an integro differential equation modelling a newtonian dynamics and its scaling limit we consider an integro differential equation describing a newtonian dynamics with long range interaction for a continuous distribution of mass in r first we deduce unique existence and regularity properties of its solution locally in time and then we investigate a scaling limit as limit dynamics a nonlinear wave equation is determined technically we rely on the connection of the newtonian dynamics to a system of an integro differential equation and a partial differential equation basic for our considerations is the study of the regularity properties of the solution of that system for that purpose we exploit its similarity to a certain strongly hyperbolic system of partial differential equations

quantitative analysis for covering based rough sets through the upper approximation number coverings are a useful form of data while covering based rough sets provide an effective tool for dealing with this data covering based rough sets have been widely used in attribute reduction and rule extraction however few quantitative analyses for covering based rough sets have been conducted while many advances for classical rough sets have been obtained through quantitative tools in this paper the upper approximation number is defined as a measurement to quantify covering based rough sets and a pair of upper and lower approximation operators are constructed using the approximation number the operators not only inherit some important properties of existing approximation operators but also exhibit some new quantitative characteristics it is interesting to note that the upper approximation number of a covering approximation space is similar to the dimension of a vector space or the rank of a matrix

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

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

rough set theory applied to fuzzy ideal theory we use covers of the universal set to define approximation operators on the power set of the given set in section 1 we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets we define a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of the fuzzy prime spectrum of a ring and rough set theory can simultaneously be brought to bear on the study of fuzzy ideals of a ring

rules in incomplete information systems abstract a new method of computing all optimal certain rules from an incomplete information system is presented and proved the method does not require changing the size of the original incomplete system additionally several existing rough set methods of computing decision rules from incomplete information systems are analyzed and compared we show which of these methods are capable of generating all optimal certain rules or a class of optimal certain rules and which methods may lead to generation of false rules

almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small bv initial data abstract in the present paper the author investigates the initial problem for genuinely nonlinear quasilinear hyperbolic systems of conservation laws under small bv perturbations of the riemann initial data where the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms combining the techniques employed by li and kong with the modified glimm s functional the author obtains the almost global existence and lifespan of classical discontinuous solutions to the above problem this result is also applied to the system of one dimensional isentropic flow

the generalized nonlinear initial boundary riemann problem for linearly degenerate quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work in the present paper we study the generalized nonlinear initial boundary riemann problem with small bv data for linearly degenerate quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space t x t 0 x 0 we prove the global existence and uniqueness of piecewise c 1 solution containing only contact discontinuities to a class of the generalized nonlinear initial boundary riemann problem which can be regarded as a small bv perturbation of the corresponding nonlinear initial boundary riemann problem for general n n linearly degenerate quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to the one of the self similar solution u u x t to the corresponding nonlinear initial boundary riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in the string theory and high energy physics are also given

a new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets traditional rough set theory is mainly used to extract rules from and reduce attributes in databases in which attributes are characterized by partitions while the covering rough set theory a generalization of traditional rough set theory does the same yet characterizes attributes by covers in this paper we propose a way to reduce the attributes of covering decision systems which are databases characterized by covers first we define consistent and inconsistent covering decision systems and their attribute reductions then we state the sufficient and the necessary conditions for reduction finally we use a discernibility matrix to design algorithms that compute all the reducts of consistent and inconsistent covering decision systems numerical tests on four public data sets show that the proposed attribute reductions of covering decision systems accomplish better classification performance than those of traditional rough sets

large systems of interacting particles and the porous medium equation abstract we study the empirical processes of systems of interacting particles whose time evolution is given by coupled ordinary differential equations in particular as the population size tends to infinity we derive different versions of the porous medium equation as limit dynamics

simulation of the solution of a viscous porous medium equation by a particle method to solve a particular partial differential equation namely a viscous porous medium equation we discuss a particle method which is based on the concept of moderately interacting many particle systems our approach may be classified as a combination of a smoothed particle hydrodynamics method and a particle mesh method quantitatively it is assessed in terms of estimates on the approximation error

a law of large numbers for moderately interacting diffusion processes we consider two special models of interacting diffusion processes and derive in the limit as the number of different processes tends to infinity and the interaction is rescaled in a suitable moderate way a law of large numbers for the empirical processes as limit dynamics we obtain certain nonlinear diffusion equations

fuzzy probabilistic approximation spaces and their information measures rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information by introducing probability into fuzzy approximation space a theory about fuzzy probabilistic approximation spaces is proposed in this paper which combines three types of uncertainty probability fuzziness and roughness into a rough set model we introduce shannon s entropy to measure information quantity implied in a pawlak s approximation space and then present a novel representation of shannon s entropy with a relation matrix based on the modified formulas some generalizations of the entropy are proposed to calculate the information in a fuzzy approximation space and a fuzzy probabilistic approximation space respectively as a result uniform representations of approximation spaces and their information measures are formed with this work

