response of an sdof system to periodic external and parametric excitations with random phase modulations a single degree of freedom system is considered which is excited simultaneously by external and parametric time variant loadings both these dynamic loads are assumed to be periodic in time with some random disorder or phase modulations response analysis is made for this system by using stochastic averaging with subsequent application of the method of moments to the resulting set of the shortened ito sdes the results of steady state mean square response analysis are presented in terms of the corresponding amplification factor illustrating its dependence on excitation system bandwidth ratios and detuning between expected excitation frequencies and the system s natural frequency

parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity in this paper the parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity are analyzed the two dimensional lindstedt poincare perturbation technique applied for finding an approximate solution of linear parametrically excited systems is extended for analyzing a strong nonlinear oscillator based on the solution of a nonlinear differential equation with constant coefficients an approximative solution is introduced the transition curves and transient surfaces along which periodic solutions exist are obtained their strong dependence on the initial conditions is evident to prove the analytical solution the numerical experiment is done for certain values initial conditions and parameter values the time history diagrams for the oscillator are plotted

moment lyapunov exponent and stability index for linear conservative system with small random perturbation asymptotic expansion series for the moment lyapunov exponent and stability index are constructed and justified for the two dimensional linear stochastic system close to a harmonic oscillator as an example a one degree of freedom mechanical system parametrically excited in stiffness and damping is considered and several terms of the expansion are obtained

moment lyapunov exponents of the stochastic parametrical hill s equation abstract the lyapunov exponent and moment lyapunov exponents of hill s equation with frequency and damping coefficient fluctuated by white noise stochastic process are investigated a perturbation approach is used to obtain explicit expressions for these exponents in the presence of small intensity noises the results are applied to the study of the almost sure and the moment stability of the stationary solutions of the thin simply supported beam subjected to axial compressions and time varying damping which are small intensity stochastic excitations

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

moment lyapunov exponents of a two dimensional system under bounded noise parametric excitation the moment lyapunov exponents of a two dimensional system under bounded noise parametric excitation are studied in this paper the method of regular perturbation is applied to obtain weak noise expansions of the moment lyapunov exponent lyapunov exponent and stability index in terms of the small fluctuation parameter

witt spaces a geometric cycle theory for ko homology at odd primes introduction this paper studies a class of stratified piecewiselinear pseudomanifolds which we call witt spaces characterized by natural local intersection homology conditions 11 we compute the cobordism groups by introducing an invariant taking values in the witt group of symmetric bilinear forms over the rationals w q these pseudomanifolds solve a problem posed by d sullivan 25 to construct a class of p l cycles with signature which represent the connected version of ko homology at odd primes ko 0d z 1 2 the result was one of the first applications of the intersection homology theory of goresky and macpherson 11 specifically the rational intersection homology groups of witt spaces satisfy a poincare duality theorem to each witt space x we associate a p l invariant w x with values in w q this invariant generalizes the signature of manifolds and satisfies cobordism invariance additivity and a product formula adapting classical surgery spherical modification to this setting we prove that w x determines the cobordism class of x and obtain an explicit description of the witt cobordism groups the only nontrivial groups occur in dimensions 4k and for k 0 they are w q sullivan 25 27 has shown that a class of p l pseudomanifolds equipped with such an invariant possesses canonical orientations in ko 0 z 1 2 the orientations induce a natural transformation it of homology theories from witt space bordism to ko 0 z 1 2 the structure of w q is known 14 and we conclude that it is an equivalence at odd primes in this paper we study the cobordism theory of a class of stratified p l pseudomanifolds by means of the recent intersection homology theory of goresky and macpherson 11 goresky and macpherson were interested in finding a class of spaces with cobordism invariant signature for the purpose of extending the hirzebruch l class to the setting of manifolds with

stochastic stability of coupled oscillators simple and combination resonances in coupled oscillators under a random parametric excitation are studied an efficient numerical method for obtaining the regions of mean square stability is proposed based on the method stability diagrams for different values of the excitation parameter and for four form of the coupling parameters are presented it is found that the random excitation can have a stabilizing effect under certain conditions

