summationn.²

Brit.

/sʌˈmeɪʃn/, U.S.

/səˈmeɪʃ(ə)n/

Origin: Formed within English, by derivation. Etymons: sum v.¹, -ation suffix.

Etymology: < sum v.¹ + -ation suffix. Compare earlier sum n.¹, summary n., summing n., and later summate v.Compare post-classical Latin summation- , summatio (9th cent. and 14th cent. in apparently isolated attestations), Middle French sommacion , French sommation sum, calculation (late 15th cent.), summing-up, summary (1601 in the passage translated in quot. 1608). Specific senses. In quot. 1608 at sense 1a after French sommation. In sense 6b after German Summierung (1893 or earlier in this sense in Freud).

a. An act of summarizing the main or essential points of something; a result of this, a summary. rare before the 20th cent.

ΘΚΠ

the mind > attention and judgement > judgement or decision > [noun] > conclusion

culorum1362

conclusionc1385

conjecturec1386

issuea1393

deduction1532

overplus1536

gatheringa1555

deducement1605

summation1608

therefore1641

offcome1655

deductivea1676

empiricism1724

wrap-up1960

inference1972

1608 E. Grimeston tr. J. F. Le Petit Gen. Hist. Netherlands ix. 440 Besides that your sergeant hath made no signification, summation [Fr. sommation], or insinuation of his exploit to mee.

1896 Liverpool Mercury 8 Jan. 5/1 A brief summation of the divisions of the Suite is that the Prelude is bold in its virility..the Valse is elegant.

1908 Daily Chron. 26 Feb. 3/3 Such is Mr. Wyndham's summation of Scott.

1977 Chem. Week (Nexis) 7 Dec. 57 That's a neat summation of the European plastics scene.

2011 Jrnl. Midwest Mod. Lang. Assoc. 46 97 Readers may not agree with Carroll or his summation of the current state of literary criticism.

b. spec. A final speech made by a counsel or judge near the end of a trial, summarizing the evidence and main points of the case for the jury. Cf. summing up n. 2a.

ΚΠ

1848 Morning Post 29 Jan. 2/4 A legal summation was then made in the usual manner, but without result.

1959 Jrnl. Illinois State Hist. Soc. 52 150 One of the defense counsel, delivered a summation, characterized by Stephen T. Logan as ‘a short but strong and sensible speech’, which contributed mightily to the result.

2005 Globe & Mail (Toronto) 14 Dec. a16/2 Chief prosecutor Bev Richards is then expected to produce some brief ‘reply evidence’ and, after summations, judge Watt will consider his verdict.

2. Mathematics. The process of finding the sum of an infinite series. See sum n.¹ 5b(a).

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > finding sum of

summation1742

1742 Daily Gazetteer 20 Sept. Several new Methods for the Summation of Series.

1845 T. Tate Treat. Factorial Anal. Introd. p. iii. The summation of series, by the method of definite integrals, first employed by Euler, has been extended by Poisson, W. S. B. Woolhouse, and other writers.

1936 S. Glasstone Recent Adv. Gen. Chem. ii. 76 By replacing summation with integration and using the method of asymptotic expansion..it has been possible to diminish the labour involved in obtaining the partition functions for relatively simple polyatomic molecules.

2014 A. Zagoskin Quantum Theory of Many-body Syst. (ed. 2) iii. 109 The causal Green's function is essentially nonanalytic, and thus cannot be obtained by summation of a series.

3. The calculation of the value or amount of something abstract or non-material; (also) an instance of this. Now rare.

ΚΠ

1753 J. Balfour Delineation of Nature & Obligation of Morality 171 Far less will he estimate the quantity of his virtue by the sordid summation of the profit of pleasure it may procure.

1797 J. Wilde Sequel Addr. to Soc. Friends of People 32 Will not the summation of doubts make a doubtful whole?

1856 P. E. Dove Logic Christian Faith v. i. 262 Our conception of duty is either ‘Yea’, or ‘Nay’ without..summations of advantages.

