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Simple cycloalkanes have a prefix "cyclo-" to distinguish them from alkanes. Cycloalkanes are named as per their acyclic counterparts with respect to the number of carbon atoms in their backbones, e.g., cyclopentane (C5H10) is a cycloalkane with 5 carbon atoms just like pentane (C5H12), but they are joined up in a five...
The following trivial names are retained in the IUPAC system: Some non-IUPAC trivial names are occasionally used: Physical properties. All alkanes are colorless. Alkanes with the lowest molecular weights are gases, those of intermediate molecular weight are liquids, and the heaviest are waxy solids. Boiling point. Alka...
On the other hand, cycloalkanes tend to have higher boiling points than their linear counterparts due to the locked conformations of the molecules, which give a plane of intermolecular contact. Melting points. The melting points of the alkanes follow a similar trend to boiling points for the same reason as outlined abo...
While these effects operate in opposing directions, the first effect tends to be slightly stronger, leading even-numbered alkanes to have slightly higher melting points than the average of their odd-numbered neighbors. This trend does not apply to methane, which has an unusually high melting point, higher than both eth...
Their solubility in nonpolar solvents is relatively high, a property that is called lipophilicity. Alkanes are, for example, miscible in all proportions among themselves. The density of the alkanes usually increases with the number of carbon atoms but remains less than that of water. Hence, alkanes form the upper layer...
Bond lengths and bond angles. An alkane has only C–H and C–C single bonds. The former result from the overlap of an sp3 orbital of carbon with the 1s orbital of a hydrogen; the latter by the overlap of two sp3 orbitals on adjacent carbon atoms. The bond lengths amount to 1.09 × 10−10 m for a C–H bond and 1.54 × 10−10 m...
Spectroscopic properties. Spectroscopic signatures for alkanes are obtainable by the major characterization techniques. Infrared spectroscopy. The C-H stretching mode gives a strong absorptions between 2850 and 2960 cm−1 and weaker bands for the C-C stretching mode absorbs between 800 and 1300 cm−1. The carbon–hydrogen...
Mass spectrometry. Since alkanes have high ionization energies, their electron impact mass spectra show weak currents for their molecular ions. The fragmentation pattern can be difficult to interpret, but in the case of branched chain alkanes, the carbon chain is preferentially cleaved at tertiary or quaternary carbons...
Acid-base behavior. The acid dissociation constant (p"K"a) values of all alkanes are estimated to range from 50 to 70, depending on the extrapolation method, hence they are extremely weak acids that are practically inert to bases (see: carbon acids). They are also extremely weak bases, undergoing no observable protonat...
The standard enthalpy change of combustion, Δc"H"⊖, for alkanes increases by about 650 kJ/mol per CH2 group. Branched-chain alkanes have lower values of Δc"H"⊖ than straight-chain alkanes of the same number of carbon atoms, and so can be seen to be somewhat more stable. Biodegradation. Some organisms are capable of met...
In the Reed reaction, sulfur dioxide and chlorine convert hydrocarbons to sulfonyl chlorides under the influence of light. Under some conditions, alkanes will undergo Nitration. C-H activation. Certain transition metal complexes promote non-radical reactions with alkanes, resulting in so C–H bond activation reactions. ...
Isomerization and reformation. Dragan and his colleague were the first to report about isomerization in alkanes. Isomerization and reformation are processes in which straight-chain alkanes are heated in the presence of a platinum catalyst. In isomerization, the alkanes become branched-chain isomers. In other words, it ...
Occurrence of alkanes on Earth. Traces of methane gas (about 0.0002% or 1745 ppb) occur in the Earth's atmosphere, produced primarily by methanogenic microorganisms, such as Archaea in the gut of ruminants. The most important commercial sources for alkanes are natural gas and oil. Natural gas contains primarily methane...
Alkanes have a low solubility in water, so the content in the oceans is negligible; however, at high pressures and low temperatures (such as at the bottom of the oceans), methane can co-crystallize with water to form a solid methane clathrate (methane hydrate). Although this cannot be commercially exploited at the pres...
Alkanes play a negligible role in higher organisms, with rare exception. Some yeasts, e.g., "Candida tropicale", "Pichia" sp., "Rhodotorula" sp., can use alkanes as a source of carbon or energy. The fungus "Amorphotheca resinae" prefers the longer-chain alkanes in aviation fuel, and can cause serious problems for aircr...
