Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.* This work is supported by the National Science Fund of Bulgaria under Grant No. D002-146/16.12.2008

The Effects of Encouraging Student-Faculty Interaction on Academic Success, Identity Development, and Student Retention in the First Year of College

The study presented in this dissertation was designed to investigate the effects of a brief intervention encouraging student-faculty interaction among college students on their academic achievement, college adjustment and intent to withdraw. Additionally, the effects of identity style on academic achievement, college adjustment, and student-faculty interaction were examined. Two hundred and five first year students participated in a four-part study, measuring the frequency and quality of student-faculty interaction, college adjustment, and identity development at three different time points. Students were randomly assigned to one of three experimental groups; only one group received the advice to meet with faculty outside of the classroom at the beginning of the fall semester. Intent to withdraw was measured at the end of the semester, and first-semester GPA was obtained during the spring semester. Results indicated a significant effect of the experimental treatment on one key outcome variable: level of institutional commitment. Students who received the advice to interact with faculty reported higher institutional commitment than the other groups, and in turn, institutional commitment was the only predictor of intent to withdraw. Academic achievement in the first semester was predicted by first generation status, quality and frequency of student-faculty interaction, and academic efficacy. In terms of identity development, students using the information orientation were better equipped to handle the demands of the first year in college than those using the diffuse orientation

An Algorithm for Projecting a Reference Direction onto the Nondominated Set of Given Points

In this paper, we consider the problem of searching nondominated alternatives in a discrete multiple criteria problem. The search procedure is based on the use of a reference direction. A reference direction reflects the desire of the decision maker (DM) to specify a search direction. To find a set of given alternatives related somehow to the reference direction specified by the DM, the reference direction has to be projected onto the set of nondominated alternatives. Our purpose is to develop an efficient algorithm for making this projection. The projection of each given reference direction determines a nondominated ordered subset. The set is provided to a decision maker for evaluation. The decision maker will choose the most preferred alternative from this subset and continues the search from this alternative with a new reference direction. The search will end when no direction of of improvement is found. A critical point in the procedure is the efficiency of the projection operation. This efficiency of our algorithm is considered theoretically and numerically. The projection is made by parametrizing an achievement scalarizing function originally proposed by Wierzbicki (1980) to project any single point onto the nondominated set

NEED AND EXPECTATIONS FOR LEARNING IN A STEM ENVIRONMENT

In the last decade, the need for specialists in the field of engineering and exact sciences emerged in Bulgaria and around the world. This led to the launch of a National Program for the construction of stem centers in schools. From the Veliko Tarnovo region, 16 schools joined the program at different stages, where STEM centers are being built or are already functioning in various subjects, which significantly support the preparation of quality personnel for the Bulgarian economy. A review and analysis of the expectations of teachers and students from work in centers with an engineering focus and training in natural sciences was made. At the next stage, an analysis and evaluation of the effect of the implementation of these innovative centers will be done.

Some Properties of AgI Suspensions Formed by the Dilution Method

The complex solution of Ag! in concentrated KI was added to water or to diluted KI solution to give pl = 2 in the final system. Time tyndallograms (obtained by measuring turbidity as a function of time) of the Ag! sols thus obtained were analysed. By a radiometric technique adsorption-desorption equilibria in the systems thus obtained were determined. The results show that sols with a smaller degree of dispersion than sols in statu nascendi (by mixing precipitation components) formed under the same final chemical conditions (pl = 2) were obtained. The colloid particles grow faster and the process of the particles growth is the fastest after the mixing of the precipitation components. The measurement of the adsorption capacity (meq/gram) gave an equilibrium value which is one tenth of the capacity of sols obtained in statu nascendi. The mode of mixing reaction components also markedly influences the stability and the growth of Ag! sol particles

The complementary role of the WTO in the enhancement of the base erosion and profit shifting project

The current rules on international tax do not function properly due to the gaps which allow for tax manipulation. Whereas most tax agreements largely contribute to the prevention of double taxation, they do not effectively approach double non-taxation matters arising from tax competition based on the agreements’ bilateral nature. In order to tackle this issue, the Base Erosion and Profit Shifting project was introduced. Developed under the Organization for Economic Co-Operation and Development framework, the Base Erosion and Profit Shifting project deals with tax avoidance practices that use mismatches and gaps in tax rules. Nevertheless, the success of this new soft law initiative requires a forum that can promote and enforce its recommendations. The structural nature of the Organisation for Economic Co-operation and Development has led to the consideration of the World Trade Organization to be this forum by many. However, the World Trade Organization covered agreements are drafted in a way that includes some of the tax competition matters but not others, including traditional tax havens. This paper aims to bridge the gaps in the area of the international tax regime. By examining the international trade and international tax regimes, it is shown that there is space for variations in the World Trade Organization broadly drafted agreements for such matters to find a resolution. It is argued that the World Trade Organization can play a complementary role in the enforcement of the new international tax rules

Statistical Numerical Methods for Eigenvalue Problem. Parallel Implementation

MSC subject classification: 65C05, 65U05.The problem of evaluating the smallest eigenvalue of real symmetric matrices using statistical numerical methods is considered

TRENDS, STYLE AND VISION - OWN TOPIC

Téma mé diplomové práce jsou TRENDY, STYL A VIZE - VLASTNÍ TÉMA, Autorská kolekce, ucelená kolekce oděvů. Tato témata mi umožnilo prozkoumat aktuální módní trendy a jejich pozadí. V době plné nepředvídatelných událostí ovlivněných pandemií COVID-19 jsem se zaměřila na to, jak ovlivnila naše životy. Museli jsme se uchýlit do ústraní s našimi blízkými a strávit nějaký čas jen v naší mysli, která se stala mou největší inspirace sama o sobě. Lidskou mysl jsem se snažila zobrazit návrhem vlastního dezénu a použitím objemů a řesení. Používala jsem hlavně přírodní látky jako je bavlna a hedvábí. Chtěl jsem pojmout svou kolekci způsobem, který nás přiměje opět snít a nabídne hlubší pohled do hloubi naší mysli. Forma modelů odkazuje na symetrii fyzického těla a bohatost a objem nehmotného.ObhájenoThe theme of my thesis is TRENDS, STYLE AND VISION - OWN TOPIC Author's collection. These topic allowed me to explore current fashion trends and it ´s own backround. In a time full of unpredictable events affected by pandemic COVID-19 and war in Ukraine I was focused on how it affected our lives. We had to close up at home with our loved ones and we had lot of time with just our own minds which become my biggest inspiration itself. I depicted the human mind by designing my own print and by application of voluminius form. I used mainly nature fabrics such as cotton and silk. I wanted to conceive my collection in a way that made us dream and offer a deeper look to the core of our minds. The form of models refers to the symmetry of the physical body and the richness and volume of the intangible

NATURAL IMMUNITY AND ALLERGY. A STUDY OF SERUM LYSOZYME IN ALLERGIC PATIENTS

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