optimal resource allocation for detection of a gaussian process using a mac in wsns we analyze a binary hypothesis testing problem built on a wireless sensor network wsn for detecting a stationary random process distributed both in space and time with a circularly symmetric complex gaussian distribution under the neyman pearson np framework using an analog scheme the sensors transmit different linear combinations of their measurements through a multiple access channel mac to reach the fusion center fc whose task is to decide whether the process is present or not considering an energy constraint on each node transmission and a limited amount of channel uses we compute the miss error exponent of the proposed scheme using large deviation theory ldt and show that the proposed strategy is asymptotically optimal when the number of sensors approaches infinity among linear orthogonal schemes we also show that the proposed scheme obtains meaningful energy saving in the low signal to noise ratio regime which is the typical scenario of wsns finally a monte carlo simulation of a 2 dimensional process in space validates the analytical results

symmetries and global solvability of the isothermal gas dynamics equations we study the cauchy problem associated with the system of two conservation laws arising in isothermal gas dynamics in which the pressure and the density are related by the law equation p with 1 our results complete those obtained earlier for 1 we prove the global existence and compactness of entropy solutions generated by the vanishing viscosity method the proof relies on compensated compactness arguments and symmetry group analysis interestingly we make use here of the fact that the isothermal gas dynamics system is invariant modulo a linear scaling of the density this property enables us to reduce our problem to that with a small initial density

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

singular limits of stiff relaxation and dominant diffusion for nonlinear systems abstract we are concerned with singular limits of stiff relaxation and dominant diffusion for general 2 2 nonlinear systems of conservation laws that is the relaxation time tends to zero faster than the diffusion parameter e o e e 0 we establish the following general framework if there exists an a priori l bound that is uniformly with respect to e for the solutions of a system then the solution sequence converges to the corresponding equilibrium solution of this system our results indicate that the convergent behavior of such a limit is independent of either the stability criterion or the hyperbolicity of the corresponding inviscid quasilinear systems which is not the case for other type of limits this framework applies to some important nonlinear systems with relaxation terms such as the system of elasticity the system of isentropic fluid dynamics in eulerian coordinates and the extended models of traffic flows the singular limits are also considered for some physical models without l bounded estimates including the system of isentropic fluid dynamics in lagrangian coordinates and the models of traffic flows with stiff relaxation terms the convergence of solutions in l p to the equilibrium solutions of these systems is established provided that the relaxation time tends to zero faster than e

on the connection between hamiltonian many particle systems and the hydrodynamical equations we consider certain hamiltonian systems with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles it is shown that the empirical processes of the positions and the velocities respectively converge to solutions of the continuity equation and the euler equation in the limit as the particle number tends to infinity

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

l1 convergence rates to the barenblatt solution for the damped compressible euler equations abstract in our previous work 17 it is shown that any l weak entropy solution of damped compressible euler equation converges to the barrenblatt s solution with finite mass in l 1 norm with a convergence rate for 1 3 in this paper by introducing an elaborate iterative method and using the intensive entropy analysis we prove the l 1 convergence to the barrenblatt s solution for any large 3 furthermore we get better l 1 convergence rate for 2 3

a stochastic system of particles modelling the euler equations we consider a system of n spheres interacting through elastic collisions at a stochastic distance in the limit n for a suitable rescaling of the interaction parameters we prove that the one particle distribution function converges to a local maxwellian whose gross density velocity and temperature satisfy the euler equation

approaches to knowledge reduction based on variable precision rough set model this paper deals with approaches to knowledge reduction based on variable precision rough set model the concepts of lower distribution reduct and upper distribution reduct based on variable precision rough sets vprs are first introduced their equivalent definitions are then given and the relationships among lower and upper distribution reducts and alternative types of knowledge reduction in inconsistent systems are investigated it is proved that for some special thresholds lower distribution reduct is equivalent to the maximum distribution reduct whereas upper distribution reduct is equivalent to the possible reduct the judgement theorems and discernibility matrices associated with the lower and upper distribution reducts are also established from which we can obtain the approaches to knowledge reduction in vprs

uncoded transmission is exactly optimal for a simple gaussian sensor network a single memoryless gaussian source is observed by many terminals subject to independent gaussian observation noises the terminals are linked to a fusion center via a standard gaussian multiple access channel the fusion center needs to recover the underlying gaussian source with respect to mean squared error in this correspondence a theorem of witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission i e each terminal s channel input is merely a scaled version of its noisy observation

