a new phenomenon in the critical exponent for structurally damped semi linear evolution equations abstract in this paper we find the critical exponent for global small data solutions to the cauchy problem in r n for dissipative evolution equations with power nonlinearities u p or u t p u t t u t u u p u t p here n 0 with 2 we show that the critical exponent for each of the two nonlinearities is related to each of the two possible asymptotic profiles of the linear part of the equation which are described by the diffusion equations v t v 0 w t w 0 the nonexistence of global solutions in the critical and subcritical cases is proved by using the test function method under suitable sign assumptions on the initial data and lifespan estimates are obtained by assuming small initial data in sobolev spaces we prove the existence of global solutions in the supercritical case up to some maximum space dimension n and we derive l q estimates for the solution for q 1 for 2 the result holds in any space dimension n 1 the existence result also remains valid if and or are fractional

improved hardy inequalities for grushin operators we show that the hardy inequality for grushin operators like x 1 2 x 2 y on a bounded domain containing the origin can be refined by adding remainder terms such as the improvement of brezis vazquez vazquez zuazua and filippas tertikas

chaotic functions with zero topological entropy on caracterise la classe m c i i des applications chaotiques en ce sens on montre que m contient certaines appliquations qui ont a la fois une entropie topologique nulle et des attracteurs infinis on montre que le complement de m consiste en applications qui ont seulement des trajectoires approchables par des cycles

transforming real valued sequences fast fourier versus fast hartley transform algorithms five programs for efficient computation of dft of real valued data are analyzed with respect to their operation counts vis a vis run times on weak and powerful floating point processors the results help dispose of the claims of superiority of fht over corresponding real valued fft the bruun 1978 algorithm turns out to be a best performer

global existence for the one dimensional second order semilinear hyperbolic equations abstract the aim of the paper is to study necessary and sufficient conditions for the existence of the global solution of the one dimensional semilinear equation appearing in the boundary value problems of gas dynamics we investigate the cauchy problem for such equation in the domain where the operator is weakly hyperbolic we obtain the necessary condition for the existence of the self similar solutions for the semilinear gellerstedt type equation the approach used in the paper is based on the fundamental solution of the linear gellerstedt operator and the l p l q estimates

comparison principles uniqueness and symmetry results of solutions of quasilinear elliptic equations and inequalities abstract we prove comparison principles uniqueness regularity and symmetry results for p regular distributional solutions of quasilinear very weak elliptic equations of coercive type and to related inequalities the simplest model examples are p u u q 1 u h on r n where q p 1 0 and div u 1 u 2 u q 1 u h on r n with q 0 and h l l o c 1 r n

the fast hartley transform algorithm the fast hartley transform fht is similar to the cooley tukey fast fourier transform fft but performs much faster because it requires only real arithmetic computations compared to the complex arithmetic computations required by the fft through use of the fht discrete cosine transforms dct and discrete fourier transforms dft can be obtained the recursive nature of the fht algorithm derived in this paper enables us to generate the next higher order fht from two identical lower order fht s in practice this recursive relationship offers flexibility in programming different sizes of transforms while the orderly structure of its signal flow graphs indicates an ease of implementation in vlsi

an analysis of real fourier domain based adaptive algorithms implemented with the hartley transform using cosine sine symmetries the least mean squared lms algorithm and its variants have been the most often used algorithms in adaptive signal processing however the lms algorithm suffers from a high computational complexity especially with large filter lengths the fourier transform based block normalized lms fbnlms reduces the computation count by using the discrete fourier transform dft and exploiting the fast algorithms for implementing the dft even though the savings achieved with the fbnlms over the direct lms implementation are significant the computational requirements of fbnlms are still very high rendering many real time applications like audio and video estimation infeasible the hartley transform based bnlms hbnlms is found to have a computational complexity much less than and a memory requirement almost of the same order as that of the fbnlms this paper is based on the cosine and sine symmetric implementation of the discrete hartley transform dht which is the key in reducing the computational complexity of the fbnlms by 33 asymptotically with respect to multiplications the parallel implementation of the discrete cosine transform dct in turn can lead to more efficient implementations of the hbnlms

a finite element approximation for a class of degenerate elliptic equations in this paper we exhibit a finite element method fitting a suitable geometry naturally associated with a class of degenerate elliptic equations usually called grushin type equations in a plane region and we discuss the related error estimates

