Density theorems for generalized Henig proper efficiency

We develop a new, simple technique of proof for density theorems (i.e.,for the sufficient conditions to guarantee that the proper efficient points of a set are dense in the efficient frontier) in an ordered topological vector space. The results are the following: (i) the set of proper efficient points of any compact setQ is dense in the set of efficient points with respect to the original topology of the space whenever the ordering coneK is weakly closed and admits strictly positive functionals; moreover, ifK is not weakly closed, then there exists a compact set for which the density statement fails; (ii) ifQ is weakly compact, then we have only weak density, but ifK has a closed bounded base, then we can assert the density with respect to the original topology, (iii) there exists a similar possibility to assert the strong density for weakly compactQ if additional restrictions are placed onQ instead ofK. These three results are obtained in a unified way as corollaries of the same statement. In this paper, we use the concept of proper efficiency due to Henig. We extend his definition to the setting of a Hausdorff topological vector space.Research of the first author was supported by the Foundation of Fundamental Research of the Republic of Belarus. Authors are grateful to Professor Valentin V. Gorokhovik for suggesting the problem studied in this paper and for numerous fruitful conversations.     

An improvement of fixed point algorithms by using a good triangulation

We consider measures for triangulations ofR ⁿ. A new measure is introduced based on the ratio of the length of the sides and the content of the subsimplices of the triangulation. In a subclass of triangulations, which is appropriate for computing fixed points using simplicial subdivisions, the optimal one according to this measure is calculated and some of its properties are given. It is proved that for the average directional density this triangulation is optimal (within the subclass) asn goes to infinity. Furthermore, we compare the measures of the optimal triangulation with those of other triangulations. We also propose a new triangulation of the affine hull of the unit simplex. Finally, we report some computational experience that confirms the theoretical results.     

Some statistical properties of the kernel-diffeomorphism estimator

The kernel density estimation method is not so attractive when the density has its support confined to a bounded space U of R^d. In a recent paper, we suggested a new nonparametric probability density function (p.d.f.) estimator called the ‘kernel-diffeomorphism estimator’, which suppressed border convergence difficulties by using an appropriate regular change of variable. The present paper gives more asymptotic theory (uniform consistency, normality). An invariance criterion for p.d.f. estimators is discussed. The invariance of the kernel diffeomorphism estimator under special affine motion (a translation followed by any member of the special linear group SL(d, R) is proved. © 1997 by John Wiley & Sons, Ltd.     

Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System

In this paper for the M(n)/M(n)/s+GI system, i.e. for a s-server queueing system where the calls in the queue may leave the system due to impatience, we present new asymptotic results for the intensities of calls leaving the system due to impatience and a Markovian system approximation where these results are applied. Furthermore, we present a new proof for the formulae of the conditional density of the virtual waiting time distributions, recently given by Movaghar for the less general M(n)/M/s+GI system. Also we obtain new explicit expressions for refined virtual waiting time characteristics as a byproduct.     

Zariski density in lie groups

In [7] Furstenberg gave a proof of Borel’s density theorem [1], which depended not on complete reducibility but rather on properties of the action of a minimally almost periodic group on projective space. In [9] and [10] the basic idea of this proof was extended in various ways to deal with other particular classes of Lie groupsG and closed subgroupsH of cofinite volume. In [5] Dani gives a more general form of the density theorem in whichH need only be non-wandering. In the present paper we define the condition ofk-minimal quasiboundedness, and prove that this condition is necessary and sufficient for the density theorem to hold ((2.4) and (2.6)). Here we replace the arguments of [9] and [10] simply by proofs that the groups considered there satisfy this condition (2.10). We extend the results of [9] and [10] by considering groups which are analytic rather than algebraic, and in the solvable case we completely characterize thek-minimally quasibounded groups (2.9). In the last section we give two applications of the density theorem.     

On the Density of 2-Saturated Lattice Packings of Discs

 In a recent paper of G. Fejes Tóth, G. Kuperberg and W. Kuperberg [1] a conjecture has been published concerning the greatest lower bound of the density of a 2-saturated packing of unit discs in the plane. (A packing of unit discs is said to be 2-saturated if none of the discs could be replaced by two other ones of the same size to generate a new packing. A packing of the unit disc is a lattice packing if the centers form a point lattice.) In the present note we study this problem for lattice packings, however, in a more general form in which the removed unit disc is replaced by two discs of radius r. A corollary of our results supports the above conjecture proving that a lattice packing cannot be 2-saturated except if its density is larger than the conjectured bound. (Received 6 December 2000; in revised form March 29, 2001)     

