SUMMARY / RELATED TOPICS

In mathematics, the phrase up to is used to convey the idea that some objects in the same class — while distinct — may be considered to be equivalent under some condition or transformation. It appears in discussions about the elements of a set, the conditions under which some of those elements may be considered to be equivalent. More given two elements a and b of a set S, "a and b are equivalent up to X" means that a and b are equivalent, if criterion X, such as rotation or permutation, is ignored. In which case, the elements of S can be arranged in subsets known as "equivalence classes", sets whose elements are equivalent to each other up to X. In some cases, this might mean that a and b can be transformed into one another—if a transformation corresponding to X is applied. If X is some property or process the phrase "up to X" can be taken to mean "disregarding a possible difference in X". For instance, the statement "an integer's prime factorization is unique up to ordering" means that the prime factorization is unique—when we disregard the order of the factors.

One might say "the solution to an indefinite integral is f, up to addition by a constant", meaning that the focus is on the solution f rather than the added constant, that the addition of a constant is to be regarded as a background information. Further examples include "up to isomorphism", "up to permutations" and "up to rotations", which are described in the Examples section. In informal contexts, mathematicians use the word modulo for similar purposes, as in "modulo isomorphism". A simple example is "there are seven reflecting tetrominoes, up to rotations", which makes reference to the seven possible contiguous arrangements of tetrominoes and which are thought of as the seven Tetris pieces; this could be written as "there are five tetrominoes, up to reflections and rotations", which would take into account the perspective that L and J can be thought of as the same piece when reflected. The Tetris game does not allow reflections, so the former notation is to seem more natural. To add in the exhaustive count, there is no formal notation for the number of pieces of tetrominoes.

However, it is common to write that "there are seven reflecting tetrominoes up to rotations". Here, Tetris provides an excellent example, as one might count 7 pieces × 4 rotations as 28, where some pieces have fewer than four rotation states. In the eight queens puzzle, if the eight queens are considered to be distinct there are 3709440 distinct solutions. However, the queens are considered to be identical, one says "there are 92 unique solutions up to permutations of the queens", or that "there are 92 solutions mod the names of the queens", signifying that two different arrangements of the queens are considered equivalent if the queens have been permuted, but the same squares on the chessboard are occupied by them. If, in addition to treating the queens as identical and reflections of the board were allowed, we would have only 12 distinct solutions up to symmetry and the naming of the queens, signifying that two arrangements that are symmetrical to each other are considered equivalent; the regular n-gon, for given n, is unique up to similarity.

In other words, if all similar n-gons are considered instances of the same n-gon there is only one regular n-gon. In group theory, one may have a group G acting on a set X, in which case, one might say that two elements of X are equivalent "up to the group action"—if they lie in the same orbit. Another typical example is the statement that "there are two different groups of order 4 up to isomorphism", or "modulo isomorphism, there are two groups of order 4"; this means that there are two equivalence classes of groups of order 4—assuming that one considers groups to be equivalent if they are isomorphic. A hyperreal x and its standard part st are equal up to an infinitesimal difference. In computer science, the term up-to techniques is a defined notion that refers to certain proof techniques for bisimulation, to relate processes that only behave up to unobservable steps. Abuse of notation Adequality All other things being equal Essentially unique List of mathematical jargon Modulo Quotient group Quotient set Synecdoche Up-to Techniques for Weak Bisimulation

The Colombo Rowing Club is the premier boat club in Sri Lanka having been founded in 1864. Its clubhouse and boat house are located on the edge of the northern Beira Lake, at Sir Chittapalam A. Gardiner Mawatha, in Colombo. Since its inception the Colombo Rowing Club has progressed into one of the most prestigious and active private member clubs in Sri Lanka. A distinctive feature has been that while the club's main sporting focus remains in rowing, social interaction and fellowship is an important aspect; the club claims to be the cradle of rowing in Sri Lanka since most affiliated clubs of the Amateur Rowing Association of Sri Lanka, governing body for rowing in Sri Lanka, started from the facilities and infrastructure, available at the Colombo Rowing Club. The club was founded on the July 15, 1864 by Sir Edward Creasy, the former Chief Justice of Ceylon and based on available records, the CRC claims to be the oldest club in the island; the Colombo Rowing Club adopted the club colours of Oxford: White.

