DIFERENCIALNE ENAČBE, DIFERENČNE ENAČBE IN MEHKA LOGIKA V UPRAVLJANJU DINAMIČNIH SISTEMOV

In this article, the use of certain mathematical tools to create a dynamic system control is described; such a control could be applied to a power supply system. In continuous dynamic systems, the control of the system is described by one or more differential equations; however, in discrete dynamic systems, this control is described by one or more difference equations. Both differential and difference equations are highly effective tools in conventional mathematical analysis. In the previous twenty years, algorithmic principles of fuzzy logic in the control of the dynamic systems have been very useful. In this article, the applications of all three approaches are presented. In the case of the fuzzy logic approach, there is an example of the energy efficiency in the employment of biomass with an emphasis on developing the environmental sustainable biomass index.V članku so predstavljene matematične metode pri kreiranju upravljanja sinamičnega sistema, ki je lahko tudi energetski sistem. V primeru dinamičnih sistemov je upravljanje opisano z eno ali več diferencialnimi enačbami, v primeru diskretnih sistemov pa je njihovo upravljanje opisano z eno ali več diferenčnimi enačbami. Oboje, diferencialne in diferenčne enačbe, so izjemno uporabno orodje v klasični matematični analizi. V zadnjih dvajsetih letih pa se je kot zelo uporabna algoritmična osnova upravljanja dinamičnih sistemov uveljavila uporaba principov mehke logike. Kot hibridni pristop upravljanju dinamičnih sistemov se v zadnjih letih uveljavlja tudi možnost sinteze diferencialnih/diferenčnih enačb ter mehke logike. V članku prikazujemo možnosti uporabe vseh treh pristopov. Za uporabo mehke logike in mehkega sklepanja je podan numerični primer za energetsko izrabo biomase s poudarkom na trajnostnem indeksom varovanja okolja

UPRAVLJANJE SISTEMA V POGOJIH ZVEZNEGA SLUČAJNOSTNEGA VHODNEGA PROCESA

In this article, a mathematical model of the control of a continuous stochastic production system is described. This system can also be a power supply system. An analytical model has been developed todescribe the influence of production and stock on hierarchical spatial pattern and demand. In production systems where the concept of inventories/stocks does not have a standard meaning in terms ofproduct storage, as in an energy system, they take on the role of supply of additional capacities that are optimally released according to demand. A system of differential equations describing the dynamics of a continuous system is solved using a Laplace transformation. Due to the stochastic nature of system inputs, the optimality criteria with the Wiener filter are satisfied. The Wiener-Hopf equation is solved by the spectral factorization method. The results of the presented mathematical model can be used as relevant information for the process of decision making in the operation of business systems,including energy systems. The operation of a mathematical model and the analysis of the results is illustrated with two examples of different demand functions.V članku je predstavljen matematični model upravljanja zveznega stohastičnega proizvodnega sistema. Ta sistem je lahko tudi energetski sistem. Razvit je analitični model, s katerim opišemo medsebojni vpliv proizvodnje ter zalog na hiearhično porazdeljeno prostorsko dogajanje/porabo oziroma povpraševanje. V proizvodnih sistemih, kjer pojem zalog nima standardnega pomena v smislu skladiščenja izdelkov, tak pa je tudi energetski sistem, prevzamejo vlogo zalog dodatne kapacitete, ki jih optimalno sproščamo glede na povpraševanje. Sistem diferencialnih enačb, ki opisujejo dinamiko zveznega sistema, rešimo z uporabo Laplaceove transformacije. Pogoju optimalnosti lahko zaradi stohastičnih vhodov sistema zadostimo z uporabo Wienerjevega filtra. To vodi do izpeljave Wiener‐Hopfove enačbe, ki jo rešimo z metodo spektralne faktorizacije. Rezultati prikazanega matematičnega modela se lahko uporabijo kot pomembne informacije odločevalcu pri v procesu sprejemanja odločitev v delovanju poslovnih sistemov, kamor sodi tudi energetski sistem. Delovanje matematičnega modela in analiza rezultatov je ilustrirano z dvema primeroma funkcije povpraševanja

