identifying acoustical coupling by measurements and prediction models for st peter s basilica in rome st peter s basilica is one of the largest buildings in the world having a huge volume resulting from the addition of different parts consequently sound propagation cannot be interpreted using a conventional approach and requires experimental measures to be compared with statistical acoustics and geometrical predictions in order to explain the interplay between shape materials and sound waves better in previous research one of the most evident effects the surprisingly low reverberation time was believed to result from acoustical coupling phenomena taking advantage of more refined measuring techniques available today an acoustic survey was carried out and the results were analyzed using different methods including bayesian parameter estimation of multiple slope decays and directional energy plots which showed that coupling effects actually take place even though measured reverberation times were longer than those given in previous studies in addition experimental results were compared with geometrical and statistical acoustic models of the basilica which showed that careful selection of input data and in statistical models the inclusion of phenomena such as direct sound radiation and non diffuse energy transfer allow obtaining accurate results finally both models demonstrated that reduced reverberation depends more on increased absorption of decorated surfaces than on coupling effects

genus bounds for minimal surfaces arising from min max constructions in this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3 dimensional manifold constructed via min max arguments a stronger estimate was announced by pitts and rubinstein but to our knowledge its proof has never been published our proof follows ideas of simon and uses an extension of a famous result of meeks simon and yau on the convergence of minimizing sequences of isotopic surfaces this result is proved in the second part of the paper

evaluation of decay times in coupled spaces bayesian decay model selection this paper applies bayesian probability theory to determination of the decay times in coupled spaces a previous paper n xiang and p m goggans j acoust soc am 110 1415 1424 2001 discussed determination of the decay times in coupled spaces from schroeder s decay functions using bayesian parameter estimation to this end the previous paper described the extension of an existing decay model n xiang j acoust soc am 98 2112 2121 1995 to incorporate one or more decay modes for use with bayesian inference bayesian decay time estimation will obtain reasonable results only when it employs an appropriate decay model with the correct number of decay modes however in architectural acoustics practice the number of decay modes may not be known when evaluating schroeder s decay functions the present paper continues the endeavor of the previous paper to apply bayesian probability inference for comparison and selection of an appropriate decay model based upon measured data following a summar

lebesgue and saks decompositions of σ finite fuzzy measures two kinds of absolute continuity of fuzzy measures are distinguished and relations between them are established the scope of fuzzy measures under our consideration is limited in a family of those that are finite and absolute continuous with respect to a finite autocontinuous fuzzy measure under this restriction lebesgue decomposition and saks decomposition are proved

exhaustivity and absolute continuity of fuzzy measures in this paper we further investigate the concept of absolute continuity of fuzzy measures and monotone functions defined by fuzzy integral by using the concept of exhaustivity the equivalencies among several different types of absolute continuity of fuzzy measures are established

regularity and autocontinuity of set multifunctions in this paper we study different types of regularity for monotone uniformly autocontinuous set multifunctions defined on a ring of subsets of a locally compact hausdorff space t and taking values in the family of closed nonvoid sets of a real normed space x

embedded minimal surfaces exotic spheres and manifolds with positive ricci curvature let n be a three dimensional riemannian manifold let e be a closed embedded surface in n then it is a question of basic interest to see whether one can deform in its isotopy class to some canonical embedded surface from the point of view of geometry a natural canonical surface will be the extremal surface of some functional defined on the space of embedded surfaces the simplest functional is the area functional the extremal surface of the area functional is called the minimal surface such minimal surfaces were used extensively by meeks yau my21 in studying group actions on three dimensional manifolds in my2 the theory of minimal surfaces was used to simplify and strengthen the classical dehn s lemma loop theorem and the sphere theorem in the setting there one minimizes area among all immersed surfaces and proves that the extremal object is embedded in this paper we minimize area among all embedded surfaces isotopic to a fixed embedded surface in the category of these surfaces we prove a general existence theorem theorem 1 a particular consequence of this theorem is that for irreducible manifolds an embedded incompressible surface is isotopic to an embedded incompressible surface with minimal area we also prove that there exists an embedded sphere of least area enclosing a fake cell provided the complementary volume is not a standard ball and provided there exists no embedded one sided rp2 by making use of the last result and a cutting and pasting argument we are able to settle a well known problem in the theory of three dimensional manifolds we prove that the covering space of any irreducible orientable three dimensional manifold is irreducible it is possible to exploit our existence theorem to study

