No description available.

This study is concerned with the vertical combinations resulting from late sixteenth century cadential formulae and in passages immediately preceding these formulae. The investigation is limited to Masses dating from the last half of the sixteenth century and utilizes compositions from the following composers: Handl, Kerle, Lassus, Merulo, Monte, and Palestrina, Victoria. This study concludes that the progressions I-V-I and I-IV-I appear to be the only two root progressions receiving high enough percentages to be regarded as significant. These percentages are tempered by the fact that I-V-I and I-IV-I may be interpreted as repetitions of standardized cadential formulae found in the sixteenth century. The study also concludes that root motion by fifth accounts for no less than 67.35 per cent of the root movements analyzed during the investigation. The percentage differential between root movement by fifth and root movement by second (the interval receiving the next highest percentage) at no time drops below 40.41 per cent. The evidence indicates that root movement by fifth does account for the majority of the root motion analyzed in final cadential passages of Masses dating from the late sixteenth century. The percentage differential between root motion by second and root motion by third decreases as the chord progressions become longer. None of the differential percentages were judged to be high enough as to merit placing any significance of root motion by second over root motion by third.

The purpose of this study was to examine the effect of bottom chord extensions on deflections and vibration characteristics of joist supported floor systems when joist bottom chord extensions are installed. To understand the effect of bottom chord extensions on deflections, natural frequency, damping, mode shape and effective mass, extensive analytical and experimental studies were conducted on single span and three span joist supported laboratory footbridges with different bottom chord extension configurations. Finite element computer models were created to simulate and compare the results of stiffness and vibration tests. Testing was done with a) the bottom chord extensions in-place before the concrete was placed, b) with all or part of the bottom chord extensions removed, and c) after the bottom chord extensions had been reinstalled with jacking for the single span footbridge and without jacking for the three-span footbridge. Results from the stiffness tests indicate that re-installing the bottom chord extensions to the joists of the single span footbridge with cured concrete with the center of the span raised helps to reduce the uniform load deflections to some extent, but not as much as placing the bottom chord extensions before the concrete placement. Likewise, for the three span footbridge, placing the bottom chord extensions before the concrete placement is observed to be a better solution. Results from the dynamic tests indicate that the effect of bottom chord extensions on the single span footbridge is consistent for natural frequency, 20 psf live load deflections, sinusoidal excitations with high amplitudes, quarter point heel drop excitations, walking excitations, and effective mass values. The effect of bottom chord extensions on the three span footbridge is consistent for the natural frequency and 20 psf deflections. However, the FRF (Frequency Response Function) peaks of chirp, heel drop, sinusoidal excitations, accelerations from walking data, and the MEScope and Finite Element model effective mass results do not follow a common trend. It can be concluded that even though the footbridge was stiffened by the bottom chord extensions, that does not necessarily mean that the acceleration levels, and hence the frequency response function peaks, decrease. However, bottom chord extensions do increase the natural frequencies for all the three governing bending modes. / Ph. D.

