fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

aspects of total variation regularized l1 function approximation the total variation based image denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 has been generalized and modified in many ways in the literature one of these modifications is to use the l1 norm as the fidelity term we study the interesting consequences of this modification especially from the point of view of geometric properties of its solutions it turns out to have interesting new implications for data driven scale selection and multiscale image decomposition

semidirect products and reduction in mechanics this paper shows how to reduce a hamiltonian system on the cotangent bundle of a lie group to a hamiltonian system in the dual of the lie algebra of a semidirect product the procedure simplifies unifies and extends work of greene guillemin holm holmes kupershmidt marsden morrison ratiu sternberg and others the heavy top compressible fluids magnetohydrodynamics elasticity the maxwell vlasov equations and multifluid plasmas are presented as examples starting with lagrangian variables our method explains in a direct way why semidirect products occur so frequently in examples it also provides a framework for the systematic introduction of clebsch or canonical variables

bases in max algebra for n tuples over the algebraic system r r max concepts such as linear dependence space and basis may be defined by analogy with classical linear algebra whenever a space is finitely generated it possesses a basis and all its bases are trivially related and therefore have the same cardinality however for any given n 2 spaces with bases of arbitrary cardinality may be constructed as well as spaces with no basis

fuzzy matrices of permanent one abstract we study the n n fuzzy matrices of permanent one hall matrices which are generalizations of the reflexive fuzzy matrices we give some necessary and sufficient conditions for a hall matrix to have a generalized inverse in the semigroup hn of n n hall matrices as applications we also study the fuzzy linear maps and the principal left ideals of hn

invertible incline matrices and cramer s rule over inclines inclines are the additively idempotent semirings in which the products are less than or equal to factors thus inclines generalize boolean algebra fuzzy algebra and distributive lattice and the boolean matrices the fuzzy matrices and the lattice matrices are the prototypical examples of the incline matrices i e the matrices over inclines in this paper the complete description of the invertible incline matrices is given some necessary and sufficient conditions for an incline matrix to be invertible are studied cramer s rule over inclines is presented and the group of invertible incline matrices is investigated the main results in the present paper generalize and develop the corresponding results in the literatures for the boolean matrices the fuzzy matrices and the lattice matrices

the solution sets of infinite fuzzy relational equations with sup conjunctor composition on complete distributive lattices this paper deals with sup conjunctor composition fuzzy relational equations in infinite domains and on complete distributive lattices when its right hand side is a continuous join irreducible element or has an irredundant continuous join decomposition a necessary and sufficient condition describing an attainable solution resp an unattainable solution is formulated and some properties of the attainable solution resp the unattainable solution are shown further the structure of solution sets is investigated

on compositions of lattice matrices in this paper we give some properties of compositions of matrices whose elements belong to a distributive lattice we also construct an idempotent matrix from a given matrix and factor a matrix into a product of a square matrix and a rectangular matrix of the same dimension this square matrix has reflexivity and transitivity the main results obtained in this paper are generalizations of previous results on fuzzy matrices by ragab emam and hashimato

bases in semimodules over commutative semirings abstract in this paper the bases of a semimodule over a commutative semiring r are investigated some properties and characterizations of the bases are discussed and some equivalent conditions for a basis to be a free basis in a finitely generated free semimodule over r are given the different possible cardinalities for a basis in a finitely generated free semimodule over r are considered and some equivalent descriptions are obtained for a commutative semiring r satisfying the property that any two bases for a finitely generated free r semimodule have the same cardinality partial results obtained in the paper develop and generalize the corresponding results for commutative join semirings and for commutative zerosumfree semirings

algebraic analysis of fuzzy systems in this paper we have developed an algebraic theory suitable for the analysis of fuzzy systems we have used the notions of semiring and semimodule introduced the notion of semilinear space have given numerous examples of them and defined also the notions of linear dependence and independence we have shown that the composition operation which plays an essential role in the analysis of fuzzy systems because of its role in the compositional rule of inference can be interpreted as a homomorphism between special semimodules consequently this operation is in a certain sense a linear operation this property formally explains why fuzzy systems are attractive for applications

a method of relational fuzzy clustering based on producing feature vectors using fastmap the first stage of organizing objects is to partition them into groups or clusters the clustering is generally done on individual object data representing the entities such as feature vectors or on object relational data incorporated in a proximity matrix this paper describes another method for finding a fuzzy membership matrix that provides cluster membership values for all the objects based strictly on the proximity matrix this is generally referred to as relational data clustering the fuzzy membership matrix is found by first finding a set of vectors that approximately have the same inter vector euclidian distances as the proximities that are provided these vectors can be of very low dimension such as 5 or less fuzzy c means fcm is then applied to these vectors to obtain a fuzzy membership matrix in addition two dimensional vectors are also created to provide a visual representation of the proximity matrix this allows comparison of the result of automatic clustering to visual clustering the method proposed here is compared to other relational clustering methods including nerfcm rouben s method and windhams a p method various clustering quality indices are also calculated for doing the comparison using various proximity matrices as input simulations show the method to be very effective and no more computationally expensive than other relational data clustering methods the membership matrices that are produced by the proposed method are less crisp than those produced by nerfcm and more representative of the proximity matrix that is used as input to the clustering process

matrices over semirings introducing the concept of semi invertibility of square matrices over semirings some sufficient conditions for semi invertibility of square matrices over various kinds of semirings are obtained also a necessary and sufficient condition for semi invertibility of square matrices over semirings is obtained

blind motion deblurring using multiple images recovery of degraded images due to motion blurring is a challenging problem in digital imaging most existing techniques on blind deblurring are not capable of removing complex motion blurring from the blurred images of complex structures one promising approach is to recover the clear image using multiple images captured for the scene however in practice it is observed that such a multi frame approach can recover a high quality clear image of the scene only after multiple blurred image frames are accurately aligned during pre processing which is a very challenging task even with user interactions in this paper by exploring the sparsity of the motion blur kernel and the clear image under certain domains we propose an alternative iteration approach to simultaneously identify the blur kernels of given blurred images and restore a clear image our proposed approach is not only robust to image formation noises but is also robust to the alignment errors among multiple images a modified version of linearized bregman iteration is then developed to efficiently solve the resulting minimization problem experiments show that our proposed algorithm is capable of accurately estimating the blur kernels of complex camera motions with minimal requirements on the accuracy of image alignment as a result our method is capable of automatically recovering a high quality clear image from multiple blurred images

indices and periods of incline matrices abstract inclines are the additively idempotent semirings in which products are less than or equal to factors thus inclines generalize boolean algebra fuzzy algebra and distributive lattice and the boolean matrices the fuzzy matrices and the lattice matrices are the prototypical examples of the incline matrices i e the matrices over inclines this paper studies the power sequence of incline matrices in detail a necessary and sufficient condition for the incline matrix to have index is given and the indices of some incline matrices with indices are estimated it is proved that the period of n n incline matrix with index is a divisor of n and that the set of periods of n n incline matrices with indices is not bounded from above in the sense of a power of n for all n an equivalent condition and some sufficient conditions for the incline matrix to converge in finite steps are established the stability of the orbits of an incline matrix is considered and a theorem in fuzzy sets and systems 81 1996 227 is pointed out being false the results in the present paper include some previous results in the literatures which were obtained for the boolean matrices the fuzzy matrices and the lattice matrices among their special cases

eigenvalues and eigenvectors for matrices over distributive lattices abstract let l be a complete and completely distributive lattice a vector is said to be an eigenvector of a square matrix a over the lattice l if a for some l the elements are called the associated eigenvalues in this paper we characterize the eigenvalues and the eigenvectors and also the roots of the characteristic equation of a

eigen fuzzy sets and fuzzy relations abstract when r is a fuzzy relation between the elements of a finite set x the fuzzy sets a of x such that r a a max min composition are called eigen fuzzy sets the main result of this paper is the determination of the greatest eigen fuzzy set associated with a given fuzzy relation and we give three methods illustrated by an example we then state that the greatest eigen fuzzy set associated with r the transitive closure of r is exactly the one associated with r finally we describe how to obtain all fuzzy relations keeping invariant a given fuzzy set

invertible and nilpotent matrices over antirings abstract in this paper we characterize invertible matrices over an arbitrary commutative antiring s with 1 and find the structure of gl n s we find the number of nilpotent matrices over an entire commutative finite antiring we prove that every nilpotent n n matrix over an entire antiring can be written as a sum of log 2 n square zero matrices and also find the necessary number of square zero summands for an arbitrary trace zero matrix to be expressible as their sum

infinite fuzzy relational equations on a complete brouwerian lattice abstract let i be a finite and j an infinite index sets a a ij i j and b b i i i a given matrix and a column vector with elements from a complete brouwerian lattice in this paper the problem of a minimal solution of a fuzzy relational equation a x b where is the sup inf composite operation is investigated

some properties of infinite fuzzy relational equations on complete brouwerian lattices this paper deals with fuzzy relational equations email protected x b where both a a j j j and b are known b has an irredundant continuous join decomposition x x j j j t is unknown represents sup inf composition j is an infinite index set on complete brouwerian lattices at first a necessary and sufficient condition for existence of the attainable solutions the unattainable solutions respectively and some properties of the attainable solutions the unattainable solutions respectively are formulated then the solution set of the fuzzy relational equations is described

minimal join decompositions and their applications to fuzzy relation equations over complete brouwerian lattices this paper deals with the existence of minimal solutions of fuzzy relation equations over complete brouwerian lattices from the viewpoint of join decompositions first the concept of a minimal join decomposition is introduced then the existence conditions and properties of such decomposition are discussed as their applications the conditions for the existence of minimal solutions of fuzzy relation equations over complete brouwerian lattices and complete lattices are given respectively

generalized fuzzy h bi ideals and h quasi ideals of hemirings a new kind of generalized fuzzy h ideals of a hemiring namely the set membership variant set membership variantlogical orq fuzzy h bi ideal resp h quasi ideal is studied and the relationships between these generalized fuzzy h ideals are described some characterization theorems of prime and semiprime set membership variant set membership variantlogical orq fuzzy h bi ideals resp h quasi ideals of a hemiring are also given in particular we show that the h hemiregular hemirings and h intra hemiregular hemirings can be described by using some of their generalized fuzzy h ideals finally the implication based fuzzy h bi ideals resp h quasi ideals of a hemiring are considered

determinant theory for fuzzy matrices abstract we study determinant theory for fuzzy square matrices including some boolean matrices and consider the cayley hamilton theorem for these matrices we prove that det a adj a det a det adj a a where adj a denotes the adjoint matrix of a fuzzy matrix a

inversion of matrices over a commutative semiring it is a well known consequence of the elementary theory of vector spaces that if a and b are n by n matrices over a field or even a skew field such that ab 1 then ba 1 this result remains true for matrices over a commutative ring however it is not in general true for matrices over noncommutatives rings in this paper we show that if a and b are n by n matrices over a commutative semiring then the equation ab 1 implies ba 1 we give two proofs one algebraic in nature the other more combinatorial both proofs use a generalization of the familiar product law for determinants over a commutative semiring

on matrices over an arbitrary semiring and their generalized inverses abstract in this paper we consider matrices with entries from a semiring s we first discuss some generalized inverses of rectangular and square matrices we establish necessary and sufficient conditions for the existence of the moore penrose inverse of a regular matrix for an m n matrix a an n m matrix p and a square matrix q of order m we present necessary and sufficient conditions for the existence of the group inverse of qap with the additional property that p q a p q is a 1 2 inverse of a the matrix product used here is the usual matrix multiplication the result provides a method for generating elements in the set of 1 2 inverses of an m n matrix a starting from an initial 1 inverse of a we also establish a criterion for the existence of the group inverse of a regular square matrix we then consider a semiring structure m m n s made up of m n matrices with the addition defined entry wise and the multiplication defined as in the case of the hadamard product of complex matrices in the semiring m m n s we present criteria for the existence of the drazin inverse and the moore penrose inverse of an m n matrix when s is commutative we show that the hadamard product preserves the hermitian property and provide a schur type product theorem for the product a c c of a positive semidefinite n n matrix a and an n n matrix c

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

regular matrices in the semigroup of hall matrices abstract we study the regular matrices in the semigroup h n of hall matrices boolean matrices with positive permanent we study some necessary and sufficient conditions for a hall matrix to be regular in h n in terms of idempotent matrices adjoint matrices and identifying permutation matrices

bases in semilinear spaces over zerosumfree semirings this paper investigates the cardinality of a basis and the characterizations of a basis in semilinear space of n dimensional vectors over zerosumfree semirings first it discusses the cardinality of a basis and gives some necessary and sufficient conditions that each basis has the same number of elements then it presents some conditions that a set of vectors is a basis and that a set of linearly independent vectors can be extended to a basis in the end it shows a necessary and sufficient condition that two semilinear spaces are isomorphic

