Papers by costas christodoulides
Analysis and Presentation of Experimental Results, 2017
The three basic probability distributions, Binomial or Bernoulli, Poisson and Normal or Gaussian,... more The three basic probability distributions, Binomial or Bernoulli, Poisson and Normal or Gaussian, are briefly examined.
In three-dimensional Euclidean space, the square of the distance between the two points \( (x_{1}... more In three-dimensional Euclidean space, the square of the distance between the two points \( (x_{1} ,\,y_{1} ,\,z_{1} ) \) and \( (x_{2} ,\,y_{2} ,\,z_{2} ) \) is given by the Pythagorean theorem.
Analysis and Presentation of Experimental Results, 2017
The laws of Statistics find applications in the phenomenon of radioactivity. The disintegration o... more The laws of Statistics find applications in the phenomenon of radioactivity. The disintegration of a nucleus is a random event which is not affected by the history of the nucleus or the conditions external to the nucleus. The probabilities that govern radioactive decay are evaluated.
Analysis and Presentation of Experimental Results, 2017
The method of least squares is developed. The application of the method in the fitting of the bes... more The method of least squares is developed. The application of the method in the fitting of the best straight line or curve to a series of experimental results, with the aim of determining the relationship existing between two variables. The method is also used in finding the optimal solutions of systems of overdetermined linear equations.
Analysis and Presentation of Experimental Results, 2017
The matter of the rejection of a measurement is examined. Criteria, such as Chauvenet’s criterion... more The matter of the rejection of a measurement is examined. Criteria, such as Chauvenet’s criterion for the rejection of data are discussed.
Analysis and Presentation of Experimental Results, 2017
Analysis and Presentation of Experimental Results, 2017
Analysis and Presentation of Experimental Results, 2017
Quite often, it is necessary to calculate the value of a quantity that was not measured directly ... more Quite often, it is necessary to calculate the value of a quantity that was not measured directly but is expressed on terms of one or more quantities which have been measured and whose means and standard deviations are known. The evaluation of the standard deviation of this quantity is done taking into account the so-called propagation of errors from the quantities that have been measured to the derived quantity.
The general principles of the Theory of Errors are examined. This chapter provides new theoretica... more The general principles of the Theory of Errors are examined. This chapter provides new theoretical tools which may be used in the development of techniques in the analysis of experimental results.
The way in which the results of experimental measurements can be best used in the extraction of c... more The way in which the results of experimental measurements can be best used in the extraction of conclusions relating to the magnitude measured is presented. The understanding of the concepts and methods presented in this chapter possibly constitute the main benefit the reader may derive from studying this book.
Journal of Polymer Science Part B: Polymer Physics, 1996
Equilibrium and dynamic sorption isotherm measurements, differential scanning calorimetry (DSC) m... more Equilibrium and dynamic sorption isotherm measurements, differential scanning calorimetry (DSC) measurements, and, mainly, dielectric relaxation spectroscopy (DRS) measurements by means of the thermally stimulated depolarization currents (TSDC) method were used to investigate the hydration properties of linear segmented polyurethane copolymers. Three types of samples were investigated with various fractions of hard and soft block segments. They were based on polyethylene adipate (PEA), 4,4'-diphenylmethane diisocyanate (MDI) and 1,4-butanediol (BDO). At 20°C the water content h of the samples at various values of relative humidity rh increases in proportion to the weight fraction of soft block segments phase. At saturation (rh = 100%) the ratio of sorbed water molecules to polar carbonyl polyester groups is 0.13. At saturation a t 20°C there is no fraction of freezable water. The glass transition temperature, Tg, measured by DSC and by TSDC, shifts to lower temperature with increasing h by about 8-10 K at saturation at 20°C. A dielectric relaxation mechanism related to interfacial polarization in the phase-separated morphology is also plasticized by water in a way similar to that observed for the main ( a ) relaxation. 0 1996 John Wiley & Sons, Inc.
European Polymer Journal, 2010
The way in which numerical results should be presented are discussed. The S.I. system of units is... more The way in which numerical results should be presented are discussed. The S.I. system of units is also presented, as well as the basic rules that must be followed in its use for the presentation of experimental results.
In order to describe certain processes and introduce some useful terms, the results of a thought ... more In order to describe certain processes and introduce some useful terms, the results of a thought experiment are examined in detail. By the term ‘experiment’ we mean here a series of successive measurements of the same magnitude, under identical experimental conditions. The ‘results’ of the measurements in this thought experiment were found using random numbers.
Analysis and Presentation of Experimental Results
In order to understand the theory of errors, as well as the methods of analysis and presentation ... more In order to understand the theory of errors, as well as the methods of analysis and presentation of experimental results, knowledge of the basic concepts of Probability Theory and Statistics is required. The purpose of this chapter is the concise presentation of the basic concepts from these fields that will be used in the book. Obviously, the treatment will not be in great detail and the reader should consult the relevant bibliography for this purpose. Those readers who have a satisfactory knowledge of these subjects may omit this chapter and consult it whenever necessary. 1.1 Tables, Distributions and Histograms Let us assume that we have performed N measurements x i ði ¼ 1; 2;. . .; NÞ of a magnitude x, keeping the experimental conditions constant as far as possible. These measurements may be considered to be a sample which was taken from a parent population of the infinite number of measurements of this magnitude that may be performed under the particular conditions. In Table 1.1, the results of 100 such measurements have been recorded. This is the form in which the results appear immediately after the measurements, although the number of measurements is very rarely as high as this, except perhaps when they are acquired by an automated method. If the number of the measurements is large enough, there may be values which appear more than once. If we count the frequency of appearance of each value, we may construct a table of this number, n r , as a function of the numerical value x r of the measurement, such as Table 1.2. In this table, the values x r have been recorded in order of increasing magnitude and the number r is given in the first column of the table. The value of n r is the frequency of appearance of the r-th value. Obviously,
The presentation of the results of an experiment in written form is examined. The basic rules of ... more The presentation of the results of an experiment in written form is examined. The basic rules of this presentation for a report of the results of an experiment in an educational laboratory are given. An example of the written report of an actual experiment is presented.
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Papers by costas christodoulides