Background.

Following a series of disagreements between Philip VI of France () and Edward III of England (), on 24 May 1337 Philip's Great Council in Paris agreed that the lands held by Edward in France should be taken back into Philip's hands on the grounds that Edward was in breach of his obligations as a vassal. This marked the start of the Hundred Years' War, which was to last 116 years. In 1340 Edward claimed the French Crown, proclaiming himself the rightful heir through his mother, Isabella of France.  The English campaigned frequently on the continent, gaining a long run of military successes against larger forces across France. In 1356 a large French army was decisively defeated at the Battle of Poitiers, in which King John II of France (), the son and successor of King Philip, was captured. This eventually led to peace being agreed, and the Treaty of Brétigny was signed in 1360. It ceded large parts of south-west France to England as its sovereign territory, while Edward renounced all claims to the French throne. The terms of Brétigny were meant to untangle the feudal responsibilities that had caused so much conflict, and, as far as the English were concerned, would concentrate their territory in an expanded version of Aquitaine. This had been part of the English royal estate in France since the reign of Henry II (), and by the treaty it and Poitou became fiefdoms of Edward's oldest son, Edward the Black Prince. John was to pay three million écus as his ransom. The French were deeply unhappy with this arrangement.  In 1369, on the pretext that Edward had failed to observe the terms of the treaty, Charles V (), the son and heir of King John, declared war once again. In August a French offensive attempted to recapture castles in Normandy. Men who had fought in earlier English campaigns and had already won fortune and fame, were summoned from their retirements and new, younger men were given commands. Events went poorly for England almost from the start: James Audley and John Chandos, two important English commanders, were killed in the first six months; while the French made territorial gains in the west, re-occupying the strategic provincial capital of Poitiers and capturing many castles.

French strategy.

This period of the Hundred Years' War, starting in 1369 and known as the Carolinian phase, was significantly different from the previous one. The French were well prepared militarily, and immediately went on the offensive. Charles was well situated in terms of financial and human resources. Edward III was growing senile, his heir was crippled by illness, and once the turmoil of the previous phase of the war had subsided Charles was able to benefit from France having three times the population and wealth of England. The French also benefited from technological improvements, such as in barding, the armouring of horses.  Fighting during this phase took place largely in Aquitaine, meaning the English had extremely long borders to defend. These were easy for small French parties to penetrate, which they did to great effect. They relied on Fabian tactics: avoiding pitched battles and using attrition to wear down the English and only attacking dispersed or isolated English forces. This was now an offensive war for the French, and the English were ill-prepared for it.

English strategy.

The English planned to use two armies. One would operate out of Aquitaine in south-west France and be commanded by the experienced Black Prince. It would concentrate on reversing recent French gains in Poitou. This force was hampered by the Black Prince being so ill that he had to be transported in a litter. As a result, he was unable to lead the campaign personally and needed to delegate the command. The other English force would operate out of the English enclave of Calais in north-east France.  The north-eastern army was to be commanded by Robert Knolles, a veteran with considerable experience of independent command in the previous phase of the war and in the Breton War of Succession. Knolles contracted on 20 June to lead the King's army, although a week earlier he had agreed to share the command with Sir Alan Buxhull, Sir Thomas Grandison and Sir John Bourchier. On 1 July they were jointly appointed King's lieutenants. Both the King and his council were aware of the problems that could be caused by giving the overall command to Knolles, whose social status was lower than that of his peers. To prevent the English army from dividing and going separate waysand in what the historian Jonathan Sumption calls "a prescient precaution"the captains were required to sign a contract before they left agreeing not only to serve the King faithfully, but also not to allow any divisions to open up between them, and to make decisions collectively.

Prelude.

English movements.

Knolles landed at Calais in August 1370 with an army of between 4,000 and 6,000 mounted men. There he awaited further orders from the King. None were forthcoming, so he proceeded on a "meandering" plundering raid through northern France. According to the historian T. F. Tout, the French allowed Knolles and his army "to wander where he would". Knolles crossed north-eastern France using what by now was a traditional English tactic, the a large-scale mounted raid. This was intended not only to inflict as much destruction as possible on the countryside they passed through, but, by doing so, draw out the French army into a pitched battle. Journeying through the Somme region, Knolles made a show of force outside Reims, marched to Troyes, and then swung west to approach Paris from the direction of Nemours. As they marched, Knolles's army captured many towns, which they would then raze if the French refused to pay the ransoms the English demanded. He reached Paris on 24 September, but the city was well garrisoned and well defended. Knolles could not enter, and the French defenders would not leave their positions. He tried to draw them out to fight them in the open, but the French would not take the bait. The contemporary describes how, even though "the said English set fire to a great number of villages around Paris... the King was advised, for the better, that they should not then be fought with."  By October Knolles had moved south and was marching towards Vendôme. He captured and garrisoned castles and monasteries between the Rivers Loir and Loire and positioned himself to be able to march into either Poitou or southern Normandy. The former would enable him to support the Black Prince; the latter might be necessary if Edward concluded an agreement with Charles of Navarre, who was offering his lands in northern Normandy as a base for the English. Many of the subordinate captains, who considered themselves better-born than Knolles, deplored his apparent lack of martial spirit. They found a leader in Sir John Minsterworth, an ambitious but unstable knight from the Welsh Marches, who mocked Knolles as "the old freebooter". Much of Knolles's strategy was based on that employed in the campaigns of the 1340s and 1350s; particularly the capturing of enemy fortresses, to either garrison them with English troops or levy a ransom. Meanwhile, the English campaign in the west, which was nominally commanded by the Black Prince and actually by John of Gaunt and the Earl of Pembroke, captured Limoges after a five-day siege, taking many prisoners whom they held for ransom and seizing much booty.

Divisions among the English.

The English system of shared leadership led to jealousies between their captains regarding how the booty and the many ransoms they had collected should be distributed. In November 1370 acrimony broke out among the English captains over the issue of where to spend the winter. Knolles was aware that the French were closing in, and of the risk this posed. Not wishing to stay encamped in an area where a surprise attack was possible, he proposed withdrawing westward into Brittany. His captains, led by Sir Alan Buxhull, strongly disagreed, preferring to find winter quarters where they were. This would enable them to be able to continue raiding the surrounding countryside. They were confident they could defeat any French attack. Their concern to keep pillaging the countryside was in large part forced upon them: the government had only paid their and their army's wages for thirteen weeks, and they were expected not just to live off the land, but pay themselves from it.  Knolles threatened to leave, and when the other English commanders refused to join him, did so, taking the largest retinue from the army with him"doubtless with considerable booty", remarks the medievalist Kenneth Fowler. With Knolles gone, the remaining 4,000 men of the English force divided into three forces. One was under the dual command of Thomas Grandison and Hugh Calveley, the other two were commanded by Walter Fitzwalter and John Minsterworth. These three forces, in turn, went separate ways, which maximised their opportunities to forage for supplies and to loot. Fowler suggests that Minsterworth was probably the first to leave. On the evening of 3 December, Knolles was some way to the west, Grandison's force of between 600 and 1,200 was spread out along a river between Pontvallain and Mayet, and Fitzwalter was several miles to the south. The location of Minsterworth's force is no longer known.

French movements.

Bertrand du Guesclin was appointed constable of France on 2 October, in direct response to Knolles's campaign. Charles considered that Guesclin had the necessary skills in leading small forces and in irregular warfare to implement the Fabian approach he had decided on. On 24 October, Guesclin sealed a "pact of brotherhood-in-arms" with Olivier de Clisson, an experienced Breton commander, and by 6 November Guesclin was in Caen raising an army. Guesclin concentrated his forces at Caen during November, and was joined there by reinforcements under the Marshals Mouton de Blainville and Arnoul d'Audrehem as well as a Breton contingent under de Clisson. Guesclin thus concentrated about 4,000 men.  A second force of about 1,200 men assembled at Châtellerault, under Marshal Sancerre. This then moved towards the English from the east, while Guesclin began to move on him from the north. On 1 December Guesclin left Caen with his army"One of those marches of which he had the secret", said a contemporary chronicler,and marched south. One of the most important aspects of the Pontvallain campaign was the speed with which the French moved: Guesclin and his forces reached Le Mans, a journey of, two days later.

Battle.

Battle of Pontvallain.

At Le Mans, Guesclin received intelligence that Grandison's force was nearby at Mayet, but was on the move in an attempt to join with Knolles. Guesclin, however, outmanoeuvred him. Despite his army being near-exhausted, Guesclin commenced a night march, which brought him to Pontvallain by the early morning of 4 December. The French were able to attack Grandison's army with no warning, which was a great psychological advantage to them. The English were taken by surprise and Sumption speculates that Grandison may only have had time to form rough lines with his men before fierce close-quarters fighting began. In the earlier phase of the war, English longbowmen had largely neutralised the French cavalry but in this encounter, the barding (armouring) of the French horses rendered the English archery largely ineffective. The English attempted an escape through the woods, but were unable to retreat northwards, where the slightly higher ground may have provided them with a defensible position. Soon, with heavy losses on both sides, Grandison's force was penned in and wiped out beneath the walls of the Château de la Faigne.  Among the French casualties was the Marshal of France, Arnoul d'Audrehem, who was mortally wounded. The English army died almost to a man. Grandison and his captains, who included Philip Courtenay and Hugh Despenser, were among the few survivors, and were taken prisoner by Guesclin. With Grandison's defeat, the largest remaining English force in the area was Fitzwalter's. Sancerre, who was still "a few hours march away", on receiving news of the battle at Pontvallain turned south to confront Fitzwalter. Guesclin, meanwhile, organised his prisoners, sent a portion of his army to chase Knolles, and moved towards Fitzwalter with the balance. Fitzwalter managed to avoid being surprised in open ground as Grandison had been, and marched south, intending to take refuge within the fortified Vaas Abbey.

Battle of Vaas.

The abbey at Vaas was garrisoned by Knolles's men, and Fitzwalter's men assumed it to be a haven. However, the French forces led by Sancerre reached the abbey at nearly the same time as the English. The garrison were unable to organise a proper defence before they had to attempt to fend off an immediate assault from Sancerre. According to Sumption, it is likely that Fitzwalter's force managed to enter the outer gate, but after bitter fighting Sancerre's troops forced their way into the abbey. The English defence, such as it was, collapsed. The arrival of Guesclin effectively put an end to the battle, which became a rout. What Sumption considers reliable estimates attested the English losses to be over 300, exclusive of prisoners. These included Fitzwalter himself, captured by the seneschal of Toulouse, and most of his lieutenants. Guesclin held Fitzwalter as his personal prisoner; possibly, Sumption adds, like the contemporary Pierre d'Orgemont when he related the tale, Guesclin believed Fitzwalter to be the marshal of England.

Aftermath.

The few English survivors of the battles still at large scattered in confusion. John Minsterworth's force, which had not been engaged at either battle, immediately removed itself to Brittany. Others made their way to Saint-Saveur, south of the Loire. Caveley returned to Poitou. Around 300 of the English remnants joined together and overran Courcillon Castle, near Château-du-Loir, and then marched to the Loire, closely pursued by Sancerre. Many of Knolles's men abandoned their positions garrisoning castles, including Rillé and Beaufort la Vallée, and also headed to the Loire. This group, which included many wounded men and pillagers, joined up with the other English force, making it "several hundred" in strength.  Guesclin maintained his close pursuit, and his constant ambushes and raids depleted the English numbers. They eventually reached the relative safe haven of the ford at Saint-Maur. Calveley's force, which had taken no part in either of the battles, had already crossed. A little beyond the ford was a strong English garrison at a fortified abbey, garrisoned by the English. Here, some of the English went east, while the majority continued towards Bordeaux. This group continued to be pursued by Guesclin, now joined again by Sancerre, deep into Poitou, where it was eventually run to ground outside Bressuire Castle. This was also occupied by an English garrison, but, fearing that if they opened the gates they would admit the French army alongside the English, they refused to do so. As a result, what remained of this remnant of the Pontvallain army was wiped out under the walls.  Sancerre proceeded to regain the castles previously captured by Knolles during his. Guesclin made his way back to Saint-Maur where he negotiated with the English inside the abbey – led by Sir John Cresswell and Calveleyand arranged their release on payment of a ransom. The price of freedom for the English is unknown. Soon after, Guesclin returned to Le Mans.  There is uncertainty as to exactly where in Brittany Knolles retired to with the booty he had garnered. Whether to Derval, to Concarneau, or to one and then to the other, he was soon joined by Minsterworth. They decided to return to England with most of their force early the following year. They made their way to the port of Pointe Saint-Mathieu, repeatedly ambushed by the French en route. When they arrived there were only two small ships available, inadequate for the several hundred men with Knolles and Minsterworth. Their numbers were swollen by English garrisons which had abandoned their posts and independently made their way to the port. Minsterworth was one of the relative few who could buy a passage; most of those who remained, possibly amounting to around 500 men, were massacred by the French, who soon caught up with them.  The return of Minsterworth to England "began a long period of recrimination", politically. Although he was as culpable as Knolles or any of the other commanders, Minsterworth attempted to avoid almost all the blame for the military disaster that had befallen them by putting the responsibility on to Knolles. In July 1372 the King's council effectively agreed with him, and condemned Knolles for the defeat. The English nobility also blamed Knolles, because of his lower social status. Despite this, Minsterworth was unable to exculpate himself completely, and the council later had him arrested and charged with traducing Knolles.  Sumption argues that the Pontvallain campaign and its aftermath should be seen as a "spectacular demonstration of Du Guesclin’s capacity to be everywhere at once" and an "extraordinary demonstration of [his] unconventional skills as a commander". Many knights were captured by the French, including John Clanvowe, Edmund Daumarle and William Neville, and were conveyed to Paris in open carts and strictly imprisoned. Others spent great sums evading capture, often borrowing money from colleagues to do so. Fitzwalter was held prisoner until he was able to raise a ransom by mortgaging his Cumberland estates to Edward III's mistress Alice Perrers on ruinous terms.

Legacy.

Knolles's campaign has been estimated to have cost Edward at least £66,667 (), based on his known requests for loans. The historian May McKisack suggests that the that preceded the battle yielded "plunder but little military benefit". Maurice Keen notes that even though Knolles had reached the gates of Paris, "he had little to show for it when he reached Brittany", which illustrated how much the Hundred Years' War had changed in character. According to Christopher Allmand, "the days of Crécy and Poitiers were over". Pontvallain, argues Alexander Gillespie, "destroyed the reputation the English had for invincibility on the battlefield".  England continued losing territory in Aquitaine until 1374, and as they lost land, they lost the allegiance of the local lords. Pontvallain ended King Edward's short-lived strategy of promoting an alliance with Charles, King of Navarre. It also marked the last use of great companieslarge forces of mercenariesby England in France; most of their original leaders had been killed. Mercenaries were still considered useful, but they were increasingly absorbed into the main armies of both sides.  Five hundred years later, when the French lost Alsace-Lorraine to Germany, the Pontvallain campaign was used jingoistically by the French as an example of a spectacular recovery of territory, to keep alive hope of eventually similarly recovering Alsace-Lorraine.

The Battle of Pontvallain, part of the Hundred Years' War, took place in the Sarthe region of north-west France on 4 December 1370, when a French army under Bertrand du Guesclin heavily defeated an English force which had broken away from an army commanded by Sir Robert Knolles. The French numbered 5,200 men, and the English force was approximately the same size.


History.

The CBC announced on February 17, 1959 that they would appear before the BBG (predecessor to the CRTC) in Ottawa on March 18 to apply for a license to extend Radio-Canada's television signal into the Winnipeg area. CBWFT first signed on at 3 p.m. on April 24, 1960, using channel 6 with an EIRP of 2,800 watts. At the same time two VTRs, worth $75,000 each were installed at the station. It was the first francophone television station west of Ontario. Its opening broadcast was a ceremony held at the Notre Dame Auditorium in St. Boniface. Dignitaries included in attendance were Lieutenant-Governor Errick Willis, Premier Duff Roblin, CBC President Alphonse Ouimet, Marcel Ouimet, general manager of Radio-Canada, J. R. Finlay, CBC Prairie Region Director, and Leo Remillard, CBWFT's program director.  At first, CBWFT's broadcast day ran between 6 and 12 hours, with a longer programming day on weekends. Over the years, this was extended to encompass most of the day. Initially, Radio-Canada's microwave link did not reach as far as Winnipeg. Instead, videotapes and films were "bicycled" from Montreal and delayed by one week, except for news and live events like "La Soirée du hockey". On November 15, 1964, it swapped frequencies with CBWT and a higher-powered transmitter was installed at the new site near Starbuck. From 1964 till the early 1980s, it referred to itself simply as "CBWFT canal 3 Winnipeg". During the early 1980s, CBWFT was known as "CBWFT 3/10", signifying its position on Channel 3, Cable 10 in Winnipeg. On January 1, 1986, it became known as "Radio-Canada Manitoba".  By October 31, 1966, CBWFT was connected to the Radio-Canada microwave signal, allowing the live feed of "Le Téléjournal" at 6 p.m. Prior to this the newscast consisted of Radio-Canada's radio news with locally inserted images. Several months after the first Anik A satellite was launched in 1972, CBWFT switched to the satellite feed of Radio-Canada and dropped the microwave feed, except to distribute its signal within its coverage area, Manitoba and Northwestern Ontario, and part of Saskatchewan. In 1976, a rebroadcaster of CBWFT programming in Regina became CBKFT. In 1985, CBKFT was issued a separate license to broadcast its own "Ce Soir" regional news program.

Transmitters.

CBWFT operated 11 analogue television retransmitters in Manitoba (e.g. Brandon) and Northwestern Ontario (in the parts of that region which fall in the Central Time Zone, e.g. Kenora). Due to federal funding reductions to the CBC, in April 2012, the CBC responded with substantial budget cuts, which included shutting down CBC's and Radio-Canada's remaining analog transmitters on July 31, 2012. None of CBC or Radio-Canada's television rebroadcasters were converted to digital.

News operation.

In 2005, the long-running "Ce Soir" news program was renamed to "Le Téléjournal", which is the same name of the French national news program on Radio-Canada. The "Téléjournal" local edition is normally 30 minutes in length, however the Wednesday edition is 60 minutes. The program is also rebroadcast at 11 p.m.

Digital television.

Analogue-to-digital conversion.

CBWFT switched from analogue to digital television broadcasting on December 9, 2011, from its Winnipeg transmitter atop the Richardson Building, after several delays, due to an "unforeseen delay that is outside of the Corporation's control," involving antenna erection. CBWFT's digital signal operates on UHF channel 51. Through the use of PSIP, digital television receivers will display CBWFT's virtual channel as 3.1.

CBWFT-DT, virtual channel 3 (UHF digital channel 51), is an Ici Radio-Canada Télé owned-and-operated station licensed to Winnipeg, Manitoba, Canada, serving the province's Franco-Manitoban population. The station is owned by the Canadian Broadcasting Corporation (known in French as "Société Radio-Canada"), as part of a twinstick with CBC Television station CBWT-DT (channel 6). The two stations share studios on Portage Avenue and Young Street in Downtown Winnipeg; CBWFT-DT's transmitter is located near Red Coat Trail/Highway 2) in Macdonald. On cable and satellite, the station is available on Shaw Cable and MTS TV channel 10, and Bell TV channel 118. There is a high definition feed offered on Shaw Cable digital channel 214 and MTS TV channel 448.


Biography.

A native of Burgundy, Marc Meneau has never really left his native region. Gone in 1961 to Strasbourg to join a hotel school, he then came back soon after to take the grocery store of his mother Marguerite located in Saint-Père in the town of Vézelay. With the help of his wife Françoise (daughter of a Burgundian restaurant owner) and to seduce her, as a self-taught cooking chef, he transformed it in a restaurant and started inventing recipes published soon after. He was eager to learn and started looking at books of old cuisine chefs, which gave him the opportunity to become a famous chef specialized in old cuisine.

Career as chef.

In 1972, he received his first Michelin star and decided to move his restaurant in a larger place that he named "L'Espérance". In 1975, he received his second Michelin star. In 1983, he was elected the best French chef of the year (Meilleur Cuisinier Français de l'Année) and received a third Michelin star and the grade of 19/20 at the Gault et Millau. He planted 16 hectares of vine to give another life to the famous wine Bourgogne-Vézelay (AOC). In 1999 however, he lost his third Michelin star.  In 2003, he created the EntreVignes, a bistro just at the opposite of his restaurant, an idea given by Serge Gainsbourg, a familiar of the area. In 2004, Marc Meneau finally had his third Michelin star back.  In 2007, he had several financial problems and the bankruptcy of his society. After that announcement, the Guide Michelin deleted it of his 2007 edition, thinking that the society of Marc Meneau was about to close. In 2008 however, "L'Espérance" appeared again in the Guide Michelin with its two stars. In 2010, Marc Meneau planted his own kitchen garden certified bio, in the park of his restaurant "L'Espérance".

Followers.

These chefs were formed by Marc Meneau

Marc Meneau (born March 16, 1943) is a French chef, two stars at the Guide Michelin (former three stars). He is the chef of the restaurant "L'Espérance" located in Saint-Père, Yonne.


Zonohedra that tile space.

The original motivation for studying zonohedra is that the Voronoi diagram of any lattice forms a convex uniform honeycomb in which the cells are zonohedra. Any zonohedron formed in this way can tessellate 3-dimensional space and is called a primary parallelohedron. Each primary parallelohedron is combinatorially equivalent to one of five types: the rhombohedron (including the cube), hexagonal prism, truncated octahedron, rhombic dodecahedron, and the rhombo-hexagonal dodecahedron.

Zonohedra from Minkowski sums.

Let {v, v,...} be a collection of three-dimensional vectors. With each vector v we may associate a line segment {xv|0≤x≤1}. The Minkowski sum {Σxv|0≤x≤1} forms a zonohedron, and all zonohedra that contain the origin have this form. The vectors from which the zonohedron is formed are called its generators. This characterization allows the definition of zonohedra to be generalized to higher dimensions, giving zonotopes.  Each edge in a zonohedron is parallel to at least one of the generators, and has length equal to the sum of the lengths of the generators to which it is parallel. Therefore, by choosing a set of generators with no parallel pairs of vectors, and by setting all vector lengths equal, we may form an equilateral version of any combinatorial type of zonohedron.  By choosing sets of vectors with high degrees of symmetry, we can form in this way, zonohedra with at least as much symmetry. For instance, generators equally spaced around the equator of a sphere, together with another pair of generators through the poles of the sphere, form zonohedra in the form of prism over regular formula_1-gons: the cube, hexagonal prism, octagonal prism, decagonal prism, dodecagonal prism, etc. Generators parallel to the edges of an octahedron form a truncated octahedron, and generators parallel to the long diagonals of a cube form a rhombic dodecahedron.  The Minkowski sum of any two zonohedra is another zonohedron, generated by the union of the generators of the two given zonohedra. Thus, the Minkowski sum of a cube and a truncated octahedron forms the truncated cuboctahedron, while the Minkowski sum of the cube and the rhombic dodecahedron forms the truncated rhombic dodecahedron. Both of these zonohedra are simple (three faces meet at each vertex), as is the truncated small rhombicuboctahedron formed from the Minkowski sum of the cube, truncated octahedron, and rhombic dodecahedron.

Zonohedra from arrangements.

The Gauss map of any convex polyhedron maps each face of the polygon to a point on the unit sphere, and maps each edge of the polygon separating a pair of faces to a great circle arc connecting the corresponding two points. In the case of a zonohedron, the edges surrounding each face can be grouped into pairs of parallel edges, and when translated via the Gauss map any such pair becomes a pair of contiguous segments on the same great circle. Thus, the edges of the zonohedron can be grouped into zones of parallel edges, which correspond to the segments of a common great circle on the Gauss map, and the 1-skeleton of the zonohedron can be viewed as the planar dual graph to an arrangement of great circles on the sphere. Conversely any arrangement of great circles may be formed from the Gauss map of a zonohedron generated by vectors perpendicular to the planes through the circles.  Any simple zonohedron corresponds in this way to a simplicial arrangement, one in which each face is a triangle. Simplicial arrangements of great circles correspond via central projection to simplicial arrangements of lines in the projective plane, which were studied by Grünbaum (1972). He listed three infinite families of simplicial arrangements, one of which leads to the prisms when converted to zonohedra, and the other two of which correspond to additional infinite families of simple zonohedra. There are also many known examples that do not fit into these three families.

Types of zonohedra.

Any prism over a regular polygon with an even number of sides forms a zonohedron. These prisms can be formed so that all faces are regular: two opposite faces are equal to the regular polygon from which the prism was formed, and these are connected by a sequence of square faces. Zonohedra of this type are the cube, hexagonal prism, octagonal prism, decagonal prism, dodecagonal prism, etc.  In addition to this infinite family of regular-faced zonohedra, there are three Archimedean solids, all omnitruncations of the regular forms:  In addition, certain Catalan solids (duals of Archimedean solids) are again zonohedra:  Others with congruent rhombic faces:  There are infinitely many zonohedra with rhombic faces that are not all congruent to each other. They include:

Dissection of zonohedra.

Although it is not generally true that any polyhedron has a dissection into any other polyhedron of the same volume (see Hilbert's third problem), it is known that any two zonohedra of equal volumes can be dissected into each other.

Zonohedrification.

Zonohedrification is a process defined by George W. Hart for creating a zonohedron from another polyhedron.  First the vertices of any polyhedron are considered vectors from the polyhedron center. These vectors create the zonohedron which we call the zonohedrification of the original polyhedron. For any two vertices of the original polyhedron, there are two opposite planes of the zonohedrification which each have two edges parallel to the vertex vectors.

Zonotopes.

The Minkowski sum of line segments in any dimension forms a type of polytope called a zonotope. Equivalently, a zonotope formula_2 generated by vectors formula_3 is given by formula_4. Note that in the special case where formula_5, the zonotope formula_2 is a (possibly degenerate) parallelotope.  The facets of any zonotope are themselves zonotopes of one lower dimension; for instance, the faces of zonohedra are zonogons. Examples of four-dimensional zonotopes include the tesseract (Minkowski sums of "d" mutually perpendicular equal length line segments), the omnitruncated 5-cell, and the truncated 24-cell. Every permutohedron is a zonotope.

Zonotopes and Matroids.

Fix a zonotope formula_2 defined from the set of vectors formula_8 and let formula_9 be the formula_10 matrix whose columns are the formula_11. Then the vector matroid formula_12 on the columns of formula_9 encodes a wealth of information about formula_2, that is, many properties of formula_2 are purely combinatorial in nature.  For example, pairs of opposite facets of formula_2 are naturally indexed by the cocircuits of formula_17 and if we consider the oriented matroid formula_17 represented by formula_19, then we obtain a bijection between facets of formula_2 and signed cocircuits of formula_17 which extends to a poset anti-isomorphism between the face lattice of formula_2 and the covectors of formula_17 ordered by component-wise extension of formula_24. In particular, if formula_9 and formula_26 are two matrices that differ by a projective transformation then their respective zonotopes are combinatorially equivalent. The converse of the previous statement does not hold: the segment formula_27 is a zonotope and is generated by both formula_28 and by formula_29 whose corresponding matrices, formula_30 and formula_31, do not differ by a projective transformation.

Tilings.

Tiling properties of the zonotope formula_2 are also closely related to the oriented matroid formula_17 associated to it. First we consider the space-tiling property. The zonotope formula_2 is said to "tile" formula_35 if there is a set of vectors formula_36 such that the union of all translates formula_37 (formula_38) is formula_35 and any two translates intersect in a (possibly empty) face of each. Such a zonotope is called a "space-tiling zonotope." The following classification of space-tiling zonotopes is due to McMullen: The zonotope formula_2 generated by the vectors formula_41 tiles space if and only if the corresponding oriented matroid is regular. So the seemingly geometric condition of being a space-tiling zonotope actually depends only on the combinatorial structure of the generating vectors.  Another family of tilings associated to the zonotope formula_2 are the "zonotopal tilings" of formula_2. A collection of zonotopes is a zonotopal tiling of formula_2 if it a polyhedral complex with support formula_2, that is, if the union of all zonotopes in the collection is formula_2 and any two intersect in a common (possibly empty) face of each. Many of the images of zonohedra on this page can be viewed as zonotopal tilings of a 2-dimensional zonotope by simply considering them as planar objects (as opposed to planar representations of three dimensional objects). The Bohne-Dress Theorem states that there is a bijection between zonotopal tilings of the zonotope formula_2 and "single-element lifts" of the oriented matroid formula_17 associated to formula_2.

Volume.

Zonohedra, and "n"-dimensional zonotopes in general, are noteworthy for admitting a simple analytic formula for their volume.  Let formula_50 be the zonotope formula_4 generated by a set of vectors formula_52. Then the n-dimensional volume of formula_50 is given by formula_54.  The determinant in this formula makes sense because (as noted above) when the set formula_55 has cardinality equal to the dimension formula_56 of the ambient space, the zonotope is a parallelotope.  Note that when formula_57, this formula simply states that the zonotope has n-volume zero.

A zonohedron is a convex polyhedron with point symmetry, every face of which is a polygon with point symmetry. Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as the three-dimensional projection of a hypercube. Zonohedra were originally defined and studied by E. S. Fedorov, a Russian crystallographer. More generally, in any dimension, the Minkowski sum of line segments forms a polytope known as a zonotope.


Payments.

Straight-through processing exists in numerous areas of financial services, such as payments processing.  Payments may be non-STP due to various reasons such as missing information, information which that is not in a machine "understandable" form (such as name and address rather than a code), or human-readable instructions "Please credit urgently") or simply falls outside of rules for which the bank allows automatic processing (for example, payments of large value or in exotic currencies).  Traditionally, making payments involves many departments in a bank. Both initiating a payment to be sent and processing a received payment may take days. In the past, payments were initiated through numerous "human-friendly" (aka paper-based) means, such as a human through a paper order, over the phone, or via fax. The payment order was input into the bank's payment system, then confirmed by a supervisor. This confirmation ensured an accurate match of input versus order before sending the payment. When multiple banks, countries or currencies were involved, the process often took several hours. When the complexity of the payment was higher, the amount of labor increased and additional human intervention resulted in more risk of errors, longer processing time, and higher costs.  In most cases, banks levy charges for non-STP payments or for manual repairs. Alternatively, banks may not charge on a "per repair" basis, but rather levy heavier fees for correspondents that provide lower quality (lower STP) payments.

Equities trading.

The process before STP was very antiquated: sales traders would have to fill in a deal ticket, blue for buy and red for sell. The order was invariably scribbled and mostly unreadable. Upon receiving the order, the trader would often execute an incorrect investment on the market. A runner picking up the ticket to input the order into the system in order to send out a contract note. For example, if the client wished to purchase 100,000 shares, but the trader only executed 10,000, the runner would send out the contract for 1,000. In those days, there was a T10 settlement so any errors were "fixable". However, with the new introduction of T5, the settlement arena changed, and STP was born. To reduce the exposure of risk, failed settlement, there could only be one "golden source" of information and that it was the responsibility of the sales trader to be correct as they had the power to correct any discrepancies with the client directly.  The goal of STP is to reduce the time it takes to process a transaction, in order to increase the likelihood that a contract or an agreement is settled on time. The concept has also been transferred into other sectors including energy (oil, gas) trading and banking, and financial planning.  Currently, the entire trade lifecycle, from initiation to settlement, is a complex labyrinth of manual processes that take several days. Such processing for equities transactions is commonly referred to as T+2 (trade date plus two days) processing, as it usually takes two business days from the "trade" being executed to the trade being settled. This means investors who are selling a security must deliver the certificate within two business days, and investors who are buying securities must send payment within two business days. But this process comes with higher risks through the occurrence of unsettled trades. Market conditions fluctuate, meaning a two-day window brings an inherent risk of unexpected losses that investors may be unable to pay for, or settle, their transactions.  Industry practitioners, particularly in the United States, viewed STP as meaning "same-day" settlement or faster, ideally minutes or even seconds. The goal was to minimise settlement risk for the execution of a trade and its settlement and clearing to occur simultaneously. However, for this to be achieved, multiple market participants must realize high levels of STP. In particular, transaction data would need to be made available on a just-in-time basis, which is a considerably harder goal to achieve for the financial services community than the application of STP alone. After all, STP itself is merely an efficient use of computers for transaction processing.  In the past, STP methods were used to help financial market firms move to one-day trade settlement of equity transactions, as well as to meet the global demand resulting from the rapid growth of online trading. Now the concepts of STP are applied to reduce systemic and operational risk and to improve certainty of settlement and minimize operational costs.

Common misconceptions.

There is often confusion within the trading world between STP and an electronic communication network (ECN). Although they are similar initiatives, ECN connects orders with those of other traders as well as staff liquidity provides. An ECN is also typically a bigger pool of orders than a standard STP.  When fully implemented, STP is able to provide asset managers, brokers and dealers, custodians, banks and other financial services with benefits including shorter processing cycles, reduced settlement risk, and lower operating costs. Some industry analysts believe that STP is not an achievable goal in the sense that firms are unlikely to find the cost/benefit to reach 100% automation. Instead, they promote the idea of improving levels of internal STP within a firm while encouraging groups of firms to work together to improve the quality of the automation of transaction information between themselves, either bilaterally or as a community of users (external STP). Other analysts, however, believe that STP will be achieved with the emergence of business process interoperability.

Straight-through processing (STP) is a method used by financial companies to speed up financial transactions by processing without manual intervention (straight-through).


History.

The city of Helena was founded by European Americans in 1833, as a port along the Mississippi River. Crowleys Ridge provided elevation and some protection against flooding, a rare feature along the right/west bank of the lower Mississippi River.  During the Civil War, the Union Army occupied Helena prior to the Battle of Helena in 1863. In the early morning hours of July 4, 1863, Confederate forces attempted to retake Helena in order to help relieve pressure on the strategic river town of Vicksburg, Mississippi. Confederate forces in Vicksburg had already arranged to surrender to General U.S. Grant on the morning of July 4. Many of the former battle sites are still intact. Helena may benefit from developing and protecting these historic areas for destination tourism.  Prior to consolidation, Helena contained 6,323 people within 23.1 km2. Neighboring West Helena had 8,689 people in 11.5 km2. Merger proposals began as early as 2002, and a March 2005 vote among citizens of both cities approved the merger. The surrounding rural county is one of the poorest of Arkansas' 75 counties. Proponents of the consolidation said that combining the cities would strengthen their bargaining power for the surrounding region in competing for projects to improve the overall economy and standard of living. Among the combined city's council's first tasks was the hiring of a new police chief. They chose Vincent Bell.

Demographics.

Based on U.S. Census reports for both cities prior to the merger, the 2000 population of the area comprising Helena–West Helena was 15,012. There were 5,516 households, and 3,765 families residing in the city. The racial makeup of the city was 31.85% White, 66.63% African American, 0.19% Native American, 0.47% Asian, 0.01% Pacific Islander, 0.27% from other races, and 0.58% from two or more races. Hispanics or Latinos of any race were 0.89% of the population.  The median income for a household in the city was $19,896, and the median income for a family was $23,274. Males had a median income of $25,087 versus $17,238 for females. The per capita income for the city was $12,131.

Helena.

As of the census of 2000, there were 6,323 people, 2,312 households, and 1,542 families residing in the city of Helena. The population density was 710.7 people per square mile (274.3/km2). There were 2,710 housing units at an average density of 304.6/sq mi (117.6/km2). The racial makeup of the city was 30.59% White, 67.93% Black or African American, 0.13% Native American, 0.60% Asian, 0.17% from other races, and 0.59% from two or more races. Hispanic or Latino of any race were 0.73% of the population.  There were 2,312 households out of which 32.7% had children under the age of 18 living with them, 33.8% were married couples living together, 28.5% had a female householder with no husband present, and 33.3% were non-families. 30.0% of all households were made up of individuals and 13.4% had someone living alone who was 65 years of age or older. The average household size was 2.62 and the average family size was 3.28.  In the city, the population was spread out with 32.5% under the age of 18, 10.0% from 18 to 24, 22.1% from 25 to 44, 20.0% from 45 to 64, and 15.5% who were 65 years of age or older. The median age was 32 years. For every 100 females there were 83.3 males. For every 100 females age 18 and over, there were 75.5 males.  The median income for a household in the city was $18,662, and the median income for a family was $21,534. Males had a median income of $27,203 versus $17,250 for females. The per capita income for the city was $13,028. About 38.4% of families and 41.4% of the population were below the poverty line, including 54.9% of those under age 18 and 24.1% of those age 65 or over.

West Helena.

As of the census of 2000, there were 8,689 people, 3,204 households, and 2,223 families residing in the city of West Helena. The population density was 1,956.6 people per square mile (755.6/km2). There were 3,518 housing units at an average density of 792.2/sq mi (305.9/km2). The racial makeup of the city was 32.77% White, 65.69% Black or African American, 0.23% Native American, 0.38% Asian, 0.02% Pacific Islander, 0.33% from other races, and 0.58% from two or more races. Hispanic or Latino of any race were 1.01% of the population.  There were 3,204 households out of which 36.0% had children under the age of 18 living with them, 36.8% were married couples living together, 29.2% had a female householder with no husband present, and 30.6% were non-families. 27.6% of all households were made up of individuals and 11.5% had someone living alone who was 65 years of age or older. The average household size was 2.71 and the average family size was 3.32.  In the city, the population was spread out with 34.1% under the age of 18, 10.1% from 18 to 24, 23.9% from 25 to 44, 19.6% from 45 to 64, and 12.3% who were 65 years of age or older. The median age was 30 years. For every 100 females there were 80.7 males. For every 100 females age 18 and over, there were 71.5 males.  The median income for a household in the city was $21,130, and the median income for a family was $25,014. Males had a median income of $22,971 versus $17,225 for females. The per capita income for the city was $11,234. About 30.9% of families and 35.4% of the population were below the poverty line, including 49.5% of those under age 18 and 27.2% of those age 65 or over.

Economy.

With a median income of $19,896 for a household, the city is one of the poorest in the nation. One potential advance for the combined city, as reported by the "Arkansas Democrat-Gazette" on July 12, 2006, is an ethanol fuel refinery to be built by Las Vegas-based E-Fuels. Whether the consolidation had any bearing on the decision is not certain. If the project is developed, it is expected to bring several new jobs and a significant increase in traffic to the region's port on the Mississippi River.  In 2006, the city announced plans to reopen the regional landfill, from which Helena–West Helena could earn fees.  Helena–West Helena's chief economic base continues to be agriculture, specifically cotton cultivation. Mechanization and large industrial farms have reduced the need for farm labor since the first half of the 20th century. Barge traffic at the city's port on the Mississippi River is another source of jobs and revenues, in addition to retail and tourism.

Media.

"The Helena-West Helena World" is the local newspaper.

Arts and culture.

Musical history.

In the 1940s and 1950s, Helena attracted blacks from rural Arkansas and the Mississippi Delta, who came for the jobs. Some also worked full-time as musicians. By then Helena was 70% black, and juke joints employed such blues pianist as Sunnyland Slim, Memphis Slim and Roosevelt Sykes.  In November 1941, a white businessman put together the staff for the town's first radio station KFFA. A group of blues musicians were given a one-hour radio spot on the condition that they gain a sponsor. King Biscuit Flour agreed to do. The King Biscuit Entertainers were sponsored, as well as the show "King Biscuit Time," featuring blues musicians.  The King Biscuit Blues Festival was organized in the late 20th century as an annual October event. It was renamed as the Arkansas Blues and Heritage Festival in 2005, and is one of the largest blues festivals in the world. The celebration is held in downtown Helena on Cherry Street in early October. It was renamed in 2010 as the King Biscuit Blues Festival at a 25th anniversary performance of renowned musician B.B. King.  The lyrics of "Stand Up Guy" by Mark Knopfler make reference to West Helena.  The Helena–West Helena School District operates public schools. operates a group of charter schools in the municipality. Helena previously had a Catholic grade school for black children, St. Cyprian School; it closed in 1963.

Helena–West Helena is the county seat of and the largest city within Phillips County, Arkansas, United States. The current city was consolidated, effective January 1, 2006, from the two Arkansas cities of Helena and West Helena. Helena is sited on lowlands between the Mississippi River and the eastern side of Crowley's Ridge. West Helena is located on the western side of Crowley's Ridge, a geographic anomaly in the typically flat Arkansas Delta. The Helena Bridge, one of Arkansas' four Mississippi River bridges, carries U.S. Route 49 across to Mississippi. The combined population of the two cities was 15,012 at the 2000 census and at the 2010 census, the official population was 12,282.


Biography.

Shikha was born to father Mahesh (who was a table-tennis player for India) and mother Madhu in Mumbai, Maharashtra, India. Her family moved to Princeton, New Jersey when she was an infant. She has one older sister (Diya) and three younger sisters (Neha, Nikita and Nimita). Her four sisters are also tennis players, but of all, Shikha is by far the most successful, and the only one to represent India (the other sisters represent the United States).  She was named the Zee Astitva Athlete of the Year 2007. She was one of the top-10 fastest servers in the world. She earned her bachelor's degree from Princeton University in Anthropology and South Asian Studies. She graduated with high academic standing while winning Princeton's prestigious Kit Harris Memorial Award for Leadership and Ethics.  Shikha launched her media and lifestyle company, SDU Seva, Inc. As of 2013, she is currently creating and producing international social issue television shows, and is a social entrepreneur. She speaks internationally at various diplomatic conferences on female empowerment through sport. She has recently been invited to sit on the board of directors of the World Economic Forum's "Global Shapers Initiative" for Bhopal. She is also a news and sports presenter and coaches all levels of tennis and fitness.

Tennis career.

She turned pro in August 2003. Though she has not won any WTA Tour event till date, Uberoi has three ITF Women's Circuit singles titles to her name- one in Harrisonburg in 2003 and two in Fort Worth and Edmond in 2004.  At the 2004 US Open, Uberoi became the second ever Indian female player in the modern era to feature and win a round at a main draw Grand Slam Tournament, defeating Japan's Saori Obata. (The first was Nirupama Vaidyanathan at the 1998 Australian Open.)  In 2005, Shikha reached 2 WTA doubles finals partnering sister Neha, one in Kolkata and one in Guangzhou.  In 2006, Uberoi represented India at the 2006 Asian Games where she defeated Linda Ahmad of Bahrain in Round 1, but retired in the second round to Zheng Jie of China.  In 2007, Shikha was the finalist in Auckland, partnering Su-Wei Hsieh.  She was also the India Fed Cup Team leader.

Shikha Devi Uberoi (; born 5 April 1983) is a former Indian-American professional tennis player and a former Indian No. 1. After Nirupama Sanjeev, she is the second Indian female player in history to crack the top 200 WTA rankings, as well as the second to feature and win a round at a Grand Slam tournament.


History.

In 1873 Ernst Abbe reported that conventional lenses are incapable of capturing some fine details of any given image. The super lens is intended to capture such details. The limitation of conventional lenses has inhibited progress in the biological sciences. This is because a virus or DNA molecule cannot be resolved with the highest powered conventional microscopes. This limitation extends to the minute processes of cellular proteins moving alongside microtubules of a living cell in their natural environments. Additionally, computer chips and the interrelated microelectronics are manufactured to smaller and smaller scales. This requires

Theory.

Image formation.

An image of an object can be defined as a tangible or visible representation of the features of that object. A requirement for image formation is interaction with fields of electromagnetic radiation. Furthermore, the level of feature detail, or image resolution, is limited to a length of a wave of radiation. For example, with optical microscopy, image production and resolution depends on the length of a wave of visible light. However, with a superlens, this limitation may be removed, and a new class of image generated.  Electron beam lithography can overcome this resolution limit. Optical microscopy, on the other hand cannot, being limited to some value just above 200 nanometers. However, new technologies combined with optical microscopy are beginning to allow increased feature resolution (see sections below).  One definition of being constrained by the resolution barrier, is a resolution cut off at half the wavelength of light. The

Conventional lens.

The conventional glass lens is pervasive throughout our society and in the sciences. It is one of the fundamental tools of optics simply because it interacts with various wavelengths of light. At the same time, the wavelength of light can be analogous to the width of a pencil used to draw the ordinary images. The limit becomes noticeable, for example, when the laser used in a digital video system can only detect and deliver details from a DVD based on the wavelength of light. The image cannot be rendered any sharper beyond this limitation.  Thus, when an object emits or reflects light there are two

Subwavelength imaging.

This has led to the desire to view live biological cell interactions in a real time, natural environment, and the need for "subwavelength imaging". Subwavelength imaging can be defined as optical microscopy with the ability to see details of an object or organism below the wavelength of visible light (see discussion in the above sections). In other words, to have the capability to observe, in real time, below 200 nanometers. Optical microscopy is a non-invasive technique and technology because everyday light is the transmission medium. Imaging below the optical limit in optical microscopy (subwavelength) can be engineered for the cellular level, and nanometer level in principle.  For example, in 2007 a technique was demonstrated where a metamaterials-based lens coupled with a conventional

Early subwavelength imaging.

"Metamaterial lenses" ("Superlens") are able to reconstruct nanometer sized images by producing a negative refractive index in each instance. This compensates for the swiftly decaying evanescent waves. Prior to metamaterials, numerous other techniques had been proposed and even demonstrated for creating super-resolution microscopy. As far back as 1928, Irish physicist Edward Hutchinson Synge, is given credit for conceiving and developing the idea for what would ultimately become near-field scanning optical microscopy.  In 1974 proposals for two-dimensional fabrication techniques were presented. These proposals included contact imaging to create a pattern in relief, photolithography, electron lithography, X-ray lithography, or ion bombardment, on an appropriate planar substrate. The shared technological goals of the metamaterial lens and the variety of lithography aim to optically resolve features having dimensions much

Analysis of the diffraction limit.

The original problem of the perfect lens: The general expansion of an EM field emanating from a source consists of both propagating waves and near-field or evanescent waves. An example of a 2-D line source with an electric field which has S-polarization will have plane waves consisting of propagating and evanescent components, which advance parallel to the interface. As both the propagating and the smaller evanescent waves advance in a direction parallel to the medium interface, evanescent waves decay in the direction of propagation. Ordinary (positive index) optical elements can refocus the propagating

The diffraction limit as restriction on resolution.

The performance limitation of conventional lenses is due to the diffraction limit. Following Pendry (2000), the diffraction limit can be understood as follows. Consider an object and a lens placed along the z-axis so the rays from the object are traveling in the +z direction. The field emanating from the object can be written in terms of its angular spectrum method, as a superposition of plane waves:  where formula_2 is a function of formula_3:  Only the positive square root is taken as the energy is going in the +"z" direction. All of the components of the angular spectrum of the image for which formula_2 is real are transmitted and re-focused by an ordinary lens. However, if

Effects of negative index of refraction.

Normally, when a wave passes through the interface of two materials, the wave appears on the opposite side of the normal. However, if the interface is between a material with a positive index of refraction and another material with a negative index of refraction, the wave will appear on the same side of the normal. Pendry's idea of a perfect lens is a flat material where "n"=−1. Such a lens allows near-field rays, which normally decay due to the diffraction limit, to focus once within the lens and once outside the lens, allowing subwavelength imaging.

Development and construction.

Superlens construction was at one time thought to be impossible. In 2000, Pendry claimed that a simple slab of left-handed material would do the job. The experimental realization of such a lens took, however, some more time, because it is not that easy to fabricate metamaterials with both negative permittivity and permeability. Indeed, no such material exists naturally and construction of the required metamaterials is non-trivial. Furthermore, it was shown that the parameters of the material are extremely sensitive (the index must equal −1); small deviations make the subwavelength resolution unobservable. Due to the resonant nature of metamaterials, on which many (proposed) implementations of superlenses depend, metamaterials are highly dispersive. The sensitive nature of the superlens to the material parameters causes superlenses based on metamaterials to have a limited usable frequency range. This initial theoretical superlens design consisted of a metamaterial that compensated for wave decay and reconstructs images in the near field. Both propagating and evanescent waves could contribute to the resolution of the image.  Pendry also suggested that a lens having only one negative parameter would form an approximate superlens, provided that the distances involved are also very small and provided that the source polarization is appropriate. For visible light this is a useful substitute, since engineering metamaterials with a negative permeability at the frequency of visible light is difficult. Metals are then a good alternative as they have negative permittivity (but not negative permeability). Pendry suggested using silver due to its relatively low loss at the predicted wavelength of operation (356 nm). In 2003 Pendry's theory was first experimentally demonstrated at RF/microwave frequencies. In 2005, two independent groups verified Pendry's lens at UV range, both using thin layers of silver illuminated with UV light to produce "photographs" of objects smaller than the wavelength. Negative refraction of visible light was experimentally verified in an yttrium orthovanadate (YVO) bicrystal in 2003.  It was discovered that a simple superlens design for microwaves could use an array of parallel conducting wires.  In 2004, the first superlens with a negative refractive index provided resolution three times better than the diffraction limit and was demonstrated at microwave frequencies. In 2005, the first near field superlens was demonstrated by N.Fang "et al.", but the lens did not rely on negative refraction. Instead, a thin silver film was used to enhance the evanescent modes through surface plasmon coupling. Almost at the same time Melville and Blaikie succeeded with a near field superlens. Other groups followed. Two developments in superlens research were reported in 2008. In the second case, a metamaterial was formed from silver nanowires which were electrochemically deposited in porous aluminium oxide. The material exhibited negative refraction. The imaging performance of such isotropic negative dielectric constant slab lenses were also analyzed with respect to the slab material and thickness. Subwavelength imaging opportunities with planar uniaxial anisotropic lenses, where the dielectric tensor components are of the opposite sign, have also been studied as a function of the structure parameters.  The superlens has not yet been demonstrated at visible or near-infrared frequencies (Nielsen, R. B.; 2010). Furthermore, as dispersive materials, these are limited to functioning at a single wavelength. Proposed solutions are metal–dielectric composites (MDCs) and multilayer lens structures. The multi-layer superlens appears to have better subwavelength resolution than the single layer superlens. Losses are less of a concern with the multi-layer system, but so far it appears to be impractical because of impedance mis-match.  While the evolution of nanofabrication techniques continues to push the limits in fabrication of nanostructures, surface roughness remains an inevitable source of concern in the design of nano-photonic devices. The impact of this surface roughness on the effective dielectric constants and subwavelength image resolution of multilayer metal–insulator stack lenses has also been studied.

See also.

Metamaterials scientists

A superlens, or super lens, is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is a feature of conventional lenses and microscopes that limits the fineness of their resolution. Many lens designs have been proposed that go beyond the diffraction limit in some way, but constraints and obstacles face each of them.


History.

The organization was formed in 1994 by Michael Hill and others, including attorney Jack Kershaw. The League of the South was named in reference to the League of United Southerners, a group organized in 1858 to shape Southern public opinion and the Lega Nord (Northern League), a very successful populist movement in Northern Italy from which the group took inspiration.  The LOS' first meeting was represented with a group of 40 men, 28 of whom formed an organization then known as The Southern League. The name was changed to The League of the South in 1996 in order to avoid confusion with the Southern League of Minor League Baseball. Among the early members were Southern professors, including president Michael Hill. Hill was a British history professor and specialist in Celtic history at Stillman College, a historically black school in Tuscaloosa. However, Hill has since left his teaching position.  In 2000, the group supported Pat Buchanan and the Reform Party.  Since 2007, The League's main publication has been "The Free Magnolia", a quarterly tabloid.

Views.

The League has been described as using "Celtic" mythology "belligerently against what is perceived as a politically correct celebration of multicultural Southern diversity".  The group believes that the Southern United States should be an independent country ruled by white men.  In 2001 they asked US congress to pay $5 billion in reparations for "property" (which at the time included human beings) which was taken or destroyed by Union forces during the Civil War. The group's legal counsel Jack Kershaw said their proposal included paying reparations to African-Americans due to the supposed negative effect the end of slavery had on their ancestors: "Blacks were better off in antebellum times in the South than they were anywhere else. [...] They lost a lot too when that lifestyle was destroyed."

Culture.

The League defines Southern culture as profoundly Christian and anti-abortion. The League describes Southern Culture as being inherently Anglo-Celtic in nature (originating in the British Isles), and they believe the South's core Anglo-Celtic culture should be preserved.  According to the League, the South has had a Marxist and egalitarian society "impressed upon it". The "League's Core Beliefs Statement" advocates the stigmatization of "perversity and all that seeks to undermine marriage and the family."

Politics.

The League believes that what it calls "the Southern people" have the right to secede from the United States, and that they "must throw off the yoke of imperial [federal, or central government] oppression". The League promotes a Southern Confederation of sovereign, independent States. The League favors strictly limited immigration, opposes standing armies and any regulation whatsoever of firearms. This proposed independent nation is described by League publications as part of a process to convince "the Southern people" that they have a unique identity.  The League focuses on recruiting and encouraging "cultural secession". In November 2006 its representatives attended the First North American Secessionist Convention of secessionists from a different parts of the country. In October 2007 it co-hosted the Second North American Secessionist Convention in Chattanooga, Tennessee.  In 2015, the group announced it would be holding an event celebrating the assassination of Abraham Lincoln, while honoring John Wilkes Booth as a hero. On April 11, 2015, it was organized by the vice chairman of the Maryland-Virginia chapter of the League, Shane Long. The LOS's main Facebook page put it bluntly: "Join us in April to celebrate the great accomplishment of John Wilkes Booth. He knew a man who needed killing when he saw him!"  The League has attempted to form paramilitary groups on more than one occasion.  The League of the South is opposed to fiat currency, personal income taxation, central banking, property taxes and most state regulation of business. The League supports sales taxes and user fees.

Charges of racism.

In the summer of 2000, the Southern Poverty Law Center (SPLC) labeled the League of the South a "racist hate group" and issued a report filled with allegations of racist statements, especially by the League's President Michael Hill. Hill responded by dismissing the label as being politically motivated, claiming that he welcomed the designation as a "badge of honor" and expressing his belief that the designation was designed to discredit the League of the South.  During the 2006 First North American Secessionist Convention, when the issue of the League of the South and racism was raised, Don Kennedy, identified as "a leader of the League of the South", stated: "How can you believe in liberty and discriminate against your neighbor? Equality before the law is something we want, and we're on the record for that." News stories about the Second North American Secessionist Convention also mentioned the SPLC's allegations, as well as skeptical responses from convention attendees. Convention organizer Kirkpatrick Sale responded: "They call everybody racists. There are, no doubt, racists in the League of the South, and there are, no doubt, racists everywhere."  In response to the 2016 Orlando nightclub shooting Hill wrote on the League's website that "In a free & independent South, Islam would be banned, Muslims deported, and all mosques closed down. The ownership of firearms, including military grade, would be encouraged for all Southern citizens in order to protect the public from such incidents as occurred overnight in Orlando, Florida".  In a 2017 decision, the Tennessee Court of Appeals ruled that a blog post describing a family as white supremacist, based on a photo showing a League of the South bumper sticker on the family car, was not defamatory because it was an opinion based on disclosed facts.

Members.

The League's Board of Directors is composed of Michael Hill, Mark Thomey, Mike Crane, Sam Nelson, and John Cook. Among the founding members were Thomas Fleming, Thomas Woods, Grady McWhiney, Clyde Wilson, and Forrest McDonald.

The League of the South (LS) is a white nationalist, Neo-Confederate, white supremacist organization, headquartered in Killen, Alabama, which states that its ultimate goal is "a free and independent Southern republic". The group defines the Southern United States as the states that made up the former Confederacy (Alabama, Arkansas, Florida, Georgia, Louisiana, Mississippi, North Carolina, South Carolina, Texas, Tennessee and Virginia). It claims to also be a religious and social movement, advocating a return to a more traditionally conservative, Christian-oriented Southern culture.


Biography.

Allouez was born in Saint-Didier-en-Velay in the département of Haute-Loire in south-central France. In 1639, he graduated from the College of Le Puy, and became a Jesuit novice in Toulouse, France. In 1655, he was ordained a priest of the Roman Catholic Church. Allouez arrived in Quebec in 1658 and immediately began a study of the Wyandot and Anishinaabe languages to prepare himself for work as a missionary among the American Indian tribes along the St. Lawrence River.  In 1660 he became the superior of the mission at Trois-Rivières, Quebec. His stay there lasted until 1663 when he was named vicar general of a part of the diocese of Quebec that is now the central region of the United States. This appointment was made by Bishop François de Laval, the first bishop of New France.  From 1665 through 1669 Allouez made a missionary tour of the western missions. In 1667 visited the village of the Nipissing Indians who had fled there during the Iroquois onslaught of 1649-50 and celebrated the first mass beside the Nipigon River May 29, 1667. He went back to Quebec in search of assistants, and immediately returned to the missions.  On December 3, 1669 Allouez said the first Mass in Oconto. He served as a missionary to the Potawatomi. The Menominee began participating in the fur trade network and converting to Christianity. The next year he was with the Mesquakie, establishing St. Mark's Mission, and founding the mission of St. James among the Miami and Mascouten Indians, finally returning to Green Bay later that year.  Because of his fluency in native languages and the prestige in which he was held by the Indian nations, in Sault Ste. Marie, Michigan, he was a principal speaker at the ceremony that formally declared the Great Lakes and the Mississippi River valley as territory of the King of France. In 1671 he founded the St. Francis Xavier Mission at the last set of rapids on the Fox River before entering the Green Bay. The site was known as Rapides Des Pères (rapids of the fathers) which became modern day De Pere, Wisconsin. This became his base until word arrived of the death of Jacques Marquette, and Allouez was assigned to continue Marquette's work among the Illinois. In February 1676, on his way to Lake Michigan, his companions rigged a sail on the canoe to sail over the ice. By March he was at Whitefish Bay and reached Kaskaskia by the end of the month.  He continued Marquette's evangelizing of the Indians until his death in 1689, near what is today Niles, Michigan just north of South Bend, Indiana. He is buried in Niles.  A good portion of Father Allouez's written work from the time has been preserved. It provides insight into the missions of the time and provides a record that is extensive and important of the Catholic Church in mid-America. It also contains the first documented accounts of the Illinois Indians. He is reputed to have baptized around 10,000 neophytes.

Claude Jean Allouez (June 6, 1622 – August 28, 1689) was a Jesuit missionary and French explorer of North America. He established a number of missions among the indigenous people living near Lake Superior.


Club career.

Glentoran.

Born in Belfast, Elliott started his career at St Andrews FC, from Belfast, then moved on to Glentoran (also in Northern Ireland) before joining Scottish Premier League club Motherwell.

Motherwell.

He became a fans favourite at Fir Park and his impressive performances earned him his first cap for Northern Ireland against Malta in September 2002. In May 2002, Motherwell went into administration and as a result had to sell many of their best players. During his time at the club, Elliott scored 22 goals in 77 appearances.

Hull City.

Elliott joined Hull City for £230,000 and in his first season finished as the club's top scorer in 2002/03 with 12 goals. In 2003/04, he continued to impress and again hit double figures for his club. As Hull City clinched a place in The Championship in 2004/05, Elliott enjoyed a fantastic season netting 27 goals in the league (which earned him the golden boot, albeit shared with Dean Windass) as well as 2 in the cup, while also starring for Northern Ireland. This goal scoring tally is perhaps made all the more impressive given that Elliott does not play as a striker and was out for 6 weeks with an injury during mid-season.  Perhaps unsurprisingly, Elliott was unable to maintain this incredible goal scoring form in the Championship. In fact, he found himself in-and-out of the team, but despite this he still finished 2005/06 as Hull's top scorer with 7 league goals. In 2006 it was revealed that he was suffering from a form of exercise-induced asthma, which affects his ability to perform for the full ninety minutes. In 2006/07 he was mainly used as an 'impact player' coming off the bench late in the game, such as in the 13 January match against QPR when he came on with eleven minutes to go and scored twice to give the Tigers a 2–1 victory.

Doncaster Rovers.

On 31 January 2008, Elliott signed for Doncaster Rovers on loan until the end of the season with a view to a permanent deal. Elliott had already snubbed moves to Southend United and Darlington, citing a desire to remain in the local area. He signed a 2-year deal with Doncaster Rovers on 1 July. On 27 September 2008, Elliott became one of three men in the Rovers team to successfully hit the bar on the "Crossbar Challenge" on "Soccer AM". On 8 January 2009 Elliott joined Grimsby Town on a one-month loan deal, this was extended for another month with Elliott eventually returning on 8 March.

Hamilton Academical.

Elliot was released by Doncaster on 1 January 2010 and signed for Hamilton Academical two days later until the end of the season. He was then loaned to Stirling Albion two months later.  In August 2010, Elliott announced that he wished his contract cancelled to be able to concentrate on his faith, with a view to perhaps entering ministry.

Return to Glentoran.

Elliott returned to former club Glentoran in September 2012. He made his first appearance since returning to the club on 1 October, coming off the bench as Glentoran lost 3–2 to Linfield in the County Antrim Shield. He made his first league appearance on 6 October, coming off the bench as Glentoran lost 2–0 to Crusaders. He scored his first (and indeed only) goal since his return to Glentoran in an IRN-BRU League Cup game against Institute. The goal was described as an "unstoppable 20 yard shot". Glentoran went on to win the game 4–2 on penalties after a 2–2 draw. After making only 7 appearances and scoring 1 goal in all competitions, Elliott was released by Glentoran after the turn of the year.

International career.

Elliott earned 39 caps for Northern Ireland, scoring 4 goals including an impressive free kick against Azerbaijan. He played in Northern Ireland's famous victory over England but soon after began to struggle for his place in the team due to emerging young talents Sammy Clingan and Chris Brunt.

Personal life.

He is a born-again Christian, belonging to Living Hope Christian Church in Hull, where he is a frequent speaker and their newest pastor. There are only three churches of this denomination in the world; these being in Belfast, Motherwell and Hull, which by coincidence, correspond exactly to where he played the majority of his club football.

Stuart Elliott (born 23 July 1978) is a Northern Irish former professional footballer who played as a midfielder from 1998 to 2013.


Hunting behaviour and bioluminescence.

In 2005, a Japanese research team headed by Tsunemi Kubodera managed to film "T. danae" in its natural habitat for the first time. The video footage, shot in deep water off Chichi-jima in the northern Pacific Ocean, shows "T. danae" emitting blinding flashes of light from photophores on its arms as it attacks its prey. It is believed that this highly maneuverable squid uses the bright flashes to disorientate potential prey. These flashes may also serve to illuminate the prey to make for easier capture as well as a courtship and territorial display.  As well as a predatorial characteristic, Dana bioluminescence has also been suggested to be a defense mechanism. Juveniles of this species have been observed moving rapidly in the direction of potential predators, as if hunting, to disorientate and startle the threat with a mock attack.  In 2012, "Taningia danae" was filmed twice more during a search for the giant squid for the Discovery Channel Special, "Monster Squid: The Giant Is Real".  Remains of Dana octopus squid have, on occasion, been found washed ashore on beaches. In 2008, a mantle of "T. danae" was discovered by students in Bermuda's Grape Bay, while tentacle remnants were found further along the shore. In early 2013, a specimen with a length (excluding arms) of was trawled at a depth of off the coast of Estaca de Bares, Galicia, Spain. It was loaned to the Spanish Institute of Oceanography.

Ecology.

N ratios showed that this squid is a top predator. In turn, they are eaten by the sperm whale.

Taningia danae, the Dana octopus squid, is a species of squid in the family Octopoteuthidae. It is one of the largest known squid species, reaching a mantle length of and total length of. The largest known specimen, a mature female, weighed.


Life.

Born Marcus Henry Kellogg on March 31, 1831, in Brighton, Ontario, Canada, Kellogg was the third of ten children. Kellogg's family moved a number of times in his youth before they eventually settled in La Crosse, Wisconsin. While there Kellogg learned to operate a telegraph and went to work for both the Northwestern Telegraph Company and the Atlantic and Pacific Telegraph Company.  He married Martha J. Robinson in 1861 and they had two daughters. During the years of the American Civil War, Kellogg became the assistant editor for the "La Crosse Democrat" newspaper. He also unsuccessfully ran for the office of city clerk in 1867 and played shortstop on one of the town's baseball teams.  In 1867 Kellogg's wife died. Leaving his daughters to be raised by an aunt, Kellogg began drifting around the upper Midwest, working as a reporter and editorial assistant in places such as Council Bluffs, Iowa, and Brainerd, Minnesota. While living in Brainerd he ran for election to the Minnesota Legislature, but was defeated. He also worked as a string correspondent for the "St. Paul Dispatch", with his articles often published under the pen name of "Frontier."  In the early 1870s, he moved to Bismarck, North Dakota, where in 1873 he helped editor Clement A. Lounsberry found "The Bismarck Tribune". Even though Kellogg was only an editorial assistant for the paper, he substituted for Lounsberry as editor of the "Tribune" second, third and fourth issues.

Battle of the Little Bighorn.

When Lounsberry learned that a military column (including the 7th U.S. Cavalry Regiment commanded by Lt. Col. George Armstrong Custer) would soon leave Fort Abraham Lincoln for the Montana Territory, he agreed to accompany Custer and provide news coverage. However, at the last minute Lounsberry's wife fell ill, so the editor asked Kellogg to take his place. Lounsberry expected Kellogg would cover nothing more than a sensational military victory.  Kellogg sent three dispatches back to Lounsberry, the last one four days before the battle when they were near the mouth of the Rosebud River. His last dispatch read, "By the time this reaches you we would have met and fought the red devils, with what result remains to be seen. I go with Custer and will be at the death." Kellogg was not predicting his own death or Custer's defeat; instead, "at the death" is a phrase borrowed from fox hunting meaning "present at the kill" ("viz"., of the pursued).  Four days after that dispatch, the Battle of the Little Bighorn was fought, resulting in the deaths of Custer and the 208 soldiers, scouts, and civilians riding with him, including Kellogg.

Aftermath.

Colonel John Gibbon, whose men arrived at the battle on Tuesday, June 27, and also helped bury the dead, said he found Kellogg's body in a ravine where a number of men from Company E died. Kellogg's body was scalped and missing an ear; he was identified by the boots he wore.  When Clement Lounsberry learned of the defeat of Custer's force and Kellogg's death, he "worked tirelessly throughout the night" to produce a special edition of "The Bismarck Tribune". Published on July 6, 1876, the article was the battle's first full account. Lounsberry also telegraphed the news, including Kellogg's correspondence, to a number of eastern newspapers, including the "New York Herald". Two letters written by Kellogg were published posthumously by the "Herald" on July 11, 1876.  As a newspaper stringer whose reports were picked up around the country, Kellogg is considered the first Associated Press correspondent to die in the line of duty.  Some of Kellogg's diary and notes survived the battle and these, along with his news accounts, are one of the primary historical sources for information on the days preceding the battle. His notes are now in the possession of the State Historical Society of North Dakota. His satchel, pencil, and eyeglasses are on display in the Newseum in Washington, DC.

Mark Kellogg (March 31, 1831 – June 25, 1876) was a newspaper reporter killed at the Battle of the Little Bighorn. Kellogg rode with George Armstrong Custer during the battle. His dispatches were the only press coverage of Custer and his men in the days leading up to the battle. As a newspaper stringer whose reports were picked up around the country, Kellogg is considered the first Associated Press correspondent to die in the line of duty.


Prehistory.

On the island is a prehistoric site, an "allée couverte" (gallery grave), known as "Ty Liac'h", built in the Neolithic period. It is in the central part of the ridge of the island. There are ten upright stones, supporting three horizontal slabs. There are other stones on the ground which once were supporting stones; there was at least one other horizontal slab. The original length was, and it had a lateral entrance on the north side.  It is south of an adjacent field in which, from aerial photographs, traces have been detected of about twenty prehistoric circular huts.

History.

It is thought that St Miliau, in the 6th century, stayed here; he evangelized the local area, and founded the parish of Ploumilliau.  There is a farmhouse on the island (now converted into a "gîte"), of which the earliest parts date from medieval times. In the north-eastern gable-end is a relatively well-preseved medieval monastic cell. It measures by and its height is. The interior is formed with slabs about wide.

Maison Aristide Briand.

Mademoiselle Uro-Lalès, also known as Lucie Jourdan (1883–1957), bought the island from Count Anatole James in 1911. It remained her property until 1942. In 1920 she had a villa built here; she was the mistress of the politician Aristide Briand, and the villa was known as Maison Aristide Briand. During the Second World War, the building was occupied by German soldiers. In more recent years it became derelict, and it was demolished in 2009.

Île Milliau ("Enez Miliev" in Breton) is an island on the coast of Brittany, France, in the commune of Trébeurden (department of Côtes-d'Armor). It is the property of the "Conservatoire du littoral". It is a short distance west of the port of Trébeurden, and is accessible on foot at low tide. Its length is about and is about in area. There is moorland, with ferns and maritime shrubs.