the existence of a global fundamental solution for homogeneous hormander operators via a global lifting method we prove the existence of a global fundamental solution x y with pole x for any hormander operator l i 1mxi2 on rn which is homogeneous of degree 2 here homogeneity is meant with respect to a family of non isotropic diagonal maps of the form x 1x1 nxn with 1 1 n due to a global lifting method for homogeneous operators proved by folland comm partial differential equations 2 1977 161 207 there exists a carnot group g and a polynomial surjective map g rn such that l is related to a sub laplacian lg on g we show that it is always possible to perform a global change of variable on g such that the lifting map becomes the projection of g rn rp onto rn we prove that an integration argument over the non compact fibers of provides a fundamental solution for l indeed if g x x y y x y rn x y rp is the fundamental solution of lg we show that g x 0 y y is always integrable with respect to y rp and its y integral is a fundamental solution for l

representation formulae and inequalities for solutions of a class of second order partial differential equations let l be a possibly degenerate second order differential operator and let n d 2 q be its fundamental solution at here d is a suitable distance in this paper we study necessary and sufficient conditions for the weak solutions of lu f u 0 on r n to satisfy the representation formula r u r n f u we prove that r holds provided f is superlinear without any assumption on the behavior of u at infinity on the other hand if u satisfies the condition lim inf f r d 2r u d 0 then r holds with no growth assumptions on f

liouville type theorem for quasi linear elliptic inequality δpu uσ 0 on riemannian manifolds abstract we studied the uniqueness of a nonnegative solution of the quasi linear elliptic inequality p u u 0 on a connected geodesically complete riemannian manifold x where is a parameter and p u div u p 2 u we proved that if p 1 p 1 and for some x 0 x lim inf t 0 t p 1 1 b x 0 r r p 1 p 1 p 1 p t 2 p 1 d r then inequality has no nontrivial nonnegative weak solutions we also studied the weighed case and the sharpness of the main result

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

fractional cosine sine and hartley transforms in previous papers the fourier transform ft has been generalized into the fractional fourier transform frft the linear canonical transform lct and the simplified fractional fourier transform sfrft because the cosine sine and hartley transforms are very similar to the ft it is reasonable to think they can also be generalized by the similar way we introduce several new transforms they are all the generalization of the cosine sine or hartley transform we first derive the fractional cosine sine and hartley transforms frct frst frht they are analogous to the frft then we derive the canonical cosine and sine transforms cct cst they are analogous to the lct we also derive the simplified fractional cosine sine and hartley transforms sfrct sfrst sfrht they are analogous to the sfrft and have the advantage of real input real output we also discuss the properties digital implementation and applications e g the applications for filter design and space variant pattern recognition of these transforms the transforms introduced in this paper are very efficient for digital implementation we can just use one half or one fourth of the real multiplications required for the frft and lct to implement them when we want to process even odd or pure real imaginary functions we can use these transforms instead of the frft and lct besides we also show that the frct frst cct cst and sfrct sfrst are also useful for the one sided t spl isin 0 spl infin signal processing

nonexistence of nonnegative solutions of elliptic systems of divergence type abstract in this paper we deal with noncoercive elliptic systems of divergence type that include both the p laplacian and the mean curvature operator and whose right hand sides depend also on a gradient factor we prove that any nonnegative entire weak solution is necessarily constant the main argument of our proofs is based on previous estimates given in filippucci 2009 12 for elliptic inequalities actually the main technique for proving the central estimate has been developed by mitidieri and pohozaev 2001 23 and relies on the method of test functions no use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions are required

a generalized approach to direction finding with reference to the recently developed estimation of signal parameters using a rotational invariance techniques esprit it is pointed out that other operators can be used to generate the matrix pencil by way of example the moving window operator is discussed

fast hartley transform pruning the discrete hartley transform dht is discussed as a tool for the processing of real signals fast hartley transform fht algorithms which compute the dht in a time proportional to n log sub 2 n exist in many applications such as interpolation and convolution of signals a significant number of zeros are padded to the nonzero valued samples before the transform is computed it is shown that for such situations significant savings in the number of additions and multiplications can be obtained by pruning the fht algorithm the modifications in the fht algorithm as a result of pruning are developed and implemented in an fht subroutine the amount of savings in the operation is determined

