One important motivation for the implementation of the Water Framework Directive is the creation of non-market environmental benefits such as improved ecological quality, or greater opportunities for open-access river recreation via microbial pollution remediation. Pollution sources impacting on ecological or recreational water quality can be uncorrelated but non-market benefits arising from riverine improvements are typically conflated within benefit valuation studies. Using stated preference choice experiments, we seek to disaggregate these sources of value for different river users, thereby allowing decision makers to understand the consequences of adopting alternative investment strategies. Our results suggest anglers derive greater value from improvements to the ecological quality of river water, in contrast to swimmers and rowers for whom greater value is gained from improvements to recreational quality. We also find three distinct groups of respondents: a majority preferring ecological over recreational improvements, a substantial minority holding opposing preference orderings and a small proportion expressing relatively low values for either form of river quality enhancement. As such, this research demonstrates that the non-market benefits which may accrue from different types of water quality improvements are nuanced in terms of their potential beneficiaries and, by inference, their overall value and policy implications.

Keywords: liquid alloys, microstratification, dispersed particles, spontaneous dispersion, criteria for true (entropic) spontaneous dispersion, mechanisms of quasi-spontaneous dispersion, methods and results for assessing size of dispersed particles.

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

It is claimed that classical mechanics (CM) in terms of its equivalent Koopman-von Neumann formulation (KvN) is indeed a ’real’ quantum theory since the formalism of quantum mechanics (FQM) does not, nor need it, exclude it as a such. This claim is made manifest by suggesting a common structure of which both KvN and ordinary quantum mechanics (OQM) correspond to unitary representations of, although unitarily inequivalent such. It is shown that OQM is obtained by enforcing the extra physical condition of quantized energy levels, which by itself does not constitute the ’quantum mystery’. It is furthermore shown that KvN in a physically realizable sense contain the hallmark quantum behavior of quantum interference. It is hence concluded that both CM and OQM are subjected to the same foundational issues. As the central part of both KvN and OQM is the introduction of probabilities via FQM it is suggested that the foundational issues regarding FQM are less about FQM itself and more about the concept of probability.

Melting phase relations of the diamond-forming system olivine (Ol) – jadeite (Jd) – diopside (Di) – (Mg, Fe, Ca, Na)-carbonates (Carb*) – (C-O-H-fluid) are studied in experiments at 6.0 GPa in the polythermal section Ol74Carb*18.5(C-O-H)7.5 - Omp74Carb*18.5(C-O-H)7.5, where Ol = Fo80Fa20, Omp (omphacite) = Jd62Di38 and Carb* = (MgCO3)25(FeCO3)25(CaCO3)25(Na2CO3)25. Peritectic reaction of olivine and jadeite-bearing melt with formation of garnet has been determined as a physico-chemical mechanism of ultrabasiс-basiс evolution of the diamond-forming system. In the process CO2-component of the supercritical C-O-H-fluid can react with silicate components to form additional carbonates of Mg, Fe, Ca and Na. Solidus temperature of the diamond-forming system is depressed to 1000-1020°C by joint effect of the H2O-fluid and carbonate constituents thereof. The experimentally recognized peritectic mechanism of ultrabasiс-basiс evolution of the diamond-forming system explains the origin of the associated paragenetic inclusions of peridotite and eclogite minerals in diamonds as well as the xenoliths of diamond-bearing peridotites and eclogites of the kimberlitic deposits of diamond. The diamond-forming systems have formed with the use of material of the upper mantle native peridotite rocks. In this case the capacity of the rocks to run the peritectic reaction of olivine was transmitted with silicate components to the diamond-forming systems.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.