coordinate algebras of extended affine lie algebras of type a1 abstract the cores of extended affine lie algebras of reduced types were classified except for type a1 in this paper we determine the coordinate algebra of extended affine lie algebras of type a1 it turns out that such an algebra is a unital z n graded jordan algebra of a certain type called a jordan torus we classify jordan tori and get five types of jordan tori

locally loop algebras and locally affine lie algebras abstract in this study we investigate a new class of lie algebras i e tame locally extended affine lie algebras of nullity 1 which are an infinite rank analog of affine lie algebras this type of algebra is called a locally affine lie algebra a certain ideal of a locally affine lie algebra called a core is a universal extension of a local version of a loop algebra which is called a locally loop algebra we classify locally loop algebras and locally affine lie algebras

the effect of exit radii on intraglottal pressure distributions in the convergent glottis phonation depends upon the dynamic distribution of glottal air pressures that act upon the vocal folds as well as tissue properties of the vocal folds the glottal wall pressures depend upon the shape size and diameter of the glottis for a given flow this study examined how the radius of curvature of the glottal exit in the converging glottis affects the wall pressures in the glottis the following exit radii were used 0 0908 cm 0 0454 cm and 0 0050 cm for the 10 case and 0 0841 cm 0 021 025 cm and 0 0050 cm for the 20 case minimal glottal diameter and flow were held constant at 0 02 cm and 73 2 cm3 s respectively the computational fluid dynamics code fluent was used to obtain the pressure profiles both the transglottal and intraglottal pressures increased as the exit radius decreased resulting in an increase in flow resistance and an increase in the outward pressure forces on the vocal folds the results suggest that the glottal exit curvature should be well specified when building computational or physical models of the vocal folds

theoretical and experimental study of quasisteady flow separation within the glottis during phonation application to a modified two mass model most flow models used in numerical simulation of voiced sound production rely for the sake of simplicity upon a certain number of assumptions while most of these assumptions constitute reasonable first approximations others appear more doubtful in particular it is implicitly assumed that the air flow through the glottal channel separates from the walls at a fixed point since this assumption appears quite unrealistic and considering that the position of the separation point is an important parameter in phonation models in this paper a revised fluid mechanical description of the air flow through the glottis is proposed in which the separation point is allowed to move this theoretical model as well as the assumptions made are validated using steady and unsteady flow measurements combined with flow visualizations in order to evaluate the effective impact of the revised theory we then present an application to a simple mechanical model of the vocal cords derived from the classical two mass model as expected implementation of a moving separation point appears to be of great importance for the modeling of glottal signals it is further shown that the numerical model coupled with a more realistic description of the vocal cord collision can lead to signals surprisingly close to those observed in real speech by inverse filtering

reflectable bases for affine reflection systems abstract the notion of a root base together with its geometry plays a crucial role in the theory of finite and affine lie theory however it is known that such a notion does not exist for the recent generalizations of finite and affine root systems such as extended affine root systems and affine reflection systems in this work we consider the notion of a reflectable base for an affine reflection system r a reflectable base for r is a minimal subset of roots such that the non isotropic part of the root system can be recovered by reflecting roots of relative to the hyperplanes determined by we give a full characterization of reflectable bases for tame irreducible affine reflection systems of reduced types excluding types e 6 7 8 as a by product of our results we show that if the root system under consideration is locally finite then any reflectable base is an integral base

a theoretical study of the hysteresis phenomenon at vocal fold oscillation onset offset this paper presents a theoretical study on the differences in the biomechanical parameters of the vocal folds between oscillation onset and offset the dynamics of the oscillation is analyzed from the perspective of the theory of nonlinear dynamical systems using a mucosal wave model of the vocal folds with the subglottal pressure and the vocal fold half width as control parameters it is shown that the oscillation onset occurs through a hopf bifurcation of the subcritical type at which an unstable limit cycle is generated also the oscillation offset occurs at a cyclic fold bifurcation at which the unstable limit cycle and a stable limit cycle the actual vocal fold oscillation coalesce and cancel each other both bifurcations combine to form an oscillation hysteresis phenomenon common in cases of flow induced oscillations an analytical expression for the onset offset ratio of parameters is derived the onset offset ratio is in the range of 0 5 1 in agreement with the experimental evidence this value depends on the phase delay in motion of the upper edge of the vocal folds versus the lower edge and on the particular model adopted for airflow separation within the glottis

