We analyze the geometry and regularity of the largest subsolution of a Free Boundary Problem. We showed that the largest subsolution is a viscosity solution of (1) with Lipschitz and Non-Degenerate properties under a very general free boundary condition. In addition to this, we provide density bounds for the positivity set and its complement near the free boundary. / text

The steel industry is the foundation that country marches toward modern of development of civilization. According to the International Iron and Steel Institute (IISI) has announced that world crude steel output reached 1,239.5 million metric tons for the year 2006. In 1996, Mainland China produced 101.2 million metric ton of crude steel. By 2001 this had risen to 150.9 million metric ton, an increase of 49.1%. In 2006, China produced 418.8 million metric ton of crude steel, an increase of 313.8% in just ten years. China¡¦s share of world crude steel production has also increased exponentially. In 1996, China became the largest steel producing country in the world. China remains the largest single market and the strongest growth area. Steel use will increase by 13% in 2007 followed by another 10% in 2008 taking the total to 443 million ton by 35% of the world total. Subject that several important environments of steel marketing change, While China poses a severe threat to Taiwan in the Steel market, Taiwanese Steel manufacturers have to move to higher ground ahead of the rising tide of mainland competition. Grounded Theory (GT) is a research method most often associated with the social sciences, (Glaser & Strauss, 1967). Thereafter Strauss in 1990 published Basics of Qualitative Research: Grounded Theory Procedures and Techniques together with Juliet Corbin. Grounded theory was developed as a systematic methodology, and its name underscores the generation of theory from data. When the principles of grounded theory are followed, a researcher using this approach will formulate a theory, either substantive (setting specific) or formal, about the phenomena they are studying that can be evaluated. To research and investigate the changing of supply-chain by interviewing decisive persons in the business, its purpose is to make this thesis more deliberate in study structure and procedures and operational logic. This research can be classified into four main groups, such as raw material suppliers,horizontal competitor,down-stream user and co-opetition(co-operation and competition). The iron and steel industry is combined with four groups, this thesis focus on iron and steel producers. Taiwanese steel industry was forced to face several critical issues from market changing in Mainland China. 1. The industrial down-streamers in Taiwan move to Mainland China. 2.The developments of upper-streamers in China that brings an extra option for purchasing raw material. 3.An increasing stress comes from excess of new established steel companies in Mainland China. 4.The lower- cost substitutes in China invade worldwide steel market. But under the special political situation and common in language and culture, both Taiwan and China industries could have more strategically options in cooperation or competition. It is influencing the key element that this research is probing into China's Mainland and interacting with steel industry of Taiwan, utilize and take Grounded Theoretical research, sum up 129 open coding altogether , sum up 14 axial coding and five selective coding progressively . In order to understand the key elements of the steel industries of both sides of Taiwan Strait.

We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the vertices that is obtained by breadth-first search. This structure is uniquely determined up to isomorphism. We also show that the maximum eigenvalue in such classes of trees is strictly monotone with respect to majorization. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

We characterize trees that have greatest maximum p-Laplacian eigenvalue among all trees with a given degree sequence. We show that such extremal trees can be obtained by breadth-first search where the vertex degrees are non-increasing. These trees are uniquely determined up to isomorphism. Moreover, their structure does not depend on p. / Series: Research Report Series / Department of Statistics and Mathematics

Those who practice poor meal timing habits such as irregular day-to-day eating, eating late at night, and have a short overnight fast are more at risk for weight gain, reduced weight loss with weight loss attempts, and increased risk for developing and/or worsening health conditions such as type 2 diabetes mellitus and cardiovascular disease and/or risk factors for said conditions. Recent studies have identified possible factors that influence meal timing, one of which is hunger. Hunger is defined as a physiologic need to eat, and can be triggered by a rise in the hormone ghrelin. Hunger in general, or greater hunger at certain times of day, may lead to poor meal timing and/or difficulty adhering to meal timing recommendations made in behavioral interventions. The goal of our study was to determine if the overall hunger level and time of onset of greatest hunger were associated with poor meal timing cross-sectionally and lower adherence to meal timing recommendations. The meal timing behaviors we examined were eating late at night, having a longer overnight fast, and an earlier ingestive period midpoint based on published evidence suggesting these are important for weight control. We hypothesized that a greater overall hunger level and later onset of greatest hunger would be inversely associated with poor meal timing cross-sectionally and a lower adherence to potential meal timing recommendations to be applied to future interventions. Our cross-sectional study was a secondary analysis of data from a previous study on diet and energy regulation in 116 healthy adults (mean BMI 24.3 kg/m2; SD 3.8, mean age 29.4 years; SD 11.9). Both continuous and categorical meal timing outcomes were examined. The continuous outcomes were eating late at night (defined as eating past 20:00 h), length of overnight fast (defined as the length of time between the last meal consumed before bedtime and first eating occasion after waking), and timing of the largest meal, which we measured using the midpoint of the ingestive period. Categorical outcomes, which had cutoff values determined based on evidence from published research, were: not eating after 20:00, achieving an overnight fast of ≥13 hours, and having the midpoint of the ingestive period before 15:00. Associations of hunger variables with continuous meal timing outcomes were examined in three separate models using analysis of covariance, with hunger variables as the independent variables and the meal timing patterns as the dependent variables. Associations of hunger variables with categorical (bivariate) outcomes had the same independent variables but were examined with logistic regression analysis. Covariates included in both continuous and categorical models were age, sex, race, physical activity level, weighted average bedtime on weekdays and weekends, dietary restraint score, dietary disinhibition score, sleep duration, and sleep quality. After inclusion of all covariates, a higher hunger score was associated with having an overnight fast lasting ≥13 hours (p=0.026), suggesting that participants were able to achieve a longer overnight fast despite being hungrier. There was no significant association between hunger variables and eating late at night or midpoint of ingestive period (p>0.05), although the p-value was marginally non-significant with eating late at night (p=0.080). Time of greatest hunger was not associated with any of the meal timing variables (p>0.05). As previous studies have shown that a longer overnight fast improves weight loss, a possible application of our findings, namely the length of overnight fast, is for individuals who aim to achieve an overnight fast of ≥13 hours to lose weight by consuming a greater proportion energy in the morning/afternoon as opposed to dinner/later at night.. This suggestion is based on previous studies showing eating a larger breakfast decreases feelings of hunger at night. Additionally, including more protein and fiber in the diet can increase satiety at any time of day. Future studies are needed to examine relationships between hunger score and a longer overnight fast, in larger, more diverse populations and with randomized controlled designs, as our study was cross-sectional and was unable to determine causality.

We consider random symmetric Toeplitz matrices of size n. Assuming that the entries on the diagonals are independent centered random variables with finite γ-th moment (γ>2), a law of large numbers is established for the largest eigenvalue. Following the approach of Sen and Virág (2013), in the limit of large n, the largest rescaled eigenvalue is shown to converge to the limit 0.8288... . The background theory is explained and some symmetry results on the eigenvectors of the Toeplitz matrix and an auxiliary matrix are presented. A numerical investigation illustrates the rate of convergence and the oscillatory nature of the eigenvectors of the Toeplitz matrix. Finally, the possibility of proving a limiting distribution for the largest eigenvalue is discussed, and suggestions for future research are made. / Vi betraktar stokastiska Toeplitz-matriser av storlek n. Givet att elementen på diagonalerna är oberoende, centrerade stokastiska variabler med ändligt γ-moment (γ>2), fastställer vi ett stora talens lag för det största egenvärdet. Med metoden från Sen och Virág (2013) visar vi att det största omskalade egenvärdet konvergera mot gränsen 0.8288... . Bakgrundsteorin förklaras och några symmetriresultat för Toeplitz-matrisens egenvektorer presenteras. En numerisk undersökning illustrerar konvergenshastigheten och Toeplitz-matrisens egenvektorers periodiska natur. Slutligen diskuteras möjligheten att bevisa en asymptotisk fördelning för de största egenvärderna och förslag för fortsatt forskning läggs fram.

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The spatiality of a viewer. A comparative exhibition analysis of Hilma af Klint's work The ten largestthrough two different spatialities.I have studied a viewer’s encounter with Hilma af Klint’s work The ten largest through two differentspatialities, the exhibition room at Moderna Museet Malmö and Moderna Museet Malmös Instagramaccount. With my research, I have wanted to get an insight into how a digital room such as an Instagramaccount can function as an exhibition room for art in a time when more and more is digitalized, whichescalated during the year when physical experiences were limited due to a global pandemic. Through acomparative exhibition analysis of the two different spaces and with the help of phenomenological theoryprimarily based on Maurice Merleau-Ponty further developed by Bia Mankell and phenomenologicaltheory in the digital based on Emmanuel Alloa, the Instagram account has been set in relation to theexhibition room at the museum. This comparative analysis showed that the two spatialities as exhibitionroom for the same work is both two separated exhibitions with characteristics influenced by space theyare shown through but also as two inevitably intertwined exhibitions and spaces influenced by each otherand each other's characteristics. / Populärvetenskaplig sammanfattningI den här uppsatsen har jag undersökt en betraktares möte med Hilma af Klints verk De tio största genomtvå olika rumsligheter, visningsrummet på Moderna Museet Malmö samt Moderna Museet Malmösinstagramkonto. Jag har med min undersökning velat få en inblick i hur ett digitalt rum så som ettinstagramkonto kan fungera så ett visningsrum för konst i en tid då mer och mer digitaliseras, vilket underåret eskalerat då fysiska upplevelser begränsats på grund av en global pandemi. Genom en komparativutställningsanalys av de två olika rumsligheterna och med hjälp av fenomenologisk teori framföralltutifrån Maurice Merleau-Ponty vidareutvecklad av Bia Mankell och fenomenologisk teori i det digitalautifrån Emmanuel Alloa har instagramkontot satts i relation till visningsrummet på museet. Dennakomparativa analys ledde fram till en syn på de två rumsligheterna för samma verk både som två separatautställningar med egenskaper påverkade av det rum de visas genom men även som två oundvikligensammanflätade utställningar och rum påverkade av varandra och varandras egenskaper.

Trees that have greatest maximum p-Laplacian eigenvalue among all trees with a given degree sequence are characterized. It is shown that such extremal trees can be obtained by breadth-first search where the vertex degrees are non-increasing. These trees are uniquely determined up to isomorphism. Moreover, their structure does not depend on p.

This study investigates whether family ownership impacts firms’ dividend payout policies by examining firms publicly listed on the Stockholm Stock Exchange (OMX Stockholm) during the years 2013–2018 (1,363 firm-year observations). The investigation is made by performing multiple regression analyses including the dependent variable DIVIDEND PAYOUT. The findings reveal that family firms distribute higher dividend payouts than non-family firms, suggesting that dividends are used as a corporate governance mechanism to mitigate agency problems. Family firms without a second blockholder present have the highest dividends. A family second blockholder appears to collude with the controlling family resulting in lower dividends. A separation between ownership and control results in higher dividends as it implies a worse corporate governance structure. In sum, the results imply that family ownership positively impacts firms’ dividend payout policies in Sweden.