dispersive decay for the magnetic schrodinger equation abstract we obtain a dispersive long time decay in weighted norms for solutions of 3d schrodinger equation with generic magnetic and scalar potentials the decay extends the results obtained by jensen and kato for the schrodinger equation without magnetic potentials for the proof we develop the spectral theory of agmon jensen and kato extending the high energy decay of the resolvent to the magnetic schrodinger equation our methods allows us extend the result to all dimension n 3

false discovery rate adjusted charting schemes for multistage process monitoring and fault identification most statistical process control research focuses on single stage processes this article considers the problem of multistage process monitoring and fault identification this problem is formulated as a multiple hypotheses testing problem however as the number of stages increases the detection power of multiple hypotheses testing methods that seek to control the type i error rate decreases dramatically to maintain the detection power we use a false discovery rate fdr control approach which is widely used in microarray research two multistage process monitoring and fault identification schemes an fdr adjusted shewhart chart and an fdr adjusted cumulative sum cusum chart are established to apply the fdr approach the distribution of the cusum statistics are obtained based on markov chain theory and brownian motion with drift models the detection and fault identification power of the new schemes are evaluated by the monte carlo method the results indicate that the novel fdr adjusted approaches

self replicating loop with universal construction after a survey of the theory and some realizations of self replicating machines this paper presents a novel self replicating loop endowed with universal construction properties based on the hardware implementation of the so called tom thumb algorithm the design of this loop leads to a new kind of cellular automaton made of a processing and a control units the self replication of the lsl acronym serves as an artificial cell division example of the loop and results in a new and straightforward methodology for the self replication of computing machines of any dimensions

decay estimates for the wave equation in two dimensions abstract we establish strichartz estimates both reversed and some direct ones pointwise decay estimates and weighted decay estimates for the linear wave equation in dimension two with an almost scaling critical potential in the case when there is no resonance or eigenvalue at the edge of the spectrum we also prove some simple applications

multivariate quality control based on regression adjusted variables when performing quality control in a situation in which measures are made of several possibly related variables it is desirable to use methods that capitalize on the relationship between the variables to provide controls more sensitive than those that may be made on the variables individually the most common methods of multivariate quality control that assess the vector of variables as a whole are those based on the hotelling t 2 between the variables and the specification vector although t 2 is the optimal single test statistic for a general multivariate shift in the mean vector it is not optimal for more structured mean shifts for example shifts in only some of the variables measures based on quadratic forms like t 2 also confound mean shifts with variance shifts and require quite extensive analysis following a signal to determine the nature of the shift this article proposes shewhart and cumulative sum cusum controls based on the vector z of scaled residuals from the regression of each varia

global in time strichartz estimates for the fractional schrodinger equations on asymptotically euclidean manifolds in this paper we prove global in time strichartz estimates for the fractional schrodinger operators namely e it lambda sigma g with sigma in 0 infty backslash 1 and lambda g delta g where delta g is the laplace beltrami operator on asymptotically euclidean manifolds mathbb r d g let f 0 in c infty 0 mathbb r be a smooth cutoff equal 1 near zero we firstly show that the high frequency part 1 f 0 p e it lambda sigma g satisfies global in time strichartz estimates as on mathbb r d of dimension d geq 2 inside a compact set under non trapping condition on the other hand under a moderate trapping assumption the high frequency part also satisfies the global in time strichartz estimates outside a compact set we next prove that the low frequency part f 0 p e it lambda sigma g satisfies global in time strichartz estimates as on mathbb r d of dimension d geq 3 without using any geometric assumption on g as a byproduct we prove global in time strichartz estimates for the fractional schrodinger and wave equations on mathbb r d g d geq 3 under non trapping condition

a note on multivariate cusum procedures cumulative sum cusum procedures are among the most powerful tools for detecting a shift from a good quality distribution to a bad quality distribution this article discusses the natural application of cusum procedures to the multivariate normal distribution it discusses two cases detecting a shift in the mean vector and detecting a shift in the covariance matrix as an example the procedure is applied to measurements taken on optical fibers

carleman estimates and absence of embedded eigenvalues let l w be a schrodinger operator with a potential w in l frac n 1 2 mathbb r n n geq 2 we prove that there is no positive eigenvalue the main tool is an l p l p prime carleman type estimate which implies that eigenfunctions to positive eigenvalues must be compactly supported the carleman estimate builds on delicate dispersive estimates established in 7 we also consider extensions of the result to variable coefficient operators with long range and short range potentials and gradient potentials

multivariate cusum quality control procedures it is a common practice to use simultaneously several one sided or two sided cusum procedures of the type proposed by page 1954 in this article this method of control is considered to be a single multivariate cusum mcusum procedure methods are given for approximating parameters of the distribution of the minimum of the run lengths of the univariate cusum charts using a new method of comparing multivariate control charts it is shown that an mcusum procedure is often preferable to hotelling s tz procedure for the case in which the quality characteristics are bivariate normal random variables

smoothing estimates for the schrodinger equation with unbounded potentials abstract we prove a local in time smoothing estimate for a magnetic schrodinger equation with coefficients growing polynomially at spatial infinity the assumptions on the magnetic field are gauge invariant and involve only the first two derivatives the proof is based on the multiplier method and no pseudodifferential techniques are required

hotelling s t2 charts with variable sample size and control limit abstract the ideas of variable sampling interval vsi variable sample size vss variable sample size and sampling interval vssi and variable parameters vp in the univariate case have been successfully applied to the multivariate case to improve the efficiency of hotelling s t 2 chart with fixed sampling rate fsr in detecting small process shifts however the main disadvantage in using most of these control schemes is an increasing in the complexity due to the adaptive changes in sampling intervals in this paper retaining the lengths of sampling intervals constant a variable sample size and control limit vssc t 2 chart is proposed and described the statistical efficiency of the vssc t 2 chart in terms of the average time to signal a shift in process mean vector is compared with that of the vp vssi vss vsi and fsr t 2 charts from the results of comparison it shows that the vssc t 2 chart for a very small shift in the process mean vector gives a better performance than the vssi vss vsi and fsr t 2 charts meanwhile it presents a similar performance to the vp t 2 chart furthermore from the viewpoint of practicability it is more convenient for administrating the control chart than the vsi vssi and vp t 2 chart thus it may provide a good option for quick response to small shifts in a multivariate process

multivariate bayesian process control for a finite production run abstract most industrial products and processes are characterized by several typically correlated measurable variables which jointly describe the product or process quality various control charts such as hotelling s t2 ewma and cusum charts have been developed for multivariate quality control where the values of the chart parameters namely the sample size sampling interval and the control limits are determined to satisfy given economic and or statistical requirements it is well known that this traditional non bayesian approach to a control chart design is not optimal but very few results regarding the form of the optimal bayesian control policy have appeared in the literature all limited to a univariate chart design in this paper we consider a multivariate bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent normally distributed vectors of random variables the problem is formulated in the pomdp partially observable markov decision process framework and the objective is to determine a control policy minimizing the total expected cost it is proved that under standard operating and cost assumptions the control limit policy is optimal cost comparisons with the benchmark chi squared chart and the mewma chart show that the bayesian chart is highly cost effective the savings are larger for smaller values of the critical mahalanobis distance between the in control and out of control process mean

the state of statistical process control as we proceed into the 21st century 2000 the state of statistical process control as we proceed into the 21st century journal of the american statistical association vol 95 no 451 pp 992 998

perturbation of resonances in quantum mechanics schrodinger operators on l2 r3 of the form v with potentials v real analytic in are discussed the analytic structure in v and k with k2 the energy variable of the resolvent kernel the eigenvalues and resonances is exhibited and we obtain in particular convergent perturbation expansions for the resonances and the corresponding resonance functions the lower order expansion coefficients are computed explicitly the resonances and the corresponding functions are also computed for a particle moving under the action of n point interactions this gives asymptotic low energy information about schrodinger hamiltonians with short range potentials the perturbation theory of resonances eigenvalues and of the corresponding functions for hamiltonians describing n point interactions perturbed by a potential is also given

multivariate generalizations of cumulative sum quality control schemes this article presents the design procedures and average run lengths for two mulativariater cumulative sum cusum quality control procedures the first cusum procedure reduces each multivariate observation to a scalar and then forms a cusum of the scalars the second cusum procedure forms a cusum vector directly from the observations these two procedures are compared with each other and with the multivariate shewhart chart other multivariate quality control procedures are mentioned robustness the fast initial response feature for cusum schemes and combined shewhart cusum schemes are discussed

scattering matrices for dissipative quantum systems abstract we consider a quantum system s interacting with another system s and susceptible of being absorbed by s the effective dissipative dynamics of s is supposed to be generated by an abstract pseudo hamiltonian of the form h h 0 v i c c the generator of the free dynamics h 0 is self adjoint v is symmetric and c is bounded we study the scattering theory for the pair of operators h h 0 we establish a representation formula for the scattering matrices and identify a necessary and sufficient condition to their invertibility this condition rests on a suitable notion of spectral singularity our main application is the nuclear optical model where h is a dissipative schrodinger operator and spectral singularities correspond to real resonances

multivariate statistical process control using lasso this article develops a new multivariate statistical process control spc methodology based on adapting the lasso variable selection method to the spc problem the lasso method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling which is especially useful in cases where the number of nonzero coefficients is small in multivariate spc applications process mean vectors often shift in a small number of components our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components using this connection between the two problems we propose a lasso based multivariate test statistic and then integrate this statistic into the multivariate ewma charting scheme for phase ii multivariate process monitoring we show that this approach balances protection against various shift levels and shift directions and thus provides an effective tool for multivariate spc applications this article

analysis and generalisation of a multivariate exponential smoothing model the multivariate exponential smoothing model of enns machak spivey and wrobleski is examined and it is found that its structure is such that it can be estimated by using techniques designed for a univariate exponential smoothing model similarly forecasts can be made using algorithms for the univariate model the model can therefore be handled very easily a more general univariate time series model which can include polynomial trends and seasonal factors is then set up and a multivariate generalisation analogous to the multivariate exponential smoothing model is introduced it is shown that this model can also be handled using algorithms designed for the univariate case

monitoring general linear profiles using multivariate exponentially weighted moving average schemes we propose a statistical process control scheme that can be implemented in industrial practice in which the quality of a process can be characterized by a general linear profile we start by reviewing the general linear profile model and the existing monitoring methods based on this we propose a novel multivariate exponentially weighted moving average monitoring scheme for such a profile we introduce two other enhancement features the variable sampling interval and the parametric diagnostic approach to further improve the performance of the proposed scheme throughout the article we use a deep reactive ion etching example from semiconductor manufacturing which has a profile that fits a quadratic polynomial regression model well to illustrate the implementation of the proposed approach

monitoring profiles based on nonparametric regression methods the use statistical process control spc in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries the spc problem with a nonlinear profile is particularly challenging this article proposes a novel scheme to monitor changes in both the regression relationship and the variation of the profile online it integrates the multivariate exponentially weighted moving average procedure with the generalized likelihood ratio test based on nonparametric regression the proposed scheme not only provides an effective spc solution to handle nonlinear profiles which are common in industrial practice but it also resolves the latent problem in popular parametric monitoring methods of being unable to detect certain types of changes due to a misspecified out of control model our simulation results demonstrate the effectiveness and efficiency of the proposed monitoring scheme in addition a systematic diagnostic approach is provided to locate t

the inertial properties of quality control charts many types of control charts have an ability to detect process changes that can weaken over time depending on the past data observed this is often referred to as the inertia problem we propose a new measure of inertia the signal resistance to be the largest standardized deviation from target not leading to an immediate out of control signal we calculate the signal resistance values for several types of univariate and multivariate charts our conclusions support the recommendation that shewhart limits should be used with exponentially weighted moving average charts especially when the smoothing parameter is small

dispersive estimates for principally normal pseudodifferential operators the aim of these notes is to describe some recent re sults concerning dispersive estimates for principally normal pseu dodifferential operators the main motivation for this comes from unique continuation problems such estimates can be used to prove l q carleman inequalities which in turn yield unique continuation results for various partial differential operators with rough poten tials dispersive estimates are l q estimates for nonelliptic partial differ ential operators which are a consequence of the decay properties of their fundamental solutions these decay properties follow from spa tial spreading of the singularities of the solutions since solutions prop agate in directions conormal to the characteristic set of the operator this spreading can be related to nonzero curvatures of the characteristic set dispersive estimates for constant coefficient operators are closely related to the restriction theorem in harmonic analysis various types of dispersive estimates are known to be true for op erators such as the wave operator the schrodinger operator and the linear kdv see ginibre velo 4 keel tao 11 they have proved to be useful in the study of nonlinear problems as well as of problems with unbounded potentials more recently similar estimates have been obtained for wave op erators with variable coefficients beginning with the smooth case in kapitanskii 10 mockenhaupt seeger and sogge 14 up to operators with c 2 coefficients in smith 15 and tataru 21 23 similar results were obtained for the schrodinger equation in staffilani tataru 19 c 2 coefficients and in burq gerard tzvetkov 1 smooth coeffic ients in the variable coefficient elliptic case one should also mention sogge s l q

asymptotic expansions in time for solutions of schrodinger type equations let ia i p d v be a dissipative operator in l2 rn where p d is an elliptic differential operator of order m with real constant coefficients and v is a compact operator from the weighted sobolev space hm s rn to h0 p s rn s r for some m 1 let r z be the resolvent of a then an asymptotic expansion of r z as z approaches a critical value of the polynomial p is given the coefficient operators in the expansion are computed explicitly by using the resolvent expansion and the results of m murata 9 an asymptotic expansion of e ita as t is given

