Lucille Ball

Lucille Désirée Ball was an American actress, model, entertainment studio executive and producer. She was the star of the self-produced sitcoms I Love Lucy, The Lucy Show, Here's Lucy, Life with Lucy, as well as comedy television specials aired under the title The Lucy-Desi Comedy Hour. Ball's career began in 1929. Shortly thereafter, she began her performing career on Broadway using the stage names Diane Belmont and Dianne Belmont, she appeared in several minor film roles in the 1930s and 1940s as a contract player for RKO Radio Pictures, being cast as a chorus girl or in similar roles. During this time, she met Cuban bandleader Desi Arnaz, the two eloped in November 1940. In the 1950s, Ball ventured into television. In 1951, she and Arnaz created the sitcom I Love Lucy, a series that became one of the most beloved programs in television history; the same year, Ball gave birth to their first child, Lucie Arnaz, followed by Desi Arnaz Jr. in 1953. Ball and Arnaz divorced in May 1960, she married comedian Gary Morton in 1961.

Following the end of I Love Lucy, Ball appeared in a Broadway musical, for a year from 1960 to 1961. However, the show received lukewarm reviews and had to be shut down permanently when Ball became ill for a brief time. After Wildcat, Ball reunited with I Love Lucy co-star Vivian Vance for the aforementioned Lucy Show, which Vance left in 1965 but which continued for three years with longtime friend of Ball's Gale Gordon who had a recurring role on the program; the Lucy Show ended its run in 1968 and Ball began appearing in a new series, Here's Lucy, with Gordon, frequent guest on her shows Mary Jane Croft, Lucie and Desi Jr.. In 1962, Ball became the first woman to run a major television studio, Desilu Productions, which produced many popular television series, including Mission: Impossible and Star Trek. Ball did not back away from acting completely. In 1985, she took on a dramatic role in Stone Pillow; the next year she starred in Life with Lucy. She appeared in film and television roles for the rest of her career until her death in April 1989 from an abdominal aortic dissection at the age of 77.

Ball was nominated for 13 Primetime Emmy Awards, winning four times. In 1960, she received two stars for her work in television on the Hollywood Walk of Fame. In 1977, Ball was among the first recipients of the Women in Film Crystal Award, she was the recipient of the Golden Globe Cecil B. DeMille Award in 1979, was inducted into the Television Hall of Fame in 1984, received the Lifetime Achievement Award from the Kennedy Center Honors in 1986, the Governors Award from the Academy of Television Arts & Sciences in 1989. Born at 69 Stewart Avenue, New York, Lucille Désirée Ball was the daughter of Henry Durrell Ball and Désirée "DeDe" Evelyn Ball, her family lived in Wyandotte, for a time. She sometimes claimed that she had been born in Butte, where her grandparents had lived. A number of magazines reported inaccurately that she had decided that Montana was a more romantic place to be born than New York and repeated a fantasy of a "western childhood". However, her father had moved the family to Anaconda, for his work, where they lived among other places.

Her family belonged to the Baptist church. Her ancestors were English, but a few were Scottish and Irish; some were among the earliest settlers in the Thirteen Colonies, including Elder John Crandall of Westerly, Rhode Island, Edmund Rice, an early emigrant from England to the Massachusetts Bay Colony. In February 1915, when Lucille was three years old, her 27-year-old father died of typhoid fever. Henry Ball was a lineman for Bell Telephone Company and was transferred; the family had moved from Jamestown to Anaconda, to Trenton, New Jersey. At the time of Henry's death, DeDe Ball was pregnant with Frederick. Ball recalled little from the day her father died, but remembered a bird getting trapped in the house. From that day forward, she suffered from ornithophobia. After Ball's father died, her mother returned to New York. Ball and her brother, Fred Henry Ball, were raised by their mother and maternal grandparents in Celoron, New York, a summer resort village on Lake Chautauqua, 2.5 miles west of downtown Jamestown.

Lucy loved one of the best amusement areas in the United States at that time. Its boardwalk had a ramp to the lake that served as a children's slide, the Pier Ballroom, a roller-coaster, a bandstand, a stage where vaudeville concerts and regular theatrical shows were presented which made Celoron Park a popular resort. Four years after Henry Ball's death, DeDe Ball married Edward Peterson. While her mother and stepfather looked for work in another city, Peterson's parents cared for her and her brother. Ball's stepgrandparents were a puritanical Swedish couple who banished all mirrors from the house except one over the bathroom sink; when the young Ball was caught admiring herself in it, she was chastised for being vain. This period of time affected Ball so that, in life, she said that it lasted seven or eight years. Peterson was a Shriner; when his organization needed female entertainers for the chorus line of their next show, he encouraged his 12-year-old stepdaughter to audition. While Ball was onstage, she realized performing was a great way to gain recognition.

