convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

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

clustering in complex networks i general formalism we develop a full theoretical approach to clustering in complex networks a key concept is introduced the edge multiplicity that measures the number of triangles passing through an edge this quantity extends the clustering coefficient in that it involves the properties of two and not just one vertices the formalism is completed with the definition of a three vertex correlation function which is the fundamental quantity describing the properties of clustered networks the formalism suggests different metrics that are able to thoroughly characterize transitive relations a rigorous analysis of several real networks which makes use of this formalism and the metrics is also provided it is also found that clustered networks can be classified into two main groups the weak and the strong transitivity classes in the first class edge multiplicity is small with triangles being disjoint in the second class edge multiplicity is high and so triangles share many edges as we shall see in the following paper the class a network belongs to has strong implications in its percolation properties

on computing the edge connectivity of an uncertain graph uncertain graphs are employed to describe graph models with imprecise expert data in uncertain graphs due to the existence of uncertain edges edge connectivity is essentially an uncertain variable different from that in a deterministic graph it is more suitable to investigate the possibility uncertain measure that an uncertain graph is k edge connected which is the main aim of this paper we first deduce a theoretical formula to calculate the uncertain measure and on this basis we then propose an algorithm which is derived from maximum flow algorithms to numerically calculate the uncertain measure the proposed algorithm is also proved to be a polynomial time algorithm and its effectiveness and efficiency are illustrated by numerical examples

oscillatory critical amplitudes in hierarchical models we study the oscillatory critical amplitudes of theq states potts model on a diamond hierarchical lattice we consider an example of the generic case finite critical index as well as the degenerate case essential singularity in both cases we compare the magnitude of the oscillations with geometrical characteristics of the julia set of zeroes of the partition function

efficient pattern matching on big uncertain graphs a significant amount of research has been devoted to seeking efficient solutions to the problem of pattern matching over graphs this interest is largely due to the many applications that require such efficient solutions including protein complex prediction social network analysis and structural pattern recognition however in many real applications the graph data are often noisy incomplete and inaccurate in other words there exist many uncertain graphs therefore in this paper we study pattern matching in the context of large uncertain graphs specifically we want to retrieve all qualified matches of a query pattern in the uncertain graph though pattern matching over uncertain graphs is np hard we employ a filtering and verification framework to speed up the search in the filtering phase we propose a probabilistic matching tree pm tree built from match cuts obtained by a cut selection process based on the pm tree we devise a collective pruning strategy to prune a large number of unqualified matches during the verification phase we develop an efficient sampling algorithm to validate the remaining candidates extensive experimental results demonstrate the effectiveness and efficiency of the proposed algorithms finally we show how our solution can be applied to querying knowledge graphs

rough set theory for the interval valued fuzzy information systems the notion of a rough set was originally proposed by pawlak z pawlak rough sets international journal of computer and information sciences 11 5 1982 341 356 later on dubois and prade d dubois h prade rough fuzzy sets and fuzzy rough sets international journal of general system 17 2 3 1990 191 209 introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets this paper deals with an interval valued fuzzy information system by means of integrating the classical pawlak rough set theory with the interval valued fuzzy set theory and discusses the basic rough set theory for the interval valued fuzzy information systems in this paper we firstly define the rough approximation of an interval valued fuzzy set on the universe u in the classical pawlak approximation space and the generalized approximation space respectively i e the space on which the interval valued rough fuzzy set model is built secondly several interesting properties of the approximation operators are examined and the interrelationships of the interval valued rough fuzzy set models in the classical pawlak approximation space and the generalized approximation space are investigated thirdly we discuss the attribute reduction of the interval valued fuzzy information systems finally the methods of the knowledge discovery for the interval valued fuzzy information systems are presented with an example

applications of the galton watson process to human dna evolution and demography we show that the problem of existence of a mitochondrial eve can be understood as an application of the galton watson process and presents interesting analogies with critical phenomena in statistical mechanics in the approximation of small survival probability and assuming limited progeny we are able to find for a genealogic tree the maximum and minimum survival probabilities over all probability distributions for the number of children per woman constrained to a given mean as a consequence we can relate existence of a mitochondrial eve to quantitative demographic data of early mankind in particular we show that a mitochondrial eve may exist even in an exponentially growing population provided that the mean number of children per woman n is constrained to a small range depending on the probability p that a child is a female assuming that the value p 0 488 valid nowadays has remained fixed for thousands of generations the range where a mitochondrial eve occurs with sizeable probability is 2 0492 n 2 0510 we also consider the problem of joint existence of a mitochondrial eve and a y chromosome adam we remark why this problem may not be treated by two independent galton watson processes and present some simulation results suggesting that joint existence of eve and adam occurs with sizeable probability in the same n range finally we show that the galton watson process may be a useful approximation in treating biparental population models allowing us to reproduce some results previously obtained by chang and derrida et al

uncertain wave equation with infinite half boundary wave equation is a type of second order and hyperbolic partial differential equation it is a commonly used tool to model many kinds of wave propagations such as sound wave electromagnetic wave water wave and string vibration propagations similarly uncertain wave equation is a type of uncertain partial equation driven by liu process which is widely used to model the wave propagation with uncertain noise such as vibrating string in uncertain environment the existing literature has studied uncertain wave equation with infinite boundary since infinite boundary is a much ideal condition this paper aims at studying the uncertain wave equation with infinite half boundary