on the weak continuity of elliptic operators and applications to potential theory in this paper we establish weak continuity results for quasilinear elliptic and subellip tic operators of divergence form acting on corresponding classes of subharmonic functions these results are analogous to our earlier results for fully nonlinear fc hessian operators from the weak continuity we derive various potential theoretic results including capacity estimates potential esti mates and the wiener criterion for regular boundary points our methods make substantial use of harnack inequalities for solutions 1 introduction there are numerous papers on the local behavior of solu tions subsolutions and supersolutions of second order quasilinear elliptic diver gence structure partial differential equations as well as extensions to degenerate elliptic and subelliptic equations in this paper we show that many properties including the quasi continuity of subharmonic functions asymptotic behavior of fundamental solutions removability of singularities wiener criteria for regular boundary points can be derived via harnack inequalities for solutions the two main ingredients in our approach which follow from our treatment of the fully nonlinear hessian operators in 45 46 47 together with that of labutin 30 are a weak convergence result and a pointwise potential estimate for subharmonic functions the weak convergence result is analogous to that for hessian operators 45 46 while the potential estimate extends that found for quasilinear elliptic operators by kilpelainen and maly 27 weak convergence results in the theory of nonlinear partial differential equa tions have been addressed in the survey 13 in this paper we treat nonlinear elliptic divergence structure operators for which harnack type inequalities are available to state our result we need an appropriate notion of subharmonic func tion in the fully nonlinear case 46 we employed the viscosity notion based on differential inequalities for smooth test functions for quasilinear divergence structure equations the traditional definition using the homogeneous equation is more convenient accordingly we shall say that a continuous function w in a domain q in euclidean space ir is harmonic with respect to an operator or c harmonic in short if it is a solution of the homogeneous equation c u 0

on nonnegative solutions of the inequality δ u uσ 0 on riemannian manifolds we study the uniqueness of a nonnegative solution of the differential inequality u u 0 on a complete riemannian manifold where 1 is a parameter we prove that if for some x0 m and all large enough r volb x0 r crplnqr where p 2 1 q 1 1 and b x r is a geodesic ball then the only nonnegative solution of is identically 0 we also show the sharpness of the above values of the exponents p q 2014 wiley periodicals inc

fast computation of the discrete cosine transform and the discrete hartley transform a new factorization of the discrete hartley transform dht is presented it is used to derive new algorithms for the dht and the discrete cosine transform dct with reduced number of multiplications

the vector split radix algorithm for 2d dht a decimation in frequency vector split radix algorithm is proposed to decompose an n n 2d discrete hartley transform dht into one n 2 n 2 dht and twelve n 4 dhts the proposed algorithm possesses the in place property and needs no matrix transpose its computational structure is very regular and is simpler than those of all existing nonseparable 2d dhts

nonlinear liouville theorems for grushin and tricomi operators the aim of this paper is to study necessary conditions for existence of weak solutions of the inequality l x y dx dy u u q x 1 y 2 x rd y rk where l is a quasi homogeneous differential operator q 1 1 2 r and k d 1 as special cases our results can be applied when l is tricomi or grushin type operators

regularity and chaos in recurrent fuzzy systems abstract in this paper we shall present a mathematical definition of recurrent fuzzy systems and begin to systematically investigate the underlying theory involved unlike static fuzzy systems recurrent fuzzy systems are equipped with time delayed feedback of their output and allow representing knowledge based dynamic processes that may be stated in the form of if then rules we study their relationship to automata and show that they have an automaton like behavior when appropriately designed in other cases recurrent fuzzy system may exhibit chaotic behavior we present sufficient conditions for the occurrence of chaos in recurrent fuzzy systems that can easily be checked solely on the basis of the qualitative linguistically formulated models we also discuss the extent to which state graphs may be used for describing the behaviors of recurrent fuzzy systems

entire solutions of completely coercive quasilinear elliptic equations ii abstract a famous theorem of sergei bernstein says that every entire solution u u x x r 2 of the minimal surface equation div d u 1 d u 2 0 is an affine function no conditions being placed on the behavior of the solution u bernstein s theorem continues to hold up to dimension n 7 while it fails to be true in higher dimensions in fact if x r n with n 8 there exist entire non affine minimal graphs bombieri de giorgi and giusti our purpose is to consider an extensive family of quasilinear elliptic type equations which has the following strong bernstein liouville property that u 0 for any entire solution u no conditions whatsoever being placed on the behavior of the solution outside of appropriate regularity assumptions in many cases moreover no conditions need be placed even on the dimension n we also study the behavior of solutions when the parameters of the problem do not allow the bernstein liouville property and give a number of counterexamples showing that the results of the paper are in many cases best possible

uniqueness result for non negative solutions of semi linear inequalities on riemannian manifolds abstract we consider certain semi linear partial differential inequalities on complete connected riemannian manifolds and provide a simple condition in terms of volume growth for the uniqueness of a non negative solution we also show the sharpness of this condition

unified parallel lattice structures for time recursive discrete cosine sine hartley transforms unified efficient computations of the discrete cosine transform dct discrete sine transform dst discrete hartley transform dht and their inverse transforms employing the time recursive approach are considered unified parallel lattice structures that can dually generate the dct and dst simultaneously as well the dht are developed these structures can obtain the transformed data for sequential input time recursively with a throughput rate of one per clock cycle the total number of multipliers required is a linear function of the transform size n with no constraint on n the resulting architectures are regular modular and without global communication so that they are very suitable for vlsi implementation for high speed applications it is shown that the dct dst dht and their inverse transforms share an almost identical lattice structure the tradeoff between time and area for the block data processing is considered

julia fatou sullivan theory for real one dimensional dynamics our aim is to show that the julia fatou sullivan structure theory for the dynamics of rational maps is also valid for smooth endomorphisms of the circle and of the interval under extremely mild smoothness and non flatness conditions in order to stress the similarity between real and complex one dimensional dynamics let us recall the main results from the fatou julia sullivan theory if f is a rational map then there is a dynamical decomposition of the riemann sphere into the disjoint union of two totally invariant i e both forward and backward invariant sets j f f f here f f is the domain of normality of the family of iterates of f and is called the fatou set its complement which is called the julia set off is a compact set which contains all the complications of the dynamics off the connected components of the open set f f are mapped onto each other by f hence the orbit of a component of f f is the union of some components of f f julia proved in the beginning of the century that if a component of f f is periodic and contains an attracting periodic point then the orbit of this component must contain a critical point sullivan in the remarkable paper su showed via quasi conformal deformations that the components are eventually periodic and fall into finitely many orbits let n be either the circle s j or a compact interval of the real line and f n n be a smooth endomorphism a critical point of f is a point where the derivative vanishes a critical point is non flat if some higher derivative is non zero a critical point is an inflection point if it has a neighbourhood where f is monotone otherwise it is called a turning point assume f is not a homeomorphism i f f is a homeomorphism then these maps correspond to degree 1 rational maps of the riemann sphere and the situation is

hartley transforms over finite fields a general framework is presented for constructing transforms in the field of the input which have a convolution like property the construction is carried out over finite fields but is shown to be valid over the real and complex fields as well it is shown that these basefield transforms can be viewed as projections of the discrete fourier transform dft and that they exist for all lengths n for which the dft is defined the convolution property of the basefield transforms is derived and a condition for such transforms to have the self inverse property is given also fast algorithms for these basefield transforms are developed showing gains when compared to computations using the fft application of the methodology to hartley transforms over r leads to a simple derivation of fast algorithms for computing real hartley transforms

a hardy type inequality in the half space on rn and heisenberg group abstract we prove a hardy type inequality in the half space on the heisenberg group and show that a hardy inequality given by j tidblm in j tidblm a hardy inequality in the half space j funct anal 221 2005 482 492 is sharp

improved fourier and hartley transform algorithms application to cyclic convolution of real data this paper highlights the possible tradeoffs between arithmetic and structural complexity when computing cyclic convolution of real data in the transform domain both fourier and hartley based schemes are first explained in their usual form and then improved either from the structural point of view or in the number of operations involved namely we first present an algorithm for the in place computation of the discrete fourier transform on real data a decimation in time split radix algorithm more compact than the previously published one second we present a new fast hartley transform algorithm with a reduced number of operations a more regular convolution scheme based on fft s is also proposed finally we show that hartley transforms belong to a larger class of algorithms characterized by their generalized convolution property

assessing the hartley transform the fast algorithm for the real hartly transform is discussed in relation to the established fast algorithm for the complex fourier transform the two transforms are compared by timing comparably written programs on a given machine and the discipline of timing is discussed as an adjunct to complexity analysis with real data one hartley transform program can economically replace such packages as a complex valued unilateral fourier transform combined with a real valued unilateral inverse fourier transform the hartley transform is favorable for fast convolution of real data sets the utility of spectral analysis into fourier series throughout physics suggested that the hartley transform might have less physical significance but the construction of hartley diffraction planes in the microwave and optical laboratories where electromagnetic phase is encoded as real valued field amplitudes has revealed interesting complementarity

adaptive filtering using hartley transform and overlap save method a novel method of implementing fir finite impulse response adaptive filters using the discrete hartley transform dht and the overlap save method is proposed it not only has the advantage of fast convergence for highly correlated input signals but also provides a significant reduction in computation over the conventional time domain and frequency domain least mean square lms adaptive filters compared with the previously proposed unconstrained frequency domain flms algorithm the convergence performance is similar but an approximate saving of 30 in computation can be obtained for the usual filter length

bessel integrals and fundamental solutions for a generalized tricomi operator abstract the method of partial fourier transform is used to find explicit formulas for two remarkable fundamental solutions for a generalized tricomi operator these fundamental solutions reflect clearly the mixed type of the tricomi operator in proving these results we establish explicit formulas for fourier transforms of some functions involving bessel functions

unveiling and exemplifying the unitary equivalence of discrete time quantum walk models the two major discrete time formulations for quantum walks coined and scattering are unitarily equivalent for arbitrary position dependent transition amplitudes and any topology andrade et al 2009 phys rev a 80 052301 although the proof explicitly describes the mapping obtention its high technicality may hinder relevant physical aspects involved in the equivalence discussing concrete examples the most general constructions for the line square and honeycomb lattices here we unveil the similarities and differences of these two versions of quantum walks we moreover show how to derive the dynamics of one from the other by means of proper projections we perform calculations for different probability amplitudes such as hadamard grover discrete fourier transform and the uncommon in the area but interesting discrete hartley transform comparing the evolutions our study illustrates the models interplay an important issue for implementations and applications of such systems

a comment on on prime factor mapping for the discrete hartley transform lun and sin see ieee trans signal processing vol 40 no 6 p 1399 1411 1982 describe a method of computing prime factor decomposed discrete hartley transform dht over n points with 2n less additions compared to the existing algorithms of bracewell and sorensen 1976 the author shows how the method of lun and siu ran be extended to eliminate the 2n extra additions in the algorithms of bracewell and sorenson

the use of the hartley transform in geophysical applications the hartley transform ht is an integral transform similar to the fourier transform ft it has most of the characteristics of the ft several authors have shown that fast algorithms can be constructed for the fast hartley transform fht using the same structures as for the fast fourier transform however the ht is a real transform and for this reason since one complex multiplication requires four real multiplications the discrete ht dht is computationally faster than the discrete ft dft consequently any process requiring the dft such as amplitude and phase spectra can be performed faster by using the dht the general properties of the dht are reviewed first and then an attempt is made to use the fht in some seismic data processing techniques such as one dimensional filtering forward seismic modeling and migration the experiments show that the hartley transform is two times faster than the fourier transform

radix 2 spl times 2 spl times 2 algorithm for the 3 d discrete hartley transform the discrete hartley transform dht has proved to be a valuable tool in digital signal image processing and communications and has also attracted research interests in many multidimensional applications although many fast algorithms have been developed for the calculation of one and two dimensional 1 d and 2 d dht the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention hence the multidimensional hartley transform is usually calculated through the row column approach however proper multidimensional algorithms can be more efficient than the row column method and need to be developed therefore it is the aim of this paper to introduce the concept and derivation of the three dimensional 3 d radix 2 spl times 2 spl times 2 algorithm for fast calculation of the 3 d discrete hartley transform the proposed algorithm is based on the principles of the divide and conquer approach applied directly in 3 d it has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row column approach based on similar algorithms

on computing the discrete hartley transform the discrete hartley transform dht is a real valued transform closely related to the dft of a real valued sequence bracewell has recently demonstrated a radix 2 decimation in time fast hartley transform fht algorithm in this paper a complete set of fast algorithms for computing the dht is developed including decimation in frequency radix 4 split radix prime factor and winograd transform algorithms the philosophies of all common fft algorithms are shown to be equally applicable to the computation of the dht and the fht algorithms closely resemble their fft counterparts the operation counts for the fht algorithms are determined and compared to the counts for corresponding real valued fft algorithms the fht algorithms are shown to always require the same number of multiplications the same storage and a few more additions than the real valued fft algorithms even though computation of the fht takes more operations in some situations the inherently real valued nature of the discrete hartley transform may justify this extra cost

