a class of superrigid group von neumann algebras we prove that for any group g in a fairly large class of generalized wreath product groups the associated von neumann algebra lg completely remembers the group g more precisely if lg is isomorphic to the von neumann algebra l of an arbitrary countable group then must be isomorphic to g this represents the rst superrigidity result pertaining to group von neumann algebras

on ii1 factors arising from 2 cocycles of w rigid groups we consider ii1 factors l g arising from 2 cocyles h2 g t on groups g containing infinite normal subgroups h g with the relative property t i e g w rigid we prove that given any separable ii1 factor m the set of 2 cocycles h h2 h t with the property that l g is embeddable into m is at most countable we use this result the relative property t of z2 z2 for sl 2 z non amenable and the fact that every cocycle h2 z2 t t extends to a cocycle on z2 sl 2 z to show that the one parameter family of ii1 factors m l z2 t are mutually non isomorphic modulo countable sets and cannot all be embedded into the same separable ii1 factor other examples and applications are discussed

ergodic actions of compact groups on operator algebras i general theory we introduce some general machinery for studying ergodic actions of compact groups on operator algebras the most important tool being that of the multiplicity map this theory is used subsequently in 42 to prove that a von neumann algebra on which su 2 acts ergodically is necessarily of type i

on the fractional adams method the generalized adams bashforth moulton method often simply called the fractional adams method is a useful numerical algorithm for solving a fractional ordinary differential equation d ay t f t y t y k 0 y 0 k k 0 1 n 1 where a 0 email protected email protected is the first integer not less than a and d ay t is the ath order fractional derivative of y t in the caputo sense although error analyses for this fractional adams method have been given for a 0 1 email protected c 1 a 0 t c 0 1 email protected c 3 g there are still some unsolved problems i the error estimates for email protected 0 1 email protected c 3 g ii the error estimates for email protected 0 1 email protected c 2 g iii the solution y t having some special forms in this paper we mainly study the error analyses of the fractional adams method for the fractional ordinary differential equations for the three cases i iii numerical simulations are also included which are in line with the theoretical analysis

a numeric analytic method for approximating a giving up smoking model containing fractional derivatives smoking is one of the main causes of health problems and continues to be one of the world s most significant health challenges in this paper the dynamics of a giving up smoking model containing fractional derivatives is studied numerically the multistep generalized differential transform method for short msgdtm is employed to compute accurate approximate solutions to a giving up smoking model of fractional order the unique positive solution for the fractional order model is presented a comparative study between the new algorithm and the classical runge kutta method is presented in the case of integer order derivatives the solutions obtained are also presented graphically

analytical and numerical solutions of a nonlinear alcoholism model via variable order fractional differential equations abstract in this paper we analyze an alcoholism model which involves the impact of twitter via liouville caputo and atangana baleanu caputo fractional derivatives with constant and variable order two fractional mathematical models are considered with and without delay special solutions using an iterative scheme via laplace and sumudu transform were obtained we studied the uniqueness and existence of the solutions employing the fixed point postulate the generalized model with variable order was solved numerically via the adams method and the adams bashforth moulton scheme stability and convergence of the numerical solutions were presented in details numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient therefore by including both the fractional derivatives and finite time delays in the alcoholism model studied we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking

some unique group measure space decomposition results using an approach emerging from the theory of closable deriva tions on von neumann algebras we exhibit a class of groups cr satisfying the following property given any groups 1 2 2 cr then any free ergodic measure preserving action on a probability space 1 2 y x gives rise to a von neumann algebra with unique group measure space cartan subalgebra pairing this result with popa s orbit equivalence superrigidity theorem we obtain new examples of w superrigid actions

a new predictor corrector method for fractional differential equations we present a new predictor corrector method to solve non linear fractional differential equations involving caputo derivative the proposed method is compared with the fractional adams method numerous illustrative examples discussed here demonstrate that the new method is more accurate and time efficient a detailed error analysis given points to the higher accuracy of the new method furthermore the proposed method when applied to fractional analog of chaotic system introduced by bhalekar and daftardar gejji unravels the underlying rich dynamics of the system

some oe and w rigidity results for actions by wreath product groups we use deformation rigidity theory in the von neumann algebra framework to study probability measure preserving actions by wreath product groups in particular we single out large families of wreath product groups satisfying various types of orbit equivalence oe rigidity for instance we show that whenever h k are icc property t groups such that h and k admit stably orbit equivalent action and such that h and k are ergodic then automatically is stably orbit equivalent to and h is stably orbit equivalent to k rigidity results for von neumann algebras arising from certain actions of such groups i e w rigidity results are also obtained

