ترغب بنشر مسار تعليمي؟ اضغط هنا

Fa`a di Brunos note on eponymous formula, trilingual version

83   0   0.0 ( 0 )
 نشر من قبل Julyan Arbel
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English
 تأليف Julyan Arbel




اسأل ChatGPT حول البحث

About 160 years ago, the Italian mathematician Fa`a di Bruno published two notes dealing about the now eponymous formula giving the derivative of any order of a composition of two functions. We reproduce here the two original notes, Fa`a di Bruno (1855, 1857), written respectively in Italian and in French, and propose a translation in English.

قيم البحث

اقرأ أيضاً

222 - P. Duarte , M. J. Torres 2008
We derive some formulas that rule the behaviour of finite differences under composition of functions with vector values and arguments.
99 - Anthony B. Morton 2008
This mathematical recreation extends the analysis of a recent paper, asking when a traveller at a bus stop and not knowing the time of the next bus is best advised to wait or to start walking toward the destination. A detailed analysis and solution i s provided for a very general class of probability distributions of bus arrival time, and the solution characterised in terms of a function analogous to the hazard rate in reliability theory. The note also considers the question of intermediate stops. It is found that the optimal strategy is not always the laziest, even when headways are not excessively long. For the common special case where one knows the (uniform) headway but not the exact timetable, it is shown that one should wait if the headway is less than the walking time (less bus travel time), and walk if the headway is more than twice this much. In between it may be better to wait or to walk, depending on ones confidence in being able to catch up to a passing bus.
In this report we provide an improvement of the significance adjustment from the FA*IR algorithm of Zehlike et al., which did not work for very short rankings in combination with a low minimum proportion $p$ for the protected group. We show how the m inimum number of protected candidates per ranking position can be calculated exactly and provide a mapping from the continuous space of significance levels ($alpha$) to a discrete space of tables, which allows us to find $alpha_c$ using a binary search heuristic.
359 - Milan Batista 2018
The article presents a generalization of Sherman-Morrison-Woodbury (SMW) formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).
This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation for multi plicative (ratio) pairwise comparisons has been provided. Counterexamples have been provided to support the theory. In our opinion, the scientific community must be made aware of the limitations of using the group theory in pairwise comparisons. Groups, which are not torsion free, cannot be used for ratios by Levis theorems.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا