a new two dimensional fast cosine transform algorithm the discrete cosine transform 2 d dct is based on a one dimensional fast cosine transform 1 d fct algorithm instead of computing the 2 d transform using the row column method the 1 d algorithm is extended by means of the vector radix approach derivation based on both the sequence splitting and kronecker matrix product method are discussed the sequence splitting approach has the advantage that all the underlying operations are shown clearly while the matrix product representations are more compact and readily generalized to higher dimensions the bit reversal operations are placed before the recursive additions so that the recursive operations can be performed in a very regular manner this greatly simplifies the indexing problem in the software implementation of the algorithms the vector radix algorithm saves 25 multiplications as compared with the row column method

fast algorithm for computing discrete cosine transform an efficient method for computing the discrete cosine transform dct is proposed based on direct decomposition of the dct the recursive properties of the dct for an even length input sequence is derived which is a generalization of the radix 2 dct algorithm based on the recursive property a new dct algorithm for an even length sequence is obtained the proposed algorithm is very structural and requires fewer computations when compared with others the regular structure of the proposed algorithm is suitable for fast parallel algorithm and vlsi implementation

a fast recursive algorithm for computing the discrete cosine transform the discrete cosine transform dct is widely applied in various fields including image data compression because it operates like the karhunen loeve transform for stationary random data this paper presents a recursive algorithm for dct with a structure that allows the generation of the next higher order dct from two identical lower order dct s as a result the method for implementing this recursive dct requires fewer multipliers and adders than other dct algorithms

on the multiplicative complexity of discrete cosine transforms the multiplicative complexity of discrete cosine transforms dcts of arbitrary dimensions on input sizes which are powers of two are obtained new upper bounds on the multiplicative complexity of scaled dcts on input sizes which are powers of two are also obtained

travelling fronts and entire solutions of the fisher kpp equation in ℝn this paper is devoted to time global solutions of the fisher kpp equation in n where f is a c 2 concave function on 0 1 such that f 0 f 1 0 and f 0 on 0 1 it is well known that this equation admits a finite dimensional manifold of planar travelling fronts solutions by considering the mixing of any density of travelling fronts we prove the existence of an infinite dimensional manifold of solutions in particular there are infinite dimensional manifolds of nonplanar travelling fronts and radial solutions furthermore up to an additional assumption a given solution u can be represented in terms of such a mixing of travelling fronts

nonplanar traveling fronts in reaction diffusion equations with combustion and degenerate fisher kpp nonlinearities abstract this paper is concerned with nonplanar traveling fronts in reaction diffusion equations with combustion nonlinearity and degenerate fisher kpp nonlinearity our study contains two parts in the first part we establish the existence of traveling fronts of pyramidal shape in r 3 and in the second part we establish the existence and stability of v shaped traveling fronts in r 2

scaled dct s on input sizes that are composite given efficient scaled discrete cosine transforms dct s of size p and q where p and q are relatively prime we present methods for constructing fast algorithms to compute scaled dct s and scaled inverse dct s of size pq extensions to multidimensional transforms are also given

the evolution of reaction diffusion waves in a class of scalar reaction diffusion equations algebraic decay rates in this paper we consider an initial boundary value problem for the generalized fisher kolmogorov petrovskii piscounov fkpp equation of order m 1 with the non negative initial data being of o x at large x dimensionless distance where 1 m 1 the corresponding problem when 1 m 1 having been considered in detail by needham and barnes nonlinearity 12 1999 41 58 using matched asymptotic expansions we are able to obtain the complete structure of the solution to the initial boundary value problem for large t time which exhibits the formation of a permanent form reaction diffusion travelling wave structure this being in contrast to the case when 1 m 1 where the large t time structure exhibits the formation of an accelerating phase wave

bistable transition fronts in rn abstract this paper is chiefly concerned with qualitative properties of some reaction diffusion fronts the recently defined notions of transition fronts generalize the standard notions of traveling fronts in this paper we show the existence and the uniqueness of the global mean speed of bistable transition fronts in r n this speed is proved to be independent of the shape of the level sets of the fronts the planar fronts are also characterized in the more general class of almost planar fronts with any number of transition layers these qualitative properties show the robustness of the notions of transition fronts but we also prove the existence of new types of transition fronts in r n that are not standard traveling fronts thus showing that the notions of transition fronts are broad enough to include other relevant propagating solutions

periodic traveling curved fronts in reaction diffusion equation with bistable time periodic nonlinearity abstract this paper is concerned with the existence and stability of periodic traveling curved fronts for reaction diffusion equations with time periodic bistable nonlinearity in two dimensional space by constructing supersolution and subsolution we prove the existence of periodic traveling wave fronts furthermore we show that the front is globally stable

the uniqueness and asymptotic stability of pyramidal traveling fronts in the allen cahn equations abstract this paper studies the uniqueness and the asymptotic stability of a pyramidal traveling front in the three dimensional whole space for a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity for this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces moreover we characterize the pyramidal traveling front in another way that is we write it as a combination of two dimensional v form waves on the edges this characterization also uniquely determines a pyramidal traveling front

on traveling wave solutions of fisher s equation in two spatial dimensions it is shown for the quadratic fisher equation in two spatial dimensions that along with a plane wave there exist several other traveling waves with nontrivial front geometry some of the solutions are found in explicit form others are constructed approximately the dispersion relationship and velocity curvature dependence generated by these solutions are studied

variable temporal length 3 d discrete cosine transform coding three dimensional discrete cosine transform 3 d dct coding has the advantage of reducing the interframe redundancy among a number of consecutive frames while the motion compensation technique can only reduce the redundancy of at most two frames however the performance of the 3 d dct coding will be degraded for complex scenes with a greater amount of motion this paper presents a 3 d dct coding with a variable temporal length that is determined by the scene change detector our idea is to let the motion activity in each block be very low while the efficiency of the 3 d dct coding could be increased experimental results show that this technique is indeed very efficient the present approach has substantial improvement over the conventional fixed length 3 d dct coding and is also better than that of the moving picture expert group mpeg coding