moment lyapunov exponents of a two dimensional system under combined harmonic and real noise excitations abstract the moment lyapunov exponents and the lyapunov exponents of a two dimensional system under combined excitations of harmonic and real noise which is modelled as an ornstein uhlenbeck process are studied the moment lyapunov exponents and the lyapunov exponents are important characteristics determining the moment and almost sure stability of a stochastic dynamical system the eigenvalue problem governing the moment lyapunov exponent is established a regular perturbation method is applied to solve the eigenvalue problem to obtain second order weak noise expansions of the moment lyapunov exponents the influence of the real noise excitation on the parametric resonance due to the harmonic excitation is investigated

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

a class of improved hybrid hochberg hommel type step up multiple test procedures summary in this paper we derive a new p value based multiple testing procedure that improves upon the hommel procedure by gaining power as well as having a simpler step up structure similar to the hochberg procedure the key to this improvement is that the hommel procedure can be improved by a consonant procedure exact critical constants of this new procedure can be numerically determined the zeroth order approximations to the exact critical constants albeit slightly conservative are simple to use and need no tabling and hence are recommended in practice the proposed procedure is shown to control the familywise error rate under independence among the p values simulations empirically demonstrate familywise error rate control under positive and negative dependence power superiority of the proposed procedure over competing ones is also empirically demonstrated illustrative examples are given

computing twisted signatures and l classes of non witt spaces in previous joint work with cappell and shaneson we have established an atiyah lusztig meyer type multiplicative characteristic class formula for the twisted signature and more generally the twisted l class of a stratified witt space the present paper shows that these formulae hold even when the stratified space does not satisfy the witt condition it constitutes one of the first applications of signature homology

moment stability for linear systems with a random parametric excitation moment stability for linear systems with a nonwhite parametric noise is considered a method of reduction of the study of this stability to the study of stability for large scale matrices is proposed mean square stability diagrams for random harmonic oscillator are presented

fast closed testing for exchangeable local tests summarymultiple hypothesis testing problems arise naturally in science this note introduces a new fast closed testing method for multiple testing which controls the familywise error rate controlling the familywise error rate is state of the art in many important application areas and is preferred over false discovery rate control for many reasons including that it leads to stronger reproducibility the closure principle rejects an individual hypothesis if all global nulls of subsets containing it are rejected using some test statistics it takes exponential time in the worst case when the tests are symmetric and monotone the proposed method is an exact algorithm for computing the closure is quadratic in the number of tests and is linear in the number of discoveries our framework generalizes most examples of closed testing such as holm s method and the bonferroni method as a special case of the method we propose the simes and higher criticism fusion test which is powerful both for detecting a few strong signals and for detecting many moderate signals

chaotic motion of van der pol mathieu duffing system under bounded noise parametric excitation abstract the chaotic behavior of van der pol mathieu duffing oscillator under bounded noise is investigated by using random melnikov technique a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system the results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases which is further verified by the maximal lyapunov exponents of the system the effect of bounded noise on poincare map is also investigated in addition the numerical simulation of the maximal lyapunov exponents

elliptic genera of singular varieties the notions of orbifold elliptic genus and elliptic genus of singular varieties are introduced and the relation between them is studied the elliptic genus of singular varieties is given in terms of a resolution of singularities and extends the elliptic genus of calabi yau hypersurfaces in fano gorenstein toric varieties introduced earlier the orbifold elliptic genus is given in terms of the fixed point sets of the action we show that the generating function for the orbifold elliptic genus ellorb x 6n p for symmetric groups 6n acting on n fold products coincides with the one proposed by r dijkgraaf g moore e verlinde and h verlinde the two notions of elliptic genera are conjectured to coincide

large deviations and stochastic flows of diffeomorphisms previous results in the theory of large deviations for additive functionals of a diffusion process on a compact manifold m are extended and then applied to the analysis of the lyapunov exponents of a stochastic flow of diffeomorphisms of m an approximation argument relates these results to the behavior near the diagonal in m2 of the associated two point motion finally it is shown under appropriate non degeneracy conditions that the two point motion is ergodic on m2 if the top lyapunov exponent is positive

