nonlinear spectral instability of steady state flow of a viscous liquid past a rotating obstacle we show that a steady state solution to the system of equations of a navier stokes flow past a rotating body is nonlinearly unstable if the associated linear operator mathcal l has a part of the spectrum in the half plane lambda in mathbb c mathrm re lambda 0 our result does not follow from known methods mainly because the basic nonlinear operator is not bounded in the same space in which the instability is studied as an auxiliary result of independent interest we also show that the uniform growth bound of the c 0 semigroup mathrm e mathcal l t is equal to the spectral bound of operator mathcal l

axiomatics for fuzzy rough sets abstract a fuzzy t rough set consists of a set x and a t similarity relation r on x where t is a lower semi continuous triangular norm we generalize the farinas prade definition for the upper approximation operator a i x i x of a fuzzy t rough set x r given originally for the special case t min to the case of arbitrary t we propose a new definition for the lower approximation operator a i x i x of x r our definition satisfies the two important identities a a a and a a a as well as a number of other interesting properties we provide axiomatics to fully characterize those upper and lower approximations

the steady motion of a navier stokes liquid around a rigid body let mathcal r be a body moving by prescribed rigid motion in a navier stokes liquid mathcal l that fills the whole space and is subject to given boundary conditions and body force under the assumptions that with respect to a frame mathcal f attached to mathcal r these data are time independent and that their magnitude is not too large we show the existence of one and only one corresponding steady motion of mathcal l with respect to mathcal f such that the velocity field at the generic point x in space decays like x 1 these solutions are physically reasonable in the sense of finn 10 in particular they are unique and satisfy the energy equation among other things this result is relevant in engineering applications involving orientation of particles in viscous liquid 14

a monolithic multi time step computational framework for first order transient systems with disparate scales abstract developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering a desirable feature to have in a numerical formulation for multiscale transient problems is to be able to employ different time steps multi time step coupling and different time integrators and different numerical formulations mixed methods in different regions of the computational domain to this end we present two new monolithic multi time step mixed coupling methods for first order transient systems we shall employ unsteady advection diffusion reaction equation with linear decay as the model problem which offers several unique challenges in terms of non self adjoint spatial operator and rich features in the solutions we shall employ the dual schur domain decomposition technique to split the computational domain into an arbitrary number of subdomains it will be shown that the governing equations of the decomposed problem after spatial discretization will be differential algebraic equations this is a crucial observation to obtain stable numerical results two different methods of enforcing compatibility along the subdomain interface will be used in the time discrete setting a systematic theoretical analysis which includes numerical stability influence of perturbations bounds on drift along the subdomain interface will be performed the first coupling method ensures that there is no drift along the subdomain interface but does not facilitate explicit implicit coupling the second coupling method allows explicit implicit coupling with controlled but non zero drift in the solution along the subdomain interface several canonical problems will be solved to numerically verify the theoretical predictions and to illustrate the overall performance of the proposed coupling methods finally we shall illustrate the robustness of the proposed coupling methods using a multi time step transient simulation of a fast bimolecular advective diffusive reactive system

the energy equality and regularity results for the stationary navier stokes equations on the exterior of a rotating obstacle abstract consider the stationary navier stokes equations on the exterior of a rotating body which is also moving in the direction of the axis of rotation with constant velocity k e 1 for every external force f div f f l 2 the existence of a weak solution u satisfying finite dirichlet integral i e u l 2 can be obtained by means of the classical galerkin method we first prove that the weak solution u satisfies the additional regularity property u k e 1 l 4 without any condition on f except for f l 2 this regularity result is enough to ensure the validity of the generalized energy equality using these we therefore obtain the uniqueness for weak solutions under some smallness condition on the data

an application of rough sets to graph theory this paper studies the testing bipartiteness of simple undirected graphs based on generalized rough sets a new binary relation induced from a simple undirected graph is first defined the concept of quasi outer definable sets is then introduced and some of its important properties are investigated finally based on the quasi outer definable set a new algorithm is designed for testing bipartiteness of a simple undirected graph experiments show that the proposed algorithm is more efficient than the traditional one when the graph is represented by an adjacency matrix

roughness in cayley graphs in this paper rough approximations of cayley graphs are studied and rough edge cayley graphs are introduced furthermore a new algebraic definition for pseudo cayley graphs containing cayley graphs is proposed and a rough approximation is expanded to pseudo cayley graphs in addition rough vertex pseudo cayley graphs and rough pseudo cayley graphs are introduced some theorems are provided from which properties such as connectivity and optimal connectivity are derived this approach opens new research fields such as data networks

the analysis of stationary viscous incompressible flow through a rotating radial blade machine existence of a weak solution abstract the paper deals with the analysis of the mathematical model of the two dimensional stationary viscous incompressible flow through a rotating radial blade machine the flow is described and studied in the rotating frame the paper provides the classical and weak formulation of the corresponding boundary value problem the boundary condition on the outflow is the so called natural boundary condition with the nonlinear term proposed by bruneau and fabrie 1996 1 and also modified by a term arising from the rotation of the machine the existence of a weak solution is proved