universal distributed estimation over multiple access channels with constant modulus signaling a distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered the proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i i d case both for a per sensor power constraint and a total power constraint when the distributions of the sensing noise are not identical a bound on their variances is shown to establish strong consistency the estimator is shown to be asymptotically normal with a variance asv that depends on the characteristic function of the sensing noise optimization of the asv is considered with respect to a transmission phase parameter for a variety of noise distributions exhibiting differing levels of impulsive behavior the robustness of the estimator in the sense of degrading gracefully when the sensing noise deviates from the gaussian distribution to impulsive sensing noise distributions such as those with positive excess kurtosis or those that do not have finite moments is shown the proposed estimator is favorably compared with the amplify and forward scheme under an impulsive noise scenario the effect of fading and phase error at the sensors are shown to not affect the consistency of the estimator but to degrade the asymptotic variance by terms that depend on the fading and phase error distributions simulations corroborate our analytical results

rough approximations on a complete completely distributive lattice with applications to generalized rough sets the generalizations of rough sets considered with respect to similarity relation covers and fuzzy relations are main research topics of rough set theory however these generalizations have shown less connection among each other and have not been brought into a unified framework which has limited the in depth research and application of rough set theory in this paper the complete completely distributive ccd lattice is selected as the mathematical foundation on which definitions of lower and upper approximations that form the basic concepts of rough set theory are proposed these definitions result from the concept of cover introduced on a ccd lattice and improve the approximations of the existing crisp generalizations of rough sets with respect to similarity relation and covers when t similarity relation is considered the existing fuzzy rough sets are the special cases of our proposed approximations on a ccd lattice thus these generalizations of rough sets are brought into a unified framework and a wider mathematical foundation for rough set theory is established

convergence of the hamiltonian particle mesh method for barotropic fluid flow we prove convergence of the hamiltonian particle mesh hpm method initially proposed by j frank g gottwald and s reich on a pe riodic domain when applied to the irrotational shallow water equations as a prototypical model for barotropic compressible uid ow under appropriate assumptions most notably suciently fast decay in fourier space of the global smoothing operator and a strang fix condition of order 3 for the local par tition of unity kernel the hpm method converges as the number of particles tends to innity and the global interaction scale tends to zero in such a way that the average number of particles per computational mesh cell remains con stant and the number of particles within the global interaction scale tends to innity the classical sph method emerges as a particular limiting case of the hpm algorithm and we nd that the respective rates of convergence are comparable under suitable assumptions since the computational complexity of bare sph is algebraically superlinear and the complexity of hpm is logarithmically su perlinear in the number of particles we can interpret the hpm method as a fast sph algorithm

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

the further investigation of covering based rough sets uncertainty characterization similarity measure and generalized models the notion of rough sets was originally proposed by pawlak in pawlak s rough set theory the equivalence relation or partition plays an important role however the equivalence relation or partition is restrictive for many applications because it can only deal with complete information systems this limits the theory s application to a certain extent therefore covering based rough sets are derived by replacing the partitions of a universe with its coverings this paper focuses on the further investigation of covering based rough sets firstly we discuss the uncertainty of covering in the covering approximation space and show that it can be characterized by rough entropy and the granulation of covering secondly since it is necessary to measure the similarity between covering rough sets in practical applications such as pattern recognition image processing and fuzzy reasoning we present an approach which measures these similarities using a triangular norm we show that in a covering approximation space a triangular norm can induce an inclusion degree and that the similarity measure between covering rough sets can be given according to this triangular norm and inclusion degree thirdly two generalized covering based rough set models are proposed and we employ practical examples to illustrate their applications finally relationships between the proposed covering based rough set models and the existing rough set models are also made

parameter estimation for middleton class a interference processes the problem of estimating the parameters of the middleton class a interference model is considered on the assumption of the availability of a set of independent samples from class a envelope distribution the asymptotic performances of several estimation procedures are explored from this analysis estimates based on the method of moments are seen to be consistent and computationally desirable but highly inefficient whereas more efficient likelihood based estimators are seen to be computationally unwieldy however an estimator that initiates likelihood iteration with the method of moments estimates is seen to overcome these difficulties in its asymptotic performance unfortunately simulation of this third estimator for practical sample sizes reveals poor performance under these conditions to overcome this lack of small sample efficiency a similar estimator that initiates likelihood iteration with physically motivated but nonoptimal estimates is also proposed simulation of this latter estimator for practical sample sizes indicates that near optimal performance is attained by this technique

distributed snr estimation with power constrained signaling over gaussian multiple access channels a sensor network is used for distributed signal to noise ratio snr estimation in a single time snapshot sensors observe a signal embedded in noise and each observation is phase modulated using a constant modulus scheme and transmitted over a gaussian multiple access channel to a fusion center at the fusion center the mean and variance are estimated jointly using an asymptotically minimum variance estimator it is shown that this joint estimator decouples into simple individual estimators of the mean and the variance the constant modulus phase modulation scheme ensures a fixed transmit power robust estimation across several sensing noise distributions as well as an snr estimate that requires a single set of transmissions from the sensors to the fusion center the estimators are evaluated in terms of asymptotic variance which are then used to evaluate the performance of the snr estimator with gaussian and cauchy sensing noise distributions in the cases of total transmit power constraint as well as a per sensor power constraint for each sensing noise distribution the optimal phase transmission parameters are also determined the asymptotic relative efficiency of the estimators is evaluated it is shown that among the noise distributions considered the estimators are asymptotically efficient only when the noise distribution is gaussian simulation results corroborate analytical results