sampling and equidistribution theorems for elliptic second order operators lifting of eigenvalues and applications abstract we consider elliptic second order partial differential operators with lipschitz continuous leading order coefficients on finite cubes and the whole euclidean space we prove quantitative sampling and equidistribution theorems for eigenfunctions the estimates are scale free in the sense that for a sequence of growing cubes we obtain uniform estimates these results are applied to prove lifting of eigenvalues as well as the infimum of the essential spectrum and an uncertainty relation aka spectral inequality for short energy interval spectral projectors several applications including random operators are discussed in the proof we have to overcome several challenges posed by the variable coefficients of the leading term

local energy decay for the damped wave equation abstract we prove local energy decay for the damped wave equation on r d the problem which we consider is given by a long range metric perturbation of the euclidean laplacian with a short range absorption index under a geometric control assumption on the dissipation we obtain an almost optimal polynomial decay for the energy in suitable weighted spaces the proof relies on uniform estimates for the corresponding resolvent both for low and high frequencies these estimates are given by an improved dissipative version of mourre s commutators method

decay estimates and strichartz estimates of fourth order schrodinger operator abstract we study time decay estimates of the fourth order schrodinger operator h 2 v x in r d for d 3 and d 5 we analyze the low energy and high energy behaviour of resolvent r h z and then derive the jensen kato dispersion decay estimate and local decay estimate for e i t h p a c under suitable spectrum assumptions of h based on jensen kato type decay estimate and local decay estimate we obtain the l 1 l estimate of e i t h p a c in 3 dimension by ginibre argument and also establish the endpoint global strichartz estimates of e i t h p a c for d 5 furthermore using the local decay estimate and the georgescu larenas soffer conjugate operator method we prove the jensen kato type decay estimates for some functions of h

uniform resolvent estimates for schrodinger operator with an inverse square potential abstract we study the uniform resolvent estimates for schrodinger operator with a hardy type singular potential let l v v x where is the usual laplacian on r n and v x v 0 r 2 where r x x x and v 0 c 1 s n 1 is a real function such that the operator v 0 n 2 2 4 is a strictly positive operator on l 2 s n 1 we prove some new uniform weighted resolvent estimates and also obtain some uniform sobolev estimates associated with the operator l v

joint statistical design of double sampling x and s charts abstract in statistical quality control usually the mean and variance of a manufacturing process are monitored jointly by two statistical control charts e g a x chart and a r chart because of the efficiency of double sampling ds x charts in detecting shifts in process mean and ds s charts in process standard deviation it seems reasonable to investigate the joint ds x and s charts for statistical quality control in this paper a joint ds x and s chart scheme is proposed the statistical design of the joint ds x and s charts is defined and formulated as an optimization problem and solved using a genetic algorithm the performance of the joint ds x and s charts is also investigated the results of the investigation indicate that the joint ds x and s charts offer a better statistical efficiency in terms of average run length arl than combined ewma and cusum schemes omnibus ewma scheme over certain shift ranges when all schemes are optimized to detect certain shifts in comparison with the joint standard two stage samplings and variable sampling size x and r charts the joint ds charts offer a better statistical efficiency for all ranges of the shifts

problem solving during artificial selection of self replicating loops abstract past cellular automata models of self replication have generally done only one thing replicate themselves however it has recently been demonstrated that such self replicating structures can be programmed to also carry out a task during the replication process past models of this sort have been limited in that the program involved is copied unchanged from parent to child so that each generation of replicants is executing exactly the same program on exactly the same data here we take a different approach in which each replicant receives a distinct partial solution that is modified during replication under artificial selection replicants with promising solutions proliferate while those with failed solutions are lost we show that this approach can be applied successfully to solve an np complete problem the satisfiability problem bounds are given on the cellular space size and time needed to solve a given problem and simulations demonstrate that this approach works effectively these and other recent results raise the possibility of evolving self replicating structures that have a simulated metabolism or that carry out useful tasks

multivariate bayesian control chart a multivariate bayesian control chart for monitoring process mean under the assumption that the vector of process observations follows a multivariate normal distribution is considered traditional control charts such as hotelling s t2 ewma and cusum charts have been applied to control industrial processes characterized by several measurable variables it is well known that these traditional non bayesian process control techniques are not optimal but very few results regarding the structure of the bayesian control policy have been reported in the literature all dealing with the univariate finite horizon case in this paper we formulate the multivariate bayesian process control problem in the optimal stopping framework the objective is to find a stopping rule under partial observations minimizing the long run expected average cost per unit time for a given sample size and sampling interval under standard operating and cost assumptions it is proved that a control limit policy is optimal and an algorithm is presented to find the optimal control limit and the minimum average cost

endpoint resolvent estimates for compact riemannian manifolds we prove l p l p bounds for the resolvent of the laplace beltrami operator on a compact riemannian manifold of dimension n in the endpoint case p 2 n 1 n 3 it has the same behavior with respect to the spectral parameter z as its euclidean analogue due to kenig ruiz sogge provided a parabolic neighborhood of the positive half line is removed this is region is optimal for instance in the case of a sphere

