The Answers, #6051 (Boston) and #6052 (Brisbane), are correct. Marvelous, bobbym!
#6053. Amnesty International (commonly known as Amnesty and AI) is a non-governmental organisation focused on human rights with over 7 million members and supporters around the world. The stated objective of the organisation is "to conduct research and generate action to prevent and end grave abuses of human rights, and to demand justice for those whose rights have been violated." When, where and by whom was it founded?
#6054. Name the intergovernmental organization headquartered in Brussels, Belgium. Formerly called Customs Co-operation Council (CCC). It is noted for its work in areas covering the development of international conventions, instruments, and tools on topics such as commodity classification, valuation, rules of origin, collection of customs revenue, supply chain security, international trade facilitation, customs enforcement activities, combating counterfeiting in support of Intellectual Property Rights (IPR),drugs enforcement,weapans illegal trading, integrity promotion, and delivering sustainable capacity building to assist with customs reforms and modernization. The WCO maintains the international Harmonized System (HS) goods nomenclature, and administers the technical aspects of the World Trade Organization (WTO) Agreements on Customs Valuation and Rules of Origin.
The solution #5850 (two parts) are correct. Neat work, Monox D. I-Fly and bobbym!
#5851. A lot consists of 144 ball-pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy it if it is defective. The shopkeeper draws a pen at random and gives it to her. What is the probability that
(i) she will but it?
(ii) she will not buy it?
141. Otto Hahn
Otto Hahn, (born March 8, 1879, Frankfurt am Main, Ger.—died July 28, 1968, Göttingen, W.Ger.) German chemist who, with the radiochemist Fritz Strassmann, is credited with the discovery of nuclear fission. He was awarded the Nobel Prize for Chemistry in 1944 and shared the Enrico Fermi Award in 1966 with Strassmann and Lise Meitner.
Hahn was the son of a glazier. Although his parents wanted him to become an architect, he eventually decided to study chemistry at the University of Marburg. There Hahn worked hard at chemistry, though he was inclined to absent himself from physics and mathematics lectures in favour of art and philosophy, and he obtained his doctorate in 1901. After a year of military service, he returned to the university as chemistry lecture assistant, hoping to find a post in industry later on.
In 1904 he went to London, primarily to learn English, and worked at University College with Sir William Ramsay, who was interested in radioactivity. While working on a crude radium preparation that Ramsay had given to him to purify, Hahn showed that a new radioactive substance, which he called radiothorium, was present. Fired by this early success and encouraged by Ramsay, who thought highly of him, he decided to continue with research on radioactivity rather than go into industry. With Ramsay’s support he obtained a post at the University of Berlin. Before taking it up, he decided to spend several months in Montreal with Ernest Rutherford (later Lord Rutherford of Nelson) to gain further experience with radioactivity. Shortly after returning to Germany in 1906, Hahn was joined by Lise Meitner, an Austrian-born physicist, and five years later they moved to the new Kaiser Wilhelm Institute for Chemistry at Berlin-Dahlen. There Hahn became head of a small but independent department of radiochemistry.
Feeling that his future was more secure, Hahn married Edith Junghans, the daughter of the chairman of Stettin City Council, in 1913; but World War I broke out the next year, and Hahn was posted to a regiment. In 1915 he became a chemical-warfare specialist, serving on all the European fronts.
After the war, Hahn and Meitner were among the first to isolate protactinium-231, an isotope of the recently discovered radioactive element protactinium. Because nearly all the natural radioactive elements had then been discovered, he devoted the next 12 years to studies on the application of radioactive methods to chemical problems.
Discovery of nuclear fission
In 1934 Hahn became keenly interested in the work of the Italian physicist Enrico Fermi, who found that when the heaviest natural element, uranium, is bombarded by neutrons, several radioactive products are formed. Fermi supposed these products to be artificial elements similar to uranium. Hahn and Meitner, assisted by the young Strassmann, obtained results that at first seemed in accord with Fermi’s interpretation but that became increasingly difficult to understand. Meitner fled from Germany in July 1938 to escape the persecution of Jews by the Nazis, but Hahn and Strassmann continued the work. By the end of 1938, they obtained conclusive evidence, contrary to previous expectation, that one of the products from uranium was a radioactive form of the much lighter element barium, indicating that the uranium atom had split into two lighter atoms. Hahn sent an account of the work to Meitner, who, in cooperation with her nephew Otto Frisch, formulated a plausible explanation of the process, to which they gave the name nuclear fission.
The tremendous implications of this discovery were realized by scientists before the outbreak of World War II, and a group was formed in Germany to study possible military developments. Much to Hahn’s relief, he was allowed to continue with his own researches. After the war, he and other German nuclear scientists were taken to England, where he learned that he had been awarded the Nobel Prize for 1944 and was profoundly affected by the announcement of the explosion of the atomic bomb at Hiroshima in 1945. Although now aged 66, he was still a vigorous man; a lifelong mountaineer, he maintained physical fitness during the enforced stay in England by a daily run.
