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Residue theorem

In complex analysis, a discipline within mathematics, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves. It generalizes Cauchy's integral formula. From a geometrical perspective, it is a special case of the generalized Stokes' theorem; the statement is as follows: Let U be a connected open subset of the complex plane containing a finite list of points a1... an, f a function defined and holomorphic on U \. Let γ be a closed rectifiable curve in U which does not meet any of the ak, denote the winding number of γ around ak by I; the line integral of f around γ is equal to 2πi times the sum of residues of f at the points, each counted as many times as γ winds around the point: ∮ γ ⁡ f d z = 2 π i ∑ k = 1 n I ⁡ Res ⁡. If γ is a positively oriented simple closed curve, I = 1 if ak is in the interior of γ, 0 if not, so ∮ γ ⁡ f d z = 2 π i ∑ Res ⁡ with the sum over those ak inside γ; the relationship of the residue theorem to Stokes' theorem is given by the Jordan curve theorem.

The general plane curve γ must first be reduced to a set of simple closed curves whose total is equivalent to γ for integration purposes. The requirement that f be holomorphic on U0 = U \ is equivalent to the statement that the exterior derivative d = 0 on U0, thus if two planar regions V and W of U enclose the same subset of, the regions V \ W and W \ V lie in U0, hence ∫ V ∖ W d − ∫ W ∖ V d is well-defined and equal to zero. The contour integral of f dz along γj = ∂V is equal to the sum of a set of integrals along paths λj, each enclosing an arbitrarily small region around a single aj — the residues of f at. Summing over, we recover the final expression of the contour integral in terms of the winding numbers. In order to evaluate real integrals, the residue theorem is used in the following manner: the integrand is extended to the complex plane and its residues are computed, a part of the real axis is extended to a closed curve by attaching a half-circle in the upper or lower half-plane, forming a semicircle.

The integral over this curve can be computed using the residue theorem. The half-circle part of the integral will tend towards zero as the radius of the half-circle grows, leaving only the real-axis part of the integral, the one we were interested in; the integral ∫ − ∞ ∞ e i t x x 2 + 1 d x arises in probability theory when calculating the characteristic function of the Cauchy distribution. It resists the techniques of elementary calculus but can be evaluated by expressing it as a limit of contour integrals. Suppose t > 0 and define the contour C that goes along the real line from −a to a and counterclockwise along a semicircle centered at 0 from a to −a. Take a to be greater than 1, so that the imaginary unit i is enclosed within the curve. Now consider the contour integral ∫ C f d z = ∫ C e i t z z 2 + 1 d z. Since eitz is an entire function, this function has singularities only where the denominator z2 + 1 is zero. Since z2 + 1 =, that happens only where z = i or z = −i. Only one of those points is in the region bounded by this contour.

Because f is e i t z z 2 + 1 = e i t z 2 i ( 1 z − i − 1 z +

Wan Zack Haikal

Wan Zack Haikal bin Wan Noor is a Malaysian professional footballer who plays as a striker or a midfielder for Selangor in Malaysia Super League. He is a member of the Malaysia national team. Wan Zack Haikal was born in Pahang, he attended a SMK Kuala Lanar, project school of Pahang FA at Kuala Lipis and was chosen to join the Kuala Lumpur President Cup Team in 2005 at the age of 14. Though the Kuala Lumpur President Cup Team did not manage to reach the finals, Wan Zack became the top scorer with 11 goals. After playing 2 years for the Kuala Lumpur President Cup Team, He was scouted by former national team player, Reduan Abdullah and Reduan gave Wan Zack a one-year contract with the newly created Felda United in 2007 at the age of 17, he manage to score two goals in 6 appearances. Wan Zack joined Harimau Muda under Ong Kim Swee. Wan Zack was part of the Harimau Muda team. During the 2010 season, Harimau Muda was split into two teams and Haikal was chosen to be in the A team. Wan Zack and 25 other Harimau Muda A players were chosen by Azraai Khor to participate in an 8-month long, training camp in Zlaté Moravce, Slovakia.