a rank based multivariate cusum procedure we consider statistical process control when measurements are multivariate a cumulative sum cusum procedure is suggested in detecting a shift in the mean vector of the measurements which is based on the cross sectional antiranks of the measurements at each time point the measurements are ordered and their antiranks which are the indices of the order statistics are recorded when the process is in control and the joint distribution of the multivariate measurements satisfies some regularity conditions the antirank vector at each time point has a given distribution this distribution changes to some other distribution when the process is out of control and the components of the shift in the mean vector of the process are not all the same this cusum can therefore detect shifts in all directions except the one in which the components of the shift in the mean vector are all the same but not 0 the shift with equal components however can be easily detected by another univariate cusum the former cusu

a multivariate exponentially weighted moving average control chart a multivariate extension of the exponentially weighted moving average ewma control chart is presented and guidelines given for designing this easy to implement multivariate procedure a comparison shows that the average run length arl performance of this chart is similar to that of multivariate cumulative sum cusum control charts in detecting a shift in the mean vector of a multivariate normal distribution as with the hotelling s 2 and multivariate cusum charts the arl performance of the multivariate ewma chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter worst case scenarios show that hotelling s 2 charts should always be used in conjunction with multivariate cusum and ewma charts to avoid potential inertia problems examples are given to illustrate the use of the proposed procedure

control chart tests based on geometric moving averages a geometrical moving average gives the most recent observation the greatest weight and all previous observations weights decreasing in geometric progression from the most recent back to the first a graphical procedure for generating geometric moving averages is described in which the most recent observation is assigned a weight r the properties of control chart tests based on geometric moving averages are compared to tests based on ordinary moving averages

forecasting applications of an adaptive multiple exponential smoothing model this paper introduces a class of multiple exponential smoothing models useful in automated or minimal intervention industrial forecasting systems these models are an alternative to simple univariate exponential smoothing and trigg and leach type adaptive models which treat time series as unrelated and so cannot explicitly accommodate interrelationships that may exist between two or more time series moreover the multiple models are adaptive in that the smoothing matrix which is a generalization of the smoothing constant of univariate models changes from period to period maximum likelihood estimates of the model parameters including the full variance covariance structure as well as the smoothing matrix are provided thus freeing the model user from the need for making ad hoc estimates of parameter values a feature of simple univariate exponential smoothing the forecast performance of this multiple time series model is compared with that of other univariate models using automobile sales data and some promising results are obtained

strichartz estimates and local smoothing estimates for asymptotically flat schrodinger equations abstract in this article we study global in time strichartz estimates for the schrodinger evolution corresponding to long range perturbations of the euclidean laplacian this is a natural continuation of a recent article d tataru parametrices and dispersive estimates for schrodinger operators with variable coefficients amer j math 130 2008 571 634 of the third author where it is proved that local smoothing estimates imply strichartz estimates by d tataru parametrices and dispersive estimates for schrodinger operators with variable coefficients amer j math 130 2008 571 634 the local smoothing estimates are known to hold for small perturbations of the laplacian here we consider the case of large perturbations in three increasingly favorable scenarios i without non trapping assumptions we prove estimates outside a compact set modulo a lower order spatially localized error term ii with non trapping assumptions we prove global estimates modulo a lower order spatially localized error term and iii for time independent operators with no resonance or eigenvalue at the bottom of the spectrum we prove global estimates for the projection onto the continuous spectrum

on the cubic dirac equation with potential and the lochak majorana condition abstract we study a cubic dirac equation on r r 3 i t u d u v x u u u u perturbed by a large potential with almost critical regularity we prove global existence and scattering for small initial data in h 1 with additional angular regularity the main tool is an endpoint strichartz estimate for the perturbed dirac flow in particular the result covers the case of spherically symmetric data with small h 1 norm when the potential v has a suitable structure we prove global existence and scattering for large initial data having a small chiral component related to the lochak majorana condition

a self starting control chart for multivariate individual observations multivariate versions of cumulative sum exponentially weighted moving average ewma and hotelling s t2 charts typically assume knowledge of the in control process parameters or with a new or changed process use parameter estimates from an in control reference sample of preliminary observations in contrast the self starting chart begins controlling the process without the need for preliminary observations an advantage when production is slow or when the cost of early out of control production is high furthermore the use of estimated parameters substantially degrades the expected performance of conventional charts a problem avoided by the proposed chart the self starting chart uses the deviation of each observation vector from the average of all previous observations these deviations or innovations can be plotted on a t2 control chart or accumulated in a multivariate ewma mewma chart the run length performance is evaluated for step shifts occurring at various points and the mewma charts a