wavelet frame based surface reconstruction from unorganized points applications of wavelet frames to image restoration problems e g image deblurring and inpainting have been successful due to their redundancy and capability of sparsely approximating piecewise smooth functions like images see e g 13 14 8 however wavelet frames have not yet been used for surface reconstruction problems recently in 6 connections between one of the wavelet frame based image restoration model 8 28 48 and variational models e g the rof model 45 were rigorously established such connections not only grant new insights to wavelet frame based image restorations it also case a geometric explanation to wavelet frame based approaches this leads us to a wavelet frame based model as well as a fast algorithm to reconstruct implicit surfaces from unorganized point sets in r 3 we will demonstrate the effectiveness of the proposed model using several commonly used examples

relative equilibria and bifurcations in the generalized van der waals 4d oscillator abstract a uniparametric 4 dof family of perturbed hamiltonian oscillators in 1 1 1 1 resonance is studied as a generalization for several models for perturbed keplerian systems normalization by lie transforms only first order is considered here as well as geometric reduction related to the invariants associated to the symmetries is used based on the previous work of the authors a description is given for the lower dimensional relative equilibria in such normalized systems for which we introduce in this context the new concept of moment polytope in addition bifurcations of relative equilibria corresponding to 3d tori are studied in some particular cases where we focus on hamiltonian hopf bifurcations and bifurcations in the 3d van der waals and zeeman systems

inner products on semimodules over a commutative semiring abstract in this paper the inner products on the semimodules over a commutative semiring are investigated some characterizations for inner products and for orthogonal sets in the semimodules are given and standard orthogonal basis and orthogonal subsemimodule are discussed in particular an equivalent description is obtained for a semifield s satisfying the property that every standard orthogonal set in a finitely generated semimodule m over s can be extended to a standard orthogonal basis for m also the analogue of the kronecker capelli theorem is proved to be valid for a matrix equation over a commutative semiring partial results obtained in this paper generalize and develop corresponding results for semilinear spaces of n dimensional vectors over commutative zerosumfree semirings

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

on the set of solutions of composite fuzzy relation equations in this paper we introduce some algorithms which have minimization properties about the fuzziness of solutions in the maxmin fuzzy relation equations

noncommuting graphs of matrices over semirings we calculate diameters and girths of commuting graphs of the set of all nilpotent matrices over a semiring the group of all invertible matrices over a semiring and the full matrix semiring

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

solution sets of finite fuzzy relation equations with sup inf composition over bounded brouwerian lattices this paper considers the resolution of finite fuzzy relation equations with sup inf composition over a bounded brouwerian lattice the solution sets of finite fuzzy relation equations on a bounded brouwerian lattice are described in a similar way as those of linear spaces of n dimensional vectors in linear algebra

a rank theorem for vandermonde matrices we show that certain matrices built from vandermonde matrices are of full rank this result plays a key role in the construction of the limit theory of generic polynomials

dynamics of the kirchhoff equations i coincident centers of gravity and buoyancy abstract we study the kirchhoff equations for a rigid body immersed in an incompressible irrotational inviscid fluid in the case that the centers of buoyancy and gravity coincide the resulting dynamical equations form a non canonical hamiltonian system with a six dimensional phase space which may be reduced to a four dimensional two degree of freedom canonical system using the two casimir invariants of motion restricting ourselves to ellipsoidal bodies we identify several completely integrable subcases in the general case we analyze existence linear and nonlinear stability and bifurcations of equilibria corresponding to steady translations and rotations including mixed modes involving simultaneous motion along two body axes some of which we show can be stable by perturbing from the axisymmetric integrable case we show that slightly asymmetric ellipsoids are typically non integrable and we investigate their dynamics with a view to using motions along homo and heteroclinic orbits to execute specific maneuvers in autonomous underwater vehicles

wavelet frame based scene reconstruction from range data abstract how to reconstruct the scene a visible surface from a set of scattered noisy and possibly sparse range data is a challenging problem in robotic navigation and computer graphics as most real scenes can be modeled by piecewise smooth surfaces traditional surface fitting techniques e g smoothing spline generally can not preserve sharp discontinuities of surfaces based on sparse approximation of piecewise smooth functions in frame domain we propose a new tight frame based formulation for reconstructing a piecewise smooth surface from a sparse range data set which is robust to both additive noise and outliers furthermore the resulting minimization problem from our formulation can be efficiently solved by the split bregman method 1 2 the numerical experiments show that the proposed approach is capable of reconstructing a piecewise smooth surface with sharp edges from sparse range data corrupted with noise and outliers

