reckon

WordNet

take account of; "You have to reckon with our opponents"; "Count on the monsoon" (同)count
a handbook of tables used to facilitate computation (同)ready_reckoner
navigation without the aid of celestial observations
a bill for an amount due (同)tally

PrepTutorEJDIC

…‘を'『数える』,計算する《+『up』+『名,』+『名』+『up』》 / …‘を'『みなす』,考える / 《話》《『reckon』+『that節』》…であると思う(suppose) / 数える,計算する / 《話》思う
計算する人,建算者 / =ready reckoner
(いたずら・悪事・犯罪などに)制裁を加える時 / =Judgement Day
計算早見表
計算・〈U〉決算,清算・〈C〉《古》(病院・ホテルなどの)勘定書・〈U〉船の位置の推測
…‘を'気にかける,こだわる / (…を)気にかける《+『of』+『名』》

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/11/21 15:39:47」(JST)

wiki en

[Wiki en表示]

Counting is the action of finding the number of elements of a finite set of objects. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term enumeration refers to uniquely identifying the elements of a finite (combinatorial) set or infinite set by assigning a number to each element.

Counting using tally marks at Hanakapiai Beach

Counting sometimes involves numbers other than one; for example, when counting money, counting out change, "counting by twos" (2, 4, 6, 8, 10, 12, ...), or "counting by fives" (5, 10, 15, 20, 25, ...).

There is archeological evidence suggesting that humans have been counting for at least 50,000 years.^[1] Counting was primarily used by ancient cultures to keep track of social and economic data such as number of group members, prey animals, property, or debts (i.e., accountancy). The development of counting led to the development of mathematical notation, numeral systems, and writing.

Forms of counting[edit]

Further information: Prehistoric numerals and Numerical digit

Counting can occur in a variety of forms.

Counting can be verbal; that is, speaking every number out loud (or mentally) to keep track of progress. This is often used to count objects that are present already, instead of counting a variety of things over time.

Counting can also be in the form of tally marks, making a mark for each number and then counting all of the marks when done tallying. This is useful when counting objects over time, such as the number of times something occurs during the course of a day. Tallying is base 1 counting; normal counting is done in base 10. Computers use base 2 counting (0's and 1's).

Counting can also be in the form of finger counting, especially when counting small numbers. This is often used by children to facilitate counting and simple mathematical operations. Finger-counting uses unary notation (one finger = one unit), and is thus limited to counting 10 (unless you start in with your toes). Other hand-gesture systems are also in use, for example the Chinese system by which one can count 10 using only gestures of one hand. By using finger binary (base 2 counting), it is possible to keep a finger count up to 1023 = 2¹⁰ − 1.

Various devices can also be used to facilitate counting, such as hand tally counters and abacuses.

Inclusive counting[edit]

Inclusive counting is usually encountered when counting days in a calendar. Normally when counting "8" days from Sunday, Monday will be day 1, Tuesday day 2, and the following Monday will be the eighth day. When counting "inclusively," the Sunday (the start day) will be day 1 and therefore the following Sunday will be the eighth day. For example, the French phrase for "fortnight" is en quinze (in 15 [days]), and similar words are present in Greek (δεκαπενθήμερο, dekapenthímero), Spanish (quincena) and Portuguese (quinzena) - whereas "a fortnight" derives from "a fourteen-night", as the archaic "a sennight" does from "a seven-night". This practice appears in other calendars as well; in the Roman calendar the nones (meaning "nine") is 8 days before the ides; and in the Christian calendar Quinquagesima (meaning 50) is 49 days before Easter Sunday.

The Jewish people also counted^[when?] days inclusively. For instance, Jesus it is said, announced he would die and resurrect "on the third day," i.e. two days later. Scholars^[who?] most commonly place his crucifixion on a Friday afternoon and his resurrection on Sunday before sunrise, spanning three different days but a period of around 36–40 hours.^{[citation needed]}

Musical terminology also uses inclusive counting of intervals between notes of the standard scale: going up one note is a second interval, going up two notes is a third interval, etc., and going up seven notes is an octave.

Education and development[edit]

Main article: Pre-math skills

Learning to count is an important educational/developmental milestone in most cultures of the world. Learning to count is a child's very first step into mathematics, and constitutes the most fundamental idea of that discipline. However, some cultures in Amazonia and the Australian Outback do not count,^[2]^[3] and their languages do not have number words.

Many children at just 2 years of age have some skill in reciting the count list (i.e., saying "one, two, three, ..."). They can also answer questions of ordinality for small numbers, e.g., "What comes after three?". They can even be skilled at pointing to each object in a set and reciting the words one after another. This leads many parents and educators to the conclusion that the child knows how to use counting to determine the size of a set.^[4] Research suggests that it takes about a year after learning these skills for a child to understand what they mean and why the procedures are performed.^[5]^[6] In the mean time, children learn how to name cardinalities that they can subitize.