On September 2011, Slovakian club FC ViOn Zlaté Moravce have confirmed the signings of Wan Zack. He joins the club on loan for 3 months until 30 October from Harimau Muda. Struck by a 4-month injury during a national duty for the national Olympic team, Haikal failed to make an appearance during his loan, only appearing in 1 unofficially friendly match with Zlaté Moravce. After his loaned finished, he returned to his club, Harimau Muda, competing in S. League; the team was competing in the Malaysia Super League for the 2011 season. Malaysian media reported in early March 2012 that Wan Zack, along with teammate Wan Zaharulnizam Zakaria is to attend trial with Japan Football League side FC Ryukyu after impressing the Japanese side talent spotter during Malaysia's 2–0 defeat to Japan in the 2012 Olympic qualifiers match in Tosu, they completed the 2-week trial with the Japanese club in July. In March 2013, Wan Zack was offered a two-year contract, but Wan Zaharulnizam did not. Instead, 19-year-old Nazirul Naim Che Hashim was offered a contract instead.

Wan Zack and Nazirul signed a two-year playing contract with FC Ryukyu in early April 2013. Wan Zack made his full debut in a 2–1 win against Sagawa Printing, playing 80 minutes before being subbed off. Malaysian media reported in early March 2014 that Wan Zack, Joined Kelantan FA On April. After his contract with Kelantan is become to end, Wan Zack switch sides and joined FELDA United, signing a two-year contract on an undisclosed fee, he made his debut, playing 86-minutes on 21 January 2017 against PKNS in Super League matches, which FELDA United won by 1–0. After succeeded in helping FELDA United to become the 2018 Malaysia Premier League champions, Wan Zack signed a one-year contract, with the option for a second year, with Selangor, he will join the squad alongside with new coach B. Sathianathan, other teammates K. Prabakaran, Azreen Zulkafali and Farizal Harun, who joined Red Giants before him. Wan Zack was called up for 2012 AFF Suzuki Cup, he played his first AFF Suzuki Cup match against Singapore after coming off the bench.

Malaysia loses 3–0 on home ground. Wan Zack played a big role in a match against Laos which he provided a goal and an assist to help Malaysia won 4–1 on 28 November 2012 at the National Stadium, Bukit Jalil. Wan Zack showed excellent performance against Indonesia in the third match, he provided an assist to teammate Mahali Jasuli. Wan Zack was injured in that match but Malaysia won 2–0 to progress to the semi-final. Wan Zack does not play on two semi-final match against Thailand due to injury. Malaysia failed to progress to final after losing 1–3 on aggregates; as of 21 July 2018. As of match played 5 July 2018. Scores and results list Malaysia's goal tally first. Harimau Muda AMerdeka Tournament: 2013 Malaysia Premier League: 2009 International U-21 Football Tournament Thanh Nien Cup: 2012Kelantan FAMalaysia FA Cup: Runner-up 2015Felda UnitedMalaysia Super League Third place:2017 Malaysia Premier League: 2018IndividualFAM Best Young Players Awards: 2011 Merdeka Tournament's Most Valuable Player: 2013 S League Yeo's People's Choice Awards: 2012 YEO's Young Player of the Year: 2012 Goal.com Asian Best XI: November 2012 Harimau Muda A Malaysia national under-23 football team Wan Zack Haikal at Soccerway Wan Zack Haikal at J.

League

2010 Speedway Swedish Individual Championship

The 2010 Speedway Swedish Individual Championship was the 2010 edition of the Speedway Swedish Individual Championship. The Final took place on September 18 at the G&B Arena in Kalmar County; the Championship was won by the defending champion Andreas Jonsson, who beat Fredrik Lindgren, Magnus Zetterström and Thomas H. Jonasson in the final heat. All top three riders riding in the 2010 Speedway Grand Prix; the Under-21 Championship, held one day before the senior Final, was won by Dennis Andersson. Andersson beat Linus Sundström and Simon Gustafsson in the final heat. Andersson won the 2010 Individual Speedway Junior European Championship. Malmö 11 August 2010 References Målilla 18 September 2010 References Nykoeping 21 August 2010 References Målilla 17 September 2010 References Speedway Swedish Individual Championship

