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1.
The vector assignment p-median problem (VAPMP) (Weaver and Church in Transp Sci 19(1):58–74, 1985) was one of the first location-allocation models developed to handle split assignment of a demand to multiple facilities. The underlying construct of the VAPMP has been subsequently used in a number of reliable facility location and backup location models. Although in many applications the chance that a facility fails may vary substantially with locations, many existing models have assumed a uniform failure probability across all sites. As an improvement, this paper proposes a new model, the expected p-median problem as a generalization of existing approaches by explicitly considering site-dependent failure probabilities. Multi-level closest assignment constraints and two efficient integer linear programming (ILP) formulations are introduced. While prior research generally concludes that similar problems are not integer-friendly and cannot be solved by ILP software, computational results show that our model can be used to solve medium-sized location problems optimally using existing ILP software. Moreover, the new model can be used to formulate other reliable or expected location problems with consideration of site-dependent failure probabilities. 相似文献
2.
Service area research is one of the pivotal topics in Urban Geography. This article first put forward a model of urban population estimation. And on the basis we measured the size and distribution of population in downtown Shanghai, China. The population model was confirmed well by the traditional survey model. Then we extracted a 1-month actual-time data set contains geo-location by collecting in Sina Weibo data, and generated Voronoi diagram by these data which denoted the service patches. We assigned population to each patch. Second part, we proposed a shortest distance algorithm, a minimum time algorithm and an improved p-median algorithm, took advantages of these three methods to divide the service area of metro stations based on patches. Subsequently, we computed the service population in each service area. Last, we took metro line 1 and 2 as examples to research the relationship among 3 location-allocation methods in detail. The results showed that: The spatial distribution of population of the core city in Shanghai emerged a descending trend from center to periphery clearly. All indicators (including area, population, distance and time) in central city within inner ring road have changed little compared with the region between inner and outer ring road. Yet the improved p-median algorithm has a certain effect of optimization. It presented a scientific and rational travel scheme for citizens cost smallest price to select better starting metro station. The study results should contribute to theoretical and technical support for location-allocation of public service facilities. 相似文献
3.
Masashi Miyagawa 《Journal of Geographical Systems》2012,14(2):209-222
This paper derives the joint distribution of the distances to the first and the second nearest points for regular and random
patterns. Distance is measured as the Euclidean and the rectilinear distances on a continuous plane. The joint distribution
extends the kth nearest distance distribution of previous works. The kth nearest distance distribution only shows how the distance to the kth nearest point is distributed, whereas the joint distribution provides the relationship between the distances. An application
of the joint distribution can be found in a facility location problem with non-closest facility service where the distance
to the second nearest facility is also important. The joint distribution that allows us to examine the first and the second
nearest distances simultaneously is useful for evaluating the reliability of facility location when some of the existing facilities
are closed. The joint distribution of the road network distances is also obtained to confirm that the model on a continuous
plane can be applied to actual road networks. 相似文献
4.
5.
The analysis of lunar laser ranging (LLR) data enables the determination of many parameters of the Earth–Moon system, such
as lunar gravity coefficients, reflector and station coordinates which contribute to the realisation of the International
Terrestrial Reference Frame 2000 (ITRF 2000), Earth orientation parameters [EOPs, which contribute to the global EOP solutions
at the International Earth Rotation Service (IERS)] or quantities which parameterise relativistic effects in the solar system.
The big advantage of LLR is the long time span of lunar observations (1970–2000). The accuracy of the normal points nowadays
is about 1 cm.
The capability of LLR to determine tidal parameters is investigated. In principle, it could be assumed that LLR would contribute
greatly to the investigation of tidal effects, because the Moon is the most important tide-generating body. In this respect
some special topics such as treatment of the permanent tide and the effect of atmospheric loading are addressed and results
for the tidal parameters h
2 and l
2 as well as values for the eight main tides are given.
Received: 14 August 2000 / Accepted: 15 October 2001 相似文献
6.
The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points Pi{Xi,Yi,Zi}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan. 相似文献
7.