2000 Belfast News Let. (Nexis) 11 May 6 Following that assessment, the ultimate summation of the overall level of threat is now reduced as a result of last weekend's events.

4. The adding up of numbers or quantities; the calculation of a sum total.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > [noun] > summing or addition

addition?c1425

conference1610

casting1743

tot1755

summation1781

totting1823

totalization1888

1781 D. Hartley Addr. Comm. Assoc. York 10 Summation of these articles of Public Loss £. 366,000,000.

1860 J. Tyndall Glaciers of Alps i. xi. 81 The summation of distances twenty paces each must finally place us at the top.

2007 B. Bosworth et al. in S. M. Collins Brookings Trade Forum 2007 179 The net debt has actually grown more slowly than would have been expected from a simple summation of the annual current account deficits.

5. The final outcome or result of something; a culmination, a climax.

ΘΚΠ

the world > relative properties > number > enumeration, reckoning, or calculation > [noun] > result, sum

telc1000

tale?c1225

tailc1330

reckoningc1392

suma1400

aggregatec1443

count1483

sum total1549

total1557

computation1586

calculation1646

quotient1659

tally1674

amount1751

tot1755

summation1841

1841 T. Carlyle On Heroes i. 36 They are not one coherent System of Thought; but properly the summation of several successive systems.

1879 19th Cent. Sept. 500 He is the summation of Hebraism and Hellenism.

1916 H. G. Wells Mr. Britling sees it Through 35 He wanted to state England..as the amiable summation of a grotesque assembly of faults.

2016 Independent (Nexis) 29 Dec. Bach regarded his majestic Mass in B minor as the summation of his choral achievement.

a. Physiology. The arrival in close temporal or spatial proximity of two more stimuli at a nerve cell or muscle fibre; the response produced in nerve or muscle tissue by such stimuli; spec. the process by which such stimuli evoke excitation in nerve or muscle when each alone would fail to do so.

ΘΚΠ

the world > life > biology > biological processes > action of nervous system > [noun] > nerve impulse

vibration1728

nerve current1859

nerve impulse1870

summation1872

message1884

wave of stimulation1885

pattern1930

the world > life > the body > structural parts > muscle > [noun] > accumulation of stimuli

summation1872

1872 Jrnl. Anat. & Physiol. 6 222 The so-called super-maximum contractions arise from the summation of two stimuli.

1907 W. H. Howell Text-bk. Physiol. (ed. 2) 41 The greatest summation occurs when the stimuli are so spaced that the second contraction begins at the apex of the first.

1979 A. P. Spence & E. B. Mason Human Anat. & Physiol. xi. 293 During spatial summation, nerve impulses in many different stimulatory presynaptic cells..may all arrive at the postsynaptic cell very close together in time.

2005 C. S. Hill in M. Aydede Pain iii. 94 It can happen that the signal is ratcheted up as a result of temporal summation in the spinal cord.

b. Psychology. The cumulative action or effect of a repeated stimulus, process, etc.; an instance of this.

ΘΚΠ

the mind > mental capacity > psychology > theory of psychoanalysis > theories of Freud > [noun] > cumulative action

summation1920

1920 E. J. Kempf Psychopathol. i. 62 The tendency to suppress our affections may accumulate; that is, a summation of the repressing or suppressing egoistic wishes may occur.

1955 J. Strachey et al. tr. S. Freud Compl. Wks. II. ii. 174 Even a hysteric can retain a certain amount of affect that has not been dealt with; if, owing to the occurrence of similar provoking causes, that amount is increased by summation to a point beyond the subject's tolerance, the impetus to conversion is given.

2004 K. Jordens & F. Van Overwalle in G. Haddock & G. R. Maio Contemp. Perspectives Psychol. Attitudes xv. 369 Implicit attitude formation is guided by a summation of valences, whereas explicit attitude formation is driven by an averaging of valences.

7. Electronics and Physics. The combination of two or more signals, waveforms, etc., via superposition.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > [noun] > summing or addition > of measurable quantities

summation1921

the world > matter > physics > electromagnetic radiation > electronics > electronic phenomena > processes > [noun] > addition of voltages, signals, etc.

summation1921

1921 Brit. Patent 170,941 2/1 The negative resistance applied is a function of the amplitude, and in consequence when two signals arrive together summation of signals is altered.

