MATHEMATICAL STUDY OF THE PLANAR OSCILLATIONS OF A HEAVY, ALMOST HOMOGENEOUS LIQUID IN A CONTAINER

Author(s):  
P. CAPODANNO ◽  
D. VIVONA
Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.


Molecules ◽  
2021 ◽  
Vol 26 (8) ◽  
pp. 2277
Author(s):  
Piotr M. Kuś ◽  
Igor Jerković

Recently, we proposed a new sample preparation method involving reduced solvent and sample usage, based on dehydration homogeneous liquid–liquid extraction (DHLLE) for the screening of volatiles and semi-volatiles from honey. In the present research, the method was applied to a wide range of honeys (21 different representative unifloral samples) to determine its suitability for detecting characteristic honey compounds from different chemical classes. GC-FID/MS disclosed 130 compounds from different structural and chemical groups. The DHLLE method allowed the extraction and identification of a wide range of previously reported specific and nonspecific marker compounds belonging to different chemical groups (including monoterpenes, norisoprenoids, benzene derivatives, or nitrogen compounds). For example, DHLLE allowed the detection of cornflower honey chemical markers: 3-oxo-retro-α-ionols, 3,4-dihydro-3-oxoedulan, phenyllactic acid; coffee honey markers: theobromine and caffeine; linden honey markers: 4-isopropenylcyclohexa-1,3-diene-1-carboxylic acid and 4-(2-hydroxy-2-propanyl)cyclohexa-1,3-diene-1-carboxylic acid, as well as furan derivatives from buckwheat honey. The obtained results were comparable with the previously reported data on markers of various honey varieties. Considering the application of much lower volumes of very common reagents, DHLLE may provide economical and ecological advantages as an alternative sample preparation method for routine purposes.


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