Incremental Calculus and its Applications

Incremental calculus is a powerful and flexible tool for theanalysis of system behaviour, dependent on variables which aresubject to discrete changes. This is of particular interestwhen attention is focused on the relative changes that takeplace, namely on the ratio of an increment of a variable (ora function) to its original value prior to the change. Suchcircumstances are common in the business world, and this iswhy incremental calculus can be widely applied for managerialpurposes, both for diagnosing past events and for planning anddecision making. The basic operational rules of incrementalcalculus are introduced, and their use is demonstrated by severalexamples. Although the examples concentrate on problems of concernto managers and business analysts, the methodology describedin this paper can be easily applied in many fields of scienceand technology.     

Angular distribution of cosmic muons using INO–ICAL prototype detector at TIFR

The India-based Neutrino Observatory Collaboration is planning to set up a magnetized 50 kt iron calorimeter (ICAL) with resistive plate chambers (RPC) as active detectors to study neutrino oscillations and precisely measure its parameters.?A prototype detector stack is set up at TIFR (18°54??N, 72°48??E) to track cosmic ray muons.?Using the muon data, angular distribution of cosmic ray muons at the sea level is studied here.     

Data Dependent Triangulations for Piecewise Linear Interpolation

Given a set of data points in R² and corresponding data values,it is clear that the quality of a piecewise linear interpolationover triangles depends on the specific triangulation of thedata points. While conventional triangulation methods dependonly on the distribution of the data points in R² in this paperwe suggest that the triangulation should depend on the datavalues as well. Several data dependent criteria for definingthe triangulation are discussed and efficient algorithms forcomputing these triangulations are presented. It is shown fora variety of test cases that data dependent triangulations canimprove significantly the quality of approximation and thatlong and thin triangles, which are traditionally avoided, aresometimes very suitable.