Her appetite for recognition was awakened at an early age. In 1927, her family suffered misfortune, their house and furnishings were lost to se

Polish–Swedish War (1621–1625)

The Polish–Swedish War of 1621 to 1625 was a war in a long-running series of conflicts between the Polish–Lithuanian Commonwealth and the Swedish Empire. It began with a Swedish invasion of the Polish–Lithuanian fiefdom Livonia. Swedish forces succeeded in taking the city of Riga after a siege; the Commonwealth, focussed on war with the Ottoman Empire, was unable to send significant forces to stop Gustav Adolf, signed a truce favorable to Sweden. The Commonwealth ceded Livonia north of the Dvina river, retained only nominal control over Riga; the new truce in Mitau was signed and lasted from November 1622 to March 1625. The Polish–Swedish War of 1617–18) showed that the Swedish Army, despite several reforms, was still unable to defeat the Polish–Lithuanian Commonwealth. Furthermore, King Gustav Adolf was still regarded in Europe as a usurper. To safeguard the Swedish crown for himself, Gustav Adolf decided to force Sigismund III Vasa to relinquish it. With help from Axel Oxenstierna, the Swedish king introduced a widespread program of military and social reforms, which resulted in creation of a well trained army, based on native recruits.

These further reforms and the ongoing conflict between the Commonwealth and the Ottoman Empire, offered Gustav Adolf a further chance to defeat the Commonwealth. While the Polish–Lithuanian army was concentrated in Podolia, in the south of the Commonwealth, a Swedish army landed near Pärnu, August 19, 1621, it was carried by a fleet of 148 vessels. Gustav Adolf had 3,150 cavalry and 375 cannons; the Swedes marched towards Riga, started a siege on 29 August. The capital of Livonia was defended by a garrison of 300 soldiers, plus 3,700 armed residents. Lithuanian Field Hetman Krzysztof Radziwiłł had only 1,500 soldiers at his disposal, as most units were in Podolia and Red Ruthenia. Riga capitulated after three assaults. On October 2, the Swedes captured the fortress of Dunamunde; the invaders, marching through marshes and forests to avoid Lithuanian cavalry, entered the Duchy of Courland and Semigallia, capturing its capital, Mitau without resistance. The Swedes tried to capture the fortress of Koknese, but failed to do so, after a skirmish with Lithuanian cavalry of Aleksander Gosiewski.

In early January 1622, the Swedes captured Valmiera, together with several smaller Livonian castles. Meanwhile, the forces under Hetman Radziwiłł grew to 3,000, which enabled the Lithuanians to respond better to Swedish attacks. On January 7, Radziwiłł recaptured Mitau, but because of a lack of artillery, he failed to seize its castle, whose garrison did not capitulate until July 6. A few weeks in late July 1622, main Swedish forces reached Mittau, a prolonged battle ensued. Since the battle turned into a stalemate, on August 10, 1622, both sides signed a truce, which in 1623 was prolonged until March 1625. During the negotiations, envoys of Gustav Adolf suggested a Swedish–Lithuanian union; the Swedish insisted on a truce due to financial problems of the Swedish Empire, as the costs of the war were too high for their treasury. Furthermore, in the autumn of 1621, the Polish–Ottoman War ended, the army of the Commonwealth was ready to march to Livonia; the truce, signed by the Lithuanians, enraged King Sigismund III Vasa, who planned to transfer all forces northwards, hoping that with the help of the Spanish Navy, he would be able to invade Sweden itself.

Polish nobility and leaders such as Krzysztof Radziwiłł and Krzysztof Zbaraski disagreed with the royal plans. They wanted the King to agree to Swedish terms, to relinquish the Swedish throne in exchange for a permanent peace treaty and Livonia. Radziwiłł emphasized the fact that after the reforms, the Swedish army was difficult to defeat, Poland–Lithuania needed a major overhaul of its armed forces the infantry and artillery; the Commonwealth needed a strong navy and specialized units of engineers, trained in erection of field fortifications. Regardless of the opinion of his generals, Sigismund III ordered construction of a fleet, with help from the Spanish Empire, was to transport the invading army to Sweden. In 1623, the Polish King met with the Starosta of Jan Wejher, telling him to build the fleet. However, from the beginning, this was questioned by the powerful and semi-independent city of Gdańsk, whose government, under Swedish pressure, opposed the idea of a Commonwealth fleet, did not allow it to be anchored in its port.

Under these circumstances, Sigismund III Wasa decided to expand the shipyard of Puck. In 1624-1626, seven medium size ships were built here, with tonnage ranging from 200 to 400 tons, they were manned by local Kashubian fishermen, while marine infantry consisted of English mercenaries, employed by the Polish King since 1621. The biggest ship of the new fleet was the galleon Król Dawid. Before the end of the truce, Gustav Adolf initiated talks with Muscovy and the Ottoman Empire, hoping for a joint attack on Poland–Lithuania. Furthermore, he sent his envoys to Sich, trying to incite the Zaporozhian Cossacks, who were Polish subjects, to attack Turkey, provoke another Polish–Ottoman war. On June 27, 1625, Gustav Adolf landed in Livonia with an army of 20,000; the main Swedish corps of 10,000 marched upwards the Daugava River, besieged Koknese, capturing it after sixteen days. On August 27, Swedes captured Tartu, soon afterwards, Mitau. In early September 1625, Swedish forces invaded the Grand Duchy of Lithuania, capturing Biržai on September 7.

This success cut links between Polish–Li

Bellman–Ford algorithm

The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers; the algorithm was first proposed by Alfonso Shimbel, but is instead named after Richard Bellman and Lester Ford Jr. who published it in 1958 and 1956, respectively. Edward F. Moore published the same algorithm in 1957, for this reason it is sometimes called the Bellman–Ford–Moore algorithm. Negative edge weights are found in various applications of graphs, hence the usefulness of this algorithm. If a graph contains a "negative cycle", reachable from the source there is no cheapest path: any path that has a point on the negative cycle can be made cheaper by one more walk around the negative cycle. In such a case, the Bellman -- Ford algorithm can report the negative cycle. Like Dijkstra's algorithm, Bellman–Ford proceeds by relaxation, in which approximations to the correct distance are replaced by better ones until they reach the solution.

In both algorithms, the approximate distance to each vertex is always an overestimate of the true distance, is replaced by the minimum of its old value and the length of a newly found path. However, Dijkstra's algorithm uses a priority queue to greedily select the closest vertex that has not yet been processed, performs this relaxation process on all of its outgoing edges. In each of these repetitions, the number of vertices with calculated distances grows, from which it follows that all vertices will have their correct distances; this method allows the Bellman–Ford algorithm to be applied to a wider class of inputs than Dijkstra. Bellman–Ford runs in O time, where | V | and | E | are the number of vertices and edges respectively. Function BellmanFord is::distance, predecessor // This implementation takes in a graph, represented as // lists of vertices and edges, fills two arrays // about the shortest path // from the source to each vertex // Step 1: initialize graph for each vertex v in vertices do distance:= inf // Initialize the distance to all vertices to infinity predecessor:= null // And having a null predecessor distance:= 0 // The distance from the source to itself is, of course, zero // Step 2: relax edges for i from 1 to size−1 do //just |V|−1 repetitions.

For all edges, if the distance to the destination can be shortened by taking the edge, the distance is updated to the new lower value. At each iteration i that the edges are scanned, the algorithm finds all shortest paths of at most length i edges. Since the longest possible path without a cycle can be | V | − 1 edges, the edges must be scanned | V | − 1 times to ensure the shortest path has been found for all nodes. A final scan of all the edges is performed and if any distance is updated a path of length | V | edges has been found which can only occur if at least one negative cycle exists in the graph; the correctness of the algorithm can be shown by induction: Lemma. After i repetitions of for loop, if Distance is not infinity, it is equal to the length of some path from s to u. Proof. For the base case of induction, consider i=0 and the moment before for loop is executed for the first time. For the source vertex, source.distance = 0, correct. For other vertices u, u.distance = infinity, correct because there is no path from source to u with 0 edges.

For the inductive case, we first prove the first part. Consider a moment when a vertex's distance is updated by v.distance:= u.distance + uv.weight. By inductive assumption, u.distance is the length of some path from source to u. U.distance + uv.weight is the length of the path from source to v that follows the path from source to u and goes to v. For the second part, consider a shortest path P from source to u with at most i edges. Let v be the last vertex before u on this path; the part of the path from source to v is a shortest path f