on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

homogenization of the boundary value for the neumann problem in this paper we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating neumann boundary data such a problem raised due to its importance for higher order approximation in homogenization theory high order approximation gives rise to the so called boundary layer phenomenon as a consequence we obtain the pointwise and w1 p convergence results our techniques are based on fourier analysis

general form of lattice valued fuzzy sets under the cutworthy approach in this note a new solution of problem of synthesis of fuzzy sets is presented in other words necessary and sufficient conditions are formulated under which for a given family of subsets f of a set x and a fixed complete lattice l there is a fuzzy set m x l such that the collection of cuts of m coincides with f moreover it is proved that the general form of lattice valued fuzzy sets considering families of cuts are the type of fuzzy sets having the codomain 0 1 c for a suitable chosen cardinal c

operations on fuzzy ideals in this paper we give suitable definitions of the operations of l fuzzy ideals in a ring as intersection addition multiplication and residual division and we prove some fundamental properties of the operations analogous to those that hold for the operations of ordinary ideals see 3

geometric regularity criteria for incompressible navier stokes equations with navier boundary conditions abstract we study the regularity criteria for weak solutions to the 3d incompressible navier stokes equations in terms of the direction of vorticity taking into account the boundary conditions a boundary regularity theorem is proved on regular curvilinear domains with a family of oblique derivative boundary conditions provided that the directions of vorticity are coherently aligned up to the boundary as an application we establish the boundary regularity for weak solutions to navier stokes equations in round balls half spaces and right circular cylindrical ducts subject to the classical navier and kinematic boundary conditions

on fuzzy subalgebras the aim of this paper is to find all fuzzy subalgebras of low dimensional simple algebras over the field of real numbers

optimal design of nonlinear phase fir filters with prescribed phase error constrained least squares design and constrained chebyshev design of one and two dimensional nonlinear phase fir filters with prescribed phase error are considered in this paper by a unified semi infinite positive definite quadratic programming approach in order to obtain unique optimal solutions we propose to impose constraints on the complex approximation error and the phase error by introducing a sigmoid phase error constraint bound function the group delay error can be greatly reduced a goldfarb idnani based algorithm is presented to solve the semi infinite positive definite quadratic program resulting from the constrained least squares design problem and then applied after some modifications to the constrained chebyshev design problem which is proved in this paper to be equivalent also to a semi infinite positive definite quadratic program through design examples the proposed method is compared with several existing methods simulation results demonstrate the effectiveness and efficiency of the proposed method

existence and uniqueness of fuzzy ideals let r be a commutative ring the idea of identifying a fuzzy ideal of r with its corresponding chain of level ideals and its range of values although widely used in the literature for the study of fuzzy ideals has never been investigated in a general setting before we investigate in this paper the more general problem of characterization of all those fuzzy ideals that can be identified with a given arbitrary family c of subsets of r together with a given arbitrary subset s of 0 1 necessary and sufficient conditions for the existence and uniqueness of such fuzzy ideals are established in particular we obtain that uniqueness always holds true for artinian rings moreover examples are presented to further support our results and shed more light on the above mentioned problem of identification we finish by raising a natural question that is left as an open problem for further investigation

the homomorphic image of a fuzzy subgroup is always a fuzzy subgroup let l be a completely distributive complete lattice with universal bound 0 and 1 and x any group we will prove that the image of a fuzzy group x l under a homomorphism f x y is always a fuzzy group without any restriction on and f

on the roughness induced effective boundary conditions for an incompressible viscous flow abstract we consider the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities it is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channel after studying the corresponding boundary layers we obtain rigorously the navier friction condition it is valid when the size and amplitude of the imperfections tend to zero furthermore the coefficient in the law is determined through an auxiliary boundary layer type problem and the tangential drag force and the effective mass flow are determined up to order o e3 2 the value of the effective coefficient is shown to be independent with respect to the position of the mean surface in the range of o e

on t fuzzy subfield and t fuzzy vector subspaces abstract in this paper we improve the definition of t fuzzy subfield and observe some of its properties the concept of t fuzzy vector subspaces of a t fuzzy subfield of a field will also be investigated and we further introduce the concept of t fuzzy subalgebra