The membership of club was predominately made up on colonialists affiliated with the many government departments and plantations in the island. In 1898, the first Boat Race took place between the Colombo Rowing Club and the Madras Boat Club and rivalry prevails until the present day. Thus, the boat race is considered second in vintage only to the prestigious Oxford and Cambridge boat race, the world's oldest, continuing inter-institutional event. With Ceylon gaining independence the club was opened up to more locals and Alavi Mohomed was selected as the first Ceylonese captain of the Club. In the 1950s and 1960s the club helped to introduce the sport to Royal College, S' Thomas' College and University of Colombo; the Club has hosted the annual Royal Thomian Regatta since 1962. The club commemorated its centenary year in 1964; the Colombo Rowing Club and the surrounding Beira Lake have hosted the Sri Lanka National Rowing Championships on twenty-four occasions till 2008. The National Championships have since moved to Bolgoda Lake which boasts a 2000m international distance course.

There are 14 institutions using the facilities at the Colombo Rowing Club and the club extends all levels of support for the development of rowing. The club hosts many as 7 regattas throughout the year catering to novices and senior oarsmen/women; the current president is Dinesh Deheragoda with Ruven Weerasinghe as captain. The current Manager of the club is Thishan Gammanpila CRC won the overall championship at the Amateur Rowing Association of East Regatta 2011, hosted by the Bolgoda Lake Rowing Club, Sri Lanka Inaugural Regatta South-West Monsoon Regatta Head of the Beira Regatta Ranfer Sprints Inter-Monsoon Regatta North East Monsoon Regatta Closing Regatta Madras-Colombo Regatta Karachi-Colombo Regatta Amateur Rowing Association of East Regatta Royal Thomian Regatta University of Colombo vs University of Moratuwa Ladies College vs Musaeus College Ananda College vs Asian International School Janaka Peiris, fondly known as Peiris, has been a boat boy of the rowing club for over 30 years and is considered a permanent fixture of the club with many members and oarsmen having their own "Peiris story" Colombo Rowing Club wins regatta with easehttp://colomborowingclub.org/

An arithmetic logic unit is a combinational digital electronic circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit. An ALU is a fundamental building block of many types of computing circuits, including the central processing unit of computers, FPUs, graphics processing units. A single CPU, FPU or GPU may contain multiple ALUs; the inputs to an ALU are the data to be operated on, called operands, a code indicating the operation to be performed. In many designs, the ALU has status inputs or outputs, or both, which convey information about a previous operation or the current operation between the ALU and external status registers. An ALU has a variety of input and output nets, which are the electrical conductors used to convey digital signals between the ALU and external circuitry; when an ALU is operating, external circuits apply signals to the ALU inputs and, in response, the ALU produces and conveys signals to external circuitry via its outputs.

A basic ALU has three parallel data buses consisting of a result output. Each data bus is a group of signals; the A, B and Y bus widths are identical and match the native word size of the external circuitry. The opcode input is a parallel bus that conveys to the ALU an operation selection code, an enumerated value that specifies the desired arithmetic or logic operation to be performed by the ALU; the opcode size determines the maximum number of different operations. An ALU opcode is not the same as a machine language opcode, though in some cases it may be directly encoded as a bit field within a machine language opcode; the status outputs are various individual signals that convey supplemental information about the result of the current ALU operation. General-purpose ALUs have status signals such as: Carry-out, which conveys the carry resulting from an addition operation, the borrow resulting from a subtraction operation, or the overflow bit resulting from a binary shift operation. Zero, which indicates all bits of Y are logic zero.

Negative, which indicates the result of an arithmetic operation is negative. Overflow, which indicates the result of an arithmetic operation has exceeded the numeric range of Y. Parity, which indicates whether an or odd number of bits in Y are logic one. At the end of each ALU operation, the status output signals are stored in external registers to make them available for future ALU operations or for controlling conditional branching; the collection of bit registers that store the status outputs are treated as a single, multi-bit register, referred to as the "status register" or "condition code register". The status inputs allow additional information to be made available to the ALU when performing an operation; this is a single "carry-in" bit, the stored carry-out from a previous ALU operation. An ALU is a combinational logic circuit, meaning that its outputs will change asynchronously in response to input changes. In normal operation, stable signals are applied to all of the ALU inputs and, when enough time has passed for the signals to propagate through the ALU circuitry, the result of the ALU operation appears at the ALU outputs.