Children with Williams syndrome often display serious delays in learning to count.^{[citation needed]}

Counting in mathematics[edit]

In mathematics, the essence of counting a set and finding a result n, is that it establishes a one to one correspondence (or bijection) of the set with the set of numbers {1, 2, ..., n}. A fundamental fact, which can be proved by mathematical induction, is that no bijection can exist between {1, 2, ..., n} and {1, 2, ..., m} unless n = m; this fact (together with the fact that two bijections can be composed to give another bijection) ensures that counting the same set in different ways can never result in different numbers (unless an error is made). This is the fundamental mathematical theorem that gives counting its purpose; however you count a (finite) set, the answer is the same. In a broader context, the theorem is an example of a theorem in the mathematical field of (finite) combinatorics—hence (finite) combinatorics is sometimes referred to as "the mathematics of counting."

Many sets that arise in mathematics do not allow a bijection to be established with {1, 2, ..., n} for any natural number n; these are called infinite sets, while those sets for which such a bijection does exist (for some n) are called finite sets. Infinite sets cannot be counted in the usual sense; for one thing, the mathematical theorems which underlie this usual sense for finite sets are false for infinite sets. Furthermore, different definitions of the concepts in terms of which these theorems are stated, while equivalent for finite sets, are inequivalent in the context of infinite sets.

The notion of counting may be extended to them in the sense of establishing (the existence of) a bijection with some well understood set. For instance, if a set can be brought into bijection with the set of all natural numbers, then it is called "countably infinite." This kind of counting differs in a fundamental way from counting of finite sets, in that adding new elements to a set does not necessarily increase its size, because the possibility of a bijection with the original set is not excluded. For instance, the set of all integers (including negative numbers) can be brought into bijection with the set of natural numbers, and even seemingly much larger sets like that of all finite sequences of rational numbers are still (only) countably infinite. Nevertheless there are sets, such as the set of real numbers, that can be shown to be "too large" to admit a bijection with the natural numbers, and these sets are called "uncountable." Sets for which there exists a bijection between them are said to have the same cardinality, and in the most general sense counting a set can be taken to mean determining its cardinality. Beyond the cardinalities given by each of the natural numbers, there is an infinite hierarchy of infinite cardinalities, although only very few such cardinalities occur in ordinary mathematics (that is, outside set theory that explicitly studies possible cardinalities).

Counting, mostly of finite sets, has various applications in mathematics. One important principle is that if two sets X and Y have the same finite number of elements, and a function f: X → Y is known to be injective, then it is also surjective, and vice versa. A related fact is known as the pigeonhole principle, which states that if two sets X and Y have finite numbers of elements n and m with n > m, then any map f: X → Y is not injective (so there exist two distinct elements of X that f sends to the same element of Y); this follows from the former principle, since if f were injective, then so would its restriction to a strict subset S of X with m elements, which restriction would then be surjective, contradicting the fact that for x in X outside S, f(x) cannot be in the image of the restriction. Similar counting arguments can prove the existence of certain objects without explicitly providing an example. In the case of infinite sets this can even apply in situations where it is impossible to give an example; for instance there must exists real numbers that are not computable numbers, because the latter set is only countably infinite, but by definition a non-computable number cannot be precisely specified.

The domain of enumerative combinatorics deals with computing the number of elements of finite sets, without actually counting them; the latter usually being impossible because infinite families of finite sets are considered at once, such as the set of permutations of {1, 2, ..., n} for any natural number n.

References[edit]

^ An Introduction to the History of Mathematics (6th Edition) by Howard Eves (1990) p.9
^ Butterworth, B., Reeve, R., Reynolds, F., & Lloyd, D. (2008). Numerical thought with and without words: Evidence from indigenous Australian children. Proceedings of the National Academy of Sciences, 105(35), 13179–13184.
^ Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496–499.
^ Fuson, K.C. (1988). Children's counting and concepts of number. New York: Springer–Verlag.
^ Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105, 395–438.
^ Le Corre, M., Van de Walle, G., Brannon, E. M., Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52(2), 130–169.

External links[edit]

History of Counting-PlainMath.Net

English Journal

Systematic review on antibiotic therapy for pneumonia in children between 2 and 59 months of age.