1993 Proc. IEEE Ultrasonics Symp. 627/2 The displacement field results from the summation of the waveforms generated by each line source, with the proper time delay.

2013 N. W. Draw Visual Devel. (ed. 3) iii. 43/1 According to signal-noise theory, detectability improves with summation of two signals if they have separate sources of noise.

Compounds

C1. General use as a modifier (in various senses).

ΚΠ

1875 Trans. Edinb. Obstetr. Soc. 1871–4 340 The gross effect of, or the summation result of the combined contractions of the entire contractile tissues of the uterus.

1901 E. B. Titchener Exper. Psychol. I. ii. 90 If we are not satisfied with this ‘summation’ theory, we may..suppose that the gaps in sensation are filled out by association.

1916 Jrnl. Amer. Chem. Soc. 38 2296 This magnitude varies with the specific heats of the reacting substances..according to the equation dU/dT = ΣnC the summation sign indicating an algebraic summation (reactants positive, resultants negative) of the molecular heats of the substances.

1918 Geogr. Rev. 6 77 The ‘summation process’..consists in adding together the mean daily air temperatures during the life phase of a crop in order to find the thermal requirement.

1967 Brain 90 445 A summation effect occurred, items of information relevant to previous stimuli being included in the perseveratory response.

1975 E. R. Hilgard & J. R. Hilgard Hypnosis in Relief of Pain ii. 34 The pattern theory, or summation theory, proposes that pain depends upon a summation of neural inputs that must reach a critical level for pain to be felt.

2006 P. J. Nahin Dr. Euler's Fabulous Formula iv. 161 The summation index k runs through all the integers, positive and negative.

C2.

summation check n. now rare any of several procedures that use addition to check the accuracy or integrity of data; esp.: (a) a procedure used with tabulated data, in which totals are calculated for each column and the sum of these compared with that of the total column (now rare) (b) (Computing and Telecommunications) a procedure in which the sum of the digits of a number is compared with a pre-calculated value in order to check for data corruption; (also) the pre-calculated value used in this procedure (= checksum n. at check- comb. form Additions).

ΘΚΠ

society > computing and information technology > data > database > data entry > [noun] > error check

summation check1926

checksum1940

parity check1950

Hamming distance1954

redundancy check1955

sum check1956

validity check1957

1926 Trans. Actuarial Soc. Amer. 27 37 The several summation checks, which detect errors early, also eliminate the need for review or independent working.

1951 Insurance Law Jrnl. No. 12 955/1 Continuous methods [for mass calculations] often have the further advantage of permitting simple summation checks.

1962 Automatic Data Processing Gloss. (U.S. Bureau of Budget) 9/1 Check-sum, the sum used in a summation check.

2010 O. R. Whittington & P. R. Delaney Wiley CPA Exam Rev. 2011 112/2 A parity check is a summation check in which the binary digits of a character are added to determine whether the sum is odd or even.

summation network n. Electronics (in a circuit) a system of components that produces an output voltage proportional to the sum of that of two or more inputs (cf. network n. 4b).

ΚΠ

1942 U.S. Patent 2,283,566 3/2 For determining that fraction of the total generated millivoltage that may be applied to an instrument or to the potentiometer, not shown, of a summation network.

2015 IEEE Trans. Signal Processing 63 284/2 The delay-adjusted scanline data for the 16 neighboring scanlines is then fed forward to the summation network.

summation notation n. the notation used to denote a series (series n. 8); an instance of such notation.Summation notion expresses series in the form Σⁿ_{i = m}x_i, where x_i represents the general term of the series, and the values of m and n specify respectively the starting and stopping points of the sum; e.g. Σ⁵_{i = 3}x_i represents the series x₃ + x₄ + x₅.

ΚΠ

1909 Michigan Technic Feb. 45 The general reduced equation is expressed directly in the summation notation.

1969 Planetary & Space Sci. 17 67 The summation notation in Equations (17) and (19) indicates that contribution from all species of thermal particles be taken.

