Introductions

An introduction to the Symposium and an introduction to Blockchain technology in preparation for the topics of the rest of the symposium

Periodic Ising Correlations

In this paper, we first rework B. Kaufman's 1949 paper, "Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis", by using representation theory. Our approach leads to a simpler and more direct way of deriving the spectrum of the transfer matrix for the finite periodic Ising model. We then determine formulas for the spin correlation functions that depend on the matrix elements of the induced rotation associated with the spin operator in a basis of eigenvectors for the transfer matrix. The representation of the spin matrix elements is obtained by considering the spin operator as an intertwining map. We exhibit the "new" elements V+ and V- in the Bugrij-Lisovyy formula as part of a holomorphic factorization of the periodic and anti-periodic summability kernels on the spectral curve associated with the induced rotation for the transfer matrix.Comment: 36 page

Mesoscopic effects in superconductor-ferromagnet-superconductor junctions

We show that at zero temperature the supercurrent through the superconductor - ferromagnetic metal - superconductor junctions does not decay exponentially with the thickness $L$ of the junction. At large $L$ it has a random sample-specific sign which can change with a change in temperature. In the case of mesoscopic junctions the phase of the order parameter in the ground state is a random sample-specific quantity. In the case of junctions of large area the ground state phase difference is $\pm \pi/2$.Comment: 4 pages, 1 figur

Origin of matter out of pure curvature

We propose a mechanism for origin of matter in the universe in the framework of Einstein-Gauss-Bonnet gravity in higher dimensions. The recently discovered new static black hole solution by the authors \cite{md2006} with the Kaluza-Klein split up of spacetime as a product of the usual {\ma M}^4 with a space of negative constant curvature is indeed a pure gravitational creation of a black hole which is also endowed with a Maxwell-like {\it gravitational charge} in four-dimensional vacuum spacetime. Further it could be envisioned as being formed from anti-de Sitter spacetime by collapse of radially inflowing charged null dust. It thus establishes the remarkable reciprocity between matter and gravity - as matter produces gravity (curvature), gravity too produces matter.Comment: 8 pages, 1 Fig, Received Honorable Mention in 2007 GRF Essay Competition, Summary of the talk given at Himalayan Relativity Dialogue at Mirik, April 18-20, 200

The experience of Southern European countries in the implementation of the policy of preservation of health

Analyzes the group of Southern European countries concerning the introduction of policies for the preservation of health. It is noted that health systems are reformed and developed in accordance with social changes and processes that occur in the health care system in the world is very dynamic and versatile.It refers to the importance of political decisions in the implementation of measures for the preservation of health. The main program of each country, their directions and features. Defined groups of countries with high and low levels of political consciousness in maintaining health. The conclusion is drawn on expediency of introduction of positive experience in politics for the preservation of health in Ukraine. Key words: politics, preservation of health, system health, a healthy lifestyle, preventive activities, the national program, the Beveridge modelАналізується група країн Південної Європи на предмет запровадження політики збереження здоров’я. Наголошується на тому, що системи охорони здоров’я реформуються та розвиваються відповідно до суспільних змін а процеси, які відбуваються у системі охорони здоров’я світу вельми динамічні та різнобічні. Вказується на важливості політичних рішень у реалізації заходів по збереженню здоров’я. Наведені  основні прграми кожної країни, їх напрямки та особливості. Визначено групи країн з високим та низьким рівнем політичної свідомості у питаннях збереження здоров’я. Зроблено висновок про доцільність запровадження позитивного досвіду у політиці збереження здоров’я в Україні.Ключові слова: політика, збереження здоров’я, ситема охорони здоров’я, здоровий спосіб життя, профілактичні заходи, національна програма, модель БеверіджаАнализируется группа стран Южной Европы на предмет введения политики сохранения здоровья. Отмечается, что системы здравоохранения реформируются и развиваются в соответствии с общественными изменениями а процессы, которые происходят в системе здравоохранения мира весьма динамичны и разносторонние. Указывается на важность политических решений в реализации мероприятий по сохранению здоровья. Приведены основные программы каждой страны, их направления и особенности. Определены группы стран с высоким и низким уровнем политической сознательности в вопросах сохранения здоровья. Сделан вывод о целесообразности внедрения положительного опыта в политике сохранения здоровья в Украине. Ключевые слова: политика, сохранение здоровья, ситема здравоохранения, здоровый образ жизни, профилактические мероприятия, национальная программа, модель Бевериджаservation of health, system health, a healthy lifestyle, preventive activities, the national program, the Beveridge model

Characterisation and representation of non-dissipative electromagnetic medium with a double light cone

We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each cotangent space on N, the medium defines a Fresnel surface. Essentially, the Fresnel surface is a tensorial analogue of the dispersion equation that describes the response of the medium for signals in the geometric optics limit. For example, in isotropic medium the Fresnel surface is at each point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L. Bergamin introduced a condition that constrains the polarisation for plane waves. In this paper we show (under suitable assumptions) that a slight strengthening of this condition gives a pointwise characterisation of all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. This is for example the behaviour of uniaxial medium like calcite. Moreover, using the representation formulas from Lindell et al. we obtain a closed form representation formula that pointwise parameterises all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. Both the characterisation and the representation formula are tensorial and do not depend on local coordinates

Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the "almost-isolated" trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons.Comment: 39 pages, 6 figures, version to appear in PRD : a few minor changes and many typos corrected in equation

Phase coherent transport in SrTiO3/LaAlO3 interfaces

The two dimensional electron gas formed between the two band insulators SrTiO3 and LaAlO3 exhibits a variety of interesting physical properties which make it an appealing material for use in future spintronics and/or quantum computing devices. For this kind of applications electrons have to retain their phase memory for sufficiently long times or length. Using a mesoscopic size device we were able to extract the phase coherence length, and its temperature variation. We find the dephasing rate to have a power law dependence on temperature. The power depends on the temperature range studied and sheet resistance as expected from dephasing due to strong electron-electron interactions.Comment: Submitted to Phys. Rev

Scratching the Bose surface

This is a `News and Views' article discussing recent proposals for ground states of many boson systems which are neither superfluids nor Mott insulators.Comment: 4 pages, 1 figur

Ostrogradski approach for the Regge-Teitelboim type cosmology

We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of {\it geodetic gravity}. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt Wheeler equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.Comment: 11 pages, 2 figures, accepted for publication in Phys. Rev.