Lassi ZS, Das JK, Haider SW, Salam RA, Qazi SA, Bhutta ZA.Author information Division of Women and Child Health, The Aga Khan University, , Karachi, Pakistan.AbstractCommunity-acquired pneumonia (CAP) remains a force to reckon with, as it accounts for 1.1 million of all deaths in children less than 5 years of age globally, with disproportionately higher mortality occurring in the low and middle income-countries (LMICs) of Southeast Asia and Africa. Existing strategies to curb pneumonia-related morbidity and mortality have not effectively translated into meaningful control of pneumonia-related burden. In the present systematic review, we conducted a meta-analysis of trials conducted in LMICs to determine the most suitable antibiotic therapy for treating pneumonia (very severe, severe and non-severe). While previous reviews, including the most recent review by Lodha et al, have focused either on single modality of antibiotic therapy (such as choice of antibiotic) or children under the age of 16 years, the current review updates evidence on the choice of drug, duration, route and combination of antibiotics in children specifically between 2 and 59 months of age. We included randomised controlled trials (RCTs) and quasi-RCTs that assessed the route, dose, combination and duration of antibiotics in the management of WHO-defined very severe/severe/non-severe CAP. Study participants included children between 2 and 59 months of age with CAP. All available titles and abstracts were screened for inclusion by two review authors independently. All data was entered and analysed using Review Manager 5 software. The review identified 8122 studies on initial search, of which 22 studies which enrolled 20 593 children were included in meta-analyses. Evidence from these trials showed a combination of penicillin/ampicillin and gentamicin to be effective for managing very severe pneumonia in children between 2 and 59 months of age, and oral amoxicillin to be equally efficacious, as other parenteral antibiotics for managing severe pneumonia in children of this particular age group. Oral amoxicillin was also found to be effective in non-severe pneumonia as well. The review further found a short 3 day course of antibiotics to be equally beneficial as 5 day course for managing non-severe pneumonia in children between 2 and 59 months of age. This review updates evidence on the general spectrum of antibiotic recommendation for CAP in children between 2 and 59 months of age, which is an age group that warrants special focus owing to its high disease and mortality burden. Evidence derived from the review found oral amoxicillin to be equally effective as parenteral antibiotics for severe pneumonia in the 2-59 month age group, which holds important implications for LMICs where parenteral drug administration is an issue. Also, the review's finding that 3 day course of antibiotic is equally effective as 5 day course for non-severe pneumonia for 2-59 months of age is again beneficial for LMICs, as a shorter therapy will be associated with a lower cost. The review addresses some research gaps in antibiotic treatment for CAP as well, and this crucial information is presented with the aim of providing a targeted cure for the middle and low income setting.
Archives of disease in childhood.Arch Dis Child.2014 Jan 15. doi: 10.1136/archdischild-2013-304023. [Epub ahead of print]
Community-acquired pneumonia (CAP) remains a force to reckon with, as it accounts for 1.1 million of all deaths in children less than 5 years of age globally, with disproportionately higher mortality occurring in the low and middle income-countries (LMICs) of Southeast Asia and Africa. Existing stra
PMID 24431417

E6 protein of human papillomavirus 16 (HPV16) expressed in Escherichia coli sans a stretch of hydrophobic amino acids, enables purification of GST-ΔE6 in the soluble form and retains the binding ability to p53.

Verma RR, Sriraman R, Rana SK, Ponnanna NM, Rajendar B, Ghantasala P, Rajendra L, Matur RV, Srinivasan VA.Author information R&D Centre, Indian Immunologicals Ltd., Rakshapuram, Gachibowli P.O., Hyderabad 500032, India.AbstractRecombinant E6 expressed in Escherichia coli is known to form recalcitrant inclusion bodies even when fused to the soluble GST protein. This study describes the modification of the HPV genotype-16 oncogenic protein E6 in order to obtain it in the soluble form. The modified protein (ΔE6) was expressed in E. coli BL21 as an N-terminal fusion with GST (GST-ΔE6). ΔE6 was constructed by deleting the nucleotide sequences coding for IHDIIL (31-36 a.a), one of the highly hydrophobic peptide stretches, using splicing by overextension polymerase chain reaction (SOE-PCR). The removal of IHDIIL residues rendered the GST-ΔE6 soluble and amenable for purification involving a two step process a preliminary glutathione-GST affinity chromatography followed by gel-filtration chromatography. Evaluation of purified protein fractions by HPLC suggests that GST-ΔE6 exists as a monomer. Further, the ΔE6 in GST-ΔE6 seemed to retain the binding ability to p53 as determined by the glutathione-GST capture ELISA. Purified GST-ΔE6 we reckon, might find use as an essential reagent in immunological assays, in sero-epidemiological studies, and also in studies to delineate the structure and function of HPV16 E6.
Protein expression and purification.Protein Expr Purif.2013 Nov;92(1):41-7. doi: 10.1016/j.pep.2013.08.010. Epub 2013 Sep 6.
Recombinant E6 expressed in Escherichia coli is known to form recalcitrant inclusion bodies even when fused to the soluble GST protein. This study describes the modification of the HPV genotype-16 oncogenic protein E6 in order to obtain it in the soluble form. The modified protein (ΔE6) was express
PMID 24012792

The value of the seagrass Posidonia oceanica: a natural capital assessment.