Edible vegetable oils also typically contain small fractions of biogenic alkanes with a wide spectrum of carbon numbers, mainly 8 to 35, usually peaking in the low to upper 20s, with concentrations up to dozens of milligrams per kilogram (parts per million by weight) and sometimes over a hundred for the total alkane fr...
Ecological relations. One example, in which both plant and animal alkanes play a role, is the ecological relationship between the sand bee ("Andrena nigroaenea") and the early spider orchid ("Ophrys sphegodes"); the latter is dependent for pollination on the former. Sand bees use pheromones in order to identify a mate;...
Production. Petroleum refining. The most important source of alkanes is natural gas and crude oil. Alkanes are separated in an oil refinery by fractional distillation. Unsaturated hydrocarbons are converted to alkanes by hydrogenation: Another route to alkanes is hydrogenolysis, which entails cleavage of C-heteroatom b...
Laboratory preparation. Rarely is there any interest in the synthesis of alkanes, since they are usually commercially available and less valued than virtually any precursor. The best-known method is hydrogenation of alkenes. Many C-X bonds can be converted to C-H bonds using lithium aluminium hydride, Clemmenson reduct...
Precursors to chemicals. By the process of cracking, alkanes can be converted to alkenes. Simple alkenes are precursors to polymers, such as polyethylene and polypropylene. When the cracking is taken to extremes, alkanes can be converted to carbon black, which is a significant tire component. Chlorination of methane gi...
Appellate procedure in the United States United States appellate procedure involves the rules and regulations for filing appeals in state courts and federal courts. The nature of an appeal can vary greatly depending on the type of case and the rules of the court in the jurisdiction where the case was prosecuted. There ...
The specific procedures for appealing, including even whether there is a right of appeal from a particular type of decision, can vary greatly from state to state. The right to file an appeal can also vary from state to state; for example, the New Jersey Constitution vests judicial power in a Supreme Court, a Superior C...
The appellant in the new case can be either the plaintiff (or claimant), defendant, third-party intervenor, or respondent (appellee) from the lower case, depending on who was the losing party. The winning party from the lower court, however, is now the respondent. In unusual cases the appellant can be the victor in the...
In tort, equity, or other civil matters either party to a previous case may file an appeal. In criminal matters, however, the state or prosecution generally has no appeal "as of right". And due to the double jeopardy principle, the state or prosecution may never appeal a jury or bench verdict of acquittal. But in some ...
Direct or collateral: Appealing criminal convictions. Many jurisdictions recognize two types of appeals, particularly in the criminal context. The first is the traditional "direct" appeal in which the appellant files an appeal with the next higher court of review. The second is the collateral appeal or post-conviction ...
In most jurisdictions the normal and preferred way of seeking appellate review is by filing an appeal of the final judgment. Generally, an appeal of the judgment will also allow appeal of all other orders or rulings made by the trial court in the course of the case. This is because such orders cannot be appealed "as of...
In Anglo-American common law courts, appellate review of lower court decisions may also be obtained by filing a petition for review by prerogative writ in certain cases. There is no corresponding right to a writ in any pure or continental civil law legal systems, though some mixed systems such as Quebec recognize these...
State post-conviction relief: collateral appeal. All States have a post-conviction relief process. Similar to federal post-conviction relief, an appellant can petition the court to correct alleged fundamental errors that were not corrected on direct review. Typical claims might include ineffective assistance of counsel...
The specific rules of the legal system will dictate exactly how the appeal is officially begun. For example, the appellant might have to file the notice of appeal with the appellate court, or with the court from which the appeal is taken, or both. Some courts have samples of a notice of appeal on the court's own web si...
Appellate procedure. Generally speaking the appellate court examines the record of evidence presented in the trial court and the law that the lower court applied and decides whether that decision was legally sound or not. The appellate court will typically be deferential to the lower court's findings of fact (such as w...
Another situation is where appeal is by way of "re-hearing". Certain jurisdictions permit certain appeals to cause the trial to be heard afresh in the appellate court. Sometimes, the appellate court finds a defect in the procedure the parties used in filing the appeal and dismisses the appeal without considering its me...