resolution of matrix equations over arbitrary brouwerian lattices this paper studies the problem of solving a matrix equation over an arbitrary not necessarily complete brouwerian lattice a criterion for the solvability and a method for finding all solutions of the equation are obtained over an arbitrary self dual brouwerian lattice an equivalent condition for the unique solution a necessary and sufficient condition for the minimal solution and a procedure for constructing minimal solutions less than or equal to any given solution of the equation are presented it is shown that the results of the paper can be applied to the determination of generalized inverses of a matrix over an arbitrary brouwerian lattice

conditions under which the solution sets of fuzzy relational equations over complete brouwerian lattices form lattices it is well known that the solution set of a fuzzy relational equation with sup inf composition is a join semilattice in general not a meet semilattice this paper investigates the conditions under which the solution sets of fuzzy relational equations with sup inf composition over complete brouwerian lattices form lattices we first give some properties of the decompositions of elements in complete lattices then present a necessary and sufficient condition that the meet of a solution with any other solution is again a solution finally we show some necessary and sufficient conditions that the solution sets are lattices

nonlinear stability of the equilibria in a double bar rotating system we study the nonlinear stability of the equilibria corresponding to the motion of a particle orbiting around a two finite orthogonal straight segment the potential is a logarithmic function and may be considered as an approximation to the one generated by irregular celestial bodies using arnold s theorem for non definite quadratic forms we determine the nonlinear stability of the equilibria for all values of the parameter of the problem moreover the resonant cases are determined and the stability is investigated

method of solution to fuzzy equations in a complete brouwerian lattice abstract up to now how to solve a fuzzy relation equation in a complete brouwerian lattice is still an open problem as di nola et al point out to this problem the key problem is whether there exists a minimal element in the solution set when a fuzzy relation equation is solvable in this paper we first show that there is a minimal element in the solution set of a fuzzy relation equation a x b where a a 1 a 2 a n and b are known and x x 1 x 2 x n t is unknown when its solution set is nonempty and b has an irredundant finite join decomposition further we give the method to solve a x b in a complete brouwerian lattice under the same conditions finally a method to solve a more general fuzzy relation equation in a complete brouwerian lattice when its solution set is nonempty is also given under similar conditions

minimal orderings and quadratic forms on a free module over a supertropical semiring abstract this paper is a sequel to 6 in which we introduced quadratic forms on a module over a supertropical semiring r and analyzed the set of bilinear companions of a single quadratic form v r in case the module v is free any semi module over a semiring gives rise to what we call its minimal ordering which is a partial order iff the semiring is upper bound any polynomial map q or quadratic form then induces a pre order which can be studied in terms of q minimal elements which are elements a which cannot be written in the form b c where b a but q b q a we determine the q minimal elements by examining their support but the class of all polynomial maps in up to rank v variables is itself a module over r so the basic properties of the minimal ordering are applied to this r module or its submodule quad v consisting of quadratic forms on v this is a significant initial step in the classification of quadratic forms over semirings arising in tropical mathematics quad v is the sum of two disjoint submodules ql v and rig v consisting of the quasilinear and the rigid quadratic forms on v respectively cf 6 both ql v and rig v are free with explicitly known bases but quad v itself is almost never free

solution sets of fuzzy relational equations on complete brouwerian lattices this work studies the problem of solving a fuzzy relational equation with composition on a complete brouwerian lattice where is a pseudo t norm two necessary and sufficient conditions that solution sets are nonempty are obtained when is normal and the solution set of the equation is nonempty a sufficient condition that there exists maximal solutions is given further the solution set of the equation is presented

latticized linear optimization on the unit interval this paper considers the latticized linear optimization llo problem and its variants which are a special class of optimization problems constrained by fuzzy relational equations or inequalities we show that an optimal solution to such a problem can be obtained in polynomial time as long as the objective function is a max separable function with continuous monotone components we further show that the set of all optimal solutions is fully determined by one maximum optimal solution and a finite number of minimal optimal solutions the maximum optimal solution can be constructed in polynomial time once the optimal objective value is known while the detection of all minimal optimal solutions in an efficient manner remains as a challenging problem the relation between llo and max separable optimization and related issues are also investigated

restoration of chopped and nodded images by framelets in infrared astronomy an observed image from a chop and nod process can be considered as the result of passing the original image through a high pass filter here we propose a restoration algorithm which builds up a tight framelet system that has the high pass filter as one of the framelet filters our approach reduces the solution of restoration problem to that of recovering the missing coefficients of the original image in the tight framelet decomposition the framelet approach provides a natural setting to apply various sophisticated framelet denoising schemes to remove the noise without reducing the intensity of major stars in the image a proof of the convergence of the algorithm based on convex analysis is also provided simulated and real images are tested to illustrate the efficiency of our method over the projected landweber method