Battery Park City Ferry Terminal

The Battery Park City Ferry Terminal is a passenger ferry terminal in Battery Park City, serving ferries along the Hudson River in New York City and northeastern New Jersey. It provides slips to ferries, water taxis, sightseeing boats in the Port of New York and New Jersey; the floating dock is moored at the foot of Vesey Street. There are four bow-loading and two side loading slips at the terminal; the mono-hull structure is the largest of its type in the world, covering 0.75 acres acres, its two towers anchored to bedrock 75 feet below the water's surface. It is near the World Financial Center, as such, is called the World Financial Center Terminal or WFC Ferry Terminal. Regular ferry service between lower Manhattan and the Village of Communipaw dates back to at least 1661 with the founding of the Communipaw ferry during the Dutch colonial period; the Jersey City Ferry began service in July 1764 between Paulus Hook to Mesier's dock, located at the foot of Courtland Street. Both ferries continued to operate into the 19th and 20th centuries and docked at Liberty Street Ferry Terminal and the Cortland Street Ferry Depot respectively.

When these ferry slips were closed in the 1950s and 1960s they were demolished and the slips were filled in to create Battery Park City. In 1986 NY Waterway restarted ferry service across the Hudson River and a ferry slip was opened at Battery Park City in 1989. Port Authority of New York and New Jersey commissioned the construction of the current terminal, which opened in 2009, replaced the landing, to which service began in 1989. NY Waterway and Liberty Water Taxi operate services to the terminal. Goldman Sachs commissions two ferries between its offices on either side of the river, which are used by both employees and non-employees. SeaStreak operates peak hour shuttle service to Pier 11/Wall Street for connecting service to the Raritan Bayshore. Service on the St. George route of the NYC Ferry system will begin in 2020. Since June 2013, ferries using the terminal, in accordance with the disregarded Rule 34, sound their horns to indicate their actions, creating what many local residents perceive as noise pollution.

List of ferries across the Hudson River to New York City Liberty Street Ferry Terminal Cortlandt Street Ferry Depot Media related to Battery Park City Ferry Terminal at Wikimedia Commons

Shelby D. Hunt

Shelby D. Hunt is an American organizational theorist, the Jerry S. Rawls and P. W. Horn Professor of Marketing at the Texas Tech University, a cited marketing researcher, his is noted for his contributions to the resource-advantage view. Hunt studied mechanical engineering at the University of Ohio, graduating with a Bachelor of Science in 1962, he received his PhD from Michigan State University in 1968. After working as a technical sales representative for Hercules Plastics Inc, he began his academic career at the University of Wisconsin-Madison in 1969, he chaired the Marketing Department from 1974 to 1980. In 1980, he took up an academic position in the graduate school of the Texas Tech University and is the Jerry S. Rawls and P. W. Horn Professor of Marketing at the Texas Tech University, he was the Editor of the Journal of Marketing from 1984 to 1987. His research interests are in the fields of "Competition, Marketing Theory, Ethics and Philosophy of Science." He has authored dozens of books and more than 150 articles and is one of the 250 most cited authors in business and economics.

He and his work are the subject of the publication, Legends in Marketing: Shelby D. Hunt, edited by Jagdish N. Sheth and published in 2011. Hunt is the recipient of multiple awards for his scholarship and services to education, including: 1976 The Harold H. Maynard Award for the “best article on marketing theory” for “The Nature and Scope of Marketing” published in the Journal of Marketing 1983 The Harold H. Maynard Award for the “best article on marketing theory” for “General Theories and Fundamental Explananda of Marketing” published in the Journal of Marketing 1986 The Paul D. Converse Award from the American Marketing Association for his contributions to marketing scholarship 1989 The Charles C. Slater Award for “Reification and Realism in Marketing: in Defense of Reason,” published in the Journal of Macromarketing 1987 The Outstanding Marketing Educator Award from the Academy of Marketing Science 1992 The Distinguished Marketing Educator Award from the American Marketing Association/Richard D.

Irwin 1995 recipient of the Harold H. Maynard Award for the “best article on marketing theory” for “The Comparative Advantage Theory of Competition” published in the Journal of Marketing 2000 recipient of the Elsevier Science Exceptional Quality and High Scholarly Impact award for “Ethics and Marketing Management,” Journal of Business Research 2002 The Distinguished Scholar Award from the Society for Marketing Advances/Elsevier Science 2017 Named as a “Marketing Legend” by the American Marketing Association Books 1971, with Urban B. Ozanne, The Economic Effects of Franchising, Washington: United States Senate, U. S. Government Printing Office 1976, Marketing Theory: Conceptual Foundations of Research in Marketing, Columbus: Grid Publishing, Inc. 1982, with Ronald Bush, Marketing Theory: Philosophy of Science Perspectives, Chicago: American Marketing Association. 1983, Marketing Theory: The Philosophy of Marketing Science, Illinois: Richard D. Irwin, Inc. 1991, Modern Marketing Theory: Critical Issues in the Philosophy of Marketing Science, Cincinnati: SouthWestern Publishing Co.

2000, A General Theory of Competition: Resources, Productivity, Economic Growth. Thousand Oaks, CA: Sage Publications 2002, Foundations of Marketing Theory: Toward a General Theory of Marketing, Armonk, NY: M. E. Sharpe, Inc. 2003, Controversy in Marketing Theory: For Reason, Realism and Objectivity, Armonk, NY: M. E. Sharpe, Inc. 2010, Marketing Theory: Foundations, Strategy, Resource-Advantage Theory, Armonk, NY: M. E. Sharpe, Inc. Articles/ Chapters 1994, "The Commitment-trust Theory of Relationship Marketing," Journal of Marketing, Vol. 58, pp 20-38 1995, “The Comparative Advantage Theory of Competition,” Journal of Marketing, Vol. 59, April, pp 1-15 1996, “The Resource-advantage Theory of Competition: Dynamics, Path Dependencies, Evolutionary dimensions,” Journal of Marketing, Vol. 60, October, pp 107-114 1997, "Competing Through Relationships: Grounding Relationship Marketing in Resource-Advantage Theory," Journal of Marketing Management, Vol. 13, pp 431-445 1999, “The Strategic Imperative and Sustainable Competitive advantage: Public Policy and Resource Advantage Theory,” Journal of Academy of Marketing Science, Vol. 27, No.

2, pp 144-5 2000, “The Competence-based, Resource-advantage, Neoclassical Theories of Competition: Toward a synthesis”, in Sanchez, R. and Heene, A. Competence-based Strategic Management: Theory and Research, JAI Press, Greenwich, CT, pp 177-208 2001, “A General Theory of Competition: Issues, an Invitation”, European Journal of Marketing, Vol. 35, Nos 5/6, pp 524-48 2002, “Determining Marketing Strategy: A Cybernetic Systems Approach to Scenario Planning,” European Journal of Marketing, Vol. 36 No. 4, pp 450-78 2003, "Resource-Advantage Theory and Embeddedness: Explaining R-A Theory’s Explanatory Success," Journal of Marketing Theory and Practice, Vol. 11, No. 1, pp 1-17 2004, "Market Segmentation Strategy, Competitive Advantage, Public Policy: Grounding Segmentation Strategy in Resource-Advantage Theory," Australasian Journal of Marketing, Vol. 12, no. 1, 2004, pp 7-25 2008, "Grounding Supply Chain Management in Resource-Advantage Theory," Volume 44, No. 1, 2008, pp 10–21 2011, "Sustainable marketing and economic growth: a esource-advantage, economic freedom approach," Journal of the Academy of Marketing Science, Vol. 39, pp 7- 20 2011, "Develop

Hanover High School (New Hampshire)