The appellant has the opportunity to present arguments for the granting of the appeal and the appellee (or respondent) can present arguments against it. Arguments of the parties to the appeal are presented through their appellate lawyers, if represented, or "pro se" if the party has not engaged legal representation. Th...
In some cases, an application for "trial de novo" effectively erases the prior trial as if it had never taken place. The Supreme Court of Virginia has stated that '"This Court has repeatedly held that the effect of an appeal to circuit court is to "annul the judgment of the inferior tribunal as completely as if there h...
In cases where a judge rather than a jury decided issues of fact, an appellate court will apply an "abuse of discretion" standard of review. Under this standard, the appellate court gives deference to the lower court's view of the evidence, and reverses its decision only if it were a clear abuse of discretion. This is ...
A lawyer traditionally starts an oral argument to any appellate court with the words "May it please the court." After an appeal is heard, the "mandate" is a formal notice of a decision by a court of appeal; this notice is transmitted to the trial court and, when filed by the clerk of the trial court, constitutes the fi...
Answer (law) In law, an answer was originally a solemn assertion in opposition to someone or something, and thus generally any counter-statement or defense, a reply to a question or response, or objection, or a correct solution of a problem. In the common law, an answer is the first pleading by a defendant, usually fil...
Appellate court An appellate court, commonly called a court of appeal(s), appeal court, court of second instance or second instance court, is any court of law that is empowered to hear a case upon appeal from a trial court or other lower tribunal. Appellate courts other than supreme courts are sometimes named as Interm...
In common law jurisdictions, an appellate court reviewing an issue of fact ordinarily gives deference to the trial court's findings. It is the duty of trial judges or juries to find facts, view the evidence firsthand, and observe witness testimony. When reviewing lower decisions on an issue of fact, courts of appeal ge...
Before hearing any case, the court must have jurisdiction to consider the appeal. The authority of appellate courts to review the decisions of lower courts varies widely from one jurisdiction to another. In some areas, the appellate court has limited powers of review. Generally, an appellate court's judgment provides t...
Appellate courts by country. Australia. The High Court has appellate jurisdiction over all other courts. Leave must be granted by the court, before the appeal matter is heard. The High Court is paramount to all federal courts. Further, it has an constitutionally entrenched general power of appeal from the Supreme Court...
Philippines. The Court of Appeals of the Philippines is the principal intermediate appellate court of that country. The Court of Appeals is primarily found in Manila, with three divisions each in Cebu City and Cagayan de Oro. Other appellate courts include the Sandiganbayan for cases involving graft and corruption, and...
In most U.S. states, and in U.S. federal courts, parties before the court are allowed one appeal as of right. This means that a party who is unsatisfied with the outcome of a trial may bring an appeal to contest that outcome. However, appeals may be costly, and the appellate court must find an error on the part of the ...
Historically, certain jurisdictions have titled their appellate court a court of errors (or court of errors and appeals), on the premise that it was intended to correct errors made by lower courts. Examples of such courts include the New Jersey Court of Errors and Appeals (which existed from 1844 to 1947), the Connecti...
Arraignment Arraignment is a formal reading of a criminal charging document in the presence of the defendant, to inform them of the criminal charges against them. In response to arraignment, in some jurisdictions, the accused is expected to enter a plea; in other jurisdictions, no plea is required. Acceptable pleas var...
Canada. In British Columbia, arraignment takes place in one of the first few court appearances by the defendant or their lawyer. The defendant is asked whether they plead guilty or not guilty to each charge. France. In France, the general rule is that one cannot remain in police custody for more than 24 hours from the ...
South Africa. In South Africa, arraignment is defined as the calling upon the accused to appear, the informing of the accused of the crime charged against them, the demanding of the accused whether they plead guilty or not guilty, and the entering of their plea. United Kingdom. In England, Wales, and Northern Ireland, ...
United States. The Sixth Amendment to the United States Constitution grants criminal defendants the right to be notified of the charges against them. Under the United States' Federal Rules of Criminal Procedure, arraignment shall consist of an open reading of the indictment (and delivery of a copy) to the defendant, an...
In California, arraignments must be conducted without unnecessary delay and, in any event, within 48 hours of arrest, excluding weekends and holidays. Form of the arraignment. The wording of the arraignment varies from jurisdiction to jurisdiction. However, it generally conforms with the following principles: Video arr...
Guilty and not-guilty pleas. If the defendant pleads guilty, an evidentiary hearing usually follows. The court is not required to accept a guilty plea. During the hearing, the judge assesses the offense, the mitigating factors, and the defendant's character, and passes sentence. If the defendant pleads not guilty, a da...
America the Beautiful "America the Beautiful" is a patriotic American song. Its lyrics were written by Katharine Lee Bates and its music was composed by church organist and choirmaster Samuel A. Ward at Grace Episcopal Church in Newark, New Jersey, though the two never met. Bates wrote the words as a poem, originally t...
On the pinnacle of that mountain, the words of the poem started to come to her, and she wrote them down upon returning to her hotel room at the original Antlers Hotel. The poem was initially published two years later in "The Congregationalist" to commemorate the Fourth of July. It quickly caught the public's fancy. An ...
Ward died in 1903, not knowing the national stature his music would attain. The song's popularity was well established by the time of Bates's death in 1929. It is included in songbooks in many religious congregations in the United States. At various times in the more than one hundred years that have elapsed since the s...
Notable performances. Elvis Presley performed it many times in concerts starting in 1976. Bing Crosby included the song in a medley on his album "101 Gang Songs" (1961). Frank Sinatra recorded the song with Nelson Riddle during the sessions for "The Concert Sinatra" in February 1963, for a projected 45 single release. ...
Barbra Streisand released an official music video footage during Norman Lear's Special in 1982. The song has been sung before many editions of the WWE's flagship annual show WrestleMania beginning at WrestleMania 2 in 1986, interchangeably with The Star-Spangled Banner. The song has been performed by artists such as Ra...
The hymn has been featured in the pregame for a number of Super Bowls, the championship game for each NFL season. It is sung along with the "Star-Spangled Banner" and, more recently, the hymn "Lift Every Voice and Sing," commonly referred to as the "Black national anthem". For Super Bowl XLVIII, The Coca-Cola Company a...
The song, performed by 5 Alarm Music, is featured heavily in a dystopian action horror franchise The Purge in both trailers and films. In 2016, American five-piece girl group Fifth Harmony performed a rendition to honor the United States women's national soccer team on defeating Japan 5–2 in the Final to win the 2015 F...
In 2023, Cécile McLorin Salvant performed the song at the US Open woman's final. In her rendition, Salvant notably skipped ahead to the lyrics of the second half of the second verse while singing the first verse (replacing "God shed His grace on thee..." with "God mend thine every flaw...", etc.). Jazz Critic Nate Chin...
"Purple mountain majesties" refers to the shade of Pikes Peak in Colorado Springs, Colorado, which inspired Bates to write the poem. The idiom inspired the Colorado Rockies to have purple as one of its team colors. In 2003, Tori Amos appropriated the phrase "for amber waves of grain" to create a personification for her...
Assistive technology Assistive technology (AT) is a term for assistive, adaptive, and rehabilitative devices for people with disabilities and the elderly. Disabled people often have difficulty performing activities of daily living (ADLs) independently, or even with assistance. ADLs are self-care activities that include...
A recent study from India led by Dr Edmond Fernandes et al. from Edward & Cynthia Institute of Public Health which was published in WHO SEARO Journal informed that geriatric care policies which address functional difficulties among older people will ought to be mainstreamed, resolve out-of-pocket spending for assis...
Occupational therapy and assistive technology. Occupational Therapy (OT) utilizes everyday occupations as a therapeutic tool for enhancing or enabling participation in healthy occupations to promote health and well-being (AOTA, 2020). Occupations include activities of daily living (ADLs), instrumental activities of dai...
Mobility impairments. Wheelchairs. Wheelchairs are devices that can be manually propelled or electrically propelled, and that include a seating system and are designed to be a substitute for the normal mobility that most people have. Wheelchairs and other mobility devices allow people to perform mobility-related activi...
Transfer devices. Patient transfer devices generally allow patients with impaired mobility to be moved by caregivers between beds, wheelchairs, commodes, toilets, chairs, stretchers, shower benches, automobiles, swimming pools, and other patient support systems (i.e., radiology, surgical, or examining tables). The most...
Walkers. A walker or walking frame or Rollator is a tool for disabled people who need additional support to maintain balance or stability while walking. It consists of a frame that is about waist high, approximately twelve inches deep and slightly wider than the user. Walkers are also available in other sizes, such as ...
Prosthesis. A prosthesis, prosthetic, or prosthetic limb is a device that replaces a missing body part. It is part of the field of biomechatronics, the science of using mechanical devices with human muscular, musculoskeletal, and nervous systems to assist or enhance motor control lost by trauma, disease, or defect. Pro...
The terms "prosthetic" and "orthotic" are adjectives used to describe devices such as a prosthetic knee. The terms "prosthetics" and "orthotics" are used to describe the respective allied health fields. An Occupational Therapist's role in prosthetics include therapy, training and evaluations. Prosthetic training includ...
Positioning devices have been developed to aid in allowing people to stand and bear weight on their legs without risk of a fall. These standers are generally grouped into two categories based on the position of the occupant. Prone standers distribute the body weight to the front of the individual and usually have a t...
Visual impairments. Many people with serious visual impairments live independently, using a wide range of tools and techniques. Examples of assistive technology for visually impairment include screen readers, screen magnifiers, Braille embossers, desktop video magnifiers, and voice recorders. Screen readers. Screen rea...
Braille and braille technology. Braille is a system of raised dots formed into units called braille cells. A full braille cell is made up of six dots, with two parallel rows of three dots, but other combinations and quantities of dots represent other letters, numbers, punctuation marks, or words. People can then use th...
Desktop video magnifier. Desktop video magnifiers are electronic devices that use a camera and a display screen to perform digital magnification of printed materials. They enlarge printed pages for those with low vision. A camera connects to a monitor that displays real-time images, and the user can control settings su...
Large-print and tactile keyboards. A large-print keyboard has large letters printed on the keys. On the keyboard shown, the round buttons at the top control software which can magnify the screen (zoom in), change the background color of the screen, or make the mouse cursor on the screen larger. The "bump dots" on the k...
Wearable technology. Wearable technology are smart electronic devices that can be worn on the body as an implant or an accessory. New technologies are exploring how the visually impaired can receive visual information through wearable devices. Some wearable devices for visual impairment include: OrCam device, eSight an...
In human–computer interaction, computer accessibility (also known as accessible computing) refers to the accessibility of a computer system to all people, regardless of disability or severity of impairment, examples include web accessibility guidelines. Another approach is for the user to present a token to the compute...
Hearing aids. A hearing aid or deaf aid is an electro-acoustic device which is designed to amplify sound for the wearer, usually with the aim of making speech more intelligible, and to correct impaired hearing as measured by audiometry. This type of assistive technology helps people with hearing loss participate more f...
Amplified telephone equipment. This type of assistive technology allows users to amplify the volume and clarity of their phone calls so that they can easily partake in this medium of communication. There are also options to adjust the frequency and tone of a call to suit their individual hearing needs. Additionally, th...
Cognitive impairments. Assistive Technology for Cognition (ATC) is the use of technology (usually high tech) to augment and assist cognitive processes such as attention, memory, self-regulation, navigation, emotion recognition and management, planning, and sequencing activity. Systematic reviews of the field have found...
A 2017 Cochrane Review highlighted the current lack of high-quality evidence to determine whether assistive technology effectively supports people with dementia to manage memory issues. Thus, it is not presently sure whether or not assistive technology is beneficial for memory problems. Educational software. Educationa...
In sports. Assistive technology in sports is an area of technology design that is growing. Assistive technology is the array of new devices created to enable sports enthusiasts who have disabilities to play. Assistive technology may be used in adaptive sports, where an existing sport is modified to enable players with ...
In education. In the United States there are two major pieces of legislation that govern the use of assistive technology within the school system. The first is Section 504 of the Rehabilitation Act of 1973 and the second being the Individuals with Disabilities Education Act (IDEA) which was first enacted in 1975 under ...
Assistive technology listed is a student's IEP is not only recommended, it is required (Koch, 2017). These devices help students both with and without disabilities access the curriculum in a way they were previously unable to (Koch, 2017). Occupational therapists play an important role in educating students, parents an...
Computer accessibility. One of the largest problems that affect disabled people is discomfort with prostheses. An experiment performed in Massachusetts used 20 people with various sensors attached to their arms. The subjects tried different arm exercises, and the sensors recorded their movements. All of the data helped...
