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1.
A. Miele T. Wang P. N. Williams 《Journal of Optimization Theory and Applications》2005,127(3):605-625
The Hohmann transfer theory, developed in the 19th century, is the kernel of orbital transfer with minimum propellant mass
by means of chemical engines. The success of the Deep Space 1 spacecraft has paved the way toward using advanced electrical
engines in space. While chemical engines are characterized by high thrust and low specific impulse, electrical engines are
characterized by low thrust and hight specific impulse. In this paper, we focus on four issues of optimal interplanetary transfer
for a spacecraft powered by an electrical engine controlled via the thrust direction and thrust setting: (a) trajectories
of compromise between transfer time and propellant mass, (b) trajectories of minimum time, (c) trajectories of minimum propellant
mass, and (d) relations with the Hohmann transfer trajectory. The resulting fundamental properties are as follows:
The above properties are verified computationally for two cases (a) ascending transfer from Earth orbit to Mars orbit; and
(b) descending transfer from Earth orbit to Venus orbit. The results are obtained using the sequential gradient- restoration
algorithm in either single-subarc form or multiple-subarc form.
Portions of this paper were presented by the senior author at the 54th International Astro-nautical Congress, Bremen, Germany,
29 September–3 October 2003 (Paper IAC-03-A.7.02).
This research was supported by NSF Grant CMS-02-18878 and NSF Cooperative Agreement HRD-98-17555 as part of the Rice University
AGEP Program. 相似文献
| (a) Flight Time/Propellant Mass Compromise. For interplanetary orbital transfer (orbital period of order year), an important objective of trajectory optimization is a compromise between flight time and propellant mass. The resulting trajectories have a three-subarc thrust profile: the first and third subarcs are characterized by maximum thrust; the second subarc is characterized by zero thrust (coasting flight); for the first subarc, the normal component of the thrust is opposite to that of the third subarc. When the compromise factor shifts from transfer time (C=0) toward propellant mass (C=1), the average magnitude of the thrust direction for the first and third subarcs decreases, while the flight time of the second subarc (coasting) increases; this results into propellant mass decrease and flight time increase. | |
| (b) Minimum Time. The minimum transfer time trajectory is achieved when the compromise factor is totally shifted toward the transfer time (C=0). The resulting trajectory is characterized by a two-subarc thrust profile. In both subarcs, maximum thrust setting is employed and the thrust direction is transversal to the velocity direction. In the first subarc, the normal component of the thrust vector is directed upward for ascending transfer and downward for descending transfer. In the second subarc, the normal component of the thrust vector is directed downward for ascending transfer and upward for descending transfer. | |
| (c) Minimum Propellant Mass. The minimum propellant mass trajectory is achieved when the compromise factor is totally shifted toward propellant mass (C=1). The resulting trajectory is characterized by a three-subarc (bang-zero-bang) thrust profile, with the thrust direction tangent to the flight path at all times. | |
| (d) Relations with the Hohmann Transfer. The Hohmann transfer trajectory can be regarded as the asymptotic limit of the minimum propellant mass trajectory as the thrust magnitude tends to infinity. The Hohmann transfer trajectory provides lower bounds for the propellant mass, flight time, and phase angle travel of the minimum propellant mass trajectory. |
2.
Marcel Erné 《Algebra Universalis》1993,30(4):538-580
We study several kinds of distributivity for concept lattices of contexts. In particular, we find necessary and sufficient conditions for a concept lattice to be
In cases (2), (4) and (5), our criteria are first order statements on objects and attributes of the given context. Several applications are obtained by considering the completion by cuts and the completion by lower ends of a quasiordered set as special types of concept lattices. Various degrees of distributivity for concept lattices are expressed by certain separation axioms for the underlying contexts. Passing to complementary contexts makes some statements and proofs more elegant. For example, it leads to a one-to-one correspondence between completely distributive lattices and so-called Cantor lattices, and it establishes an equivalence between partially ordered sets and doubly founded reduced contexts with distributive concept lattices. 相似文献
| (1) | distributive, |
| (2) | a frame (locale, complete Heyting algebra), |
| (3) | isomorphic to a topology, |
| (4) | completely distributive, |
| (5) | superalgebraic (i.e., algebraic and completely distributive). |
3.
G. Forst 《Inventiones Mathematicae》1976,34(2):135-150
Continuing earlier work on construction of harmonic spaces from translation invariant Dirichlet spaces defined on locally compact abelian groups, it is shown that the potential kernel for a non-symmetric translation invariant Dirichlet form on a locally compact abelian group under the extra assumptions that
相似文献
| (i) | the potential kernel is absolutely continuous and the canonical l.s.c. density is continuous in the complement of the neutral element. |
| (ii) | the theory is of local type. |
| (iii) | the underlying group is not discrete, can be interpreted as the potential kernel for a translation invariant axiomatic theory of harmonic functions, in which (among other properties) the domination axiom is fulfilled. |
4.
