Mountain Pass Solutions for a Double-Well Energy

We establish the existence of a mountain pass solution for a variational integral involving a quasiconvex function with a double-well structure in the geometrically linear elasticity setting. We show that under small dead-load perturbations, the Neumann boundary value problem has at least three solutions, a global minimizer, a local minimizer and a mountain pass solution. We show that our variational integral satisfies a Weak Palais-Smale condition (WPS) hence the mountain pass lemma applies.     

Ascent properties for pairs of modules

Given a flat local ring homomorphism \({R \rightarrow S}\) and two finitely generated R-modules M and N, we describe conditions under which the modules \({{\rm Tor}^{R}_{i}(M,N)}\) and \({{\rm Ext}^{i}_{R}(M,N)}\) have S-module structures that are compatible with their R-module structures.     

Optimal Guidance for Quasi-planar Lunar Ascent

The minimum-time controls (thrust pitch angle and thrust yaw angle) for the three-dimensional transfer of a constant-thrust rocket from one state to another over a flat moon are used to develop guidance laws for operation over a spherical moon. The objective is to evaluate the effect of making approximations on the size of the thrust pitch angle on the suitability of the resulting control law as a guidance law. After assuming small out-of-plane motion (small yaw angle), three pitch angle control laws (exact, first-order, and zeroth-order) are developed. The three laws are employed in the sample and hold guidance of a lunar ascent vehicle. All three laws satisfy the final conditions and give essentially the same pitch and yaw control histories. Since the zeroth-order law can be obtained completely analytically (no iteration processes), it merits consideration for ascent guidance.     

Ascent of properties for absolutely flat homomorphisms

We show that if A – B is an absolutely flat homomorphism of consultative rings and A is arithmetical, then B is such, thus generalising a previous result (see [9]) on valutation rings.

To prove the above theorem we show first that it is true when A is a local ring and B is a local ind-étale homomorphism (in par ticular if B is a strict henselization of A ) , and we apply the following general fact:a local property which ascends to strict henselization and descends by faithful flatness ascends also by ab solutely flat homomorphlsms. This last result also applies to other properties, such as locally noetherian, geometrically unibranche, R_n,S_n, Cohen-Macaulay.     

Rado's Conjecture and Ascent Paths of Square Sequences

This is a continuation of our paper 12 where we show that Rado's Conjecture can trivialize ‐sequences in some cases when ? is not necessarily a successor cardinal.     

Minimizing Fusion Frame Potential

Fusion frames are an emerging topic of frame theory, with applications to encoding and distributed sensing. However, little is known about the existence of tight fusion frames. In traditional frame theory, one method for showing that unit norm tight frames exist is to characterize them as the minimizers of an energy functional, known as the frame potential. We generalize the frame potential to the fusion frame setting. In particular, we introduce the fusion frame potential, and show how its minimization is equivalent to the minimization of the traditional frame potential over a particular domain. We then study this minimization problem in detail. Specifically, we show that if the desired number of fusion frame subspaces is large, and if the desired dimension of these subspaces is small compared to the dimension of the underlying space, then a tight fusion frame of those dimensions will necessarily exist, being a minimizer of the fusion frame potential.     

Minimizing symmetric submodular functions

We describe a purely combinatorial algorithm which, given a submodular set functionf on a finite setV, finds a nontrivial subsetA ofV minimizingf[A] + f[V A]. This algorithm, an extension of the Nagamochi—Ibaraki minimum cut algorithm as simplified by Stoer and Wagner [M. Stoer, F. Wagner, A simple min cut algorithm, Proceedings of the European Symposium on Algorithms ESA '94, LNCS 855, Springer, Berlin, 1994, pp. 141–147] and by Frank [A. Frank, On the edge-connectivity algorithm of Nagamochi and Ibaraki, Laboratoire Artémis, IMAG, Université J. Fourier, Grenbole, 1994], minimizes any symmetric submodular function using O(|V|³) calls to a function value oracle. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.A preliminary version of this paper was presented at the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) in January 1995. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.     

Optimal Ascent Trajectories and Feasibility of Next-Generation Orbital Spacecraft

This paper deals with the optimization of the ascent trajectories for single-stage-to-orbit (SSTO) and two-stage-to-orbit (TSTO) rocket-powered spacecraft. The maximum payload weight problem is studied for various combinations of initial thrust-to-weight ratio, engine specific impulse, and spacecraft structural factor. For TSTO rocket-powered spacecraft, two cases are studied: uniform structural factor and nonuniform structural factor between stages.The main conclusions are that: the design of SSTO configurations might be comfortably feasible, marginally feasible, or unfeasible, depending on the parameter values assumed; the design of TSTO configurations is not only feasible, but the payload appears to be considerably larger than that of SSTO configurations; for the case of a nonuniform structural factor, the most attactive TSTO design appears to be a first-stage structure made of only tanks and a second-stage structure made of engines, tanks, electronics, and so on.Improvements in engine specific impulse and spacecraft structural factor are desirable and crucial for SSTO feasibility; indeed, aerodynamic improvements do not yield significant improvements in payload weight.For SSTO configurations, the maximum payload weight behaves almost linearly with respect to the engine specific impulse and the spacecraft structural factor. The same property holds for TSTO configurations as long as the ratio of the structural factors of Stage 2 and Stage 1 is held constant. With reference to the specific impulse/structural factor domain, this property leads to the construction of a zero-payload line separating the feasibility region (positive payload) from the unfeasibility region (negative payload).     