several logarithmic caffarelli kohn nirenberg inequalities and applications abstract in this paper based on the caffarelli kohn nirenberg inequalities on the euclidean space and the weighted holder inequality we establish the logarithmic caffarelli kohn nirenberg inequalities and parameter type logarithmic caffarelli kohn nirenberg inequalities and give applications for the weighted ultracontractivity of positive strong solutions to a kind of evolution equations we also prove corresponding logarithmic caffarelli kohn nirenberg inequalities and parameter type logarithmic caffarelli kohn nirenberg inequalities on the heisenberg group and related to generalized baouendi grushin vector fields some applications are provided

representation formulae of solutions of second order elliptic inequalities abstract we prove various representation formulae of solutions of second order differential inequalities on r n as an outcome we obtain positivity results of the solutions of l u 0 where l is a general second order elliptic operator in divergence form results of this type are very useful for studying related liouville theorems of second order semilinear inequalities

a prime factor fast w transform algorithm a method for converting any nesting dft algorithm to the type i discrete w transform dwt i is introduced a nesting algorithm that differs from either the windograd fourier transform algorithm wfta or the prime factor fft algorithm pfa is presented new small n dets which are suitable for this nesting algorithm are developed based on using sparse matrix decomposition the proposed algorithm is more efficient that either wfta or pfa for large n and it is more flexible for the choice of transform length because 32 points are used for 2d processing the proposed algorithm is more efficient than the polynomial transform

a new critical curve for a class of quasilinear elliptic systems abstract we study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms the main model cases are given by the p laplacian operator as well as the mean curvature operator in nonparametric form we prove that if the exponents lie under a certain curve then the system has only the trivial solution these results hold without any restriction provided the possible solutions are more regular the underlying framework is the classical euclidean case as well as the carnot groups setting

some new liouville type results for fully nonlinear pdes on the heisenberg group abstract we prove new sharp liouville type properties via degenerate hadamard three sphere theorems for fully nonlinear equations structured over heisenberg vector fields as model examples we cover the case of pucci s extremal operators perturbed by suitable semilinear and gradient terms extending to the heisenberg setting known contributions valid in the euclidean framework

fundamental solution of a higher step grushin type operator abstract we examine a class of grushin type operators p k where k n 0 defined in 1 1 the operators p k are non elliptic and degenerate on a sub manifold of r n l geometrically they arise via a submersion from a sub laplace operator on a nilpotent lie group of step k 1 we explain the geometric framework and prove some analytic properties such as essential self adjointness the main purpose of the paper is to give an explicit expression of the fundamental solution of p k our methods rely on an appropriate change of coordinates and involve the theory of bessel and modified bessel functions together with weber s second exponential integral

calculation of multidimensional hartley transforms using one dimensional fourier transforms in the processing of real valued data a purely real transform such as the hartley transform is more desirable than the complex fourier transform because it avoids unnecessary complex computations this advantage is most significant in multidimensional transformations where a large amount of data has to be processed a multidimensional fast hartley transform algorithm is described that successively applies 1d fourier transforms redundant operations are reduced to a minimum special indexing schemes parity operators are introduced to avoid unscrambling procedures

existence of entire large positive solutions of semilinear elliptic systems abstract we show that entire large positive radial solutions exist for the semilinear elliptic system u p x v v q x u on r n n 3 for positive and provided that the nonnegative functions p and q are continuous c positive and satisfy the decay conditions 0 tp t dt 0 tq t dt and greater than unity and 0 tp t dt and 0 tq t dt if neither nor is greater than one

quasilinear elliptic systems in rn with multipower forcing terms depending on the gradient in this paper we deal with noncoercive elliptic multipower systems of divergence type which include p laplacian type operators as well as mean curvature operators and whose right hand sides depend on the product of both components of the solution and on a gradient factor we prove that any nonnegative nontrivial entire weak solution nonnecessarily radial is constant for nontrivial solutions we intend that both components are nontrivial the paper improves former results due to clement fleckinger mitidieri de thelin 2000 in 4 to bidaut veron and pohozaev 2001 in 3 where no gradient terms are considered on the other hand the paper contains as subcases also some recent results of filippucci 2011 12 in which systems with gradient dependence for the forcing terms are treated but not of multipower type the key ingredient of the proof technique is the method of test functions employed by mitidieri and pohozaev for studying systems in mitidieri and pohozaev 1999 17 no use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions is required

generalized discrete hartley transforms the discrete hartley transform is generalized into four classes in the same way as the generalized discrete fourier transform fast algorithms for the resulting transforms are derived the generalized transforms are expected to be useful in applications such as digital filter banks fast computation of the discrete hartley transform for any composite number of data points fast computations of convolution and signal representation the fast computation of skew circular convolution by the generalized transforms for any composite number of data points is discussed in detail

nonexistence of solutions to parabolic differential inequalities with a potential on riemannian manifolds we are concerned with nonexistence results of nonnegative weak solutions for a class of quasilinear parabolic problems with a potential on complete noncompact riemannian manifolds in particular we highlight the interplay between the geometry of the underlying manifold the power nonlinearity and the behavior of the potential at infinity

automatic generation of fast discrete signal transforms this paper presents an algorithm that derives fast versions for a broad class of discrete signal transforms symbolically the class includes but is not limited to the discrete fourier and the discrete trigonometric transforms this is achieved by finding fast sparse matrix factorizations for the matrix representations of these transforms unlike previous methods the algorithm is entirely automatic and uses the defining matrix as its sole input the sparse matrix factorization algorithm consists of two steps first the symmetry of the matrix is computed in the form of a pair of group representations second the representations are stepwise decomposed giving rise to a sparse factorization of the original transform matrix we have successfully demonstrated the method by computing automatically efficient transforms in several important cases for the dft we obtain the cooley tukey 1965 fft for a class of transforms including the dct type ii the number of arithmetic operations for our fast transforms is the same as for the best known algorithms our approach provides new insights and interpretations for the structure of these signal transforms and the question of why fast algorithms exist the sparse matrix factorization algorithm is implemented within the software package arep

split radix fast hartley transform in one and two dimensions a simple matrix decomposition is provided as a derivation of the one dimensional split radix fast hartley transform fht the method is then extended in a straightforward manner to the two dimensional fht 2 d fht by implementing the vector radix approach as a result the proposed algorithm requires many fewer computational operations than the nonsplit vector radix 2 d fht method

existence of entire explosive positive radial solutions for a class of quasilinear elliptic systems abstract we show the existence of entire explosive positive radial solutions for quasilinear elliptic systems div u m 2 u p x g v div v n 2 v q x f u on r n where f and g are positive and non decreasing functions on 0 satisfying the keller osserman condition

a structure theorem in one dimensional dynamics on considere la classe 7b a des applications c f 0 1 0 1 telles que f 0 f 1 0 et f a un unique point critique c 0 1 si le point critique de f 7b a est non plat alors f n a pas d intervalle errant

structured fast hartley transform algorithms the flowgraph originally proposed for the computation of the radix 2 fast hartley transform fht is restructured for clarity and ease of implementation with hardware and software by applying the transposition theorem to the newly formed flowgraph which corresponds to a decimation in time algorithm a decimation in frequency algorithm with a similar flowgraph is obtained the number of operations for the two algorithms is the same because of an existing symmetry which is also identical to that of another fht algorithm recently proposed

fast dht algorithms for length n q 2 sup m this article presents an improved split radix algorithm that can flexibly compute the discrete hartley transforms dht of length q 2 sup m where q is an odd integer comparisons with previously reported algorithms show that savings on the number of arithmetic operations can be made furthermore a wider range of choices on different dht lengths is naturally provided

an efficient prime factor algorithm for the discrete cosine transform and its hardware implementations the prime factor decomposition is a fast computational technique for many important digital signal processing operations such as the convolution the discrete fourier transform the discrete hartley transform and the discrete cosine transform dct the authors present a new prime factor algorithm for the dct they also design a prime factor algorithm for the discrete sine transform based on the prime factor dct algorithm hardware implementations for the prime factor dct are also studied they are especially interested in the hardware designs which are suitable for the vlsi implementations they show three hardware designs for the prime factor dct including a vlsi circuit fabricated directly according to the signal flow graph a linear systolic array and a mesh connected systolic array these three designs show the trade off between cost and performance the methodology which deals with general n sub 1 spl times n sub 2 point dcts where n sub 1 and n sub 2 are mutually prime is illustrated by converting a 15 point dct problem into a 3 spl times 5 point 2d dct problem