This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewittdecomposition theorem for this kind of vector measures. The major results are(a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain;(b) Every orthogonal vector measure can be represented as the sum of two orthogonal vectormeasures, one of which is countably additive, and the other is purely finitely additive. Furthermore,these vector measures are completely perpendicular to each other. 相似文献
5.
6.
We construct a self-avoiding process taking values in the finite Sierpinski gasket, and study its properties. We then study continuum limit processes that are suggested by the statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We prove that there are three types of continuum limit processes according to the parameters defining the statistical mechanics of self-avoiding paths:
相似文献
| (i) | the self-avoiding process we construct in this paper; |
| (ii) | a deterministic motion along a Peano curve on the finite Sierpinski gasket; |
| (iii) | a deterministic motion along a line segment. |
7.
Ronen Peretz 《Israel Journal of Mathematics》1999,109(1):181-187
LetF(X, Y) be a two dimensional polynomial map overC. We show how to use the notion of induced resultants in order to give short and elementary proofs to the following three
theorems:
相似文献
| 1. | If the Jacobian of F is a non-zero constant, then the image of F contains all of C2 except for a finite set. |
| 2. | If F is invertible, then the inverse map is determined by the free terms of the induced resultants. |
| 3. | If F is invertible, then the degree of F equals the degree of its inverse. |
8.
A. A. Tuganbaev 《Mathematical Notes》1998,64(1):116-120
Rings over which every nonzero right module has a maximal submodule are calledright Bass rings. For a ringA module-finite over its centerC, the equivalence of the following conditions is proved:
Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 136–142, July, 1998.This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00627. 相似文献
| (1) | A is a tight Bass ring; |
| (2) | A is a left Bass ring; |
| (3) | A/J(A) is a regular ring, andJ(A) is a right and leftt-nilpotent ideal. |
9.
A family of complementarity problems is defined as extensions of the well-known linear complementarity problem (LCP). These are:
A number of well-known mathematical programming problems [namely, quadratic programming (convex, nonconvex, pseudoconvex, nonconvex), linear variational inequalities, bilinear programming, game theory, zero-one integer programming, fixed-charge problem, absolute value programming, variable separable programming] are reformulated as members of this family of four complementarity problems. A brief discussion of the main algorithms for these four problems is presented, together with some computational experience. 相似文献
| (i) | second linear complementarity problem (SLCP), which is an LCP extended by introducing further equality restrictions and unrestricted variables; |
| (ii) | minimum linear complementarity problem (MLCP), which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized; |
| (iii) | second minimum linear complementarity problem (SMLCP), which is an MLCP, but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. |
10.
We present a new pivot-based algorithm which can be used with minor modification for the enumeration of the facets of the
convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary
dimension. The algorithm has the following properties:
For example, the algorithm finds thev vertices of a polyhedron inR
d defined by a nondegenerate system ofn inequalities (or, dually, thev facets of the convex hull ofn points inR
d, where each facet contains exactlyd given points) in timeO(ndv) andO(nd) space. Thev vertices in a simple arrangement ofn hyperplanes inR
d can be found inO(n
2
dv) time andO(nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming. 相似文献
| (a) | Virtually no additional storage is required beyond the input data. |
| (b) | The output list produced is free of duplicates. |
| (c) | The algorithm is extremely simple, requires no data structures, and handles all degenerate cases. |
| (d) | The running time is output sensitive for nondegenerate inputs. |
| (e) | The algorithm is easy to parallelize efficiently. |
11.
We consider smooth non-degenerate surfaces in ℙ4, and prove that there is a finite number of such surfaces which are:
A complete list is given in both cases. 相似文献
| (a) | sectionally non-special, i.e.h1(O C(1))=0, where C is a general hyperplane section of S; or |
| (b) | not of general type and non-special (i.e. h1(O C(1))=0. |
12.
T. E. Armstrong 《International Journal of Game Theory》1991,20(1):65-90
We consider games in coalition function form on a, generally infinite, algebra of coalitions. For finite algebras the additive part mappingv E(v ¦) is the usual. The concern here is the analogue for infinite algebras. The useful construction is the finitely additive stochastic process of additive parts of the game on the filtration
f
of finite subalgebras of.It is shown that
is an isomorphism between:
相似文献
| a) | Additive games and martingales |
| b) | Superadditive games and supermartingales |
| c) | Shapley's games of bounded deviationBD() in his (1953) dissertation and bounded F-processes of Armstrong (1983) |
| d) | Gilboa's spaceBS() (1989) and bounded processes of Armstrong (1983) |
13.
