Lifting Problem Research Articles

Comparison of cocycles of measured equivalence relations and lifting problems

Let be an ergodic discrete equivalence relation on a Lebesgue space and . We say that an automorphism of if it preserves the cohomology class of . We introduce a quasi-order relation on the set of all cocycles of by means of comparison of the corresponding groups of all automorphisms being compatible with them. We find simple necessary and sufficient conditions under which two cocycles of a hyperfinite measure-preserving equivalence relation with values in compact (possibly different) groups are connected by this relation. Next, given an ergodic subrelation , we investigate the problem of extending -cocycles up to -cocycles and improve the recent results of Gabriel–Lemańczyk–Schmidt. As an application we study the problem of lifting of automorphisms of up to automorphisms of the skew product , provide new short proofs of some known results and answer several questions from [ALV, ALMN].

Lifting Theorem as a Special Case of Abstract Interpolation Problem

Using properties of the de Branges-Rovnyak spaces we include the classical lifting problem into the general scheme of the abstract interpolation problem.

Extremally disconnected spaces, subspaces and retracts

A characterization of compact subspaces of extremally disconnected spaces is given which is similar to Gleason's characterization that the extremally disconnected spaces are projective for the class of compact spaces. An equivalence is established between the questions of whether every basically disconnected space is embeddable into an extremally disconnected space and the Borel lifting problems for the category algebras of generalized Cantor cubes. We study an inductive method of strengthening the product topology on the Cantor cubes to extremally disconnected topologies and use this to establish, from CH, that every compact F-space of weight c + embeds into an extremally disconnected space.

C(K, X) as an M-ideal inWC(K, X)

In this paper we study the classes of Banach spacesX for which the space of continuousX-valued functions forms an M-ideal in the space of weakly continuous functions. We also study a lifting problem for weakly continuous functions.

ON THE K-THEORY OF QUARTER-PLANE TOEPLITZ ALGEBRAS

Given a C*-algebra A which is filtered by a collection of closed ideals Ai, there is a spectral sequence which relates the K-theory of A to the K-theory of the various quotient algebras Ai/Ai−1. The d1 differentials in this spectral sequence are familiar index invariants, but the higher differentials are not well-understood. Considering the case of Toeplitz C*-algebras associated with certain cones in Z2, it is shown that a d2 differential in the spectral sequence is non-trivial. This differential turns out to be an obstruction to a classical lifting problem in operator theory. Analysis of this obstruction leads to necessary and sufficient conditions for the lifting problem. It is hoped that this example will illuminate the role of higher differentials in the K-theory spectral sequence.

The Lifting Problem for Affine Structures in Nilpotent Lie Groups

Affine manifolds occur in several situations in pure and applied mathematics, (e.g. leaves of Lagrangian foliations, completely integrable Hamiltonian systems, linear representations of virtually polycyclic groups, geometric quantization and so on). This work is devoted to left invariant affinely flat structures in Lie groups. We are mainly concerned with the following situation. Let $G$ and ${G_0}$ be nilpotent Lie groups of dimension $n + 1$ and $n$ , respectively and let $h:G \to {G_0}$ be a continuous homomorphism from $G$ onto ${G_0}$ . Given a left invariant affinely flat structure $({G_0},{\nabla _0})$ the lifting problem is to discover whether $G$ has a left invariant affinely flat structure $(G,\nabla )$ such that $h$ becomes an affine morphism. In the present work we answer positively when $({G_0},{\nabla _0})$ is "normal". Therefore the existence problem for a left invariant complete affinely flat structure in nilpotent Lie groups is solved by applying the following subsequent results. Let $\mathfrak {A}f({G_0})$ be the set of left invariant affinely flat structures in the nilpotent Lie group ${G_0},({1^ \circ })\;\mathfrak {A}f({G_0}) \ne \emptyset$ implies the existence of normal structure $({G_0},{\nabla _0}) \in \mathfrak {A}f({G_0});({2^ \circ })\;h:G \to {G_0}$ being as above every normal structure $({G_0},{\nabla _0})$ has a normal lifted in $\mathfrak {A}f(G)$.

A lifting theorem for compact symplectic manifolds

It is shown that the Lie algebra of globally Hamiltonian vector fields on a compact symplectic manifold can be lifted to a Lie algebra of smooth functions on the manifold under Poisson bracket. This implies that any algebra of symmetries of a classical mechanical system described by such a manifold may be realised as an algebra of observables (smooth functions). Parallels between lifting problems in classical and quantum mechanics are explored.

The manual lifting problem: The illusive solution

Ayoub, M.A., 1982. The manual lifting problem: the illusive solution. Journal of Occupational Accidents, 4: 1–23. Much has been written and discussed concerning the hazards of manual lifting tasks. The literature, the industrial experience and the injury statistics all support the inevitable conclusion that the problem is real and that its far-reaching roots in the workplace are unparalleled in industry. Yet we still have to find a remedy which can either be implemented in industry or which can at least be effective under all task and workplace conditions. In the interim, however, the literature offers three solution approaches that can be used separately or collectively for controlling lifting hazards: (a) hazard control through training in safe lifting, (b) control of employee exposure through pre-employment strength testing, and (c) control of job demands through the adoption of workloads acceptable for the industrial population. The principles and philosophies of each of the three approaches are detailed and discussed. The strengths and weaknesses of each approach are also summarized and assessed.