Lorenzo Iorio 《Journal of Geodesy》2006,80(3):128-136
In this paper, we quantitatively discuss the impact of the current uncertainties in the even zonal harmonic coefficients J
l
of the Newtonian part of the terrestrial gravitational potential on the measurement of the general relativistic Lense–Thirring effect. We use a suitable linear combination of the nodes Ω of the laser-ranged LAGEOS and LAGEOS-II satellites. The one-sigma systematic error due to mismodelling of the J
l
coefficients ranges from ~ 4% for the EIGEN−GRACE02S gravity field model to ~ 9% for the GGM02S model. Another important source of systematic error of gravitational origin is represented by the secular variations j
l
of the even zonal harmonics. While the relativistic and J
l
signals are linear in time, the shift due to j
l
is quadratic. We quantitatively assess their impact on the measurement of the Lense–Thirring effect with numerical simulations obtaining a 10−20% one-sigma total error over 11 years for EIGEN-GRACE02S. Ciufolini and Pavlis (Nature 431:958–960, 2004) claim a total error of 5% at the one-sigma level. 相似文献
8.
非球形冰晶的毫米波k-Ze关系研究 总被引：1，自引：0，他引：1
针对毫米波雷达处理数据的实际需要,应用离散偶极子近似法DDA,获得了非球形冰晶的后向散射及衰减截面并进行了参数化,并主要基于细化的冰云模型,假设冰晶粒子谱为Γ分布,通过模拟取样各1330次（代表1330种粒子分布）,分别计算得到了W波段（94 GHz）与Ka波段（35 GHz）毫米波雷达探测的冰云衰减系数k及雷达反射率因子Ze,而且利用数值模拟的方法,建立了k-Ze关系的具体表达式。计算表明,非球形和非瑞利散射对W波段毫米波雷达衰减的影响较大,而且在同样滴谱分布条件下,W波段毫米波雷达的衰减比Ka波段毫米波雷达的大几倍,此外细化的冰云模型对k-Ze关系具有影响。本研究对中纬度非降水性冰云的毫米波雷达的衰减订正具有参考价值,并对中国的毫米波雷达应用具有借鉴作用。 相似文献
9.
10.
Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration 总被引：6，自引：0，他引：6
Ten days of GPS data from 1998 were processed to determine how the accuracy of a derived three-dimensional relative position
vector between GPS antennas depends on the chord distance (denoted L) between these antennas and on the duration of the GPS observing session (denoted T). It was found that the dependence of accuracy on L is negligibly small when (a) using the `final' GPS satellite orbits disseminated by the International GPS Service, (b) fixing
integer ambiguities, (c) estimating appropriate neutral-atmosphere-delay parameters, (d) 26 km ≤ L ≤ 300 km, and (e) 4 h ≤T ≤ 24 h. Under these same conditions, the standard error for the relative position in the north–south dimension (denoted S
n
and expressed in mm) is adequately approximated by the equation S
n
=k
n
/T
0.5 with k
n
=9.5 ± 2.1 mm · h0.5 and T expressed in hours. Similarly, the standard errors for the relative position in the east–west and in the up-down dimensions
are adequately approximated by the equations S
e
=k
e
/T
0.5 and S
u
=k
u
/T
0.5, respectively, with k
e
=9.9 ± 3.1 mm · h0.5 and k
u
=36.5 ± 9.1 mm · h0.5.
Received: 5 February 2001 / Accepted: 14 May 2001 相似文献
11.
C. C. Tscherning 《Journal of Geodesy》1999,73(6):332-336
A reproducing-kernel Hilbert space (RKHS) of functions harmonic in the set outside a sphere with radius R
0, having a reproducing kernel K
0(P,Q) is considered (P, Q, and later P
n
being points in the set of harmonicity). The degree variances of this kernel will be denoted σ0
n
.
The set of Riesz representers associated with the evaluation functionals (or gravity functionals) related to distinct points
P
n
,n = 1,…,N, on a two-dimensional surface surrounding the bounding sphere, will be linearly independent. These functions are used to
define a new N-dimensional RKHS with kernel (a
n
>0)
If the points all are located on a concentric sphere with radius R
1>R
0, and form an ε-net covering the sphere, and a
n
are suitable area elements (depending on N), then this kernel will converge towards an isotropic kernel with degree variances
Consequently, if K
N
(P,Q) is required to represent an isotropic covariance function of the Earth's gravity potential, COV(P,Q), σ0
n
can be selected so that σ
n
becomes equal to the empirical degree variances.
If the points are chosen at varying radial distances R
n
>R
0, then an anisotropic kernel, or equivalent covariance function representation, can be constructed. If the points are located
in a bounded region, the kernel may be used to modify the original kernel
Values of anisotropic covariance functions constructed based on these ideas are calculated, and some initial ideas are presented
on how to select the points P
n
.
Received: 24 September 1998 / Accepted: 10 March 1999 相似文献
12.