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

extensions and intentions in the rough set theory abstract the approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension it is different from the well known approaches in the literature in that the upper approximations and the lower approximations of unknown sets are considered as certain families of known sets this approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets which are analogous to classical operations on sets the basic results presented in this paper based on certain ideas of the second author were formulated by the first author in his doctoral dissertation prepared under the supervision of the third author

on existence and uniqueness of solutions to a boussinesq system with nonlinear and mixed boundary conditions abstract we study a boussinesq system in a bounded domain with an outlet boundary portion where fluid can leave or re enter on this boundary part we consider a do nothing condition for the fluid flow and a new artificial condition for the heat transfer that couples nonlinearly the fluid velocity and temperature the latter can be further adjusted if convective or conductive phenomena are dominant we prove existence and in some cases uniqueness of weak solutions to stationary and evolutionary problems by a fixed point strategy under suitable assumptions on the data a variety of numerical tests shows the improved performance of the new artificial condition with respect to other standard choices in the literature

on the structure of rough prime primary ideals and rough fuzzy prime primary ideals in commutative rings this paper is a continuation of ideas presented by davvaz roughness in rings inform sci 164 2004 147 163 roughness based on fuzzy ideals inform sci 176 2006 2417 2437 we introduce the notions of rough prime primary ideals and rough fuzzy prime primary ideals in a ring and give some properties of such ideals also we discuss the relations between the upper and lower rough prime primary ideals and the upper and lower approximations of their homomorphism images

a mixed multiscale finite element method for elliptic problems with oscillating coefficients the recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large scale structure of the solutions without resolving all the fine scale structures motivated by the numerical simulation of flow transport in highly heterogeneous porous media we propose a mixed multiscale finite element method with an over sampling technique for solving second order elliptic equations with rapidly oscillating coefficients the multiscale finite element bases are constructed by locally solving neumann boundary value problems we provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic while such a simplifying assumption is not required by our method it allows us to use homogenization theory to obtain the asymptotic structure of the solutions numerical experiments are carried out for flow transport in a porous medium with a random log normal relative permeability to demonstrate the efficiency and accuracy of the proposed method

roughness of a fuzzy set an integration between the theories of fuzzy sets and rough sets has been attempted by providing a measure of roughness of a fuzzy set several properties of this new measure are established some of the possible applications for handling uncertainties in the field of pattern recognition are mentioned

large time behavior of a generalized oseen evolution operator with applications to the navier stokes flow past a rotating obstacle consider the motion of a viscous incompressible fluid in a 3d exterior domain d when a rigid body mathbb r 3 setminus d moves with prescribed time dependent translational and angular velocities for the linearized non autonomous system l q l r smoothing action near t s as well as generation of the evolution operator t t s t ge s ge 0 was shown by hansel and rhandi j reine angew math 694 1 26 2014 under reasonable conditions in this paper we develop the l q l r decay estimates of the evolution operator t t s as t s rightarrow infty and then apply them to the navier stokes initial value problem

the navier stokes equations in ℝn with linearly growing initial data consider the equations of navier stokes on n with initial data u0 of the form u0 x u0 x mx where m is an n n matrix with constant real entries and u0 lp n it is shown that under these assumptions the equations of navier stokes admit a unique local solution in lp n moreover if etm 1 for all t 0 then this mild solution is even analytic in x this is surprising since the underlying semigroup of ornstein uhlenbeck type is not analytic in contrast to the stokes semigroup

on the ornstein uhlenbeck operator in spaces of continuous functions we study the realization of the ornstein uhlenbeck operator a in the space of the uniformly continuous and bounded functions in rn we prove that it generates a semigroup which is neither strongly continuous nor analytic but enjoys nice smoothing properties such properties are used to prove a schauder type theorem for the elliptic equation u au f

relational interpretations of neighborhood operators and rough set approximation operators this paper presents a framework for the formulation interpretation and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations a special class of neighborhood systems called 1 neighborhood systems is introduced three extensions of pawlak approximation operators are analyzed properties of neighborhood and approximation operators are studied and their connections are examined

a short note on algebraic t rough sets our aim in this paper is to introduce the concept of a set valued homomorphism for groups which is a generalization of ordinary homomorphism then using the definitions of lower inverse and upper inverse we introduce the definition of uniform set valued homomorphism and prove that every set valued homomorphism is uniform finally the concept of probabilistic t rough set is defined

on coupled navier stokes and energy equations in exterior like domains we investigate a class of nonlinear evolution systems modeling time dependent flows of incompressible viscous and heat conducting fluids with temperature dependent transport coefficients in three dimensional exterior like domains we prove a local existence theorem for the fully coupled parabolic system with a source term involving the square of the velocity gradient and a combination of dirichlet and artificial boundary conditions

constructive and axiomatic approaches of fuzzy approximation operators this paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized fuzzy rough and rough fuzzy respectively approximation operators is first defined the representations of both fuzzy rough approximation operators and rough fuzzy approximation operators are then presented the connections between fuzzy and crisp respectively relations and fuzzy rough and rough fuzzy respectively approximation operators are further established in axiomatic approach various classes of fuzzy approximation operators are characterized by different sets of axioms the minimal axiom sets of fuzzy approximation operators guarantee the existence of certain types of fuzzy or crisp relations producing the same operators

a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity abstract mathematical models for flow through porous media typically enjoy the so called maximum principles which place bounds on the pressure field it is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations that is one needs to satisfy discrete maximum principles dmp unfortunately many of the existing formulations for flow through porous media models do not satisfy dmp this paper presents a robust scalable numerical formulation based on variational inequalities vi to model non linear flows through heterogeneous anisotropic porous media without violating dmp vi is an optimization technique that places bounds on the numerical solutions of partial differential equations to crystallize the ideas a modification to darcy equations by taking into account pressure dependent viscosity will be discretized using the lowest order raviart thomas rt0 and variational multi scale vms finite element formulations it will be shown that these formulations violate dmp and in fact these violations increase with an increase in anisotropy it will be shown that the proposed vi based formulation provides a viable route to enforce dmp moreover it will be shown that the proposed formulation is scalable and can work with any numerical discretization and weak form a series of numerical benchmark problems are solved to demonstrate the effects of heterogeneity anisotropy and non linearity on dmp violations under the two chosen formulations rt0 and vms and that of non linearity on solver convergence for the proposed vi based formulation parallel scalability on modern computational platforms will be illustrated through strong scaling studies which will prove the efficiency of the proposed formulation in a parallel setting algorithmic scalability as the problem size is scaled up will be demonstrated through novel static scaling studies the performed static scaling studies can serve as a guide for users to be able to select an appropriate discretization for a given problem size

on the navier stokes flows for heat conducting fluids with mixed boundary conditions abstract we consider a coupled model for steady flows of viscous incompressible heat conducting fluids with temperature dependent material coefficients in a fixed three dimensional open cylindrical channel we introduce the banach spaces x and y to be the space of possible solutions of this problem and the space of its data respectively we show that the corresponding operator of the problem acting between x and y is frechet differentiable applying the local diffeomorphism theorem we get the local solvability results for a variational formulation

roughness in mv algebras in this paper by considering the notion of an mv algebra we consider a relationship between rough sets and mv algebra theory we introduce the notion of rough ideal with respect to an ideal of an mv algebra which is an extended notion of ideal in an mv algebra and we give some properties of the lower and the upper approximations in an mv algebra

a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint we present a novel computational framework for diffusive reactive systems that satisfies the non negative constraint and maximum principles on general computational grids the governing equations for the concentration of reactants and product are written in terms of tensorial diffusion reaction equations we restrict our studies to fast irreversible bimolecular reactions if one assumes that the reaction is diffusion limited and all chemical species have the same diffusion coefficient one can employ a linear transformation to rewrite the governing equations in terms of invariants which are unaffected by the reaction this results in two uncoupled tensorial diffusion equations in terms of these invariants which are solved using a novel non negative solver for tensorial diffusion type equations the concentrations of the reactants and the product are then calculated from invariants using algebraic manipulations the novel aspect of the proposed computational framework is that it will always produce physically meaningful non negative values for the concentrations of all chemical species several representative numerical examples are presented to illustrate the robustness convergence and the numerical performance of the proposed computational framework we will also compare the proposed framework with other popular formulations in particular we will show that the galerkin formulation which is the standard single field formulation does not produce reliable solutions and the reason can be attributed to the fact that the single field formulation does not guarantee non negative solutions we will also show that the clipping procedure which produces non negative solutions but is considered as a variational crime does not give accurate results when compared with the proposed computational framework

variational inequality for the rotating navier stokes equations with subdifferential boundary conditions a steady viscous incompressible fluid through a rotating channel satisfies the rotating navier stokes equations subdifferential boundary conditions are imposed a variational inequality is derived for this system furthermore under some assumptions the weak solution of the variational inequality exists and is unique

a hybrid multi time step framework for pore scale and continuum scale modeling of solute transport in porous media abstract in this paper we propose a computational framework which is based on a domain decomposition technique to employ both finite element method which is a popular continuum modeling approach and lattice boltzmann method which is a popular pore scale modeling approach in the same computational domain to bridge the gap across the disparate length and time scales we first propose a new method to enforce continuum scale boundary conditions i e dirichlet and neumann boundary conditions onto the numerical solution from the lattice boltzmann method this method is based on maximization of entropy and preserve the non negativity of discrete distributions under the lattice boltzmann method the proposed computational framework allows different grid sizes orders of interpolation and time steps in different subdomains this allows for different desired resolutions in the numerical solution in different subdomains through numerical experiments the effect of grid and time step refinement disparity of time steps in different subdomains domain partitioning and the number of iteration steps on the accuracy and rate of convergence of the proposed methodology are studied finally to showcase the performance of this framework in porous media applications we use it to simulate the dissolution of calcium carbonate in a porous structure

generalized fuzzy rough sets this paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized approximation operators is defined the connections between fuzzy relations and fuzzy rough approximation operators are examined in axiomatic approach various classes of fuzzy rough approximation operators are characterized by different sets of axioms axioms of fuzzy approximation operators guarantee the existence of certain types of fuzzy relations producing the same operators