fuzzy direct sums of fuzzy rings abstract in this paper we introduce the concepts of the fuzzy weak direct sum and the fuzzy complete direct sum of fuzzy subrings of commutative rings we prove some basic properties analogous to those of ordinary rings

on the lattice of fuzzy ideals of a ring abstract first we prove that in the lattice of all fuzzy left right ideals with the same tip t using the technique of strong cut by this we obtain the following results 1 we point out that the lattice of all fuzzy ideals of a ring is not distributive thus the main theorem l f1 r is distributive in majumdar and sultana 1996 is erroneous 2 the lattice of all fuzzy left right ideals with same tip t of a ring r is modular this generalizes the main theorem in ajmal and thomas 1995

average of the navier s law on the rapidly oscillating boundary we study the flow of newtonian fluid in a domain with periodically wrinkled boundary with slip navier s boundary condition the goal of this paper is to replace a microscopic boundary condition posed on the rough boundary by some macroscopic boundary condition posed on the middle surface of the oscillating boundary depending on the shape of wrinkles and the friction coefficient we get four different effective models

fuzzy groups with sup property we investigate the inner structure of fuzzy subgroups with sup property we provide a characterization of this type of fuzzy subgroups in terms of their level subsets it is shown that the property of being a fuzzy subgroup with sup property is invariant under homomorphism and the homomorphic preimage of a fuzzy subgroup with sup property is also a fuzzy subgroup with sup property moreover we investigate the lattice structure of the class lnt of fuzzy normal subgroups of a group g each of which assumes the same value t at the identity of g it is proved that the subclass lnst of fuzzy subgroups with sup property of lnt constitutes a sublattice of lnt the modularity of lnst is derived as a consequence of the modularity of lnt

a multiscale finite element method for partial differential equations posed in domains with rough boundaries we propose and analyze a finite element scheme of multiscale type to deal with elliptic partial differential equations posed in domains with rough boundaries there is no need to assume that the boundary is periodic in any sense so the method is quite general on the other hand if the boundary is periodic we prove convergence of the scheme

tensor products of semilattices and fuzzy ideals we study complete fuzzy ideals on semilattices from the point of view of tensor products of semilattices we show that the lattice of all complete fuzzy ideals on a semilattice is an extension of tensor product we define the notion of semicomplete bi ideals and show that the lattice of all fuzzy ideals on a distributive lattice is isomorphic to the lattice of all semicomplete bi ideals moreover we show that the lattice of all complete fuzzy ideals on a distributive algebraic lattice is distributive

flows of incompressible viscous liquids with anisotropic wall slip abstract this paper deals with a boundary value problem for the stokes equations with a general direction dependent navier type slip boundary condition this problem models the steady laminar flow of an incompressible linearly viscous liquid in a bounded domain with an impermeable rough boundary with variable and anisotropic roughness it is proved that the problem has a unique weak solution

fuzzy primary representations of fuzzy ideals abstract let r be a commutative ring with identity and let a be a fuzzy ideal of r then a is said to have a fuzzy primary representation if a is the intersection of a finite number of fuzzy primary ideals we show that every fuzzy ideal a of r such that a 0 1 has a fuzzy primary representation if and only if r is artinian we show that uniqueness properties for reduced primary representations of ideals in the usual sense carry over to fuzzy ideals

roughness based on fuzzy ideals the theory of rough set proposed by pawlak and the theory of fuzzy set proposed by zadeh are complementary generalizations of classical set theory many sets are naturally endowed with two binary operations addition and multiplication one concept which does this is a ring this paper concerns a relationship between rough sets fuzzy sets and ring theory it is a continuation of ideas presented by kuroki and wang n kuroki p p wang the lower and upper approximations in a fuzzy group inform sci 90 1996 203 220 we consider a ring as a universal set and we assume that the knowledge about objects is restricted by a fuzzy ideal in fact we apply the notion of fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring some characterizations of the above approximations are made and some examples are presented

