Informal description.

The following characterization may be easier to understand than the usual formal definition: an affine space is what is left of a vector space after you've forgotten which point is the origin (or, in the words of the French mathematician Marcel Berger, "An affine space is nothing more than a vector space whose origin we try to forget about, by adding translations to the linear maps"). Imagine that Alice knows that a certain point is the actual origin, but Bob believes that another point—call it —is the origin. Two vectors, and, are to be added. Bob draws an arrow from point to point and another arrow from point to point, and completes the parallelogram to find what Bob thinks is, but Alice knows that he has actually computed  Similarly, Alice and Bob may evaluate any linear combination of and, or of any finite set of vectors, and will generally get different answers. However, if the sum of the coefficients in a linear combination is 1, then Alice and Bob will arrive at the same answer.  If Alice travels to then Bob can similarly travel to  Under this condition, for all coefficients, Alice and Bob describe the same point with the same linear combination, despite using different origins.  While only Alice knows the "linear structure", both Alice and Bob know the "affine structure"—i.e. the values of affine combinations, defined as linear combinations in which the sum of the coefficients is 1. A set with an affine structure is an affine space.

Definition.

An "affine space" is a set together with a vector space formula_1, and a transitive and free action of the additive group of formula_1 on the set. The elements of the affine space are called "points", and the elements of the associated vector space formula_1 are called "vectors", "translations", or sometimes "free vectors". Explicitly, the definition above means that the action is a mapping, generally denoted as an addition,  that has the following properties.  The first two properties are simply defining properties of a (right) group action. The third property characterizes free and transitive actions, the onto character coming from transitivity, and then the injective character follows from the action being free. There is a fourth property that follows from 1, 2 above:  Property 3 is often used in the following equivalent form. Another way to express the definition is that an affine space is a principal homogeneous space for the action of the additive group of a vector space. Homogeneous spaces are by definition endowed with a transitive group action, and for a principal homogeneous space such a transitive action is by definition free.

Subtraction and Weyl's axioms.

The properties of the group action allows for the definition of subtraction for any given ordered pair of points in, producing a vector of formula_1. This vector, denoted formula_16 or formula_17, is defined to be the unique vector in formula_1 such that Existence follows from the transitivity of the action, and uniqueness follows because the action is free.  This subtraction has the two following properties, called Weyl's axioms:  In Euclidean geometry, the second Weyl's axiom is commonly called the "parallelogram rule".  Affine spaces can be equivalently defined as a point set, together with a vector space formula_1, and a subtraction satisfying Weyl's axioms. In this case, the addition of a vector to a point is defined from the first Weyl's axioms.

Affine subspaces and parallelism.

An "affine subspace" (also called, in some contexts, a "linear variety", a flat, or, over the real numbers, a "linear manifold") of an affine space is a subset of such that, given a point formula_25, the set of vectors formula_26 is a linear subspace of formula_1. This property, which does not depend on the choice of, implies that is an affine space, which has formula_28 as its associated vector space.  The affine subspaces of are the subsets of of the form where is a point of, and a linear subspace of formula_1.  The linear subspace associated with an affine subspace is often called its "", and two subspaces that share the same direction are said to be "parallel".  This implies the following generalization of Playfair's axiom: Given a direction, for any point of there is one and only one affine subspace of direction, which passes through, namely the subspace.  Every translation formula_31 maps any affine subspace to a parallel subspace.  The term "parallel" is also used for two affine subspaces such that the direction of one is included in the direction of the other.

Affine map.

Given two affine spaces and whose associated vector spaces are formula_1 and formula_28, an "affine map" or "affine homomorphism" from to is a map such that is a well defined linear map. By formula_36 being well defined is meant that implies.  This implies that, for a point formula_9 and a vector formula_38, one has  Therefore, since for any given in, for a unique, is completely defined by its value on a single point and the associated linear map formula_40.

Vector spaces as affine spaces.

Every vector space may be considered as an affine space over itself. This means that every element of may be considered either as a point or as a vector. This affine space is sometimes denoted for emphasizing the double role of the elements of. When considered as a point, the zero vector is commonly denoted (or, when upper-case letters are used for points) and called the "origin".  If is another affine space over the same vector space (that is formula_41) the choice of any point in defines a unique affine isomorphism, which is the identity of and maps to. In other words, the choice of an origin in allows us to identify and up to a canonical isomorphism. The counterpart of this property is that the affine space may be identified with the vector space in which "the place of the origin has been forgotten".

Relation to Euclidean spaces.

Definition of Euclidean spaces.

Euclidean spaces (including the one-dimensional line, two-dimensional plane, and three-dimensional space commonly studied in elementary geometry, as well as higher-dimensional analogues) are affine spaces.  Indeed, in most modern definitions, a Euclidean space is defined to be an affine space, such that the associated vector space is a real inner product space of finite dimension, that is a vector space over the reals with a positive-definite quadratic form. The inner product of two vectors and is the value of the symmetric bilinear form The usual Euclidean distance between two points and is  In older definition of Euclidean spaces through synthetic geometry, vectors are defined as equivalence classes of ordered pairs of points under equipollence (the pairs and are "equipollent" if the points (in this order) form a parallelogram). It is straightforward to verify that the vectors form a vector space, the square of the Euclidean distance is a quadratic form on the space of vectors, and the two definitions of Euclidean spaces are equivalent.

Affine properties.

In Euclidean geometry, the common phrase "affine property" refers to a property that can be proved in affine spaces, that is, it can be proved without using the quadratic form and its associated inner product. In other words, an affine property is a property that does not involve lengths and angles. Typical examples are parallelism, and the definition of a tangent. A non-example is the definition of a normal.  Equivalently, an affine property is a property that is invariant under affine transformations of the Euclidean space.

Affine combinations and barycenter.

Let be a collection of points in an affine space, and formula_44 be elements of the ground field.  Suppose that formula_45. For any two points and one has Thus this sum is independent of the choice of the origin, and the resulting vector may be denoted  When formula_48, one retrieves the definition of the subtraction of points.  Now suppose instead that the field elements satisfy formula_49. For some choice of an origin, denote by formula_50 the unique point such that One can show that formula_50 is independent from the choice of. Therefore, if one may write The point formula_50 is called the barycenter of the formula_56 for the weights formula_57. One says also that formula_50 is an affine combination of the formula_56 with coefficients formula_57.

Affine span and bases.

For any subset of an affine space, there is a smallest affine subspace that contains it, called the affine span of. It is the intersection of all affine subspaces containing, and its direction is the intersection of the directions of the affine subspaces that contain.  The affine span of is the set of all (finite) affine combinations of points of, and its direction is the linear span of the for and in. If one chooses a particular point, the direction of the affine span of is also the linear span of the for in.  One says also that the affine span of is generated by and that is a generating set of its affine span.  A set of points of an affine space is said to be affinely independent or, simply, independent, if the affine span of any strict subset of is a strict subset of the affine span of. An or barycentric frame (see, below) of an affine space is a generating set that is also independent (that is a minimal generating set).  Recall the "dimension" of an affine space is the dimension of its associated vector space. The bases of an affine space of finite dimension are the independent subsets of elements, or, equivalently, the generating subsets of elements. Equivalently, } is an affine basis of an affine space if and only if } is a linear basis of the associated vector space.

Coordinates.

There are two strongly related kinds of coordinate systems that may be defined on affine spaces.

Barycentric coordinates.

Let be an affine space over a field of dimension, and formula_62 be an affine basis of. The properties of an affine basis imply that for every in there is a unique -tuple formula_63 of elements of such that and  The formula_57 are called the barycentric coordinates of over the affine basis formula_62. If the are viewed as bodies that have weights (or masses) formula_57, the point is thus the barycenter of the, and this explains the origin of the term "barycentric coordinates".  The barycentric coordinates define an affine isomorphism between the affine space and the affine subspace of defined by the equation formula_64.  For affine spaces of infinite dimension, the same definition applies, using only finite sums. This means that for each point, only a finite number of coordinates are non-zero.

Affine coordinates.

An affine frame of an affine space consists of a point, called the "origin", and a linear basis of the associated vector space. More precisely, for an affine space with associated vector space formula_1, the origin belongs to, and the linear basis is a basis of formula_1 (for simplicity of the notation, we consider only the case of finite dimension, the general case is similar).  For each point of, there is a unique sequence formula_44 of elements of the ground field such that or equivalently  The formula_57 are called the affine coordinates of over the affine frame.  Example: In Euclidean geometry, Cartesian coordinates are affine coordinates relative to an orthonormal frame, that is an affine frame such that is an orthonormal basis.

Relationship between barycentric and affine coordinates.

Barycentric coordinates and affine coordinates are strongly related, and may be considered as equivalent.  In fact, given a barycentric frame one deduces immediately the affine frame and, if are the barycentric coordinates of a point over the barycentric frame, then the affine coordinates of the same point over the affine frame are  Conversely, if is an affine frame, then is a barycentric frame. If are the affine coordinates of a point over the affine frame, then its barycentric coordinates over the barycentric frame are  Therefore, barycentric and affine coordinates are almost equivalent. In most applications, affine coordinates are preferred, as involving less coordinates that are independent. However, in the situations where the important points of the studied problem are affinity independent, barycentric coordinates may lead to simpler computation, as in the following example.

Example of the triangle.

The vertices of a non-flat triangle form an affine basis of the Euclidean plane. The barycentric coordinates allows easy characterization of the elements of the triangle that do not involve angles or distance:  The vertices are the points of barycentric coordinates, and. The lines supporting the edges are the points that have a zero coordinate. The edges themselves are the points that have a zero coordinate and two nonnegative coordinates. The interior of the triangle are the points whose all coordinates are positive. The medians are the points that have two equal coordinates, and the centroid is the point of coordinates.

Properties of affine homomorphisms.

Image and fibers.

Let be an affine homomorphism, with as associated linear map.  The image of is the affine subspace of, which has formula_86 as associated vector space. As an affine space does not have a zero element, an affine homomorphism does not have a kernel. However, for any point of, the inverse image of is an affine subspace of, of direction formula_87. This affine subspace is called the fiber of.

Projection.

An important example is the projection parallel to some direction onto an affine subspace. The importance of this example lies in the fact that Euclidean spaces are affine spaces, and that this kind of projections is fundamental in Euclidean geometry.  More precisely, given an affine space with associated vector space formula_88, let be an affine subspace of direction formula_89, and be a complementary subspace of formula_89 in formula_88 (this means that every vector of formula_88 may be decomposed in a unique way as the sum of an element of formula_89 and an element of ). For every point of, its projection to parallel to is the unique point in such that  This is an affine homomorphism whose associated linear map formula_95 is defined by for and in.  The image of this projection is, and its fibers are the subspaces of direction.

Quotient space.

Although kernels are not defined for affine spaces, quotient spaces are defined. This results from the fact that "belonging to the same fiber of an affine homomorphism" is an equivalence relation.  Let be an affine space, and be a linear subspace of the associated vector space formula_88. The quotient of by is the quotient of by the equivalence relation  This quotient is an affine space, which has formula_99 as associated vector space.  For every affine homomorphism formula_100, the image is isomorphic to the quotient of by the kernel of the associated linear map. This is the first isomorphism theorem for affine spaces.

Axioms.

Affine space is usually studied as analytic geometry using coordinates, or equivalently vector spaces. It can also be studied as synthetic geometry by writing down axioms, though this approach is much less common. There are several different systems of axioms for affine space.  Affine planes satisfy the following axioms : (in which two lines are called parallel if they are equal or disjoint): As well as affine planes over fields (or division rings), there are also many non-Desarguesian planes satisfying these axioms. gives axioms for higher-dimensional affine spaces.

Relation to projective spaces.

Affine spaces are subspaces of projective spaces: an affine plane can be obtained from any projective plane by removing a line and all the points on it, and conversely any affine plane can be used to construct a projective plane as a closure by adding a line at infinity whose points correspond to equivalence classes of parallel lines.  Further, transformations of projective space that preserve affine space (equivalently, that leave the hyperplane at infinity invariant as a set) yield transformations of affine space. Conversely, any affine linear transformation extends uniquely to a projective linear transformation, so the affine group is a subgroup of the projective group. For instance, Möbius transformations (transformations of the complex projective line, or Riemann sphere) are affine (transformations of the complex plane) if and only if they fix the point at infinity.

Affine algebraic geometry.

In algebraic geometry, an affine variety (or, more generally, an affine algebraic set) is defined as the subset of an affine space that is the set of the common zeros of a set of so-called "polynomial functions over the affine space". For defining a "polynomial function over the affine space", one has to choose an affine frame. Then, a polynomial function is a function such that the image of any point is the value of some multivariate polynomial function of the coordinates of the point. As a change of affine coordinates may be expressed by linear functions (more precisely affine functions) of the coordinates, this definition is independent of a particular choice of coordinates.  The choice of a system of affine coordinates for an affine space formula_101 of dimension over a field induces an affine isomorphism between formula_101 and the affine coordinate space. This explains why, for simplification, many textbooks write formula_103, and introduce affine algebraic varieties as the common zeros of polynomial functions over.  As the whole affine space is the set of the common zeros of the zero polynomial, affine spaces are affine algebraic varieties.

Ring of polynomial functions.

By the definition above, the choice of an affine frame of an affine space formula_101 allows one to identify the polynomial functions on formula_101 with polynomials in variables, the "i"th variable representing the function that maps a point to its th coordinate. It follows that the set of polynomial functions over formula_101 is a -algebra, denoted formula_107, which is isomorphic to the polynomial ring formula_108.  When one changes coordinates, the isomorphism between formula_107 and formula_110 changes accordingly, and this induces an automorphism of formula_108, which maps each indeterminate to a polynomial of degree one. It follows that the total degree defines a filtration of formula_112, which is independent from the choice of coordinates. The total degree defines also a graduation, but it depends on the choice of coordinates, as a change of affine coordinates may map indeterminates on non-homogeneous polynomials.

Zariski topology.

Affine spaces over topological fields, such as the real or the complex numbers, have a natural topology. The Zariski topology, which is defined for affine spaces over any field, allows use of topological methods in any case. Zariski topology is the unique topology on an affine space whose closed sets are affine algebraic sets (that is sets of the common zeros of polynomials functions over the affine set). As, over a topological field, polynomial functions are continuous, every Zariski closed set is closed for the usual topology, if any. In other words, over a topological field, Zariski topology is coarser than the natural topology.  There is a natural injective function from an affine space into the set of prime ideals (that is the spectrum) of its ring of polynomial functions. When affine coordinates have been chosen, this function maps the point of coordinates formula_113 to the maximal ideal formula_114. This function is a homeomorphism (for the Zariski topology of the affine space and of the spectrum of the ring of polynomial functions) of the affine space onto the image of the function.  The case of an algebraically closed ground field is especially important in algebraic geometry, because, in this case, the homeomorphism above is a map between the affine space and the set of all maximal ideals of the ring of functions (this is Hilbert's Nullstellensatz).  This is the starting idea of scheme theory of Grothendieck, which consists, for studying algebraic varieties, of considering as "points", not only the points of the affine space, but also all the prime ideals of the spectrum. This allows gluing together algebraic varieties in a similar way as, for manifolds, charts are glued together for building a manifold.

Cohomology.

Like all affine varieties, local data on an affine space can always be patched together globally: the cohomology of affine space is trivial. More precisely, formula_115 for all coherent sheaves F, and integers formula_116. This property is also enjoyed by all other affine varieties. But also all of the etale cohomology groups on affine space are trivial. In particular, every line bundle is trivial. More generally, the Quillen–Suslin theorem implies that "every" algebraic vector bundle over an affine space is trivial.

In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

En géométrie, la notion d'espace affine généralise la notion d'espace issue de la géométrie euclidienne en omettant les notions d'angle et de distance. Dans un espace affine, on peut parler d'alignement, de parallélisme, de barycentre. Sous la forme qui utilise des rapports de mesures algébriques, qui est une notion affine, le théorème de Thalès et le théorème de Ceva sont des exemples de théorèmes de géométrie affine plane réelle (c'est-à-dire n'utilisant que la structure d'espace affine du plan réel). Un espace affine peut aussi être vu comme un espace vectoriel « dont on a oublié l'origine ». Ainsi les translations de vecteur non nul sont des transformations affines (c'est-à-dire qu'elles conservent la structure d'espace affine), mais pas vectorielles. Les homothéties (de centre un point quelconque de l'espace), mais aussi par exemple les transvections ou les dilatations sont des applications affines.


Early life and education.

Azad was born as Humayun Kabir on 28 April 1947 in Rarhikhal village in Bikrampur which village is now under the Sreenagar sub-district of Munshiganj district. Notable scientist Jagadish Chandra Bose was born in the same village. He passed the secondary examination from Sir Jagadish Chandra Basu Institute in 1962 and higher secondary examination from Dhaka College in 1964. He earned BA and MA degrees in Bengali language and literature from the University of Dhaka in 1967 and 1968 respectively. He obtained his PhD in linguistics submitting his thesis titled "Pronominalisation in Bangla" from the University of Edinburgh in 1976. Azad changed his surname from Kabir to Azad on 28 September 1988 by the magistrate of Narayanganj District.

Career.

Azad started his career in 1969 by joining the Chittagong College. He joined the University of Chittagong as a lecturer on 11 February 1970 and Jahangirnagar University in 1972. He was appointed as an associate professor of Bengali at the University of Dhaka on 1 November 1978 and got promoted to the post of professor in 1986.

Literary works.

Azad's first published book was about collection of poems written by himself, the book was titled as "Aloukik Istimar" (), this was published in 1973, in which year he went to Scotland for studying Ph.D in Linguistics from University of Edinburgh. He wrote a short-story in 1979 called "Onoboroto Tusharpat" () which was inspired from his newly-wed life with his Dhaka University class-mate Latifa Kohinoor, he took Latifa Scotland after the marriage in 1975, in Britain one day among heavy snowing Azad was driving a car with his wife which became the main plot of the short story; so many years later Azad included this short-story in his 1996 book "Jadukorer Mrityu" () which book is the collection of his own-written five short-stories.  Towards the end of the 1980s, he started to write newspaper column focusing on contemporary sociopolitical issues. His commentaries continued throughout the 1990s and were later published as books as they grew in numbers. Through his writings of the 1990s and early 2000s he established himself as a novelist.  In 1992 Azad published the first comprehensive feminist book in Bengali titled "Naree" (). "Naree" received both positive and negative reviews as a treatise, it was considered the first full fledged feminist book after the independence of Bangladesh. In this work Azad mentioned the pro-women contributions of the British India's two famous Bengali socio-political reformers: Raja Rammohan Roy and Ishwar Chandra Vidyasagar, he criticized Rabindranath Tagore, a famous Bengali poet and Nobel laureate, and Bankim Chandra Chatterjee, a famous Bengali novelist of the 19th century. The work, critical of the patriarchal and male-chauvinistic attitude of society towards women, attracted negative reactions from many Bangladeshi readers. The Government of Bangladesh banned the book in 1995. The ban was eventually lifted in 2000, following a legal battle that Azad won in the High Court of the country.  In the year of 1994 he published his first novel which was titled as "Chhappanno Hazar Borgomile" (). The novel was about military rule in Bangladesh. He got special recognition for his second novel "Sab Kichu Bhene Pare" (1995) which was based on interpersonal relationship of Bangladeshi society. He wrote "Ekti Khuner Shopno" (), an unrequited love-based novel where the main male protagonist lives in Salimullah Muslim Hall of Dhaka University where Azad lived during his student life, it was Azad's last novel published in 2004 in which year he died.

Assassination attempt.

On 27 February 2004, near the campus of the University of Dhaka during the annual Bangla Academy book fair, two assailants, armed with chopping knives, hacked Azad several times on the jaw, lower part of the neck and hands. Azad was taken to the nearby Dhaka Medical College and Hospital. He was then sent to the Combined Military Hospital (CMH), Dhaka and later to Bumrungrad International Hospital in Thailand where he recovered.  Azad had been fearing for his life ever since excerpts of his novel, "Pak Sar Jamin Sad Bad" () were first published in "The Daily Ittefaq Newspaper"s Eid supplement in 2003. In that novel, he indecorously criticised the political ideologies of the Islamic extremists of Bangladesh. After that book had been published, he started receiving various threats from the Islamist fundamentalists.  A week prior to Azad's assault, Delwar Hossain Sayeedi, one of the members of parliament of Bangladesh said in the parliament, that Azad's political satire "Pak Sar Jamin Sad Bad" must be banned; he also wanted infliction of the blasphemy law of Bangladesh for this kind of book. In 2006, one of the leaders of the fundamentalist organization Jama'atul Mujahideen Bangladesh (JMB) admitted to the RAB interrogators that his operatives carried out the attack on writer Azad, as well as two other murders, bomb blasts, and attacks on cinemas.

Death.

On 12 August 2004, Azad was found dead in his apartment in Munich, Germany, where he had arrived a week earlier to conduct research on the nineteenth century German romantic poet Heinrich Heine, several months after the Islamists' machete attack on him at a book fair, which had left him grievously injured. His family demanded an investigation, alleging that the extremists who had attempted the earlier assassination had a role in this death. While alive, Azad had expressed his wish to donate his body to medical college after his death. But he was buried in Rarhikhal, his village home in Bangladesh, as doctors denied to take his body for medical research, as several days had passed to reach his body to Bangladesh from Germany. The first death anniversary of Azad was observed with respect in Rarhikhal village on Friday, the 12 August 2005.

Personal life.

Azad married Latifa Kohinoor on 12 October 1975 whom he first met 1968 when studying M.A. in Dhaka University. Together they had two daughters, Smita and Mouli, and one son, Anannya.

Humayun Azad (; born Humayun Kabir; 28 April 1947 – 12 August 2004) was a Bangladeshi poet, novelist, short-story writer, critic, researcher, linguist and professor of Dhaka University. He wrote more than seventy titles. He was awarded the Bangla Academy Literary Award in 1986 for his contributions to Bengali linguistics. In 2012, the Government of Bangladesh honored him with Ekushey Padak posthumously.

Humayun Azad (Rari Khal, Raj britannique, – Munich, Allemagne, ) était un chercheur et auteur bangladais prolifique d'une soixantaine de livres dont 10 romans, 7 recueils de poésie, 7 livres de littérature comparée, 2 livres pour enfants et de nombreux articles. Il était récipiendaire du "Bangla Academy Award" (1996) et du "Shishu Academy Award for literature".


The Great Inflation.

The term "stagflation", a portmanteau of "stagnation" and "inflation", was first coined during a period of inflation and unemployment in the United Kingdom. The United Kingdom experienced an outbreak of inflation in the 1960s and 1970s. Inflation rose in the 1960s and 1970s, UK policy makers failed to recognize the primary role of monetary policy in controlling inflation. Instead, they attempted to use non-monetary policies and devices to respond to the economic crisis. Policy makers also made "inaccurate estimates of the degree of excess demand in the economy, [which] contributed significantly to the outbreak of inflation in the United Kingdom in the 1960s and 1970s.  Stagflation was not limited to the United Kingdom, however. Economists have shown that stagflation was prevalent among seven major market economies from 1973 to 1982. After inflation rates began to fall in 1982, economists' focus shifted from the causes of stagflation to the "determinants of productivity growth and the effects of real wages on the demand for labor".

Causes.

Economists offer two principal explanations for why stagflation occurs. First, stagflation can result when the economy faces a supply shock, such as a rapid increase in the price of oil. An unfavorable situation like that tends to raise prices at the same time as it slows economic growth by making production more costly and less profitable.  Second, the government can cause stagflation if it creates policies that harm industry while growing the money supply too quickly. These two things would probably have to occur simultaneously because policies that slow economic growth do not usually cause inflation, and policies that cause inflation do not usually slow economic growth.  Both explanations are offered in analyses of the 1970s stagflation in the West. It began with a huge rise in oil prices, but then continued as central banks used excessively stimulative monetary policy to counteract the resulting recession, causing a price/wage spiral.

Postwar Keynesian and monetarist views.

Early Keynesianism and monetarism.

Up to the 1960s, many Keynesian economists ignored the possibility of stagflation, because historical experience suggested that high unemployment was typically associated with low inflation, and vice versa (this relationship is called the Phillips curve). The idea was that high demand for goods drives up prices, and also encourages firms to hire more; and likewise high employment raises demand. However, in the 1970s and 1980s, when stagflation occurred, it became obvious that the relationship between inflation and employment levels was not necessarily stable: that is, the Phillips relationship could shift. Macroeconomists became more skeptical of Keynesian theories, and Keynesians themselves reconsidered their ideas in search of an explanation for stagflation.  The explanation for the shift of the Phillips curve was initially provided by the monetarist economist Milton Friedman, and also by Edmund Phelps. Both argued that when workers and firms begin to expect more inflation, the Phillips curve shifts up (meaning that more inflation occurs at any given level of unemployment). In particular, they suggested that if inflation lasted for several years, workers and firms would start to take it into account during wage negotiations, causing workers' wages and firms' costs to rise more quickly, thus further increasing inflation. While this idea was a severe criticism of early Keynesian theories, it was gradually accepted by most Keynesians, and has been incorporated into New Keynesian economic models.

Neo-Keynesianism.

Neo-Keynesian theory distinguished two distinct kinds of inflation: demand-pull (caused by shifts of the aggregate demand curve) and cost-push (caused by shifts of the aggregate supply curve). Stagflation, in this view, is caused by cost-push inflation. Cost-push inflation occurs when some force or condition increases the costs of production. This could be caused by government policies (such as taxes) or from purely external factors such as a shortage of natural resources or an act of war.  Contemporary Keynesian analyses argue that stagflation can be understood by distinguishing factors that affect aggregate demand from those that affect aggregate supply. While monetary and fiscal policy can be used to stabilise the economy in the face of aggregate demand fluctuations, they are not very useful in confronting aggregate supply fluctuations. In particular, an adverse shock to aggregate supply, such as an increase in oil prices, can give rise to stagflation.

Supply theory.

Fundamentals.

Supply theories are based on the neo-Keynesian cost-push model and attribute stagflation to significant disruptions to the supply side of the supply-demand market equation, such as when there is a sudden real or relative scarcity of key commodities, natural resources, or natural capital needed to produce goods and services. Other factors may also cause supply problems, for example, social and political conditions such as policy changes, acts of war, extremely restrictive government control of production. In this view, stagflation is thought to occur when there is an adverse supply shock (for example, a sudden increase in the price of oil or a new tax) that causes a subsequent jump in the "cost" of goods and services (often at the wholesale level). In technical terms, this results in contraction or negative shift in an economy's aggregate supply curve.  In the resource scarcity scenario (Zinam 1982), stagflation results when economic growth is inhibited by a restricted supply of raw materials. That is, when the actual or relative supply of basic materials (fossil fuels (energy), minerals, agricultural land in production, timber, etc.) decreases and/or cannot be increased fast enough in response to rising or continuing demand. The resource shortage may be a real physical shortage, or a relative scarcity due to factors such as taxes or bad monetary policy influencing the "cost" or availability of raw materials. This is consistent with the cost-push inflation factors in neo-Keynesian theory (above). The way this plays out is that after supply shock occurs, the economy first tries to maintain momentum. That is, consumers and businesses begin paying higher prices to maintain their level of demand. The central bank may exacerbate this by increasing the money supply, by lowering interest rates for example, in an effort to combat a recession. The increased money supply props up the demand for goods and services, though demand would normally drop during a recession.  In the Keynesian model, higher prices prompt increases in the supply of goods and services. However, during a supply shock (i.e., scarcity, "bottleneck" in resources, etc.), supplies do not respond as they normally would to these price pressures. So, inflation jumps and output drops, producing stagflation.

Explaining the 1970s stagflation.

Following Richard Nixon's imposition of wage and price controls on 15 August 1971, an initial wave of cost-push shocks in commodities were blamed for causing spiraling prices. The second major shock was the 1973 oil crisis, when the Organization of Petroleum Exporting Countries (OPEC) constrained the worldwide supply of oil. Both events, combined with the overall energy shortage that characterized the 1970s, resulted in actual or relative scarcity of raw materials. The price controls resulted in shortages at the point of purchase, causing, for example, queues of consumers at fuelling stations and increased production costs for industry.

Recent views.

Through the mid-1970s, it was alleged that none of the major macroeconomic models (Keynesian, New Classical, and monetarist) were able to explain stagflation.  Later, an explanation was provided based on the effects of adverse supply shocks on both inflation and output. According to Blanchard (2009), these adverse events were one of two components of stagflation; the other was "ideas"—which Robert Lucas, Thomas Sargent, and Robert Barro were cited as expressing as "wildly incorrect" and "fundamentally flawed" predictions (of Keynesian economics) which, they said, left stagflation to be explained by "contemporary students of the business cycle". In this discussion, Blanchard hypothesizes that the recent oil price increases could trigger another period of stagflation, although this has not yet happened (pg. 152).

Neoclassical views.

A purely neoclassical view of the macroeconomy rejects the idea that monetary policy can have real effects. Neoclassical macroeconomists argue that real economic quantities, like real output, employment, and unemployment, are determined by real factors only. Nominal factors like changes in the money supply only affect nominal variables like inflation. The neoclassical idea that nominal factors cannot have real effects is often called "monetary neutrality" or also the "classical dichotomy".  Since the neoclassical viewpoint says that real phenomena like unemployment are essentially unrelated to nominal phenomena like inflation, a neoclassical economist would offer two separate explanations for'stagnation' and 'inflation'. Neoclassical explanations of stagnation (low growth and high unemployment) include inefficient government regulations or high benefits for the unemployed that give people less incentive to look for jobs. Another neoclassical explanation of stagnation is given by real business cycle theory, in which any decrease in labour productivity makes it efficient to work less. The main neoclassical explanation of inflation is very simple: it happens when the monetary authorities increase the money supply too much.  In the neoclassical viewpoint, the real factors that determine output and unemployment affect the aggregate supply curve only. The nominal factors that determine inflation affect the aggregate demand curve only. When some adverse changes in real factors are shifting the aggregate supply curve left at the same time that unwise monetary policies are shifting the aggregate demand curve right, the result is stagflation.  Thus the main explanation for stagflation under a classical view of the economy is simply policy errors that affect both inflation and the labour market. Ironically, a very clear argument in favour of the classical explanation of stagflation was provided by Keynes himself. In 1919, John Maynard Keynes described the inflation and economic stagnation gripping Europe in his book "The Economic Consequences of the Peace". Keynes wrote:  Lenin is said to have declared that the best way to destroy the Capitalist System was to debauch the currency. By a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens. By this method they not only confiscate, but they confiscate arbitrarily; and, while the process impoverishes many, it actually enriches some. [...] Lenin was certainly right. There is no subtler, no surer means of overturning the existing basis of society than to debauch the currency. The process engages all the hidden forces of economic law on the side of destruction, and does it in a manner which not one man in a million is able to diagnose.  Keynes explicitly pointed out the relationship between governments printing money and inflation.  The inflationism of the currency systems of Europe has proceeded to extraordinary lengths. The various belligerent Governments, unable, or too timid or too short-sighted to secure from loans or taxes the resources they required, have printed notes for the balance.  Keynes also pointed out how government price controls discourage production.  The presumption of a spurious value for the currency, by the force of law expressed in the regulation of prices, contains in itself, however, the seeds of final economic decay, and soon dries up the sources of ultimate supply. If a man is compelled to exchange the fruits of his labours for paper which, as experience soon teaches him, he cannot use to purchase what he requires at a price comparable to that which he has received for his own products, he will keep his produce for himself, dispose of it to his friends and neighbours as a favour, or relax his efforts in producing it. A system of compelling the exchange of commodities at what is not their real relative value not only relaxes production, but leads finally to the waste and inefficiency of barter.  Keynes detailed the relationship between German government deficits and inflation.  In Germany the total expenditure of the Empire, the Federal States, and the Communes in 1919–20 is estimated at 25 milliards of marks, of which not above 10 milliards are covered by previously existing taxation. This is without allowing anything for the payment of the indemnity. In Russia, Poland, Hungary, or Austria such a thing as a budget cannot be seriously considered to exist at all. Thus the menace of inflationism described above is not merely a product of the war, of which peace begins the cure. It is a continuing phenomenon of which the end is not yet in sight.

Keynesian in the short run, classical in the long run.

While most economists believe that changes in money supply can have some real effects in the short run, neoclassical and neo-Keynesian economists tend to agree that there are no long-run effects from changing the money supply. Therefore, even economists who consider themselves neo-Keynesians usually believe that in the long run, money is neutral. In other words, while neoclassical and neo-Keynesian models are often seen as competing points of view, they can also be seen as two descriptions appropriate for different time horizons. Many mainstream textbooks today treat the neo-Keynesian model as a more appropriate description of the economy in the short run, when prices are'sticky', and treat the neoclassical model as a more appropriate description of the economy in the long run, when prices have sufficient time to adjust fully.  Therefore, while mainstream economists today might often attribute short periods of stagflation (not more than a few years) to adverse changes in supply, they would not accept this as an explanation of very prolonged stagflation. More prolonged stagflation would be explained as the effect of inappropriate government policies: excessive regulation of product markets and labor markets leading to long-run stagnation, and excessive growth of the money supply leading to long-run inflation.

Alternative views.

As differential accumulation.

Political economists Jonathan Nitzan and Shimshon Bichler have proposed an explanation of stagflation as part of a theory they call differential accumulation, which says firms seek to beat the average profit and capitalisation rather than maximise. According to this theory, periods of mergers and acquisitions oscillate with periods of stagflation. When mergers and acquisitions are no longer politically feasible (governments clamp down with anti-monopoly rules), stagflation is used as an alternative to have higher relative profit than the competition. With increasing mergers and acquisitions, the power to implement stagflation increases.  Stagflation appears as a societal crisis, such as during the period of the oil crisis in the 70s and in 2007 to 2010. Inflation in stagflation, however, does not affect all firms equally. Dominant firms are able to increase their own prices at a faster rate than competitors. While in the aggregate no one appears to profit, differentially dominant firms improve their positions with higher relative profits and higher relative capitalisation. Stagflation is not due to any actual supply shock, but because of the societal crisis that hints at a supply crisis. It is mostly a 20th and 21st century phenomenon that has been mainly used by the "weapondollar-petrodollar coalition" creating or using Middle East crises for the benefit of pecuniary interests.

Demand-pull stagflation theory.

Demand-pull stagflation theory explores the idea that stagflation can result exclusively from monetary shocks without any concurrent supply shocks or negative shifts in economic output potential. Demand-pull theory describes a scenario where stagflation can occur following a period of monetary policy implementations that cause inflation. This theory was first proposed in 1999 by Eduardo Loyo of Harvard University's John F. Kennedy School of Government.

Supply-side theory.

Supply-side economics emerged as a response to US stagflation in the 1970s. It largely attributed inflation to the ending of the Bretton Woods system in 1971 and the lack of a specific price reference in the subsequent monetary policies (Keynesian and Monetarism). Supply-side economists asserted that the contraction component of stagflation resulted from an inflation-induced rise in real tax rates (see bracket creep)

Austrian School of economics.

Adherents to the Austrian School maintain that creation of new money ex nihilo benefits the creators and early recipients of the new money relative to late recipients. Money creation is not wealth creation; it merely allows early money recipients to outbid late recipients for resources, goods, and services. Since the actual producers of wealth are typically late recipients, increases in the money supply weakens wealth formation and undermines the rate of economic growth. Says Austrian economist Frank Shostak:  "The increase in the money supply rate of growth coupled with the slowdown in the rate of growth of goods produced is what the increase in the rate of price inflation is all about. (Note that a price is the amount of money paid for a unit of a good.) What we have here is a faster increase in price inflation and a decline in the rate of growth in the production of goods. But this is exactly what stagflation is all about, i.e., an increase in price inflation and a fall in real economic growth. Popular opinion is that stagflation is totally made up. It seems therefore that the phenomenon of stagflation is the normal outcome of loose monetary policy. This is in agreement with [Phelps and Friedman (PF)]. Contrary to PF, however, we maintain that stagflation is not caused by the fact that in the short run people are fooled by the central bank. Stagflation is the natural result of monetary pumping which weakens the pace of economic growth and at the same time raises the rate of increase of the prices of goods and services."

Jane Jacobs and the influence of cities on stagflation.

In 1984, journalist and activist Jane Jacobs proposed the failure of major macroeconomic theories to explain stagflation was due to their focus on the nation as the salient unit of economic analysis, rather than the city. She proposed that the key to avoiding stagflation was for a nation to focus on the development of "import-replacing cities" that would experience economic ups and downs at different times, providing overall national stability and avoiding widespread stagflation. According to Jacobs, import-replacing cities are those with developed economies that balance their own production with domestic imports—so they can respond with flexibility as economic supply and demand cycles change. While lauding her originality, clarity, and consistency, urban planning scholars have criticized Jacobs for not comparing her own ideas to those of major theorists (e.g., Adam Smith, Karl Marx) with the same depth and breadth they developed, as well as a lack of scholarly documentation. Despite these issues, Jacobs' work is notable for having widespread public readership and influence on decision-makers.

Responses.

Stagflation undermined support for the Keynesian consensus.  Federal Reserve chairman Paul Volcker very sharply increased interest rates from 1979–1983 in what was called a "disinflationary scenario". After U.S. prime interest rates had soared into the double-digits, inflation did come down; these interest rates were the highest long-term prime interest rates that had ever existed in modern capital markets. Volcker is often credited with having stopped at least the inflationary side of stagflation, although the American economy also dipped into recession. Starting in approximately 1983, growth began a recovery. Both fiscal stimulus and money supply growth were policy at this time. A five- to six-year jump in unemployment during the Volcker disinflation suggests Volcker may have trusted unemployment to self-correct and return to its natural rate within a reasonable period.

In economics, stagflation or recession-inflation is a situation in which the inflation rate is high, the economic growth rate slows, and unemployment remains steadily high. It presents a dilemma for economic policy, since actions intended to lower inflation may exacerbate unemployment.

La stagflation est la situation d'une économie qui souffre simultanément d’une croissance économique faible ou nulle et d'une forte inflation (c’est-à-dire une croissance rapide des prix). Cette situation est souvent accompagnée d'un taux de chômage élevé, ce qui contredit ce qu'énonce le Carré magique de Kaldor.


Backward compatibility.

The LSB is designed to be binary-compatible and produce a stable application binary interface (ABI) for independent software vendors. To achieve backward compatibility, each subsequent version is purely additive. In other words, interfaces are only added, not removed. The LSB adopted an interface deprecation policy to give application developers enough time in case an interface is removed from the LSB.  This allows the developer to rely on every interface in the LSB for a known time and also to plan for changes, without being surprised. Interfaces are only removed after having been marked "deprecated" for at least three major versions, or roughly eleven years.  LSB 5.0 is the first major release that breaks backward compatibility with earlier versions.

ISO standard.

The LSB is registered as an official ISO standard. The main parts of it are:  There is also ISO/IEC TR 24715:2006 which identifies areas of conflict between ISO/IEC 23360 (the Linux Standard Base 3.1 specification) and the ISO/IEC 9945:2003 (POSIX) International Standard.  ISO/IEC 23360 and ISO/IEC TR 24715 can be freely downloaded from ISO website.

Reception.

While the LSB is a standard and without a competitor, it is followed only by few Linux distributions. For instance, only 21 distribution releases (versions) are certified for LSB version 4.0, notably Red Flag Linux Desktop 6.0, Red Hat Enterprise Linux 6.0, SUSE Linux Enterprise 11, and Ubuntu 9.04 (Jaunty Jackalope); even fewer are certified for version 4.1.  The LSB has been criticized for not taking input from projects, most notably the Debian project, outside the sphere of its member companies.

Choice of the RPM package format.

The LSB specifies that software packages should either be delivered as an LSB-compliant installer, or (preferably) be delivered in a restricted form of the RPM Package Manager format.  This choice of package format precludes the use of the many other, existing package formats not compatible with RPM. To address this, the standard does not dictate which package format the system must use for its own packages, merely that RPM must be supported to allow packages from third-party distributors to be installed on a conforming system.

Limitations on Debian.

Debian has included optional support for the LSB early on, at version 1.1 in "woody" (3.0; ), 2.0 in "sarge" (3.1; ), 3.1 in "etch" (4.0; ), 3.2 in "lenny" (5.0; ) and 4.1 in "wheezy" (7; ). To use foreign LSB-compliant RPM packages, the end-user needs to use Debian's Alien program to transform them into the native package format and then install them.  The LSB-specified RPM format has a restricted subset of RPM features—to block usage of RPM features that would be untranslatable to.deb with Alien or other package conversion programs, and vice versa, as each format has capabilities the other lacks. In practice, not all Linux binary packages are necessarily LSB-compliant, so while most can be converted between.rpm and.deb, this operation is restricted to a subset of packages.  By using Alien, Debian is LSB-compatible for all intents and purposes, but according to the description of their lsb package, the presence of the package "does not imply that we believe that Debian fully complies with the Linux Standard Base, and should not be construed as a statement that Debian is LSB-compliant."  Debian strived to comply with the LSB, but with many limitations. However, this effort ceased around July 2015 due to lack of interest and workforce inside the project. In September 2015, the Debian project confirmed that while support for Filesystem Hierarchy Standard (FHS) would continue, support for LSB had been dropped. Ubuntu followed Debian in November 2015.

Quality of compliance test suites.

Additionally, the compliance test suites have been criticized for being buggy and incomplete—most notably, in 2005 Ulrich Drepper criticized the LSB for poorly written tests which can cause incompatibility between LSB-certified distributions when some implement incorrect behavior to make buggy tests work, while others apply for and receive waivers from complying with the tests. He also denounced a lack of application testing, pointing out that testing only distributions can never solve the problem of applications relying on implementation-defined behavior.  For the vendors considering LSB certifications in their portability efforts, the Linux Foundation sponsors a tool that analyzes and provides guidance on symbols and libraries that go beyond the LSB.

The Linux Standard Base (LSB) is a joint project by several Linux distributions under the organizational structure of the Linux Foundation to standardize the software system structure, including the Filesystem Hierarchy Standard used in the Linux kernel. The LSB is based on the POSIX specification, the Single UNIX Specification (SUS), and several other open standards, but extends them in certain areas.

La Linux Standard Base (abréviation : LSB) est un projet joint par nombre de distributions Linux sous la structure organisationnelle du afin de concevoir et standardiser la structure interne des systèmes d'exploitation basés sur GNU/Linux. La LSB est basée sur les spécifications POSIX, la « spécification unique d'UNIX », ainsi que sur d'autres nombreux standards ouverts, mais l'étend dans certains domaines.


Biography.

Early life and political career.

He was born at Pontedera, Tuscany, and was an early member of the Christian Movement founded by the Catholic priest don Romolo Murri in 1902. He obtained his first degree in literature and philosophy at the "Scuola Normale Superiore di Pisa". Between 1911 and 1915 he then worked as a high-school teacher of classics in several Italian towns (Parma, Massa di Carrara, Bergamo and Monza).  He volunteered for military service in the First World War and when it was over he became in 1919 one of the founding members of the Catholic Italian Popular Party. He was elected to represent Pisa in both the parliamentary elections of 1919 and 1921. A trade-union leader in the Italian Confederation of Christian Workers, in 1922–1923 he served in the first government of Benito Mussolini as Under-secretary for Industry and Commerce. In April 1923, however, a national meeting of the Popular Party held in Turin decided to withdraw all PPI representatives from the government. He then went back to his role in the leadership of the Catholic trade unions, and tried to face the daily violence brought against them by the fascist squads.  In 1924, after Luigi Sturzo had resigned as Secretary of the PPI, Gronchi became leader of the party, together with two other "triumvirs", (Spataro and Rodinò). Re-elected to Parliament in the same year, he joined the anti-fascist opposition of the so-called Aventine Secession (from the hill in Rome where the opposition withdrew from Parliament). In 1926 he was expelled from Parliament by the new regime.  In the years between 1925 and 1943 he thus interrupted his political career. In order to avoid having to become a member of the Fascist Party, he also resigned his position as a schoolteacher, and earned his living as a successful businessman, first as a salesman and then as an industrialist.

After the Second World War.

