is PERSIANN-CCS, a satellite-based QPE. The second is a meteorological radar with Doppler capabilities that works in the C band. Pixel-to-point comparisons are made between the values offered by the QPEs and those obtained by two networks of rain gauges. The results obtained indicate that both QPEs were well below the rain gauge values, especially in extreme rainfall time slots. There seems to be a weak linear association between the value of the discrepancies and the precipitation value of the QPEs. It does not seem that radar is more accurate than PERSIANN-CCS, despite its larger spatial resolution and its commonly higher effectiveness. The main conclusion is that neither PERSIANN-CCS nor radar, without empirical calibration, are acceptable QPEs for the real-time monitoring of meteorological extremes in the southeast of the Iberian Peninsula.

Background. Asbestos has been used for thousands of years but in a large industrial scale for about 100–150 years. The first identified disease was asbestosis, a type of incurable pneumoconiosis caused by asbestos dust and fibres. The latest estimate of global number of asbestosis deaths from the Global Burden of Disease estimate 2016 is 3495. Asbestos caused cancer was identified in the late 1930’s but despite of today’s overwhelming evidence of the strong carcinogenicity of all asbestos types including chrysotile it is still widely used globally. Various estimates have been made over time including those of WHO and ILO 107,000–112,000 deaths. Present estimates are radically higher. This special edition of the Journal summarizes key aspects of the past and present of the asbestos problem globally. Methods. Documentation on milestones of asbestos related diseases, ARDs, their recognition, reporting, compensation and prevention efforts were examined, in particular from the regulatory and prevention point of view. Estimated global numbers of incidence and mortality of ARDs were looked at. Results. Asbestos causes an estimated 257,000 deaths (243,223–270,635) annually according to latest knowledge. Work-related exposures are responsible for 235,000 deaths (222,322–247,363) of those. In the European Union, USA and in other High income economies (WHO regional classification) the direct costs for sickness, early retirement and death, including production losses, have been estimated to be very high, in the Western European countries and EU equivalent of 0.70% of the GDP or 114.9*109 USD. Intangible costs could be much higher. When applying the Value of Statistical Life (VSL) of 4 million EUR per cancer death used by the European Commission we arrived 5at 410*109 USD while the human suffering and loss of life is impossible to quantify. The numbers and costs are increasing practically in every country and region in the world. Asbestos has been banned in 55 countries but used widely today, some 2,030,000 tons consumed annually according to latest available consumption data. Every 20 tons of asbestos produced and consumed kills a person somewhere in the world. Buying 1 kg asbestos powder format e.g. in Asia costs some 0.38 USD and 20 tons would cost in such retail market 7600 USD. Conclusions. Present efforts to eliminate this man-made problem, in fact an epidemiological disaster, and preventing exposures leading to it are insufficient in most countries in the world. Applying programmes and policies, such as those on the elimination of all kind of asbestos use—that is banning of new asbestos use and tight control and management of existing structures containing asbestos—need revision and resources. The ILO/WHO Joint Programme for the Elimination of Asbestos-related Diseases need to be revitalized. Exposure limits do not protect properly against cancer but for asbestos removal and equivalent exposure elimination work we propose a limit value of 1000 fibres/m³.

Generally, stochastic functional differential equations (SFDEs) pose a challenge as they often lack explicit exact solutions. Consequently, it becomes necessary to seek certain favorable conditions under which numerical solutions can converge towards the exact solutions. This article aims to delve into the convergence analysis of solutions for stochastic functional differential equations by employing the framework of G-Brownian motion. To establish the goal, we find a set of useful monotone type conditions and work within the space Cr((−∞,0];Rn). The investigation conducted in this article confirms the mean square boundedness of solutions. Furthermore, this study enables us to compute both LG2 and exponential estimates.

The quantile estimation of extreme wind speed is needed in various environmental fields such as climatology, design of structures, renewable energy sources and agricultural operations. These calculations are crucial for the coding of wind speed. In this study, the required wind speed series of 16 stations in Khyber Pakhtunkhwa, Pakistan, was obtained from the NASA official website and measured in meters per second (m/s) at a 10-meter distance. A Regional Frequency Analysis of 16 AMWS stations was performed using L-moments. The quantile estimates of extreme wind speed are needed for various areas of interest using Regional Frequency Analysis (RFA) and extreme value theory. These calculations are crucial for the coding of wind speed. The data was taken from the NASA official website at a 10-meter distance and measured in meter per second (m/s). A Regional Frequency Analysis of AMWS using L-moments is performed utilizing wind speed data from sixteen sites (16) in Pakistan's Khyber Pakhtunkhwa province. There are no sites that are found to be discordant. The wards method is used to construct a homogenous region and make two homogenous regions from 16 sites. The heterogeneity test justifies that both clusters are homogeneous. The most appropriate probability distribution from the Generalized Normal (GNO), Generalized Logistic (GLO), Pearson Type-3 (P3), Generalized Pareto (GPA), and Generalized Extreme Value (GEV) distributions are chosen to calculate regional quantiles. According to the L-moments diagram and Z statistics, GEV for Cluster- Ι and GLO for Cluster- ΙΙ are the best suggestions from the others. Both clusters’ robustness is measured utilizing Relative Bias (RB) and Relative Root Mean Square Error (RRMSE). Overall, GEV distribution is fit for cluster-Ι, and the GLO distribution is fit for cluster-ΙΙ. Utilizing the site mean and median as index parameters, we can also find at-site quantiles from regional quantiles. The study’s quantile estimates can be employed in codified structural designs with policy consequences.

Macrophytes and seagrasses play a crucial role with a variety of the functions in the marine ecosystem and respond synchronized-promptly to the changing climate, followed by ecological status. Monitoring of the seagrasses was one of the paramount topics at the marine environment. One of the fast monitoring techniques is the vegetation acoustics with the advantages compared to the other remote sensing techniques. The acoustic method alone is ambitious to sea-truth identities of the backscatterers at the sea. Therefore, a package of computer programs was developed to identify, estimate leaf biometrics (leaf length and biomass) of one of the common seagrasses, Posidonia oceanica. Some troubleshooting in the acoustical data were fixed and then solved to reach the estimates regarding to the matters encountered for the vegetation as well as fisheries and plankton acoustics. One of the trouble was the “Lost” bottom which occurred during the data collection and post-processing due to occurrence of the acoustical noises, reverberations, interferences and intense scatterers suchlike fish schools. Another problem to remove was the occurrence as studying the near-bottom echoes belonging to submerged vegetations such as seagrasses, followed by spurious echoes. Last one was recognition of the seagrass to estimate leaf length and biomass calibrating the sheaths/vertical rhizome of the seagrass and establishing relationships between acoustical units and biometrics, respectively. As a consequence, an autonomous package of the code written in language MatLab was developed to perform all processes, and the name of the package was abbreviated as POSIBIOM, POSIdonia BIOMass. This study presented the algorithms, methodology, acoustics-biometrics relation, and mapping of the biometrics for the first time, and discussed advantages and disadvantages of the package compared to the software purposed for the bottom types, habitat and vegetation acoustic. The future studies were recommended to improve the package.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

Accurate and consistent rainfall observations are vital for climatological studies in support of better planning and decision making. However, estimation of accurate spatial rainfall is limited by sparse rain gauge distributions. Satellite rainfall products can thus potentially play a role in spatial rainfall estimation but their skill and uncertainties need to be under-stood across spatial-time scales. This study aimed at assessing the temporal and spatial performance of seven satellite products (TARCAT (Tropical Applications of Meteorology using SATellite and ground-based observations (TAMSAT) African Rainfall Climatology And Time series), Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS), Tropical Rainfall Measuring Mission (TRMM-3B43), Climate Prediction Center (CPC) Morphing (CMORPH), the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks- Climate Data Record (PERSIANN-CDR), CPC Merged Analysis of Precipitation (CMAP) and Global Precipitation Climatology Project (GPCP) using gridded (0.05o) rainfall data over East Africa for 15 years(1998-2012). The products’ error distributions were qualitatively compared with large scale horizontal winds (850 mb) and elevation patterns with respect to corresponding rain gauge data for each month during the ‘long’ (March-May) and ‘short’ (October-December) rainfall seasons. For validation only rainfall means extracted from 284 rain gauge stations were used, from which qualitative analysis using continuous statistics of Root Mean Squared Difference, Standard deviations, Correlations, coefficient of determinations (from scatter plots) were used to evaluate the products’ performance. Results revealed rainfall variability dependence on wind flows and modulated by topographic influences. The products’ errors showed seasonality and dependent on rainfall intensity and topography. Single sensor and coarse resolution products showed lowest performance on high ground areas. All the products showed low skills in retrieving rainfall during ‘short’ rainfall season when orographic processes were dominant. CHIRPS, CMORPH and TRMM performed well, with TRMM showing the best performance in both seasons. There is need to reduce products’ errors before applications.

