a hypothesis testing approach toward identifying active contrasts the problem of identifying the active contrasts in an unreplicated fractional factorial design is approached from a hypothesis testing point of view the null hypothesis that all contrasts are inactive is first tested and if rejected the active contrasts causing rejection are identified and estimated the method is illustrated with examples from box and meyer compared with the confidence interval approach of dong and lenth and found to be a worthy competitor

compact finite difference method for the fractional diffusion equation high order compact finite difference scheme for solving one dimensional fractional diffusion equation is considered in this paper after approximating the second order derivative with respect to space by the compact finite difference we use the grunwald letnikov discretization of the riemann liouville derivative to obtain a fully discrete implicit scheme we analyze the local truncation error and discuss the stability using the fourier method then we prove that the compact finite difference scheme converges with the spatial accuracy of fourth order using matrix analysis numerical results are provided to verify the accuracy and efficiency of the proposed algorithm

fractional calculus a new approach to the analysis of generalized fourth order diffusion wave equations the homotopy perturbation method is applied to the generalized fourth order fractional diffusion wave equations the problem is formulated in the caputo sense moreover a reliable scheme for calculating nonlinear operators is proposed the results reveal that the present method is very effective and convenient

the fate of the wilson fisher fixed point in non commutative ϕ4 in this article we study non commutative vector sigma model with the most general 4 interaction on moyal weyl spaces we compute the 2 and 4 point functions to all orders in the large n limit and then apply the approximate wilson renormalization group recursion formula to study the renormalized coupling constants of the theory the non commutative wilson fisher fixed point interpolates between the commutative wilson fisher fixed point of the ising universality class which is found to lie at zero value of the critical coupling constant a of the zero dimensional reduction of the theory and a novel strongly interacting fixed point which lies at infinite value of a corresponding to maximal non commutativity beyond which the two sheeted structure of a as a function of the dilation parameter disappears

parametric representation of covariant noncommutative qft models we extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call covariant because their power counting is definitely more difficult to obtain this class of theories is important since it includes gauge theories which should be relevant for the quantum hall effect

a compact finite difference scheme for the fractional sub diffusion equations in this paper a compact finite difference scheme for the fractional sub diffusion equations is derived after a transformation of the original problem the l1 discretization is applied for the time fractional part and fourth order accuracy compact approximation for the second order space derivative the unique solvability of the difference solution is discussed the stability and convergence of the finite difference scheme in maximum norm are proved using the energy method where a new inner product is introduced for the theoretical analysis the technique is quite novel and different from previous analytical methods finally a numerical example is provided to show the effectiveness and accuracy of the method

identifying active contrasts by stepwise testing unreplicated fractional factorial designs are frequently used in industrial experimentation and are characterized by the absence of degrees of freedom for estimation of the error variance this article presents step down and step up testing procedures that efficiently identify the active contrasts significant effects in such experiments and simultaneously provide an accurate estimate of the error variance the methods allow the user to restrict the experimentwise error rate to a prespecified level use of the new methods is illustrated in terms of standard examples from the literature simulation shows that a version of the step up procedure outperforms its competitors

a preconditioned fast quadratic spline collocation method for two sided space fractional partial differential equations abstract quadratic spline collocation methods for the one and two dimensional fractional diffusion equations are proposed by carefully exploring the mathematical structure of the coefficient matrix we propose a matrix free fast krylov subspace iterative solver for the corresponding quadratic spline collocation scheme and then preconditioning technique is applied to further accelerate the convergence of the fast krylov subspace iterative method it shows that the fast quadratic spline collocation scheme has greatly reduced the computational cost from o n 2 to o n log n per iteration and memory requirement from o n 2 to o n while still well approximates the fractional diffusion equations without any accuracy lost numerical experiments are given to demonstrate the efficiency and effectiveness of the fast method

compact difference schemes for the modified anomalous fractional sub diffusion equation and the fractional diffusion wave equation in this paper compact finite difference schemes for the modified anomalous fractional sub diffusion equation and fractional diffusion wave equation are studied schemes proposed previously can at most achieve temporal accuracy of order which depends on the order of fractional derivatives in the equations and is usually less than two based on the idea of weighted and shifted grunwald difference operator we establish schemes with temporal and spatial accuracy order equal to two and four respectively

constructive renormalization for φ24 theory with loop vertex expansion in this paper we construct the two dimensional euclidean 4 quantum field theory using the method of loop vertex expansion we reproduce the results of standard constructive theory for example the borel summability of the schwinger functions in the coupling constant our method should be also suitable for the future construction of grosse wulkenhaar models on non commutative space time