The external circuitry connected to the ALU is responsible for ensuring the stability of ALU input signals throughout the operation, for allowing sufficient time for the signals to propagate through the ALU before sampling the ALU result. In general, external circuitry controls an ALU by applying signals to its inputs; the external circuitry employs sequential logic to control the ALU operation, paced by a clock signal of a sufficiently low frequency to ensure enough time for the ALU outputs to settle under worst-case conditions. For example, a CPU begins an ALU addition operation by routing operands from their sources to the ALU's operand inputs, while the control unit applies a value to the ALU's opcode input, configuring it to perform addition. At the same time, the CPU routes the ALU result output to a destination register that will receive the sum; the ALU's input signals, which are held stable until the next clock, are allowed to propagate through the ALU and to the destination register while the CPU waits for the next clock.

When the next clock arrives, the destination register stores the ALU result and, since the ALU operation has completed, the ALU inputs may be set up for the next ALU operation. A number of basic arithmetic and bitwise logic functions are supported by ALUs. Basic, general purpose ALUs include these operations in their repertoires: Add: A and B are summed and the sum appears at Y and carry-out. Add with carry: A, B and carry-in are summed and the sum appears at Y and carry-out. Subtract: B is subtracted from A and the difference appears at Y and carry-out. For this function, carry-out is a "borrow" indicator; this operation may be used to compare the magnitudes of A and B. Subtract with borrow: B is subtracted from A with borrow and the difference appears at Y and carry-

Lo Man Kam is a teacher of the Chinese martial art of Wing Chun. Lo was born in 1933 in Hong Kong. During the Qing dynasty in Guangdong, members of the Lo family were government officials, as were many of their ancestors in many generations. Thus, the Lo family lived in the housing provided to government officials which were guarded by the Qing Green Standard Army; the lobby of this Lo family residence has pair of royal plaques bestowed by Emperor of the Qing dynasty. During the two major wars in China, everything was destroyed. Owing to this, Lo family members temporarily stayed with the younger brother of Yip Man, Yip Ten, in his large mansion in Mulberry Garden. After the war, the Lo family moved back to Hong Kong. After Ip Man moved back to Hong Kong in 1949, he taught Wing Chun in the office of the Kowloon Hotel Union, it was at that time. When Lo first started to learn Wing Chun in Hong Kong, there were only 5-7 students of Yip Man, including senior disciple Leung Shueng, Lok Yiu, Chu Shong-tin, Chan Kau, little brother Yip.

Lo was encouraged by Yip Man to teach in Taiwan. When Lo first moved to Taiwan, he underwent special military academy training. After graduation, Lo was appointed to work at the Ministry of National Defense in Taiwan. In 1975, he retired as a Major and opened his Wing Chun Kung Fu school in Neihu, Taiwan. After opening the school, he had students named Daniel Duby and James; these students were the first foreign disciples to participate in the "Bai Si Lai" in the Taiwanese wushu community. In 1990, due to a speech given by Lo, the Taiwan Special Police Force First Corps leader Dr. Lu, who recognized the value of Lo's talent, appointed him to be a Taiwan Special Police Force instructor. In 1992, when the Republic of China-Taiwan started its first SWAT team, Lo was appointed to be the first SWAT team head instructor. In 1993, Dr. Lu from the Special Police Force got promoted to the principal of the Taiwan Police College. Lo joined him at the Police College and continued teach and train future police officers and training instructors.

Lo helped the Police College by authoring the text book “Police Kung Fu”, which focuses on hand-to-hand combat techniques. This book has been translated to English and sold in the US and translated to Russian as well. At this time, director of Taiwan National Security Bureau had appointed Lo to teach Taiwan CIA hand-to-hand combat training, to write Bureau of Investigation teaching materials. Lo worked as training instructor for the Taiwan National Security Bureau 10 years. Lo helped the Taiwan Judicial Yuan by authoring material for the Judicial police hand book and other training material, as well as serving as Taiwan Judicial Yuan training instructor. Lo's position at the Police College, beginning with the term of Principle Dr. Lu, continuing through the term of 5 other principals, lasted 18 years; every now and he is invited back to give special training lessons. In terms of family legacy of Wing Chun Kung Fu, Lo's son Gorden Lu, has been teaching Wing Chun in Virginia Beach in the United States for more than 10 years.

Students of Lo Man Kam from many parts of the world such as Europe, New Zealand, the US and many other countries have come all the way to Taiwan to enter the door of the Lo Man Kam Wing Chun Kung Fu family. Many of Lo's students have themselves become Sifu, are teaching the 3rd generation of students in the Lo Man Kam lineage; the Lo Man Kam Wing Chun Kung Fu Federation has students and schools in more than 40 countries, in Europe and South America, Asia and Australia. Lo Man Kam lead the Federation in Taiwan and created many Associations in other countries; the European countries and their Associations found the European Association as their common leadership. Lo Man kams son Gorden Lu is the president and Los long time student Marc Debus is vicepresident of that organisation. Police Kung Fu: The Personal Combat Handbook of the Taiwan National Police book written by Lo Man Kam Publisher: Tuttle Publishing.