Estimation of the density of regression errors by pointwise model selection

This paper presents two results: a density estimator and an estimator of regression error density. We first propose a density estimator constructed by model selection, which is adaptive for the quadratic risk at a given point. Then we apply this result to estimate the error density in a homoscedastic regression framework Y _i = b(X _i ) + ε _i from which we observe a sample (X _i , Y _i ). Given an adaptive estimator $ \hat b $ \hat b of the regression function, we apply the density estimation procedure to the residuals $ \hat \varepsilon _i = Y_i - \hat b(X_i ) $ \hat \varepsilon _i = Y_i - \hat b(X_i ) . We get an estimator of the density of ε _i whose rate of convergence for the quadratic pointwise risk is the maximum of two rates: the minimax rate we would get if the errors were directly observed and the minimax rate of convergence of $ \hat b $ \hat b for the quadratic integrated risk.     

Global solutions to isentropic planar magnetohydrodynamic equations with density‐dependent viscosity

In this paper, we study the isentropic compressible planar magnetohydrodynamic equations with viscosity depending on density and with free boundaries. Precisely, when the viscosity coefficient λ(ρ) is proportional to ρ^θ with θ > 0, where ρ is the density, we establish the existence of global solutions under certain assumptions on the initial data by deriving some new a priori estimates.     

A class of solvable nonlinear filters

The purpose of this paper is to present a new class of nonlinear filters that can be explicitly computed. The systems have drift satisfying a Riccati equation f + f ² = V where V is Fourier transform of an arbitrary complex even Borel measure on U and we give an explicit formula for the unnormalized conditional density, as a convergent series each term of which depends only on a finite number of statistics.     

Linguistic modelling and information coarsening based on prototype theory and label semantics

The theory of prototypes provides a new semantic interpretation of vague concepts. In particular, the calculus derived from this interpretation results in the same calculus as label semantics proposed by Lawry. In the theory of prototypes, each basic linguistic label L has the form ‘about P’, where P is a set of prototypes of L and the neighborhood size of the underlying concept is described by the word ‘about’ which represents a probability density function δ on [0,+∞). In this paper we propose an approach to vague information coarsening based on the theory of prototypes. Moreover, we propose a framework for linguistic modelling within the theory of prototypes, in which the rules are concise and transparent. We then present a linguistic rule induction method from training data based on information coarsening and data clustering. Finally, we apply this linguistic modelling method to some benchmark time series prediction problems, which show that our linguistic modelling and information coarsening methods are potentially powerful tools for linguistic modelling and uncertain reasoning.     

Localization results for densities associated with stable small-noise diffusions

Summary This paper concerns asymptotic properties of the stationary density associated with small-noise diffusion processes, such as considered in the well-known work of Ventcel and Freidlin [12]. We assume that the origin is a globally attracting asymptotically stable equilibrium point of the underlying deterministic flow. For a bounded domain D, containing the origin, we derive estimates which establish the asymptotic independence, as the size of the noise vanishes, of the equilibrium density in D from the coefficients of the process outside D. These results are applied to generalize a result of Sheu [10] on an asymptotic representation of the equilibrium density.     

On density properties of certain subgroups with boundedness conditions

LetG be a locally compact group acting on a topological space. Here we define some boundedness conditions for the action. For a nondiscrete locally compact vector spaceV andgG L (V), layering structures forV and the projective spaceP (V) ofV are obtained. From the layering structures, we derive then density properties of subgroups ofG with boundedness conditions. We generalize the Borel density theorem and Prasad's theorem on automorphisms of algebraic semi-simple groups. Some new results onp-adic groups are added.Partially supported by N. S. F. Grant 7702168.     

New decision rules for exact search in N-Queens

This paper presents a set of new decision rules for exact search in N-Queens. Apart from new tiebreaking strategies for value and variable ordering, we introduce the notion of ‘free diagonal’ for decision taking at each step of the search. With the proposed new decision heuristic the number of subproblems needed to enumerate the first K solutions (typically K = 1, 10 and 100) is greatly reduced w.r.t. other algorithms and constitutes empirical evidence that the average solution density (or its inverse, the number of subproblems per solution) remains constant independent of N. Specifically finding a valid configuration was backtrack free in 994 cases out of 1,000, an almost perfect decision ratio. This research is part of a bigger project which aims at deriving new decision rules for CSP domains by evaluating, at each step, a constraint value graph G _c . N-Queens has adapted well to this strategy: domain independent rules are inferred directly from G _c whereas domain dependent knowledge is represented by an induced hypergraph over G _c and computed by similar domain independent techniques. Prior work on the Number Place problem also yielded similar encouraging results.     