MEHKI MODEL NAPOVEDI OGROŽENOSTI Z BOLEZNIJO COVID-19

The present paper presents a fuzzy model for predicting the risk of a community (country) to being infected by the coronavirus Covid-19. The research is not the medical field, where favourable news about vaccines against this disease is just emerging from the research community. Instead, it presents a relatively simple mathematical model based on the use of fuzzy logic. The model is created as a fuzzy system, in which the basic postulates of fuzzy logic and fuzzy inference are used. The presented model is, of course, only one possibility for describing and predicting the threat to the population due to the Covid-19 disease.V članku je predstavljen mehki model napovedi ogroženosti prebivalcev neke skupnosti (države) z boleznijo Covid-19. Raziskava se ne spušča na medicinski področje, kjer se v svetovni raziskovalni skupnosti ravnokar pojavljajo ugodne vesti o cepivu proti tej bolezni. Raziskava predstavlja relativno preprost matematični model, ki temelji na uporabi mehke logike. Model je kreiran kot mehki sistem, kjer uporabljamo osnovne postulate mehkega sklepanja. Predstavljeni model je seveda le ena od možnosti opisovanja in predvidevanja ogroženosti prebivalcev zaradi bolezni Covid-19

GENERALIZIRANO MEHKO LINEARNO PROGRAMIRANJE

Linear programming is one of the widely used methods for optimising business systems, which includes organisational, financial, logistic and control subsystems of energy systems in general. It is possible to express numerous real-world problems in a form of linear program and then solve by simplex method [1]. In the development of linear programming, we are facing a number of upgrades and generalisations, as well as replenishment. Particularly interesting in recent years is an option that decision variables and coefficients are fuzzy numbers. In this case we are dealing with fuzzy linear programming. If we also include in a fuzzy linear program a generalisation with respect to Wolfe’s modified simplex method [1], we obtain a generalised fuzzy linear program (GFLP). Usenik and Žulj introduced methods for solving those programs and proved the existence of the optimal solution in [2]. In the article, the simplex algorithm which enables the determining of an optimal solution for GFLP is described. There is a numerical example at the end of the article that illustrates the algorithm.Linearno programiranje je najbolj uporabljena metoda optimizacije poslovnih sistemov, med katere štejemo tudi organizacijske, finančne, logistične in nasploh upravljalne podsisteme energetskega sistema. Veliko praktičnih problemov je mogoče izraziti v obliki linearnega programa, ki ga nato rešimo s simpleksno metodo [1]. Razvoj linearnega programiranja je doživel vrsto nadgradenj, posplošitev in dopolnitev. V zadnjih letih je še posebej zanimiva možnost, da so odločitvene spremenljivke in koeficienti mehka števila – v tem primeru gre za mehko linearno programiranje. Ko pa v ta program uvedemo še pojem generalizacije v Wolfejev pomenu [1], govorimo o generaliziranem mehkem linearnem programiranju (GMLP). Usenik in Žulj [2] sta razvila postopke reševanja takšnih programov in dokazala eksistenco optimalne rešitve. V članku opišemo algoritem simpleksnega postopka za GMLP, ki omogoča izračun optimalne rešitve, in na koncu dodamo numerični primer, ki ilustrira izvedeni algoritem

Thermodynamics of complexation of alkaline-earth metal cations by a fluorescent phenathridine-based calix[4]arene derivate

