The strength of Ramsey Theorem for coloring relatively large sets

We characterize the computational content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called {\em exactly large} sets. An {\it exactly large} set is a set X\subset\Nat such that \card(X)=\min(X)+1. The theorem we analyze is as follows. For every infinite subset $M$ of \Nat, for every coloring $C$ of the exactly large subsets of $M$ in two colors, there exists and infinite subset $L$ of $M$ such that $C$ is constant on all exactly large subsets of $L$. This theorem is essentially due to Pudl\`ak and R\"odl and independently to Farmaki. We prove that --- over Computable Mathematics --- this theorem is equivalent to closure under the $\omega$ Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. Our results give a complete characterization of the theorem from the point of view of Computable Mathematics and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey Theorem. We also show that analogous results hold for a related principle based on the Regressive Ramsey Theorem. In addition we give a further characterization in terms of truth predicates over Peano Arithmetic. We conjecture that analogous results hold for larger ordinals

Eta Epsilon Chapter Spring Initiation, 2016

Report on the spring 2016, initiation for the Eta Epsilon chapter of Sigma Gamma Epsilon at Southern Utah University

Vision of international relations in islamist ideology

Islamism is one of the currents in the political thought of the Islamic world. It considers religion an ideology and uses it in political struggle. Its goal is to develop a model of socio-political development based on Islamic norms. Islamism is a socio-political thought deeply engraved in the minds of the inhabitants of the Near and Middle East and a very popular ideology due to the social order it envisages. For decades, in the Arab Middle East, Islamism as a political movement was pushed down into the political underground, but the events of 2011, referred to as the Arab Spring, have given to Islamist groups, new opportunities to take political action. Islamism presents its own vision of international relations

Slavery in the Gulf in the First of the 20th Century: a study based on records from the British Archives

This book is on slavery in the Persian Gulf in the early 20th century, as documented in the official reports of British officials as well as the slaves' statements made at the British Agencies. Giving a statement was a prerequisite of manumission the slaves were applying for in front of the British officials. In the course of the research 949 statements made between 1907 and 1949 were found and their analysis sheds a light on various aspects of the social, economic and political life in the Gulf in this period. Slavery was an important part of the socio-economic system of the region, which was based on pearl diving and the cultivation of palm trees. The system had existed for ages but it was threatened by a deep crisis in the 1920s and 1930s. This fact had significant implications for slavery.Grant 1 H016 048 30 of the Polish Ministry of Science and Higher Educatio

Simulation of an offset wall turbulent jet flow

Jet flows are commonly observed in many real-world situations, such as in the exhaust plume from a rocket, the airflow from a jet engine or combustion equipment. The jet flow is a high-speed stream of fluid expelled from a relatively narrow orifice into a surrounding fluid with a lower velocity. Factors such as the jet velocity and pressure, size and shape of the orifice, and the properties of the surrounding fluid influence the behavior and characteristics of jet flows. The turbulent offset jet is a fundamental problem due to the development of an adverse pressure gradient that causes the jet stream to deviate from the jet centerline (recirculation zone) and get in direct contact with the wall (impingement zone), both leading to increased turbulence, mixing and potentially reduced efficiency, and source of significant heat transfer or fluid-wall interactions, respectively. This study aims to model the fluid flow phenomena of a jet flow offset from a wall using Computational Fluid Dynamics (CFD) and to validate the model with experimental data published in the literature. The jet model is a 2D, incompressible and turbulent flow in which the jet is discharged into still air. Due to the presence of a lateral wall, it deflects and impinges onto a flat surface. Several RANS (Reynolds-averaged Navier–Stokes equations) turbulence and wall treatment models are tested and compared with the experimental data. The validation process was verified, and the turbulence models agreed with the experimental data. The k-ε model shows a better agreement with the experimental model to the detriment of the k-ω model. Using the k-ε model to describe 2D turbulent incompressible jet flows has shown to be a good choice according to the experimental data

Junior Recital: Katie Zdanowski, Tuba; Patricia Foltz, Piano; March 18, 2010

Kemp Recital HallMarch 18, 2010Thursday Evening8:30 p.m

Islam - Zachód: jaka przyszłość?

Praca recenzowana / Peer-reviewed pape

Państwo na muzułmańskim Bliskim Wschodzie: procesy genezy i czynniki trwania

Bliski Wschód jest regionem o jednych z najstarszych tradycji państwowości. Sięgają one czwartego i trzeciego tysiąclecia przed naszą erą, kiedy to neolityczne wspólnoty osiadłe dały początek miastom-państwom związanym z ośrodkami kultu oraz imperialnym społecznościom rolniczo-miejskim. Procesy genezy państw na Bliskim Wschodzie należy wiązać z kilkoma czynnikami: segmentacją i integracją organizmów plemiennych, wzrostem produktywności we wspólnotach osiadłych, ruchami podboju połączonymi najczęściej z krzewieniem islamu, kolonializmem oraz narodzinami idei świeckiego narodu. Można mówić o kilku typach państwa: plemiennych szejkanatach, państwach-osadach, państwach imperialnych, państwach kolonialnych i państwach narodowych.Projekt badawczy NCN nr N N108 09414

Tragedia bliskowschodnich Chrześcijan – Mroczne oblicze Arabskiej Wiosny

The article refers to the problem of the extinction of Christianity and other religious minorities in the Middle East. This process began in the 19th century in the Balkans and continued with Jews in the Arab countries, Jews and Bahais in Iran, and the Chaldo-Assyrian Christians in Iraq and Syria. The events of 2011 provoked a new wave of anti-Christian feelings in the Arab world with the worst anti-Christian violence against Copts in Egypt. The other question discussed in the article is why the Western press and political elites have ignored or under-reported this persecution

Szyici w Al-Ahsie. Stosunki religijno-polityczne w Arabii Saudyjskiej

"Arabia Saudyjska jako państwo wyrosła z emiratu Nadżdu - struktury protopaństwowej utworzonej w centralnej części Półwyspu Arabskiego w XVIII w. przez ród Su’udów. Spoiwem ideologicznym tej struktury był wahhabizm, a właściwie tauhidyzm (dosł. jedynobóstwo), będący specyficzną interpretacją islamu dokonaną przez teologa Muhammada ibn Abd al-Wahhaba. Wahhabizm głosił konieczność powrotu do „pierwotnej postaci” islamu i wzywał do prostoty oraz ascetycznego trybu życia. Wahhabici występowali przeciwko mistycyzmowi muzułmańskiemu, zwalczali lokalne kulty świętych i opowiadali się za restrykcyjnym przestrzeganiem najbardziej surowej - hanbalickiej szkoły prawa muzułmańskiego. Cechowała ich też wrogość do niemuzułmanów oraz muzułmanów wszystkich innych - poza hanbalicką - szkół prawa muzułmańskiego. Szczególnie wrogo wahhabizm odnosił się do szyizmu."(...