Mathematical foundation of the MFS for certain elliptic systems in linear elasticity

The method of fundamental solutions (MFS) is a Trefftz–type technique in which the solution of an elliptic boundary value problem is approximated by a linear combination of translates of fundamental solutions with singularities placed on a pseudo–boundary, i.e., a surface embracing the domain of the problem under consideration. In this work, we develop a mathematical framework for the numerical implementation of the MFS in elliptic systems. We obtain density results, with respect to the C ^ℓ-norms, which establish the applicability of the method in certain systems arising from the theory of elastostatics and thermo-elastostatics. The domains in our density results may possess holes and they satisfy the segment condition. This work was supported by a grant of the University of Cyprus.     

Stable ergodicity and julienne quasi-conformality

In this paper we dramatically expand the domain of known stably ergodic, partially hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property are stably ergodic. Our main tools are the new concepts – julienne density point and julienne quasi-conformality of the stable and unstable holonomy maps. Julienne quasi-conformal holonomy maps preserve all julienne density points. Received June 14, 1999 / final version received October 25, 1999     

Geometric heuristics for rural radio maps approximation

Given a terrain T and an antenna A located on it, we would like to approximate the Radio Map of A over T, namely, to associate a signal strength for each point p∈T as received from A. This work presents a new Radio Map approximation algorithm using an adaptive radial sweep-line technique. The suggested radar-like algorithm (RLA) uses a pipe-line method for computing the signal strength along points on a ray, and an adaptive method for interpolating the signal strength over regions between two consecutive rays. Whenever the difference between two consecutive rays is above a certain threshold, a middle ray is created. Thus, the density of the sampling rays is sensitive to the shape of the terrain. Finally, we report on an experiment which compares the new algorithm with other well-known methods. The main conclusion is that the new RLA is significantly faster than the others, i.e., its running time is 3–15 times faster for the same approximation accuracy.     

On the Intersection Density of Flat Processes

Stationary POISSON r-flat processes in the d-dimensional Euclidean space (d/2 ≦ r ≦ d ? 1) induce a process of (2r ? d)-flats each of which is the intersection of two r-flats of the original processes. The intensity of the induced (2r ? d)-flat process is called intersection density of the original POISSON r-flat process. The problem of maximizing the intersection density for given intensity is considered. A new approach to earlier results of THOMAS and the author is presented.     

Analytic density in Lie groups

A subgroupH of an analytic groupG is said to beanalytically dense if the only analytic subgroup ofG containingH isG itself. The main purpose of this paper is to give sufficient conditions onG (analogous to those of [8], [9], and [7] in the case of Zariski density) which guarantee the analytic density of cofinite volume subgroupsH. First we consider the case of arbitrary cofinite volume subgroups (Theorem 5 and its corollaries). Then we specialize to lattices, and prove the following result (Theorem 8):Let G be an analytic group whose radical is simply connected and whose Levi factor has no compact part and a finite center. Then any lattice in G is analytically dense. In proving this use is made of a result of Montgomery which also implies that for any simply connected solvable group, cocompactness of a closed subgroup implies analytic density. In the case of a solvable group with real roots this means analytic density and cocompactness are equivalent and thus completes a circle of ideas raised in Saito [13]. In Corollary 9 we deal with a related local condition. Finally in Theorem 10 and its corollaries we apply these considerations to prove a homomorphism extension theorem and an isomorphism theorem for 1-dimensional cohomology.     

Global classical solution to 1D compressible Navier–Stokes equations with no vacuum at infinity

C. Miao In this paper, we are concerned with the 1D Cauchy problem of the compressible Navier–Stokes equations with the viscosity μ(ρ) = 1+ρ^β(β≥0). The initial density can be arbitrarily large and keep a non‐vacuum state at far fields. We will establish the global existence of the classical solution for 0≤β < γ via a priori estimates when the initial density contains vacuum in interior interval or is away from the vacuum. We will show that the solution will not develop vacuum in any finite time if the initial density is away from the vacuum. To study the well‐posedness of the problem, it is crucial to obtain the upper bound of the density. Some new weighted estimates are applied to obtain our main results. Copyright © 2015 John Wiley & Sons, Ltd.     

Charge density fluctuation of low frequency in a dusty plasma

The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity of the dusty plasma, has been studied by kinetic theory. The results show that theP value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle Ω _c , which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation of low frequency. For a dusty plasma ofP≪1, when the charging frequency Ω _c , is much smaller than the dusty plasma frequency ω_d, there is a strong charge density fluctuation which is of character of dust acoustic eigenwave. For a dusty plasma ofP≫1, when the frequency Ω _c , is much larger than ω _d there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist.