On quantitative hypocoercivity estimates based on Harris-type theorems

This review concerns recent results on the quantitative study of convergence towards the stationary state for spatially inhomogeneous kinetic equations. We focus on analytical results obtained by means of certain probabilistic techniques from the ergodic theory of Markov processes. These techniques are sometimes referred to as Harris-type theorems. They provide constructive proofs for convergence results in the $L^1$ (or total variation) setting for a large class of initial data. The convergence rates can be made explicit (both for geometric and sub-geometric rates) by tracking the constants appearing in the hypotheses. Harris-type theorems are particularly well-adapted for equations exhibiting non-explicit and non-equilibrium steady states since they do not require prior information on the existence of stationary states. This allows for significant improvements of some already-existing results by relaxing assumptions and providing explicit convergence rates. We aim to present Harris-type theorems, providing a guideline on how to apply these techniques to the kinetic equations at hand. We discuss recent quantitative results obtained for kinetic equations in gas theory and mathematical biology, giving some perspectives on potential extensions to nonlinear equations.Comment: 40 pages, typos are corrected, new references are added and structure of the paper has change

Modification Of Pendant Anthracene And Azide Functionalized Polycarbonates Via Double Click Reactions

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2014Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2014Antrasen ve azid fonksiyonlu halkalı karbonat monomerleri sentezlenerek, ko-polimerizasyonu, benzil alkol başlatıcılığında, 1,8-diazabisiklo[5.4.0]undek-7-en ve 1-(3,5-bis(trifloromethil)fenil)-3-siklohekzil tiyoüre katalizörlüğündeki halka açılma polimerizasyonu ile gerçekleştirilmiştir.  Çalışmanın sonraki kısmında antrasen ve azid fonksiyonlu polikarbonat zincirine bakır katalizli azid-alkin siklokatılma (CuAAC) reaksiyonu ile Alkin-PCL ve Diels-Alder (DA) reaksiyonu ile maleimid uç fonksiyonlu PEG takılarak PC-g-PCL/PEG aşı kopolimeri elde edildi. Aşı kopolimerleri için Diels-Alder reaksiyon etkinliği UV-Vis spektroskopisi yardımıyla belirlendi. Elde edilen monomerler, öncü bileşikler, başlangıç polimerleri ve sonuç polimerler 1H NMR, UV, FT-IR ve GPC kullanılarak analiz edilmiştir.In this study, anthracene and azide functional cyclic carbonate monomers are synthesized, the co-polymerization of these was carried out successfully via ring-opening polymerization (ROP) using benzyl alcohol as initiator, 1,8-diazabicyclo[5.4.0]undec-7-ene and 1-(3,5-bis(trifluorometh1-(3,5-bis(trifluoromethyl))-3-cyclohexyl-2-thiourea, as catalyst system.  Subsequently, anthracene and azide functional polycarbonate chain, copper catalyzed azide-alkyne cycloaddition (CuAAC) by reaction of Alkyne-PCL, and Diels-Alder (DA) by reaction maleimide end-functionalized PEG attaching and  PC-g-PCL/PEG heterograft copolymer was obtained. Diels-Alder click reaction efficiency for graft copolymerization was monitored by UV-Vis spectroscopy. The structures of all monomers, initiators, polymer precursors and final polymers were confirmed exactly using GPC, 1H NMR, UV-Vis and FT-IR analyses.Yüksek LisansM.Sc

A Seventeenth Century Mevlevi Poet: Sabir Parsa (His Biography and Works)

Sâbir Pârsâ, a seventeenth century Mevlevi poet, was born in Gelibolu. He joined the way of Mevlevi by means of his uncle Ağa-zade Muhammed Efendi. After his uncle's death Sâbir became the sheykh of Gelibolu Mevlevi-hane in place of his because of the prohibition of ''sema'" he left this task and became professor and judge in different places. So me time later, he turned to form er his duty. He was successful in Persian poetry as well as in Turkish poetry. In this study Sabir Parsa's life. art and works will be described and assessed

The Relationship between Intellectual Thinking Tendencies and Creative Leadership of Primary School Administrators

This study aimed to determine the relationship between intellectual thinking tendencies and creative leadership of primary school administrators. In this context, it was tried to investigate how intellectual thinking tendencies influence creative leadership. The study was conducted in the general survey model, which is widely used in quantitative research methods. The participants of study consist of school administrators working in primary schools affiliated to Manisa, Yunusemre District Directorate of National Education. The study was conducted in the fall term of 2022-2023 academic year. The data was collected by “Intellectual Thinking Tendency Scale” and “Creative Leadership Scale” and was analyzed with SPSS 25 package program by taking the significance level as.05. Parametric analysis techniques were used in the analysis of the data. In this meaning: by minimum, maximum, arithmetic mean, and standard deviation values for descriptive statistics; by independent sample t-test for the differences in genders, administrative duties, and administrative seniorities; by One-way ANOVA Analysis for the differences of professional seniorities and professional fields were analyzed. The relation between intellectual thinking tendencies and creative leadership was analyzed with Pearson Correlation Coefficient. According to the results, primary school administrators’ intellectual thinking tendencies and creative leadership levels were found as high; according to their genders, administrative duties, administrative seniorities, professional seniorities, and professional fields, no meaningful differences were found. As the last result, the relationship between intellectual thinking tendencies and creative leadership of primary school administrators was observed in high scores

SOME NOTES ON KENMOTSU MANIFOLD

In the present paper, we deal with a Kenmotsu manifold $M$. Firstly, we study the notion of torse-forming vector field on such a manifold. Then, we investigate some curvature conditions such as $Q.\mathcal{M}=0$ and $C.Q=0$ on such a manifold and obtain some necessary conditions for such a manifold given as to be Einstein and $\eta-$Einstein. Also, we study a Kenmotsu manifold $M$ admitting a Ricci soliton and give an example for this manifold

A cross-diffusion system obtained via (convex) relaxation in the JKO scheme

In this paper, we start from a very natural system of cross-diffusion equations which, unfortunately, is not well-posed as it is the gradient flow for the Wasserstein distance of a functional which is not lower semi-continuous due to lack of convexity of the integral. We then compute the convexification of the integral and prove existence of a solution in a suitable sense for the gradient flow of the corresponding relaxed functional. This gradient flow has also a cross-diffusion structure but the mixture between two different regimes which are determined by the convexification makes this study non-trivial.Comment: 38 pages, 2 figure