geometry of human vocal folds and glottal channel for mathematical and biomechanical modeling of voice production current models of the vocal folds derive their shape from approximate information rather than from exactly measured data the objective of this study was to obtain detailed measurements on the geometry of human vocal folds and the glottal channel in phonatory position a non destructive casting methodology was developed to capture the vocal fold shape from excised human larynges on both medial and superior surfaces two female larynges each in two different phonatory configurations corresponding to low and high fundamental frequency of the vocal fold vibrations were measured a coordinate measuring machine was used to digitize the casts yielding 3d computer models of the vocal fold shape the coronal sections were located in the models extracted and fitted by piecewise defined cubic functions allowing a mathematical expression of the 2d shape of the glottal channel left right differences between the cross sectional shapes of the vocal folds were found in both the larynges

irreducible representations for toroidal lie algebras abstract in this work a large number of irreducible representations with finite dimensional weight spaces are constructed for some toroidal lie algebras to accomplish this we develop a general theory of z n graded lie algebras with polynomial multiplication we construct modules by the standard inducing procedure and study their irreducible quotients using the vertex operator technics

linearly recursive sequences and operator polynomials abstract operator polynomials i e polynomials over endomorphism algebras of vector spaces are studied in the framework of polynomial modules and their comodule duals i e the comodules of linearly recursive sequences the subcomodules which replace the concept of jordan matrix pairs contain enough information to recover the polynomials up to unit factors

universal central extensions of direct limits of lie superalgebras abstract we show that the universal central extension of a direct limit of perfect lie superalgebras l i is isomorphic to the direct limit of the universal central extensions of l i as an application we describe the universal central extensions of some infinite rank lie superalgebras

the effect of glottal angle on intraglottal pressure intraglottal pressure distributions depend upon glottal shape size and diameter this study reports the effects of varying glottal angle on intraglottal and transglottal pressures using a three dimensional plexiglas model with a glottis having nine symmetric glottal angles and a constant minimal glottal diameter of 0 06cm the empirical data were supported by computational results using fluent the results suggested that 1 the greater the convergent glottal angle the greater outward driving forces higher intraglottal pressures on the vocal folds 2 flow resistance was greatest for the uniform glottis and least for the 10 divergent glottis 3 the greatest negative pressure in the glottis and therefore the greatest pressure recovery for diverging glottal shapes occurred for an angle of 10 4 the smaller the convergent angle the greater the flow resistance 5 fluent was highly accurate in predicting the empirical pressures of this model 6 flow separation locations given by fluent for

the classification of locally finite split simple lie algebras one of the great early achievements in lie theory is the classification of the finite dimensional simple complex lie algebras by w killing and e cartan more than 50 years later new aspects were added to this classification by the theory of coxeter groups and the visualization of the classification in terms of dynkin diagrams furthermore serre s description of the simple lie algebras by generators and relations provided a direct way to construct the lie algebras from the cartan matrix corresponding to the choice of a root base i e a system of simple roots

classification and construction of quasisimple lie algebras abstract we study a class of possibly infinite dimensional lie algebras called the quasisimple lie algebras qsla s and generalizing semisimple and affine kac moody lie algebras they are characterized by the existence of a finite dimensional cartan subalgebra a non degenerate symmetric ad invariant killing form and nilpotent rootspaces attached to non isotropic roots we are then able to derive a classification theorem for the possible irreducible elliptic quasisimple root systems moreover we construct explicit realizations of some of them as untwisted and twisted current algebras generalizing the affine loop algebras

quantum tori and the structure of elliptic quasi simple lie algebras abstract we study and classify those tame irreducible elliptic quasi simple lie algebras which are simply laced and of rankl 3 the first step is to identify the core of such an algebra up to central isogeny by identifying the coordinates when the type isdorethe coordinates are laurent polynomials in variables while for typeathe coordinates can be any quantum torus in variables the next step is to study the universal central extension as well as the derivation algebra of the core these are related to the first connes cyclic homology group of the coordinates the final step is to use this information to give constructions of lie algebras which we then prove yield representatives of all isomorphism classes of the above types of algebras

intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees human phonation does not always involve symmetric motions of the two vocal folds asymmetric motions can create slanted or oblique glottal angles this study reports intraglottal pressure profiles for a plexiglas model of the larynx with a glottis having a 10 degree divergence angle and either a symmetric orientation or an oblique angle of 15 degrees for the oblique glottis one side was divergent and the other convergent the vocal fold surfaces had 14 pressure taps the minimal glottal diameter was held constant at 0 04 cm results indicated that for either the symmetric or oblique case the pressure profiles were different on the two sides of the glottis except for the symmetric geometry for a transglottal pressure of 3 cm h2o for the symmetric case flow separation created lower pressures on the side where the flow stayed attached to the wall and the largest pressure differences between the two sides of the channel were 5 6 of the transglottal pressure for the oblique case pressures were lower

locally extended affine lie algebras abstract we propose a new simplified definition of extended affine lie algebras ealas for short and also discuss a general version of extended affine lie algebras called locally extended affine lie algebras local ealas for short we prove a conjecture by v kac for local ealas it turns out that the root system of a local eala becomes a locally finite version of an extended affine root system several examples of new ealas and local ealas are introduced and finally we classify local ealas of nullity 0 and show the connection to locally finite split simple lie algebras

influence of collision on the flow through in vitro rigid models of the vocal folds measurements of pressure in oscillating rigid replicas of vocal folds are presented the pressure upstream of the replica is used as input to various theoretical approximations to predict the pressure within the glottis as the vocal folds collide the classical quasisteady boundary layer theory fails it appears however that for physiologically reasonable shapes of the replicas viscous effects are more important than the influence of the flow unsteadiness due to the wall movement a simple model based on a quasisteady bernoulli equation corrected for viscous effect combined with a simple boundary layer separation model does globally predict the observed pressure behavior

an algebraic approach to multiparameter spectral theory root subspaces for multiprameter eigenvalue problems are described using coalgebraic techniques an algorithm is given to construct bases for the root subspaces

extended affine root supersystems abstract the interaction of a lie algebra l having a weight space decomposition with respect to a nonzero toral subalgebra with its corresponding root system forms a powerful tool in the study of the structure of l this in particular suggests a systematic study of the root system apart from its connection with the lie algebra although there have been a lot of researches in this regard on lie algebra level such an approach has not been considered on lie superalgebra level in this work we introduce and study extended affine root supersystems which are a generalization of both affine reflection systems and locally finite root supersystems extended affine root supersystems appear as the root systems of the super version of extended affine lie algebras and invariant affine reflection algebras including affine lie superalgebras this work provides a framework to study the structure of this kind of lie superalgebras refereed to as extended affine lie superalgebras

vertex representations for n toroidal lie algebras and a generalization of the virasoro algebra vertex representations are obtained for toroidal lie algebras for any number of variables these representations afford representations of certainn variable generalizations of the virasoro algebra that are abelian extensions of the lie algebra of vector fields on a torus

lie algebras graded by 3 graded root systems and jordan pairs covered by grids let r be an irreducible root system a lie algebra l is called graded by r if l is graded with grading group the root lattice of r such that the only nonzero homogeneous subspaces of l have degree 0 or a root in r the grading is induced by the adjoint action of a split cartan subalgebra of a finite dimensional simple lie subalgebra of l with root system r and l is generated by the homogeneous subspaces of nonzero degree this class of lie algebras was introduced and studied by s berman and r moody in invent math 108 1992 where in particular a classification up to central equivalence is given in the simply laced case the doubly laced cases have recently been classified by g benkart and e zelmanov let r be a 3 graded root system i e r is not of type e 8 f 4 or g 2 in this paper lie algebras graded by r are described in a unified way without case by case considerations namely it is shown that a lie algebra l is 3 graded if and only if l is a central extension of the tits kantor koecher algebra of a jordan pair covered by a grid whose associated 3 graded root system is isomorphic to r this result is then used to classify lie algebras graded by r we give the classification of jordan pairs covered by a grid and describe their tits kantor koecher algebras one of the advantages of this approach is that it works over rings containing 1 2 and 1 3 and also for infinite root systems another application is the description of slodowy s intersection matrix algebras arising from multiply affinized cartan matrices