the comparison of the riemann solutions in gas dynamics in this paper we compare two riemann solution constructions of isentropic and nonisentropic gas dynamic equations with the same initial values we obtain that when rarefaction waves occur in the non isentropic solution the same family rarefaction waves occur in the isentropic solution however when advancing or reflected shock waves occur in the isentropic case the same kind shock waves occur in the nonisentropic case moreover by numerical calculation it can be found that the wave intensities of the two solutions are quite close our conclusion reflects that almost non isentropic gas dynamic process can be simulated by isentropic gas dynamic process in practice c 2015 elsevier inc all rights reserved

uniqueness and stability of riemann solutions with large oscillation in gas dynamics we prove the uniqueness of riemann solutions in the class of entropy solutions in with arbitrarily large oscillation for the 3 3 system of euler equations in gas dynamics the proof for solutions with large oscillation is based on a detailed analysis of the global behavior of shock curves in the phase space and the singularity of centered rarefaction waves near the center in the physical plane the uniqueness of riemann solutions yields their inviscid large time stability under arbitrarily large perturbation of the riemann initial data as long as the corresponding solutions are in l and have local bounded total variation satisfying a natural condition on its growth with time no specific reference to any particular method for constructing the entropy solutions is needed the uniqueness result for riemann solutions can easily be extended to entropy solutions u x t piecewise lipschitz in x for any t 0 with arbitrarily large oscillation

relations of reduction between covering generalized rough sets and concept lattices the reduction theory plays an important role in data analysis this paper studies the relation between the reduction of a covering and the attribute reduction of a concept lattice the reduction of a covering from the perspective of concept lattices is investigated conversely the attribute reduction of a formal context is studied in the framework of covering generalized rough sets the results in this paper show that the reduction of a covering can be viewed as the attribute reduction of a derivative formal context moreover every reduct of a given formal context can be seen as the reduct of an induced covering as an application of the theoretical results an approach to the attribute reduction of concept lattices based on covering generalized rough sets is proposed furthermore experiments are given to show the effectiveness of the proposed method

linear coherent decentralized estimation we consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center due to power and bandwidth limitations each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center in this context we study the linear decentralized estimation of the source vector where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages we adopt the mean squared error mse as the performance criterion when the channels between sensors and the fusion center are orthogonal it has been shown previously that the complexity of designing the optimal encoding matrices is np hard in general in this paper we study the optimal linear decentralized estimation when the multiple access channel mac is coherent for the case when the source and observations are scalars we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation simulations show that the proposed power scheduling improves the mse performance by a large margin when compared to the uniform power scheduling we also show that under a finite network power budget the asymptotic mse performance when the total number of sensors is large critically depends on the multiple access scheme for the case when the source and observations are vectors we study the optimal linear decentralized estimation under both bandwidth and power constraints we show that when the mac between sensors and the fusion center is noiseless the resulting problem has a closed form solution which is in sharp contrast to the orthogonal mac case while in the noisy mac case the problem can be efficiently solved by semidefinite programming sdp

maps of convex sets and invariant regions for finite difference systems of conservation laws general results about maps of convex sets in r n are proved we outline their extensions to an infinite dimensional context such extensions have applications in nonlinear analysis such as in the study of the invariance of convex sets under nonlinear maps here we explore applications only in the finite dimensional context more specifically we apply the general results to the problem of finding sufficient conditions for a region of the state space to be globally or locally invariant under finite difference schemes applied to systems of conservation laws in several space variables in particular we establish a final characterization of the invariant regions under the lax friedrichs scheme and also give sufficient conditions for the local invariance further we give sufficient conditions for the global and local invariance of regions under flux splitting finite difference schemes an example of the multi dimensional euler equations for non isentropic gas dynamics is discussed

knowledge reduction based on the equivalence relations defined on attribute set and its power set one of the key problems of knowledge discovery is knowledge reduction this paper proposes a new method for knowledge reduction in information systems first two families of closed sets c r and c r are defined where r and r are equivalence relations defined on the attribute set and its power set respectively the properties of c r and c r are also discussed the necessary and sufficient condition for c r c r is then given and employed to construct an approach to attribute reduction in information systems it is also proved that under the condition c r c r the proposed approach to knowledge reduction is equivalent to the well accepted one in reference w x zhang y leung w z wu information systems and knowledge discovery science publishing company beijing 2003

existence of global weak solutions to a special system of euler equation with a source ii general case abstract in this paper we apply the maximum principle and the theory of compensated compactness to establish an existence theorem for global weak solutions to the cauchy problem of the non strictly hyperbolic system a special system of euler equation with a general source term