monotone finite volume schemes for diffusion equations on unstructured triangular and shape regular polygonal meshes we consider a non linear finite volume fv scheme for stationary diffusion equation we prove that the scheme is monotone i e it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients the scheme is extended to regular star shaped polygonal meshes and isotropic heterogeneous coefficients

on axiomatic characterisations of crisp approximation operators abstract in rough set theory one can find the result that the upper approximation defines a closure operator on the power set of the universe fixed in the paper presented first we have solved the problem under which additional assumptions a given closure operator can be represented by an upper approximation within the concepts of rough set theory second we have solved this problem within modal logic for a diamond operator represented by an arbitrary binary relation on the universe finally we have generalized these problems to lower approximations and modal box operators to rough approximations of fuzzy sets rough fuzzy sets to fuzzy approximations of crisp sets fuzzy rough sets and fuzzy approximations of fuzzy sets fuzzy diamond and fuzzy box

topological characterizations of covering for special covering based upper approximation operators the relationships among properties of covering approximation operators and their corresponding coverings have attracted intensive research in recent years in particular those among topological properties have drawn special attention because of their important applications in rough set theory in this paper we give topological characterizations of covering c for covering based upper approximation operators fh sh th and rh to be closure operators we also give intuitive characterizations of covering c and describe covering based approximation space u c as certain types of information exchange systems when sh or rh is a closure operator by applying our new characterizations we give inequalities about the relationship between the number of members in c and the number of elements in u and discuss relationships among conditions for different covering based upper approximation operators to be closure operators to the best of our knowledge it is the first time that such characterizations descriptions inequalities and discussions are systematically considered in the literature of rough set theory furthermore in this paper we also give several characterizations of unary coverings an important type of coverings in studying relationships among basic concepts in covering based rough sets by the relationships among different types of covering base approximation operators

some mathematical structures for computational information abstract this paper is about the basic underlying mathematical structures of various types of imprecise information set theory and probability measures are basic ingredients in extracting some specific type of information and in reasoning with uncertain knowledge but in this era of information technology it is desirable to consider also more complex types of information for example information coming from human perception see e g l a zadeh ieee trans circuits and systems 45 1 1999 105 119 as a first approximation the classical ingredients could be generalized to adequately model new types of information as such we will describe in this paper four types of non classical sets namely random sets rough sets conditional sets and fuzzy sets as well as their associated non additive measures

l p theory of the navier stokes flow in the exterior of a moving or rotating obstacle in this paper we describe two recent approaches for the lp theory of the navier stokes flow in the exterior of a moving or rotating obstacle

preprocessing for quadratic programming techniques for the preprocessing of not necessarily convex quadratic programs are discussed most of the procedures extend known ones from the linear to quadratic cases but a few new preprocessing techniques are introduced the implementation aspects are also discussed numerical results are finally presented to indicate the potential of the resulting code both for linear and quadratic problems the impact of insisting that bounds of the variables in the reduced problem be as tight as possible rather than allowing some slack in these bounds is also shown to be numerically significant

on the local solvability in morrey spaces of the navier stokes equations in a rotating frame abstract we prove local in time non uniform solvability for the rotating navier stokes equations in morrey spaces m p r 3 these spaces contain singular and nondecaying functions which are of interest in statistical turbulence we give an algebraic relation between the size of existence time and angular velocity the evolution of velocity u is analyzed in suitable kato fujita spaces based on morrey spaces we show the asymptotic behavior u w in l 0 t m p r 3 as 0 where w is the solution for the navier stokes equations with the same data u 0 particularly for 3 p the solution is approximately self similar for small when u 0 is homogeneous of degree 1

lp lq estimate of the stokes operator and navier stokes flows in the exterior of a rotating obstacle we consider the motion of a viscous fluid filling the whole three dimensional space exterior to a rotating obstacle with constant angular velocity we develop the l p l q estimates and the similar estimates in the lorentz spaces of the stokes semigroup with rotation effect we next apply them to the navier stokes equation to prove the global existence of a unique solution which goes to a stationary flow as t with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in l3 weak l3 space

adaptive spacetime discontinuous galerkin method for hyperbolic advection diffusion with a non negativity constraint summary applications where the diffusive and advective time scales are of similar order give rise to advection diffusion phenomena that are inconsistent with the predictions of parabolic fickian diffusion models non fickian diffusion relations can capture these phenomena and remedy the paradox of infinite propagation speeds in fickian models in this work we implement a modified frame invariant form of cattaneo s hyperbolic diffusion relation within a spacetime discontinuous galerkin advection diffusion model an h adaptive spacetime meshing procedure supports an asynchronous patch by patch solution procedure with linear computational complexity in the number of spacetime elements this localized solver enables the selective application of optimization algorithms in only those patches that require inequality constraints to ensure a non negative concentration solution in contrast to some previous methods we do not modify the numerical fluxes to enforce non negative concentrations thus the element wise conservation properties that are intrinsic to discontinuous galerkin models are defined with respect to physically meaningful riemann fluxes on the element boundaries we present numerical examples that demonstrate the effectiveness of the proposed model and we explore the distinct features of hyperbolic advection diffusion response in subcritical and supercritical flows copyright 2015 john wiley sons ltd

strong lp solutions to the navier stokes flow past moving obstacles the case of several obstacles and time dependent velocity consider the navier stokes flow past several moving or rotating obstacles with possible time dependent velocity it is shown that under suitable assumptions on the data there exists a unique local strong solution in the l p l q setting for suitable p q 1 moreover it is proved that this strong solution coincides with the known mild solution in the very weak sense

topological properties of generalized approximation spaces rough set theory is a powerful mathematical tool for dealing with inexact uncertain or vague information the core concepts of rough set theory are information systems and approximation operators of approximation spaces approximation operators draw close links between rough set theory and topology this paper concerns generalized approximation spaces via topological methods and studies topological properties of rough sets classical separation axioms compactness and connectedness for topological spaces are extended to generalized approximation spaces relationships among separation axioms for generalized approximation spaces and relationships between topological spaces and their induced generalized approximation spaces are investigated an example is given to illustrate a new approach to recover missing values for incomplete information systems by regularity of generalized approximation spaces

on a ktb modal fuzzy logic abstract an extension of the classical ktb modal logic to the fuzzy case is considered a new notion of similarity is introduced and a fuzzy logic based on this relation is proposed also the validity of formulas is defined by introducing a notion of logical consequence then the decision procedure of this logic is described in the tableau method

variational inequality approach to enforcing the non negative constraint for advection diffusion equations abstract predictive simulations are crucial for the success of many subsurface applications and it is highly desirable to obtain accurate non negative solutions for transport equations in these numerical simulations to this end optimization based methodologies based on quadratic programming qp have been shown to be a viable approach to ensuring discrete maximum principles and the non negative constraint for anisotropic diffusion equations in this paper we propose a computational framework based on the variational inequality vi which can also be used to enforce important mathematical properties e g maximum principles and physical constraints e g the non negative constraint we demonstrate that this framework is not only applicable to diffusion equations but also to non symmetric advection diffusion equations an attractive feature of the proposed framework is that it works with any weak formulation for the advection diffusion equations including single field formulations which are computationally attractive a particular emphasis is placed on the parallel and algorithmic performance of the vi approach across large scale and heterogeneous problems it is also shown that qp and vi are equivalent under certain conditions state of the art qp and vi solvers available from the petsc library are used on a variety of steady state 2d and 3d benchmarks and a comparative study on the scalability between the qp and vi solvers is presented we then extend the proposed framework to transient problems by simulating the miscible displacement of fluids in a heterogeneous porous medium and illustrate the importance of enforcing maximum principles for these types of coupled problems our numerical experiments indicate that vis are indeed a viable approach for enforcing the maximum principles and the non negative constraint in a large scale computing environment also provided are firedrake project files as well as a discussion on the computer implementation to help facilitate readers in understanding the proposed framework

the oseen navier stokes flow in the exterior of a rotating obstacle the non autonomous case consider the navier stokes flow past a rotating obstacle with a general time dependent angular velocity and a time dependent outflow condition at infinity sometimes called an oseen condition by a suitable change of coordinates the problem is transformed to an non autonomous problem with unbounded drift terms on a fixed exterior domain r d it is shown that the solution to the linearized problem is governed by a strongly continuous evolution system ft t s gts 0 on l p for 1 p 1 moreover l p l q smoothing properties and gradient estimates of t t s 0 st are obtained these results are the key ingredients to show local in time existence of mild solutions to the full nonlinear problem for pd and initial value in l p

constructive and algebraic methods of the theory of rough sets this paper reviews and compares constructive and algebraic approaches in the study of rough sets in the constructive approach one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation different classes of rough set algebras are obtained from different types of binary relations in the algebraic approach one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators various classes of rough set algebras are characterized by different sets of axioms axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators

a stabilized mixed finite element method for darcy flow based on a multiscale decomposition of the solution recently masud and hughes proposed a stabilized mixed finite element formulation for darcy flow an interesting feature of this formulation is that there are no mesh dependent parameters in the present work we provide a derivation of this formulation based on a multiscale decomposition of the solution we also extend the work of masud and hughes to three dimensional problems and show the convergence rates for various three dimensional finite elements we also show that this formulation passes three dimensional constant flow patch tests for distorted element geometries i e elements with non constant jacobian robustness of this formulation is illustrated by performing numerical simulations on complex geometries

decay estimates of gradient of a generalized oseen evolution operator arising from time dependent rigid motions in exterior domains let us consider the motion of a viscous incompressible fluid past a rotating rigid body in three dimensions where the translational and angular velocities of the body are prescribed but time dependent in a reference frame attached to the body we have the navier stokes system with the drift and one half of the coriolis terms in a fixed exterior domain the existence of the evolution operator t t s in the space l q generated by the linearized non autonomous system was proved by hansel and rhandi j reine angew math 694 1 26 2014 and the large time behavior of t t s f in l r for t s rightarrow infty was then developed by hishida math ann 372 915 949 2018 when f is taken from l q with q leqq r the contribution of the present paper concerns such l q l r decay estimates of nabla t t s with optimal rates which must be useful for the study of stability attainability of the navier stokes flow in several physically relevant situations our main theorem completely recovers the l q l r estimates for the autonomous case stokes and oseen semigroups those semigroups with rotating effect in three dimensional exterior domains which were established by hishida and shibata arch ration mech anal 193 339 421 2009 iwashita math ann 285 265 288 1989 kobayashi and shibata math ann 310 1 45 1998 maremonti and solonnikov ann sc norm super pisa 24 395 449 1997 and shibata in amann arendt hieber neubrander nicaise von below eds functional analysis and evolution equations the gunter lumer volume birkhauser basel pp 595 611 2008