unstable minimal surfaces and heegaard splittings in recent years minimal surfaces have played an important role in the study of three dimensional manifolds least area surfaces which minimize area in their isotopy 15 homotopy 23 or homology 10 classes have been used to make progress towards the understanding of three manifolds which contain such surfaces such surfaces can be shown to exist and to have strong regularity properties under the assumption that the homotopy isotopy or homology class in which they minimize area is non trivial however these techniques tend not to be applicable to the study of surfaces which are not essential in one of the above classes or to the study of manifolds which contain only such nonessential surfaces recently developed techniques open the way for the use of a new class of surfaces in three dimensional manifolds namely the class of unstable embedded minimal surfaces pitts and rubinstein have established the existence of unstable minimal submanifolds which arise from a heegaard splitting in such a way that their genus is less than or equal to that of the heegaard splitting 19 in this paper we extend their result to obtain greater topological control of the resulting minimal surface and apply the resulting theorem to purely topological problems relating to heegaard splittings of a three manifold a compact manifold is a handlebody if it is homeomorphic to a regular neighborhood of a graph in r 3 a heegaard splitting of a three manifold m is a triple f h1 h2 where f is an embedded connected orientable surface in m h1 and h 2 are handlebodies embedded in m m h 1 w h 2 and h c h2 f o h i o h 2 f is called a heegaard surface we say that two heegaard splittings of m f h1 h2 and f h i h are equivalent if there is a homeomorphism h m m such that f f f f h o h i and f h2 h by considering neighborhoods of triangulations one can show that any closed orientable three manifold admits a heegaard splitting of particular interest are the splittings with heegaard surface of smallest possible genus the genus of such a splitting is called the heegaard genus of the three manifold

erratum to non atomicity and the darboux property for fuzzy and non fuzzy borel baire multivalued set functions fuzzy sets and systems 160 2009 1308 1317

efficient estimation of decay parameters in acoustically coupled spaces using slice samplinga room acoustic energy decay analysis of acoustically coupled spaces within the bayesian framework has proven valuable for architectural acoustics applications this paper describes an efficient algorithm termed slice sampling monte carlo ssmc for room acoustic decay parameter estimation within the bayesian framework this work combines the ssmc algorithm and a fast search algorithm in order to efficiently determine decay parameters their uncertainties and inter relationships with a minimum amount of required user tuning and interaction the large variations in the posterior probability density functions over multidimensional parameter spaces imply that an adaptive exploration algorithm such as ssmc can have advantages over the exiting importance sampling monte carlo and metropolis hastings markov chain monte carlo algorithms this paper discusses implementation of the ssmc algorithm its initialization and convergence using experimental data measured from acoustically coupled spaces

evaluation of decay times in coupled spaces reliability analysis of bayeisan decay time estimation this paper discusses quantitative tools to evaluate the reliability of decay time estimates and inter relationships between multiple decay times for estimates made within a bayesian framework previous works xiang and goggans j acoust soc am 110 1415 1424 2001 113 2685 2697 2003 have applied bayesian framework to cope with the demanding tasks in estimating multiple decay times from schroeder decay functions measured in acoustically coupled spaces a parametric model of schroeder decay function xiang j acoust soc am 98 2112 2121 1995 has been used for the bayesian model based analysis the relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within bayesian framework using schroeder decay function data this paper will first address the estimation of global variance of the residual errors between the schroeder function data and its model moreover this paper discusses how the landscape shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates their associated variances and their inter relationships this paper uses experimental results from measured room impulse responses in real halls to describe a model based sampling method for an efficient estimation of decay times and their individual variances these parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces

a set valued egoroff type theorem in this paper an egoroff type theorem for a fuzzy multimeasure defined on a s algebra of subsets of an abstract space and taking values in the family of all nonvoid closed subsets of a real normed space is established some necessary and or sufficient conditions under which egoroff s theorem is valid are also presented

continuity properties and alexandroff theorem in vietoris topology in several previous papers we introduced and studied various continuity properties in the set valued case precisely we established results concerning increasing decreasing convergence exhaustivity order continuity and regularity in hausdorff topology for closed set valued monotone set multifunctions on a real normed space in this paper taking as starting point of a previous work we introduce and study from another point of view corresponding continuity properties in vietoris topology for more general monotone set multifunctions on a hausdorff linear topological space thus we obtain generalizations of some previous results which in turn generalize to the set valued case well known results from classical fuzzy i e monotone measure theory an alexandroff theorem in vietoris topology and its converse are also established

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

non atomicity and the darboux property for fuzzy and non fuzzy borel baire multivalued set functions in this paper we establish results concerning non atomicity and the darboux property for multisubmeasures fuzzy multivalued set functions defined on the baire respectively borel d ring b 0 respectively b of a locally compact hausdorff space

on set valued fuzzy integrals abstract in the paper we extend fuzzy integrals of point valued functions which were defined by ralescu and adams to set valued functions some properties similar to auman integrals are shown and these include convexity monotonicity fatou s lemma lebesgue convergence theorem etc