new split radix algorithm for the discrete hartley transform this paper presents a split radix algorithm that can flexibly compute the discrete hartley transforms of various sequence lengths comparisons with previously reported algorithms are made in terms of the required number of additions and multiplications it shows that the length 3 2 sup m dhts need a smaller number of multiplications than the length 2 sup m dhts however they both require about the same computational complexity in terms of the total number of additions and multiplications optimized computation of length 12 16 and 24 dfts are also provided

fast algorithm for the 3 d dct ii recently many applications for three dimensional 3 d image and video compression have been proposed using 3 d discrete cosine transforms 3 d dcts among different types of dcts the type ii dct dct ii is the most used in order to use the 3 d dcts in practical applications fast 3 d algorithms are essential therefore in this paper the 3 d vector radix decimation in frequency 3 d vr dif algorithm that calculates the 3 d dct ii directly is introduced the mathematical analysis and the implementation of the developed algorithm are presented showing that this algorithm possesses a regular structure can be implemented in place for efficient use of memory and is faster than the conventional row column frame rcf approach furthermore an application of 3 d video compression based 3 d dct ii is implemented using the 3 d new algorithm this has led to a substantial speed improvement for 3 d dct ii based compression systems and proved the validity of the developed algorithm

a new class of quasi newtonian methods for optimal learning in mlp networks in this paper we present a new class of quasi newton methods for an effective learning in large multilayer perceptron mlp networks the algorithms introduced in this work named lqn utilize an iterative scheme of a generalized bfgs type method involving a suitable family of matrix algebras l the main advantages of these innovative methods are based upon the fact that they have an o nlogn complexity per step and that they require o n memory allocations numerical experiences performed on a set of standard benchmarks of mlp networks show the competitivity of the lqn methods especially for large values of n

comments on fast computation of the discrete cosine transform and the discrete hartley transform by h s malvar the commenter shows that the algorithm presented in the above paper ibid vol assp 35 no 10 p 1484 5 oct 1987 requires exactly the same number of multiplications as but more additions than prevalent methods for the computation of the dht discrete hartley transform by existing methods contrary to the author s claim

split vector radix fast fourier transform the split radix approach for computing the discrete fourier transform dft is extended for the vector radix fast fourier transform fft to two and higher dimensions it is obtained by further splitting the n 2 n 2 transforms with twiddle factors in the radix 2 2 fft algorithm the generalization of this split vector radix fft algorithm to higher radices and higher dimensions is also presented by introducing a general approach for constructing the fast hartley transform fht from the corresponding fft new vector and split vector radix fht algorithms with the same desirable properties as their fft counterparts are obtained

liouville type theorem for nonlinear elliptic system involving grushin operator abstract we study the degenerate elliptic system of the form g u v p g v u q on r n r n 1 r n 2 where g x x 2 y is the grushin operator 0 and p q 1 we establish some liouville type results for stable solutions of the system in particular we prove the comparison principle a crucial step to establish such results as consequences we obtain a liouville type theorem for the scalar equation and provide a counterpart of the previous result in c cowan 2013 7

liouville theorems for anisotropic quasilinear inequalities abstract the purpose of this paper is to prove some nonexistence results for nonnegative weak solutions of differential inequalities l u u q or l u u q or l u 0 on r n here l is a quasilinear operator belonging to a wide class of operators including the anisotropic pseudo m laplacian operator the m laplacian operator the mean curvature operator acting in euclidean setting as well as their counterparts in carnot groups setting

fast hartley transforms for image processing the fast hartley transform fht is used to transform two dimensional image data because the hartley transform is real valued it does not require complex operations both spectra and autocorrelations of two dimensional ultrasound images of normal and abnormal livers were computed

a note on 2 d hartley transform in recent years the application of the hartley transform originally introduced by hartley 1942 has gained importance in seismic signal processing and interpretation saatcilar et al 1990 1992 the hartley transform is similar to the fourier transform but is computationally much faster than even the fast fourier transform bracewell 1983 bracewell et al 1986 sorensen et al 1985 pei and wu 1985 duhamel and vetterli 1987 zhou 1992 surprisingly we have not seen a clear definition of the 2 d hartley transform in the published literature