generalized selection combining based on the log likelihood ratio we propose a generalized selection combining gsc scheme for binary signaling in which a subset of diversity branches providing the largest magnitude of log likelihood ratio llr are selected and combined it is shown that the bit error probability with maximum ratio combining mrc or square law combining of l branches is identical to that with llr based gsc of l 2 branches we also propose a simple but suboptimal gsc based on a noncoherent envelope detection and discuss its potential advantages over the conventional signal to noise ratio based gsc and mrc

noether s theorem of fractional birkhoffian systems abstract in this paper we study noether type symmetry theorem to fractional birkhoffian systems with riemann liouville derivatives this theorem provides an explicit algorithmic way to compute a constant for any birkhoffian systems admitting a symmetry finally we extend our noether s theorem to fractional birkhoffian systems base on caputo or riesz derivatives

robust m tests without consistent estimation of the asymptotic covariance matrix we extend the kvb approach of kiefer vogelsang and bunzel 2000 to constructing robust m tests without consistent estimation of the asymptotic covariance matrix we demonstrate that when model parameters have to be estimated the normalizing matrix computed using a full sample estimator is able to eliminate the nuisance parameters when there is no estimation effect but not otherwise to circumvent the problem of estimation effect we propose using recursive estimators to compute the normalizing matrix and show that the resulting m test is asymptotically pivotal this m test is thus robust not only to heteroscedasticity and serial correlations of unknown form but also to the presence of an estimation effect as examples we consider robust tests for serial correlations and robust information matrix tests the former tests extend that of lobato 2001 and are applicable to model residuals for testing higher order moments we find that the latter tests are also robust when a lower order moment is miss

a bootstrapped spectral test for adequacy in weak arma models this paper proposes a cramer von mises cm test statistic to check the adequacy of weak arma models without posing a martingale difference assumption on the error terms the asymptotic null distribution of the cm test is obtained moreover this cm test is consistent and has nontrivial power against the local alternative of order n 1 2 due to the unknown dependence of error terms and the estimation effects a new block wise random weighting method is constructed to bootstrap the critical values of the test statistic the new method is easy to implement and its validity is justified the theory is illustrated by a small simulation study and an application to s p 500 stock index

testing that a dependent process is uncorrelated an analysis is presented of a new testing procedure for the null hypothesis that a stochastic process is uncorrelated when the process is possibly dependent unlike with existing procedures the user does not need to choose any arbitrary number to implement the proposed test the asymptotic null distribution of the proposed test statistic is not standard but it is tabulated by means of simulations the test is compared with two alternative test procedures that require selection of user chosen numbers on the basis of asymptotic local power and finite sample behavior although the asymptotic local power of the proposed test is lower than those corresponding to the alternative tests in a monte carlo study i show that in small samples the test typically better controls the type i error and that the loss of power is not substantial

new fractional operators and application to fractional variational problem abstract motivated by hilfer fractional derivative a class of generalized fractional integral and derivative operators is discussed the generalized fractional integrals are the counterparts of generalized fractional derivatives we study their semigroup property and fractional integration by parts formulae which play an important role in deducing the euler lagrange equation of extremal problem involving generalized fractional operators as applications we discuss a minimizing functional problem and an isoperimetric problem containing these new operators numerical simulations based on polynomial approximation and galerkin approach are presented our study shows that the polynomial approximation and galerkin approach can be easily applied to fractional variational problem depending on both left and right generalized fractional integrals and derivatives

inference for autocorrelations under weak assumptions abstract in this article we consider the large sample behavior of estimates of autocorrelations and autoregressive moving average arma coefficients as well as their distributions under weak conditions specifically the usual text book formulas for variances of these estimates are based on strong assumptions and should not be routinely applied without careful consideration such is the case when the time series follows an arma process with uncorrelated innovations that may not be assumed to be independent and identically distributed as a specific case it is well known that if the process is independent and identically distributed then the sample autocorrelation estimates scaled by the square root of the sample size are asymptotically standard normal this result is used extensively as a diagnostic check on the residuals of a fitted model or as an initial test on the observed time series to determine whether further model fitting is warranted in this article we show that this result can be quite

fractional sturm liouville problem in this paper we define some fractional sturm liouville operators fslos and introduce two classes of fractional sturm liouville problems fslps namely regular and singular fslp the operators defined here are different from those defined in the literature in the sense that the operators defined here contain left and right riemann liouville and left and right caputo fractional derivatives for both classes we investigate the eigenvalue and eigenfunction properties of the fslos in the class of regular fslps we discuss two types of fslps as an operator for the class of singular fslps we introduce a fractional legendre equation fle and discuss its solution it is shown that the legendre polynomials resulting from an fle are the same as those obtained from the integer order legendre equation however the eigenvalues of the two equations differ using the legendre integral transform we demonstrate some applications of our results by solving two fractional differential equations one ordinary and the other partial it is our hope that this paper will initiate new research in the area of fslps and many of its variations

collocation method with convergence for generalized fractional integro differential equations abstract in this paper we study a numerical approach for some class of generalized fractional integro differential equations gfides defined in terms of the b operators presented recently we develop collocation method for linear and nonlinear forms of gfides the numerical approach uses the idea of collocation methods for solving integral equations legendre polynomials are used to approximate the solution in finite dimensional space with convergence analysis the obtained approximate solution recovers the solution of the fractional integro differential equation fide defined using caputo derivatives in a special case fides containing convolution type kernels appear in diverse area of science and engineering applications therefore some test examples varying the kernel in the b operator are considered to perform the numerical investigations the numerical results validate the presented scheme and provide good accuracy using few legendre basis functions

generalized variational problems and euler lagrange equations this paper introduces three new operators and presents some of their properties it defines a new class of variational problems called generalized variational problems or gvps in terms of these operators and derives euler lagrange equations for this class of problems it is demonstrated that the left and the right fractional riemann liouville integrals and the left and the right fractional riemann liouville caputo riesz riemann liouville and riesz caputo derivatives are special cases of these operators and they are obtained by considering a special kernel further the euler lagrange equations developed for functional defined in terms of the left and the right fractional riemann liouville caputo riesz riemann liouville and riesz caputo derivatives are special cases of the euler lagrange equations developed here examples are considered to demonstrate the applications of the new operators and the new euler lagrange equations the concepts of adjoint differential operators and adjoint differential equations defined in terms of the new operators are introduced a new class of generalized lagrangian hamiltonian and action principles are presented in special cases these formulations lead to fractional adjoint differential operators and adjoint differential equations and fractional lagrangian hamiltonian and action principle thus the new operators introduce a generalized approach to many problems in classical mechanics in general and variational calculus in particular possible extensions of the subject and the concepts discussed here are also outlined

diagnostic checking in multivariate arma models with dependent errors using normalized residual autocorrelations in this paper we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise we propose new portmanteau statistics

generalized euler lagrange equations for fractional variational problems with free boundary conditions in this article we are going to present necessary conditions which must be satisfied to make the fractional variational problems fvps with completely free boundary conditions have an extremum the fractional derivatives are defined in the caputo sense first we present the necessary conditions for the problem with only one dependent variable and then we generalize them to problems with multiple dependent variables we also find the transversality conditions for when each end point lies on a given arbitrary curve in the case of a single variable or a surface in the case of multiple variables it is also shown that in special cases such as those with specified and unspecified boundary conditions and problems with integer order derivatives the new results reduce to the known necessary conditions some examples are presented to demonstrate the applicability of the new formulations

a numerical technique for solving a class of fractional variational problems this paper presents a numerical method for solving a class of fractional variational problems fvps with multiple dependent variables multi order fractional derivatives and a group of boundary conditions the fractional derivative in the problem is in the caputo sense in the presented method the given optimization problem reduces to a system of algebraic equations using polynomial basis functions an approximate solution for the fvp is achieved by solving the system the choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed we extensively discuss the convergence of the method and finally present illustrative examples to demonstrate validity and applicability of the new technique