Sustavno je istraženo kompleksiranje kationa zemnoalkalijskih metala s derivatom kaliks[4]arena koji na donjem obodu posjeduje dvije fluorescentne fenantridinske podjedinice i dva supstituenta s tercijarnim amidnim skupinama, koji zajedno čine efikasno vezno mjesto za katione. U svrhu detaljnijeg proučavanja utjecaja otapala na ravnoteže procesa kompleksiranja, provedena su istraživanja reakcija u acetonitrilu, metanolu i etanolu. Kompleksiranje je istraženo spektrofotometrijskim, fluorimetrijskim te izotermnim mikrokalorimetrijskim izravnim i kompeticijskim titracijama. Određene su konstante stabilnosti nastalih kompleksa (i iz njih izračunane odgovarajuće standardne reakcijske Gibbsove energije) te standardne reakcijske entalpije i entropije. Proučavani kaliksaren pokazuje iznimno velik afinitet prema zemnoalkalijskim kationima u acetonitrilu, daleko manji u etanolu te još manji u metanolu. U acetonitrilu termodinamički je najstabilniji kompleks s Ca2+, dok u metanolu i etanolu najveća konstanta stabilnosti odgovara kompleksu sa Sr2+. Razlike u afinitetima za vezanje kationa uglavnom su posljedica različite solvatacije vrsta prisutnih u otopini i kompatibilnosti veličine kationa i veznog mjesta liganda. U acetonitrilu su u svim slučajevima i entalpijski i entropijski doprinos standardnoj reakcijskoj Gibbsovoj energiji povoljni, dok su u metanolu i etanolu reakcije kompleksiranja endotermne i entropijski kontrolirane. Istraživani ligand pokazao se vrlo efikasnim i osjetljivim fluorescentnim receptorom za Ca2+ i Sr2+ u acetonitrilu.The complexation of alkaline-earth metal cations with tertiary-amide lower-rim fluorescent calix[4]arene derivative comprising two phenanthridine moieties was studied by means of spectrophotometric, fluorimetric, and microcalorimetric direct and competitive titrations. In order to investigate the solvent effect on cation-binding processes, the complexation reactions were studied in acetonitrile, methanol, and ethanol, whereby the complex stability constants (and derived standard reaction Gibbs energies) as well as standard reaction enthalpies and entropies of complexation reactions were determined. The investigated calixarene exhibited high affinity towards alkaline-earth metal cations in acetonitrile, with low selectivity and peak affinity corresponding to Ca2+, whereas the complex stabilities were significantly lower in ethanol and methanol, in which the affinity for Sr2+ was highest. The differences in cation-binding abilities were a consequence of the differences in solvation of the species present in solution as well in compatibility of the cation and binding-site sizes. The extensive solvent effect could be, at least partially, rationalized by much more favourable cation solvation in methanol and ethanol, as compared to acetonitrile. The binding reactions were enthalpically controlled in acetonitrile, as opposed to methanol and ethanol in which the reactions were endothermic and entropically driven. The investigated ligand was proven to be very effective and rather sensitive fluorescent receptor for Ca2+ and Sr2+ in acetonitrile

Online professional development for librarians in the workplace and the problem of multitasking

Objective. This survey aimed to identify which activities that can lead to multitasking librarians do at the same time as their online professional development at work, and how often they perform them. Approach/Methodology/Design. The survey was conducted using quantitative methodology, with a survey questionnaire as the measurement instrument, which examined the age of the respondents, the type of library where they work, the location from where they attend online professional development and the activities they carry out during their online professional development. The survey included 593 librarians employed in 2024 in one of the different types of libraries included in the COBISS system. Results. The results indicate that participants do perform additional tasks during their professional development sessions, but only occasionally or rarely. The performance of additional activities varies statistically significantly between participants according to the type of library they work in and their age, and the performance of some activities also varies according to the location where they are receiving the training. The most frequently reported multi-tasking activities during the online professional development are additional work tasks, interaction with co-workers and reading and writing e-mails unrelated to the training. Participants with the highest reported rates of multitasking are from the national library and special and higher education libraries. In terms of age, younger participants (aged between 20 and 39) were the most frequent multitaskers. Limitations. The data were not collected immediately following a single online professional development session and was gathered retrospectively, which may have caused participants to have difficulty recalling information. Additionally, the use of a survey questionnaire may introduce response bias. Practical Application. The results of the survey can help us to be aware of these issues when planning online professional development sessions. Social Significance. Addressing the problem of multitasking may help discourage such behaviour among learners, and alert online professional development planners to the problem of an inappropriate learning environment that allows too many distractions. Originality/Value. The article presents previously unknown information and data about the implementation of multitasking performed by librarians from various types of libraries while engaging in online professional development at the workplace