properties and power spectral densities of cp based oqam ofdm systems offset quadrature amplitude modulation ofdm oqam ofdm systems have low sidelobes but require complex receivers for broadband channels to deal with this problem cyclic prefix cp based oqam ofdm systems have been proposed in the literature in this paper we study oqam ofdm and two existing cp based oqam ofdm systems and propose a new cp based system with good spectrum performance we investigate their properties and analyze their power spectral densities psds we show that the continuous time transmitted cp oqam ofdm signal after the cp insertion is equivalent to a truncated signal obtained by inserting cp and cyclic suffix cs to the discrete time input data symbols in the oqam ofdm system which simplifies the calculation of the psd of the transmitted cp oqam ofdm signal and also implies that the psd of the cp oqam ofdm may be affected by the truncation we show that the perfect reconstruction pr condition for the cp oqam ofdm system is actually the same as that for the oqam ofdm system when the length of the prototype filter is not more than the length of the transmitted cp oqam ofdm signal of each block excluding the cp we also compare three cp based oqam ofdm systems with windowed cp ofdm systems numerical results show that the theoretical and simulated psds of the transmitted signals match well cp based oqam ofdm systems perform better than windowed cp ofdm systems considering both the psd and bit error rate ber performances and the newly proposed cp based oqam ofdm system has the best psd performance in the three cp based oqam ofdm systems with an increase of the data rate overhead

vanishing viscosity limit for the 3d magnetohydrodynamic system with a slip boundary condition abstract this work investigates the solvability regularity and vanishing viscosity limit of the 3d viscous magnetohydrodynamic system in a class of bounded domains with a slip boundary condition

the lattice of fuzzy ideals of a ring the set of all fuzzy ideals of a ring r is partially ordered with respect to the natural ordering of fuzzy sets in r it has been shown that this is a lattice but not a sublattice of the lattice of all fuzzy sets in r this lattice of all fuzzy ideals of r is complete distributive and bounded and has neither atoms nor dual atoms

fuzzy intersection equations and primary representations abstract let r be a commutative ring we show that if every ideal of r has a primary representation then a finitely generated fuzzy ideal of r has a fuzzy primary representation which contains a primary representation of the support of we show how this result can be applied to a system of fuzzy intersection equations in order to display the crisp part and the fuzzy part of the solution

homogenization of parabolic equation in an evolving domain with an oscillating boundary abstract in this article we study the existence uniqueness and homogenization of the heat equation in a domain with highly oscillating and evolving time dependent boundary and an inhomogeneous time dependent data on the oscillating part of boundary motivated by fluid structure interaction problems we rewrite the parabolic equation in a reference configuration which transforms the boundary oscillations into rapidly oscillating coefficients finally we obtain the effective coefficients and corrector results in the reference configuration

a metatheorem for deriving fuzzy theorems from crisp versions a metatheorem is developed that allows theorems containing references to crisp substructures to be reformulated to refer to fuzzy substructures theorems concerning fuzzy substructures in semigroups rings and lattices are derived in concise fashion from analogous theorems that concern crisp substructures the modularity of the lattice of fuzzy normal subgroups of a group is concisely derived from the modularity of its lattice of crisp normal subgroups the fundamental tool used is a function that represents the algebra of fuzzy subsets of a set as a subdirect product of copies of the algebra of crisp subsets

fuzzy equivalence relation redefined abstract in this note a weak fuzzy equivalence relation is defined generally superseding most of the established results the concept is discussed in the setting where the min transitivity of a fuzzy relation is replaced by the general t norm transitivity

characterizations of monoids by the properties of their fuzzy subsystems abstract in this paper we initiate the study of fuzzy subsystems of an s system where s is a monoid with zero and s systems are representations of s we introduce the notions of pure fuzzy purely fuzzy maximal and purely fuzzy prime ideals of a monoid s it is shown that the set of purely fuzzy prime ideals of s admits the structure of a topological space called the pure fuzzy spectrum of s we also define a pure fuzzy subsystem of an s system and call an s system fuzzy normal if each of its subsystems is pure fuzzy monoids of which all s systems are fuzzy normal are characterized it is shown among other results that such monoids are right weakly regular