On his return to Germany he was elected president of the former Kaiser Wilhelm Society (renamed the Max Planck Society for the Advancement of Science) and became a respected public figure, a spokesman for science, and a friend of Theodor Heuss, the first president of the Federal Republic of Germany. He campaigned against further development and testing of nuclear weapons. Honours came to him from all sides; in 1966 he, Meitner, and Strassmann shared the prestigious Enrico Fermi Award. This period of his life was saddened, however, by the loss of his only son, Hanno, and his daughter-in-law, who were killed in an automobile accident in 1960. His wife never recovered from the shock. Hahn died in 1968, after a fall; his wife survived him by only two weeks.
#6049. What does the acronym 'AWACS' signify? (Derived from the Boeing 707, it provides all-weather surveillance, command, control, and communications, and is used by the United States Air Force, NATO, Royal Air Force, French Air Force, and Royal Saudi Air Force. The E-3 is distinguished by the distinctive rotating radar dome above the fuselage. Production ended in 1992 after 68 aircraft had been built.)
#6050. What does the acronym 'FLAG' signify? ( a 28,000-kilometer-long optical fiber mostly-submarine communications cable that connects the United Kingdom, Japan, and many places in between. The cable is operated by Global Cloud Xchange. The system runs from the eastern coast of North America to Japan. Its Europe-Asia segment was the fourth longest cable in the world in 2008.)
The solution #5848(a) is correct. Neat work!
#5849. A box contains 90 discs which are numbered from 1 to 90. If 1 disc is drawn at random from the box, find the probability that is bears
(i) a two-digit number.
(ii) a perfect square number.
(iii) a number which is divisible by 5.
140. Carl Friedrich Gauss, original name Johann Friedrich Carl Gauss (born April 30, 1777, Brunswick [Germany]—died February 23, 1855, Göttingen, Hanover) German mathematician, generally regarded as one of the greatest mathematicians of all time for his contributions to number theory, geometry, probability theory, geodesy, planetary astronomy, the theory of functions, and potential theory (including electromagnetism).
Gauss was the only child of poor parents. He was rare among mathematicians in that he was a calculating prodigy, and he retained the ability to do elaborate calculations in his head most of his life. Impressed by this ability and by his gift for languages, his teachers and his devoted mother recommended him to the duke of Brunswick in 1791, who granted him financial assistance to continue his education locally and then to study mathematics at the University of Göttingen from 1795 to 1798. Gauss’s pioneering work gradually established him as the era’s preeminent mathematician, first in the German-speaking world and then farther afield, although he remained a remote and aloof figure.
Gauss’s first significant discovery, in 1792, was that a regular polygon of 17 sides can be constructed by ruler and compass alone. Its significance lies not in the result but in the proof, which rested on a profound analysis of the factorization of polynomial equations and opened the door to later ideas of Galois theory. His doctoral thesis of 1797 gave a proof of the fundamental theorem of algebra: every polynomial equation with real or complex coefficients has as many roots (solutions) as its degree (the highest power of the variable). Gauss’s proof, though not wholly convincing, was remarkable for its critique of earlier attempts. Gauss later gave three more proofs of this major result, the last on the 50th anniversary of the first, which shows the importance he attached to the topic.
Gauss’s recognition as a truly remarkable talent, though, resulted from two major publications in 1801. Foremost was his publication of the first systematic textbook on algebraic number theory, Disquisitiones Arithmeticae. This book begins with the first account of modular arithmetic, gives a thorough account of the solutions of quadratic polynomials in two variables in integers, and ends with the theory of factorization mentioned above. This choice of topics and its natural generalizations set the agenda in number theory for much of the 19th century, and Gauss’s continuing interest in the subject spurred much research, especially in German universities.
The second publication was his rediscovery of the asteroid Ceres. Its original discovery, by the Italian astronomer Giuseppe Piazzi in 1800, had caused a sensation, but it vanished behind the Sun before enough observations could be taken to calculate its orbit with sufficient accuracy to know where it would reappear. Many astronomers competed for the honour of finding it again, but Gauss won. His success rested on a novel method for dealing with errors in observations, today called the method of least squares. Thereafter Gauss worked for many years as an astronomer and published a major work on the computation of orbits—the numerical side of such work was much less onerous for him than for most people. As an intensely loyal subject of the duke of Brunswick and, after 1807 when he returned to Göttingen as an astronomer, of the duke of Hanover, Gauss felt that the work was socially valuable.
Similar motives led Gauss to accept the challenge of surveying the territory of Hanover, and he was often out in the field in charge of the observations. The project, which lasted from 1818 to 1832, encountered numerous difficulties, but it led to a number of advancements. One was Gauss’s invention of the heliotrope (an instrument that reflects the Sun’s rays in a focused beam that can be observed from several miles away), which improved the accuracy of the observations. Another was his discovery of a way of formulating the concept of the curvature of a surface. Gauss showed that there is an intrinsic measure of curvature that is not altered if the surface is bent without being stretched. For example, a circular cylinder and a flat sheet of paper have the same intrinsic curvature, which is why exact copies of figures on the cylinder can be made on the paper (as, for example, in printing). But a sphere and a plane have different curvatures, which is why no completely accurate flat map of the Earth can be made.