In 1943–1944 he was a co-founder of the new Christian-Democratic party (DC), and became a leader of its left-wing faction, together with men like Giorgio La Pira, Giuseppe Dossetti and Enrico Mattei (the future boss of ENI, the Italian government-owned petrochemical giant). He was also a member of the Comitato di Liberazione Nazionale, the multi-party committee of the Italian Resistance, as a representative of his party.  Although often in conflict with his party’s majority and its Secretary Alcide De Gasperi, he served as Industry minister in 1944–1946 and as a member of the Constituent Assembly in 1946. In 1947, as the Cold War began, he vehemently opposed his party’s decision to expel the Italian Communist and Socialist parties from the national government. From 1948 to 1955 he was elected President of the Italian Chamber of Deputies (the lower branch of Parliament).

President of the Republic.

In 1955 Luigi Einaudi’s term as first President of the Italian Republic came to an end, and Parliament had to choose his successor. The new Secretary of the DC, Amintore Fanfani, was promoting for the job the liberal Cesare Merzagora, who was then President of the Senate. However the extreme right-wing of the party – led by Giuseppe Pella, Guido Gonella, Salvatore Scoca and Giulio Andreotti – joined hands with the trade-unionist left – led by Giovanni Pastore, Giorgio Bo and Achille Marazza – in an "uprising" against the party leadership, in order to get Giovanni Gronchi ("Parliament's man") elected instead. The move had the support of the Communist and Socialist parties, and also of the monarchic and neo-fascist right. After a bitter battle and the final crumbling of the centrist front, on 29 April 1955 Gronchi was elected President of the Republic with 658 votes out of 883. He was the first Catholic politician to become Head of the Italian State.  His period in office lasted until 1962. It was marked by the ambition to bring about a gradual “opening to the left”, whereby the Socialists and the Communist Party would be brought back into the national government, and Italy would abandon NATO, becoming a non-aligned country. There was however stiff parliamentary opposition to this project, particularly by the small Italian Liberal Party, which was deemed a necessary ingredient of any viable majority.  In an attempt to escape the deadlock, in 1959 Gronchi appointed as prime minister a trusted member of his own Catholic left-wing faction, Fernando Tambroni, sending him to Parliament with a “President’s government” but no pre-arranged majority. However Tambroni found himself surviving in Parliament only thanks to neo-fascist votes. This unforeseen “opening to the right” had serious consequences. In 1960 there were bad riots in several towns of Italy, particularly at Genoa, Licata and Reggio Emilia, where the police opened fire on demonstrators, killing five people. The Tambroni government thus ended in ignominy; forced to resign, it was followed by an all-DC government, with a traditionally centrist parliamentary majority.  The unhappy Tambroni experiment tarnished Gronchi’s reputation for good, and until the end of his period of office he remained a lame-duck President. In 1962 he attempted to get a second mandate, with the powerful help of Enrico Mattei, but the attempt failed and Antonio Segni was elected instead. As he ceased to be Head of State, he became a life senator by right, according to the Italian Constitution. He died in Rome on 17 October 1978 at the age of 91.

Assessment.

For an overall historical assessment of his presidency it must certainly kept in mind the Tambroni failure, with its suggestion of an authoritarian approach. Yet an “opening to the left” of sorts did in fact happen soon after his mandate was over. Indeed, the first center-left coalition was formed by Aldo Moro as soon as 1964, when the Socialists (but not the Communists) entered the government. In the 1970s, the Christian Democrats and Communists made efforts toward what was called the Historic Compromise. On this basis he might be credited with some important foresight and a lasting influence.  Still, it is hard to maintain that his political project had really very much to do with the center-left governments that followed each other between 1964 and 1992. During most of this period the Communists were isolated even more tightly than before, due to the loss of their former Socialist allies and the bitter conflict that followed with them, particularly after Bettino Craxi became the Socialist leader. Outside influences were later revealed to be at work as well. A 2000 Parliament Commission report concluded that the strategy and operations by the clandestine, US-supported, "stay-behind" Gladio was designed to "stop the PCI, and to a certain degree also the PSI [Italian Socialist Party], from achieving executive power in the country". In any case, Italy kept its socio-economic structure as a market economy and its foreign policy alignment.

Personal life.

In 1941, Gronchi married Carla Bissatini (2 September 1912 – 14 August 1993) and had one son and one daughter.

Giovanni Gronchi (; 10 September 1887 – 17 October 1978) was a Christian Democratic Italian politician who served as the third President of Italy from 1955 to 1962 and was marked by a controversial and failed attempt to bring about an "opening to the left" in Italian politics. He was reputed the real holder of the executive power in Italy from 1955 to 1962, backward the various Prime Ministers of this time.

Giovanni Gronchi, né le à Pontedera, près de Pise, et mort le à Rome, est un homme d'État italien, d'obédience démocrate-chrétienne. Plusieurs fois ministre, il est président de la Chambre des députés de 1948 à 1955, puis président de la République italienne de 1955 à 1962. Il est également sénateur à vie de 1962 à 1978.


Description.

It has a narrow, creeping stem that readily roots at the nodes. The trifoliate leaves are subdivided into three rounded leaflets and resemble a clover in shape. Some varieties have green leaves, while others, like "Oxalis corniculata" var. "atropurpurea", have purple. The leaves have inconspicuous stipules at the base of each petiole.  The fruit is a narrow, cylindrical capsule, long, and noteworthy for its explosive discharge of the contained seeds, long. Pollen is about 34 microns in diameter.

Distribution.

This species probably comes from southeastern Asia. It was first described by Linnaeus in 1753 using specimens from Italy, and it seems to have been introduced to Italy from the east before 1500. It is now cosmopolitan in its distribution and is regarded as a weed in gardens, agricultural fields, and lawns.

Uses.

The leaves of woodsorrel are quite edible, with a tangy taste of lemons. A drink can be made by infusing the leaves in hot water for about 10 minutes, sweetening and then chilling. The entire plant is rich in vitamin C. Any woodsorrel is safe in low dosages, but if eaten in large quantities over a length of time can inhibit calcium absorption by the body.  As a hyperaccumulator of copper, it can be used for phytoremediation. The 1491 Ming Dynasty text, "Precious Secrets of the Realm of the King of Xin", describes how to locate underground copper deposits by extracting trace elements of copper from the plant.

Oxalis corniculata, the creeping woodsorrel, also called procumbent yellow sorrel or sleeping beauty, resembles the common yellow woodsorrel, "Oxalis stricta". It is a somewhat delicate-appearing, low-growing, herbaceous plant in the family Oxalidaceae.

L'Oxalide corniculée ou Oxalis corniculé (Oxalis corniculata) est une petite plante vivace du genre des Oxalis de la famille des Oxalidacées, adventice des jardins, utilisée dans les médecines traditionnelles.


History.

University Lyon 3 was established in the early 1970s (26 July 1973), a division of teachers following the events of May 68 that rocked the academic world. There are also departments of geography-planning, the engineer of the countryside in Annecy and history, and a faculty of philosophy with more than 90 doctoral students. All three public universities in Lyon (Lyon 1, Lyon 2, Lyon 3) are derivative of the former University of Lyon established in 1896.  The university has steadily expanded its international relations and has relations with universities in various countries.  Because of past extreme-right tendencies of some of its staff, the university was accused in the 1980s and 1990s of complacency with regard anti-Semitic and racist elements. The Report on racism and Holocaust denial at the University Jean Moulin-Lyon 3, prepared under the direction of Henry Rousso at the request of the Minister of Education and released in October 2004, showed that the number of teachers involved was limited.

Campuses.

The university is located on three different campuses: the first one, called "Les Quais", is by the Rhône (river), the second, called "Manufacture des Tabacs" in the SE part of Lyon, and the last one in Bourg-en-Bresse (Ain department).

Faculty of Law.

The Lyon Law School, was created by decree issued on 29 October 1875, by Marshal Mac Mahon, was inaugurated by French President Felix Faure on 1 May 1896. The Faculty of Law of Lyon celebrates 130 years, largest centre for law students from the city of Lyon, it has all the legal training of the first year Degree tray until 8 (or more). The Lyon Law school enjoys a national and international reputation of distinction. In the latest edition of the Gourman Report (6th ed, 1993), it was ranked 1st among France's provincial universities, and 5th among European universities, behind Paris, Oxford, Cambridge and Heidelberg.  The Law School has always been in touch with foreign legal systems. Before the First World War, the Lyon Law School founded the Law school of Beirut, in Lebanon. These two cities, Lyon and Beirut, were both on one of Silk Roads, which started in China and ended in Lyon ; intellectual, artistic and industrial interests converged. The Institute of Comparative Law was created by Édouard Lambert in 1920, and now bears his name. Just before he passed away, this great comparative law specialist wrote the Egyptian Civil Code, which is still in effect today and has hardly been amended. Cambodia was also the scene of the development of the Lyon Law School, before the Vietnam War. Quite frequently, the Dean of the Lyon Law School had previously been or was to become a Dean in Beirut or Phnom Penh.  The law school is known for research of history of law and family law. It is also famous in the field of Business Law, thanks to its master's degree in Business and Tax law, coupled with the most famous degree in the field of business Law in France: (DJCE stands for "Diplôme de Juriste Conseil en Entreprise" or Corporate Jurist Diploma in English). The Faculty of law also proposes the preparation of master 2 business and financial engineering ranked 7th, Master 2 audiovisual & media law ranked 4th among the best master's degrees by SMBG 2015. The Law faculty also includes the department of political science : international relations (international security, diplomacy, francophone studies) propose the preparation of master 2 international relations ranked 5th among the best master's degrees in international security and defense by SMBG ranking 2015. In 2008, it launched its own LL.M in International and European Law. The law school offers several joint programs in business law with EM Lyon business school, in criminal science with the faculty of medicine of university of Lyon, in security studies with France’s National Police College.  The faculty organise conferences with INTERPOL, and Handicap International on a regular basis..