an ergodic control problem for constrained diffusion processes existence of optimal markov control an ergodic control problem for a class of constrained diffusion processes is considered the goal is the almost sure minimization of long term cost per unit time the main result of the paper is that there exists an optimal markov control for the considered problem it is shown that under the assumption of regularity of the skorohod map and the assumption that the drift vector field takes values in a certain cone of stability the class of controlled diffusion processes considered have strong uniform in control stability properties the role of the boundary is critical in obtaining the stability and ergodic control results for the class of controlled constrained diffusion processes considered in this work since the domains are unbounded and the corresponding unconstrained diffusions are typically transient these stability properties are key in obtaining appropriate tightness estimates once these estimates are available the remaining work lies in identifying weak limits of a certain family of occupation measures in this regard an extension to the echeverria weiss kurtz characterization of invariant measures of markov processes to the case of constrained controlled processes considered in this paper is proved this characterization result is also crucially used in proving the compactness of the family of invariant measures of markov processes corresponding to all possible markov controls

existence and global stability of traveling curved fronts in the allen cahn equations abstract this paper is concerned with existence and stability of traveling curved fronts for the allen cahn equation in the two dimensional space by using the supersolution and the subsolution we construct a traveling curved front and show that it is the unique traveling wave solution between them our supersolution can be taken arbitrarily large which implies some global asymptotic stability for the traveling curved front

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

traveling waves with multiple and nonconvex fronts for a bistable semilinear parabolic equation we construct new examples of traveling wave solutions to the bistable and balanced semilinear parabolic equation in input amssym bbb r n 1 our first example is that of a traveling wave solution with two non planar fronts that move with the same speed our second example is a traveling wave solution with a nonconvex moving front to our knowledge no existence results of traveling fronts with these type of geometric characteristics have been previously known our approach explores a connection between solutions of the semilinear parabolic pde and eternal solutions to the mean curvature flow in input amssym bbb r n 1

the structure of vector radix fast fourier transforms a general form of the matrix representation for multidimensional vector radix fast fourier transform fft algorithms using decimation in frequency is presented a structure theorem is devised to construct systematically various vector radix decimation in frequency fft algorithms from their 1 d counterparts logic diagrams are provided to facilitate the software and hardware implementation of the algorithms the computational complexity of several of the algorithms is considered

transition fronts of time periodic bistable reaction diffusion equations in rn abstract this paper is concerned with the existence and qualitative properties of transition fronts for time periodic bistable reaction diffusion equations in r n we first show that any almost planar transition front is actually planar regardless of the number of transition layers then we prove that all transition fronts admit a global mean speed and it holds c where c is the speed of the planar traveling front finally we establish the existence of a transition front in r n that is not a standard traveling front such a front behaves like three moving time periodic planar fronts as time goes to and like a time periodic v shaped traveling front as time goes to

pyramidal traveling fronts in a nonlocal delayed diffusion equation abstract recently there have been great progresses on the study of nonplanar traveling wave solutions of reaction diffusion equations in this paper we study the pyramidal traveling fronts of nonlocal delayed diffusion equation in r n with n 2 by using the comparison principle and establishing super and subsolution since the effect of nonlocal delay we show that nonlocal delayed diffusion equation in n dimensional space has a pyramidal traveling front u t x v x x n s t toward x n axis for each s c 0 in particular two dimensional traveling curved front and three dimensional pyramidal fronts for nonlocal delayed diffusion equation in r 2 and r 3 are also established respectively moreover we also extend our results to generally nonlocal delayed reaction diffusion equation

a new algorithm to compute the discrete cosine transform a new algorithm is introduced for the 2m point discrete cosine transform this algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms and it makes the system simpler

one and two dimensional constant geometry fast cosine transform algorithms and architectures this paper presents general radix one and two dimensional 1 d and 2 d constant geometry fast cosine transform algorithms and architectures suitable for vlsi owing to their regular structures a constant geometry algorithm is obtained by shuffling the rows and columns of each decomposed dct matrix that corresponds to a butterfly stage the 1 d algorithm is derived and then it is extended to the 2 d case based on the derived algorithms the architectures with a flexible degree of parallelism are discussed

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

symmetry of traveling wave solutions to the allen cahn equation in mathbb r 2 in this paper we prove even symmetry of monotone traveling wave solutions to the balanced allen cahn equation in the entire plane related results for the unbalanced allen cahn equation are also discussed

two dimensional curved fronts in a periodic shear flow abstract this paper is devoted to the study of traveling fronts of reaction diffusion equations with periodic advection in the whole plane r 2 we are interested in curved fronts satisfying some conical conditions at infinity we prove that there is a minimal speed c such that curved fronts with speed c exist if and only if c c moreover we show that such curved fronts are decreasing in the direction of propagation that is they are increasing in time we also give some results about the asymptotic behaviors of the speed with respect to the advection diffusion and reaction coefficients

curved fronts in the belousov zhabotinskii reaction diffusion systems in r 2 in this paper we consider a diffusion system with the belousov zhabotinskii bz for short chemical reaction following brazhnik and tyson 4 and perez munuzuri et al 45 who predicted v shaped fronts theoretically and discovered v shaped fronts by experiments respectively we give a rigorous mathematical proof of their results we establish the existence of v shaped traveling fronts in r 2 by constructing a proper supersolution and a subsolution furthermore we establish the stability of the v shaped front in r 2 c 2018 elsevier inc all rights reserved