strong solutions to the navier stokes equations around a rotating obstacle we study the existence of strong solutions to the three dimensional navier stokes initial boundary value problem in the domain exterior to a rigid body that rotates with constant angular velocity we show that when the initial data u0 are prescribed in an appropriate functional class a strong solution exists at least in some finite time interval moreover the solution exists for all times provided u0 in suitable norm and the magnitude of do not exceed a certain constant depending only on the kinematic viscosity and on the regularity of in this latter case we also show that the velocity field converges to the velocity field of the corresponding steady state solution

non negative mixed finite element formulations for a tensorial diffusion equation we consider the tensorial diffusion equation and address the discrete maximum minimum principle of mixed finite element formulations in particular we address non negative solutions which is a special case of the maximum minimum principle of mixed finite element formulations it is well known that the classical finite element formulations like the single field galerkin formulation and raviart thomas variational multiscale and galerkin least squares mixed formulations do not produce non negative solutions that is they do not satisfy the discrete maximum minimum principle on arbitrary meshes and for strongly anisotropic diffusivity coefficients in this paper we present two non negative mixed finite element formulations for tensorial diffusion equations based on constrained optimization techniques these proposed mixed formulations produce non negative numerical solutions on arbitrary meshes for low order i e linear bilinear and trilinear finite elements the first formulation is based on the raviart thomas spaces and the second non negative formulation is based on the variational multiscale formulation for the former formulation we comment on the effect of adding the non negative constraint on the local mass balance property of the raviart thomas formulation we perform numerical convergence analysis of the proposed optimization based non negative mixed formulations we also study the performance of the active set strategy for solving the resulting constrained optimization problems the overall performance of the proposed formulation is illustrated on three canonical test problems

existence of the solution to stationary navier stokes equations with nonlinear slip boundary conditions abstract the stationary navier stokes equations with nonlinear slip boundary conditions are investigated in this paper because the boundary conditions include the subdifferential property on the part boundary the variational formulation of this problem is the variational inequality problem of the second kind with navier stokes operator the main purpose of the paper is to study the existence of the weak solution and the strong solution to this variational inequality problem in terms of the yosida s regularity method

pointwise decay of stationary rotational viscous incompressible flows with nonzero velocity at infinity we consider a stationary viscous incompressible flow around a translating and rotating body optimal rates of decay are derived for the velocity and its gradient on the basis of a representation formula involving a fundamental solution constructed by r b guenther and e a thomann the fundamental solution of the linearized navier stokes equations for spinning bodies in three spatial dimensions time dependent case j math fluid mech 8 2006 77 98 for a linearized system

steady solutions with finite kinetic energy for a perturbed navier stokes system in r3 abstract consider a navier stokes liquid filling the three dimensional space exterior to a moving rigid body and subject to an external force using a coordinates system attached to the body the equations of the fluid can be written in a time independent domain which results in a perturbed navier stokes system where the extra terms depend on the velocity of the rigid body in this paper we consider the related whole space problem and construct a strong solution with finite kinetic energy for the corresponding steady state equations for this appropriate conditions on the external force have to be imposed for instance that it is a function with compact support and null average together with a smallness condition involving the viscosity of the fluid first a linearized version of the problem is analysed by means of the fourier transform and then a strong solution to the full nonlinear problem is obtained by a fixed point procedure we also show that such a solution satisfies the energy equation and is unique within a certain class

l q l r estimates for solutions of the nonstationary stokes equations in an exterior domain and the navier stokes initial value problems inl q spaces

on stability of steady circular flows in a two dimensional exterior disk we study the stability of some exact stationary solutions to the two dimensional navier stokes equations in an exterior domain to the unit disk these stationary solutions are known as a simple model of the flow around a rotating obstacle while their stability has been open due to the difficulty arising from their spatial decay in a scale critical order in this paper we affirmatively settle this problem for small solutions that is we will show that if these exact solutions are small enough then they are asymptotically stable with respect to small l2 perturbations

the boundary integral method for the linearized rotating navier stokes equations in exterior domain abstract in this paper we apply the boundary integral method to the linearized rotating navier stokes equations in exterior domain introducing some open ball which decomposes the exterior domain into a finite domain and an infinite domain we obtain a coupled problem by the linearized rotating navier stokes equations in finite domain and a boundary integral equation without using the artificial boundary condition for the coupled problem we show the existence and uniqueness of solution finally we study the finite element approximation for the coupled problem and obtain the error estimate between the solution of the coupled problem and its approximation solution