linear independence in bottleneck algebras abstract let r be a linearly ordered set a bottleneck algebra is the set r together with two operations a b max a b and a b min a b in this paper we suggest various definitions of linear independence of sets of n tuples over r study their characteristics and interrelations

deconvolution a wavelet frame approach this paper devotes to analyzing deconvolution algorithms based on wavelet frame approaches which has already appeared in chan et al siam j sci comput 24 4 1408 1432 2003 appl comput hormon anal 17 91 115 2004a int j imaging syst technol 14 91 104 2004b as wavelet frame based high resolution image reconstruction methods we first give a complete formulation of deconvolution in terms of multiresolution analysis and its approximation which completes the formulation given in chan et al siam j sci comput 24 4 1408 1432 2003 appl comput hormon anal 17 91 115 2004a int j imaging syst technol 14 91 104 2004b this formulation converts deconvolution to a problem of filling the missing coefficients of wavelet frames which satisfy certain minimization properties these missing coefficients are recovered iteratively together with a built in denoising scheme that removes noise in the data set such that noise in the data will not blow up while iterating this approach has already been proven to be efficient in solving various problems in high resolution image reconstructions as shown by the simulation results given in chan et al siam j sci comput 24 4 1408 1432 2003 appl comput hormon anal 17 91 115 2004a int j imaging syst technol 14 91 104 2004b however an analysis of convergence as well as the stability of algorithms and the minimization properties of solutions were absent in those papers this paper is to establish the theoretical foundation of this wavelet frame approach in particular a proof of convergence an analysis of the stability of algorithms and a study of the minimization property of solutions are given

sufficient conditions for a nondegenerate hopf bifurcation in a generalized lagrange poisson problem in this paper we provide sufficient conditions for the existence of a nondegenerate hamiltonian hopf bifurcation at the equilibria corresponding to the rotation around the vertical axis of a symmetric gyrostat with a fixed point under the effect of an axially symmetric potential

max plus algebra based wavelet transforms and their fpga implementation for image coding in the present paper we propose new image coding methods based on max plus algebra based wavelet transforms mp wavelets max plus algebra is an algebraic structure on the set of integers endowed with maximum minimum and standard addition as operations the proposed wavelet decomposition schemes are novel classes of morphological wavelets which in contrast to the existing approaches involve only integers and only max min and addition in their computation since they do not involve floating point calculations and multiplications mp wavelets have a very low computational complexity and they are suitable for efficient hardware implementation through image coding experiments using 10 000 images extracted from low resolution web crawled misc database the characteristics of the proposed mp wavelets are presented furthermore we show a computational complexity analysis to compare mp wavelets to one of the fastest wavelet transforms the conventional haar wavelet the applicability of mp wavelets in video coding is also confirmed by image coding experiments using residual frames finally the field programmable gate arrays fpga implementation of mp wavelets is presented to confirm suitability of mp wavelets for hardware implementation

standard orthogonal vectors in semilinear spaces and their applications abstract this paper investigates the standard orthogonal vectors in semilinear spaces of n dimensional vectors over commutative zerosumfree semirings first we discuss some characterizations of standard orthogonal vectors then as applications we obtain some necessary and sufficient conditions that a set of vectors is a basis of a semilinear subspace which is generated by standard orthogonal vectors prove that a set of linearly independent nonstandard orthogonal vectors cannot be orthogonalized if it has at least two nonzero vectors and show that the analog of the kronecker capelli theorem is valid for systems of equations

invertible matrices and semilinear spaces over commutative semirings this paper deals with invertible matrices and semilinear spaces over commutative semirings some necessary and sufficient conditions for matrices to be invertible over commutative semirings are obtained the condition under which the cardinality of each basis of semilinear space of n dimensional vectors is n is given in the end the factor rank of matrices over semirings is investigated

on invertible matrices over antirings abstract an antiring is a semiring which is zerosumfree i e a b 0 implies a b 0 for any a b in this semiring in this paper the complete description of the invertible matrices over a commutative antiring is given and some necessary and sufficient conditions for a matrix over a commutative antiring to be invertible are obtained also cramer s rule over commutative antirings is presented the main results in this paper generalize and develop the corresponding results for the boolean matrices the fuzzy matrices the lattice matrices and the incline matrices