numerical approximation of laminar flows over rough walls with sharp asperities abstract we consider a viscous incompressible fluid filling an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rough wall the latter is assumed to consist of a plane wall covered with periodically distributed asperities whose size depends on a small parameter e 0 the assumption of sharp asperities is made that is the height of the asperities does not vanish as e 0 the rough wall is at rest and the plane wall is moving at a constant horizontal velocity we assume that the flow is governed by the stationary stokes equations we give an asymptotic approximation of the stokes flow under the rugose region by a couette flow depending on the size e of the asperities we then build a numerical approximation of the couette flow based on a partial domain decomposition method

couette flows over a rough boundary and drag reduction we consider the couette flow between two plates the lower plate is fixed and has periodically placed riblets of the characteristic size on it in the limit 0 we find the effective couette navier flow as an o 2 approximation for the effective mass flow and an o 2 l 1 approximation for the velocity in the effective solution the effect of roughness enters through the navier slip condition with the matrix coefficient in front of the effective shear stress calculated using a boundary layer problem furthermore an o 2 approximation for the tangential drag force is found in all estimates explicit dependence on the kinematic viscosity the velocity of the upper plate and the distance between the plates l 3 is kept also the uniqueness of the solution is expressed through a non linear algebraic condition linking and l 3 then the result is applied to the viscous sub layers around immersed bodies strictly containing the surface riblets it is found that for the riblets of the characteristic size being of the order smaller or equal to the approximation obtained for the tangential drag could be applied we compare and for realistic data and our results lead to the conclusion that the riblets reduce significantly tangential drag which may explain their presence on the skin of nektons

embedding lattices of fuzzy subalgebras into lattices of crisp subalgebras abstract given a universal algebra a we define an algebra a where a and a are of the same type and generate the same variety of algebra next we define a map e lf a lc a where lf a is the lattice of fuzzy subalgebras of a and lc a is the lattice of crisp subalgebras of a for many algebras a the map e is shown to be a lattice embedding as a corollary of this fact we derive the results that the lattice of fuzzy normal subgroups of a group and the lattice of fuzzy ideals of a ring are both modular lattices

viscous boundary layers for the navier stokes equations with the navier slip conditions we tackle the issue of the inviscid limit of the incompressible navier stokes equations when the navier slip with friction conditions are prescribed on impermeable boundaries we justify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in prandtl s theory and a linear behavior this analysis holds for general regular domains in both dimensions two and three

effective boundary condition for stokes flow over a very rough surface abstract the main purpose of this paper is to derive a wall law for a flow over a very rough surface we consider a viscous incompressible fluid filling a 3 dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a very rough wall the latter consists in a plane wall covered with periodically distributed asperities which size depends on a small parameter e 0 and with a fixed height we assume that the flow is governed by the stationary stokes equations using asymptotic expansions and boundary layer correctors we construct and analyze an asymptotic approximation of order o e 3 2 0 being arbitrary small in the h 1 norm for the velocity and in the l 2 norm for the pressure we derive an effective boundary condition of navier type then expressing the boundary layer terms in terms of the homogenized solution and the solution of a cell problem we obtain an effective approximation in the whole domain of the flow

analysis and design of ofdm oqam systems based on filterbank theory a discrete time analysis of the orthogonal frequency division multiplex offset qam ofdm oqam multicarrier modulation technique leading to a modulated transmultiplexer is presented the conditions of discrete orthogonality are established with respect to the polyphase components of the ofdm oqam prototype filter which is assumed to be symmetrical and with arbitrary length fast implementation schemes of the ofdm oqam modulator and demodulator are provided which are based on the inverse fast fourier transform non orthogonal prototypes create intersymbol and interchannel interferences isi and ici that in the case of a distortion free transmission are expressed by a closed form expression a large set of design examples is presented for ofdm oqam systems with the number of subcarriers going from four up to 2048 which also allows a comparison between different approaches to get well localized prototypes

some results on l fuzzy modules abstract an l fuzzy quotient module of a module is redefined and a modular complete pseudo complemented lattice structure is given to the set of all l fuzzy modules of a given module some isomorphisms between the lattices or posets of l fuzzy modules are obtained finally a galois connection is established between two lattices of l fuzzy modules of homomorphic modules