Minimizing makespan in parallel flowshops

In this study, a new class of proportional parallel flow shop problems with the objective of minimizing the makespan has been addressed. A special case for this problem in which jobs are processed on only one machine as opposed to two or more machines in a flow shop, is the well-known multiple processor problem which is NP-complete. The parallel processor problem is a restricted version of the problems addressed in this paper and hence are NP-complete. We develop and test heuristic and simulation approaches to solve large scale problems, while using exact procedures for smaller problems. The performance of the heuristics relative to the LP lower bound as well as a comparison with the truncated integer programming solution are reported. The performance of the heuristics and the simulation results were encouraging.     

Minimizing coincidence in positive codimension

Let f and g be maps between smooth manifolds M and N of dimensions n + m and n, respectively (where m > 0 and n > 2). Suppose that the image (fxg)(M) intersects the diagonal N × N in finitely many points, whose preimages are smooth m-submanifolds inM. The problem of minimizing the coincidence set Coin(f, g) of the maps f and g with respect to these preimages and/or their components is considered. The author’s earlier results are strengthened. Namely, sufficient conditions under which such a coincidence m-submanifold can be removed without additional dimensional constraints are obtained.     

Minimizing breaks by maximizing cuts

We propose to solve the break minimization problem in sports scheduling by transforming it into a maximum cut problem in an undirected graph and applying a branch-and-cut algorithm. Our approach outperforms previous approaches with constraint programming and integer programming techniques.     

Two-Dimensional Multiple-Valued Dirichlet Minimizing Functions

We give some remarks on two-dimensional multiple-valued Dirichlet minimizing functions, including frequency, classification of branch points and their connections. As an application, we prove that blowing-up functions of a two-dimensional multiple-valued Dirichlet minimizing function are unique. This article is concluded with a boundary regularity theorem for two-dimensional multiple-valued Dirichlet minimizing functions.     

MCD-finite Domains and Ascent of IDF Property in Polynomial Extensions

An integral domain is said to have the IDF property when every non-zero element of it has only a finite number of non-associate irreducible divisors. A counterexample has already been found showing that the IDF property does not necessarily ascend in polynomial extensions. In this paper, we introduce a new class of integral domains, called MCD-finite domains, and show that for any domain D, D[X] is an IDF domain if and only if D is both IDF and MCD-finite. This result entails all the previously known sufficient conditions for the ascent of the IDF property. Our new characterization of polynomial domains with the IDF property enables us to use a different construction and build another counterexample which strengthen the previously known result on this matter.     

On the Ascent of Properties Related to Unique Factorization Domains

In this article, we develop equivalent conditions for a certain class of monoidal transform to inherit either the property of being a completely integrally closed domain that satisfies the ascending chain condition on principal ideals, the property of being a Mori domain, the property of being a Krull domain, or the property of being a unique factorization domain, respectively. Such a class of monoidal transform is given in terms of an (analytically) independent set that forms a prime ideal in the base domain. Characterizations are provided illustrating the necessity of the “prime ideal” hypothesis when the base domain is a Noetherian unique factorization domain.     

Minimizing Sequences in Class-Qualified Deposit Problems

We study multidimensional control problems involving first-order partial differential equations. To ensure the existence of sufficiently regular multipliers (from the space ) in the first-order necessary optimality conditions, some restrictions of the feasible domain have to be added. In particular, we investigate ‘class-qualified’ problems where the weak derivatives of can be represented within a Baire function class. In the present paper, we prove conditions under which the original and the modified problems possess the same minimal values.     

Minimizing makespan in re-entrant permutation flow-shops

A re-entrant flow-shop (RFS) describes situations in which every job must be processed on machines in the order of M₁, M₂, …, M _m , M₁, M₂, …,M _m , …, and M₁, M₂, …,M _m . In this case, every job can be decomposed into L levels and each level starts on M₁, and finishes on M _m . In a RFS case, if the job ordering is the same on any machine at each level, then it is said that no passing is allowed since any job is not allowed to pass any previous job. The RFS scheduling problem where no passing is allowed is called the re-entrant permutation flow-shop (RPFS) problem. This paper proposes three extended mixed BIP formulations and six extended effective heuristics for solving RPFS scheduling problems to minimize makespan.     

Minimizing the delay at traffic lights

Vehicles holding at traffic lights is a typical queuing problem.At crossings the vehicles experience delay in both directions.Longer periods with green lights in one direction are disadvantageousfor the vehicles coming from the other direction. The totaldelay for getting through the traffic point is what counts.This article presents an expression to calculate the optimaltime periods of red lights and green lights starting from afixed-cycle time. The solution is optimal if it makes the trafficjam delay at the road crossing minimal. As these solutions dependon the number of cars arriving in the different directions,which is not constant during the day, the application can beenlarged to a system where the time periods of red and greenlights change during the day.