Gauss published works on number theory, the mathematical theory of map construction, and many other subjects. In the 1830s he became interested in terrestrial magnetism and participated in the first worldwide survey of the Earth’s magnetic field (to measure it, he invented the magnetometer). With his Göttingen colleague, the physicist Wilhelm Weber, he made the first electric telegraph, but a certain parochialism prevented him from pursuing the invention energetically. Instead, he drew important mathematical consequences from this work for what is today called potential theory, an important branch of mathematical physics arising in the study of electromagnetism and gravitation.
Gauss also wrote on cartography, the theory of map projections. For his study of angle-preserving maps, he was awarded the prize of the Danish Academy of Sciences in 1823. This work came close to suggesting that complex functions of a complex variable are generally angle-preserving, but Gauss stopped short of making that fundamental insight explicit, leaving it for Bernhard Riemann, who had a deep appreciation of Gauss’s work. Gauss also had other unpublished insights into the nature of complex functions and their integrals, some of which he divulged to friends.
In fact, Gauss often withheld publication of his discoveries. As a student at Göttingen, he began to doubt the a priori truth of Euclidean geometry and suspected that its truth might be empirical. For this to be the case, there must exist an alternative geometric description of space. Rather than publish such a description, Gauss confined himself to criticizing various a priori defenses of Euclidean geometry. It would seem that he was gradually convinced that there exists a logical alternative to Euclidean geometry. However, when the Hungarian János Bolyai and the Russian Nikolay Lobachevsky published their accounts of a new, non-Euclidean geometry about 1830, Gauss failed to give a coherent account of his own ideas. It is possible to draw these ideas together into an impressive whole, in which his concept of intrinsic curvature plays a central role, but Gauss never did this. Some have attributed this failure to his innate conservatism, others to his incessant inventiveness that always drew him on to the next new idea, still others to his failure to find a central idea that would govern geometry once Euclidean geometry was no longer unique. All these explanations have some merit, though none has enough to be the whole explanation.
Another topic on which Gauss largely concealed his ideas from his contemporaries was elliptic functions. He published an account in 1812 of an interesting infinite series, and he wrote but did not publish an account of the differential equation that the infinite series satisfies. He showed that the series, called the hypergeometric series, can be used to define many familiar and many new functions. But by then he knew how to use the differential equation to produce a very general theory of elliptic functions and to free the theory entirely from its origins in the theory of elliptic integrals. This was a major breakthrough, because, as Gauss had discovered in the 1790s, the theory of elliptic functions naturally treats them as complex-valued functions of a complex variable, but the contemporary theory of complex integrals was utterly inadequate for the task. When some of this theory was published by the Norwegian Niels Abel and the German Carl Jacobi about 1830, Gauss commented to a friend that Abel had come one-third of the way. This was accurate, but it is a sad measure of Gauss’s personality in that he still withheld publication.
Gauss delivered less than he might have in a variety of other ways also. The University of Göttingen was small, and he did not seek to enlarge it or to bring in extra students. Toward the end of his life, mathematicians of the calibre of Richard Dedekind and Riemann passed through Göttingen, and he was helpful, but contemporaries compared his writing style to thin gruel: it is clear and sets high standards for rigour, but it lacks motivation and can be slow and wearing to follow. He corresponded with many, but not all, of the people rash enough to write to him, but he did little to support them in public. A rare exception was when Lobachevsky was attacked by other Russians for his ideas on non-Euclidean geometry. Gauss taught himself enough Russian to follow the controversy and proposed Lobachevsky for the Göttingen Academy of Sciences. In contrast, Gauss wrote a letter to Bolyai telling him that he had already discovered everything that Bolyai had just published.
After Gauss’s death in 1855, the discovery of so many novel ideas among his unpublished papers extended his influence well into the remainder of the century. Acceptance of non-Euclidean geometry had not come with the original work of Bolyai and Lobachevsky, but it came instead with the almost simultaneous publication of Riemann’s general ideas about geometry, the Italian Eugenio Beltrami’s explicit and rigorous account of it, and Gauss’s private notes and correspondence.
The solution #5847 is correct. Neat work, bobbym!
#5848. (i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?
#6047. When is 'World Information Society Day' proclaimed? (The day had previously been known as World Telecommunication Day to commemorate the founding of the International Telecommunication Union on 1865.)
#6048. When is 'World No Tobacco Day' (WNTD) is observed around the world every year? ( It is intended to encourage a 24-hour period of abstinence from all forms of tobacco consumption around the globe. The day is further intended to draw attention to the widespread prevalence of tobacco use and to negative health effects, which currently lead to nearly 6 million deaths each year worldwide, including 600,000 of which are the result of non-smokers being exposed to second-hand smoke.)
The solutions in #5846 are correct. Neat work, bobbym!
#5847. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at the pen and tell weather or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.