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41.
The origin of the function concept is usually traced to Galileo's work on motion. We argue that specific proto-function concepts appeared in the work of Tartaglia a century before the publication of Galileo's Two New Sciences. The study of Tartaglia's ideas can be used in the classroom as a historical introduction to various function concepts, and certain modern extensions of Tartaglia's optimal range problem and inverse range problem are sources of enrichment for undergraduate courses in analysis, mathematical modeling and computation.  相似文献   
42.
This paper demonstrates one way to approach mathematical remediation with dignity for faculty and students alike. It illustrates specific ways in which student deficiencies can be improved while simultaneously developing creative, significant and stimulating approaches to teaching basic mathematical concepts. In order to aid students who have not mastered even the addition and multiplication of rational numbers, examples will be provided to show how these deficiencies can be improved within mathematical formats that lead naturally to the principles of algebra, progressions, powers and roots, symbolism, number theory, probability theory, linear programming, information theory, etc. An integral part of this approach to mathematical remediation involves the selection of appropriate research problems by the students.  相似文献   
43.
Selected algorithms of three famous mathematicians are expressed in recursive computer programmes using a programming language (APL). Specifically: (a) Euclid's greatest common divisior algorithm; (b) Fibonacci's ‘ golden ‘ number series; (c) Pascal's triangle.

The programmes are designed to be viewed directly by students in order to elucidate the algorithms. Such programmes can be stimulants for learning mathematics.  相似文献   
44.
Even-numbered 1-alkanols from butanol to tetradecanol were evaluated for solubilizing and microemulsifying methanol in triolein and for their effectiveness on water tolerances of the hybrid fuels. Photon correlation spectroscopy determinations indicated molecular dispersions formed rather than nonaqueous microemulsions, but the addition of water to the solubilized systems did produce certain quarternary compositions that exhibited microemulsion properties. 1-Octanol imparted optimal, whereas 1-butanol and 1-tetradecanol imparted minimal, water tolerance for the hybrid fuels. Among four isomeric octanols studied, the 1- and 4-octanols were superior to the 2- and 3-octanols for water tolerance. This superiority is attributed to stronger hydrogen bonding and greater association in the 1-and 4-isomers compared to the 2- and 3-isomers.  相似文献   
45.
Hydrolysis and condensation of monomolecular alkyloxysilane films by the Langmuir technique is presented. Octadecyltrimethoxysilane formed monolayers on aqueous subphases with different properties depending on the bulk pH. At pH 1 a solid condensed film was directly formed with a molecular area of 23 Å2 and a surface pressure/surface area variation similar to that on non-ionized stearic acid. At pH 5.6 and 11 several phase transitions were observed during the compression of the monolayer with a final collapse at a molecular area of 20 Å2. Relaxation measurements confirmed the stability of the films for longer than 12 hours at different surface pressures below a critical value.  相似文献   
46.
E. Daloia  G. Lim  J. Melton  J. Roubie 《合成通讯》2013,43(18):2617-2622
Successive treatment of (Z)-(2-aminothiazol-4-yl) -2-methoxyiminoacetic acid, 1, with 0.9 to 1.0 equiv. of hydrogen chloride and 1.04 equiv. (chloromethylene) dimethylammonium chloride provides (Z) - (2-aminothiazol-4-yl) -2-methoxyiminoacetyl-chloride hydrochloride, 3, in high yield.  相似文献   
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In this paper we construct and study a class of Markov processes whose sample paths are piecewise deterministic and whose random jumps can have limiting points in finite time intervals. A characterization of the infinitesimal generators of such processes will be given  相似文献   
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