sequential decentralized parameter estimation under randomly observed fisher information we consider the problem of decentralized scalar parameter estimation using wireless sensor networks with gaussian noise specifically we propose a novel framework based on level triggered sampling a non uniform sampling strategy and sequential estimation the proposed estimator can be used as an asymptotically optimal fixed sample size decentralized estimator when the observed fisher information i e fisher information without expectation is deterministic as an alternative to the one shot estimators commonly found in the literature it can also be used as an asymptotically optimal sequential decentralized estimator when the observed fisher information is random we show that the optimal centralized estimator under gaussian noise which is the maximum likelihood estimator is characterized by two processes namely the observed fisher information ut and the observed correlation vt it is noted that vt is always random even when ut is not in the proposed scheme each sensor computes its local random processes and sends a single bit to the fusion center fc whenever the local random processes passes certain predefined levels the fc upon receiving a bit from a sensor updates its approximation to the corresponding global random process and accordingly its estimate the sequential estimation process terminates when ut or the approximation to it reaches a target value we provide an asymptotic analysis for the proposed estimator and the one based on conventional uniform in time sampling under both deterministic and random ut and determine the conditions under which they are asymptotically optimal consistent and asymptotically unbiased analytical results together with simulation results demonstrate the superiority of the proposed estimator based on level triggered sampling over the traditional decentralized estimator based on uniform sampling

cauchy problem for an isentropic magnetogasdynamic system abstract this paper investigates the cauchy problem for an isentropic magnetogasdynamic system under certain reasonable hypotheses on the initial data we obtain the global existence and uniqueness of the c 1 solution to the system meanwhile when the hypotheses on the initial data do not hold we obtain the blow up phenomena of the c 1 solution to the system the bounds of the solution are shown to depend on the parameter which characterizes a one dimensional plane flow 0 or a three dimensional cylindrically symmetric flow 1 it is shown that the existence of the finite time singularity is significantly influenced by the magnetic field strength present in the flow along with the initial data

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

finite energy method for compressible fluids the navier stokes korteweg model this is the first of a series of papers devoted to the initial value problem for the one dimensional euler system of compressible fluids and augmented versions containing higher order terms in the present paper we are interested in dispersive shock waves and analyze the zero viscosity capillarity limit associated with the navier stokes korteweg system specifically we establish the existence of finite energy solutions as well as their convergence toward entropy solutions to the euler system our method of proof combines energy and effective energy estimates a nonlinear sobolev inequality high integrability properties for the mass density and for the velocity and compactness properties based on entropies 2015 wiley periodicals inc

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

universal decentralized estimation in a bandwidth constrained sensor network consider a situation where a set of distributed sensors and a fusion center wish to cooperate to estimate an unknown parameter over a bounded interval u u each sensor collects one noise corrupted sample performs a local estimation and transmits a message to the fusion center while the latter combines the received messages to produce a final estimate this correspondence investigates optimal local estimation and final fusion schemes under the constraint that the communication from each sensor to the fusion center must be a one bit message such a binary message constraint is well motivated by the bandwidth limitation of the communication links fusion center and by the limited power budget of local sensors in the absence of bandwidth constraint and assuming the noises are bounded to the interval u u additive independent but otherwise unknown the classical estimation theory suggests that a total of o u2 epsi2 sensors are necessary and sufficient in order for the sensors and the fusion center to jointly estimate the unknown parameter within epsi root mean squared error mse it is shown in this correspondence that the same remains true even with the binary message constraint furthermore the optimal decentralized estimation scheme suggests allocating 1 2 of the sensors to estimate the first bit of the unknown parameter 1 4 of the sensors to estimate the second bit and so on

topological approaches to covering rough sets rough sets a tool for data mining deal with the vagueness and granularity in information systems this paper studies covering based rough sets from the topological view we explore the topological properties of this type of rough sets study the interdependency between the lower and the upper approximation operations and establish the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation lastly axiomatic systems for the lower approximation operation and the upper approximation operation are constructed

type based estimation over multiaccess channels we study the problem of communicating sensor readings over a gaussian multiaccess channel we focus on the scenario that each sensor observes a single random variable and transmits it using certain signaling in a shared channel the objective is the design of channel waveforms i e the signal constellation to facilitate the estimation of field parameters from the channel output we propose a communication scheme in which sensors transmit according to the type of their observations type based multiple access tbma and show that the tbma is asymptotically optimal in the limit of large number of sensors if the sensor channel gains are identical in particular we show that tbma together with a variant of the maximum likelihood estimator achieves the cramer rao bound asymptotically we then extend the asymptotic analysis of tbma to fading channels and compare the performance of tbma with other orthogonal allocation methods such as time division multiple access

existence of global entropy solutions of a nonstrictly hyperbolic system in this paper we use the theory of compensated compactness coupled with some basic ideas of the kinetic formulation by lions perthame souganidis tadmor lps lpt to establish an existence theorem for global entropy solutions of the nonstrictly hyperbolic system 1

rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations abstract in this paper we initially present and compile the tools and theories that are necessary for a rough set analysis of a general type of fuzzy data from this study we have developed two original contributions that can enhance the application of fuzzy rough sets techniques to data that may be affected by several sources of uncertainty in its measurement process for this type of analysis we have first considered the construction of homogeneous granules in which reflexivity symmetry and a certain transitivity property are satisfied this has encouraged us to study the application of t similarity relations in this framework and to examine the available theorems that permit us to aggregate this type of relations as a part of this study we have also developed a new theorem that allows us to use the dual of the generalized means as an aggregation operator in the fuzzy rough sets context another theoretical development that tries to respond to a practical problem is the concept of precision aggregation we use this new notion to export ziarko s variable precision rough set model to the analysis of fuzzy data a generalization that becomes a necessity for the fuzzy rough sets analysis of large databases the utility of this approach is demonstrated with an application example in the vehicle database donated by the turing institute

on the classical solutions to the hydrodynamic model for semiconductors abstract this paper mainly deals with the multidimensional hydrodynamic model for semiconductors inspired by the previous papers y shizuta s kawashima systems of equations of hyperbolic parabolic type with applications to the discrete boltzmann equation hokkaido math j 14 1985 249 275 s kawashima w a yong dissipative structure and entropy for hyperbolic systems of balance laws arch ration mech anal 174 2004 345 364 w a yong entropy and global existence for hyperbolic balance laws arch ration mech anal 172 2004 247 266 we develop some new frequency localization estimates to establish the global existence and exponential stability of small classical solutions in a class of critical besov spaces which are different from estimates in our recent paper d y fang j xu t zhang global exponential stability of classical solutions to the hydrodynamic model for semiconductors math models methods appl sci 17 2007 1507 1530 furthermore this new method can also be applied to the multidimensional euler equations with damping the analytic tool used is the littlewood paley decomposition

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

on lower and upper intension order relations by different cover concepts in this paper the concept of intension is used to introduce two types of ordering relations based on information that generates a cover for the universal set these types of ordering relations are distinct from the well known ordering relation based on set inclusion for these ordering relations we consider the algebraic structures that arise in various types of covers we show that in the case of a representative cover the algebraic structure resulting from the lower intension inclusion is a double stone algebra while in the case of a reduced cover it is a boolean algebra in addition the algebraic structure resulting from the upper intension inclusion in the case of a representative cover is a boolean algebra and in the case of a reduced cover the two boolean algebraic structures from lower and upper intension inclusions are isomorphic

decay of almost periodic solutions of conservation laws we consider the asymptotic behavior of solutions of systems of inviscid or viscous conservation laws in one or several space variables which are almost periodic in the space variables in a generalized sense introduced by stepanoff and wiener which extends the original one of h bohr we prove that if u x t is such a solution whose inclusion intervals at time t with respect to 0 satisfy l epsiv t t 0 as t and such that the scaling sequence u t x t u t x t t is pre compact as t in l loc 1 d 1 then u x t decays to its mean value which is independent of t as t the decay considered here is in l 1 loc of the variable x t which implies as we show that as t where m x denotes taking the mean value with respect to x in many cases we show that if the initial data are almost periodic in the generalized sense then so also are the solutions we also show in these cases how to reduce the condition on the growth of the inclusion intervals l t with t as t for fixed 0 to a condition on the growth of l 0 with as 0 which amounts to imposing restrictions only on the initial data we show with a simple example the existence of almost periodic non periodic functions whose inclusion intervals satisfy any prescribed growth condition as 0 the applications given here include inviscid and viscous scalar conservation laws in several space variables some inviscid systems in chromatography and isentropic gas dynamics as well as many viscous 2 2 systems such as those of nonlinear elasticity and eulerian isentropic gas dynamics with artificial viscosity among others in the case of the inviscid scalar equations and chromatography systems the class of initial data for which decay results are proved includes in particular the l generalized limit periodic functions our procedures can be easily adapted to provide similar results for semilinear and kinetic relaxations of systems of conservation laws

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

convergence of the viscosity method for a nonstrictly hyperbolic conservation law a convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic systemvt vu x 0 u t left frac 1 2 u 2 mathop smallint limits v s s delta r 3 ds right x 0 0 r 3 is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

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

distributed estimation and detection with bounded transmissions over gaussian multiple access channels a distributed inference scheme which uses bounded transmission functions over a gaussian multiple access channel is considered when the sensor measurements are decreasingly reliable as a function of the sensor index the conditions on the transmission functions under which consistent estimation and reliable detection are possible is characterized for the distributed estimation problem an estimation scheme that uses bounded transmission functions is proved to be strongly consistent provided that the variances of the noise samples are bounded and that the transmission function is one to one the proposed estimation scheme is compared with the amplify and forward technique and its robustness to impulsive sensing noise distributions is highlighted in contrast to amplify and forward schemes it is also shown that bounded transmissions suffer from inconsistent estimates if the sensing noise variance goes to infinity for the distributed detection problem similar results are obtained by studying the deflection coefficient simulations corroborate our analytical results

