Stability analysis of continuous-time periodic systems via theharmonic analysis

Asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems is studied by harmonic analysis. It is first shown that stability can be examined with what we call the harmonic Lyapunov equation. Another necessary and sufficient stability criterion is developed via this generalized Lyapunov equation, which reduces the stability test into that of an approximate FDLCP model whose transition matrix can be determined explicitly. By extending the Gerschgorin theorem to linear operators on the linear space l₂, yet another disc-group criterion is derived, which is only sufficient. Stability of the lossy Mathieu equation is analyzed as a numerical example to illustrate the results     

Automatic conversion from lexical words to prosodic words for mandarin text-to-speech system

In real speech, not like lexical words (LWs), prosodic words (PWs) are basic rhythmic units. The naturalness of a Text-to-Speech (TTS) system is directly influenced by the segmentation of the PWs. Most of the PWs are the combination of several LWs. In this paper, three Lexical Combination Models are proposed to combine LWs into PWs, including a Directed Acyclic Graph Model, a Segmentation Model and a Markov Model (MM). To cope with the situation where some long LWs should be segmented into two or more PWs, a Lexical Split Model (LSM) is applied to the long LWs. Experimental results prove that relatively constant results with various training data can be obtained from a MM. The Transformation-Based Error Driven Learning (TBED) algorithm, for its high performance of individual property, is applied in combination with the MM to improve the precision of PW segmentation. Experiments show that among the three proposed models, the MM combined with TBED and LSM, leads to the best performance, in which a precision of 93.00% and a recall of 93.23% are achieved. The perception test indicates that by using PWs as the lowest prosodic units a speech sounds more natural and acceptable than by using LWs. This paper is supported by NSFC Project (60503071); 973 Natural Basic Research Program of China (2004CB318102); Postdoctor Science Foundation of P. R. China (20070420275).     

Parameters evaluation of SOLA algorithm for time scale modification

Successful operation of the Synchronous Overlap and Add (SOLA) algorithm for Time Scale Modification (TSM) of speech is closely tied to the proper choice of parameters. This paper investigates the quality of time scale modified speech under different values of primary parameters. Based on Mean Opinion Score (MOS) tests and Bark Spectral Distortion (BSD) measure, the proper choices of synthesis shift (Ss) and the duration of the shift search interval (K _max?) are given experimentally. The conclusions can be helpful for operating the SOLA algorithm for time scale modification of speech.     

Critical Configurations for 1-View in Projections from ℙ<Superscript>k</Superscript> → ℙ<Superscript>2</Superscript>

In this paper we describe, from a theoretical point of view, critical configurations for the projective reconstruction of a set of points, for a single view, i.e. for calibration of a camera, in the case of projections from ℙ^k to ℙ² for k ≥ 4. We give first a general result describing these critical loci in ℙ^k, which, if irreducible, are algebraic varieties of dimension k−2 and degree 3. If k=4 they can be either a smooth ruled surface or a cone and if k = 5 they can be a smooth three dimensional variety, ruled in planes, or a cone. If k≥ 6, the variety is always a cone, the vertex of which has dimension at least k − 6. The reducible cases are studied in Appendix A. These results are then applied to determine explicitly the critical loci for the projections from ℙ^k which arise from the dynamic scenes in ℙ³ considered in [13]. Marina Bertolini is currently Associate Professor of Geometry at the Department of Mathematics at the Università degli Studi di Milano, Italy. Her main field of research is Complex Projective Algebraic Geometry, with particular interest for the classification of projective varieties and for the geometry of Grassmann varieties. On these topics M. Bertolini has published more than twenty reviewed papers on national and international journals. She has been for some years now interested also in applications of Algebraic Geometry to Computer Vision problems. Cristina Turrini is Associate Professor of Geometry at the Department of Mathematics of Università degli Studi di Milano, Italy. Her main research interest is Complex Projective Algebraic Geometry: subvarieties of Grassmannians, special varieties, automorphisms, classification. In the last two years she has started to work on applications of Algebraic Geometry to problems of Computer Vision. She is author or co-author of about thirty reviewed papers. She is also involved in popularization of Mathematics, and on this subject she is co-editor of some books.     

The hot blow forming of AZ31 Mg sheet: Formability assessment and application development

The hot blow forming of magnesium sheet offers significant opportunity for forming complex, lightweight parts for automotive applications. This paper characterizes the elevated-temperature formability of AZ31 magnesium sheet materials and the effect of processing conditions on the performance of these materials. In addition, magnesium sheet application development at General Motors Corporation is reviewed.     

Simulation of Strength Distribution in Ground Ceramics by Incorporating Residual Stress Effect

Strength of ground ceramics may be affected by residual stress as well as surface flaws induced by grinding. Strength prediction for ground ceramics is convenient for mechanical design of ceramic components. In this article, a numerical procedure based on fracture mechanics was proposed to estimate strength distribution of ground ceramics by considering grinding-induced residual stress. Bending strength and residual stress of ground ceramics were measured for three grinding-conditions. By comparison of simulated results with experimental ones, it was revealed that strength characteristics in experiments were well simulated by using the proposed procedure.     

Identification of a class of nonlinear state-space models using RPEtechniques

The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator