Uncertain numbers

Interval A kind of uncertain number consisting of the set of all real numbers lying between two fixed numbers called the endpoints of the interval. In this book, intervals are always closed so that the endpoints are always considered part of the set. 

Probability box A kind of uncertain number representing both incertitude and variability. A probability box can be specified by a pair of functions serving as bounds about an imprecisely known cumulative distribution function. The probability box is identified with the class of distribution functions that would be consistent with (i.e., bounded by) these distributions. 

The periodicity of chemical properties arises from filling of successive quantum mechanical shells of electrons. For example, filling of the s,p shells, with capacities of 8 electrons each, and the d shells, which can hold up to 10 electrons, is associated with the main group and transition elements, respectively (Fig. 1.1). Before the advent of quantum theory, two classes of elements were known that seemed not to fit the Mendeleyevian scheme an uncertain number of rare earth elements or lanthanides— metallic elements, discovered throughout the 1800s, that form oxides of... 

Some of the discrepancies in the reported recoveries of different solutes from various waters by different investigators who have used the same functional polymers from different manufacturers can be rationalized by considering the discussions of pore size and surface area. Even when the pore sizes and surface areas are specified, awareness of the uncertainty in their determination is needed. Two polymers having the same listed pore size and surface area can behave quite differently as accumulators of organic solutes surface area does not specify surface orientation for adsorption pore size is not uniform, so the quoted value is an average and experimentally uncertain number. 

What is the net sample rate and its uncertainty This raises the general question of calculating the uncertainty in the result of some mathematical operations on an uncertain number. If we consider two independently determined numbers and their uncertainties (standard deviations), A + [Pg.572]

This chapter summarizes the most recent compilations of carbonate reservoir size in the ocean and sediments, as well as the particulate and dissolved fluxes (Fig. 9.5) provided by the above mentioned authors. Coral reefs are probably the best documented shallow-water carbonate environment. Carbonate production on reef flats range as high as 10.000 g CaCOj m yr , with a global mean of about 1800 g CaCOj myr . Totally this amounts to 24.5 10 molyr (Table 9.1) from which 14.5-10 mol yr accumulate and 10-10 mol yr are transported to the deep-sea either by particulate or dissolved export. One of the most uncertain numbers in all these budget calculations are the estimates of the global carbonate production in... 

Note that the first two digits in each measurement are the same regardless of who made the measurement these are called the certain numbers of the measurement. However, the third digit is estimated and can vary it is called an uncertain number. When one is making a measurement, the custom is to record all of the certain numbers plus the first uncertain number. It would not make any sense to try to measure the pin to the third decimal place (thousandths of a centimeter), because this mler requires an estimate of even the second decimal place (hundredths of a centimeter). 

Why is the answer limited by the term with the smallest number of decimal places Recall that the last digit reported in a measurement is actually an uncertain number. Although 18,18.0, and 18.00 are treated as the same quantities by your calculator, they are different to a scientist. The problem above can be thought of as follows ... 

When a measurement is made, the certain numbers plus the first uncertain number are called the of the measurement. 

Nuclear collisions. When elementary particles collide with each other or with a photon, other particles can be created that are often unstable, i.e., they decay into other particles and continue to do so until they reach a state where only stable particles result. Such a process is called a cascade. Common intermediate and final particles are the pion, the muon, the photon, and the neutrino. The pion comes in various forms, charged and uncharged, the muon is always charged, and the neutrino is always neutral. The neutrino is characterized by a very small interaction cross section with matter. Thepions have a mass, again in energy equivalents, of about 140 MeV, the muons of about 106 MeV, and the neutrinos of about 0.03 eV, a still rather uncertain number. 

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