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

a non polynomial numerical scheme for fourth order fractional diffusion wave model abstract in this paper we tackle the numerical treatment of a fourth order fractional diffusion wave problem by using parametric quintic spline in the spatial dimension and an approximation of caputo derivatives at half points we propose a numerical scheme and rigorously prove its solvability convergence and stability in maximum norm it is shown that the theoretical convergence order improves those of earlier work to confirm simulation is carried out to demonstrate the numerical efficiency of the proposed scheme as well as the better performance over other methods

on finite difference methods for fourth order fractional diffusion wave and subdiffusion systems abstract in this paper firstly the finite difference method is explored for the fourth order fractional diffusion wave system the method is proved to be uniquely solvable stable and convergent in l norm by the energy method then we examine a subdiffusion system and present the numerical analysis using a different method numerical experiments are provided to demonstrate the accuracy and efficiency of the proposed schemes

renormalisation of noncommutative ϕ 4 theory by multi scale analysis in this paper we give a much more efficient proof that the real euclidean 4 model on the four dimensional moyal plane is renormalisable to all orders we prove rigorous bounds on the propagator which complete the previous renormalisation proof based on renormalisation group equations for non local matrix models on the other hand our bounds permit a powerful multi scale analysis of the resulting ribbon graphs here the dual graphs play a particular role because the angular momentum conservation is conveniently represented in the dual picture choosing a spanning tree in the dual graph according to the scale attribution we prove that the summation over the loop angular momenta can be performed at no cost so that the power counting is reduced to the balance of the number of propagators versus the number of completely inner vertices in subgraphs of the dual graph

modified riemann liouville derivative and fractional taylor series of nondifferentiable functions further results the paper gives some results and improves the derivation of the fractional taylor s series of nondifferentiable functions obtained recently in the form f g h e a h ad g a f g 0 a 1 where e a is the mittag leffier function here one defines fractional derivative as the limit of fractional difference and by this way one can circumvent the problem which arises with the definition of the fractional derivative of constant using riemann liouville definition as a result a modified riemann liouville definition is proposed which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one s in order to support this f taylor series one shows how its first term can be obtained directly in the form of a mean value formula the fractional derivative of the dirac delta function is obtained together with the fractional taylor s series of multivariate functions the relation with irreversibility of time and symmetry breaking is exhibited and to some extent this f taylor s series generalizes the fractional mean value formula obtained a few years ago by kolwantar

a new conservative finite difference scheme for the rosenau equation a conservative difference scheme is given for the kdv like rosenau equation the unique solvability of numerical solutions is shown a priori bound convergence and stability of the difference scheme are proved

control of error rates in adaptive analysis of orthogonal saturated designs individual and simultaneous confidence intervals using the data adaptively are constructed for the effects in orthogonal saturated designs under the assumption of effect sparsity the minimum coverage probabilities of the intervals are equal to the nominal level 1

a permutation test for effects in an unreplicated factorial design a permutation test is proposed for examining the significance of effects in unreplicated factorial experiments the procedure tests each effect with a separate sampling distribution using a test statistic that is equivalent to the optimal invariant decision rule of birnbaum the proposed test is more flexible than other methods proposed for the same situation because it requires no a priori assumptions regarding the underlying distribution of the data nor does it impose any practical restriction on the number of potentially significant effects present

inference for effect saturated fractional factorials industrial scientists and engineers often use experimental designs in which all degrees of freedom are used to estimate effects and consequently no classical estimate of the error is possible robust scale estimates provide an alternative measure of the error in this study several such scale estimators are evaluated based on the power or related significance tests the pseudo standard error method of lenth provides the best overall performance lenth s t approximation for critical values was found to be inaccurate however so new tables are provided additional recommendations are made according to the experimenter s prior belief in the number of likely important factors

a novel expansion iterative method for solving linear partial differential equations of fractional order in this manuscript we implement a relatively new analytic iterative technique for solving time space fractional linear partial differential equations subject to given constraints conditions based on the generalized taylor series formula the solution methodology is based on generating the multiple fractional power series expansion solution in the form of a rapidly convergent series with minimum size of calculations this method can be used as an alternative to obtain analytic solutions of different types of fractional linear partial differential equations applied in mathematics physics and engineering some numerical test applications were analyzed to illustrate the procedure and to confirm the performance of the proposed method in order to show its potentiality generality and accuracy for solving such equations with different constraints conditions numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm

a survey on parametric spline function approximation this survey paper contains a large amount of material and indeed can serve as an introduction to some of the ideas and methods for the solution of ordinary and partial differential equations starting from schoenberg s work quart appl math 4 1946 345 369 the parametric spline function which depends on a parameter w 0 is reduces to the ordinary cubic or quintic spline for w 0 a note on parametric spline function approximation which is special case of this work has been published in comp math applics 29 1995 67 73 this article deals with the odd order parametric spline relations

step up simultaneous tests for identifying active effects in orthogonal saturated designs a sequence of null hypotheses regarding the number of negligible effects zero effects in orthogonal saturated designs is formulated two step up simultaneous testing procedures are proposed to identify active effects nonzero effects under the commonly used assumption of effect sparsity it is shown that each procedure controls the experimentwise error rate at a given a level in the strong sense

