Tauberian theorems for the wavelet transform

We make a complete wavelet analysis of asymptotic properties of distributions. The study is carried out via Abelian and Tauberian type results, connecting the boundary asymptotic behavior of the wavelet transform with local and non-local quasiasymptotic properties of elements in the Schwartz class of tempered distributions. Our Tauberian theorems are full characterizations of such asymptotic properties. We also provide precise wavelet characterizations of the asymptotic behavior of elements in the dual of the space of highly time-frequency localized functions over the real line. For the use of the wavelet transform in local analysis, we study the problem of extensions of distributions initially defined on R\ {0} to R; in this extension problem, we explore the asymptotic properties of extensions of a distribution having a prescribed asymptotic behavior. Our results imply intrinsic properties of functions and measures as well, for example, we give a new proof of the classical Littlewood Tauberian theorem for power series

Multiresolution expansions and wavelets in Gelfand-Shilov spaces

We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand-Shilov spaces. Important examples of multiresolution analyses for which our results apply arise in particular from Dziuba\'{n}ski-Hern\'{a}ndez construction of band-limited wavelets with subexponential decay. Our results are twofold. Firstly, we obtain approximation properties of multiresolution expansions of Gelfand-Shilov functions and (ultra)distributions. Secondly, we establish convergence of wavelet series expansions in the same regularity framework.Comment: 15 page

Slope stability analyses using limit equilibrium and strength reduction methods

Slope stability analyses using limit equilibrium and strength reduction methods This paper presents results of comparative slope stability analyses conducted by limit equilibrium and strength reduction methods. Several slopes, taken either from geotechnical practice or literature review, are considered. The influence of tension, distributed load, finite element size and model parameters is analysed in relation to the location, shape of the critical failure surface and the corresponding value of the factor of safety. Both methods provide similar results if they are correctly applied using appropriate software programs. Analize stabilnosti pokosa metodama granične ravnoteže i smanjenja parametara čvrstoće U ovom su radu predstavljeni rezultati usporedne analize stabilnosti pokosa metodama granične ravnoteže i smanjenja parametara čvrstoće tla. Razmatrano je nekoliko pokosa uzetih iz literature ili iz geotehničke prakse. Analiziran je utjecaj vlačnog naprezanja, raspodijeljenog opterećenja, veličina konačnog elementa i parametri modela na lokaciji te oblik kritičnog loma i odgovarajuće vrijednosti faktora sigurnosti. Obje navedene metode daju slične rezultate ako se ispravno primijene u odgovarajućim računalnim programima

Solid-phase extraction as promising sample preparation method for compound of emerging concerns analysis

Today’s environment is under the influence of numerous substances and most of them are not covered by current national and international regulations. Substances that are classified as contaminants of emerging concern, CECs, are not regulated nor systematically controlled in the environment, and they belong to the different chemical classes such as pesticides in current use, pharmaceutically active compounds (PhACs), personal care products, illicit drugs, hormones, micro- and nano-plastics, per- and poly-fluoroalkyl substances (PFAS), and many others. Once released CECs end up in surface water where they can be either accumulated or transported to the other environmental compartments, i.e. soil (by irrigation), underground water, or drinking water. The aim of the research was to investigate the efficiency of different selected solid-phase extraction (SPE) cartridges for preparation of water samples for simultaneous analysis of several CECs. For this purpose, a model mix solution of selected CECs in concentration relevant to environmental appearance was used. The selected CECs (14 PhACs, 11 pesticides in current use, and 4 PFAS) represented emerging contaminants with different properties, including polarities, and varying adverse effect on the environment and human health. Different types of sorbents were investigated: (i) commercial single-layer HLB, (ii) homemade multi-layer I: HLB plus a mix of WAX, WCX, and PPL, and (iii) multi-layer II: mix of WAX, WCX, and PPL plus HLB. The results revealed that the single-layer sorbent showed better efficiency in extraction of the analyzed CECs. Multi-layer sorbent should be further investigated to elucidate the possible reason for the poor extraction of some compounds, as development of a balanced extraction for a wider range of contaminants with different polarities, especially for non-target analysis of chemical residues, is required in order to capture the occurrence of the full profile of micropollutants

Quantifying acidity and basicity of oxides: a calorimetric approach

Given the great many applications of heterogeneous acid-base catalysis, the acidity and basicity of solid oxide catalysts (non-porous, such as ceria, zirconia or titania, or porous, such as zeolites) are considered crucial, among various characteristics which influence their performance. Namely, the concentration of acid/basic sites, their nature and their strengths are the most important parameters. Different methods are routinely being applied in the study of acidity/basicity, most often infrared spectroscopy and temperature programmed desorption. However, in terms of exact quantitative data on acidic/basic site strength distributions, a calorimetric method stands out as exceptional. It is designed to simultaneously record adsorption isotherms of basic (NH3) or acidic (SO2) probe molecules and the related thermal effects, via coupling of a calorimeter and a calibrated volumetric line equipped with pressure gauges. Microcalorimetric-volumetric measurements of adsorption yield several sets of results: the total number of sites (µmol/g), the concentration of irreversibly adsorbed probe molecules (number of “strong” sites, µmol/g), integral heats of adsorption (J/g) and differential heats of adsorption (kJ/mol), i.e. the distribution of strengths of the acid/basic sites. Examples of these unique results, which provide a fully quantitative image of acidity/basicity of oxide materials, unparalleled by any other technique, will be presented.X Serbian Ceramic Society Conference - Advanced Ceramics and Application : new frontiers in multifunctional material science and processing : program and the book of abstracts; September 26-27, 2022; Belgrad

Application of geological strength index for characterization of weathering-induced failures

This study investigates weathering indded failures of the heterogeneous fissile rock mass consisting of sandstone and shale. Discontinuity data was collected and the geological strength index (GSI) value was determined immediately after excavation based on the quantified GSI chart. Slake durability tests were performed up to the fifth cycle. Samples were exposed to natural climatic conditions during a twelve-month period, in order to quantify slaking process by means of disintegration ratio. As a consequence of exposure, samples disintegrated into smaller fragments. On these bases, the model aimed at addressing delayed failure of cuts is proposed in the paper

Slope stability analyses using limit equilibrium and strength reduction methods

U ovom su radu predstavljeni rezultati usporedne analize stabilnosti pokosa metodama granične ravnoteže i smanjenja parametara čvrstoće tla. Razmatrano je nekoliko pokosa uzetih iz literature ili iz geotehničke prakse. Analiziran je utjecaj vlačnog naprezanja, raspodijeljenog opterećenja, veličina konačnog elementa i parametri modela na lokaciji te oblik kritičnog loma i odgovarajuće vrijednosti faktora sigurnosti. Obje navedene metode daju slične rezultate ako se ispravno primijene u odgovarajućim računalnim programima.This paper presents results of comparative slope stability analyses conducted by limit equilibrium and strength reduction methods. Several slopes, taken either from geotechnical practice or literature review, are considered. The influence of tension, distributed load, finite element size and model parameters is analysed in relation to the location, shape of the critical failure surface and the corresponding value of the factor of safety. Both methods provide similar results if they are correctly applied using appropriate software programs

PRIMJENA PARAMETARA STIŠLJIVOSTI U ANALIZI SLIJEGANJA KOMUNALNOG OTPADA

Da bi se omogućilo točnije modeliranje i numerička simulacija dugotrajnog ponašanja odlagališta otpada, što je veoma važno prilikom projektiranja pokrovnog sustava i zatvaranja odlagališta otpada, neophodno je poznavanje parametara stišljivosti. Za razliku od prirodnog tla, glavnu komponentu ukupnog slijeganja komunalnog otpada predstavlja sekundarna kompresija. Zato je određivanje indeksa sekundarne kompresije ili modificiranog indeksa sekundarne kompresije posebno važno. U radu su prikazani neki od rezultata laboratorijskih ispitivanja uzoraka komunalnog otpada dobiveni u edometarskom uređaju, kao i njihova uloga u analizi slijeganja komunalnog otpada. Ispitivanja su izvršena na umjetno pripremljenim uzorcima, uz uvažavanje preporuka koje se odnose na dimenzije korištenih uređaja i veličinu najvećih frakcija u uzorku (EN 1997-2, ASTM 2007-a, 2007-b). Primjenom različitih modela, koji se najčešće koriste za prognozu slijeganja odlagališta komunalnog otpada, izvršena je analiza slijeganja korištenjem dobivenih parametara stišljivosti

Chronopotentiometric determination of metamitron comparing classical and Box-Behnken optimization approaches

This paper describes an optimization procedure for determination of the herbicide metamitron by chronopotentiometry. Two different working electrodes were use in the experiments: glassy carbon and thin film mercury electrode. The analytical signal of metamitron was the result of irreversible reduction on the working electrodes in Britton-Robinson buffer as the supporting electrolyte, and one reduction peak was obtained on both working electrodes. Operating conditions, involving several chemical and instrumental parameters such as: pH of Britton-Robinson buffer, initial potential and reduction current were optimized by the classical method, where one parameter is changing while others are constant, and by using Box-Behnken experimental design. In both optimization procedures, the maximum height of the metamitron analytical signal was requested. Obtained results from this study revealed that there were no differences between the two optimization methods