The only cases where exact distributions of estimates are known is for samples from exponential families, and then only for special functions of the parameters. So statistical inference was traditionally based on the asymptotic normality of estimates. To improve on this we need the {\it Edgeworth expansion} for the distribution of the standardized estimate. This is an expansion in $n^{-1/2}$ about the normal distribution, where $n$ is typically the sample size. The 1st few terms of this expansion were originally given for the special case of a sample mean. In earlier work we derived it for {\it any } standard estimate, hugely expanding its application. We call an estimate $\hat{w}$ of an unknown vector $w\in R^p$, a {\it standard estimate}, if $E\ \hat{w}\rightarrow w$ as $n\rightarrow \infty$, and for $r\geq 1$ the $r$th order cumulants of $\hat{w}$ have magnitude $n^{1-r}$ and can be expanded in $n^{-1}.$ Here we give another huge extension. We give the expansion of the distribution of {\it any smooth function} of $\hat{w}$, say $t(\hat{w})\in R^q,$ giving its distribution to $n^{-5/2}$. We do this by showing that $t(\hat{w})$, is a standard estimate of $t(w)$. This provides far more accurate approximations for the distribution of $t(\hat{w})$ than its asymptotic normality. %NOT USED: The building blocks of the Edgeworth expansions are the {\it cumulant coefficients } of the estimate. These cumulant coefficients are also needed for bias reduction, Bayes estimates and confidence regions. We give {\it chain rules} for the cumulant coefficients of $t(\hat{w})$ in terms of those of $\hat{w}$ and the derivatives of $t(w)$, up to those needed for 5th order Edgeworth expansions for $t(\hat{w})$ and its {\it tilted expansion}, useful for the tail of the distribution.

Australia is a unique continent surrounded by the ocean and the majority of catchments flow to the coast. Some of these catchments are gauged and others are ungauged. There are 405 gauged catchments covering 2,549,000 km2 across the coastal regions of 12 drainage divisions in Australia. Whereas there are 771 catchments conceptualised as ungauged covering additional 835,000 km2. The mean annual rainfall and PET and its spatial and temporal distribution vary significantly from one drainage division to another. We developed a continuous daily streamflow time series of all gauged and ungauged catchments from 1993 onwards. We applied the GR4J lumped conceptual model to these catchments. The performance of gauged catchments was analysed through (i) visual inspection of daily hydrographs, flow duration curves and daily scatter plots, and (ii) performance metrics including NSE and PBias. Based on the NSE and PBias, performance ratings of 80% and 96% of the models respectively were found 'good'. There was no relationship found between the catchment area and model performance. The ungauged catchments were divided into four categories based on distance from potential donor catchments where observed data are available for GR4J model calibration, and Köppen climate zone. The total ungauged catchments represent 24.7% of the total drainage division areas. The streamflow from ungauged catchments was estimated using GR4J model based on the parameters of their donor catchments. Overall, runoff ratios from ungauged catchments were found to be higher compared to their donor gauged catchments, likely driven by their higher rainfall and less PET. This tendency was particularly evident in two drainage divisions – the Carpentaria Coast (CC) and Tanami-Timor Sea Coast (TTS) where ungauged areas comprised 51% and 43% respectively. The mean gauged annual streamflow varied significantly across drainage divisions – 230 GL from South Australian Gulf (SAG) to 146,150 GL in TTS. The streamflow from all ungauged catchments was estimated at 232,200 GL per year. Overall, the average streamflow from all drainage divisions, including gauged and ungauged areas, across the coastal regions of Australia was estimated at 419,950 GL per year. This nationwide estimate of streamflow dataset could potentially enhance our understanding of coastal processes and improvements of marine modelling systems and tools.

In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.

The aim of the paper is to identify the most likely factors that determine the demand for Renewa-ble Energy Consumption (R.E.C.) in European countries. Although in Europe a high environmen-tal awareness is omnipresent, countries differ in scope and share of R.E.C. due to historical ener-getic policies and dependencies, investments into renewable and traditional energetic sectors, R&D development, structural changes required by energetic policy change, and many other fac-tors. The study refers to a set of macroeconomic, institutional, and social factors affecting energetic renewable policy and R.E.C. in selected European countries in two points of time: i.e., before and after the Paris Agreement. The Bayesian Average Classical Estimates (BACE) is applied to indicate the most likely factors affecting R.E.C. in 2015 and 2018. The comparison of the results reveals that the G.D.P. level, nuclear and hydro energy consumption were the determinants significant in both analyzed years. Furthermore, it became clear that in 2015 the R.E.C. depended strongly on the energy consumption structure, while in 2018, the foreign direct investment and trade openness played their role in increasing renewable energy consumption. The direction of changes is positive and complies with sustainable development goals (S.D.G.s).

In this work the close relation between vorticity and micro-rotation in micropolar flows in Rn (n = 2 or 3) is identified and used to explain the faster decay by t^(-1/2) of the angular velocity of the micro-rotation of fluid particles, as well as establishing its optimality. For this purpose important upper and lower bounds for Leray solutions in homogeneous Sobolev spaces are derived, using the monotonicity approach recently introduced by the authors for dissipative systems in general. Several related results of interest are also given along the discussion.