含瞬时态、具有突变率的广义生-灭Q-矩阵(Ⅱ)

研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,在Q_(E_0)非零流出下,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是遍历的,并求出其遍历测度以及给出诚实Q过程可配称的充要条件。最后给出两个例子以说明本文的结果易于验证。     

On the unboundedness of facility layout problems

Facility layout problems involve the location of facilities in a planar arrangement such that facilities that are strongly connected to one another are close to each other and facilities that are not connected may be far from one another. Pairs of facilities that have a negative connection should be far from one another. Most solution procedures assume that the optimal arrangement is bounded and thus do not incorporate constraints on the location of facilities. However, especially when some of the coefficients are negative, it is possible that the optimal configuration is unbounded. In this paper we investigate whether the solution to the facility layout problem is bounded or not. The main Theorem is a necessary and sufficient condition for boundedness. Sufficient conditions that prove boundedness or unboundedness are also given.     

The choice of spectral element basis functions in domains with an axis of symmetry

New spectral element basis functions are constructed for problems possessing an axis of symmetry. In problems defined in domains with an axis of symmetry there is a potential problem of degeneracy of the system of discrete equations corresponding to nodes located on the axis of symmetry. The standard spectral element basis functions are modified so that the axial conditions are satisfied identically. The modified basis is employed only in spectral elements that are adjacent to the axis of symmetry. This modification of the spectral element method ensures that the nodes are the same in each element, which is not the case in other methods that have been proposed to tackle the problem along the axis of symmetry, and that there are no nodes along the axis of symmetry. The problems of Stokes flow past a confined cylinder and sphere are considered and the performance of the original and modified basis functions are compared.     

TOPOLOGY WITHOUT POINTS

Abstract

Other theories that develop topology without points are either excessively artificial or suffer from a lack of rigor. In this paper it is assumed that worlds W are composed of parts that form a complete Boolean algebra [xbar] and that the collection [Wbar] of all points of W is a certain subcollection of all filters defined over [xbar]. Two axioms are given for points which, given suitable definitions, convert [Wbar] into a compact Hausdorff space. Nearness collections of parts of W are defined which satisfy all the axioms of Herrlich for nearness except that closure is defined without mentioning points and consequently one may define closed and open parts. A category of worlds is defined in which the objects are lattices of closed parts of a world and the arrows are roughly speaking the far-preserving mps. It is shown that the category of compact T₁-spaces is a reflective subcategory of the category of worlds.     

The whispering surface effect

The representation theory of symmetry groups, together with variational and functional-topological methods, are used in a two-dimensional formulation to investigate the waveguide properties of one-dimensionally periodic surfaces (OPS) and interfaces. It is established that all surfaces on which the Neumann condition is satisfied possess the waveguide property—they are open waveguides. This means that there are waves localized in the neighbourhood of the surface which propagate along it without attenuation—waveguide modes. It is shown that for any hard OPS there is always a transmission band of waveguide frequencies, localized in the neighbourhood of zero—the whispering surface effect. Anomalous oscillations localized around OPSs on which the Neumann condition is satisfied are observed and investigated. Examples of surfaces for which anomalous oscillations exist and others for which none exist are presented. It is proved that OPSs on which the Dirichlet condition holds do not have a transmission band for waveguide frequencies in the neighbourhood of zero, and for some frequency bands they do not have waveguide and anomalous properties. It is shown that one-dimensionally periodic interfaces of two media possess waveguide and anomalous properties, provided that the parameters satisfy certain relationships. It is established that if the interface has the waveguide property, then transmission band of frequencies will always exist localized in the neighbourhood of zero—the whispering interface effect. An example is presented in which anomalous oscillations are investigated, dispersion relations are derived and pass and stop bands for waveguide modes are determined.     

Functional role semantics and reflective equilibrium

In this paper it is argued that functional role semantics can be saved from criticisms, such as those raised by Putnam and Fodor and Lepore, by indicating which beliefs and inferences are more constitutive in determining mental content. The Scylla is not to use vague expressions; the Charybdis is not to endorse the analytic/synthetic distinction. The core idea is to use reflective equilibrium as a strategy to pinpoint which are the beliefs and the inferences that constitute the content of a mental state. The beliefs and the inferences that are constitutive are those that are in reflective equilibrium in the process of attributing mental states to others.     