the lattices of fuzzy ideals of a ring we investigate the lattice structure of various sublattices of the lattice of fuzzy subrings of a given ring we prove that a special class of fuzzy ideals forms a modular sublattice of the lattice of fuzzy ideals of a ring

prototype filter optimization to minimize stopband energy with npr constraint for filter bank multicarrier modulation systems recently filter bank multicarrier fbmc modulations have attracted increasing attention the filter banks of fbmc are derived from a prototype filter that determines the system performance such as stopband attenuation intersymbol interference isi and interchannel interference ici in this paper we formulate a problem of direct optimization of the filter impulse response coefficients for the fbmc systems to minimize the stopband energy and constrain the isi ici unfortunately this filter optimization problem is nonconvex and highly nonlinear nevertheless observing that all the functions in the optimization problem are twice differentiable we propose using the alpha based branch and bound alpha bb algorithm to obtain the optimal solution however the convergence time of the algorithm is unacceptable because the number of unknowns i e the filter coefficients in the optimization problem is too large the main contribution of this paper is that we propose a method to dramatically reduce the number of unknowns of the optimization problem through approximation of the constraints so that the optimal solution of the approximated optimization problem can be obtained with acceptable computational complexity numerical results show that the proposed approximation is reasonable and the optimized filters obtained with the proposed method achieve significantly lower stopband energy than those with the frequency sampling and windowing based techniques

a shape hessian based boundary roughness analysis of navier stokes flow the influence of boundary roughness characteristics on the rate of dissipation in a viscous fluid is analyzed using shape calculus from the theory of optimal control of systems governed by partial differential equations to study the mapping mathscr d from surface roughness topography to the dissipation rate of a navier stokes flow expressions for the shape gradient and hessian are determined using the velocity method in the case of couette and poiseuille flows a flat boundary is a local minimum of the dissipation rate functional thus for small roughness heights the behavior of mathscr d is governed by the flat wall shape hessian operator whose eigenfunctions are shown to be the fourier modes for stokes flow the shape hessian is determined analytically and its eigenvalues are shown to grow linearly with the wavenumber of the shape perturbation for navier stokes flow the shape hessian is computed numerically and the ratio of its eigenvalues to those of a stokes flow depend only on the re

the lattices of fuzzy subgroups and fuzzy normal subgroups abstract here we discuss various types of sublattices of the lattice of fuzzy subgroups of a given group we prove that a special class of fuzzy normal subgroups constitutes a modular sublattice of the lattice of fuzzy subgroups

a complete study of the lattices of fuzzy congruences and fuzzy normal subgroups in this paper we introduce the concepts of t fuzzy congruences and t fuzzy equivalences using these ideas we investigate completely on one hand the lattice structures of the set of fuzzy equivalence relations on a group and the set of fuzzy congruences and on the other hand the lattice structures of the set of fuzzy subgroups and fuzzy normal subgroups our study reveals some finer and interesting facts about these lattices it is proved among other results that the set ct of all t fuzzy congruences of a group g forms lattice and also the set lnt of all those fuzzy normal subgroups which assume the same value t at e the identity of g forms a lattice as an important result we prove that the lattices ct and lnt are isomorphic it is also shown that the lattices ct and lnt are modular moreover we construct various important sublattices of the lattice ct and exhibit their relationship by lattice diagrams in the process we improve and unify many results of earlier authors on fuzzy congruences

generation of optimal periodic oscillations for the control of boundary layers this paper is devoted to the optimal design problem of periodic surfaces solutions to elliptic partial differential equations occurring in oscillating domains exhibit boundary layer behavior and we intend to control the first order correctors using a mathematical framework derived from the homogenization techniques the existence of an optimal boundary layer control is proved

effective boundary conditions for laminar flows over periodic rough boundaries effective boundary conditions or wall laws are proposed for a laminar flow over a rough wall with periodic roughness elements these effective conditions are posed on a regularized boundary which allows the details of the wall to be avoided and dramatically reduces the computational cost the effective conditions stem from an asymptotic expansion of the solution which is presented here both first and second order conditions are discussed and tested numerically on bidimensional cases