infinite fuzzy relational equations with sup conjunctor on complete brouwerian lattices abstract in this paper a system of infinite fuzzy relational equations with sup conjunctor on complete brouwerian lattices is investigated some properties of attainable resp unattainable partially attainable solutions of the system are first shown which are closely related minimal solutions some necessary and sufficient conditions for attainable resp minimal solutions are then represented and in the end the set of attainable solutions is given when the right hand sides of the system either are join irreducible elements or have irredundant finite join decompositions

regular fuzzy matrices and fuzzy equations abstract there have been many researches on fuzzy relational equations in this paper under the general framework of fuzzy matrix theory we first introduce ranks and regularity properties of fuzzy matrices then for a regular matrix a mn f we study the generalized inverses of a and the solutions of a fuzzy equation x a b

the solution set of a fuzzy relational equation with sup conjunctor composition in a complete lattice this paper deals with a fuzzy relational equation with sup conjunctor composition in a complete lattice we investigate its properties and describe its solution set in particular we give a sufficient and necessary condition that the solution set is nonempty and a sufficient condition that there exist minimal elements in the solution set

inverses of l fuzzy matrices abstract inverses and generalized inverses of matrices over a brouwerian lattice are considered necessary and sufficient conditions for the existence of inverses g inverses thierrin vagner inverses minimum norm g inverses least squares g inverses and moore penrose inverses of matrices are obtained algorithms for finding all these types of generalized inverses are given

affine systems in l2 rd the analysis of the analysis operator abstract discrete affine systems are obtained by applying dilations to a given shift invariant system the complicated structure of the affine system is due first and foremost to the fact that it is not invariant under shifts affine frames carry the additional difficulty that they are global in nature it is the entire interaction between the various dilation levels that determines whether the system is a frame and not the behaviour of the system within one dilation level we completely unravel the structure of the affine system with the aid of two new notions the affine product and a quasi affine system this leads to a characterization of affine frames the induced characterization of tight affine frames is in terms of exact orthogonality relations that the wavelets should satisfy on the fourier domain several results such as a general oversampling theorem follow from these characterizations most importantly the affine product can be factored during a multiresolution analysis construction and this leads to a complete characterization of all tight frames that can be constructed by such methods moreover this characterization suggests very simple sufficient conditions for constructing tight frames from multiresolution of particular importance are the facts that the underlying scaling function does not need to satisfy any a priori conditions and that the freedom offered by redundancy can be fully exploited in these constructions an

on matrix equations in a class of complete and completely distributive lattices matrix equations of the form ax b and ya b are considered in a class of complete and completely distributive lattices where the multiplication operation of matrices is defined either by the max min or by the min max way necessary and sufficient conditions for the solvability of the equations are obtained and for the solvable case the entire solution set and the largest solution are determined by using relative pseudo or relative lower pseudocomplements in lattices the results are seen to be a generalization of 4 5 6 and in a sense also an extension of 3 as an application the g inverse and thierrin vagner inverses of matrices are considered

determinantal identities over commutative semirings abstract we present a development of determinantal identities over commutative semirings this includes a generalization of the cauchy binet and laplace theorems as well as results on compound matrices and adjoints it is further shown that laplace s theorem is a special case of the grade s adjoint identity

equilibria stability and hamiltonian hopf bifurcation of a gyrostat in an incompressible ideal fluid abstract for a gyrostat in a incompressible ideal fluid by writing kirchhoff s equations as a lie poisson system and using a non canonical hamiltonian formulation we provide the expressions of the equilibria when the gyrostatic momentum is constant with the form l 0 0 l and present necessary and sufficient conditions for the stability of some of them via the energy casimir method and the study of the linearized equations of the motion finally using a recent geometric method introduced by hanssmann and van der meer we give a sufficient condition for the existence of a non degenerate hamiltonian hopf bifurcation at those equilibria when the gyrostat is symmetric

some results in the setting of fuzzy relation equations theory abstract in this paper we point out certain theoretical aspects of fuzzy relation equations connecting some known results between composite and o fuzzy equations several theorems are obtained and some examples are provided too

dioids and semirings links to fuzzy sets and other applications besides the classical algebraic structures of groups rings and fields which have long been the almost exclusive reference concepts used in mathematical modelling other algebraic structures such as dioids and semirings have emerged in the last two or three decades in connection with modelling and solving a rich variety of non classical problems e g in decision analysis fuzzy set theory operations research automatic control and mathematical physics the present paper aims at providing an overview of applications of dioid and semiring structures stressing links with fuzzy sets and emphasizing linear algebraic problems solving linear systems computing eigenvalues and eigenvectors non classical path finding problems using algebras of endomorphisms and connections between dioid structure and nonlinear analysis in view of solving problems in mathematical physics