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

evaluation of reverberation times using a nonlinear regression approach reverberation decay curves can be obtained by the backward integration of room impulse responses proposed by m r schroeder the evaluation of reverberation times is often achieved by a linear regression line fitting the reverberation decay curves however under noisy conditions the successful application of this method requires either a careful choice of the integration limit or a precise estimate of the mean square value of the background noise in the present paper an alternative method using a nonlinear iterative regression approach for evaluating reverberation times from schroeder s decay curves is proposed a nonlinear model of the decay curves established according to the nature of schroeder s decay curves is used for the regression process rather than the linear model used in linear regression the regression process is based on the generalized least squares error principle in which a rapid convergence can be observed preliminary experiments show a slight dependence of the reverberation tim

set valued lusin type theorem for null null additive set multifunctions in a previous paper we presented a set valued egoroff type theorem for monotone set multifunctions in this paper a new version of this set valued egoroff type theorem is obtained it enables a set valued lusin type theorem for null null additive monotone continuous set multifunctions to be established several applications of this lusin type theorem are given pointing out some relationships among m measurability a measurability and totally measurability of real functions we also compare our new lusin type theorem with lusin s theorem previously obtained by the second author

a multi rate decay model to predict energy based acoustic parameters in churches multi rate decays are sometimes observed in room acoustics appearing when markedly different volumes are coupled together and resulting in nonlinear decay curves such behavior appears in several churches at the very beginning of the decay process although in conditions which cannot be explicitly referred to as coupling phenomena consequently multi rate exponential decays may be suitable to model energy distribution in this group of buildings providing a more elegant and easily applicable set of equations in place of a previously defined linear model used to adapt barron s revised theory the paper shows that the multi rate approach ensures ease of calculation without significant loss in accuracy in predicting energy based acoustic parameters

volume of minimal hypersurfaces in manifolds with nonnegative ricci curvature we establish a min max estimate on the volume width of a closed riemannian manifold with nonnegative ricci curvature more precisely we show that every closed riemannian manifold with nonnegative ricci curvature admits a pl morse function whose level set volume is bounded in terms of the volume of the manifold as a consequence of this sweep out estimate there exists an embedded closed possibly singular minimal hypersurface whose volume is bounded in terms of the volume of the manifold

quantifying uncertainty in geoacoustic inversion i a fast gibbs sampler approach this paper develops a new approach to estimating seabed geoacoustic properties and their uncertainties based on a bayesian formulation of matched field inversion in bayesian inversion the solution is characterized by its posterior probability density ppd which combines prior information about the model with information from an observed data set to interpret the multi dimensional ppd requires calculation of its moments such as the mean covariance and marginal distributions which provide parameter estimates and uncertainties computation of these moments involves estimating multi dimensional integrals of the ppd which is typically carried out using a sampling procedure important goals for an effective bayesian algorithm are to obtain efficient unbiased sampling of these moments and to verify convergence of the sample this is accomplished here using a gibbs sampler gs approach based on the metropolis algorithm which also forms the basis for simulated annealing sa although gs can be computationally slow in its basic form just as modifications to sa have produced much faster optimization algorithms the gs is modified here to produce an efficient algorithm referred to as the fast gibbs sampler fgs an automated convergence criterion is employed based on monitoring the difference between two independent fgs samples collected in parallel comparison of fgs gs and monte carlo integration for noisy synthetic benchmark test cases indicates that fgs provides rigorous estimates of ppd moments while requiring orders of magnitude less computation time

evaluation of decay times in coupled spaces an efficient search algorithm within the bayesian framework this paper discusses an efficient method for evaluating multiple decay times within the bayesian framework previous works n xiang and p m goggans j acoust soc am 110 1415 1424 2001 113 2685 2697 2003 n xiang p m goggans t jasa and m kleiner 117 3707 3715 2005 have applied the bayesian inference to cope with demanding tasks in estimating multiple decay times from schroeder decay functions measured or calculated in acoustically coupled spaces since then a number of recent works call for efficient estimation methods within the bayesian framework an efficient analysis is of practical significance for better understanding and modeling the sound energy decay process in acoustically coupled spaces or even in single spaces for reverberation time estimation this paper will first formulate the bayesian posterior probability distribution function ppdf in a matrix form to reduce the dimensionality as applied to the decay time evaluation based on existence of only global extremes o

evaluation of decay times in coupled spaces bayesian parameter estimation determination of sound decay times in coupled spaces often demands considerable effort based on schroeder s backward integration of room impulse responses it is often difficult to distinguish different portions of multirate sound energy decay functions a model based parameter estimation method using bayesian probabilistic inference proves to be a powerful tool for evaluating decay times a decay model due to one of the authors n xiang j acoust soc am 98 2112 2121 1995 is extended to multirate decay functions following a summary of bayesian model based parameter estimation the present paper discusses estimates in terms of both synthesized and measured decay functions no careful estimation of initial values is required in contrast to gradient based approaches the resulting robust algorithmic estimation of more than one decay time from experimentally measured decay functions is clearly superior to the existing nonlinear regression approach