By Eduardo H.C. Cattani, Francisco Guillen, Aroldo Kaplan, Fernando Puerta

Over the last 2O years classical Hodge idea has gone through a number of generalizations of serious curiosity in algebraic geometry. The papers during this quantity replicate the new advancements within the components of: combined Hodge thought at the cohomology of singular and open types, at the rational homotopy of algebraic types, at the cohomology of a hyperlink, and at the vanishing cycles; L -realization of the intersection cohomology for the instances of singular forms and soft kinds with degenerating coefficients; purposes of cubical hyperresolutions and of iterated integrals; asymptotic habit of degenerating adaptations of Hodge constitution; the geometric consciousness of maximal adaptations; and diversifications of combined Hodge constitution. N

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To the positive difference of the reciprocals of 4 and 12 add the reciprocal of 30. 40. Convert the following to decimals with three significant figures: (a) 5/8 (b) 11/13 (c) 318/273 (6) 3937/3600 50 COMMON FRACTIONS [CHAP. 21. 22. 23. 24. 28. 29. 34. 35. 36. 37. 38. 39. 40. 31. (a) 2/15 11 (42, 3, 4, 6, 9 (c) 4800 (b) 1; 333. (a) 3/20 (43, 3, 5, (b) 2, 3, 4, 5 , 6, 10 330. 32. 26. 27. 25. 1 TERMS Percent means by the hundred; also, in or for every hundred, that is, hundredths. If we consider that a quantity is subdivided into 100 equal parts, a certain percent of the quantity is the number of these hundredth parts involved.

A) Divide C by D to the correct number of significant figures. 142. (c) Calculate the relative error in (b). 83 Since the measured values have three significant figures each, the quotient should be expressed to the same precision. The division is carried out to one more significant figure than the least precise measurement and the last digit is rounded off. 32. 14 Since the absolute error has two significant figures, the relative error should be calculated to three figures and then rounded off to two.

25. 52 x 102 calorie. 4 x 104 BTU. The conversion factor has to be written so that BTU appears below the division line. Then the BTU will cancel out. 52 to two significant figures. 26. 6 g/cm3 to kg/m3, given that 1 kg = loo0 g, 1 m = 100 cm. 1 kg = 103g 1 m = 102cm 1 m3 = (100cm13 = 106 cm3 28 MEASUREMENT AND SCIENTIFIC NOTATION [CHAP. 2 Multiply by the conversion factors so as to cancel out the units g and cm3. 27. 0mi/h to m/min. 21 x 103 m/min. 28. 6 x 10-19)~ to two significant figures. 29.