A CLASS OF FACTORIZED QUASI-NEWTON METHODS FOR NONLINEAR LEAST SQUARES PROBLEMS

1.IntroductionThispaPerdealswiththeproblemofndniedingasumofsquaresofnonlinearfuntions-mwhereri(x),i==1,2,',maretwicecontinuouslyfferentiable,m2n'r(x)=(rl(x),rz(x),'jbe(x))"and"T"denotestranspose.NoIilinearleastSquaresproblemisakindofAnportan0ptiedationprobletnsandisaPpearedinmanyfield8suchasscientilicexperiments,mbomumlikelihoodestimation,solutionofnonlinearequaions'patternrecoghtionandetc.ThederiVativesofthefUnctionj(x)aregivenbywhereAEppxnistheJacobianmatrisofr(x)anditselementsare~=f…     

M-ideal structure in Banach algebras

It is shown that M-ideals in a Banach algebra with identity are subalgebras, and that they are ideals if the algebra is commutative. Counterexamples demonstrate that these are the strongest results available. The theory is then applied to familiar classes of Banach spaces.     

Translations in affine Klingenberg spaces

An old question regarding the world we live in concerns what is real regarding points and lines: if two distinct lines intersect, is their intersection a unique point? In this paper, we take the approach that the answer is no, that all the points in the intersection are somehow close to one another (neighbourly) and that two non-neighbourly points determine a unique line. These are the Affine Klingenberg spaces (AK-spaces). How does one put a logical structure on points and lines that reflect the preceding view of reality? History has shown that such a structure is based upon the concept of coordinatization, which leads naturally to algebraic structures that allow a faithful representation of incidence, which in turn reflects the existence of relations between points and lines that recognise incidence. The preceding view of reality is not new, and the history of this subject is of approaches that are too general (there are conditions on neighbourly points). Our approach is novel in that it is based upon a minimum number of assumptions that yield the existence of dilatations that are translations: the corner stones of coordinatization.     

Constrained control for uncertain linear systems

The linear state feedback synthesis problem for uncertain linear systems with state and control constraints is considered. We assume that the uncertainties are present in both the state and input matrices and they are bounded. The main goal is to find a linear control law assuring that both state and input constraints are fulfilled at each time. The problem is solved by confining the state within a compact and convex positively invariant set contained in the allowable state region.It is shown that, if the controls, the state, and the uncertainties are subject to linear inequality constraints and if a candidate compact and convex polyhedral set is assigned, a feedback matrix assuring that this region is positively invariant for the closed-loop system is found as a solution of a set of linear inequalities for both continuous and discrete time design problems.These results are extended to the case in which additive disturbances are present. The relationship between positive invariance and system stability is investigated and conditions for the existence of positively invariant regions of the polyhedral type are given.The author is grateful to Drs. Vito Cerone and Roberto Tempo for their comments.     

Asymptotic optimality of the static frequency caching in the presence of correlated requests

It is well known that the static caching algorithm that keeps the most frequently requested documents in the cache is optimal in case when documents are of the same size and requests are independent and identically distributed. However, it is hard to develop explicit and provably optimal caching algorithms when requests are statistically correlated. In this paper, we show that keeping the most frequently requested documents in the cache is still optimal for large cache sizes even if the requests are strongly correlated.     

Multidimensional upwind convection schemes for flow in porous media on structured and unstructured quadrilateral grids

Standard reservoir simulation schemes employ first order upwind schemes for approximation of the convective fluxes when multiple phases or components are present. These convective flux schemes rely upon upwind information that is determined according to grid geometry. As a consequence directional diffusion is introduced into the solution that is grid dependent. The effect can be particularly important for cases where the flow is across grid coordinate lines and is known as cross-wind diffusion.Truly higher dimensional upwind schemes that minimize cross-wind diffusion are presented for convective flow approximation on quadrilateral unstructured grids. The schemes are locally conservative and yield improved results that are essentially free of spurious oscillations. The higher dimensional schemes are coupled with full tensor Darcy flux approximations.The benefits of the resulting schemes are demonstrated for classical test problems in reservoir simulation including cases with full tensor permeability fields. The test cases involve a range of structured and unstructured grids with variations in orientation and permeability that lead to flow fields that are poorly resolved by standard simulation methods. The higher dimensional formulations are shown to effectively reduce the numerical cross-wind diffusion effect, leading to improved resolution of concentration and saturation fronts.     