2014 N. Loehr Adv. Linear Algebra iii. 35 Often we denote such a polynomial using the summation notation Σⁿ_{i = 0}a_ixⁱ.

summation tone n. [after German Summationston (H. Helmholtz 1856, in Ann. der Physik u. Chem. 99 518)] Acoustics and Music = sum tone n. at sum n.¹ Compounds.

ΘΚΠ

society > leisure > the arts > music > musical sound > harmony or sounds in combination > chord > [noun] > combination tone

resultant note1836

resultant tone1836

summation tone1867

summation-tone (or summational tone)1867

combinational tone1879

combination tone1889

1867 J. Tyndall Sound vii. 285 Resultant tones are of two kinds... The former are called difference tones, the latter summation tones.

1994 P. Rehfeldt New Direct. for Clarinet (rev. ed.) iii. 42 Many multiple sonorities also produce difference tones and summation tones.

This entry has been updated (OED Third Edition, September 2019; most recently modified version published online March 2022).

单词	summation
释义	† summationn.¹ Forms: late Middle English somacion, 1600s–1800s summation. Origin: A borrowing from French. Etymons: French somacion, sommacion. Etymology: < Middle French somacion, sommacion (late 13th cent. in Old French; French sommation ) < sommer to achieve, accomplish (something) (late 12th cent.), to summon (a person) (c1250; < somme sum n.¹) + -acion -ation suffix. Compare earlier summonds n., summoning n., summonition n., summons n. Obsolete. A summons (in various senses). ΘΚΠ society > authority > command > command or bidding > [noun] > summons or summoning lathingc897 summonc1330 summoningc1375 summonds1385 calla1400 summation?1473 citing1485 sanda1513 whistlea1529 provocation1542 evocation1575 bidding1810 biddance1836 whip1879 ?1473 W. Caxton tr. R. Le Fèvre Recuyell Hist. Troye (1894) I. lf. 110^v Perseus..sente danus vnto the kynge prycus to somene hym that he shold yelde the royame vnto kynge Acrisius Danus wente to Arges. And accomplisshed the somacion. 1633 E. Grimeston tr. Polybius Hist. xiv. 419 Scipio gaue many presumptions by his preparation and summation [Gk. τῶν παραγγελμάτων], that hee had some Enterprize against Bysarthe. 1769 tr. P. de Charlevoix Hist. Paraguay II. viii. 42 The summation of Don Bernardin to repair to La Plata. 1864 D. G. Mitchell Seven Stories 7 The admiring spirit with which..I yielded my pence to his impetuous summation. This entry has been updated (OED Third Edition, September 2019; most recently modified version published online June 2021). summationn.² Brit. /sʌˈmeɪʃn/, U.S. /səˈmeɪʃ(ə)n/ Origin: Formed within English, by derivation. Etymons: sum v.¹, -ation suffix. Etymology: < sum v.¹ + -ation suffix. Compare earlier sum n.¹, summary n., summing n., and later summate v.Compare post-classical Latin summation- , summatio (9th cent. and 14th cent. in apparently isolated attestations), Middle French sommacion , French sommation sum, calculation (late 15th cent.), summing-up, summary (1601 in the passage translated in quot. 1608). Specific senses. In quot. 1608 at sense 1a after French sommation. In sense 6b after German Summierung (1893 or earlier in this sense in Freud). 1. a. An act of summarizing the main or essential points of something; a result of this, a summary. rare before the 20th cent. ΘΚΠ the mind > attention and judgement > judgement or decision > [noun] > conclusion culorum1362 conclusionc1385 conjecturec1386 issuea1393 deduction1532 overplus1536 gatheringa1555 deducement1605 summation1608 therefore1641 offcome1655 deductivea1676 empiricism1724 wrap-up1960 inference1972 1608 E. Grimeston tr. J. F. Le Petit Gen. Hist. Netherlands ix. 440 Besides that your sergeant hath made no signification, summation [Fr. sommation], or insinuation of his exploit to mee. 1896 Liverpool Mercury 8 Jan. 5/1 A brief summation of the divisions of the Suite is that the Prelude is bold in its virility..the Valse is elegant. 1908 Daily Chron. 26 Feb. 3/3 Such is Mr. Wyndham's summation of Scott. 1977 Chem. Week (Nexis) 7 Dec. 57 That's a neat summation of the European plastics scene. 2011 Jrnl. Midwest Mod. Lang. Assoc. 