properties of the t2 control chart when parameters are estimated moments of the run length distribution are often used to design and study the performance of quality control charts in this article the run length distribution of the t2 chart for monitoring a multivariate process mean is analyzed it is assumed that the in control process observations are iid random samples from a multivariate normal distribution with unknown mean vector and covariance matrix it is shown that the in control run length distribution of the chart does not depend on the unknown process parameters furthermore it is shown that the out of control run length distribution of the chart depends only on the statistical distance between the in control and out of control mean vectors it follows that a performance analysis can be given without knowledge of the in control values of the parameters or their estimates the performance of charts constructed using traditional f distribution based control limits is studied recommendations are given for sample size requirements necessary to achieve desir

restriction theorems for orthonormal functions strichartz inequalities and uniform sobolev estimates we generalize the theorems of stein tomas and strichartz about surface restrictions of fourier transforms to systems of orthonormal functions with an optimal dependence on the number of functions we deduce the corresponding strichartz bounds for solutions to schr odinger equations up to the endpoint thereby solving an open problem of frank lewin lieb and seiringer we also prove uniform sobolev estimates in schatten spaces extending the results of kenig ruiz and sogge we finally provide applications of these results to a limiting absorption principle in schatten spaces to the well posedness of the hartree equation in schatten spaces to lieb thirring bounds for eigenvalues of schr odinger operators with complex potentials and to schatten properties of the scattering matrix

imbedded singular continuous spectrum for schrodinger operators 1 1 hv v x and some self adjoint boundary condition at zero the operator 1 1 describes a charged particle such as an electron in the electric field v x when v x is decaying quickly one expects the spectral and dynamical properties of hy to remain close to those of the free operator ho recall that with the operator 1 1 one can associate in a canonical way a spectral measure p see for example 6 2 which contains much information about the quantum system the classical result in this direction going back to the beginning of the century is that if v g l1 the spectral measure on the positive semi axis remains purely absolutely continuous in one dimension an absolutely continuous spectrum corresponds to the ballistic rate of propagation of the particle a natural question to ask is what are the critical rates of decay at which some changes in the spectral and dynamical properties of hy may happen as far as v x has any decay at all the essential spectrum coincides with 0 oo but the quality of the spectrum and dynamics may change in 1928 wigner and von neumann 27 showed that there exist potentials v x satisfying v x jsuch that hy has positive imbedded eigenvalue e 1 this is a purely quantum resonance phenomenon since v can be chosen arbitrarily small and the bound state originates from long range correlations in the potential rather than the usual confining effect naboko 17 and simon 25 provided constructions which show that much more drastic changes are possible if the potential decays arbitrarily slower than coulomb namely for any positive function h x which grows at infinity there exist potentials v such that v x yjgand hy has a dense set of positive eigenvalues due to some recent results 3 21 it is known that the absolutely continuous spectrum on the positive semi axis is preserved for v o c l x l 2 e and in fact for v g l2 8 more precisely for such potentials the absolutely continuous part of the spectral measure iac gives positive weight to any subset of 0 oo of positive lebesgue measure therefore the naboko

a markov chain model for the multivariate exponentially weighted moving averages control chart abstract a markov chain approximation is used to determine the run length performance of a multivariate statistical process control chart the markov chain approach is widely used in the analysis of univariate control charts we extend the advantages of this type of analysis to a multivariate exponentially weighted moving averages control chart the analysis can be applied whenever the multivariate control statistic can be modeled as a markov chain and the run length performance depends on the off target mean only through the noncentrality parameter

frequentist bayesian monte carlo test for mean vectors in high dimension abstract conventional methods for testing the mean vector of a p variate gaussian distribution require a sample size n greater than or equal to p but in high dimensional situations that is when n is smaller than p special and new adjustments are needed although bayesian empirical methods are well succeeded for testing in high dimension their performances are strongly dependent on the actual unknown covariance matrix of the gaussian random vector in this paper we introduce a hybrid frequentist bayesian monte carlo test and prove that i under the null hypothesis the performance of the proposed test is invariant with respect to the real unknown covariance matrix and ii the decision rule is valid which means that in terms of expected loss the performance of the proposed procedure can always be made as good as the exact bayesian test and in terms of type i error probability the method is always of level for arbitrary 0 1

a least angle regression control chart for multidimensional data in multidimensional applications it is very rare that all variables shift at the same time a statistical process control procedure would have superior efficiency when limited to the subset of variables likely responsible for the out of control conditions the key idea of this article consists of combining a variable selection method with a multivariate control chart to detect changes in both the mean and variability of a multidimensional process with gaussian errors in particular we develop a control chart for phase ii monitoring which integrates the least angle regression algorithm with a multivariate exponentially weighted moving average comparisons with related multivariate control schemes demonstrate the efficiency of the proposed control chart in a wide range of practical applications including profile and multistage process monitoring further the proposed scheme may also provide valuable diagnostic information for fault isolation supplemental materials including an r package are available