analysis of covariance in randomized trials more precision and valid confidence intervals without model assumptions covariate adjustment in the randomized trial context refers to an estimator of the average treatment effect that adjusts for chance imbalances between study arms in baseline variables called covariates the baseline variables could include for example age sex disease severity and biomarkers according to two surveys of clinical trial reports there is confusion about the statistical properties of covariate adjustment we focus on the analysis of covariance ancova estimator which involves fitting a linear model for the outcome given the treatment arm and baseline variables and trials that use simple randomization with equal probability of assignment to treatment and control we prove the following new to the best of our knowledge robustness property of ancova to arbitrary model misspecification not only is the ancova point estimate consistent as proved by yang and tsiatis 2001 but so is its standard error this implies that confidence intervals and hypothesis tests conducted as if the linear model were correct are still asymptotically valid even when the linear model is arbitrarily misspecified for example when the baseline variables are nonlinearly related to the outcome or there is treatment effect heterogeneity we also give a simple robust formula for the variance reduction equivalently sample size reduction from using ancova by reanalyzing completed randomized trials for mild cognitive impairment schizophrenia and depression we demonstrate how ancova can achieve variance reductions of 4 to 32

orbit equivalence rigidity and bounded cohomology we establish new results and introduce new methods in the theory of measurable orbit equivalence using bounded cohomology of group representations our rigidity statements hold for a wide uncountable class of groups arising from negative curvature geometry amongst our applications are a measurable mostow type rigidity theorems for products of negatively curved groups b prime factorization results for measure equivalence c superrigidity for orbit equivalence d the first examples of continua of type ii1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic

on the first continuous l 2 cohomology of free group factors abstract we prove that the first continuous l 2 cohomology of free group factors vanishes this answers a question by andreas thom regarding continuity properties of free difference quotients and shows that one cannot distinguish free group factors by means of first continuous l 2 betti number

on the stability and convergence of the time fractional variable order telegraph equation in this work we have generalized the time fractional telegraph equation using the concept of derivative of fractional variable order the generalized equation is called time fractional variable order telegraph equation this new equation was solved numerically via the crank nicholson scheme stability and convergence of the numerical solution were presented in details numerical simulations of the approximate solution of the time fractional variable order telegraph equation were presented for different values of the grid point

robustness of ancova in randomized trials with unequal randomization randomized trials with continuous outcomes are often analyzed using analysis of covariance ancova with adjustment for prognostic baseline covariates the ancova estimator of the treatment effect is consistent under arbitrary model misspecification in an article recently published in the journal wang et al proved the model based variance estimator for the treatment effect is also consistent under outcome model misspecification assuming the probability of randomization to each treatment is 1 2 in this reader reaction we derive explicit expressions which show that when randomization is unequal the model based variance estimator can be biased upwards or downwards in contrast robust sandwich variance estimators can provide asymptotically valid inferences under arbitrary misspecification even when randomization probabilities are not equal

ergodic actions of compact groups on operator algebras iii classification for su 2 we prove that the only ergodic actions ofsu 2 are on type i von neumann algebras using the theory developed in 8

l 2 rigidity in von neumann algebras we introduce the notion of l2 rigidity for von neumann algebras a generalization of property t which can be viewed as an analogue for the vanishing of 1 cohomology into the left regular representation of a group we show that l2 rigidity passes to normalizers and is satisfied by nonamenable ii1 factors which are non prime have property or are weakly rigid as a consequence we obtain that if m is a free product of diffuse von neumann algebras or if m l where is a finitely generated group with 1 2 0 then any nonamenable regular subfactor of m is prime and does not have properties or t in particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of n ozawa

a new iterative technique for a fractional model of nonlinear zakharov kuznetsov equations via sumudu transform abstract the main objective of this paper is to suggest a new computational technique namely new iterative sumudu transform method nistm to solve numerically nonlinear time fractional zakharov kuznetsov fzk equation in two dimensions we implemented the proposed technique on two test examples plotted the solution and compared the absolute error with the variational iterative technique vim and homotopy perturbation transform method hptm

a modified numerical scheme and convergence analysis for fractional model of lienard s equation abstract the key purpose of the present work is to constitute a numerical algorithm based on fractional homotopy analysis transform method to study the fractional model of lienard s equations the lienard s equation describes the oscillating circuits the suggested scheme is a merger of homotopy analysis technique classical laplace transform and homotopy polynomials the uniqueness and convergence analysis of the solution are also discussed the numerical and graphical results elucidate that the suggested approach is very straightforward and accurate

strong rigidity of generalized bernoulli actions and computations of their symmetry groups abstract we study equivalence relations and ii 1 factors associated with quotients of generalized bernoulli actions of kazhdan groups specific families of these actions are entirely classified up to isomorphism of ii 1 factors this yields explicit computations of outer automorphism and fundamental groups in particular every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic ii 1 factors