artificial conditions for the linear elasticity equations in this paper we consider the equations of linear elasticity in an exterior domain we exhibit artificial boundary conditions on a circle which lead to a non coercive second order boundary value problem in the particular case of an axisymmetric geometry explicit computations can be performed in fourier series proving the well posedness except for a countable set of parameters a perturbation argument allows to consider near circular domains we complete the analysis by some numerical simulations

fuzzy nil radicals and fuzzy semiprimary ideals of rings abstract an attempt is made to define a fuzzy semiprimary ideal by using the idea of the fuzzy nil radical of a fuzzy ideal the level ideals of a such a fuzzy ideal are examined and the ring of fuzzy cosets of such a fuzzy ideal is studied the algebraic nature of such fuzzy ideals under homomorphisms is also ascertained

on existence of p valued fuzzy sets with a given collection of cuts a representation theorem of families of subsets by poset valued fuzzy sets is presented namely necessary and sufficient conditions are given under which for a given family of subsets f of a set x and a fixed poset p there is a fuzzy set m x p such that the collection of cuts of m coincides with f

the lattice of fuzzy normal subgroups is modular abstract we have introduced and discussed in a recent paper 2 various sublattices such as lf lt and lfnt of the lattice l of fuzzy subgroups of a given group in particular we proved that the sublattice lfn of fuzzy normal subgroups with finite range and tip t is a modular sublattice of l here we remove all the restrictions on the choice of fuzzy normal subgroups and prove that the class of all fuzzy normal subgroups ln forms the modular sublattice of l as a tool we prove an important result that the fuzzy subgroups generated by a pair of fuzzy normal subgroups of a group is fuzzy normal

time domain channel estimation for oqam ofdm systems algorithms and performance bounds in this paper we first present a general time domain model for the channel estimation in the orthogonal frequency division multiplexing system with offset quadrature amplitude modulation oqam ofdm and utilize the frequency domain pilots to estimate the time domain channel impulse responses different form the conventional methods there is no specific requirement for the length of the symbol interval compared to the the maximum channel delay spread in the proposed scheme furthermore with the proposed time domain model the channel statistic information could be utilized to improve the performance of the channel estimation then we propose two channel estimation schemes i e linear minimum mean square error lmmse and weighted least square wls and we also derive their corresponding bayesian cramer rao bound bcrb and cramer rao bound crb bounds respectively simulation results demonstrate that the bcrb and crb bounds could be achieved by the proposed lmmse and wls methods respectively moreover simulation results show that the proposed methods are much robust to the time synchronization error compared to the conventional frequency domain methods and imply that the pulse shaping filter with waveforms concentrated in the time domain could be employed in oqam ofdm systems to improve the channel estimation performance and spectral efficiency

relevance of the slip condition for fluid flows near an irregular boundary we consider the navier stokes equation in a domain with a rough boundary the roughness is modeled by a small amplitude and small wavelength oscillation with typical scale varepsilon ll 1 for periodic oscillation it is well known that the best homogenized that is regular in varepsilon boundary condition is of navier type such result still holds for random stationary irregularities as shown recently by the first author 5 15 we study here arbitrary irregularity patterns

effective boundary condition at a rough surface starting from a slip condition abstract we consider the homogenization of the navier stokes equation set in a channel with a rough boundary of small amplitude and wavelength it was shown recently that for any non degenerate roughness pattern and for any reasonable condition imposed at the rough boundary the homogenized boundary condition in the limit e 0 is always no slip we give in this paper error estimates for this homogenized no slip condition and provide a more accurate effective boundary condition of navier type our result extends those obtained in basson and gerard varet 2008 6 and gerard varet and masmoudi 2010 13 in which the special case of a dirichlet condition at the rough boundary was examined

invertibility of morphisms in the category of l fuzzy left r modules abstract in this paper we obtain the sufficient and necessary condition for a left right invertible morphism in the category of l fuzzy left r modules and point out a mistake made in fuzzy sets and systems 21 1987 105 113