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

nonstrictly hyperbolic systems with stiff relaxation terms abstract in this paper a zero factor idea is introduced to extend the convergence framework in g q chen c d levermore t p liu hyperbolic conservation laws with stiff relaxation terms and entropy comm pure appl math 47 1994 787 830 for the singular limits of stiff relaxation from general 2 2 hyperbolic conservation systems to nonstrictly hyperbolic systems and an application of this framework on the so called system of extended traffic flow is obtained

kinetic formulation for systems of two conservation laws and elastodynamics for scalar conservation laws the kinetic formulation makes it possible to generate all the entropies from a simple kernel we show how this concept replaces and simplifies greatly the concept of young measures avoiding the difficulties encountered when working in lp the general construction of the two kinetic functions that generate the entropies of 2 2 strictly hyperbolic systems is also developed here we show that it amounts to building a universal entropy i e one that can be truncated by a kinetic value along riemann invariants for elastodynamics this construction can be completed and specialized using the additional galilean invariance this allows a full characterization of convex entropies it yields a kinetic formulation consisting of two semi kinetic equations which as usual are equivalent to the infinite family of all the entropy inequalities

global structure stability of riemann solutions of quasilinear hyperbolic systems of conservation laws shocks and contact discontinuities abstract in this paper the author proves the global structure stability of the lax s riemann solution u u x t containing only shocks and contact discontinuities of general n n quasilinear hyperbolic system of conservation laws more precisely the author proves the global existence and uniqueness of the piecewise c1 solution u u t x of a class of generalized riemann problem which can be regarded as a perturbation of the corresponding riemann problem for the quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to that of the solution u u x t combining the results in kong global structure instability of riemann solutions of quasilinear hyperbolic systems of conservation laws rarefaction waves to appear the author proves that the lax s riemann solution of general n n quasilinear hyperbolic system of conservation laws is globally structurally stable if and only if it contains only non degenerate shocks and contact discontinuities but no rarefaction waves and other weak discontinuities

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

on the derivation of reaction diffusion equations as limit dynamics of systems of moderately interacting stochastic processes we consider systems of moderately interacting particles which are divided into a finite number of different subpopulations and show that in the limit as the population size tends to infinity the empirical processes of the subpopulations converge to the solution of a system of reaction diffusion equations

covering based rough set approximations we propose a framework for the study of covering based rough set approximations three equivalent formulations of the classical rough sets are examined by using equivalence relations partitions and s algebras respectively they suggest the element based the granule based and the subsystem based definitions of approximation operators covering based rough sets are systematically investigated by generalizing these formulations and definitions a covering of universe of objects is used to generate different neighborhood operators neighborhood systems coverings and subsystems of the power set of the universe they are in turn used to define different types of generalized approximation operators within the proposed framework we review and discuss covering based approximation operators according to the element granule and subsystem based definitions

a proof of the fisher information inequality via a data processing argument the fisher information j x of a random variable x under a translation parameter appears in information theory in the classical proof of the entropy power inequality epi it enters the proof of the epi via the de bruijn identity where it measures the variation of the differential entropy under a gaussian perturbation and via the convolution inequality j x y sup 1 spl ges j x sup 1 j y sup 1 for independent x and y known as the fisher information inequality fii the fii is proved in the literature directly in a rather involved way we give an alternative derivation of the fii as a simple consequence of a data processing inequality for the cramer rao lower bound on parameter estimation

global solutions to one dimensional shallow water magnetohydrodynamic equations abstract in this paper we study the cauchy problem for the one dimensional shallow water magnetohydrodynamic equations the main difficulty is the case of zero depth h 0 since the nonlinear flux function p h is singular and the definition of solution is not clear near h 0 first assuming that h has a positive and lower bound we establish the pointwise convergence of the viscosity solutions by using the div curl lemma from the compensated compactness theory to special pairs of functions c f e and obtain a global weak entropy solution second under some technical conditions on the initial data such that the riemann invariants w z are monotonic and increasing we introduce a variant of the vanishing artificial viscosity to select a weak solution finally we extend the results to two special cases where p h is for the polytropic gas or for the chaplygin gas

relationships between covering based rough sets and relation based rough sets rough set theory is an important technique to deal with vagueness and granularity in information systems in rough set theory relation based rough sets and covering based rough sets are two important extensions of the classical rough sets this paper investigates relationships between relation based rough sets and covering based rough sets firstly we unify five types of covering based rough sets under a framework of a type of relation based rough sets and establish the equivalences between four types of covering based rough sets and the type of relation based rough sets respectively then within the proposed framework conditions required for two different coverings to generate the same approximation operators are investigated we also present some sufficient and necessary conditions for different types of covering based rough sets to be equal furthermore two examples are taken to illustrate applications of the discussion about relationships between covering based rough sets and relation based rough sets

existence of solutions to hyperbolic conservation laws with a source existence of solutions to three different systems of eqs 1 1 1 2 and 1 3 coming from physically relevant models is shown each needing a different proof which are given in sects 2 3 and 4 the unifying theme is the presence of source terms and the general method of proof is vanishing viscosity together with compensated compactness for system 1 2 entropy entropy flux pairs of lax type are constructed and estimates from singular perturbation theory of odes are used for 1 1 and 1 3 weak entropy entropy flux pairs are constructed following the compensated compactness framework set up by diperna 4

on measurements of covering rough sets based on granules and evidence theory covering rough sets generalize classical rough sets by relaxing partitions of the universe to coverings the existing research of covering rough sets mainly concentrates on comparing of different kinds of approximation operators and designing algorithms for attribute reductions of decision systems less efforts have been made in measurements of covering rough sets to enrich this field in this paper we investigate the measurements of covering rough sets based on granules and evidence theory which can be used to solve more complex practical problems firstly it is shown that the most common sixteen pairs of covering approximation operators can be grouped into five pairs of dual covering approximation operators and six pairs of non dual covering approximation operators according to definitions based on element granule and subsystem secondly we define the rough degree and precision for the purpose of characterizing the uncertainty of these summarized covering approximation operators under a unified framework the underlying uncertainty of covering rough sets results from the roughness of granulation of coverings finally we investigate the relationships between the covering approximation operators and evidence theory it shows that some kinds of covering approximation operators can be characterized by belief and plausibility functions while others do not share this property the sufficient conditions under which covering approximation operators can be measured by belief and plausibility functions are further explored and the corresponding counterexamples are given to illustrate those that cannot be measured based on above discussions we develop a basic framework of numerical characterization on measurements of covering rough sets with granules and evidence theory

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

on the asymptotic efficiency of distributed estimation systems with constant modulus signals over multiple access channels a distributed estimation problem is considered with multiple access channels between sensors and a fusion center the sensors phase modulate their noisy observations before transmitting them to the fusion center where a signal parameter is estimated the asymptotic efficiency of this estimator is then determined by using two inequalities that relate the fisher information and the characteristic function a necessary and sufficient condition for equality is found for the first time in the literature the loss in efficiency of the distributed estimation scheme relative to the centralized approach is quantified for different sensing noise distributions it is shown that this distributed estimation system does not incur an efficiency loss if and only if the sensing noise distribution is gaussian

approaches to knowledge reduction of covering decision systems based on information theory in this paper we propose some new approaches for attribute reduction in covering decision systems from the viewpoint of information theory firstly we introduce information entropy and conditional entropy of the covering and define attribute reduction by means of conditional entropy in consistent covering decision systems secondly in inconsistent covering decision systems the limitary conditional entropy of the covering is proposed and attribute reductions are defined and finally by the significance of the covering some algorithms are designed to compute all the reducts of consistent and inconsistent covering decision systems we prove that their computational complexity are polynomial numerical tests show that the proposed attribute reductions accomplish better classification performance than those of traditional rough sets in addition in traditional rough set theory mibark algorithm g y wang h hu d yang decision table reduction based on conditional information entropy chinese j comput 25 2002 1 8 cannot ensure the reduct is the minimal attribute subset which keeps the decision rule invariant in inconsistent decision systems here we solve this problem in inconsistent covering decision systems

a fluctuation theorem for moderately interacting diffusion processes we study the asymptotic behaviour of the fluctuations of the empirical processes of the second example of moderately interacting diffusion processes of 3 and show that in the limit as the number of different processes tends to infinity these fluctuations behave gaussian

the convergence of the sph method abstract in this paper we prove the convergence of a smooth particle flow to the solution of a regularized version of the euler equations describing a generic polytropic fluid this result combined with a stability property of the euler equations with respect to suitable regularizations result of the same authors of the present paper which will be published elsewhere allows to achieve the proof of the convergence of the so called smoothed particle hydrodynamics sph method

the approximation number function and the characterization of covering approximation space there is renewed interest in the topic of covering based rough sets it is important to understand the characterization of covering approximation spaces recently zhu et al presented the concept of an approximation number function which can be viewed as a quantitative tool for analyzing the covering approximation spaces we focus on this concept and show that an approximation number function can be characterized by its properties we give the axiomatic definition of an approximation number function and prove that there is a one to one correspondence between the set of all lower approximation number functions and the set of all covering approximation spaces this suggests that the concept is fundamental to the characterization of covering approximation spaces we apply approximation number functions to the existing studies on approximation spaces and a series of matroidal structures are induced in an approximation space