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PDE --- Bruxelles

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Since the end of the 19th century when the prominent Norwegian mathematician Sophus Lie created the theory of Lie algebras and Lie groups and developed the method of their applications for solving differential equations, his theory and method have continuously been the research focus of many well-known mathematicians and physicists. This book is devoted to recent development in Lie theory and its applications for solving physically and biologically motivated equations and models. The book contains the articles published in two Special Issue of the journal Symmetry, which are devoted to analysis and classification of Lie algebras, which are invariance algebras of real-word models; Lie and conditional symmetry classification problems of nonlinear PDEs; the application of symmetry-based methods for finding new exact solutions of nonlinear PDEs (especially reaction-diffusion equations) arising in applications; the application of the Lie method for solving nonlinear initial and boundary-value problems (especially those for modelling processes with diffusion, heat transfer, and chemotaxis).

Lie algebra/group --- invariance algebra of nonlinear PDE --- Lie symmetry --- nonlinear boundary-value problem --- (generalized) conditional symmetry --- symmetry of (initial) boundary-value problem --- invariant solution --- exact solution --- non-Lie solution --- Q-conditional symmetry --- representation of Lie algebra --- nonclassical symmetry --- invariance algebra of PDE

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Climatology --- Weather forecasting --- Forecasting, Weather --- Short range weather forecasting --- Weather --- Weather prediction --- Forecasting --- Geophysical prediction --- Climatology. --- Weather forecasting. --- Climate --- Climate science --- Climate sciences --- Science of climate --- Atmospheric science --- Meteorology & Climatology --- numerical methods --- stochastic processes --- pde analysis --- time series analysis --- data filtering and assimilation --- atmosphere and ocean sciences

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This Special Issue aims to provide an updated overview of the flourishing ongoing research activity in the field of the chemistry of natural and nature-inspired compounds. Ten of the submitted articles were accepted for publication after peer-review. Interestingly, the published papers cover a wide range of chemical reactions, different scaffolds, and several medicinal chemistry applications. Moreover, this Special Issue gathered contributions from all over the world, testifying the international scientific community’s interest in this topic. I would like to sincerely thank the MDPI staff, particularly Jade Lu and the editorial team of Molbank. I am particularly grateful to the authors that decided to share the results of their research by contributing their manuscript to this Special Issue, and, of course, to the reviewers for their valuable help.

Research & information: general --- quercetin --- flavonoids --- semi-synthetic --- PDE --- sildenafil --- molecular modeling --- Garcinia porrecta --- Clusiaceae --- xanthone --- Lansium domesticum --- Meliaceae --- MCF-7 --- triterpene onoceranoid --- hydrazone --- (+)-camphor --- valproic acid --- technology --- terpenoid --- anticonvulsant activity --- 1,2,3-triazole --- anticancer --- aminoquinoline --- hybrid compound --- kokosanolide --- tetranortriterpenoid --- C. dichotoma --- antidiabetic --- α-glucosidase --- α-amylase --- docking --- ADMET --- curcumin analog --- organic synthesis --- photophysical properties --- steady-state fluorescence --- DFT calculation --- 7-hydroxy-2H-chromen-2-one --- O-acylation reaction --- coumarin --- lupeol derivative --- benzylidene derivative --- α-glucosidase inhibition --- Oxone® --- n/a

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This Special Issue aims to provide an updated overview of the flourishing ongoing research activity in the field of the chemistry of natural and nature-inspired compounds. Ten of the submitted articles were accepted for publication after peer-review. Interestingly, the published papers cover a wide range of chemical reactions, different scaffolds, and several medicinal chemistry applications. Moreover, this Special Issue gathered contributions from all over the world, testifying the international scientific community’s interest in this topic. I would like to sincerely thank the MDPI staff, particularly Jade Lu and the editorial team of Molbank. I am particularly grateful to the authors that decided to share the results of their research by contributing their manuscript to this Special Issue, and, of course, to the reviewers for their valuable help.

quercetin --- flavonoids --- semi-synthetic --- PDE --- sildenafil --- molecular modeling --- Garcinia porrecta --- Clusiaceae --- xanthone --- Lansium domesticum --- Meliaceae --- MCF-7 --- triterpene onoceranoid --- hydrazone --- (+)-camphor --- valproic acid --- technology --- terpenoid --- anticonvulsant activity --- 1,2,3-triazole --- anticancer --- aminoquinoline --- hybrid compound --- kokosanolide --- tetranortriterpenoid --- C. dichotoma --- antidiabetic --- α-glucosidase --- α-amylase --- docking --- ADMET --- curcumin analog --- organic synthesis --- photophysical properties --- steady-state fluorescence --- DFT calculation --- 7-hydroxy-2H-chromen-2-one --- O-acylation reaction --- coumarin --- lupeol derivative --- benzylidene derivative --- α-glucosidase inhibition --- Oxone® --- n/a