reduction and axiomization of covering generalized rough sets this paper investigates some basic properties of covering generalized rough sets and their comparison with the corresponding ones of pawlak s rough sets a tool for data mining the focus here is on the concepts and conditions for two coverings to generate the same covering lower approximation or the same covering upper approximation the concept of reducts of coverings is introduced and the procedure to find a reduct for a covering is given it has been proved that the reduct of a covering is the minimal covering that generates the same covering lower approximation or the same covering upper approximation so this concept is also a technique to get rid of redundancy in data mining furthermore it has been shown that covering lower and upper approximations determine each other finally a set of axioms is constructed to characterize the covering lower approximation operation

rough set approach to incomplete information systems abstract in the paper we present rough set approach to reasoning in incomplete information systems we propose reduction of knowledge that eliminates only that information which is not essential from the point of view of classification or decision making in our approach we make only one assumption about unknown values the real value of a missing attribute is one from the attribute domain however we do not assume which one we show how to find decision rules directly from such an incomplete decision table which are as little non deterministic as possible and have minimal number of conditions

a rst a generalization of rough set theory the paper presents a transition from the crisp rough set theory to a fuzzy one called alpha rough set theory or in short a rst all basic concepts or rough set theory are extended i e information system indiscernibility dependency reduction core definability approximations and boundary the resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts besides the control of knowledge granularity is natural in a rst which is based on a parameterized indiscernibility relation a rst is developed to recognize non deterministic relationships using notions as a dependency a reduct and so forth on the other hand we introduce a notion of relative dependency as an alternative of the absolute definibility presented in rough set theory the extension a rst leads naturally to the new concept of alpha rough sets which represents sets with fuzzy non empty boundaries 2000 elsevier science inc all rights reserved

rough sets and boolean reasoning abstract in this article we discuss methods based on the combination of rough sets and boolean reasoning with applications in pattern recognition machine learning data mining and conflict analysis

analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems the maximum principle is one of the most important properties of solutions of partial differential equations its numerical analog the discrete maximum principle dmp is one of the most difficult properties to achieve in numerical methods especially when the computational mesh is distorted to adapt and conform to the physical domain or the problem coefficients are highly heterogeneous and anisotropic violation of the dmp may lead to numerical instabilities such as oscillations and to unphysical solutions such as heat flow from a cold material to a hot one in this work we investigate sufficient conditions to ensure the monotonicity of the mimetic finite difference mfd method on two and three dimensional meshes these conditions result in a set of general inequalities for the elements of the mass matrix of every mesh element efficient solutions are devised for meshes consisting of simplexes parallelograms and parallelepipeds and orthogonal locally refined elements as those used in the amr methodology on simplicial meshes it turns out that the mfd method coincides with the mixed hybrid finite element methods based on the low order raviart thomas vector space thus in this case we recover the well established conventional angle conditions of such approximations instead in the other cases a suitable design of the mfd method allows us to formulate a monotone discretization for which the existence of a dmp can be theoretically proved moreover on meshes of parallelograms we establish a connection with a similar monotonicity condition proposed for the multi point flux approximation mpfa methods numerical experiments confirm the effectiveness of the considered monotonicity conditions

the fujita kato approach to the navier stokes equations in the rotational framework consider the navier stokes equations in the rotational framework it is proved that these equations possess a unique global mild solution for arbitrary speed of rotation provided the initial data u 0 is small enough in the h frac12 sigma mathbb r 3 norm

a steady flow through a plane cascade of profiles with an arbitrarily large inflow_the mathematical model existence of a weak solution the paper deals with a mathematical model of a viscous stationary incompressible flow through a cascade of profiles the problem for the navier stokes system is formulated in a domain corresponding to one spatial period of the cascade we consider several types of boundary conditions on various parts of the boundary the inflow the artificial lower and upper boundaries the profile the outflow we solve the problem with an arbitrarily large inflow into the turbine we formulate the artificial boundary condition on the outflow the modification of the so called do nothing condition which enables us to prove the existence of a weak solution for any inflow

rudiments of rough sets abstract worldwide there has been a rapid growth in interest in rough set theory and its applications in recent years evidence of this can be found in the increasing number of high quality articles on rough sets and related topics that have been published in a variety of international journals symposia workshops and international conferences in recent years in addition many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs rough set theory has led to many interesting applications and extensions it seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences especially in research areas such as machine learning intelligent systems inductive reasoning pattern recognition mereology knowledge discovery decision analysis and expert systems in the article we present the basic concepts of rough set theory and point out some rough set based research directions and applications

domains of fractional powers of the stokes operator in lr spaces soit d un domaine borne de r n n 2 a frontiere lisse s soit 1 r et soit x r la fermeture dans l r d n de tous les champs vectoriels solenoidaux lisses a support compact dans d soit w r m d l espace de sobolev d ordre m et soit le laplacien on considere l operateur de stokes a r p r de domaine d a r w w r 2 d n w 5 0 mx 2 soit a un nombre reel positif pour chaque positif il y a une constante ce a telle que a r z ce a exp im z pour tout z satisfaisant a rez 0 ou a r z est la norme operateur de a r z

some properties on the surfaces of vector fields and its application to the stokes and navier stokes problems with mixed boundary conditions abstract in this paper we are concerned with the stationary and non stationary stokes and navier stokes problems with mixed boundary conditions involving velocity pressure rotation stress and normal derivative of velocity together relying on the relations among strain rotation normal derivative of velocity and shape of boundary surface we get variational formulations of the stokes and navier stokes problems with the mixed boundary conditions also we study existence and uniqueness of solutions to the problems