Faculty of Philosophy.

The professorial staff of the Faculty of Philosophy of Lyon 3 includes, or has included :

School of business administration.

The IAE, standing for Institut d'Administration des Entreprises (Institute of business administration), is the school of business of the Jean Moulin University Lyon 3. Also known as the IAE of Lyon, its main campus is located in the historical complex of the "Manufacture des Tabacs" in the heart of Lyon, France.  Founded in 1956 the IAE of Lyon has 6300 students in 2007 (including 2000 in postgraduate studies), accounting for more than 28% of the 22,300 students at Lyon 3 University.  In addition to the 150 some professors at the IAE, 400 executives from private, external companies contribute to the education.  The various courses offered include four bachelor's degrees (Licence), eight professional bachelor's degrees (Licence professionnelles), nine master's degrees (with 40 specializations) and preparatory courses for the chartered accountants examination.  The IAE of Lyon is one of the top French institutions for research and training in management. The school is highly internationalized and has an alumni network of 30,000 former students throughout the world.

Faculty of Arts.

The Faculty of Arts of Lyon complements and collaborates with the University Lyon 2 and the ENS de Lyon.  It offers courses in French literature and the Classics. The faculty also in includes departments of history, geography, and media and communication.

Faculty of languages.

The Faculty of Languages of Lyon 3 includes studies in foreign languages and civilizations (the LCE), learning of foreign literatures, cultures, history of languages.  Foreign languages:  There is also the opportunity to study applied foreign languages.

Notable alumni.

(*prior the division of the University of Lyon).  (*prior the division of the University of Lyon).

Students.

The biggest school in terms of number of students is the Faculty of Law (10,460), the Business School (IAE) with (8,578). Then comes, the Faculty of Languages (4851) and the Faculty of Arts (13%). Other students attend the Faculty of Philosophy, or programmes such as professional short-term degree. [2005 figures]

Jean Moulin University Lyon 3 (), also referred to as Jean Moulin or Lyon III, is a multidisciplinary public university in Lyon, France, based in Law and social sciences. It is under the purview of the Academy of Lyon. A total of 29,000 students study there for undergraduate and posgraduate degrees. It has three campuses in Lyon. The university is a member of the University of Lyon, the Coimbra Group and the European University Association (EUA).

L’université Jean-Moulin-Lyon-, de nom d’usage « université Jean Moulin », également dite « Lyon » ou « Lyon 3 », est une université française située à Lyon, ainsi qu'à Bourg-en-Bresse. C'est l'une des quatre universités de l'académie de Lyon. Elle est issue d’une scission organisée par plusieurs enseignants de l'université Lyon II en 1973 et est membre fondateur de l'université de Lyon.


History.

The earliest known inhabitation of the area dates back 12,000 years, according to archaeologists, evidenced by recent finds. Excavations unearthed a campsite with firepit and more than 600 artifacts including stone tool fragments and arrowheads.  The area of the present-day city of Fredericton was first used for seasonal farming by the Maliseet peoples. Maliseet cultivated food plants including: beans, pumpkins, Jerusalem artichokes, ground nuts, and maize on the river banks and islands of the Saint John River. In the mid-18th century their principal village of Aucpaque was located several kilometres upriver from the site of present-day Fredericton.

Colonial history (1690–1867).

The first European contact was by the French in the late 17th century. Joseph Robineau de Villebon received a land grant and was appointed governor of Acadia. During King William's War, Villebon built Fort Nashwaak on the north side of the Saint John River, at the mouth of the Nashwaak River. For most of the war, Fort Nashwaak served as the capital of the French colony of Acadia; forces from here conducted numerous military raids on English settlers on the New England/ Acadia border.  French and English hostilities continued along the border. Within weeks of an attack of French and Indigenous forces launched

Modern history (1867–present).

The building constructed to house the colonial-era legislative assembly in 1788 was destroyed by a fire in 1880. Two years later, the present Legislature Building was constructed.  The first major expansion of the city occurred on 1 July 1945 when it amalgamated with the town of Devon. Today the city of Fredericton comprises Fredericton proper, and the boroughs of Silverwood, Nashwaaksis, Barker's Point and Marysville, which were incorporated into the city in 1973.  The commemorative brass cenotaph plaques were stolen in October 2015, and were replaced by replicas cast by an Amherst foundry called Liberty Enterprises.  One of the communities amalgamated into Fredericton in 1973, Marysville, has a unique and distinctive history of its own. Marysville is located on the Nashwaak River, a tributary of the Saint John River, just north of pre-1973 Fredericton. The community is distinguished by its 19th-century mill and historic

Geography.

The Saint John River runs through Fredericton, with most of the city's post-war suburban development occurring on the gently sloping hills on either side of the river (although the downtown core is flat and lies low to the river).  At an altitude of about above sea level, Fredericton is nestled in the Pennsylvanian Basin. It differs markedly from the geologically older parts of the province. There are prominently two distinct areas in the region that are divided around the area of Wilsey Road, in the east end of the city. In the west side, the bedrock underneath the earth is topographically dominant, whereas the other is controlled by Pleistocene and recent deposits leading to the rivers (resulting in the area being shallow and wide). Fredericton and its surroundings are rich in water resources, which, coupled with highly arable soil, make the Fredericton region ideal for agriculture. The Saint John River and one of its major tributaries, the Nashwaak River, come together in Fredericton. The uninhabited parts of the city are heavily forested.

Climate.

Fredericton has a humid continental climate (Köppen climate classification "Dfb"). The average January low temperature is, while the average high in July is. On average, Fredericton receives approximately of precipitation per year. Snowfall is common between late November and early April, and snow usually stays on

Administration.

Municipal.

Fredericton has a mayor-council and non-partisan form of government, with the mayor and council serving fixed four-year terms (three years until 2004), and elections held in May. The current mayor is Mike O'Brien, who was elected in 2016.

Federal and provincial.

Provincially, Fredericton elected Progressive Conservatives from 1952 until electoral sweep of the Liberal Party in 1987 when they won every seat in New Brunswick under Frank McKenna. Since then there has been greater political alteration in the provincial electoral landscape in Fredericton.  In 1991, the right-wing Confederation of Regions Party won the riding of Fredericton North (along with several other nearby ridings). In 1999 Progressive Conservatives swept all three Fredericton area seats; however, in 2003, Fredericton North and Fredericton-Fort Nashwaak returned to the Liberals.  Following the electoral redistribution in 2013, the city includes the provincial ridings

Cityscape.

Architecturally, Fredericton spans more than two centuries. The city features an eclectic mix of buildings and residences ranging from classical Victorian style to modern office buildings and architecture. Fredericton's skyline is also distinguished by many historic churches. There are 12 National Historic Sites of Canada in Fredericton.  Neighbourhoods in Fredericton include:  The City of Fredericton is bisected by the Saint John River. This has created two distinctive regions of the city characterized as the "Northside" and the "Southside". The Southside is characterized by a downtown core consisting of provincial government departments, historical buildings, and numerous business establishments, banks, and law firms. Downtown also hosts many of the city's cultural attractions, such as The Playhouse, the Fredericton Region Museum (formerly the York-Sunbury Museum), the Beaverbrook Art Gallery and Science East, New Brunswick's science centre. Many notable historical buildings are also located in or near downtown, including grand Victorian-era residences, the New Brunswick Legislative Building, and Christ Church Cathedral. South of downtown, the city's elevation rises along a sloping hill (part of the river valley feature of the city).  "The Hill", as it is called, includes an area known as "College Hill", where the adjoining campuses of the University of New Brunswick and St. Thomas University are located, slightly southeast of the downtown area. Southwest of the universities on the

Culture.

Due to the presence of the universities, Fredericton is more cosmopolitan than many cities its size. This is reflected in cuisine offered by local ethnic restaurants (which include Caribbean, Chinese, Greek, Indian, Korean, Italian, Japanese, Lebanese, Mexican, Pakistani and Vietnamese foods). There are also several retail outlets that sell ethnic products and artifacts. The federal government named Fredericton the "Cultural Capital of Canada" for the year 2009. Officers' Square is an outdoor public space located at the centre of the city. It serves as a venue for outdoor concerts during the summer, featuring a variety of local and national talent. During the winter, Officers' Square is transformed into an outdoor skating rink.

Arts.

