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Differential equation

In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions represent physical quantities, the derivatives represent their rates of change, the differential equation defines a relationship between the two; because such relations are common, differential equations play a prominent role in many disciplines including engineering, physics and biology. The study of differential equations consists of the study of their solutions, of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas. If a closed-form expression for the solutions is not available, the solutions may be numerically approximated using computers; the theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy. Differential equations first came into existence with the invention of calculus by Newton and Leibniz.

In Chapter 2 of his 1671 work Methodus fluxionum et Serierum Infinitarum, Isaac Newton listed three kinds of differential equations: d y d x = f d y d x = f x 1 ∂ y ∂ x 1 + x 2 ∂ y ∂ x 2 = y In all these cases, y is an unknown function of x, f is a given function. He solves these examples and others using infinite series and discusses the non-uniqueness of solutions. Jacob Bernoulli proposed the Bernoulli differential equation in 1695; this is an ordinary differential equation of the form y ′ + P y = Q y n for which the following year Leibniz obtained solutions by simplifying it. The problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, Joseph-Louis Lagrange. In 1746, d’Alembert discovered the one-dimensional wave equation, within ten years Euler discovered the three-dimensional wave equation; the Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem.

This is the problem of determining a curve on which a weighted particle will fall to a fixed point in a fixed amount of time, independent of the starting point. Lagrange sent the solution to Euler. Both further developed Lagrange's method and applied it to mechanics, which led to the formulation of Lagrangian mechanics. In 1822, Fourier published his work on heat flow in Théorie analytique de la chaleur, in which he based his reasoning on Newton's law of cooling, that the flow of heat between two adjacent molecules is proportional to the small difference of their temperatures. Contained in this book was Fourier's proposal of his heat equation for conductive diffusion of heat; this partial differential equation is now taught to every student of mathematical physics. In classical mechanics, the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow these variables to be expressed dynamically as a differential equation for the unknown position of the body as a function of time.

In some cases, this differential equation may be solved explicitly. An example of modeling a real-world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance; the ball's acceleration towards the ground is the acceleration due to gravity minus the acceleration due to air resistance. Gravity is considered constant, air resistance may be modeled as proportional to the ball's velocity; this means that the ball's acceleration, a derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation and verifying its validity. Differential equations can be divided into several types. Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution. Used distinctions include whether the equation is: Ordinary/Partial, Linear/Non-linear, Homogeneous/heterogeneous.

This list is far from exhaustive.

Life (band)

LIFE are a US alternative rock/pop band from Hermosa Beach, made up of the founding members of Tomorrows Bad Seeds, Moises Juarez, Sean Chapman and Matthew "Mets" McEwan. Moi and Mets were friends from school and grew up together in Hermosa Beach. Life was formed in Hermosa Beach, California in 2012, by all founding members of Tomorrows Bad Seeds, Moises Juarez, Sean Chapman and Matthew "Mets" McEwan. After years of touring and recording with Tomorrows Bad Seeds, the original members felt the need to branch out musically in a direction which had more "global appeal". Though grateful for what the reggae/rock scene had done for them, the band, felt they were growing and changing musically and so started their new project "LIFE" After a chance meeting with Producer/Musical director, Michael Choi on Warped Tour in the lunch queue, they embarked on a year-long journey to write new material and develop a new sound for themselves, taking all their personal musical influences which ranged from punk rock to soul.

The band signed with indie label Urbantone Group and launched with a premiere of their first single "R. U. D. W. N.?" Via USA Today in March 2014. The single was soon followed by a 2nd track "Better Days", premiered by Yahoo! Music. In June 2014, their first EP called "R. U. D. W. N.? EP" was released. Containing 5 tracks, the EP was a mixture of various influences of the band members. Sebastian Mackay at Substream Magazine said "The end result is an EP will get into your marrow and have you innocently tapping along at one moment and singing your heart out the next". Substream gave the EP a rare 5 stars. Gregory Robson at AbsolutePunk said of the EP "R U D W N? is a first-rate work from a band that deserves both wider appeal and wider recognition."In July 2014, Life premiered the video to "Kids" on LA Magazine. The video was created by Clifford Cruz. Produced by Foolish Prophet, this first EP consists of 5 tracks: R. U. D. W. N.? Kill The Messenger Kids Better Days Burning UpAll the tracks were written by the band and Foolish Prophet with co-writes from Josiah Rosen and Emil Ogoo.

