Existence of solutions of some quadratic integral equations

In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values

Kubelka-Munk theory in describing optical properties of paper (II)

Kubelka i Munk dali su sažeti oblik i pristup s jasnim ciljem ka praktičnim metodama mjerenja. Njihova metoda je bila brzo prihvaćena u papirnoj industriji i danas ima široku primjenu u mjerenju i procjeni obojenja, svjetline i opaciteta pri proizvodnji papira. Unatoč tome navedena metoda posjeduje neke nedostatke i drugi dio članka će pokriti sustave na koje se ne može tako kvalitetno primijeniti (otisnuti i reciklirani papir). Također će biti riječi i o numeričkim modelima (simulacije putanja pojedinačnih fotona) koji se koriste kao nadopuna rezultatima dobivenima K-M metodom. Najčešće korišteni su Monte Carlo simulacijski modeli, GRACE i DORT. Većina informacija u ovom članku preuzeta je iz referenca čiji se popis nalazi na kraju članka i koje je potrebno konzultirati za detaljniju analizu.Kubelka-Munk theory was quickly adapted for use by the papermaking industry and has now been in widespread use for decades in the measurement and prediction of colour, brightness and opacity of paper sheets. Though it remains the most used in practice, it has some disadvantages and the second part of the article will cover a system that is less applicable to the theory itself (an ink-dyed sheet of paper or strongly absorbing media) as well as numerical methods (simulations of individual photon paths) which are used to improve the results obtained by the K-M theory. The most commonly used are Monte Carlo simulation model, GRACE and DORT. Most of the information reported here is taken from the references cited at the end of the article which should be consulted for a more in-depth study

Numerical performance of stability enhancing and speed increasing steps in radiative transfer solution methods

AbstractMethods for solving the radiative transfer problem, which is crucial for a number of sectors of industry, involve several numerical challenges. This paper gives a systematic presentation of the effect of the steps that are needed or possible to make any discrete ordinate radiative transfer solution method numerically efficient. This is done through studies of the numerical performance of the stability enhancing and speed increasing steps used in modern tools like Disort or Dort2002.Performance tests illustrate the effect of steps that are taken to improve the stability and speed. It is shown how the steps together give a stable solution procedure to a problem previously considered numerically intractable, and how they together decrease the computation time compared to a naive implementation with a factor 1000 in typical cases and far beyond in extreme cases. It is also shown that the speed increasing steps are not introduced at the cost of reduced accuracy. Further studies and developments, which can have a positive impact on computation time, are suggested

N-colour separation methods for accurate reproduction of spot colours

In packaging, spot colours are used to print key information like brand logos and elements for which the colour accuracy is critical. The present study investigates methods to aid the accurate reproduction of these spot colours with the n-colour printing process. Typical n-colour printing systems consist of supplementary inks in addition to the usual CMYK inks. Adding these inks to the traditional CMYK set increases the attainable colour gamut, but the added complexity creates several challenges in generating suitable colour separations for rendering colour images. In this project, the n-colour separation is achieved by the use of additional sectors for intermediate inks. Each sector contains four inks with the achromatic ink (black) common to all sectors. This allows the extension of the principles of the CMYK printing process to these additional sectors. The methods developed in this study can be generalised to any number of inks. The project explores various aspects of the n-colour printing process including the forward characterisation methods, gamut prediction of the n-colour process and the inverse characterisation to calculate the n-colour separation for target spot colours. The scope of the study covers different printing technologies including lithographic offset, flexographic, thermal sublimation and inkjet printing. A new method is proposed to characterise the printing devices. This method, the spot colour overprint (SCOP) model, was evaluated for the n-colour printing process with different printing technologies. In addition, a set of real-world spot colours were converted to n-colour separations and printed with the 7-colour printing process to evaluate against the original spot colours. The results show that the proposed methods can be effectively used to replace the spot coloured inks with the n-colour printing process. This can save significant material, time and costs in the packaging industry