Finite semifields and nonsingular tensors

In this article, we give an overview of the classification results in the theory of finite semifields (note that this is not intended as a survey of finite semifields including a complete state of the art (see also Remark 1.10)) and elaborate on the approach using nonsingular tensors based on Liebler (Geom Dedicata 11(4):455-464, 1981)

Correspondences Between Cluster Structures.

This thesis introduces quasi-homomorphisms of cluster algebras, a class of maps relating cluster algebras of the same type, but with different coefficients. The definition is given in terms of seed orbits, the smallest equivalence classes of seeds on which the mutation rules for non-normalized seeds are unambiguous. After proving basic structural results, we provide examples of quasi-homomorphisms involving familiar cluster algebras. We construct a quasi-isomorphism between cluster stuctures in Grassmannians and cluster structures in Fock-Goncharov spaces of configurations of affine flags. We explore the related notion of a quasi-automorphism, and compare the resulting group with other groups of symmetries of cluster structures. For cluster algebras from surfaces, we determine the subgroup of quasi-automorphisms inside the tagged mapping class group of the surface.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133477/1/cmfra_1.pd

Cluster algebras and discrete integrable systems

This dissertation presents connections between cluster algebras and discrete integrable systems, especially T-systems and their specializations/generalizations. We give connections between the T-system or the octahedron relation, and the pentagram map and its various generalizations. A solution to the T-system with quasi-periodic boundary conditions gives rise to a solution to a higher pentagram map. In order to obtain all the solutions of higher pentagram map, we define T-systems with principal coefficients from cluster algebra aspect. Combinatorial solutions of the T-systems with principal coefficients with respect to any valid initial condition are shown to be partition functions of perfect matchings, non-intersecting paths and networks. This also provides a solution to other systems with various choices of coefficients on T-systems including Speyer's octahedron recurrence (Speyer 2007), generalized lambda-determinants (Di Francesco 2013) and (higher) pentagram maps (Schwartz 1992, Ovsienko et al. 2010, Glick 2011, Gekhtman et al. 2016). We study a discrete dynamic on weighted bipartite graphs on a torus, analogous to dimer integrable systems of Goncharov and Kenyon 2013. We show that all Hamiltonians, partition functions of all weighted perfect matchings with a common homology class, are invariant under a move on the weighted graph. This move coincides with a cluster mutation, analog to Y-seed mutation in dimer integrable systems. Q-systems are reductions of T-systems by forgetting one of the parameters. We construct graphs for Q-systems of type A and B and show that the Hamiltonians are conserved quantities of the systems. The conserved quantities can be written as partition functions of hard particles on a certain graph. For type A, they Poisson commute under a nondegenerate Poisson bracket

Preliminary design study. Shuttle modular scanning spectroradiometer

Fundamental concepts on which to base a detailed design for a Shuttle Modular Scanning Spectroradiometer were developed, and a preliminary design is presented. The recommended design features modularity and flexibility. It includes a 75-cm f/1.7-telescope assembly in an all-reflective Schmidt configuration, a solid state scan system (pushbroom) with high resolution over a 15 deg field of view, and ten detector channels covering the spectral range from 0.45 to 12.5 micrometers. It uses charge transfer device techniques to accommodate a large number of detector elements for earth observation measurements. Methods for in-flight radiometric calibration, for image motion compensation, and for data processing are described. Recommendations for ground support equipment are included, and interfaces with the shuttle orbiter vehicle are illustrated

Материалы конференции: "Алгебра и математическая логика: теория и приложения"

Сборник содержит тезисы докладов, представленных на международную конференцию "Алгебра и математическая логика: теория и приложения" ( г. Казань 2-6 июня 2014 год) и сопутствующую молодежную летнюю школу "Вычислимость и вычислимые структуры", посвященную 210-летию Казанского университета, 80-летию со дня основания кафедры алгебры (ныне кафедры алгебры и математической логики) Казанского университета Н.Г. Чеботаревым и 70-летию со дня рождения зав. кафедрой члена-корреспондента АН РТ М.М. Арсланова.17

Critical Thinking Skills Profile of High School Students In Learning Science-Physics

This study aims to describe Critical Thinking Skills high school students in the city of Makassar. To achieve this goal, the researchers conducted an analysis of student test results of 200 people scattered in six schools in the city of Makassar. The results of the quantitative descriptive analysis of the data found that the average value of students doing the interpretation, analysis, and inference in a row by 1.53, 1.15, and 1.52. This value is still very low when compared with the maximum value that may be obtained by students, that is equal to 10.00. This shows that the critical thinking skills of high school students are still very low. One fact Competency Standards science subjects-Physics is demonstrating the ability to think logically, critically, and creatively with the guidance of teachers and demonstrate the ability to solve simple problems in daily life. In fact, according to Michael Scriven stated that the main task of education is to train students and or students to think critically because of the demands of work in the global economy, the survival of a democratic and personal decisions and decisions in an increasingly complex society needs people who can think well and make judgments good. Therefore, the need for teachers in the learning device scenario such as: driving question or problem, authentic Investigation: Science Processes