Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in 40 years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, m...

In Part I of this paper we argued that the first-order systems HP5 and EG are modest complete descriptive axiomatization of most of Euclidean geometry. In this paper we discuss two further modest complete descriptive axiomatizations: Tarksi’s for Cartesian geometry and new systems for adding π. In contrast we find Hilbert’s full second order system immodest for geometrical purposes but appropri...

The electrocardiography (ECG) artifact corrupts the surface electromyography (sEMG) signals recorded from the trunk area We assessed the effectiveness of three methods used to remove the ECG. We compared the performance of bandpass filtering methods, the commonly used mathematical morphology operator (MMO) method and the Adaptive filter on both simulationed and real sEMG data. False positive an...

The basis of musical consonance has been debated for centuries without resolution. Three interpretations have been considered: (i) that consonance derives from the mathematical simplicity of small integer ratios; (ii) that consonance derives from the physical absence of interference between harmonic spectra; and (iii) that consonance derives from the advantages of recognizing biological vocaliz...

My primary research interest is in computability and complexity theory. More specifically, I have an active research program in the area of effective dimension theory and randomness. Computability theory was first developed in the 1930s and ’40s by Alan Turing who has come to be seen, along with Gödel and Tarski, as one one of the founders of modern mathematical logic. The subject developed ove...

BACKGROUND Risk adjustment models were used to estimate health care consumption after adjusting for individual characteristics or other factors. The results of this technique were not satisfying. One reason could be that the length of time to document consumption might be associated with the mean and variance of observed health care consumption. This study aims to use a simplified mathematical ...

Set theory of the reals is a subfield of Mathematical Logic mainly concerned with the interplay between forcing and Descriptive Set Theory. One of the motivations behind Descriptive Set Theory is the strong intuition that simple sets of real numbers should not display irregular behaviour, or, in other words, they should be topologically and measure theoretically nice. In order to fill this stat...

In this paper we will consider the most known ratios control schemes ((L/D, V/B),(L/D,V/F), Ryskamp’s, and (D/(L+D),V/B)) for binary distillation column and we compare them in the basis of interactions and disturbance propagation. The models for these configurations are deuced using mathematical transformations taking the energy balance structure (LV) as a base model. The dynamic relative magni...

In this work, characteristics of various ball bearing parameters are studied under different loads and rotational speeds. By using Dimensional Analysis (DA), dimensionless parameters are computed which provides solution for a group of parameters. This analysis can be accomplished by using the Buckingham π-theorem. DA leads to reduction of the number of independent parameters involved in a probl...