The Chuvanay Range known as Chuvan Mountains, is a range of mountains in Chukotka Autonomous Okrug, Russian Far East. Administratively the range is part of Bilibino District; the village of Keperveyem is located at the feet of the range in its northwestern end, on the other side of the Maly Anyuy River. Bilibino is located about 40 kilometres further to the north; the highest point of the Chuvanay Range is 1,614 metres high mount Chuvanay. To the east and northeast the mountain range is limited by the course of the Maly Anyuy River, which makes a wide bend, flowing first northwards and again westwards. To the south the range is bound by the Kulpolney River and to the west by the valley of the Tenvelveyem —left hand tributaries of the Maly Anyuy. A few other tributaries of the Maly Anyuy have their source in the range, flowing between both and joining the left bank of the river; the ghost town of Aliskerovo, beyond which rises the Ilirney Range, lies to the northeast, on the other side of the river, near its confluence with the Egilknyveyem River.

To the south and southwest rises the Anyuy Range and to the north the smaller Kyrganay Range. The Chuvanay Range is part of the East Siberian System of mountains and is one of the subranges of the Anadyr Highlands; the general profile of the mountains is more pointed than the neighboring mountain ranges of Bilibino District, such as the Kyrganay, or the Rauchuan Range further to the north, which are characterized by a smoother relief. List of inhabited localities in Bilibinsky District Chuvans Rafting on the Small Anyuy River - Part II The Chuvanay mountains in the distance ГОРЫ СЕВЕРО-ВОСТОКА РОССИИ O. Yu. Glushkova, Late Pleistocene Glaciations in North-East Asia

The Caledonian-Record is a daily newspaper published in St. Johnsbury and circulates throughout Caledonia County, it was established in 1837. It employs a total staff of 36; the paper is distributed in the Northeast Kingdom of Vermont and the western portion of Coos County, New Hampshire. It maintains a New Hampshire office located at 263 Main Street in New Hampshire, it is published daily except some holidays. The Caledonian has focused on local news from 50 communities, which are located in three Vermont counties and two New Hampshire ones; the average daily net paid circulation has dipped from a peak of about 12,500 about 1999 to the six months ending March 2013 at 10,204. Penetration of the primary market area of St. Johnsbury and Lyndonville was under 93%. For the area surrounding St. Johnsbury the Caledonian provided coverage of 80% of the occupied households. Albert G. Chadwick began publishing the paper as a weekly in August, 1837, it is the oldest paper in the county. It started as a twenty-four column paper.

It was a Whig paper. At the time, Vermont was Whig; the paper advocated the principles of the Free Soil element and became an early adherent and unswerving supporter of the principles of the Republican Party. It was published by its founder for 18 years. George D. Rand and Charles M. Stone bought it in July 1855. Stone became the sole owner and publisher in April 1857. In 1875 it was still a weekly newspaper. Subscribers paid \$1.50 a year. In the 20th century, the paper was bought by a former Hearst reporter from Herb Smith, his son, Gordon Smith, Class of 1941 at Yale, joined the paper on the business side upon graduation and went on to own and publish the paper. Gordon brought with him as a writer; the Caledonian garnered attention in 2003 over a court case entitled Caledonian-Record Pub. Co. Inc. v. VT State College; the Caledonian wanted to have access to student disciplinary records and hearings from Lyndon State College. Lyndon state claimed that it was exempt from making the requested information public per the Vermont Public Records Act and the Open Meetings Law.

The local court sided with Lyndon State College, an appeal to the Vermont Supreme Court followed. The Vermont Supreme Court upheld the verdict. Julie Fothergill, an attorney with the Vermont League of Cities and Towns, stated that the ruling "is important for all public bodies because it indicates how the Court may interpret other exceptions to the Public Records Law." Besides the Caledonian, the paper published the Orleans County Record and the Littleton Record. In 2007 the paper employed a staff of 40. Sales ranged from \$1 to \$5 million annually. In 2007 the paper partnered with the American Society of News Editors at Lyndon Institute to publish a school newspaper, the first at the school, entitled The Campus News. In 2008 the paper outsourced the printing of the paper to Upper Valley Press in Haverhill, New Hampshire, citing equipment, quality control and personnel problems. In 2017, the paper was family owned. Official site Newspaper Pages on Chronicling America