For users with physical disabilities a large variety of switches are available and customizable to the user's needs varying in size, shape, or amount of pressure required for activation. Switch access may be placed near any area of the body which has consistent and reliable mobility and less subject to fatigue. Common ...
Assistive technology and innovation. Innovation is happening in assistive technology either through improvements to existing devices or the creation of new products. In the WIPO published 2021 report on Technology Trends, assistive products are grouped into either conventional or emerging technologies. Conventional ass...
To a great extent this « conventional » versus « emerging » classification is based on the WHO's Priority Assistive Products List and the ISO 9999 standard for assistive products for persons with disabilities, the APL delineating the absolute minimum that countries should be offering to their citizens and ISO 9999 defi...
In the past, the top patent offices for filing, and therefore perceived target markets, in assistive technology have been the U.S. and Japan. Patenting activity has, however, been declining in these two jurisdictions. At the same time, there has been a surge in patent filings in China and an increase in filings in the ...
The technology readiness level and the related patenting activity can also be explained through the following factors which contribute to a product's entry to market, such as the expected impact on a person's participation in different aspects of life, the ease of adoption (need for training, fitting, additional equipm...
Beyond the patent landscape, industrial designs have an added importance for the field of assistive technology. Assistive technology is often not adopted, or else abandoned entirely, because of issues to do with design (lack of appeal) or comfort (poor ergonomics). Design often plays a role after the patenting activity...
History. In 1988 the National institute on disability and rehabilitation research, NIDRR, awarded Gaulladet University a grant for the project "Robotic finger spelling hand for communication and access to text by deaf-blind persons". Researchers at the university developed and tested a robotic hand. Although it was nev...
Abacus An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. An abacus consists of a two-dimensional array of slidable beads (or simil...
Any particular abacus design supports multiple methods to perform calculations, including addition, subtraction, multiplication, division, and square and cube roots. The beads are first arranged to represent a number, then are manipulated to perform a mathematical operation with another number, and their final position...
Etymology. The word "abacus" dates to at least 1387 AD when a Middle English work borrowed the word from Latin that described a sandboard abacus. The Latin word is derived from ancient Greek () which means something without a base, and colloquially, any piece of rectangular material. Alternatively, without reference to...
Some scholars point to a character in Babylonian cuneiform that may have been derived from a representation of the abacus. It is the belief of Old Babylonian scholars, such as Ettore Carruccio, that Old Babylonians "seem to have used the abacus for the operations of addition and subtraction; however, this primitive dev...
Greece. The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. Demosthenes (384–322 BC) complained that the need to use pebbles for calculations was too difficult. A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Pol...
Rome. The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles () were used. Marked lines indicated units, fives, tens, etc. as in the Roman numeral system. Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin lay...
Due to Pope Sylvester II's reintroduction of the abacus with modifications, it became widely used in Europe again during the 11th century It used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster and was more easily moved. China. The earliest known written do...
The prototype of the Chinese abacus appeared during the Han dynasty, and the beads are oval. The Song dynasty and earlier used the 1:4 type or four-beads abacus similar to the modern abacus including the shape of the beads commonly known as Japanese-style abacus. In the early Ming dynasty, the abacus began to appear in...
Another possible source of the "suanpan" is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a placeholder. The zero was probably introduced to the Chinese in the Tang dynasty (618–907) when travel in the Indian Ocean and the Middle East would have provided direct contact wi...
Japan. In Japan, the abacus is called "soroban" (, lit. "counting tray"). It was imported from China in the 14th century. It was probably in use by the working class a century or more before the ruling class adopted it, as the class structure obstructed such changes. The 1:4 abacus, which removes the seldom-used second...
The four-bead abacus spread, and became common around the world. Improvements to the Japanese abacus arose in various places. In China, an abacus with an aluminium frame and plastic beads has been used. The file is next to the four beads, and pressing the "clearing" button puts the upper bead in the upper position, and...
The Nepōhualtzintzin was divided into two main parts separated by a bar or intermediate cord. In the left part were four beads. Beads in the first row have unitary values (1, 2, 3, and 4), and on the right side, three beads had values of 5, 10, and 15, respectively. In order to know the value of the respective beads of...

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