共查询到20条相似文献,搜索用时 31 毫秒
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Consider the supremal functional applied to \(W^{1,\infty }\) maps \(u:\Omega \subseteq \mathbb {R}\longrightarrow \mathbb {R}^N\), \(N\ge 1\). Under certain assumptions on \(\mathscr {L}\), we prove for any given boundary data the existence of a map which is: Our method is based on \(L^p\) approximations and stable a priori partial regularity estimates. For item ii) we utilise the recently proposed by the author notion of \(\mathcal {D}\)-solutions in order to characterise the limit as a generalised solution. Our results are motivated from and apply to Data Assimilation in Meteorology.
相似文献
$$\begin{aligned} E_\infty (u,A) := \Vert \mathscr {L}(\cdot ,u,\mathrm {D}u)\Vert _{L^\infty (A)},\quad A\subseteq \Omega , \end{aligned}$$
(1)
- (i)a vectorial Absolute Minimiser of (1) in the sense of Aronsson,
- (ii)a generalised solution to the ODE system associated to (1) as the analogue of the Euler-Lagrange equations,
- (iii)a limit of minimisers of the respective \(L^p\) functionals as \(p\rightarrow \infty \) for any \(q\ge 1\) in the strong \(W^{1,q}\) topology and
- (iv)partially \(C^2\) on \(\Omega \) off an exceptional compact nowhere dense set.
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M. Hayes 《The Journal of the Operational Research Society》1976,27(2):329-340
This paper examines the procedure by which votes are converted into seats at U.K. General Elections. In particular it seeks to answer these questions. 相似文献
- i)What is the meaning of swing when more than two parties fight an election?
- ii)How can the distribution of seats at an election be determined from a prediction of national swing?
- iii)How can swing analysis be extended to help determine an electoral strategy for political parties?
- iv)What explanation can be provided for the swing in Scotland?
- v)What explanation can be provided for variations in the English swing?
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Indranil Biswas 《Geometriae Dedicata》2009,142(1):37-46
We consider all complex projective manifolds X that satisfy at least one of the following three conditions:
- (1)There exists a pair \({(C\,,\varphi)}\) , where C is a compact connected Riemann surface anda holomorphic map, such that the pull back \({\varphi^* {\it TX}}\) is not semistable.$\varphi\,:\, C\,\longrightarrow\, X$
- (2)The variety X admits an étale covering by an abelian variety.
- (3)The dimension dim X ≤ 1.
We prove that the following classes are among those that are of the above type.
相似文献
- All X with a finite fundamental group.
- All X such that there is a nonconstant morphism from \({{\mathbb C}{\mathbb P}^1}\) to X.
- All X such that the canonical line bundle K X is either positive or negative or \({c_1(K_X)\,\in\,H^2(X,\, {\mathbb Q})}\) vanishes.
- All X with \({{\rm dim}_{\mathbb C} X\, =\,2}\).
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The paper presents a comparison of Health and Welfare O.R. in the U.K. and Ireland as represented by two registers of current projects, compiled in 1972 and 1977 respectively. The survey shows that
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- i)There appear to be very few O.R. studies of social services;
- ii)The major focus has apparently moved away from hospital-based tactical studies, towards more broadly-based strategic studies;
- iii)Related to this, the number of projects labelled as concerned with "planning" has increased;
- iv)The number of projects involving "optimisation" has decreased, whilst those involving simulation have shown some increase; and
- v)The majority of projects in both years were described as involving "applied common sense", rather than any specific technique.
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We give a complete solution of the following two problems:
相似文献
- (1)For which (n, x) does there exist a pair of hexagon triple systems of order n having x inside triples in common?
- (2)For which (n, x) does there exist a pair of hexagon triple systems having x outside triples in common?
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G. C. Beare 《The Journal of the Operational Research Society》1987,38(10):899-905
The paper describes the use of an optimizing model, together with a simulation model, to determine the most effective mix and deployment of air defence weapons to defend a given set of assets against a range of air threats. The advantages of using an optimizing model in such studies are that it: 相似文献
- a—Gives more consistent results by reducing player variance.
- b—Can generate solutions that are robust to variations in threat and environment.
- c—Ensures that good solutions are not overlooked.
- d—Reduces the total processing time required to complete the study.
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We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. We prove:
Theorem 0.1. If K is a tame AEC with amalgamation satisfying a natural definition of superstability (which follows from categoricity in a high-enough cardinal), then for all high-enough \(\lambda {:}\) Our proofs use independence calculus and a generalization of averages to this non first-order context.
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- (1)The union of an increasing chain of \(\lambda \)-saturated models is \(\lambda \)-saturated.
- (2)There exists a type-full good \(\lambda \) -frame with underlying class the saturated models of size \(\lambda \).
- (3)There exists a unique limit model of size \(\lambda \).
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We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients.
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- (1)An extension theorem, for extending flow equivalences of subshifts to flow equivalent irreducible shifts of finite type which contain them.
- (2)The classification of certain constant to one maps from SFTs via algebraic invariants of associated G-SFTs.
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The vehicle-scheduling problem involves the design of several vehicle tours to meet a given set of requirements for customers with known locations, subject to a capacity constraint for the vehicles and a distance (or time) constraint for vehicle tours. Three methods of solution are considered in this paper: The excessive computation time and computer storage required for the first method renders it impracticable for large problems. Ten problems are examined and the results suggest that method C is superior to the other two methods. 相似文献
- aA branch-and-bound approach.
- bThe "savings" approach.
- cThe 3-optimal tour method.
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B. Griffiths 《The Journal of the Operational Research Society》1961,12(4):244-260
This paper describes the techniques used in an enquiry into production planning and stock holding problems encountered by one of our member firms.The investigation of the problem falls into three parts: 相似文献
- i)The analysis of demand.
- ii)The determination of optimum stock levels.
- iii)The solution of the allocation problem which arises if the capacity available for the production of stock lines is not equal to the amount required to bring stocks back to the optimum levels. This problem has not been fully investigated, but a proposed method of solution is given in an appendix.
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Under CH we show the following results:
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- (1)There is a discrete ultrafilter which is not a \({\mathcal {Z}}_{0}\)-ultrafilter.
- (2)There is a \(\sigma \)-compact ultrafilter which is not a \({\mathcal {Z}}_{0}\)-ultrafilter.
- (3)There is a \({\mathcal {J}}_{\omega ^{3}}\)-ultrafilter which is not a \({\mathcal {Z}}_{0}\)-ultrafilter.
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S. Vajda 《The Journal of the Operational Research Society》1975,26(3):527-542
In this paper, concepts of linear programming-in particular the Simplex algorithm and the Dual Simplex algorithm-are used within a discrete renewal model for the development of a graded population, when the transfer rates between the various grades are given, and "wastage" is replaced by suitable recruiting.The following questions are dealt with: Examples are given to illustrate the procedure, and some attention is given to the possibility of alternative routes in cases (3) and (4). It is observed that if a structure is attainable (or re-attainable) after n steps, then it is not necessarily attainable (or re-attainable) after n + 1 steps. 相似文献
- 1)Which population structures (i.e. partitions into grades) can be attained from a given structure, after one or more steps?
- 2)From which structures can a given structure be attained in one or more steps?
- 3)If the present structure as well as a desired future structure are given, can the latter be attained from the former in one or more steps? If so, how?
- 4)The last problem is of special interest if the starting structure is identical with that to be attained and is called re-attaining after more than one step, or strictly maintaining after one step.
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We consider the eigenvalue problems for boundary value problems of second order difference equations(1) and(2) Comparison results for the eigenvalues of the problem (1) and the problem (2) are established. 相似文献
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Let X and Y be two Banach spaces, and f: X → Y be a standard ε-isometry for some ε ≥ 0. In this paper, by using a recent theorem established by Cheng et al. (2013–2015), we show a sufficient condition guaranteeing the following sharp stability inequality of f: There is a surjective linear operator T: Y → X of norm one so that
$$\left\| {Tf(x) - x} \right\| \leqslant 2\varepsilon , for all x \in X.$$
As its application, we prove the following statements are equivalent for a standard ε-isometry f: X → Y:
This gives an affirmative answer to a question proposed by Vestfrid (2004, 2015). 相似文献
- (i)lim inf t→∞ dist(ty, f(X))/|t| < 1/2, for all y ∈ S Y ;
- (ii)\(\tau(f)\equiv sup_{y\epsilon S_{Y}}\) lim inf t→∞dist(ty, f(X))/|t| = 0;
- (iii)there is a surjective linear isometry U: X → Y so that$$\left\| {f(x) - Ux} \right\| \leqslant 2\varepsilon , for all x \in X.$$