在音樂中，組曲是一種特別的創作形式。組曲將多首音樂段落組合排列，並且在音樂段落之間加入間奏，形成一首音樂組曲。組曲的編曲重點在於音樂段落的編排順序及段落之間的連結。平時在宴會、舞會、餐廳、賣場等場合中，往往都會連續播放多首流行音樂。利用電腦編曲自動產生流行音樂組曲，將可提升播放音樂的銜接與流暢感。 因此，本研究利用資料探勘技術及音樂編曲理論，將多首音樂重新改編成一首組曲。系統首先將每首音樂分段並找出每首音樂的代表段落。接著，系統根據代表段落間的相似度編排順序。最後，為了達到組曲中音樂段落連接的流暢性，我們以模型訓練的方式在段落連結間加入間奏。系統從訓練資料學習產生旋律發展、和弦進程與節奏的模型，接著分析代表段落的動機、旋律、和弦及節奏，使得組曲編曲後的段落連結更為流暢且完整。本研究以流行音樂鋼琴伴奏曲為測試資料，我們分別邀請三十四位受過音樂訓練與未受音樂訓練的測試者，針對本研究所提出的鋼琴伴奏節奏辨識、代表段落萃取、段落順序編排及間奏產生，評估其效果。實驗結果顯示，本研究所提出的順序編排與間奏產生技術，對於組曲的流暢感，有著相當大的幫助。 / In music, a medley is an organized piece composed from segments of existing pieces. Ordering and bridge for connection between segments are the important elements for medley arrangement. Automatic medley arrangement is helpful for playing a set of music continuously which is common in banquet, party, restaurant, shopping mall, etc.. This thesis aims to develop the automatic medley arrangement method by using data mining techniques and music arrangement theory. The proposed method first segments each music and discovers the significant segment from each music. Then, the linear arrangement based on the similarities between significant segments is generated. Finally, in order to connect segments smoothly in the medley, the bridge between two segments is generated and inserted by using model training. Three models, melody progression, chord progression and rhythm models are learned from training data. For the experiments, testing data is collected from popular piano music and thirty-four people are invited to evaluate the effectiveness of the rhythm recognition of accompaniment, the extraction of significant segment, the linear arrangement of segments, and the creation of bridge. Experimental results show that the proposed medley arrangement method performs well.

Chapter 1 introduces Jensen Inequality and its geometric interpretation. Some useful criteria for checking the convexity of functions are discussed. Many applications in various fields are also included. Chapter 2 deals with Schur Inequality, which can easily solve some problems involved symmetric inequality in three variables. The relationship between Schur Inequality and the roots and the coefficients of a cubic equation is also investigated. Chapter 3 presents Muirhead Inequality which is derived from the concept of majorization. It generalizes the inequality of arithmetic and geometric means. The equivalence of majorization and Muirhead¡¦s condition is illustrated. Two useful tricks for applying Muirhead Inequality are provided. Chapter 4 handles Majorization Inequality which involves Majorization and Schur convexity, two of the most productive concepts in the theory of inequalities. Its applications in elementary symmetric functions, sample variance, entropy and birthday problem are considered.

Η παρούσα διατριβή ανήκει στο γενικότερο θεματικό πεδίο της σεισμικής αποτίμησης, σχεδιασμού ή ανασχεδιασμού κατασκευών οπλισμένου σκυροδέματος με βάση τις μετακινήσεις. Οι σύγχρονες μέθοδοι αυτού του τύπου, στηρίζονται σε έλεγχο και σύγκριση της σεισμικής απαίτησης με την ικανότητα των μελών της κατασκευής σε όρους μετακινήσεων παρά σε όρους δυνάμεων. Δημιουργείται επομένως η ανάγκη για απλό και αξιόπιστο υπολογισμό της συμπεριφοράς μελών οπλισμένου σκυροδέματος σε κάμψη και διάτμηση, σε όρους μετακινήσεων. Το αντικείμενο της παρούσης διατριβής είναι η ανάπτυξη προσομοιωμάτων για τον υπολογισμό των βασικών χαρακτηριστικών της συμπεριφοράς καμπτόμενων μελών οπλισμένου σκυροδέματος και συγκεκριμένα: της ροπής διαρροής, της παραμόρφωσης στη διαρροή, της ενεργού δυσκαμψίας, της παραμόρφωσης στην αστοχία, της διατμητικής αντοχής σε ανακυκλιζόμενη φόρτιση, της αντοχής μελών με χαμηλό λόγο διάτμησης και της συμπεριφοράς υπό διαξονική καταπόνηση. Εξετάζονται μέλη διαφόρων τύπων και διαφορετικής διατομής, μέλη με ενίσχυση μανδύα οπλισμένου σκυροδέματος ή μανδύα