wavelet frame based algorithm for 3d reconstruction in electron microscopy in electron microscopy three dimensional 3d reconstruction is one key component in many computerized techniques for solving 3d structures of large protein assemblies using electron microscopy images of particles main challenges in 3d reconstruction include very low signal to noise ratio and very large scale of data sets involved in the computation motivated by the recent advances of sparsity based regularization in the wavelet frame domain for solving various linear inverse problems in imaging science we proposed a wavelet tight frame based 3d reconstruction approach that exploits the sparsity of the 3d density map in a wavelet tight frame system the proposed approach not only runs efficiently in terms of cpu time but also requires a much lower memory footprint than existing framelet based regularization methods the convergence of the proposed iterative scheme and the functional it minimizes is also examined together with the connection to existing wavelet frame based regularizations the numeric

necessary and sufficient conditions for existence of maximal solutions for inf α composite fuzzy relational equations on complete brouwerian lattices an inf a composite fuzzy relational equation and its equation system are investigated in finite domains a necessary and sufficient solvability condition is proposed for the equation then all its maximal solutions and the whole solution set are determined subsequently the whole solution set for the equation system is determined in infinite domains sufficient conditions for existence of a maximal solution for the equation and the equation system are shown respectively afterwards a necessary and sufficient condition that there exists a maximal solution which is more than or equal to any solution is presented for the equation

the semiring of matrices over a finite chain let l m denote the chain 0 1 2 m 1 with the usual ordering and m n l m the matrix semiring of all nxn matrices with elements in l m we firstly introduce some order preserving semiring homomorphisms from m n l m to m l k by using these homomorphisms we show that a matrix over the finite chain l m can be decomposed into the sum of some matrices over the finite chain l k where k

edge preserving image denoising and estimation of discontinuous surfaces in this paper we are interested in the problem of estimating a discontinuous surface from noisy data a novel procedure for this problem is proposed based on local linear kernel smoothing in which local neighborhoods are adapted to the local smoothness of the surface measured by the observed data the procedure can therefore remove noise correctly in continuity regions of the surface and preserve discontinuities at the same time since an image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects this procedure can be applied directly to image denoising numerical studies show that it works well in applications compared to some existing procedures

the semigroup of incline hall matrices this paper investigates the semigroup of incline hall matrices an incline hall matrix means an incline matrix which is greater than or equal to an incline invertible matrix it is proved that any incline hall matrix has index some necessary and sufficient conditions for an incline hall matrix to be regular in the semigroup of incline hall matrices are given and green s relations on the such semigroup are described also the sandwich semigroup of incline hall matrices is considered the main results in the present paper generalize some previous results on boolean matrices fuzzy matrices and lattice matrices

lagrangian relative equilibria for a gyrostat in the three body problem bifurcations and stability in this paper we consider the non canonical hamiltonian dynamics of a gyrostat in the frame of the three body problem using geometric mechanic methods we study the approximate dynamics of the truncated legendre series representation of the potential of an arbitrary order working in the reduced problem we study the existence of relative equilibria that we refer to as lagrange type following the analogy with the standard techniques we provide necessary and sufficient conditions for the linear stability of lagrangian relative equilibria if the gyrostat morphology form is close to a sphere thus we generalize the classical results on equilibria of the three body problem and many results on them obtained by the classic approach for the case of rigid bodies

high order total variation based image restoration the total variation tv denoising method is a pde based technique that preserves edges well but has the sometimes undesirable staircase effect namely the transformation of smooth regions ramps into piecewise constant regions stairs in this paper we present an improved model constructed by adding a nonlinear fourth order diffusive term to the euler lagrange equations of the variational tv model our technique substantially reduces the staircase effect while preserving sharp jump discontinuities edges we show numerical evidence of the power of resolution of this novel model with respect to the tv model in some 1d and 2d numerical examples

a heuristic method to compute the approximate postinverses of a fuzzy matrix this paper considers the problem of computing the approximate inverses of a fuzzy matrix under max min composition a polynomial time algorithm is proposed to construct an approximate postinverse by minimizing an evaluation function which balances two different distance measures the obtained approximate postinverse contains no zero columns unless the given fuzzy matrix itself contains zero rows subsequently the techniques for solving fuzzy relational equations are applied to obtain all the approximate postinverses of equal quality