fuzzy semistar operations on integral domains in this paper we introduce the notion of fuzzy semistar operation on an integral domain and relate it to the existing notion of fuzzy star operation we show that the set of all fuzzy semistar operations on the integral domain is a complete lattice we also characterize when an overring of a domain is a prufer domain and when an overring is a flat module over the domain in terms of a fuzzy semistar operation

sequential quadratic programming method for solution of electromagnetic inverse problems in this paper a new algorithm namely a reduced hessian sequential quadratic programming sqp method for solving electromagnetic inverse problems is proposed the electromagnetic inverse problem is considered to be a constrained nonlinear programming the reduced hessian sqp method finds the solution of this constrained nonlinear programming by solving a sequential of quadratic programming subproblems the reduced hessian scheme is applied to reduce the requirement of computational memory of the basic sqp method for large inverse problems numerical results are presented to demonstrate the efficiency and accuracy of the proposed method and some comparisons show that the proposed method has a better convergence and a faster speed than the previous methods

a characterization of l fuzzy prime ideals abstract in this paper the concepts of a l fuzzy prime and a l fuzzy completely prime ideal are given and some fundamental lemmas are proved in particular bijections among some of the l fuzzy prime ideals of two homomorphic rings are constructed also a characterization of a l fuzzy prime ideal of a ring is given

prime l fuzzy ideals and primary l fuzzy ideals abstract in this paper the concepts of a primary l fuzzy ideal and a prime l fuzzy ideal and p primary are introduced and some fundamental propositions proved in particular a structural theorem for a primary l fuzzy ideal belonging to a prime l fuzzy ideal is given

the lattice of l ideals of a ring is modular in this paper we extend the notion of a tip extended pair of fuzzy subgroups to l ideals of a ring we prove that the sum of two tip extended l ideals of an arbitrary pair of l ideals of a ring is the least l ideal containing the union of the given l ideals using this construction of join of l ideals we prove that the lattice of all l ideals of a given ring is modular

fuzzy semistar operations of finite character on integral domains this paper is devoted to the construction of examples of fuzzy semistar operations on integral domains a special case of interest is the fuzzy semistar operation of finite character we show that the set of fuzzy semistar operations of finite character on an integral domain is a complete lattice we also prove that the fuzzy semistar operation on an integral domain defined by a finite collection of overrings and union preserving fuzzy semistar operations of finite character on the overrings is of finite character an example is constructed to prove that if the collection of overrings is infinite the corresponding fuzzy semistar operation may not be of finite character we describe the set of fuzzy semistar operation of finite character on valuation domains

constructing wall laws with domain decomposition or asymptotic expansion techniques abstract this paper is concerned with the numerical simulation of flows of viscous fluids over rough surfaces the proposed methodology introduces consistant equivalent wall laws using domain decomposition techniques with nonmatching grids and local periodicity assumptions the paper describes this approach with its theoretical background studies its limitations and its potential applicability and compares its results to the boundary conditions that are obtained by alternative asymptotic strategies

completion of ordered structures by cuts of fuzzy sets an overview the aim of the paper is to present a role of fuzzy sets in the theory of ordered structures main algebraic properties of cuts of fuzzy sets are given and a completion of partially ordered sets to complete lattices is described it turns out that this completion is equivalent with the famous dedekind macneille completion but the algorithm presented here is much simpler

tom head s join structure of fuzzy subgroups abstract tom head formulated a metatheorem in 1995 fuzzy sets and systems 73 1995 349 with an idea of directly proving the fuzzy analogs of results of classical mathematics in the process he defined a vital concept of tip extended pair of fuzzy subgroups in this paper we use this concept to define the join of fuzzy subgroups using this definition of join we have provided a much simpler and direct proof of modularity of the lattice of fuzzy normal subgroups moreover we have also demonstrated other applications regarding quasinormality and fuzzy submonoid generated by two fuzzy submonoids using the redefined sup min product due to kim inform sci 91 1996 77