The spacetime gravitational field of a deformable body 总被引：3，自引：0，他引：3
The high-resolution analysis of orbit perturbations of terrestrial artificial satellites has documented that the eigengravitation
of a massive body like the Earth changes in time, namely with periodic and aperiodic constituents. For the space-time variation
of the gravitational field the action of internal and external volume as well as surface forces on a deformable massive body
are responsible. Free of any assumption on the symmetry of the constitution of the deformable body we review the incremental
spatial (“Eulerian”) and material (“Lagrangean”) gravitational field equations, in particular the source terms (two constituents:
the divergence of the displacement field as well as the projection of the displacement field onto the gradient of the reference
mass density function) and the `jump conditions' at the boundary surface of the body as well as at internal interfaces both
in linear approximation. A spherical harmonic expansion in terms of multipoles of the incremental Eulerian gravitational potential
is presented. Three types of spherical multipoles are identified, namely the dilatation multipoles, the transport displacement
multipoles and those multipoles which are generated by mass condensation onto the boundary reference surface or internal interfaces.
The degree-one term has been identified as non-zero, thus as a “dipole moment” being responsible for the varying position
of the deformable body's mass centre. Finally, for those deformable bodies which enjoy a spherically symmetric constitution,
emphasis is on the functional relation between Green functions, namely between Fourier-/ Laplace-transformed volume versus
surface Love-Shida functions (h(r),l(r) versus h
′(r),l
′(r)) and Love functions k(r) versus k
′(r). The functional relation is numerically tested for an active tidal force/potential and an active loading force/potential,
proving an excellent agreement with experimental results.
Received: December 1995 / Accepted: 1 February 1997 相似文献
13.
The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of M?bius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex
generated by the unknown point and the four known points. Substitution of M?bius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4.
contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gau? (1842), A. Schreiber (1908) and A.␣Ansermet (1910).
Received: 05 March 1996; Accepted: 15 October 1996 相似文献
14.
A. J. E. Smith B. A. C. Ambrosius K. F. Wakker P. L. Woodworth J. M. Vassie 《Journal of Geodesy》1997,71(11):695-703
Three years of TOPEX/POSEIDON altimeter data have been processed at Delft Institute for Earth-Oriented Space Research (DEOS)
to solve the major diurnal and semi-diurnal constituents of the global ocean tide using the two classical methods of tidal
analysis, i.e. the harmonic and response analyses. Some experiments with the parameters in the response formalism show that the tidal admittance
in both the diurnal and semi-diurnal band can be adequately described with a lag interval of 2 days and a number of lags of
three. Results of both methods are evaluated from the differences with the most recent Grenoble hydrodynamic model (FES95.2)
and from the fit with the harmonic constants of a globally distributed set of tide gauges. It was found that the solutions
of the two methods differ at the millimeter level and are thus fully equivalent, which is confirmed by the tide gauges and
the differences with FES95.2. From the comparisons with the Grenoble model it was found that the M
2 and S
2 solutions of that model likely contain bathymetric errors which are of the order of 1–2 cm for M
2 and 0.5 cm for S
2.
Received: 18 December 1996 / Accepted: 12 May 1997 相似文献
15.
Defining the distortion of a conformal map projection as the oscillation of the logarithm of its infinitesimal-scale σ, Chebyshev’s principle states that the best (minimum distortion) conformal map projection over a given region Ω of the ellipsoid is characterized by the property that σ is constant on the boundary of that region. Starting from a first map of Ω, we show how to compute the distortion δ0(Ω) of this Chebyshev’s projection. We prove that this minimum possible conformal mapping distortion associated with Ω coincides with the absolute value of the minimum of the solution of a Dirichlet boundary-value problem for an elliptic partial differential equation in divergence form and with homogeneous boundary condition. If the first map is conformal, the partial differential equation becomes a Poisson equation for the Laplace operator. As an example, we compute the minimum conformal distortion associated with peninsular Spain. Using longitude and isometric latitude as coordinates, we solve the corresponding boundary-value problem with the finite element method, obtaining δ0(Ω)=0.74869×10−3. We also quantify the distortions δl and δutm of the best conformal conic and UTM (zone 30) projections over peninsular Spain respectively. We get δl=2.30202×10−3 and δutm=3.33784×10−3. 相似文献
16.