Production started in May 2013, when Chapman suggested they should get a drummer like his hero, Josh Freese. The producer suggested asking "the man himself", so Freese became the main drummer on the EP, recording R. U. D. W. N.?, Kids and Better Days. The drums on Burning Up was recorded by the legendary drummer "JR" Robinson famed for his work with Quincy Jones and Michael Jackson; the drummer on Kill The Messenger was another legend Omar Hakim, a particular hero to Foolish Prophet due to his wide ranging work with Miles Davis, Madonna, Daft Punk etc. On percussion was another legend Luis Conte, piano was Rachel Z and horns were Nick Lane, Chuck Findley, Lee Thornburg, Tom Evans; the EP launched on June 2014 with a performance at The Roxy in West Hollywood. The band recorded their next single with drummer José Pasillas from the band Incubus. Chapman had met Pasillas through Greg Teal at Hurley and became friends after their first jam session. Pasillas has recorded 2 other tracks with the band. R. U.

D. W. N.? EP Moises Juarez Sean Chapman Matthew McEwan Official Site

Canada's National Ballet School

Canada's National Ballet School commonly known as the National Ballet School of Canada, is a classical ballet school located in Toronto, Canada. Along with the Royal Winnipeg Ballet School, it is a provider of professional ballet training in Canada. Mavis Staines has been the Artistic Director of the school since 1989; the National Ballet of Canada was formed in 1951 by the English ballet dancer Celia Franca, a dancer with ballet companies in the United Kingdom. Franca immigrated to Canada in 1951 and founded the National Ballet of Canada that same year hiring the English ballet teacher Betty Oliphant to work with the company; as the National Ballet became established and Oliphant decided to create a ballet academy to train dancers for the company. The school, modeled after Britain's Royal Ballet School, opened in 1959 in a former Quaker meeting house at 111 Maitland Street in Toronto, a building purchased for the school by the National Ballet Guild at a cost of $80,000. Oliphant became the school's first Artistic Director.

Alumni of the school include Martine van Hamel, Frank Augustyn, Neve Campbell, Anne Ditchburn, Rex Harrington, Karen Kain, James Kudelka, Veronica Tennant, Martine Lamy, John Alleyne, Mavis Staines, Kevin Pugh. In 1983, students at the school were featured in the Academy Award-winning National Film Board of Canada dance film Flamenco at 5:15. In 2000, 400 Jarvis Street, in the Wellesley-Church district, was acquired from the Canadian Broadcasting Corporation for one dollar; the existing buildings on the site were redesigned by Goldsmith Borgal & Company Ltd.. Architects. Three new buildings, dubbed Project Grand Jete, were planned and built by GBCA, along with Kuwabara Payne McKenna Blumberg Architects. Construction began in 2003, in 2005, the school relocated there; the major expansion to the school was completed in 2007 at a cost of $100 million. 111 Maitland, now known as Currie Hall, became the school's dining hall. The Margaret McCain Academic Building was built for and housed Havergal Ladies' College from 1898 until 1932, housed the Canadian Broadcasting Corporation's main radio and television studios in Toronto from 1945 until 1996.

Included as part of the school is a heritage building – the 1856 home of Sir Oliver Mowat, the longest-serving Premier of Ontario, a Father of Confederation, Ontario's Lieutenant-Governor. The mansion named Norfield House, was renamed Lozinski House and now houses the school's artistic and administrative offices; the architectural firms of Goldsmith Borgal & Company Ltd. Architects and Kuwabara Payne McKenna Blumberg Architects integrated the original buildings with three new buildings, using contemporary construction composed of glass, metal panels, concrete blocks, which appears transparent from the street façade; the three new buildings were completed in 2007: the Celia Franca Centre, a "Bar" building, a six-storey "North Tower" building, which consists of three large studio spaces, each stacked on top of the other. The Celia Franca Centre is used for multiple purposes. Twelve dance studios of various sizes, some of which are facing Jarvis Street, function are visible to passersby; the Franca Celia Centre includes a coffee shop, library/ resource centre, study areas, seating zones.