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

principal response of duffing oscillator to combined deterministic and narrow band random parametric excitation abstract the principal resonance of a duffing oscillator to combined deterministic and narrow band random parametric excitations is investigated in particular the case in which the parametric terms share close frequencies is examined the method of multiple scales is used to determine the equations of modulation of amplitude and phase the behavior stability and bifurcation of steady state response are studied by means of qualitative analyses jumps are shown to occur if the random excitation is small the effects of damping detuning and magnitudes of deterministic and narrow band parametric excitations are analyzed the theoretical analyses are verified by numerical results

moment lyapunov exponents of a two dimensional system under real noise excitation abstract the moment lyapunov exponents of a two dimensional system under real noise excitation an ornstein uhlenbeck process are studied in this paper the method of regular perturbation is applied to obtain the weak noise expansions of the moment lyapunov exponent lyapunov exponent and stability index in terms of the small fluctuation parameter

chaotic motion in the resonant separatrix bands of a mathieu duffing oscillator with a twin well potential the m 1 resonant bands in the left and right potential wells are skew symmetric and the 2m 1 resonant bands of the large orbit motion are symmetric the analytical conditions for the onset and destruction of a resonant band are developed through the incremental energy approach the numerical predictions of such onset and destruction are also completed by the energy increment spectrum method the sub resonance interaction occurs for strong excitations which needs to be further investigated these results are applicable to the small and large orbit motions of post buckled structure under a parametric excitation

ergodic solenoidal homology realization theorem we define generalized currents associated with immersions of abstract oriented solenoids with a transversal measure we realize geometrically the full real homology of a compact manifold with these generalized currents and more precisely with immersions of minimal uniquely ergodic solenoids this makes precise and geometric de rham s realization of the real homology by only using a restricted geometric subclass of currents

maximal lyapunov exponent and almost sure stability for stochastic mathieu duffing systems abstract the principal resonance of a mathieu duffing oscillator to random excitation is investigated the method of multiple scales is used to determine the equations of modulation of amplitude and phase the effects of damping detuning cubic term and magnitudes of random excitation are analyzed the explicit asymptotic formulas for the maximal lyapunov exponent is obtained the almost sure stability or instability of the stochastic mathieu duffing system depends on the sign of the maximal lyapunov exponent in the last part of the work the numerical results are obtained

comparison of some approaches to stability of a sdof system under random parametric excitation we give a rigorous comparison of the asymptotic stochastic averaging method and the moment lyapunov exponent approach in assessing the mean square stability through an example of a single degree of freedom system under small periodic parametric excitation with random phase modulation the comparison is based on an efficient numerical procedure to determine the regions of mean square stability

the sequential rejection principle of familywise error control closed testing and partitioning are recognized as fundamental principles of familywise error control in this paper we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing we present a general sequentially rejective multiple testing procedure and show that many well known familywise error controlling methods can be constructed as special cases of this procedure among which are the procedures of holm shaffer and hochberg parallel and serial gatekeeping procedures modern procedures for multiple testing in graphs resampling based multiple testing procedures and even the closed testing and partitioning procedures themselves we also give a general proof that sequentially rejective multiple testing procedures strongly control the familywise error if they fulfill simple criteria of monotonicity of the critical values and a limited form of weak familywise error control in each single step the sequential rejection principle gives a novel theoretical perspective on many well known multiple testing procedures emphasizing the sequential aspect its main practical usefulness is for the development of multiple testing procedures for null hypotheses possibly logically related that are structured in a graph we illustrate this by presenting a uniform improvement of a recently published procedure

largest lyapunov exponent for second order linear systems under combined harmonic and random parametric excitations the principal resonance of a second order linear stochastic oscillator to combined harmonic and random parametric excitations is investigated the method of multiple scales is used to determine the equations of modulation of amplitude and phase the effects of damping detuning bandwidth and magnitudes of random excitation are analyzed the method of path integration is used to obtain the steady state probability density function of the system and then the largest lyapunov exponent is calculated the almost sure stability or instability of the stochastic system depends on the sign of the largest lyapunov exponent the theoretical analyses are verified by numerical results

an extension of a theorem by cheeger and muller to spaces with isolated conical singularities the aim of this article is to extend a theorem by cheeger and muller to spaces with isolated conical singularities by generalizing the proof of bismut and zhang to the singular setting the main tools in this approach are the witten deformation and local index techniques

computing twisted signatures and l classes of stratified spaces this paper establishes an atiyah type characteristic class formula for both the twisted signature and the twisted l classes of a singular space the result in its present form applies to coefficient systems that satisfy a transversality condition near the singularities this condition is frequently automatically satisfied e g on supernormal spaces or for local systems arising in certain geometric mapping situations we obtain applications to stratified maps by combining our formula with the cappell shaneson signature formula

closure method and asymptotic expansions for linear stochastic systems a closure procedure for the hierarchy of moment equations related to linear systems of ordinary differential equations with a random parametric excitation is introduced a generalization of pringsheim s theorem for continued fractions is used in a proof of the procedure convergence the boundary function method for singular perturbation problems is applied to obtain asymptotic expansions for the moments of the solutions of such systems

superperverse intersection cohomology stratification in dependence within its traditional range of perversity parameters intersection cohomology is a topological invariant of pseudomanifolds this is no longer true once one allows superperversities perversities with open image in new window in this case intersection cohomology may depend on the choice of the stratification by which it is defined topological invariance also does not hold if one allows stratifications with codimension one strata nonetheless both errant situations arise in important situations the former in the cappell shaneson superduality theorem and the latter in any discussion of pseudomanifold bordism we show that while full invariance of intersection cohomology under restratification does not hold in this generality it does hold up to restratifications that fix the the top stratum

intersection homology ii in 19 20 we introduced topological invariants ih x called intersection homology groups for the study of singular spaces x these groups depend on the choice of a perversity p a perversity is a function from 2 3 to the non negative integers such that both c and c 2 c are positive and increasing functions of c 2 1 the group ihr is defined for spaces x called pseudomanifolds a pseudomanifold of dimension n is a space that admits a stratification x x n x n z x n 3 x 1 x 0

higher criticism for detecting sparse heterogeneous mixtures higher criticism or second level significance testing is a multiplecomparisons concept mentioned in passing by tukey it concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis tukey suggested comparing the fraction of observed significances at a given level to the expected fraction under the joint null in fact he suggested standardizing the difference of the two quantities and forming a z score the resulting z score tests the significance of the body of significance tests we consider a generalization where we maximize this z score over a range of significance levels 0 0 we are able to show that the resulting higher criticism statistic is effective at resolving a very subtle testing problem testing whether n normal means are all zero versus the alternative that a small fraction is nonzero the subtlety of this sparse normal means testing problem can be seen from work of ingster and jin who studied such problems in great detail in their studies they identified an interesting range of cases where the small fraction of nonzero means is so small that the alternative hypothesis exhibits little noticeable effect on the distribution of the p values either for the bulk of the tests or for the few most highly significant tests in this range when the amplitude of nonzero means is calibrated with the fraction of nonzero means the likelihood ratio test for a precisely specified alternative would still succeed in separating the two hypotheses we show that the higher criticism is successful throughout the same region of amplitude sparsity where the likelihood ratio test