diagnostic checking in arma models with uncorrelated errors we consider tests for lack of fit in arma models with nonindependent innovations in this framework the standard box pierce and ljung box portmanteau tests can perform poorly specifically the usual text book formulas for asymptotic distributions are based on strong assumptions and should not be applied without careful consideration in this article we derive the asymptotic covariance matrix of a vector of autocorrelations for residuals of arma models under weak assumptions on the noise the asymptotic distribution of the portmanteau statistics follows a consistent estimator of and a modification of the portmanteau tests are proposed this allows us to construct valid asymptotic significance limits for the residual autocorrelations and asymptotically valid goodness of fit tests when the underlying noise process is assumed to be noncorrelated rather than independent or a martingale difference a set of monte carlo experiments and an application to the standard poor 500 returns illustrate the p

generalized fractional calculus with applications to the calculus of variations we study operators that are generalizations of the classical riemann liouville fractional integral and of the riemann liouville and caputo fractional derivatives a useful formula relating the generalized fractional derivatives is proved as well as three relations of fractional integration by parts that change the parameter set of the given operator into its dual such results are explored in the context of dynamic optimization by considering problems of the calculus of variations with general fractional operators necessary optimality conditions of euler lagrange type and natural boundary conditions for unconstrained and constrained problems are investigated interesting results are obtained even in the particular case when the generalized operators are reduced to be the standard fractional derivatives in the sense of riemann liouville or caputo as an application we provide a class of variational problems with an arbitrary kernel that give answer to the important coherence embedding problem illustrative optimization problems are considered

direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method this paper presents an adaptive legendre gauss pseudospectral method for solving a type of constrained fractional variational problems fvps the fractional derivative is defined in the caputo sense in the presented method by dividing the domain of the problem into a uniform mesh the given fvp reduces to a nonlinear mathematical programming problem and there is no need to solve the complicated fractional euler lagrange equations the method developed in this paper adjusts both the mesh spacing and the number of collocation points on each subinterval in order to improve the accuracy the method is easy to implement and yields very accurate results some error estimates and convergence properties of the method are discussed numerical examples are included to confirm the efficiency and convergence of the proposed method

variational approach and deformed derivatives recently we have demonstrated that there exists a possible relationship between q deformed algebras in two different contexts of statistical mechanics namely the tsallis framework and the kaniadakis scenario with a local form of fractional derivative operators for fractal media the so called hausdorff derivatives mapped into a continuous medium with a fractal measure here in this paper we present an extension of the traditional calculus of variations for systems containing deformed derivatives embedded into the lagrangian and the lagrangian densities for classical and field systems the results extend the classical euler lagrange equations and the hamiltonian formalism the resulting dynamical equations seem to be compatible with those found in the literature specially with mass dependent and with nonlinear equations for systems in classical and quantum mechanics examples are presented to illustrate applications of the formulation also the conserved noether current is worked out

discussing the extension and applications of a variational approach with deformed derivatives one has recently presented an extension of the standard variational calculus to include the presence of deformed derivatives both in the lagrangian of systems of particles and in the lagrangian density of field theoretic models classical euler lagrange equations and the hamiltonian formalism have been reassessed in this approach whenever applied to a number of physical systems the resulting dynamical equations come out to be the correct ones found in the literature especially with mass dependent and with nonlinear equations for classical and quantum mechanical systems in the present contribution one extends the variational approach including a piecewise form of deformed derivatives to study higher order dissipative systems and to obtain as an option deformed equations as well applications to concrete situations are contemplated such as an accelerated point charge this is the problem of the abraham lorentz dirac force stochastic dynamics like the langevin the advection convection reaction and fokker planck equations the korteweg de vries equation the landau lifshitz gilbert problem and the caldirola kanai hamiltonian and heat transfer equation of the fourier and non fourier types by considering these different examples it is shown that the formulation proposed in this paper may be a simple but promising path for dealing for example with dissipative nonlinear stochastic systems and the anomalous heat transfer problem by adopting a variational approach one has recently presented an extension of the standard variational calculus to include the presence of deformed derivatives both in the lagrangian of systems of particles and in the lagrangian density of field theoretic models classical euler lagrange equations and the hamiltonian formalism have been reassessed in this approach whenever applied to a number of physical systems the resulting dynamical equations come out to be the correct ones found in the literature especially with mass dependent and with nonlinear equations for classical and quantum mechanical systems in the present contribution one extends the variational approach including a piecewise form of deformed derivatives to study higher order dissipative systems and to obtain as an option deformed equations as well applications to concrete situations are contemplated such as an accelerated point charge this is the problem of the abraham lorentz dirac force stochastic dynamics like the langevin the advection convection reaction and

fractional variational calculus in terms of riesz fractional derivatives this paper presents extensions of traditional calculus of variations for systems containing riesz fractional derivatives rfds specifically we present generalized euler lagrange equations and the transversality conditions for fractional variational problems fvps defined in terms of rfds we consider two problems a simple fvp and an fvp of lagrange results of the first problem are extended to problems containing multiple fractional derivatives functions and parameters and to unspecified boundary conditions for the second problem we present lagrange type multiplier rules for both problems we develop the euler lagrange type necessary conditions which must be satisfied for the given functional to be extremum problems are considered to demonstrate applications of the formulations explicitly we introduce fractional momenta fractional hamiltonian fractional hamilton equations of motion fractional field theory and fractional optimal control the formulations presented and the resulting equations are similar to the formulations for fvps given in agrawal 2002 j math anal appl 272 368 2006 j phys a math gen 39 10375 and to those that appear in the field of classical calculus of variations these formulations are simple and can be extended to other problems in the field of fractional calculus of variations

consistent testing for serial correlation of unknown form this paper proposes three classes of consistent one sided tests for serial correlation of unknown form for the residual from a linear dynamic regression model that includes both lagged dependent variables and exogenous variables the tests are obtained by comparing a kernel based normalized spectral density estimator and the null normalized spectral density using a quadratic norm the hellinger metric and the kullback leibler information criterion respectively under the null hypothesis of no serial correlation the three classes of new test statistics are asymptotically n 0 1 and equivalent the null distributions are obtained without having to specify any alternative model unlike some conventional tests for serial correlation the null distributions of our tests remain invariant when the regressors include lagged dependent variables under a suitable class of local alternatives the three classes of the new tests are asymptotically equally efficient under global alternatives however their relative efficiencies depend on the relative magnitudes of the three divergence measures our approach provides an interpretation for box and pierce s 1970 test which can be viewed as a quadratic norm based test using a truncated periodogram many kernels deliver tests with better power than box and pierce s test or the truncated kernel based test a simulation study shows that the new tests have good power against an ar 1 process and a fractionally integrated process in particular they have better power than the lagrange multiplier tests of breusch 1978 and godfrey 1978 as well as the portmanteau tests of box and pierce 1970 and ljung and box 1978 the cross validation procedure of beltrao and bloomfield 1987 and robinson 1991a works reasonably well in determining the smoothing parameter of the kernel spectral estimator and is recommended for use in practice

numerical solution of fractional oscillator equation abstract we focus on a numerical scheme applied for a fractional oscillator equation in a finite time interval this type of equation includes a complex form of left and right sided fractional derivatives its analytical solution is represented by a series of left and right fractional integrals and therefore is difficult in practical calculations here we elaborated two numerical schemes being dependent on a fractional order of the equation the results of numerical calculations are compared with analytical solutions then we illustrate convergence and stability of our schemes

a new method of dynamical stability i e fractional generalized hamiltonian method and its applications fractional generalized hamiltonian method of dynamical stability is presented six criterions for the new method of dynamical stability are given the new method s applications are studied five kinds of actual fractional dynamical models are constructed dynamical stability of the five actual fractional dynamical models is explored in the paper we present fractional generalized hamiltonian method of dynamical stability in terms of riesz riemann liouville derivative and study its applications for an actual dynamical system the fractional generalized hamiltonian method of constructing a fractional dynamical model is given and then the six criterions for fractional generalized hamiltonian method of dynamical stability are presented as applications by using the fractional generalized hamiltonian method we construct five kinds of actual fractional dynamical models which include a fractional euler poinsot model of rigid body that rotates with respect to a fixed point a fractional hojman urrutia model a fractional lorentz dirac model a fractional whittaker model and a fractional robbins lorenz model and we explore the dynamical stability of these models respectively this work provides a general method for studying the dynamical stability of an actual fractional dynamical system that is related to science and engineering