sharp counterexamples in unique continuation for second order elliptic equations we construct nontrivial solutions with compact support for the elliptic equation u v u with v lp p n 2 or v l w for n 3 and with v l1 for n 2 the same method also yields nontrivial solutions with compact support for the elliptic equation u w u with w lq p n or w lw for n 2 for the second order elliptic equations u v u in r 1 respectively u w u in r 2 we define the weak unique continuation property ucp respectively the strong unique continuation property sucp as follows let u be a solution to 1 which vanishes in an open set then u 0 ucp let u be a solution to 1 which vanishes of infinite order at some point x0 r then u 0 sucp research partially supported by the dfg and daad research partially supported by the nsf grants dms 9970297 int 9815286

multivariate control charts based on the james stein estimator abstract in this study we focus on improving parameter estimation in phase i study to construct more accurate phase ii control limits for monitoring multivariate quality characteristics for a multivariate normal distribution with unknown mean vector the usual mean estimator is known to be inadmissible under the squared error loss function when the dimension of the variables is greater than 2 shrinkage estimators such as the james stein estimators are shown to have better performance than the conventional estimators in the literature we utilize the james stein estimators to improve the phase i parameter estimation multivariate control limits for the phase ii monitoring based on the improved estimators are proposed in this study the resulting control charts js type charts are shown to have substantial performance improvement over the existing ones

multivariate exponentially weighted moving covariance matrix multivariate exponentially weighted moving average mewma charts are among the best control charts for detecting small changes in any direction the well known mewma is directed at changes in the mean vector but changes can occur in either the location or the variability of the correlated multivariate quality characteristics calling for parallel methodologies for detecting changes in the covariance matrix this article discusses an exponentially weighted moving covariance matrix for monitoring the stability of the covariance matrix of a process used together with the location mewma this chart provides a way to satisfy shewhart s dictum that proper process control monitor both mean and variability we show that the chart is competitive generally outperforming current control charts for the covariance matrix

exponential bounds and absence of positive eigenvalues for n body schrodinger operators for a large class ofn body potentialsv we prove that if is an eigenfunction of v with eigenvaluee then sup 2 e 0 exp x l2 is either a threshold or consequences of this result are the absence of positive eigenvalues and optimal l2 exponential lower bounds

weighted energy decay for 3d klein gordon equation abstract we obtain a dispersive long time decay in weighted energy norms for solutions of the 3d klein gordon equation with generic potential the decay extends the results obtained by jensen and kato for the 3d schrodinger equation for the proof we modify the spectral approach of jensen and kato to make it applicable to relativistic equations

multivariate profile charts for statistical process control the multivariate profile mp chart is a new control chart for simultaneous display of univariate and multivariate statistics it is designed to analyze and display extended structures of statistical process control data for various cases of grouping reference distribution and use of nominal specifications for each group of observations the scaled deviations from reference values are portrayed together as a modified profile plot symbol the vertical location of the symbol is determined by the multivariate distance of the vector of means from the reference values the graphical display in the mp chart enjoys improved visual characteristics as compared with previously suggested methods moreover the perceptual tasks required by the use of the mp chart provide higher accuracy in retrieving the quantitative information this graphical display is used to display other combined univariate and multivariate statistics such as measures of dispersion principal components and cumulative sums

a positive density analogue of the lieb thirring inequality the lieb thirring inequalities give a bound on the negative eigenvalues of a schrodinger operator in terms of an l p norm of the potential these are dual to bounds on the h 1 norms of a system of orthonormal functions here we extend these bounds to analogous inequalities for perturbations of the fermi sea of noninteracting particles i e for perturbations of the continuous spectrum of the laplacian by local potentials

resolvent expansion and time decay of the wave functions for two dimensional magnetic schrodinger operators we consider two dimensional schrodinger operators h b v given by eq 1 1 below we prove that under certain regularity and decay assumptions on b and v the character of the expansion for the resolvent h b v 1 as 0 is determined by the flux of the magnetic field b through mathbb r 2 subsequently we derive the leading term of the asymptotic expansion of the unitary group e ith b v as t and show how the magnetic field improves its decay in t with respect to the decay of the unitary group e ith 0 v

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

a multivariate change point model for statistical process control multivariate statistical process control spc carries out ongoing checks to ensure that a process is in control these checks on the process are traditionally done by t2 multivariate cusum and multivariate exponentially weighted moving average control charts these traditional spc charts assume that the in control true parameters are known exactly and use these assumed true values to set the control limits the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample it is increasingly recognized that this phase i study needs to involve large samples if the parameter estimates are to provide run behavior matching that of the known parameter situation but apart from the general undesirability of large and thus expensive studies preliminary to actual charting some industrial settings have a paucity of relevant data for estimating the process parameters an attractive alternative to traditional charting methods when mon

a multivariate sign ewma control chart nonparametric control charts are useful in statistical process control spc when there is a lack of or limited knowledge about the underlying process distribution especially when the process measurement is multivariate this article develops a new multivariate spc methodology for monitoring location parameters it is based on adapting a powerful multivariate sign test to online sequential monitoring the weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control ewma scheme which results in a nonparametric counterpart of the classical multivariate ewma mewma it is affine invariant and has a strictly distribution free property over a broad class of population models that is the in control ic run length distribution can attain or is always very close to the nominal one when using the same control limit designed for a multivariate normal distribution moreover when the process distribution comes from the elli

absence of embedded eigenvalues for riemannian laplacians in this paper we study absence of embedded eigenvalues for schrodinger operators on non compact connected riemannian manifolds a principal example is given by a manifold with an end possibly more than one in which geodesic coordinates are naturally defined in this case one of our geometric conditions is a positive lower bound of the second fundamental form of angular submanifolds at infinity inside the end another condition is an upper bound of the trace of this quantity while a third one is a bound of the derivatives of part of the trace some oscillatory behaviour of the trace is allowed in addition to geometric bounds we need conditions on the potential a regularity property of the domain of the schrodinger operator and the unique continuation property examples include ends endowed with asymptotic euclidean or hyperbolic metrics

unique continuation from infinity for linear waves abstract we prove various uniqueness results from null infinity for linear waves on asymptotically flat space times assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities we derive that the solution must vanish in an open set in the interior we find that the parts of infinity where we must impose a vanishing condition depend strongly on the background geometry in particular for backgrounds with positive mass such as schwarzschild or kerr the required assumptions are much weaker than the ones in the minkowski space time the results are nearly optimal in many respects they can be considered analogues of uniqueness from infinity results for second order elliptic operators this work is partly motivated by questions in general relativity

self reproduction in cellular automata abstract self reproduction in cellular automata is discussed with reference to the models of von neumann and codd the conclusion is drawn that although the capacity for universal construction is a sufficient condition for self reproduction it is not a necessary condition slightly more liberal criteria for what constitutes genuine self reproduction are introduced and a simple self reproducing structure is exhibited which satisfies these new criteria this structure achieves its simplicity by storing its description in a dynamic loop rather than on a static tape

trace class conditions for functions of schrodinger operators we consider the difference f delta v f delta of functions of schrodinger operators in l 2 mathbb r d and provide conditions under which this difference is trace class we are particularly interested in non smooth functions f and in v belonging only to some l p space this is motivated by applications in mathematical physics related to lieb thirring inequalities we show that in the particular case of schrodinger operators the well known sufficient conditions on f based on a general operator theoretic result due to v peller can be considerably relaxed we prove similar theorems for f delta v f delta frac d d alpha f delta alpha v alpha 0 our key idea is the use of the limiting absorption principle

self starting multivariate exponentially weighted moving average control charting multivariate control charts are valuable tools for industrial quality control the conventional discussion of them rests on the presumption that the in control process parameters are known a priori the more common reality is that practitioners plug in parameter estimates gathered from a special phase i sample to establish parameter values for the charts but no sample will establish the exact process parameters and quite small random errors translate into serious distortions of the run behavior particularly of sensitive charts and can affect chart performance so called self starting methods can begin the control of the process right after startup without the preliminary step of a large phase i sample univariate self starting methods for converting the unknown parameter stream of process readings into a known parameter sequence have been available for some time now this article develops a multivariate equivalent by providing a way to transform the process readings into a stream of vectors followin

weighted dispersive estimates for two dimensional schrodinger operators with aharonov bohm magnetic field abstract we consider two dimensional schrodinger operators h with an aharonov bohm magnetic field and an additional electric potential we obtain an explicit leading term of the asymptotic expansion of the unitary group e i t h for t in weighted l 2 spaces in particular we show that the magnetic field improves the decay of e i t h with respect to the unitary group of non magnetic schrodinger operators and that the decay rate in time is determined by the magnetic flux

agmon kato kuroda theorems for a large class of perturbations we prove asymptotic completeness for operators of the form h l on l2 rd d 2 where l is an admissible perturbation our class of admissible perturbations contains multiplication operators defined by real valued potentials v lq rd q d 2 d 1 2 if d 2 then we require q 1 3 2 as well as real valued potentials v satisfying a global kato condition the class of admissible perturbations also contains first order differential operators of the form a a for suitable vector potentials a our main technical statement is a new limiting absorption principle which we prove using techniques from harmonic analysis related to the stein tomas restriction theorem