Interactions Between Price Setting and Capital Investment in a Customer Market

In this essay a customer market model is constructed, where an entrepreneur-owned firm has two choice variables, namely the customer stock and the capital stock. The firm is assumed to be completely credit rationed and the investment procedure is characterised by time-to-build. The model is solved numerically to yield steady state paths for the ratio of customers to capital, investments and price. A comparative statics analysis is carried out so as to find out how price and investments respond to exogenous shocks. The model is also tested empirically with data for the Swedish manufacturing sector. The results from the theoretical model point to a close relationship between price setting and investment decisions, which is then confirmed by the empirical investigation.Price Setting; Customer Markets; Investments

Why Don't Prices Fall in a Recession? Financial Constraints, Investment, and Customer Relations

We construct a model of a financially constrained firm making pricing and investment decisions. The firm operates in a market where customers respond slowly to price changes and there are implementation lags in investment (time to build). Our model implies that the markup over marginal cost is counter-cyclical, the product price responds slowly to demand shocks, and quickly to cost shocks, and the price is strongly related to investment. Estimating the decision rules on aggregate data for Swedish industry, we find that the qualitative results are in line with our model.customer market; price rigidity; price equation; investment equation

Fouling and Cleaning During Treatment of Thermomechanical Pulp Mill Process Water

One of many possible applications for membranes in industries is to separate valuable products from wastewater. However, usage of membranes inevitably leads to fouling. Fouling means that the treated solution affects the membrane and causes a permanent decrease of the permeate flux. That means that the membrane requires cleaning so that the flux can be restored and the full potential of the membrane can be utilized. Membrane cleaning can be performed by different methods, one of them being chemical cleaning. This master thesis aims to investigate which parameters that affect how the fouling takes place, as well as which parameters that affects the chemical cleaning of the fouled membranes. The experimental work has been performed by treating an ultrafiltration membrane with process water from a thermomechanical pulp mill. The experimental work consisted of two main parts, the fouling experiments and the cleaning experiments. The fouling experiments investigated the fouling influence of temperature, duration and concentration of the treated solution. The results from the experiments showed that the fouling is influenced by the temperature and that more severe fouling is achieved at higher temperatures. The cleaning experiments showed that the efficiency of a cleaning method is dependent on both the cleaning agent concentration and the cleaning time. Two cleaning agents, Ultrasil 10 and sodium hypochlorite, were used in the cleaning experiments. A conclusion that can be drawn from this work is that it would be interesting to investigate if the fouling in membrane plants could be reduced by using lower temperatures industrially. Less fouling would lead to a reduced need for chemical cleaning, which probably would increase the membrane lifetime as chemical cleaning often is the most damaging procedure that a membrane is subjected to. A lower temperature could lead to financial savings both by an increase of the membrane lifetime, but also as the operating time between the required cleaning can increase. However, a lower filtration temperature is negative from an economical perspective as the flux is lower at lower temperatures and the production will thus be more time consuming. A way of overcoming the reduced production pace could be to increase the membrane area.Membranprocesser kan användas för att isolera värdefulla substanser i processvatten i massabruk vilket minskar brukets miljöpåverkan, och ökar dess intäkter. Men membran smutsas ned. Det är därför viktigt att effektiva rengöringsmetoder utvecklas. I examensarbetet har möjligheten att isolera värdefulla substanser i processvatten från ett termomekaniskt massabruk undersökts. Om det vore möjligt att isolera komponenter som idag tas om hand i brukets avloppsvattenreningsanläggning kan det leda till nya inkomstkällor samtidigt som förnybara råvaror skulle kunna utnyttjas. Det är sedan tidigare känt att det ultrafiltreringsmembran som använts i det experimentella arbetet kan separera de komponenter man vill skilja åt, men nedsmutsningen av membranet har identifierats som ett stort problem. I arbetet har det experimentellt undersökts vilka driftsparametrar som påverkar nedsmutsningen av membranet under filtreringen. Det visade sig att den parameter som påverkar nedsmutsningen mest var processlösningens temperatur under filtreringen. För att få riktigt smutsiga membran krävs det höga temperaturer. Utöver temperaturen undersöktes även inverkan av processlösningens koncentration och försökstiden, men de spelade inte lika stor roll för nedsmutsningen som temperaturen gjorde. Att nedsmutsningen är värre vid höga temperaturer än låga är ett intressant resultat som är värt att utreda vidare eftersom höga temperaturer normalt används i membrananläggningar. Om nedsmutsningen skulle kunna minskas genom att använda lägre temperaturer vid filtreringen skulle det vara bra eftersom nedsmutsning kräver rengöring, vilket ofta är skadligt för membranet. Tyvärr är det så att en lägre temperatur även påverkar produktionen i anläggningen, där en lägre temperatur ger minskad produktion eftersom filtreringen sker långsammare då. Nedsmutsning är inte bra eftersom det innebär att membranen inte kan användas fullt ut. Då krävs det rengöring. När membranen rengörs måste produktionen avbrytas. Därför vill man inte rengöra membranen oftare än nödvändigt. Rengöring av membran är dessutom det mest skadliga membranet utsätts för och bidrar till att membranet förstörs snabbare och behöver ersättas av ett nytt membran, vilket är kostsamt. Att undersöka hur nedsmutsningen av ett membran kan minskas och rengöringen göras mer effektiv är alltså viktigt för att spara både pengar och resurser. Det experimentella arbetet visade att både rengöringsmedlets koncentration och rengöringstiden påverkade hur effektiv rengöringen var. Högre koncentrationer och längre rengöringstider gav renare membran. Både nedsmutsning och rengöring av membran är områden där omfattande forskning är möjlig. Framförallt är det intressant att utreda nedsmutsningens temperaturberoende i förhållande till produktionen och rengöringen, för att hitta de ekonomiskt mest gynnsamma förhållandena