The Betty Oliphant Theatre has change rooms, dressing rooms and wardrobe all encompassed within the Franca Celia Centre. The Façade of the Celia Franca Centre consists of glazed curtain walls combined with cultured stone tiles tied by steel grate panel sub-structures; the choreography of the opening scene of The Nutcracker is visible in the suspended frit glass of the south pavilion facade in Benesh notation. Official website The National Ballet of Canada Prix de Lausanne The Canadian Encyclopedia: The School The Canadian Encyclopedia: The Company


The FRIDE was an independent European think tank headquartered in Madrid and Brussels. As of 2012, it was one of 55 think tanks in the country, it focused on the improvement of European views and ideas on various topics related to international development. It ceased its activities on 31 December 2015 due to economic reasons; the think tank was founded by Diego Hidalgo in 1999. Hidalgo is the founder of another think tank, Club of Rome, other similar organizations. FRIDE became part of the European Think Tanks Group which includes the German Development Institute, European Center for Development Policy Management and the Overseas Development Institute. In 2012, FRIDE was the 77th organization among top 100 non-US think tanks and the 75th among top 150 worldwide think tanks according to the global go to think tanks ranking developed by the international relations program of the University of Pennsylvania. In the same ranking, it was the 23rd Western Europe think tank among 75 institutions. FRIDE was closed down in December 2015.

The stated objective of the FRIDE was to expand the ideas on Europe's role in the international arena with special reference to multilateralism, democratic values and sustainable development. It was an international development, its major study fields includes democracy, emerging powers, development cooperation, global governance, fragile states and energy security. In addition, it focused on peace and security, human rights, democracy promotion, development and humanitarian aid; the specialization of FRIDE was on crisis and EU foreign policy and the reshaped global order, changing approaches to security and the new Middle East. The organization had a director and a deputy director; as well as a board of trustees and an advisory committee. Pedro Solbes was Giovanni Grevi the director of the organization. FRIDE realized its activities through publications, research programs and events; the FRIDE publications were policy briefs, opinion articles in the newspapers and working papers developed by its research team and publishes books.

In addition, FRIDE organized projects and analyses. In 2010, the Club of Madrid and FRIDE functioned as the advisor bodies for the G20 summit held in Seoul, its studies in the period of 2011-2012 were the 26th best policy report according to the global go to think tanks ranking. FRIDE's major financial source was private projects. In 2010, the EU funding was just 0.68% of its revenues, € 2.47 million. The Madrid regional government was one of the contributors of the FRIDE since 2008

Borislav Tsekov

Borislav Tsekov is a Bulgarian lawyer, public figure and policymaker. In 2001–2005, he served as Member of Parliament representing the NMSS and since 2004 the New Times Party. In that time he was a member of the European Integration Committee, Legal Affairs Committee and Committee on Local Self-government, Regional Policy and Urban development, he has been elected as Deputy Chairman of Religious Affairs Ad Hoc Committee on Religious Affairs and Ad Hoc Committee on Amendments to the Constitution. As Member of Bulgarian Parliament, Borislav Tsekov sponsored more than 30 bills. More than half of these bills were adopted by the Parliament, including Religious Denominations Act, Political Parties Act, State Orders and Medals Act, amendments. Tsekov served as Secretary General of the Ombudsman Institution of the Republic of Bulgaria, a constitutional authority monitoring human rights and good governance issues. In earlier stages of his professional career, Tsekov has worked as NGO and business consultant, Legal advisor at the Parliament, lecturer at the New Bulgarian University.