The twin perspective 4 point (twin P4P) problem – also called the combined three dimensional resection-intersection problem – is the problem of finding
the position of a scene object from 4 correspondence points and a scene stereopair. While the perspective centers of the left and right scene image are positioned by means of a double three dimensional resection, the position of the scene object imaged on the left and right photograph is determined by a three dimensional intersection based upon given resected perspective centers. Here we present a new algorithm solving the twin P4P problem by means of M?bius barycentric coordinates. In the first algorithmic step we determine the distances between the perspective centers and the unknown intersected point by solving a linear system of
equations. Typically, area elements of the left and right image build up the linear equation system. The second algorithmic step allows for the computation of the M?bius barycentric coordinates of the unknown intersected point which are thirdly converted into three dimensional object space coordinates {X,Y,Z} of the intersected point. Typically, this three-step algorithm based upon M?bius barycentric coordinates takes advantage of the primary double resection problem from which only distances from four correspondence points to the left and right perspective centre are needed. No orientation parameters and no coordinates
of the left and right perspective center have to be made available.
Received 1 May 1996; Accepted 13 September 1996 相似文献
17.
Arif Wismadi Mark Zuidgeest Mark Brussel Martin van Maarseveen 《Journal of Geographical Systems》2014,16(1):19-48
To determine whether the inclusion of spatial neighbourhood comparison factors in Preference Modelling allows spatial decision support systems (SDSSs) to better address spatial equity, we introduce Spatial Preference Modelling (SPM). To evaluate the effectiveness of this model in addressing equity, various standardisation functions in both Non-Spatial Preference Modelling and SPM are compared. The evaluation involves applying the model to a resource location-allocation problem for transport infrastructure in the Special Province of Yogyakarta in Indonesia. We apply Amartya Sen’s Capability Approach to define opportunity to mobility as a non-income indicator. Using the extended Moran’s I interpretation for spatial equity, we evaluate the distribution output regarding, first, ‘the spatial distribution patterns of priority targeting for allocation’ (SPT) and, second, ‘the effect of new distribution patterns after location-allocation’ (ELA). The Moran’s I index of the initial map and its comparison with six patterns for SPT as well as ELA consistently indicates that the SPM is more effective for addressing spatial equity. We conclude that the inclusion of spatial neighbourhood comparison factors in Preference Modelling improves the capability of SDSS to address spatial equity. This study thus proposes a new formal method for SDSS with specific attention on resource location-allocation to address spatial equity. 相似文献
18.
《测量评论》2013,45(6):275-284
AbstractWith the modern calculating machine in easy reach of every computer, the problem of determining the position of an occupied point from which direction observations have been made to three or more known points has become quite simple. The method outlined below is quite elegant in form and exceedingly simple on the machine. Let A, B, C be the three points whose co-ordinates (X1Y1), (X2Y2), (X3Y3) are known, and let (XY) be the co-ordinates of the point P which we wish to fix. 相似文献
19.
Analysis on the global morphology of stratospheric gravity wave activity deduced from the COSMIC GPS occultation profiles 总被引：5，自引：0，他引：5
Monthly mean global morphologies of potential energy density E
p
from stratospheric gravity waves are revealed by observations of COSMIC GPS radio occultation. The E
p
is obtained from vertical wavelengths ranging from 2 to 10 km over cells of 1° × 2° in latitude and longitude. The computed
values confirm previous results and obtain new ones. The large gravity wave E
p
values found in the tropics between 25°N and 25°S could be mainly due to the strong tropical cumulus convection; July values
are larger than those for January (2007). In mid and high latitudes, the most prominent features of the northern winter hemisphere
are the enhanced densities above the Eurasian continent and the North Atlantic and the depressed E
p
values above the North Pacific and North America for which topography, wind sources and wind filtering may be responsible.
In southern winter hemisphere, large E
p
values are found around 180° and 300° longitudes that are likely due to the topography of the Antarctic plateau, the Antarctic
Peninsula and South America. Enhanced E
p
values are found over Scandinavia. However, there is no clear evidence to show that gravity waves are localized over the
Rocky Mountains, the Himalayas and the Andes. Topography and planetary wave modulations are proposed to interpret the large-scale
longitudinal variations and inter-hemisphere asymmetry of the GW activity. 相似文献
20.
Maytham Safar 《Journal of Geographical Systems》2008,10(4):407-416
This paper addresses the problem of Group K-Nearest Neighbors (GKNN) queries in spatial network databases, and suggests a novel approach based on real network distances.
This approach essentially uses network Voronoi diagram properties together with a progressive incremental network expansion
for determining the inner network distances that are needed to obtain GKNN queries.
相似文献