Many researchers had developed polyphase sequences, so called ¡§perfect sequence¡¨ or ¡§ideal sequence¡¨, with ideal periodic auto-correlation function. There are lots of applications of communication system depends on the sequences with good auto-correlation property, i.e., synchronization, channel estimation and multiple access. These sequences cannot maintain the ideal property in implementation, because of the error of quantization in digital signal processing of transmitter. On the contrary, we develop a novel set of perfect sequences, Gaussian Integer Perfect Sequence (GIPS), which only contains Gaussian integers. In this paper, we construct them by linear combination and cyclic shift of the eight base sequences. We present the design and basic properties of the sequences. Furthermore, the design method of sequences with the smallest dynamic range is presented.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 44-46). Available also in a digital version from Dissertation Abstracts.

Thesis (M.S.)--Brigham Young University. Dept. of Civil and Environmental Engineering, 2008. / Includes bibliographical references (p. 51-54).

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, March 2003. / Thesis advisor(s): Charles W. Therrien, Charles W. Granderson. Includes bibliographical references (p. 123). Also available online.

Thesis (M.A.) in Mathematics--University of Maine, 2001. / Includes vita. Includes bibliographical references (leaves 42-43).

Η παρούσα μεταπτυχιακή διατριβή εντάσσεται ερευνητικά στην περιοχή της Στατιστικής Θεωρίας Αποφάσεων και ειδικότερα στη βελτίωση των εκτιμητών του μέτρου της διασποράς για την αντίστροφη κανονική κατανομή IG(μ,λ), όπου μ είναι η παράμετρος θέσης, ενώ το λ είναι η παράμετρος κλίμακος και εκφράζει το αντίστροφο μέτρο της διασποράς. Στο Κεφάλαιο 1 παρουσιάζονται κάποιοι χρήσιμοι, για την πορεία της μελέτης μας, ορισμοί και θεωρήματα, στο Κεφάλαιο 2 μελετάται το μοντέλο της αντίστροφης κανονικής κατανομής, δίνονται τα χαρακτηριστικά μεγέθη αυτής και υπολογίζονται γνωστοί εκτιμητές για το μέτρο της διασποράς. Στο Κεφάλαιο 3, εξετάζεται το πρόβλημα εκτίμησης του μέτρου της διασποράς , τόσο ως προς την τετραγωνική συνάρτηση ζημίας , όσο και προς την συνάρτηση ζημίας εντροπίας . Υπό ορισμένες συνθήκες, αποδεικνύεται η μη αποδεκτικότητα, του βέλτιστου αναλλοίωτου εκτιμητή, κατασκευάζοντας καλύτερους εκτιμητές τύπου Stein [1964, Ann. Inst. Statist. Math.]. Η μέθοδος κατασκευής αυτών των εκτιμητών παρουσιάστηκε στην εργασία των N. Pal and B. Sinha [1989, Statistical data analysis and inference]. Στο Κεφάλαιο 4, και για το ίδιο πρόβλημα εκτίμησης που πραγματεύεται το προηγούμενο κεφάλαιο,κατασκευάζονται καλύτεροι εκτιμητές από το βέλτιστο αναλλοίωτο εκτιμητή χρησιμοποιώντας την μεθοδολογία των Brewster and Zidek [1974, Ann. Statist.]. Η μέθοδος κατασκευής αυτών των εκτιμητών παρουσιάζεται στην εργασία των B.MacGibbon and G.Shorrock [1997, Statist. Probab. Lett.]. / The present postgraduate thesis is placed among the area of Statistical Decision Theory and especially we give improved estimators of dispersion of an inverse Gaussian distribution IG(μ,λ), where μ is the mean and λ is a parameter, known as inverse measure of dispersion. In Chapter 1 are some useful definitions and theorems are presented, in Chapter 2 the model of inverse Gaussian distribution is studied, we give some properties of the model and known estimators for the measure of dispersion , are presented. In Chapter 3, we examine the problem of estimating the measure of dispersion under quadratic and entropy losses. Under certain conditions, we derive improved estimators (Stein [1964, Ann. Inst. Statist. Math.]) of the best affine equivariant estimator for . The method of construction of these estimators is presented in the paper of N. Pal and B. Sinha [ 1989, Statistical data analysis and inference ]. In Capital 4, and for the same problem of estimating , improved estimators of the best affine equivariant estimator are derived, using the methodology of Brewster and Zidek [1974, Ann. Statist. ]. This method of construction of these estimators is presented in the paper of B. MacGibbon and G. Shorrock [1997, Statist. Probab. Lett. ].

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The following study analyzes birthweight-specific neonatal health using a combination of a mixture model and logistic regression: the extended Parametric Mixture of Logistic Regression. The data are collected from the Obstetric database at Muhimbili National Hospital in Dar es Salaam, Tanzania and the years 2009 -2013 are used in the analysis. Due to rounding in the birthweight data a novel method to adjust for rounding when estimating a mixture model is applied. The influence of rounding on the estimates is then investigated. A three-component model is selected. The variables used in the analysis of neonatal health are early neonatal mortality, if the mother has HIV, anaemia, is a private patient and if the neonate is born after 36 completed weeks of gestation. It can be concluded that the mortality rates are high especially for low birthweights (2000 or less) in the estimated first and second components. However, due to wide confidence bounds it is hard to draw conclusions from the data.

A recent study of the positronium atom showed that the energy levels could be determined numerically using an effective field theory just as easily as the underlying true theory. Here, we expand on this idea by modeling the three-body positronium-ion and four-body di-positronium molecule with low-energy effective field theories. We then compare the results obtained using the effective theories to those found in a similar manner with the true theory to determine if numerical calculations will converge more quickly using the effective field theory due to removal of the Coulomb divergence. Finally, with the necessary framework in place, we calculate a matrix element needed to evaluate the correction to the magnetic moment of the positronium-ion due to the interaction between the positron and the two electrons which form a spin singlet.