Appeasement in an international context is a diplomatic policy of making political or material concessions to an aggressive power in order to avoid conflict. The term is most applied to the foreign policy of the British governments of Prime Ministers Ramsay MacDonald, Stanley Baldwin and most notably Neville Chamberlain towards Nazi Germany and Fascist Italy between 1935 and 1939. At the beginning of the 1930s, such concessions were seen as positive due to the trauma of World War I, second thoughts about the vindictive treatment of Germany in the Treaty of Versailles, a perception that Fascism was a useful form of anti-communism. However, by the time of the Munich Pact—concluded on 30 September 1938 among Germany, Britain and Italy—the policy was opposed by the Labour Party, by a few Conservative dissenters such as Winston Churchill, Duff Cooper, Anthony Eden. Appeasement was supported by Britain's upper class, including royalty, big business, the House of Lords, media leaders such as BBC and The Times.

As alarm grew about the rise of fascism in Europe, Chamberlain resorted to news censorship to control public opinion. He confidently announced after Munich that he had secured "peace for our time"; the policies have been the subject of intense debate for more than seventy years among academics and diplomats. The historians' assessments have ranged from condemnation for allowing Hitler's Germany to grow too strong, to the judgment that Germany was so strong that it might well win a war and that postponement of a showdown was in their country's best interests. Historian Andrew Roberts argued in 2019, "Indeed, it is the accepted view in Britain today that they were right at least to have tried... Britain would not enter hostilities for many more months, admitting unreadiness to directly oppose Germany in combat, she sat and watched the invasion of France, acting only four years later." Chamberlain's policy of appeasement emerged from the failure of the League of Nations and the failure of collective security.

The League of Nations was set up in the aftermath of World War I in the hope that international cooperation and collective resistance to aggression might prevent another war. Members of the League were entitled to the assistance of other members; the policy of collective security ran in parallel with measures to achieve international disarmament and where possible was to be based on economic sanctions against an aggressor. It appeared to be ineffectual when confronted by the aggression of dictators, notably Germany's Remilitarization of the Rhineland, Italian leader Benito Mussolini's invasion of Abyssinia. In September 1931, Japan, a member of the League of Nations, invaded Manchuria in northeast China, claiming that its population was not only Chinese, but was a multi-ethnic region. China appealed to the United States for assistance; the Council of the League asked the parties to withdraw to their original positions to permit a peaceful settlement. The United States reminded them of their duty under the Kellogg–Briand Pact to settle matters peacefully.

Japan went on to occupy the whole of Manchuria. The League set up a commission of inquiry that condemned Japan, the League duly adopting the report in February 1933. In response Japan continued its advance into China. However, the U. S. issued the Stimson Doctrine and refused to recognize Japan's conquest, which played a role in shifting U. S. policy to favour China over Japan late in the 1930s. Some historians, such as David Thomson, assert that the League's "inactivity and ineffectualness in the Far East lent every encouragement to European aggressors who planned similar acts of defiance". In this 1935 pact, Britain permitted Germany to begin rebuilding its navy, including its U-boats, in spite of Hitler having violated the Treaty of Versailles. Italian Prime Minister Benito Mussolini had imperial ambitions in Abyssinia. Italy was in possession of neighboring Eritrea and Somalia. In December 1934 there was a clash between Italian and Abyssinian troops at Walwal, near the border between British and Italian Somaliland, in which Italian troops took possession of the disputed territory and in which 150 Abyssinians and 50 Italians were killed.

When Italy demanded apologies and compensation from Abyssinia, Abyssinia appealed to the League, Emperor Haile Selassie famously appealing in person to the assembly in Geneva. The League persuaded both sides to seek a settlement under the Italo-Ethiopian Treaty of 1928 but Italy continued troop movements and Abyssinia appealed to the League again. In October 1935 Mussolini launched an attack on Abyssinia; the League declared Italy to be the aggressor and imposed sanctions, but coal and oil were not included. Albania and Hungary refused to apply sanctions; the Italian economy suffered. The League considered closing off the Suez Canal which would have stopped arms to Abyssinia, thinking it would be too harsh a measure, they did not do so. Earlier, in April 1935, Italy had joined France in protest against Germany's rearmament. France was anxious to placate Mussolini so as to keep him away from an alliance with Germany. Britain was less hostile to Germany and set the pace in imposing sanctions and moved a naval fleet into the Mediterranean.

But in November 1935, the British Foreign Secretary, Sir Samuel Hoare and the French Prime Minister, Pierre Laval, had secret discussions in which they agreed to concede two-thirds of Abyssinia to Italy. However, the press leaked the content of the discussions

List of The Spectacular Spider-Man episodes

The Spectacular Spider-Man is an American animated television series based on the Marvel Comics character, Spider-Man, developed for television by Greg Weisman and Victor Cook. In terms of tone and style, the series is based principally on the original stories by Stan Lee and Steve Ditko, with a similar balance of action and comedy as well as a high school setting. However, it tends to utilize material from all eras of the comic's run and other sources such as the film series and the Ultimate Spider-Man comics; the series premiered on March 8, 2008 during the Kids' WB programming block of The CW, its second season aired on Disney XD in the United States, ended its run on November 18, 2009. Throughout its run, The Spectacular Spider-Man was acclaimed by both audiences; the entire series was broadcast in Canada on Teletoon. Following the central theme of "The Education of Peter Parker", the series is broken up into loose arcs, each consisting of three to four episodes that take place over a month within the series, with the episode titles in each arc adopting terms from specific fields of study.

Both Season One and Two consist of 13 episodes. The first three episodes are named after notions in biology, the next three are named after ones in economics, the following three are terms in chemistry, while the final four are notions in psychology; the first four episodes are named after notions from engineering, the next three are named after ones in human development, the following three are terms in criminology, while the final three are drama terminologies. The Spectacular Spider-Man – list of episodes on IMDb List of The Spectacular Spider-Man episodes at

Graver basis

In applied mathematics, Graver bases enable iterative solutions of linear and various nonlinear integer programming problems in polynomial time. They were introduced by Jack E. Graver, their connection to the theory of Gröbner bases was discussed by Bernd Sturmfels. The algorithmic theory of Graver bases and its application to integer programming is described by Shmuel Onn; the Graver basis of an m × n integer matrix A is the finite set G of minimal elements in the set under a well partial order on Z n defined by x ⊑ y when x i y i ≥ 0 and | x i | ≤ | y i | for all i. For example, the Graver basis of A = consists of the vectors, their negations. Integer programming is the problem of optimizing a linear or nonlinear objective function over the set of integer points satisfying a system of linear inequalities. Formally, it can be written in standard form: min, it is one of the most fundamental discrete optimization problems and has a broad modeling power and numerous applications in a variety of areas, but is very hard computationally as noted below.

However, given the Graver basis G of A, the problem with linear and various nonlinear objective functions can be solved in polynomial time as explained next. The most studied case, treated in, is that of linear integer programming, min, it may be assumed that all variables are bounded from below and above: such bounds either appear in the application at hand, or can be enforced without losing any optimal solutions. But with linear objective functions the problem is NP-hard and hence cannot be solved in polynomial time. However, given the Graver basis G of A it can be solved in polynomial time using the following simple iterative algorithm. Assume first that some initial feasible point x is given. While possible, repeat the following iteration: find positive integer q and element g in G such that x + qg does not violate the bounds and gives best possible improvement; the last point x is optimal and the number of iterations is polynomial. To find an initial feasible point, a suitable auxiliary program can be set up and solved in a similar fashion.

Turning to the case of general objective functions f, if the variables are unbounded the problem may in fact be uncomputable: it follows from the solution of Hilbert's 10th problem, that there exists no algorithm which, given an integer polynomial f of degree 8 in 58 variables, decides if the minimum value of f over all 58-dimensional integer vectors is 0. However, when the variables are bounded, the problem min can be solved using the Graver basis G in polynomial time for several nonlinear objective functions including: Separable-convex functions of the form f = ∑ i = 1 n f i. Consider the following optimization problem over three-dimensional tables with prescribed line sums, min { w x: x ∈ Z + l × m × n, ∑ i x i, j