σύνθετων υλικών, καθώς επίσης και μέλη με μάτιση του διαμήκους οπλισμού στην περιοχή πλαστικής άρθρωσης. Για την ανάπτυξη των προσομοιωμάτων, καθώς και για τον έλεγχο άλλων παλαιότερων, αναπτύχθηκε και αξιοποιήθηκε βάση πειραματικών δεδομένων μελών οπλισμένου σκυροδέματος με περισσότερα από 2800 πειράματα από τη διεθνή βιβλιογραφία. Για τον υπολογισμό της ροπής και της καμπυλότητας στη διαρροή, αναπτύσσονται απλές σχέσεις υπολογισμού, βασιζόμενες σε ανάλυση σε επίπεδο διατομής και καθορίζονται τα κατάλληλα κριτήρια διαρροής. Αναπτύσσονται ακολούθως σχέσεις υπολογισμού της παραμόρφωσης στη διαρροή, και συγκεκριμένα της γωνίας στροφής χορδής του μέλους στη διαρροή, θy, ως άθροισμα τριών όρων: καμπτικής παραμόρφωσης, διατμητικής παραμόρφωσης και παραμόρφωσης λόγω ολίσθησης των ράβδων διαμήκους οπλισμού από την περιοχή αγκύρωσης. Προτείνονται δε δύο εναλλακτικοί τρόποι υπολογισμού της ενεργού δυσκαμψίας, ένας θεωρητικός και ένας καθαρά εμπειρικός. Στη συνέχεια εξετάζεται η παραμόρφωση στην αστοχία και προτείνονται δύο εναλλακτικοί μέθοδοι υπολογισμού της γωνίας στροφής χορδής στην αστοχία, θu. Η 1η βασίζεται στον υπολογισμό της καμπυλότητας στην αστοχία, φu, με εφαρμογή του κατάλληλου προσομοιώματος περίσφιγξης του σκυροδέματος, και στην εφαρμογή της φu σε μήκος πλαστικής άρθρωσης ίσο με Lpl, ενώ η 2η σε καθαρά εμπειρικές εξισώσεις. Εξετάζεται ακολούθως η διατμητική αντοχή σε ανακυκλιζόμενη φόρτιση και προτείνονται προσομοιώματα για αστοχία σε διαγώνιο εφελκυσμό ή αστοχία σε λοξή θλίψη, μετά την καμπτική διαρροή. Στη συνέχεια εξετάζεται η συμπεριφορά μελών οπλισμένου σκυροδέματος υπό διαξονική καταπόνηση. Εξετάζονται επίσης μέλη με χαμηλό λόγο διάτμησης και προτείνονται νέα αντιπροσωπευτικότερα κριτήρια για τον χαρακτηρισμό ενός μέλους ως “κοντό μέλος”, καθώς και νέα μεθοδολογία υπολογισμού της αντοχής των μελών αυτών, με κατάλληλο συνδυασμό του προσομοιώματος των Shohara and Kato, 1981 και των Φαρδής και συνεργάτες 1998. Ακολούθως εξετάζονται μέλη ενισχυμένα με μανδύα σύνθετων υλικών και προτείνονται προσομοιώματα υπολογισμού της γωνίας στροφής χορδής στη διαρροή και την καμπτική αστοχία, καθώς και προσομοίωμα υπολογισμού της διατμητικής αντοχής. Στη συνέχεια εξετάζεται η συμπεριφορά μελών με μάτιση του διαμήκους οπλισμού στην περιοχή πλαστικής άρθρωσης, καθώς και η εφαρμογή μανδύα σύνθετων υλικών για την ενίσχυση της περιοχής αυτής. Τέλος εξετάζεται η συμπεριφορά στη διαρροή και στην αστοχία, μελών ενισχυμένων με μανδύα οπλισμένου σκυροδέματος. Η ανάπτυξη όλων των προτεινόμενων προσομοιωμάτων της διατριβής βασίζεται στην καλύτερη δυνατή συμφωνία με τα πειραματικά αποτελέσματα της βάσης δεδομένων, χωρίς όμως να θυσιάζεται η απλότητα και η ευχρηστία αυτών. / The present Thesis belongs in the general field of seismic assessment, design and redesign of concrete structures with displacement based procedures. Modern methods of this kind are based in controlling and comparing seismic demand with structural elements capacity in terms of displacements rather than forces. This leads in the need of estimating reinforced concrete elements performance under bending and shear, in terms of displacements. The object of the Thesis is development of models for calculating the basic performance characteristics of reinforced concrete elements under bending, in particular: yield moment, deformation at yielding, effective stiffness, deformation at ultimate, shear strength under cyclic loading, maximum strength of members with low shear ratio and behavior under biaxial loading. Members with various types of section and various characteristics are included, as also members retrofitted with FRP jacket or concrete jacket and members with lap-splice of longitudinal reinforcement in plastic hinge region. In order to develop new models and check older ones, a database of more than 2800 experiments from international literature on reinforced concrete elements was created and used here. Simple equations and procedures are suggested for calculating yield moment and corresponding curvature, based on section analysis, by specifying the appropriate yield criteria. Equations for calculating deformation at yielding, in particular chord rotation at yielding, θy as the sum of deformations due to bending, due to shear and due to slippage of longitudinal reinforcement from anchorage zone, are also developed. Calculation of effective stiffness is based on two alternative models, one theoretical and one purely empirical. Deformation at ultimate is then examined where two methods for calculating chord rotation at ultimate are suggested. 1st one is based on ultimate curvature, φu, where an appropriate concrete confinement model is used, and plastic hinge length Lpl, while 2nd one is based on purely empirical equations. Shear strength under cyclic loading is also examined and new models for calculating shear strength for shear tension and shear compression failure after flexural yield are developed. Behavior of reinforced concrete elements under biaxial loading is then examined. Elements with low shear ratio are also covered and new, more representative, criteria to characterize an element as a “short element” are suggested. A procedure based on an appropriate combination of Shohara and Kato 1981 model and Fardis et al. 1998 model is then suggested for calculating maximum strength of such “short elements”. Retrofitted members with FRP jacket are then examined and models for chord rotation at yielding and ultimate, as well as for shear strength are suggested. Behavior of members with lap-splice of longitudinal reinforcement inside plastic hinge region is then examined, including also retrofitting of this region with FRP jacket. Performance at yielding and ultimate of retrofitted members with concrete jacket is also examined. Development of all the suggested models of the Thesis is based on best fit with experimental results of the database, without sacrificing simplicity and applicability of the models.

Purpose - The paper presents a theoretical framework that describes the aerodynamics of a falling maple (Acer pseudoplatanus) seed. --- Methodology - A semi-empirical method is developed that provides a ratio stating how much longer a seed falls in air compared to freefall. The generated lift is calculated by evaluating the integral of two-dimensional airfoil elements using a preliminary falling speed. This allows for the calculation of the definitive falling speed using Blade Element Momentum Theory (BEMT); hereafter, the fall duration in air and in freefall are obtained. Furthermore, the input-variables of the calculation of lift are transformed to require only the length and width of the maple seed. Lastly, the method is applied to two calculation examples as a means of validation. --- Findings - The two example calculations gave percentual errors of 5.5% and 3.7% for the falling speed when compared to measured values. The averaged result is that a maple seed falls 9.9 times longer in air when released from 20 m; however, this result is highly dependent on geometrical parameters which can be accounted for using the constructed method. --- Research limitations - Firstly, the coefficient of lift is unknown for the shape of a maple seed. Secondly, the approximated transient state is yet to be verified by measurement. --- Originality / Value - The added value of this report lies in the reduction of simplifications compared to BEMT approaches. In this way a large amount of accuracy is achieved due to the inclusion of many geometrical parameters, even though simplicity is maintained. This has been accomplished through constructing a simple three-step method that is fundamental and essentially non-iterative.