Birge Zimmermann Huisgen 《manuscripta mathematica》1991,70(1):157-182
We show that all projective resolutions over a monomial relations algebra Λ simplify drastically at the stage of the second
syzygy; more precisely, we show that the kernel of any homomorphism between two projective left Λ-modules is isomorphic to
a direct sum of principal left ideals generated by paths. As consequences, we obtain:
This research was partially supported by a grant from the National Science Foundation. 相似文献
| (a) | a tight approximation of the finitistic dimensions of Λ in terms of the (very accessible) projective dimensions of the principal left ideals generated by paths; |
| (b) | a basis for comparison of the ‘big’ and ‘little’ finitistic dimensions of Λ, yielding in particular that these two invariants cannot differ by more than 1 and that they are equal in ‘most’ cases; |
| (c) | manageable algorithms for computation of finitistic dimensions. |
14.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid
topological groups is established. 相似文献
| (1) | If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group. |
| (2) | If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete. |
| (3) | If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property. |
| (4) | The order-bound topology on any commutative lattice group is the finest locally solid topology on it. |
15.
Yōhei Yamasaki 《Graphs and Combinatorics》1989,5(1):275-282
We have generalized the theory of Shannon's games in [10]. In this paper, we treat a game on a graph with an action of elementary abelian group but our decision of the winner is more general. Our theory can be applied for non-negative integersn andr, to the two games on a graph withn + 1 distinguished terminals whose rules are as follows:
Dedicated to Professor Sin Hitotumatu for his 60'th birthday 相似文献
| (1) | the players Short and Cut play alternately to choose an edge, |
| (2) | the former contracts it and the later deletes it |
| (3) | the former if and only if he connects the terminals into at mostn – r + 1 ones. |
16.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
| – | • is finitely generated and infinite-dimensional, but has only finitedimensional quotients; |
| – | • has a subalgebra of finite codimension, isomorphic toM 2(k); |
| – | • is prime; |
| – | • has quadratic growth, and therefore Gelfand-Kirillov dimension 2; |
| – | • is recursively presented; |
| – | • satisfies no identity; |
| – | • contains a transcendental, invertible element; |
| – | • is semiprimitive if % MathType!End!2!1! has characteristic ≠2; |
| – | • is graded if % MathType!End!2!1! has characteristic 2; |
| – | • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!; |
| – | • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!. |
17.
The star unfolding of a convex polytope with respect to a pointx on its surface is obtained by cutting the surface along the shortest paths fromx to every vertex, and flattening the surface on the plane. We establish two main properties of the star unfolding:
These two properties permit conceptual simplification of several algorithms concerned with shortest paths on polytopes, and
sometimes a worst-case complexity improvement as well:
相似文献
| 1. | It does not self-overlap: it is a simple polygon. |
| 2. | The ridge tree in the unfolding, which is the locus of points with more than one shortest path fromx, is precisely the Voronoi diagram of the images ofx, restricted to the unfolding. |
| • | The construction of the ridge tree (in preparation for shortest-path queries, for instance) can be achieved by an especially simpleO(n 2) algorithm. This is no worst-case complexity improvement, but a considerable simplification nonetheless. |
| • | The exact set of all shortest-path “edge sequences” on a polytope can be found by an algorithm considerably simpler than was known previously, with a time improvement of roughly a factor ofn over the old bound ofO(n 7 logn). |
| • | The geodesic diameter of a polygon can be found inO(n 9 logn) time, an improvement of the previous bestO(n 10) algorithm. |
18.
Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian
symmetric spaces which are not semisimple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal
modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric
space M to a triple consisting of:
That leads to a classification scheme of indecomposable nonsimple pseudo-Riemannian symmetric spaces. In addition, we obtain
a full classification of symmetric spaces of index 2 (thereby completing and correcting in part earlier classification results
due to Cahen and Parker and to Neukirchner). 相似文献
| (i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M); | |
| (ii) a semisimple orthogonal module of the Lie algebra with involution; and | |
| (iii) a quadratic cohomology class of this module. |
19.
LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:
相似文献
| (1) | Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|. |
| (2) | |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group. |
| (3) | |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group. |
20.
José Rodríguez 《Archiv der Mathematik》2007,88(1):62-70
Let X be a weakly Lindel?f determined Banach space. We prove that the following two statements are equivalent:
Some applications and related examples are given.
Received: 11 January 2006; Revised: 24 May 2006 相似文献
| (i) | Every Radon probability measure on (BX*, w*) has separable support. |
| (ii) | Every countably additive X*-valued measure with σ-finite variation has norm separable range. |