rigidity results for wreath product ii1 factors abstract we consider ii 1 factors of the form m g b g where either i b is a non hyperfinite ii 1 factor and g is an icc amenable group or ii b is a weakly rigid ii 1 factor and g is icc group and where g acts on g b by bernoulli shifts we prove that isomorphism of two such factors implies cocycle conjugacy of the corresponding bernoulli shift actions in particular the groups acting must be isomorphic as a consequence we can distinguish between certain classes of group von neumann algebras associated to wreath product groups

weak containment rigidity for distal actions abstract we prove that if a measure distal action of a countable group is weakly contained in a strongly ergodic probability measure preserving action of then is a factor of in particular this applies when is a compact action as a consequence we show that the weak equivalence class of any strongly ergodic action completely remembers the weak isomorphism class of the maximal distal factor arising in the furstenberg zimmer structure theorem

fractional differential models for anomalous diffusion abstract in this study we investigate three kinds of fractional differential models distributed order model variable order model and random order model for characterization of anomalous diffusion the characteristics physical advantages and potential applications of each model are highlighted the numerical simulations also validate our analytical and comparison results furthermore a generalized distributed variable order model and a more generalized distributed variable random order model are proposed to combine the advantages of distributed order model variable order model and random order model

analysis of a system of nonautonomous fractional differential equations involving caputo derivatives abstract we discuss existence uniqueness and stability of solutions of the system of nonlinear fractional differential equations d i y i t f i t y 1 y n y i k c k i 1 i n 1 k m i where m i i m i 1 and d i denotes caputo fractional derivative linear and nonlinear systems have been solved using banach fixed point theorem

measure equivalence rigidity and bi exactness of groups we get three types of results on measurable group theory direct product groups of ozawa s class s groups wreath product groups and amalgamated free products we prove measure equivalence factorization results on direct product groups of ozawa s class s groups as consequences monod shalom type orbit equivalence rigidity theorems follow we prove that if two wreath product groups a g b of non amenable exact direct product groups g with amenable bases a b are measure equivalent then g and are measure equivalent we get bass serre rigidity results on amalgamated free products of non amenable exact direct product groups

solvability and optimal controls of impulsive hilfer fractional delay evolution inclusions with clarke subdifferential abstract we study the solvability and optimal controls of an impulsive nonlinear hilfer fractional delay evolution inclusion in banach spaces for the main results we use fractional calculus fixed point technique semigroup theory and multivalued analysis we introduce the notion of clarke delay subdifferential to continue and extend previous works in the field we prove an existence result of optimal control pair for lagrange problem l p under appropriate set of sufficient conditions finally as application we give an impulsive control partial differential inclusion with hilfer fractional derivative

classification of type iii bernoulli crossed products abstract crossed products with noncommutative bernoulli actions were introduced by connes as the first examples of full factors of type i i i this article provides a complete classification of the factors p f n f n where f n is the free group and p is an amenable factor with an almost periodic state we show that these factors are completely classified by the rank n of the free group f n and connes s sd invariant we prove similar results for free product groups as well as for classes of generalized bernoulli actions

t property and nonisomorphic full factors of types ii and iii abstract the actions of t groups on von neumann s hyperfinite algebras are studied it is proved that there exist factors of type ii with different countable fundamental groups and hence different actions it is also proved that there exist nonisomorphic full factors of type iii 1 with any fixed invariant sd

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

stability analysis for a single degree of freedom fractional oscillator abstract this paper investigates the analytical solution asymptotical stability and bibo stability of a single degree of freedom sdof fractional oscillator by applying the laplace transform an analytical solution is provided in terms of prabhakar s function with the decomposition of state space an equivalent incommensurate fractional differential system is obtained new criteria on the asymptotical stability and bibo stability are derived based on the distribution of the characteristic roots and the poles respectively an example under three diverse cases is presented to illustrate the validity and flexibility of our main results and the memory and hereditary effects of the fractional orders

asymptotic structure of free araki woods factors the purpose of this paper is to investigate the structure of shlyakhtenko s free araki woods factors using the framework of ultraproduct von neumann algebras we first prove that all the free araki woods factors gamma h mathbb r u t prime prime are omega solid in the following sense for every von neumann subalgebra q subset gamma h mathbb r u t prime prime that is the range of a faithful normal conditional expectation and such that the relative commutant q cap m omega is diffuse we have that q is amenable next we prove that the continuous cores of the free araki woods factors gamma h mathbb r u t prime prime associated with mixing orthogonal representations u mathbb r rightarrow mathcal o h mathbb r are omega solid type mathrm ii infty factors finally when the orthogonal representation u mathbb r rightarrow mathcal o h mathbb r is weakly mixing we prove a dichotomy result for all the von neumann subalgebras q subset gamma h mathbb r u t prime prime that are globally invariant under the modular automorphism group sigma t varphi u of the free quasi free state varphi u