46 97 Readers may not agree with Carroll or his summation of the current state of literary criticism. b. spec. A final speech made by a counsel or judge near the end of a trial, summarizing the evidence and main points of the case for the jury. Cf. summing up n. 2a. ΚΠ 1848 Morning Post 29 Jan. 2/4 A legal summation was then made in the usual manner, but without result. 1959 Jrnl. Illinois State Hist. Soc. 52 150 One of the defense counsel, delivered a summation, characterized by Stephen T. Logan as ‘a short but strong and sensible speech’, which contributed mightily to the result. 2005 Globe & Mail (Toronto) 14 Dec. a16/2 Chief prosecutor Bev Richards is then expected to produce some brief ‘reply evidence’ and, after summations, judge Watt will consider his verdict. 2. Mathematics. The process of finding the sum of an infinite series. See sum n.¹ 5b(a). ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > finding sum of summation1742 1742 Daily Gazetteer 20 Sept. Several new Methods for the Summation of Series. 1845 T. Tate Treat. Factorial Anal. Introd. p. iii. The summation of series, by the method of definite integrals, first employed by Euler, has been extended by Poisson, W. S. B. Woolhouse, and other writers. 1936 S. Glasstone Recent Adv. Gen. Chem. ii. 76 By replacing summation with integration and using the method of asymptotic expansion..it has been possible to diminish the labour involved in obtaining the partition functions for relatively simple polyatomic molecules. 2014 A. Zagoskin Quantum Theory of Many-body Syst. (ed. 2) iii. 109 The causal Green's function is essentially nonanalytic, and thus cannot be obtained by summation of a series. 3. The calculation of the value or amount of something abstract or non-material; (also) an instance of this. Now rare. ΚΠ 1753 J. Balfour Delineation of Nature & Obligation of Morality 171 Far less will he estimate the quantity of his virtue by the sordid summation of the profit of pleasure it may procure. 1797 J. Wilde Sequel Addr. to Soc. Friends of People 32 Will not the summation of doubts make a doubtful whole? 1856 P. E. Dove Logic Christian Faith v. i. 262 Our conception of duty is either ‘Yea’, or ‘Nay’ without..summations of advantages. 2000 Belfast News Let. (Nexis) 11 May 6 Following that assessment, the ultimate summation of the overall level of threat is now reduced as a result of last weekend's events. 4. The adding up of numbers or quantities; the calculation of a sum total. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > [noun] > summing or addition addition?c1425 conference1610 casting1743 tot1755 summation1781 totting1823 totalization1888 1781 D. Hartley Addr. Comm. Assoc. York 10 Summation of these articles of Public Loss £. 366,000,000. 1860 J. Tyndall Glaciers of Alps i. xi. 81 The summation of distances twenty paces each must finally place us at the top. 2007 B. Bosworth et al. in S. M. Collins Brookings Trade Forum 2007 179 The net debt has actually grown more slowly than would have been expected from a simple summation of the annual current account deficits. 5. The final outcome or result of something; a culmination, a climax. ΘΚΠ the world > relative properties > number > enumeration, reckoning, or calculation > [noun] > result, sum telc1000 tale?c1225 tailc1330 reckoningc1392 suma1400 aggregatec1443 count1483 sum total1549 total1557 computation1586 calculation1646 quotient1659 tally1674 amount1751 tot1755 summation1841 1841 T. Carlyle On Heroes i. 36 They are not one coherent System of Thought; but properly the summation of several successive systems. 1879 19th Cent. Sept. 500 He is the summation of Hebraism and Hellenism. 1916 H. G. Wells Mr. Britling sees it Through 35 He wanted to state England..as the amiable summation of a grotesque assembly of faults. 2016 Independent (Nexis) 29 Dec. Bach regarded his majestic Mass in B minor as the summation of his choral achievement. 