Fredericton is an important cultural centre of the region featuring art galleries, the New Brunswick College of Craft and Design, museums and theatres which promote local artistic and literary talent. The Beaverbrook Art Gallery is New Brunswick's provincial art gallery. It was established in 1959 by Lord Beaverbrook as a gift to his native province. Fredericton is also home to several commercial art galleries.  The Playhouse hosts plays and musicals throughout the year, as well as presenting visiting comedians and musical performances by both Canadian and international artists. The Playhouse is the main venue for Theatre New Brunswick (TNB). TNB was founded by prominent Canadian director Walter Learning in 1969, and is the province's largest professional theatre company.  Every fall Fredericton hosts the Harvest Jazz & Blues Festival. The week-long festival draws artists from all over North America. Since its inception in 1991, the event has grown into a large, diverse festival which has attracted artists

Attractions.

Parks and public spaces.

Fredericton contains many public parks featuring preserved forest lands - such as Odell Park and Reading Park. Odell Park is adjacent to the Fredericton Botanic Garden. Furthermore, Fredericton features tree-lined streets and elm trees in particular which have earned the city its nickname "The City of Stately Elms". Fredericton's parks and public spaces include:

Sports.

There are no professional sports teams in Fredericton, although both universities have extensive athletic programs. The UNB Reds and St. Thomas Tommies are rivals in most sports. When their women's hockey teams play (St. Thomas University has no men's hockey program in the Atlantic University Sport), the matches are called the "Battle of the Hill". The first National Championship ever won by UNB was in the fall of 1980. The men's soccer team under the leadership of Coaches Gary Brown and Robin Hopper defeated Sir Wilfrid Laurier 3-1 on a frigid day in November. The UNB Reds men's hockey team has experienced recent success in national competition, winning Canadian Interuniversity Sport (now known as U Sports) championships in the 1997–98, 2006–07, 2008–09, 2010–11, 2012-13, 2015–16, 2016-17, and 2018-19 seasons (8 titles). They have also finished in second place in the 1996–97,1999-2000, 2003–04, 2007–2008, and 2014-15 championships. This success has produced two milestones of note: first, between 2013 and 2019 (7 years), only UNB (with 3 wins) and the Alberta Golden Bears (with 4 wins) have won the David Johnston University Cup

Demographics.

The population of the city of Fredericton is 58,220 (2016 Canada Census) and 101,760 for Greater Fredericton. Along with Moncton and Halifax, Fredericton is one of three Maritime cities to register a population increase in recent years.

Ethnicity.

Fredericton's population is predominantly white. However, a black minority has had a long presence in the city, primarily in the Barker's Point borough. Willie O'Ree, the first black player in the NHL, is from Fredericton. The largest non-white segment of Fredericton's population is made up of First Nations people, who live primarily on the Saint Mary's Reserve located in the

Language.

While a predominantly Anglophone city, the civil service has seen an increase in the city's Francophone population. This population is served by the Centre communautaire Sainte-Anne (which includes K-12 schooling, a radio station, a public library, and a cultural centre). In

Religion.

The residents of Fredericton are predominantly Christian, with Protestants forming the largest denomination. While the Roman Catholic population is not as large, the city does have the province's only

Economy.

During the 19th and early 20th centuries, the lumber industry, with its corresponding mills, was a primary sector of Fredericton's economy. Over the course of the 20th century, this industry declined and gave way to the provincial government and the universities becoming the primary employers in the city.  The policies of centralizing provincial government functions during the 1960s under New Brunswick Premier Louis Robichaud - along with the expanded role of the public sector characteristic of the 1960s/70s - led to a sizeable expansion of the city's population. It was during these decades that the Hill area on the city's Southside was largely developed and bedroom communities such as New Maryland emerged.  The 1960s also saw an expansion of the University of New Brunswick due to increased post-war university enrolment, as well as the construction of the Fredericton campus of Saint Thomas University. Also contributing to this expansion was the move of the Law School, now the University of New Brunswick Faculty of Law, from Saint John to the Fredericton area. This expansion of the post-secondary sector also contributed to Fredericton's population growth during the 1960s and 1970s. Since then, the city's population has

Education.

Primary and secondary education.

Fredericton's public schools are located in either the Anglophone West School District (formerly known as District 18, and prior to that, District 26) or the District Scolaire Francophone Sud (District 1). Fredericton is home to three public high schools, two operating in the English language and one in the French language. Fredericton High School, which was once the largest school in the Commonwealth of Nations, operates in English and primarily serves students living on Fredericton's south side. It is also one of the oldest public high schools in Canada, tracing its beginnings to 1785 – having celebrated its bicentennial in 1985. Fredericton High School is home to several sports teams – including basketball, hockey, soccer, and football – which dominated New Brunswick provincial high school sports championships during much of the 1980s and 1990s. The school motto is "Palma Non Sine Pulvere", Latin for "No Reward Without Effort" (literally "no palm without dust").  Leo Hayes High School, which opened in 1999, also operates in English and primarily serves students living on Fredericton's north side. The high

Post-secondary institutions.

Universities.

Fredericton's status as an educational centre is evident in the city's two degree-granting universities: the University of New Brunswick and St. Thomas University. The University of New Brunswick (UNB) was founded in 1785, making it the oldest public university in North America, compared to the oldest private university, Harvard University, in 1636. Built in 1826, UNB's Old Arts Building is the oldest university building still in use

Colleges.

Fredericton is also home to several colleges and similar institutions. The New Brunswick College of Craft and Design houses the province's leading programs in photography and visual arts. The Fredericton location of the New Brunswick Community College is on the campus of the University of New Brunswick. The

Other institutions.

Alongside Fredericton's more established universities, the city also is home to several online for-profit universities. University of Fredericton (UFred) and Yorkville University are operational. The University of Fredericton was founded in 2006, making it the youngest private university in Canada. It is a degree-granting online university providing certificate and graduate degree programs in business leadership. UFred offers MBA and EMBA Programs under Section 3 of the Degree Granting Act of the Province of New Brunswick in Canada. Yorkville offers graduate programs in counselling psychology and adult education. Meritus closed in 2012. These universities typically have offices downtown.

Research.

Fredericton hosts several major research centres - dealing with policy development, agriculture, forestry, and engineering. These research institutions are connected to the city's two universities as well as the provincial and federal governments.  The Hugh John Flemming Forestry Centre (including Provincial and Federal Departments) is the leading forestry research centre in Atlantic Canada. This Centre carries out major research endeavours in forestry management and scientific research. The Centre closely collaborates with the Forestry Department at the University of New Brunswick which is one of the top Forestry Departments in Canada. As well, research and development in agriculture and crop development is carried out at the Agricultural Research Station in Lincoln.

Transportation.

Air.

Air service is provided out of the Fredericton International Airport, located approximately 15 kilometres east of downtown in Lincoln. It is served by Air Canada Express, which operates direct flights to Toronto, Ottawa,

Public transit.

Fredericton Transit provides bus transit service to most areas of the city. All city buses feature bike racks so that cyclists can take advantage of bus services as well. Fredericton is also served by several taxi companies. The major companies in alphabetical order are: ABC Car Services, Checker Cab, George's Skycab, Loyal Taxi, Standard Taxi and Trius Taxi. Fredericton started installing bicycle lanes in July 2008, with a plan to establish 45 kilometres of on-street painted bicycle lanes, and 39 kilometres of signed bicycle routes, by 2011.  There is no rail service into

Roads.

Fredericton is located on the Trans-Canada Highway, which passes along the southern municipal boundary. Routes 7 and 8 (the latter being a former alignment of the Trans-Canada) also pass through the city. Two highway bridges, the Westmorland Street Bridge and the Princess Margaret Bridge, cross the Saint John River. Those bridges feed into controlled-access roads (Routes 8 and 105 serving the city's

Trail system.

Fredericton has a network of 25 trails totalling more than on both sides of the Saint John and Nashwaak Rivers. Many of the city trails are rail trails that follow old railway lines. These include the Old Train Bridge that spans across the Saint John River, providing a panoramic view of downtown Fredericton. The rail trail system in Fredericton is part of the Sentier NB Trail system and some of these trails are also part of the larger Trans-Canada Trail network. Some sections of the trail system are being paved to make it more accessible to non-motorized vehicles such as bicycles and wheelchairs.  Railway service through Fredericton was discontinued by CP Rail in fall 1993 and CN Rail in spring 1996. Following abandonment, both companies sold their right-of-ways to the provincial government which developed the trail network in partnership with the city and volunteer trail organizations. The trails are used by residents for walking, biking, and jogging and boast several scenic vistas along the Saint John and Nashwaak rivers as well as a mix of urban and wooded/natural scenery.  On the south side of the city, CP Rail's Fredericton Subdivision enters the city from Rusagonis-Waasis to the south, following the Wilsey Road and Beaverbrook Street to the former railway yard

Fredericton (; ) is the capital of the Canadian province of New Brunswick. The city is situated in the west-central portion of the province along the Saint John River, which flows west to east as it bisects the city. The river is the dominant natural feature of the area. One of the main urban centres in New Brunswick, the city had a population of 58,220 in the 2016 Canadian Census. It is the third-largest city in the province after Moncton and Saint John.

Fredericton (, ) est la capitale de la province du Nouveau-Brunswick au Canada. La ville est située sur les deux rives du fleuve Saint-Jean. La ville compte en 2011. Ses habitants sont les "Frédérictonnais(es)".