VeriaVeria (Véroia or Vérroia; Veria), officially transliterated Veroia, historically also spelled Berea or Berœa, is a city in Central Macedonia, in the geographic region of Macedonia, northern Greece, capital of the regional unit of Imathia. It is located north-northwest of the capital Athens and west-southwest of Thessaloniki. Even by the standards of Greece, Veria is an old city; first mentioned in the writings of Thucydides in 432 BC, there is evidence that it was populated as early as 1000 BC.
Computational complexity of matrix multiplicationIn theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the right amount of time it should take is of major practical relevance. Directly applying the mathematical definition of matrix multiplication gives an algorithm that requires n3 field operations to multiply two n × n matrices over that field (Θ(n3) in big O notation).
Renaissance humanismRenaissance humanism was a worldview centered on the nature and importance of humanity, that emerged from the study of Classical antiquity. This first began in Italy and then spread across Western Europe in the 14th, 15th, and 16th centuries. During the period, the term humanist (umanista) referred to teachers and students of the humanities, known as the studia humanitatis, which included the study of Latin and Ancient Greek literatures, grammar, rhetoric, history, poetry, and moral philosophy.
Completely multiplicative functionIn number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting only products of coprime numbers, and such functions are called multiplicative functions. Outside of number theory, the term "multiplicative function" is often taken to be synonymous with "completely multiplicative function" as defined in this article.
Vector (mathematics and physics)In mathematics and physics, vector is a term that refers colloquially to some quantities that cannot be expressed by a single number (a scalar), or to elements of some vector spaces. Historically, vectors were introduced in geometry and physics (typically in mechanics) for quantities that have both a magnitude and a direction, such as displacements, forces and velocity. Such quantities are represented by geometric vectors in the same way as distances, masses and time are represented by real numbers.
Byzantine architectureByzantine architecture is the architecture of the Byzantine Empire, or Eastern Roman Empire. The Byzantine era is usually dated from 330 AD, when Constantine the Great established a new Roman capital in Byzantium, which became Constantinople, until the fall of the Byzantine Empire in 1453. However, there was initially no hard line between the Byzantine and Roman Empires, and early Byzantine architecture is stylistically and structurally distinguishable from earlier Roman architecture.
MultiplicationMultiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.
Covariance and contravariance of vectorsIn physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis. In modern mathematical notation, the role is sometimes swapped. A simple illustrative case is that of a vector. For a vector, once a set of basis vectors has been defined, then the components of that vector will always vary opposite to that of the basis vectors. A vector is therefore a contravariant tensor.
Byzantine artByzantine art comprises the body of Christian Greek artistic products of the Eastern Roman Empire, as well as the nations and states that inherited culturally from the empire. Though the empire itself emerged from the decline of Rome and lasted until the Fall of Constantinople in 1453, the start date of the Byzantine period is rather clearer in art history than in political history, if still imprecise. Many Eastern Orthodox states in Eastern Europe, as well as to some degree the Islamic states of the eastern Mediterranean, preserved many aspects of the empire's culture and art for centuries afterward.
Multiplication algorithmA multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Efficient multiplication algorithms have existed since the advent of the decimal system. If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplication, sometimes called grade-school multiplication, sometimes called the Standard Algorithm: multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.