Tsekov is a National President for the World Jurist Association, based in Washington DC. Tsekov is President of the Board of Governors of the Institute of Modern Politics, he is an author of many publications on legislative issues. In February 2011 he published the book New York: The Altar of the Modern World, a kaleidoscopic mosaic of history and lifestyle of New York City. 1994 - graduated the Faculty of Law of Sofia University “St Clement of Ohrid” 1993 – Portugal: Training Program “Political Strategies and Election Campaign”, Friedrich Naumann Foundation 1996-1999: Belgium: European Law – Five Training Programs of TAIEX 1998 – USA: “International Policy Advocacy”, Advocacy Institute and School for International Training 1999 – Japan: “Human Rights and Anti-discrimination”, JICA and Japanese Foreign Ministry 2003 – Italy: “Strengthening and Capacity Building of Bulgarian Anti-corruption Institutions”, USAID and IDLO 2004 – USA: “Contemporary Political Issues – Presidential Campaign 2004”, Department of State 2006 – USA: “Promoting Tolerance” – American Jewish Committee 2007 - "John F. Kennedy" School of Government, Harvard University 2009 - "International Human Rights Academy", organized by Ghent University, Utrecht University, University of the Western Cape, American University Washington College of Law, University of Pretoria, Free University of Brussels 2016 - Ph.

D. in Constitutional Law at the Bulgarian Academy of Sciences National Assembly of the Republic of Bulgaria Sega, daily newspaper Standart, daily newspaper Center for the Study of Democracy Ombudsman of the Republic of Bulgaria Panorthodox NDSV Verbal Mosaics Blog


Sun SPOT was a sensor node for a wireless sensor network developed by Sun Microsystems announced in 2007. The device used the IEEE 802.15.4 standard for its networking, unlike other available sensor nodes, used the Squawk Java virtual machine. After the acquisition of Sun Microsystems by Oracle Corporation, the SunSPOT platform was supported but its forum was shut down in 2012; the assembled device fit in the palm of a hand. Its first processor board included an ARM architecture 32 bit CPU with ARM920T core running at 180 MHz, it had 4 MB flash memory. A 2.4 GHz IEEE 802.15.4 radio had an integrated antenna and a USB interface was included. A sensor board included a three-axis accelerometer, temperature sensor, light sensor, 8 tri-color LEDs, analog and digital inputs, two momentary switches, 4 high current output pins; the unit used a 3.7V rechargeable 750 mAh lithium-ion battery, had a 30 uA deep sleep mode, battery management provided by software. The device's use of Java device drivers is unusual since Java is hardware-independent.

Sun SPOT uses a small Java ME Squawk which ran directly on the processor without an operating system. Both the Squawk VM and the Sun SPOT code are open source. Standard Java development environments such as NetBeans can be used to create SunSPOT applications; the management and deployment of application are handled by ant scripts, which can be called from a development environment, command line, or the tool provided with the SPOT SDK, "solarium". The nodes communicate using the IEEE 802.15.4 standard including the base-station approach to sensor networking. Protocols such as Zigbee can be built on 802.15.4. Sun Labs reported implementations of RSA and elliptic curve cryptography optimized for small embedded devices. Sun Microsystems Laboratories started research on sensor networks around 2004. After some initial experience using "Motes" from Crossbow Technology, a project began under Roger Meike to design an integrated hardware and software system. Sun sponsored a project at the Art Center College of Design called Autonomous Light Air Vessels in 2005.

The first limited-production run of Sun SPOT development kits were released April 2, 2007, after months of delays. This introduction kit included two Sun SPOT demo sensor boards, a Sun SPOT base station, the software development tools, a USB cable; the software was compatible with Windows XP, Mac OS X 10.4, common Linux distributions. Some demonstration code was provided. A developer from Sun gave a demonstration in September 2007. After investigating commercial use, Sun moved to focus on educational users; the entire project, operating environment, Java virtual machine and applications, was available as open source in January 2008. Oracle Corporation acquired Sun Microsystems in 2010 and continued Sun SPOT development, through release 8 of the hardware by March 2011; the 2011 version with fewer inputs. In 2012 the forum said it would be "down for maintenance" until "mid-June". A new forum was started on the Oracle Technology Network on May 7, 2013. David G. Simmons, one of the SunSPOT developers for Sun Microsystems, maintained a blog through the end of 2010.

He opened. When the project was shut down, the lead hardware engineer for the SunSPOT project, Bob Alkire, archived the hardware design on his personal website. Official website