Формування літературно-малярського дискурсу в творчості Богдана Лепкого

Досліджено проблему взаємодії мистецтв у доробку письменника. З’ясовано, які життєві обставини зумовили зацікавлення Б. Лепкого живописом та словесністю, розглянуто чинники, що вплинули на становлення його естетичних поглядів та формування індивідуальної авторської манери

A geometric approach to approximating the limit set of eigenvalues for banded Toeplitz matrices

This article is about finding the limit set for banded Toeplitz matrices. Our main result is a new approach to approximate the limit set $\Lambda(b)$ where $b$ is the symbol of the banded Toeplitz matrix. The new approach is geometrical and based on the formula $\Lambda(b) = \cap_{\rho \in (0, \infty)} \text{sp } T(b_\rho)$. We show that the full intersection can be approximated by the intersection for a finite number of $\rho$'s, and that the intersection of polygon approximations for $\text{sp } T(b_\rho)$ yields an approximating polygon for $\Lambda(b)$ that converges to $\Lambda(b)$ in the Hausdorff metric. Further, we show that one can slightly expand the polygon approximations for $\text{sp } T(b_\rho)$ to ensure that they contain $\text{sp } T(b_\rho)$. Then, taking the intersection yields an approximating superset of $\Lambda(b)$ which converges to $\Lambda(b)$ in the Hausdorff metric, and is guaranteed to contain $\Lambda(b)$. We implement the algorithm in Python and test it. It performs on par to and better in some cases than existing algorithms. We argue, but do not prove, that the average time complexity of the algorithm is $O(n^2 + mn\log m)$, where $n$ is the number of $\rho$'s and $m$ is the number of vertices for the polygons approximating $\text{sp } T(b_\rho)$. Further, we argue that the distance from $\Lambda(b)$ to both the approximating polygon and the approximating superset decreases as $O(1/\sqrt{k})$ for most of $\Lambda(b)$, where $k$ is the number of elementary operations required by the algorithm.Comment: 20 pages, 8 figures. Submitted to SIAM Journal on Matrix Analysis and Application

Qualitative and Quantitative X-Ray Diffraction Analysis for Forensic Examination of Duct Tapes

Duct tapes are an increasingly important class of forensic evidence. This research has studied the value of using x-ray diffraction (XRD) to extend the ability of evidence examiners to gain additional information about a duct tape specimen. Duct tapes are composed of five different layers. Starting from the non-adhesive side, these layers are the release coating, backing, scrim, primer and adhesive. The release coating assists in reducing unwind tension and preventing the tape from sticking to itself when on a roll. The backing layer serves as a support for the adhesive, and is usually based on polyethylene. The scrim is a layer of fibers either embedded in the backing layer or between the backing and adhesive layers. Primers help attach the adhesive to the backing. Pressure sensitive adhesives are based on polymers such as natural or synthetic rubbers combined with tackifying resins and hydrogenated resins. Pigments and additives are added to the backing and adhesive layers in order to achieve the desired tape characteristics and appearance. A variety of instrumental methods are used to obtain information for discrimination of pressure sensitive tapes including duct tapes. Research has been reported on the evidential value of a range of physical investigations such as, physical and optical examination of thickness, weight/area, fluorescence, and birefringence, as well as instrumental chemical techniques including UV/VIS, FTIR, XRF, NAA, ICP MS, XRD, pyrolysis-GC/MS and isotope-ratio MS. XRD analyses have been used to identify minerals in duct tape but to date, only limited qualitative XRD information has been used and no systematic investigation of the further uses of XRD analysis and databases has been published. XRD analysis has the potential to offer a convenient, cost effective and non-destructive method for further characterization of the molecular or atomic make up of the tape layers. The diffractogram contains information about the qualitative and quantitative mineral composition and the crystallinity of mineral species and polymers present. This research has shown that the use of quantitative XRD analysis of duct tapes can differentiate between some duct tape samples from rolls that cannot be distinguished by current, routine analysis methods