generalized differential transform method application to differential equations of fractional order abstract in this paper we propose a new generalization of the one dimensional differential transform method that will extend the application of the method to differential equations of fractional order the new generalization is based on generalized taylor s formula and caputo fractional derivative several illustrative examples are given to demonstrate the effectiveness of the obtained results the new generalization introduces a promising tool for many linear and nonlinear models containing fractional derivatives

parametric representation of a translation invariant renormalizable noncommutative model we construct here the parametric representation of a translation invariant renormalizable scalar model on the noncommutative moyal space of even dimension d this representation of the feynman amplitudes is based on some integral form of the noncommutative propagator all types of graphs planar and non planar are analyzed the role played by noncommutativity is explicitly shown this parametric representation established allows us to calculate the power counting of the model furthermore the space dimension d is just a parameter in the formulae obtained this paves the road for the dimensional regularization of this noncommutative model

quick and easy analysis of unreplicated factorials box and meyer 1986 introduced a method for assessing the sizes of contrasts in unreplicated factorial and fractional factorial designs this is a useful technique and an associated graphical display popularly known as a bayes plot makes it even more effective this article presents a competing technique that is also effective and is computationally simple an advantage of the new method is that the results are given in terms of the original units of measurement this direct association with the data may make the analysis easier to explain

quantum field theory on quantized bergman domain we present an oscillator realization of discrete series representations of group su 2 2 we give formulas for the coherent state star product quantization of a bergman domain d a formulation of a regularized noncommutative scalar field on a quantized d is given

a new difference scheme for the time fractional diffusion equation abstract in this paper we construct a new difference analog of the caputo fractional derivative called the l 2 1 formula the basic properties of this difference operator are investigated and on its basis some difference schemes generating approximations of the second and fourth order in space and the second order in time for the time fractional diffusion equation with variable coefficients are considered stability of the suggested schemes and also their convergence in the grid l 2 norm with the rate equal to the order of the approximation error are proved the obtained results are supported by the numerical calculations carried out for some test problems

analytical treatment of differential equations with fractional coordinate derivatives this paper outlines a reliable strategy to use the homotopy perturbation method based on jumarie s derivative for solving fractional differential equations in this framework compact structures of fourth order fractional diffusion wave equations are considered as prototype examples moreover convergence of the proposed approach for these types of equations is investigated results show that the response expressions are mittag leffler stable

a conservative difference scheme for the zakharov equations a new conservative difference scheme is presented for the periodic initial value problem of zakharov equations the scheme can be implicit or semi explicit depending on the choice of a parameter the discretization of the initial condition is of second order accuracy which is consistent with the accuracy of the scheme on the basis of a priori estimates and an inequality about norms convergence of the difference solutions is proved in the energy norm numerical experiments with the schemes are done for several test cases computational results demonstrate that the new semi explicit scheme with a new initial approximation is more accurate and computationally efficient

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

loop vertex expansion for φ2k theory in zero dimension in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction

on mittag leffler type functions in fractional evolution processes abstract we review a variety of fractional evolution processes so defined being governed by equations of fractional order whose solutions turn out to be related to mittag leffler type functions the chosen equations are the simplest of the fractional calculus and include the abel integral equations of the second kind which are relevant in typical inverse problems and the fractional differential equations which govern generalized relaxation and oscillation phenomena

parametric representation of noncommutative field theory in this paper we investigate the schwinger parametric representation for the feynman amplitudes of the recently discovered renormalizable phi 4 4 quantum field theory on the moyal non commutative mathbb r 4 space this representation involves new hyperbolic polynomials which are the non commutative analogs of the usual kirchoff or symanzik polynomials of commutative field theory but contain richer topological information

power counting theorem for non local matrix models and renormalisation solving the exact renormalisation group equation a la wilson polchinski perturbatively we derive a power counting theorem for general matrix models with arbitrarily non local propagators the power counting degree is determined by two scaling dimensions of the cut off propagator and various topological data of ribbon graphs as a necessary condition for the renormalisability of a model the two scaling dimensions have to be large enough relative to the dimension of the underlying space in order to have a renormalisable model one needs additional locality properties typically arising from orthogonal polynomials which relate the relevant and marginal interaction coefficients to a finite number of base couplings the main application of our power counting theorem is the renormalisation of field theories on noncommutative d in matrix formulation

renormalization of tensorial group field theories abelian u 1 models in four dimensions we tackle the issue of renormalizability for tensorial group field theories tgft including gauge invariance conditions with the rigorous tool of multi scale analysis to prepare the ground for applications to quantum gravity models in the process we define the appropriate generalization of some key qft notions including connectedness locality and contraction of high subgraphs we also define a new notion of wick ordering corresponding to the subtraction of maximal melonic tadpoles we then consider the simplest examples of dynamical 4 dimensional tgft with gauge invariance conditions for the abelian u 1 case we prove that they are super renormalizable for any polynomial interaction