unsupervised machine learning based on non negative tensor factorization for analyzing reactive mixing abstract analysis of reactive diffusion simulations representing complex mixing processes requires a large number of independent model runs for each high fidelity model simulation the model inputs are varied and the predicted mixing behavior is represented by temporal and spatial changes in species concentration it is then required to discern how the model inputs such as diffusivity dispersion anisotropy and velocity field properties impact the mixing process this task is challenging and typically involves interpretation of large model outputs representing temporal and spatial changes of species concentration within the model domain however the task can be automated and substantially simplified by applying machine learning ml methods in this paper we present an application of an unsupervised ml method called ntf k using non negative tensor factorization ntf coupled with a custom clustering procedure based on k means to reveal the temporal and spatial features in product concentrations an attractive and unique aspect of the proposed ml method is that it ensures the extracted features are non negative which is important to obtain a meaningful deconstruction of the mixing processes the ml methodology is applied to a large set of high resolution finite element model simulations representing anisotropic reaction diffusion processes in perturbed vortex based velocity fields the applied finite element method ensures that spatial and temporal species concentration are always non negative even in the case of high anisotropic contrasts the simulated reaction is a fast irreversible bimolecular reaction a b c where species a and b react to form species c the reactive diffusion model input parameters that control mixing include properties of the velocity field such as vortex structures anisotropic dispersion and molecular diffusion we demonstrate the applicability of the ml feature extraction method to produce a meaningful deconstruction of model outputs to discriminate between different physical processes impacting the reactants their mixing and the spatial distribution of the product c the presented ml analysis allowed us to identify additive temporal and spatial features that characterize mixing behavior the application of the proposed ntf k approach is not limited to reactive mixing ntf k can be readily applied to any observed or simulated datasets that can be represented as tensors multi dimensional arrays and have separable latent signatures or features

generalized lower and upper approximations in a ring in this paper the concepts of set valued homomorphism and strong set valued homomorphism of a ring are introduced and related properties are investigated the notions of generalized lower and upper approximation operators constructed by means of a set valued mapping which is a generalization of the notion of lower and upper approximation of a ring are provided we also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by davvaz b davvaz roughness in rings information science 164 2004 147 163 in a ring and discuss some significant properties of them

global existence and uniqueness theorem to 2 d incompressible non resistive mhd system with non equilibrium background magnetic field abstract in this article we consider the global existence and uniqueness of the solution to the 2d incompressible non resistive mhd system with non equilibrium background magnetic field our result implies that a strong enough non equilibrium background magnetic field will guarantee the stability of the nonlinear mhd system beside the classical energy method the interpolation inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments

on definable concepts of rough set models in various generalized rough set models definable concepts are used to approximate other concepts based on a unified abstract rough set theory this paper investigates the mathematical structure of the set of definable concepts in several generalized rough set models such as relation based models covering based models and fuzzy based models it is shown that there exist two kinds of interesting structures for the set of definable concepts which are often used in rough set models the complementary structure and the equational structure in addition relations between different rough set models are discussed

twofold fuzzy sets and rough sets some issues in knowledge representation abstract this paper deals with the representation of sets where the membership of some elements may be ill known rather than just a matter of degree as in a fuzzy set the notion of a twofold fuzzy set is introduced when the relevant information for determining the membership status is incomplete a twofold fuzzy set is made of a nested pair of fuzzy sets the one which gathers the elements which more or less necessarily belong and the one which gathers the elements which more or less possibly belong twofold fuzzy sets are compared from a frontal and from a semantical point of view with other proposals and particularly with the notion of a rough set recently introduced by pawlak set operations of twofold fuzzy sets are discussed and the cardinality of a twofold fuzzy set is defined twofold fuzzy relations are also introduced finally various applications of twofold fuzzy sets in knowledge representation are briefly discussed

an existence theorem for the navier stokes flow in the exterior of a rotating obstacle we consider the three dimensional navier stokes initial value problem in the exterior of a rotating obstacle it is proved that a unique solution exists locally in time if the initial velocity possesses the regularity l 1 2 this regularity assumption is the same as that in the famous paper of fujita kato an essential step for the proof is the deduction of a certain smoothing property together with estimates near t 0 of the semigroup which is not an analytic one generated by the operator in the space l 2 where stands for the angular velocity of the rotating obstacle and p denotes the projection associated with the helmholtz decomposition

on existence regularity and uniqueness of thermally coupled incompressible flows in a system of three dimensional pipes abstract we study an initial boundary value problem for time dependent flows of heat conducting viscous incompressible fluids in a system of three dimensional pipes on a time interval 0 t we are motivated by the bounded domain approach with do nothing boundary conditions in terms of the velocity pressure and temperature of the fluid such flows are described by a coupled parabolic system with strong nonlinearities and including the natural boundary conditions for the velocity and temperature of the fluid on the part of the boundary where the fluid is supposed to leave the channel the present analysis is devoted to the proof of the existence regularity and uniqueness of the solution for the problem described above