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Aliquot
Aliquot ( la, a few, some, not many) may refer to: Mathematics *Aliquot part, a proper divisor of an integer *Aliquot sum, the sum of the aliquot parts of an integer *Aliquot sequence, a sequence of integers in which each number is the aliquot sum of the previous number Music *Aliquot stringing, in stringed instruments, the use of strings which are not struck to make a note, but which resonate sympathetically with struck notes *Aliquot stop, an organ stop that adds harmonics or overtones instead of the primary pitch Sciences *Aliquot of a sample, in chemistry or the other sciences, an exact portion of a sample or total amount of a liquid (e.g. exactly 25 mL of water taken from 250 ml) *Aliquot in pharmaceutics, a method of measuring ingredients below the sensitivity of a scale by proportional dilution with inactive known ingredients *Genome aliquoting, the problem of reconstructing an ancestral genome from the genomes of polyploid descendants Other uses *Aliquot part, in the US P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. Definition and overview The aliquot sequence starting with a positive integer ''k'' can be defined formally in terms of the sum-of-divisors function σ1 or the aliquot sum function ''s'' in the following way: : ''s''0 = ''k'' : ''s''n = ''s''(''s''''n''−1) = σ1(''s''''n''−1) − ''s''''n''−1 if ''s''''n''−1 > 0 : ''s''n = 0 if ''s''''n''−1 = 0 ---> (if we add this condition, then the terms after 0 are all 0, and all aliquot sequences would be infinite sequence, and we can conjecture that all aliquot sequences are convergent, the limit of these sequences are usually 0 or 6) and ''s''(0) is undefined. For example, the aliquot sequence of 10 is 10, 8, 7, 1, 0 because: :σ1(10) − 10 = 5 + 2 + 1 = 8, : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Stringing
Aliquot stringing is the use of extra, un-struck strings in the piano for the purpose of enriching the tone. Aliquot systems use an additional (hence fourth) string in each note of the top three piano octaves. This string is positioned slightly above the other three strings so that it is not struck by the hammer. Whenever the hammer strikes the three conventional strings, the aliquot string vibrates sympathetically. Aliquot stringing broadens the vibrational energy throughout the instrument, and creates an unusually complex and colorful tone. Etymology The word ''aliquot'' ultimately comes from a Latin word meaning 'some, several'. In mathematics, ''aliquot'' means 'an exact part or divisor', reflecting the fact that the length of an aliquot string forms an exact division of the length of longer strings with which it vibrates sympathetically. History Julius Blüthner invented the aliquot stringing system in 1873. The Blüthner aliquot system uses an additional (hence fourth) stri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Sum
In number theory, the aliquot sum ''s''(''n'') of a positive integer ''n'' is the sum of all proper divisors of ''n'', that is, all divisors of ''n'' other than ''n'' itself. That is, :s(n)=\sum\nolimits_d. It can be used to characterize the prime numbers, perfect numbers, "sociable numbers", deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number. Examples For example, the proper divisors of 12 (that is, the positive divisors of 12 that are not equal to 12) are 1, 2, 3, 4, and 6, so the aliquot sum of 12 is 16 i.e. (1 + 2 + 3 + 4 + 6). The values of ''s''(''n'') for ''n'' = 1, 2, 3, ... are: :0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 36, 6, 16, 13, 28, 1, 42, 1, 31, 15, 20, 13, 55, 1, 22, 17, 50, 1, 54, 1, 40, 33, 26, 1, 76, 8, 43, ... Characterization of classes of numbers The aliquot sum function can be used to characterize several notable classes of numbers: *1 is the only number whose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample (material)
In general, a sample is a limited quantity of something which is intended to be similar to and represent a larger amount of that thing(s). The things could be countable objects such as individual items available as units for sale, or an uncountable material. Even though the word "sample" implies a smaller quantity taken from a larger amount, sometimes full biological or mineralogical specimens are called samples if they are taken for analysis, testing, or investigation like other samples. They are also considered samples in the sense that even whole specimens are "samples" of the full population of many individual organisms. The act of obtaining a sample is called "sampling" and can be performed manually by a person or by automatic process. Samples of material can be taken or provided for testing, analysis, investigation, quality control, demonstration, or trial use. Sometimes, sampling may be performed continuously. Aliquot part In science, a representative liquid sample tak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Part
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer is divisible by a nonzero integer if there exists an integer such that n=km. This is written as :m\mid n. Other ways of saying the same thing are that divides , is a divisor of , is a factor of , and is a multiple of . If does not divide , then the notation is m\not\mid n. Usually, is required to be nonzero, but is allowed to be zero. With this convention, m \mid 0 for every nonzero integer . Some definitions omit the requirement that m be nonzero. General Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Stop
An organ stop is a component of a pipe organ that admits pressurized air (known as ''wind'') to a set of organ pipes. Its name comes from the fact that stops can be used selectively by the organist; each can be "on" (admitting the passage of air to certain pipes), or "off" (''stopping'' the passage of air to certain pipes). The term can also refer to the control that operates this mechanism, commonly called a stop tab, stop knob, or drawknob. On electric or electronic organs that imitate a pipe organ, the same terms are often used, with the exception of the Hammond organ and clonewheel organs, which use the term " drawbar". The term is also sometimes used as a synonym for register, referring to rank(s) of pipes controlled by a single stop. Registration is the art of combining stops to produce a certain sound. The phrase " pull out all the stops,” while once only meant to engaging all voices on the organ, has entered general usage, for deploying all available means to pursue a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pharmaceutics
Pharmaceutics is the discipline of pharmacy that deals with the process of turning a new chemical entity (NCE) or old drugs into a medication to be used safely and effectively by patients. It is also called the science of dosage form design. There are many chemicals with pharmacological properties, but need special measures to help them achieve therapeutically relevant amounts at their sites of action. Pharmaceutics helps relate the formulation of drugs to their delivery and disposition in the body. Pharmaceutics deals with the formulation of a pure drug substance into a dosage form. Branches of pharmaceutics include: *Pharmaceutical formulation *Pharmaceutical manufacturing *Dispensing pharmacy *Pharmaceutical technology *Physical pharmacy *Pharmaceutical jurisprudence Pure drug substances are usually white crystalline or amorphous powders. Before the advent of medicine as a science, it was common for pharmacists to dispense drugs ''as is''. Most drugs today are administered as p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyploid
Polyploidy is a condition in which the cells of an organism have more than one pair of ( homologous) chromosomes. Most species whose cells have nuclei ( eukaryotes) are diploid, meaning they have two sets of chromosomes, where each set contains one or more chromosomes and comes from each of two parents, resulting in pairs of homologous chromosomes between sets. However, some organisms are polyploid. Polyploidy is especially common in plants. Most eukaryotes have diploid somatic cells, but produce haploid gametes (eggs and sperm) by meiosis. A monoploid has only one set of chromosomes, and the term is usually only applied to cells or organisms that are normally diploid. Males of bees and other Hymenoptera, for example, are monoploid. Unlike animals, plants and multicellular algae have life cycles with two alternating multicellular generations. The gametophyte generation is haploid, and produces gametes by mitosis, the sporophyte generation is diploid and produces spores by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