6. a. Physiology. The arrival in close temporal or spatial proximity of two more stimuli at a nerve cell or muscle fibre; the response produced in nerve or muscle tissue by such stimuli; spec. the process by which such stimuli evoke excitation in nerve or muscle when each alone would fail to do so. ΘΚΠ the world > life > biology > biological processes > action of nervous system > [noun] > nerve impulse vibration1728 nerve current1859 nerve impulse1870 summation1872 message1884 wave of stimulation1885 pattern1930 the world > life > the body > structural parts > muscle > [noun] > accumulation of stimuli summation1872 1872 Jrnl. Anat. & Physiol. 6 222 The so-called super-maximum contractions arise from the summation of two stimuli. 1907 W. H. Howell Text-bk. Physiol. (ed. 2) 41 The greatest summation occurs when the stimuli are so spaced that the second contraction begins at the apex of the first. 1979 A. P. Spence & E. B. Mason Human Anat. & Physiol. xi. 293 During spatial summation, nerve impulses in many different stimulatory presynaptic cells..may all arrive at the postsynaptic cell very close together in time. 2005 C. S. Hill in M. Aydede Pain iii. 94 It can happen that the signal is ratcheted up as a result of temporal summation in the spinal cord. b. Psychology. The cumulative action or effect of a repeated stimulus, process, etc.; an instance of this. ΘΚΠ the mind > mental capacity > psychology > theory of psychoanalysis > theories of Freud > [noun] > cumulative action summation1920 1920 E. J. Kempf Psychopathol. i. 62 The tendency to suppress our affections may accumulate; that is, a summation of the repressing or suppressing egoistic wishes may occur. 1955 J. Strachey et al. tr. S. Freud Compl. Wks. II. ii. 174 Even a hysteric can retain a certain amount of affect that has not been dealt with; if, owing to the occurrence of similar provoking causes, that amount is increased by summation to a point beyond the subject's tolerance, the impetus to conversion is given. 2004 K. Jordens & F. Van Overwalle in G. Haddock & G. R. Maio Contemp. Perspectives Psychol. Attitudes xv. 369 Implicit attitude formation is guided by a summation of valences, whereas explicit attitude formation is driven by an averaging of valences. 7. Electronics and Physics. The combination of two or more signals, waveforms, etc., via superposition. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > [noun] > summing or addition > of measurable quantities summation1921 the world > matter > physics > electromagnetic radiation > electronics > electronic phenomena > processes > [noun] > addition of voltages, signals, etc. summation1921 1921 Brit. Patent 170,941 2/1 The negative resistance applied is a function of the amplitude, and in consequence when two signals arrive together summation of signals is altered. 1993 Proc. IEEE Ultrasonics Symp. 627/2 The displacement field results from the summation of the waveforms generated by each line source, with the proper time delay. 2013 N. W. Draw Visual Devel. (ed. 3) iii. 43/1 According to signal-noise theory, detectability improves with summation of two signals if they have separate sources of noise. Compounds C1. General use as a modifier (in various senses). ΚΠ 1875 Trans. Edinb. Obstetr. Soc. 1871–4 340 The gross effect of, or the summation result of the combined contractions of the entire contractile tissues of the uterus. 1901 E. B. Titchener Exper. Psychol. I. ii. 90 If we are not satisfied with this ‘summation’ theory, we may..suppose that the gaps in sensation are filled out by association. 1916 Jrnl. Amer. Chem. Soc. 38 2296 This magnitude varies with the specific heats of the reacting substances..according to the equation dU/dT = ΣnC the summation sign indicating an algebraic summation (reactants positive, resultants negative) of the molecular heats of the substances. 1918 Geogr. Rev. 6 77 The ‘summation process’..consists in adding together the mean daily air temperatures during the life phase of a crop in order to find the thermal requirement. 1967 Brain 90 445 A summation effect occurred, items of information relevant to previous stimuli being included in the perseveratory response. 