Utjecaj otapala na kinetiku kemijskih reakcija

Opis kinetike reakcija u otopini znatno je složeniji od reakcija u plinskoj fazi. Razlog tome je značajan broj interakcija sudionika reakcije s molekulama otapala čiji je kvantitativan opis netrivijalan. Za razmatranje kinetike reakcija u otopini je, dakle, za razliku od plinske faze, potrebno uključiti dodatne varijable vezane uz otapalo. Osim toga, interpretacija dobivenih eksperimentalnih podataka korištenjem jednostavnih kinetičkih modela daje isključivo kvalitativnu sliku o promatranom sustavu, zbog čega je za kvantitativniji opis potrebno koristiti znatno složenije modele. Osim uobičajenih varijabli koje utječu na kinetiku reakcije, kao što je primjerice temperatura, otapalo i njegove karakteristike također treba uzeti u obzir. Budući da promjena otapala nerijetko uzrokuje promjenu brzine, mehanizma i ishoda kemijske reakcije, ono je važan faktor u njezinu „usmjeravanju“. Iz tog je razloga odabir otapala izrazito važan u planiranju sinteze spojeva. Koristeći saznanja iz osnova kemijske kinetike i ponašanja tvari u otopinama moguće je na temelju pretpostavljenog mehanizma predvidjeti svojstva otapala koja bi pogodovala željenom ishodu reakcije, bilo u kontekstu brzine, prinosa, selektivnosti ili jednostavnosti provođenja i obrade reakcijske smjese. U ovom radu bit će ukratko opisana načela interakcija u otopini potrebna za daljnji opis utjecaja otapala na kinetiku reakcija. Utjecaj otapala bit će razmotren za slučaj aktivacijski kontroliranih reakcija na temelju teorije aktiviranog kompleksa, odnosno za slučaj difuzijski kontroliranih reakcija na temelju teorije sudara. Odabrani primjeri bit će dani na kraju rada kako bi pružali uvid u važnost odabira otapala za reakcije u otopini, ali i važnost prisustva malih količina otapala kod mehanokemijskih reakcija

Evaluating of some quality parameters of different apricot cultivars using HPLC method

High performance liquid chromatography (HPLC) was used for separation, identification and quantification of sugars, sugar alcohol sorbitol and non-volatile acid content in puree of 15 apricot cultivars (Prunus armeniaca L.). Sugar analyses included sucrose, glucose, fructose, xylose and sorbitol. The main organic acids characterizing apricot puree are malic, citric and fumaric acid. Variation in the content of theanalyzed compounds mentioned and also in the content of soluble solids (SS), titratable acids and pH value was found among the cultivars. Sensory evaluation showed that the content of individual organic acids and sugars as well as their relations could be crucial in forming the taste.Knowledge of the qualitative and quantitative composition of acids and sugars in apricot fruits may prove to be a powerful tool in evaluating fruit maturity and quality

Complexation of Alkali and Alkaline Earth Metal Cations by Fluorescent Glycoconjugated Calix[4]arene Derivative: Thermodynamic and Computational Studies

The affinity of novel, phenanthridine-based calix[4]arene glycoconjugate (L), bearing efficient cation-binding tertiary-amide functionalities in the coordination site, towards alkali and alkaline earth metal cations in methanol was investigated by means of spectrophotometry, microcalorimetry, and 1H NMR spectroscopy. Significant complexation-induced enhancement of the calixarene fluorescence was observed in all cases, allowing also the use of spectrofluorimetric titrations for quantitative monitoring of the complexation processes. The thermodynamic reaction parameters (complex stability constants, standard reaction enthalpies and entropies) were determined and discussed regarding the ligand structure and cation charge densities, as well as solvation effect on the studied equilibria. Compound L was found to be a considerably more efficient receptor for alkali relative to alkaline earth metal cations of similar sizes. This was mostly a consequence of stronger solvation of the latter compared to the former in methanol. Molecular dynamic simulations of L and its complexes were carried out as well, which provided additional information on their structural characteristics and the ligand cation-complexation properties