actions of rigid groups on uhf algebras let be a countably infinite property t group and let d be uhf algebra of infinite type we prove that there exists a continuum of pairwise non weakly cocycle conjugate strongly outer actions of on d the proof consists in assigning to any second countable abelian pro p group g a strongly outer action of on d whose weak cocycle conjugacy class completely remembers the group g the group g is reconstructed from the action through its weak 1 cohomology set endowed with a canonical pairing function our construction also shows the following stronger statement the relations of conjugacy cocycle conjugacy and weak cocycle conjugacy of strongly outer actions of on d are complete analytic sets and in particular not borel the same conclusions hold more generally when is only assumed to contain an infinite subgroup with relative property t and for actions on not necessarily simple separable nuclear uhf absorbing self absorbing c algebras with at least one trace finally we use the techniques of this paper to construct outer actions on r with prescribed cohomology precisely for every infinite property t group and for every countable abelian group we construct an outer action of on r whose 1 cohomology is isomorphic to

extreme values for solution to uncertain fractional differential equation and application to american option pricing model abstract uncertain fractional differential equation plays an important role of describing uncertain dynamic process this paper focuses on extreme values including supremum and infimum for solution to an uncertain fractional differential equation for the caputo type theorems for the inverse uncertain distributions of the extreme values are given based on the definition of path and then numerical algorithms for them are designed numerical examples are shown for validating the availability about algorithms the absolute errors between the numerical and analytical results are also presented to demonstrate the accuracy of the algorithms finally as an application of the extreme values an uncertain stock model is proposed on the basis of uncertain fractional differential equation of the caputo type the american option pricing formulas of such stock model are studied by using the proposed extreme theorems besides numerical calculations are also illustrated with respect to different parameters p

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

optimality variability power we provide a theoretical template for the comparison of response adaptive randomization procedures for clinical trials using a taylor expansion of the noncentrality parameter of the usual chi squared test for binary responses we show explicitly the relationship among the target allocation proportion the bias of the randomization procedure from that target and the variability induced by the randomization procedure we also generalize this relationship for more than two treatments under various multivariate alternatives this formulation allows us to directly evaluate and compare different response adaptive randomization procedures and different target allocations in terms of power and expected treatment failure rate without relying on simulation for k 2 treatments we compare four response adaptive randomization procedures and three target allocations based on multiple objective optimality criteria we conclude that the drop the loser rule and the doubly adaptive biased coin design are clearly super

some rigidity results for non commutative bernoulli shifts abstract we introduce the outer conjugacy invariants s s s for cocycle actions of discrete groups g on type ii 1 factors n as the set of real numbers t 0 for which the amplification t of can be perturbed to an action respectively to a weakly mixing action we calculate explicitly s s s and the fundamental group of f in the case g has infinite normal subgroups with the relative property t e g when g itself has the property t of kazhdan and is an action of g on the hyperfinite ii 1 factor by connes stormer bernoulli shifts of weights t i i thus s s and f coincide with the multiplicative subgroup s of r generated by the ratios t i t j i j while s z if s 1 i e when all weights are equal and s r otherwise in fact we calculate all the 1 cohomology picture of t t 0 and classify the actions g in terms of their weights t i i in particular we show that any 1 cocycle for g vanishes modulo scalars and that two such actions are cocycle conjugate iff they are conjugate also any cocycle action obtained by reducing a bernoulli action of a group g as above on n g g m n n c tr g to the algebra pnp for p a projection in n p 0 1 cannot be perturbed to a genuine action

on solid ergodicity for gaussian actions we investigate gaussian actions through the study of their crossed product von neumann algebra the motivational result is chifan and ioana s ergodic decomposition theorem for bernoulli actions chifan and ioana 2010 4 that we generalize to gaussian actions theorem a we also give general structural results theorems 3 4 and 3 8 that allow us to get a more accurate result at the level of von neumann algebras more precisely for a large class of gaussian actions x we show that any subfactor n of l x containing l x is either hyperfinite or is non gamma and prime at the end of the article we show a similar result for bogoliubov actions

orbit equivalence rigidity consider a countable group acting ergodically by measure p reserving transformations on a probability space x and let r be the corresponding orbit equivalence relation on x the following rigidity phenomenon is shown there exist group actions such that the equivalence relation r on x determines the group and the action x uniquely up to finite groups the natural action of sln z on the n torus r n z n for n 2 is one of such examples the interpretation of these results in the context of von neumann algebras provides some support to the conjecture of connes on rigidity of group algebras for groups with property t our rigidity results also give examples of countable equivalence relations of type ii1 which cannot be generated mod 0 by a free action of any group this gives a negative answer to a long standing problem of feldman and moore

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method