1975 E. R. Hilgard & J. R. Hilgard Hypnosis in Relief of Pain ii. 34 The pattern theory, or summation theory, proposes that pain depends upon a summation of neural inputs that must reach a critical level for pain to be felt. 2006 P. J. Nahin Dr. Euler's Fabulous Formula iv. 161 The summation index k runs through all the integers, positive and negative. C2. summation check n. now rare any of several procedures that use addition to check the accuracy or integrity of data; esp.: (a) a procedure used with tabulated data, in which totals are calculated for each column and the sum of these compared with that of the total column (now rare) (b) (Computing and Telecommunications) a procedure in which the sum of the digits of a number is compared with a pre-calculated value in order to check for data corruption; (also) the pre-calculated value used in this procedure (= checksum n. at check- comb. form Additions). ΘΚΠ society > computing and information technology > data > database > data entry > [noun] > error check summation check1926 checksum1940 parity check1950 Hamming distance1954 redundancy check1955 sum check1956 validity check1957 1926 Trans. Actuarial Soc. Amer. 27 37 The several summation checks, which detect errors early, also eliminate the need for review or independent working. 1951 Insurance Law Jrnl. No. 12 955/1 Continuous methods [for mass calculations] often have the further advantage of permitting simple summation checks. 1962 Automatic Data Processing Gloss. (U.S. Bureau of Budget) 9/1 Check-sum, the sum used in a summation check. 2010 O. R. Whittington & P. R. Delaney Wiley CPA Exam Rev. 2011 112/2 A parity check is a summation check in which the binary digits of a character are added to determine whether the sum is odd or even. summation network n. Electronics (in a circuit) a system of components that produces an output voltage proportional to the sum of that of two or more inputs (cf. network n. 4b). ΚΠ 1942 U.S. Patent 2,283,566 3/2 For determining that fraction of the total generated millivoltage that may be applied to an instrument or to the potentiometer, not shown, of a summation network. 2015 IEEE Trans. Signal Processing 63 284/2 The delay-adjusted scanline data for the 16 neighboring scanlines is then fed forward to the summation network. summation notation n. the notation used to denote a series (series n. 8); an instance of such notation.Summation notion expresses series in the form Σⁿ_{i = m}x_i, where x_i represents the general term of the series, and the values of m and n specify respectively the starting and stopping points of the sum; e.g. Σ⁵_{i = 3}x_i represents the series x₃ + x₄ + x₅. ΚΠ 1909 Michigan Technic Feb. 45 The general reduced equation is expressed directly in the summation notation. 1969 Planetary & Space Sci. 17 67 The summation notation in Equations (17) and (19) indicates that contribution from all species of thermal particles be taken. 2014 N. Loehr Adv. Linear Algebra iii. 35 Often we denote such a polynomial using the summation notation Σⁿ_{i = 0}a_ixⁱ. summation tone n. [after German Summationston (H. Helmholtz 1856, in Ann. der Physik u. Chem. 99 518)] Acoustics and Music = sum tone n. at sum n.¹ Compounds. ΘΚΠ society > leisure > the arts > music > musical sound > harmony or sounds in combination > chord > [noun] > combination tone resultant note1836 resultant tone1836 summation tone1867 summation-tone (or summational tone)1867 combinational tone1879 combination tone1889 1867 J. Tyndall Sound vii. 285 Resultant tones are of two kinds... The former are called difference tones, the latter summation tones. 1994 P. Rehfeldt New Direct. for Clarinet (rev. ed.) iii. 42 Many multiple sonorities also produce difference tones and summation tones. This entry has been updated (OED Third Edition, September 2019; most recently modified version published online March 2022). < n.¹?1473n.²1608
随便看	approaches approachforcing system approaching approachless approachment approbate approbate and reprobate approbated approbates approbating approbation approbations approbative approbativeness approbator approbatory approclivity approes approfound apprompt approof approofs approperate appropinquate appropinquated

† summationn.1

summationn.2

Compounds

† summationn.¹

summationn.²