Vassallo P, Paoli C, Rovere A, Montefalcone M, Morri C, Bianchi CN.Author information DISTAV, Dipartimento di Scienze della Terra, dell'Ambiente e della Vita, Genoa University, Italy.AbstractMaking nature's value visible to humans is a key issue for the XXI century and it is crucial to identify and measure natural capital to incorporate benefits or costs of changes in ecosystem services into policy. Emergy analysis, a method able to analyze the overall functioning of a system, was applied to reckon the value of main ecosystem services provided by Posidonia oceanica, a fragile and precious Mediterranean seagrass ecosystem. Estimates, based on calculation of resources employed by nature, resulted in a value of 172 € m(-2)a(-1). Sediment retained by meadow is most relevant input, composing almost the whole P. oceanica value. Remarks about economic losses arising from meadow regression have been made through a time-comparison of meadow maps. Suggested procedure represents an operative tool to provide a synthetic monetary measure of ecosystem services to be employed when comparing natural capital to human and financial capitals in a substitutability perspective.
Marine pollution bulletin.Mar Pollut Bull.2013 Oct 15;75(1-2):157-67. doi: 10.1016/j.marpolbul.2013.07.044. Epub 2013 Aug 15.
Making nature's value visible to humans is a key issue for the XXI century and it is crucial to identify and measure natural capital to incorporate benefits or costs of changes in ecosystem services into policy. Emergy analysis, a method able to analyze the overall functioning of a system, was appli
PMID 23953894

Pitch and pitch variation in lesbian women.

Van Borsel J, Vandaele J, Corthals P.Author information Ghent University, Ghent, Belgium; Universidade Veiga de Almeida, Rio de Janeiro, Brazil. john.vanborsel@ugent.beAbstractOBJECTIVES: The purpose of this study was to investigate to what extent lesbian women demonstrate pitch and pitch variation that is different from that of heterosexual women.
Journal of voice : official journal of the Voice Foundation.J Voice.2013 Sep;27(5):656.e13-6. doi: 10.1016/j.jvoice.2013.04.008. Epub 2013 Jul 19.
OBJECTIVES: The purpose of this study was to investigate to what extent lesbian women demonstrate pitch and pitch variation that is different from that of heterosexual women.STUDY DESIGN: Static group comparison.METHODS: The average pitch and pitch variation of a group of 34 self-identified lesbian
PMID 23876941

Japanese Journal

19世紀イギリスにおける動物闘技の違法性と制定法に関する基礎的研究 : 動物虐待法(1835年)と先行法との歴史的関連を中心として

松井良明
スポーツ史研究 (20), 35-50, 2007-03-15
NAID 110006242254

産業政策論に関する新視点 : 産業連関表に基づく産業構造の評価基準と労働価値量の算出方法を中心に(<特集>総合政策学)

張忠任
総合政策論叢 8, 117-123, 2004-12
In the neoclassical economics, the policy effects are usually analyzed within the framework of the general equilibrium of endogenous variables by the method of comparative statics which will be attain …
NAID 110006456360

<いのち>のどこが大切なのか? : 古代ギリシア人の死生観への一瞥

森一郎,森一郎(1962-),モリイチロウ
東京女子大学紀要論集 50(2), 29-65, 2000-03-10
… It is often said, "We must today realize the sublime value of life on earth." This is one of the most basic convictions of modern humanism-or, more strictly speaking, "humanitarianism." In fact, we reckon the dignity of life among the principles of our sense of morality. …
NAID 110006000690

製品におけるマーケットシェアの有するフラクタル性の仮説と考察

井上勝雄,安斎利典,広川美津雄
デザイン学研究 46(5), 11-16, 2000-01-31
本研究前半で行った複雑系の方法論的な考察から見い出された3つの複雑系研究の方向性の中で, 製品デザインに関係が深いマーケットシェアが, その方向性の中のひとつであるフラクタル性が見られることに注目した。その視点から, マーケットシェアが完全なる自由な市場競争である場合は, その分布点はフラクタル性を示すベキ分布をするが, 市場の内部に阻害要因があると, そのベキ分布にバラツキが現れるという仮説を導 …
NAID 110003825125