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

rene thom s work on geometric homology and bordism by the early 1950 s algebraic topology had reached great heights with serre s thesis and the calculations in the seminar of henri cartan of the cohomology of spaces with one nonzero homotopy group in terms of steenrod operations there was also the appearance of the new characteristic classes of vector bundles pontryagin classes z coefficients and chern weil classes coefficients in r joining those of stiefel whitney z mod 2 coefficients rene thom absorbed all this structure made vigorous use of it and added a geometric perspective that combined to revolutionize topology manifold theory and algebraic geometry for the unexpected and fertile results in bordism closed manifolds mod boundaries of manifolds of the 1954 paper 1 thom received the fields medal at edinburgh in 1958 many more applications of thom s ideas came even later

explanation on the importance of narrow band random excitation characters in the response of a cantilever beam a detailed theoretical investigation into the first and second mode response of a parametrically excited slender cantilever beam where the narrow band random excitation characters are taken into consideration is presented the method of multiple scales is used to determine a uniform first order expansion of the solution of the nonlinear integro differential equations the first order moment frequency and force response data curves of a specimen beam tested by other investigators are obtained further comparisons have been made and results show that whether the first order moment frequency response data curves or the first order moment force response data curves of the first two modes are all in agreement with other investigators experimental results furthermore the stochastic jump and bifurcation have been investigated for the first modal parametric principal resonance by using the stationary joint probability of amplitude and phase results show that stochastic jump occurs mainly in the region of triple valued solution for the frequency response domain if the bandwidth is a variable and others keep constant the basic phenomena indicate that the most probable motion is around the higher branch when the bandwidth is smaller whereas the most probable motion gradually approaches the lower one when the bandwidth becomes higher if the excitation central frequency f is a variable and others keep constant the basic phenomena imply that the higher is f the more probable is the jump from the higher branch to the lower one once f exceeds an certain value for the force response domain there is a region of excitation acceleration a within which the joint probability density has two peaks an upper peak and a lower peak results show that the upper peak decreases while the lower peak increases as the value of a decreases

mean square stability of a second order parametric linear system excited by a colored gaussian noise abstract the stochastic stability of a second order linear parametric oscillator whose stiffness is perturbed by a stationary zero mean colored gaussian process is investigated in this paper referring to the stability in the second response moments mean square stability the stochastic perturbation is the output of a linear filter excited by a stationary gaussian white noise stochastic process and the hypothesis of weak excitation is not formulated the first assumption allows using ito s stochastic differential calculus the moment equations of the response are written till the second order by means of ito s differential rule they form an infinite hierarchy that is the equations for the moments of order r contain moments of order larger than r in order to close the hierarchy the cumulant neglect closure method is applied herein the moment equation set is closed by neglecting the cumulants of third order nonlinear moment equations result they are linearized and the limit of stability is searched by studying the eigenvalues of the matrix of the coefficients of the linearized moment equations several numerical analyses are performed to evaluate the critical mean square value of the excitation when a system parameter is varied for the cases of both first and second order parametric excitation a first order excitation an ornstein uhlenbeck process does not cause stochastic resonance while a second order excitation does the first result was not known previously

multiple tests of a non hierarchical finite family of hypotheses this paper considers the problem of simultaneously testing a non hierarchical finite family of hypotheses several definitions have been introduced they are used to shed interesting light on the interrelationship between the four types of test that have previously been proposed

a graphical approach to sequentially rejective multiple test procedures for clinical trials with multiple treatment arms or endpoints a variety of sequentially rejective weighted bonferroni type tests have been proposed such as gatekeeping procedures fixed sequence tests and fallback procedures they allow to map the difference in importance as well as the relationship between the various research questions onto an adequate multiple test procedure since these procedures rely on the closed test principle they usually require the explicit specification of a large number of intersection hypotheses tests the underlying test strategy may therefore be difficult to communicate we propose a simple iterative graphical approach to construct and perform such bonferroni type tests the resulting multiple test procedures are represented by directed weighted graphs where each node corresponds to an elementary hypothesis together with a simple algorithm to generate such graphs while sequentially testing the individual hypotheses the approach is illustrated with the visualization of several common gatekeeping strategies a case study is used to illustrate how the methods from this article can be used to tailor a multiple test procedure to given study objectives