Hanover High School is the only public high school in the Dresden School District, in Hanover, New Hampshire, USA. In 1963 it became the first interstate high school in the country as part of a bill, the last signed into action by John F. Kennedy. Today it accepts students from several communities in New Vermont. Enrollment is 786 students, the majority of whom come from the towns of Hanover and Norwich, Vermont. 11% of the student body attends on a tuition basis from towns such as Cornish and Lyme, New Hampshire, Strafford and Hartland, Vermont. The school employs 79 full-time faculty members. Hanover High was recognized in 2009 by BusinessWeek in their "America's Best High Schools" annual article as having the "Best Overall Academic Performance" in New Hampshire, with a GreatSchools rating of 10/10; the school is accredited by the New England Association of Schools and Colleges, over 96% of students are accepted to or are planning to attend post secondary education after graduating. Of the 85 professional staff at Hanover High School, 71% hold at least a master's degree, while 18% hold a master's degree + 60 credits or a doctorate.

The academic program is divided into the traditional five departments: English, Science, Social Studies, Foreign Language. Each department offers a selection of courses; as students advance, additional opportunities become available. The school's curriculum and policies emphasize individual student freedoms. For example, seniors elect to design and complete an independent study project that academically explores a personal interest. With Dartmouth College a short walk from the school, some students attend courses at the college when they have exhausted the high school's offerings; the academic atmosphere is student-centric, with off-campus privileges available and with a council of students and community members whose governing power extends in many areas beyond that of the school principal. Hanover's physical education program, for 9th graders, has an extensive outdoor ropes course, one of the largest in the world with over 35 high ropes course elements, as well as a comprehensive indoor ropes course and climbing wall.

Begun in 1988 by physical education teacher Glyn Reinders, the outdoor education program has become the core of Hanover's physical education curriculum and is considered one of the premier high school programs in the country. The girls' cross country team was fourth in the nation during the 2007 season; the boys' varsity soccer team has won the state championship for the last six years, as well as the state sportsmanship award for the past four years. The boys' hockey and lacrosse teams are both the smallest schools in Division I, yet Hanover always makes it to the state finals in at least one of the sports, if not both; the 2009 fall campaign was successful, with field hockey, boys' cross country, girls' cross country and boys' soccer all being crowned state champions. The school boasts a large number of music ensembles, community service organizations, an official drama group "Footlighters" that puts on two shows and a musical each year, a student-organized drama group "SOS. Hanover High School is one of the few public schools in New Hampshire to have a crew team.

It is the largest sport at Hanover, with one in every six students participating. They have been recognized as one of the top public school rowing programs consecutively in New Hampshire. HHS is a democratic school revolving around the Hanover High Council; the council has the authority to act on all matters at Hanover High School not controlled by school board policy, state policy, administrative regulations established by the Superintendent of the Schools, rules and regulations published in the Student Handbook of Hanover High School. Council elections are held each spring. Hanover has a comprehensive athletics program, with players competing at both the varsity and junior varsity levels. Sports offered include baseball, cross country running, cross-country skiing, field hockey, golf, ice hockey, rugby, ski jumping, softball, tennis, track and volleyball; the boys' cross country running team won back-to-back state championships in 2008 and 2009. The boys' soccer team is perennially the most successful team at Hanover, having won the Class I state championships every year from 2005–2010, the Division I title in 2013.

They have won a state-record total of 18 overall, while the boys' ice hockey team is successful in the competitive NH Division I, where nearly all the other schools are much larger than Hanover. The boys' golf team has been one of the top programs in the state, winning over 30 state championships since the early 1980s. Many former Marauder golfers are now members of the PGA. In 1989 the golf team finished an undefeated 48-0 season under coach Glyn Reinders and were named by the Boston Globe "New England Team of the Year". Notable girls' teams include the perennial power house cross country team, which won the Class I state championship from 2004 through 2009, placed fourth at the Nike Team Nationals high school championships; the girls' soccer team has won NH Division II championships in 2014, 2015 and 2018. The girls' varsity tennis team appeared in five consecutive state championship finals from 2013 through 2017; the football team is a strong force in NH Division IV, but hasn't won a state championship since 2005, despite making it to every state final since