How Can Mathematics Students Learn to Play?

When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. We believe that if our students get used to routinely seeking out counterexamples, as they play with various mathematical ideas, they may also end up enjoying their mathematical experiences more

Civil Society, Stabilization, and Democratization: A Study of the Role of Civil Society Organizations in the Middle East

This thesis aims to explore the role of civil society in conflict and post-conflict areas of the Middle East, and the question as to whether the relationship between the political structure and political culture of a country is the primary determinant in the strength of civil society organizations. This study will examine the factors that have been known to influence the strength of civil society organizations and analyze the theory regarding the conditional relationship between political structure and political culture and its corresponding impact on the role of civil society organizations. In the following sections, I first provide an overview of the previous literature regarding the dynamic role of civil society and the factors that affect its relative strength and success. I then present a theoretical perspective positing the relationship between the political structure and political structure to be the primary determinant of the strength of civil society organizations. I explore this theory through the case studies of three Middle Eastern countries, namely Syria, Libya, and Tunisia. Lastly, I conclude with remarks from these case studies and explore prospects for future research regarding the role of civil society organizations.Bachelor of Art

Backlund transformations and Hamiltonian flows

In this work we show that, under certain conditions, parametric Backlund transformations (BTs) for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation lead to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, that indeed will be a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An application to the Toda periodic lattice is given.Comment: 19 pages, 2 figures. to appear in J. Phys.

Backlund transformations for the elliptic Gaudin model and a Clebsch system

A two-parameters family of Backlund transformations for the classical elliptic Gaudin model is constructed. The maps are explicit, symplectic, preserve the same integrals as for the continuous flows and are a time discretization of each of these flows. The transformations can map real variables into real variables, sending physical solutions of the equations of motion into physical solutions. The starting point of the analysis is the integrability structure of the model. It is shown how the analogue transformations for the rational and trigonometric Gaudin model are a limiting case of this one. An application to a particular case of the Clebsch system is given.Comment: 18 pages; the following article has been submitted to J. Math. Phys. After it is published, it will be found at http://jmp.aip.org

Discovery and Physical Characterization of a Large Scattered Disk Object at 92 au

We report the observation and physical characterization of the possible dwarf planet 2014. UZ224 ("DeeDee"), a dynamically detached trans-Neptunian object discovered at 92 au. This object is currently the second-most distant known trans-Neptunian object with reported orbital elements, surpassed in distance only by the dwarf planet Eris. The object was discovered with an r-band magnitude of 23.0 in data collected by the Dark Energy Survey between 2014 and 2016. Its 1140 year orbit has (a, e, i)=(109 au, 0.65, 26 degrees.8). It will reach its perihelion distance of 38 au in the year 2142. Integrations of its orbit show it to be dynamically stable on Gyr timescales, with only weak interactions with Neptune. We have performed follow-up observations with ALMA, using 3 hr of on-source integration time to measure the object's thermal emission in the Rayleigh-Jeans tail. The signal is detected at 7 sigma significance, from which we determine a V-band albedo of 13.1(-2.4)(+3.3)(stat)sys percent and a diameter of 635(-61)(+57)(stat)(-39)(+32)(sys) km assuming a spherical body with uniform surface properties

Ruptured appendiceal cystadenoma presenting as right inguinal hernia in a patient with left colon cancer: A case report and review of literature

BACKGROUND: Mucoceles resulting from cystadenomas of the appendix are uncommon. Although rare, rupture of the mucoceles can occur with or without causing any abdominal complaint. There are several reports associating colonic malignancy with cystadenomas of the appendix. Herein, we report an unusual and interesting case of right inguinal hernia associated with left colon cancer. CASE PRESENTATION: A case of ruptured mucocele resulting from cystadenoma of the appendix was presented as right inguinal hernia in a 70-year-old male. The patient underwent colonoscopy, x-ray, ultrasound and computed tomography. Localized pseudomyxoma peritonei associated with adenocarcinoma of the descending colon was diagnosed. The patient underwent segmental resection of the colon, appendectomy, debridement of pseudomyxoma and closure of the internal ring of right inguinal canal. He is free of symptoms in one year follow-up. CONCLUSION: Synchronous colon cancer may occur in patients with appendiceal mucoceles. In such patients, the colon should be investigated and colonoscopy can be performed meticulously in cases of ruptured mucoceles and localized pseudomyxoma peritonei. Surgical intervention is the current choice of management

In silico Identification and Expression of Protocadherin Gene Family in Octopus vulgaris

Connecting millions of neurons to create a functional neural circuit is a daunting challenge. Vertebrates developed a molecular system at the cell membrane to allow neurons to recognize each other by distinguishing self from non-self through homophilic protocadherin interactions. In mammals, the protocadherin gene family counts about 50 different genes. By hetero-multimerization, protocadherins are capable of generating an impressive number of molecular interfaces. Surprisingly, in the California two-spot octopus, Octopus bimaculoides, an invertebrate belonging to the Phylum Mollusca, over 160 protocadherins (PCDHs) have been identified. Here we briefly discuss the role of PCDHs in neural wiring and conduct a comparative study of the protocadherin gene family in two closely related octopus species, Octopus vulgaris and O. bimaculoides. A first glance at the expression patterns of protocadherins in O. vulgaris is also provided. Finally, we comment on PCDH evolution in the light of invertebrate nervous system plasticity