The Effects of Combining Observation Periods in Time Series

This paper considers what happens when 'monthly' data, which can be modelled by a linear transform function together with a noise or error term, are aggregated to form 'annual' data. It is assumed that in the monthly model noise and input are independent, and it is shown that if the parameters of the annual model are so chosen that the input and noise are uncorrelated at all lags, then the parameters are functions of the structure generating the input series. However, if the annual noise and input are uncorrelated, the resulting model leads to the same estimate of gain and average lag as the monthly model. It is pointed out that this is at variance with reported empirical studies where annual models lead to much greater average lags. An example is given to show that the explanation may lie in the over-simplification of annual models. It is frequently assumed that a monthly Koyck model implies a similar annual model. This is not so, and the omission of a lagged term in the input series accounts for the bias in the average lag.     

Angle orders

A finite poset is an angle order if its points can be mapped into angular regions in the plane so thatx precedesy in the poset precisely when the region forx is properly included in the region fory. We show that all posets of dimension four or less are angle orders, all interval orders are angle orders, and that some angle orders must have an angular region less than 180° (or more than 180°). The latter result is used to prove that there are posets that are not angle orders.The smallest verified poset that is not an angle order has 198 points. We suspect that the minimum is around 30 points. Other open problems are noted, including whether there are dimension-5 posets that are not angle orders.Research supported in part by the National Science Foundation, grant number DMS-8401281.     

The quasistatic motions of a three-body system on a plane

A controlled three-body system on a horizontal plane with dry friction is considered. The interaction forces between each pair of bodies are controls that are not subject to prior constraints but must be chosen in such a way that the motions of the system generated by them are quasistatic, that is, the total force acting on each of the bodies must be close to zero. All motions in which one body moves and the other two are fixed are found in the class of quasistatic motions. The problem of the optimal displacement of a moving body between two specified positions on a plane such that the absolute magnitude of the work of the friction forces along the trajectory is a minimum is solved. The quasistatic controllability of a three-body system is demonstrated and algorithms for bringing it into a specified position are discussed. The system considered simulates a mobile robot consisting of three bodies between which control forces act that can be realized by linear motors. The sizes of the bodies are assumed to be negligibly small compared with the distances between them so that the bodies are treated as particles.     

Orientability of matroids

In this paper we define oriented matroids and develop their fundamental properties, which lead to generalizations of known results concerning directed graphs, convex polytopes, and linear programming. Duals and minors of oriented matroids are defined. It is shown that every coordinatization (representation) of a matroid over an ordered field induces an orientation of the matroid. Examples of matroids that are orientable but not coordinatizable and of matroids that are not orientable are presented. We show that a binary matroid is orientable if and only if it is unimodular (regular), and that every unimodular matroid has an orientation that is induced by a coordinatization and is unique in a certain straightforward sense.     

On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.     

Schmidt number and partially entanglement-breaking channels in infinite-dimensional quantum systems

The Schmidt number of a state of an infinite-dimensional composite quantum system is defined and several properties of the corresponding Schmidt classes are considered. It is shown that there are states with given Schmidt number such that any of their countable convex decompositions does not contain pure states of finite Schmidt rank. The classes of infinite-dimensional partially entanglement-breaking channels are considered, and generalizations of several properties of such channels, which were obtained earlier in the finite-dimensional case, are proved. At the same time, it is shown that there are partially entanglement-breaking channels (in particular, entanglement-breaking channels) such that all the operators in any of their Kraus representations are of infinite rank.     

Possibly v. actually the case: Davidson’s omniscient interpreter at twenty

The publication of Davidson 2001, anthologizing articles from the 1980s and 1990s, encourages reconsidering arguments contained in them. One such argument is Davidson’s omniscient-interpreter argument (‘OIA’) in Davidson 1983. The OIA allegedly establishes that it is necessary that most beliefs are true. Thus the omniscient interpreter, revived in 2001 and now 20 years old, was born to answer the skeptic. In Part I of this paper, I consider charges that the OIA establishes only that it is possible that most beliefs are true; if correct, then it is also possibly the case that most beliefs are false—the skeptic’s very position. Next, I consider two responses on Davidson’s behalf, showing that each fails. In Part II, I show that the OIA establishes neither that it is necessarily merely possibly but actually the case that most beliefs are true. I then conclude that this is enough to answer the skeptic.     

On optimal trees

The merits of different shapes of trees as data storage structures are compared. Given a tree data structure, the worst-case cost of searching the tree is studied, under weak assumptions about the cost of searches. In particular, it is assumed that the cost of a search path is the sum of the costs of the nodes on it, and that the cost of a node depends only on the outdegree of that node. The main results of the paper are that there are regular trees (as defined in the paper) which are nearly optimal among trees with a given number of nodes, and that minimal-cost trees are often nearly regular.