navier stokes equations for compressible fluids global existence and qualitative properties of the solutions in the general case we consider the equations which describe the motion of a viscous compressible fluid taking into consideration the case of inflow and or outflow through the boundary by means of some a priori estimates we prove the existence of a global in time solution moreover as a consequence of a stability result we show that there exist a periodic solution and a stationary solution

model for force fluctuations in bead packs we study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials we present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile we compare our results for the force distribution function for this model including exact results for certain contact angle probability distributions with numerical simulations of force distributions in random sphere packings this model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings our model is closely related to some that have been studied in the context of self organized criticality we present evidence that in the force distribution context critical power law force distributions occur only when a parameter hidden in other interpretations is tuned our numerical mean field and exact results all indicate that for almost all contact distributions the distribution of forces decays exponentially at large forces

markov chain approach to the distribution of ancestors in species of biparental reproduction we studied how to obtain a distribution for the number of ancestors in species of sexual reproduction present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees it has been shown that it is not possible to reconstruct the genealogical history of each species along all its generations by means of a geometric progression this analysis demonstrates that it is possible to rebuild the tree of progenitors by modeling the problem with a markov chain for each generation the maximum number of possible ancestors is different this presents huge problems for the resolution we found a solution through a dilation of the sample space although the distribution defined there takes smaller values with respect to the initial problem in order to correct the distribution for each generation we introduced the invariance under a gauge local group of dilations these ideas can be used to study the interaction of several processes and provide a new approach on the problem of the common ancestor in the same direction this model also provides some elements that can be used to improve models of animal reproduction

dimension reduction of compressible fluid models over product manifolds abstract in this paper we study the dimension reduction limits of the compressible navier stokes equations over product riemannian manifolds o m f such that dim m n and dim f d are arbitrary using the method of relative entropies we establish the convergence of the suitable weak solutions of the navier stokes equations on o to the classical solution of the limiting equations on m as 0 provided the latter exists in addition we also deduce the vanishing viscosity limit the limiting equations identified through our analysis contain the weight function a m r as a parameter where a x area of the fibre f x our work is based on and generalises the results in bella et al 2016 3 bella et al 2014 4 and maltese and novotn 2014 19 and it contains as special cases the physical models of circular nozzles thin plate limits and finite length longitudinal nozzles

distribution of repetitions of ancestors in genealogical trees we calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non overlapping generations each ancestor at generation g in the past has a weight w which is up to a normalization the number of times this ancestor appears in the genealogical tree of an individual at present the distribution pg w of these weights reaches a stationary shape p1 w for large g i e for a large number of generations back in the past for small w p1 w is a power law p1 w w with a non trivial exponent which can be computed exactly using a standard procedure of the renormalization group approach some extensions of the model are discussed and the eect of these variants on the shape of p1 w are analysed c 2000 elsevier science b v all rights reserved

log periodic critical amplitudes a perturbative approach log periodic amplitudes appear in the critical behavior of a large class of systems in particular when a discrete scale invariance is present here we show how to compute these critical amplitudes perturbatively when they originate from a renormalization map which is close to a monomial in this case the log periodic amplitudes of the subdominant corrections to the leading critical behavior can also be calculated

shortest path problem with uncertain arc lengths uncertainty theory provides a new tool to deal with the shortest path problem with nondeterministic arc lengths with help from the operational law of uncertainty theory this paper gives the uncertainty distribution of the shortest path length also it investigates solutions to the a shortest path and the most shortest path in an uncertain network it points out that there exists an equivalence relation between the a shortest path in an uncertain network and the shortest path in a corresponding deterministic network which leads to an effective algorithm to find the a shortest path and the most shortest path roughly speaking this algorithm can be broken down into two parts constructing a deterministic network and then invoking the dijkstra algorithm

uncertain multi product newsboy problem with chance constraint a multi product newsboy problem with uncertain demand and uncertain storage space is investigated under a warehousing chance constraint it is assumed that indeterminacy may appear in demand and storage space due to rough estimation of their distributions by decision maker uncertainty theory provides a new tool to deal with the human uncertainty we develop an uncertain expected value programming model uevpm based on uncertainty theory uncertain variables functions from uncertainty space to the set of real numbers are used to describe subjective estimation the objective function is to maximize the expected profit of newsboy at a predetermined confidence level furthermore we convert the chance constrained uncertain programming model to its equivalent deterministic form so as to be solved by classic integer programming method finally three numerical examples are given to illustrate the potential usefulness of the study

two dimensional polymers and conformal invariance abstract the critical properties of self avoiding walks percolation clusters and critical exponents associated with the planar brownian motion are reviewed in two dimensions 2d the conformal spectrum of these geometrical critical systems is made of an infinite descrete series of scaling dimensions the latter are calculated in the framework of coulomb gas methods and conformal invariance the statistical mechanics of the same critical models on a random 2d lattice i e on a random surface namely in presence of a critically fluctuating metric in the so called 2d quantum gravity is also addressed and the above critical geometrical systems are exactly solvable in this case the new gravitational conformal spectrum is related to the standard conformal spectrum in the plane as predicted recently

reduction methods of type 2 uncertain variables and their applications to solid transportation problem uncertainty theory is a branch of mathematics for dealing with realistic uncertainties arising out of complexity changeability and non decidability of practical environments an uncertain variable is defined as a function from the uncertainty space to the set of real numbers and is characterized by an uncertainty distribution this paper proposes the definition of type 2 uncertain variables within the framework of uncertainty theory through introduction of generalized uncertain measures and focuses on more complex twofold uncertainties some uncertainty reduction methods associated with type 2 uncertain variables are also proposed for convenience of applicability including reduction of optimistic value pessimistic value and expected value moreover four classes of type 2 uncertain variables are reduced to type 1 uncertain variables with specific uncertainty distributions type 2 uncertain optimization methods are applied to solving the fixed charge solid transportation problem with the type 2 uncertain parameters where the solution methods are also provided for the proposed models finally numerical experiments are implemented to demonstrate application and sensitivity analysis of the proposed approaches

weak strong uniqueness for measure valued solutions we prove the weak strong uniqueness for measure valued solutions of the incompressible euler equations these were introduced by diperna and majda in their landmark paper commun math phys 108 4 667 689 1987 where in particular global existence to any l2 initial data was proven whether measure valued solutions agree with classical solutions if the latter exist has apparently remained open

statistical properties of genealogical trees we analyze the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and nonoverlapping generations by reconstructing the genealogy of an individual from the population evolution we measure the distribution of ancestors appearing more than once in a given tree after a transient time the probability of repetition follows up to a rescaling a stationary distribution which we calculate both numerically and analytically this distribution exhibits a universal shape with a nontrivial power law which can be understood by an exact though simple renormalization calculation some real data on human genealogy illustrate the problem which is relevant to the study of the real degree of diversity in closed interbreeding communities

the maximum flow problem of uncertain network the maximum flow problem is one of the classic combinatorial optimization problems with many applications in electrical power systems communication networks computer networks and logistic networks the goal of the problem is to find the maximum amount of flow from the source to the sink in a network a network is called uncertain if the arc capacities of the network are uncertain variables the main purpose of this paper is to solve the maximum flow in an uncertain network by under the framework of uncertainty theory

on distribution function of the diameter in uncertain graph in uncertain graphs the existence of some edges is not predetermined the diameter of an uncertain graph is essentially an uncertain variable which indicates the suitability for investigation of its distribution function the main focus of this paper is to propose an algorithm to determine the distribution function of the diameter of an uncertain graph we first discuss the characteristics of the uncertain diameter and the distribution function is derived an efficient algorithm is designed based on floyd s algorithm further some numerical examples are illustrated to show the efficiency and application of the algorithm

global solutions to the compressible euler equations with geometrical structure we prove the existence of global solutions to the euler equations of compressible isentropic gas dynamics with geometrical structure including transonic nozzle flow and spherically symmetric flow due to the presence of the geometrical source terms the existence results themselves are new especially as they pertain to radial flow in an unbounded region vec x geqq 1 and to transonic nozzle flow arbitrary data withl bounds are allowed in these results a shock capturing numerical scheme is introduced to compute such flows and to construct approximate solutions the convergence and consistency of the approximate solutions generated from this scheme to the global solutions are proved with the aid of a compensated compactness framework

non trivial exponents in coarsening phenomena abstract one of the simplest examples of stochastic automata is the glauber dynamics of ferromagnetic spin models such as ising or potts models at zero temperature if the initial condition is random one observes a pattern of growing domains with a characteristic size which increases with time like t 1 2 in this self similar regime the fraction of spins which never flip up to time t decreases like t where the exponent is non trivial and depends both on the number q of states of the potts model and on the dimension of space this exponent can be calculated exactly in one dimension similar non trivial exponents are also present in even simpler models of coarsening where the dynamical rule is deterministic

single period inventory problem under uncertain environment this paper investigates the single period inventory newsboy problem in a general uncertain environment here it is assumed that the uncertainty appears in the market demand of the product uncertain demand is used to describe a subjective estimate not estimated by random fuzzy demand linguistically expressed by demand is about x using identification functions of the uncertain variable we derive the optimum order quantity and finally the expression of total expected profit for a fixed time period the computational aspects of the model in uncertain environment and their interpretations are illustrated by some examples

uncertainty theory as a basis for belief reliability abstract belief reliability is a newly developed model based reliability metric which considers both what we know expressed as reliability models and what we don t know expressed as epistemic uncertainty in the reliability models about the reliability in this paper we show that due to the explicit representation of epistemic uncertainty belief reliability should not be regarded as a probability measure rather it should be treated as an uncertain measure in uncertainty theory a minimal cut set based method is developed to calculate the belief reliability of coherent systems a numerical algorithm is then presented for belief reliability analysis based on fault tree models the results of application show that the developed methods require less computations than the structure function based method of classical reliability theory