Graphs with many strong orientations

We establish mild conditions under which a possibly irregular, sparse graph $G$ has "many" strong orientations. Given a graph $G$ on $n$ vertices, orient each edge in either direction with probability $1/2$ independently. We show that if $G$ satisfies a minimum degree condition of $(1+c_1)\log_2{n}$ and has Cheeger constant at least $c_2\frac{\log_2\log_2{n}}{\log_2{n}}$, then the resulting randomly oriented directed graph is strongly connected with high probability. This Cheeger constant bound can be replaced by an analogous spectral condition via the Cheeger inequality. Additionally, we provide an explicit construction to show our minimum degree condition is tight while the Cheeger constant bound is tight up to a $\log_2\log_2{n}$ factor.Comment: 14 pages, 4 figures; revised version includes more background and minor changes that better clarify the expositio

Coalitions and Cliques in the School Choice Problem

The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their preference profiles in order to improve the outcome for some other students. Our second approach involves trading cliques among students where those involved improve their assignments by waiving some of their priorities. The coalition method yields the EADAM outcome among other Pareto dominations of the SOSM outcome, while the clique method yields all possible Pareto optimal Pareto dominations of SOSM. The clique method furthermore incorporates a natural solution to the problem of breaking possible ties within preference and priority profiles. We discuss the practical implications and limitations of our approach in the final section of the article

Calculation of dielectric coefficient, relaxation time and activation energy of Mn compounded PIN-PMN-PT mono crystal

Relaksör-ferroelektrik malzemeler 1950 li yıllarda keşfedilmiştir, birçok uygulamada kullanılmasına rağmen hala bazı mekanik ve elektrik özellikleri tam olarak anlaşılamamıştır. Özellikle ferroelektrik faz geçişlerindeki, mekanik ve elektriksel davranımlarının sıcaklık bağımlılıklarını tam olarak modelleyebilen bir yaklaşım eksikliği vardır. Bu çalışmada, Landau fenomonolojik teori kullanılarak, Mn katkılı PIN-PMN-PT tek kristal karışım malzemenin ferroelektrik rhombohedral-monoklinik faz geçişinde (TC=112 0C) 512 ve 584 cm-1 Raman modları için; kendiliğinden polarizasyon, dielektrik duyarlık ve gevşeme zamanı sıcaklığa bağlı olarak hesaplanmıştır. Landau fenomonolojik teoriden türetilen dielektrik duyarlık bağıntısı, deneysel veriler ile uyumlu sonuçlar vermiştir. Ayrıca, ferroelektrik rhombohedral fazda farklı sıcaklık aralıkları için aktivasyon enerjileri pseuode-spin fonon ve enerji dalgalanma model yaklaşımları kullanılarak hesaplanmıştır. Her iki model kullanılarak hesaplanan sönümleme sabiti değerlerimiz, gözlemlenen verilerle uyumlu çıkmıştır.Relaxor-ferroelectric materials were discovered in the 1950s, and although they are used in many applications, some of their mechanical and electric properties have not fully understood yet. There haven't been an adequate approach that can precisely model the temperature dependencies of their mechanical and electrical behaviour, especially in ferroelectric phase transitions yet. In this study, using Landau phenomenological theory, Mn-doped PIN-PMN-PT single crystal mixture material ferroelectric rhombohedral-monoclinic phase transition (TC=112 0C) for 512 and 584 cm-1 Raman modes; spontaneous polarization, dielectric sensitivity and relaxation time were calculated based on temperature. The dielectric precision correlation derived from Landau phenomenological theory yielded results consistent with experimental data. Furthermore, activation energies for different temperature ranges in the ferroelectric rhombohedral phase were calculated using pseudospin Phonon and energy fluctuation model approaches. Our damping constant values, which were calculated using both models, were good well consistent with the observed data