weighted hilbert spaces for the stationary exterior stokes problem with navier slip boundary conditions abstract in this paper we analyze the three dimensional exterior stokes problem with the navier slip boundary conditions describing the flow of a viscous and incompressible fluid past an obstacle where it is assumed that the fluid may slip at the boundary because the flow domain is unbounded we set the problem in weighted spaces in order to control the behavior at infinity of the solutions this functional framework also allows to prescribe various behaviors at infinity of the solutions growth or decay existence and uniqueness of solutions are shown in a hilbert setting which gives the tools for a possible numerical analysis of the problem weighted korn s inequalities are the key point in order to study the variational problem

effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions to deal with multi scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition an effective surface theory is developed which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions a typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material to develop the concept of effective surface a multi domain decomposition approach is applied in this framework velocity and concentration at micro scale are estimated with an asymptotic expansion of deviation terms with respect to macro scale velocity and concentration fields closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions the evolution of some effective properties and the impact of surface geometry peclet schmidt and damkohler numbers are investigated finally comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface for two kinds of configurations

vanishing viscous limits for the 2d lake equations with navier boundary conditions abstract the vanishing viscosity limit is considered for the viscous lake equations with navier friction boundary conditions we prove that the inviscid limit satisfies the inviscid lake equations and the results include flows generated by l p initial vorticity with 1 p

tight weyl heisenberg frames in l sup 2 z tight weyl heisenberg frames in l sup 2 z are the tool for short time fourier analysis in discrete time they are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory good resolution of short time fourier analysis in the joint time frequency plane is not attainable unless some redundancy is introduced that is the reason for considering overcomplete weyl heisenberg expansions the main result of this correspondence is a complete parameterization of finite length tight weyl heisenberg frames in l sup 2 z with arbitrary rational oversampling ratios this parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks which is introduced first

the lattice of fuzzy left right ideals of a ring is modular we use the technique of nested set to study the structure of the lattice of all fuzzy left right ideals of a given ring we give a way to depict the supremum of fuzzy left right ideals by nested set and prove that the lattice of all fuzzy left right ideals of a given ring is modular

homogenization of the brush problem with a source term in l 1 we consider a domain which has the form of a brush in 3d or the form of a comb in 2d i e an open set which is composed of cylindrical vertical teeth distributed over a fixed basis all the teeth have a similar fixed height their cross sections can vary from one teeth to another one and are not supposed to be smooth moreover the teeth can be adjacent i e they can share parts of their boundaries the diameter of every tooth is supposed to be less than or equal to e and the asymptotic volume fraction of the teeth as e tends to zero is supposed to be bounded from below away from zero but no periodicity is assumed on the distribution of the teeth in this domain we study the asymptotic behavior as e tends to zero of the solution of a second order uniformly elliptic equation with a zeroth order term which is bounded from below away from zero when the homogeneous neumann boundary condition is satisfied on the whole of the boundary first we revisit the problem where the source term belongs to l 2 this is a classical problem but our homogenization result takes place in a geometry which is more general that the ones which have been considered before moreover we prove a corrector result which is new then we study the case where the source term belongs to l 1 working in the framework of renormalized solutions and introducing a definition of renormalized solutions for degenerate elliptic equations where only the vertical derivative is involved such a definition is new we identify the limit problem and prove a corrector result

wall laws for fluid flows at a boundary with random roughness the general concern of this paper is the effect of rough boundaries on fluids we consider a stationary flow governed by incompressible navier stokes equations in an infinite domain bounded by two horizontal rough plates the roughness is modeled by a spatially homogeneous random field with characteristic size e a mathematical analysis of the flow for small e is performed the navier s wall law is rigorously deduced from this analysis this substantially extends former results obtained in the case of periodic roughness notably in 16 17 2007 wiley periodicals inc

navier wall law for nonstationary viscous incompressible flows abstract we study the navier wall law for the two dimensional initial boundary value problem of the navier stokes equations in a domain with a rough boundary the navier wall law is verified for the initial data in c 1 class under the natural compatibility condition our proof relies on the boundary layer analysis and the l theory of the navier stokes equations in the half space

r primary l representations of l ideals we examine the basic properties of prime l ideals primary l ideals and r radicals of l ideals where l is a completely distributive lattice we determine to what extent every l ideal has an r primary l representation