Global uniqueness in the disc lifting problem

Global uniqueness in the disc lifting problem

Water Drive From Interbedded Shale Compaction In Superpressured Gas Reservoirs A Model Study

The behavior of abnormally high-pressured gas reservoirs in sand formations with randomly interbedded, thin, noncontinuous shale layers is examined using numerical simulation. The relevance of the internal water drive resulting from shale compaction and the influence of mobile water generation on reservoir and well behavior are discussed. Introduction An increasing number of hydrocarbon reservoirs discovered at great depths have pressures that are significantly higher than the hydrostatic pressure. Because of the high temperatures found at great depths, a large percentage of these superpressured reservoirs are gas or percentage of these superpressured reservoirs are gas or gas-condensate types. Several authors discussed the conditions that help create superpressured reservoirs. Such reservoirs often are found in thick sedimentary basins characterized by high-velocity sedimentation. Tightly interbedded shale and sand layers (under impermeable layers) are typical of superpressured reservoirs. The compressibility of abnormally high-pressured formations is higher than normal resulting from their understressed condition. When the abnormally high-pressured formation is a hydrocarbon reservoir, the high rock compressibility and even higher compressibility of the shale layers, either interbedded or boundary, may contribute appreciably to reservoir energy. Purpose Purpose It long has been recognized that reservoir rock compaction as well as interstitial water expansion, both resulting from pressure depletion, can contribute appreciably to the energy supporting production in abnormally high-pressured gas reservoirs. Several authors pointed out that in reservoirs embedded between thick shale layers, a sensible contribution to the production mechanism may originate by water expelled from the confining shale layers. Because these shale layers are very thick, the time required for the decreasing reservoir pressure to diffuse throughout the shale body may be more than the productive life of the reservoir. When reservoir rock contains very thin, noncontinuous shale layers, randomly distributed within the sand body, the time delay for water release from interbedded shale compaction can be disregarded. Wallace presented a list of actual gas reservoirs where water released presented a list of actual gas reservoirs where water released from the compaction of interbedded shale layers did contribute relevantly to reservoir drive, thus creating what might be termed an "internal water drive." In this study, production behavior of abnormally high-pressured gas reservoirs with thin shale interbeddings was examined. The study aimsto evaluate the energy contribution to reservoir drive resulting from water released from interbedded shale compaction; andto gain information about the adverse influence that diffused generation of mobile water (resulting from shale compaction) may have on well performance, considering that water production in gas wells poses disposal and often difficult lifting problems . JPT P. 937

Steady Incompressible Variable-Thickness Shear Layer Aerodynamics

A shear flow aerodynamic theory for steady incompressible flows is presented for both the lifting and non lifting problems. The slow variation of the boundary layer thickness is considered. The slowly varying behavior is treated by using multitime scales. The analysis begins with the elementary wavy wall problem and, through Fourier superpositions over the wave number space, the shear flow equivalents to the aerodynamic transfer functions of classical potential flow are obtained. The aerodynamic transfer functions provide integral equations which relate the wall pressure and the upwash. Computational results are presented for the pressure distribution, the lift coefficient, and the center of pressure travel along a two dimensional flat plate in a shear flow. The aerodynamic load is decreased by the shear layer, compared to the potential flow. The variable thickness shear layer decreases it less than the uniform thickness shear layer based upon equal maximum shear layer thicknesses.

An integral approach to lifting wing theory at Mach one

An approach to lifting wing theory at Mach one is presented that utilizes an integral method similar to the Karman-Pohlhausen method in boundary layer theory. As in any integral method the results obtained are approximate in nature. Nonetheless, comparison with experimental data shows good agreement in cases for which experimental data are available. The method can easily be used to determine the lift on wings of finite aspect ratio and also to solve transient lifting problems. The method is demonstrated by solving for the pressure distribution on a lifting airfoil of arbitrary symmetric cross-section, the lift on a wing of rectangular planform, and the transient lift on an airfoil due to a sudden change in angle of attack. These cases were chosen to illustrate the versatility of the method and are not meant to be exhaustive of all possibilities. The computational time required to obtain numerical results is very small in all cases considered.

The primitive lifting problem in the equivalence problem for transitive pseudogroup structures: a counterexample

A transitive Lie pseudogroup Γ M {\Gamma _M} on M is a primitive extension of Γ N {\Gamma _N} if Γ N {\Gamma _N} is the quotient of Γ M {\Gamma _M} by an invariant fibration π : M → N \pi :M \to N and if the pseudogroup induced by Γ M {\Gamma _M} on the fiber of π \pi is primitive. In the present paper an example of this situation is given with the following property (counterexample to the primitive lifting property): the equivalence theorem is true for almost- Γ N {\Gamma _N} -structures but false for almost- Γ M {\Gamma _M} -structures.

A unified treatment of some basic problems in homotopy theory

0. Introduction. This note announces some new methods in algebraic topology, based on the results of [1], [2] and [3]. The relative lifting problem [5, p. 415] is fundamental to that subject. It includes the extension problem, the retraction problem, the lifting problem, the section problem, the relative section problem and the computation of [X, Y] problem, among its particular cases. These problems (excluding the last one) are usually taken to concern just the existence of extensions, retractions, etc. ; we use the terms in the wider sense, to include both the existence question and the homotopy classification question, for the respective extensions, retractions, etc. We will : (i) prove that many cases of the above problems (including the computation of the absolute and relative cohomology groups of the total space of a fibration, and the computation of certain homotopy groups) are equivalent to problems, involving the restricted fibered mapping projection (pq;a); (ii) give some examples of solutions of parallel problems. Our solutions include one lifting problem and two extension problems. The extension results have some immediate consequences; they give new derivations for the exact cohomology sequences of Serre and Wang. Gysin's sequence is derived separately. Future papers will discuss these and other applications in detail. Our argument is valid in several convenient categories, including the category of i-spaces [4], [2], [7] and the category of quasi-topological spaces [6], [1], [2]. This category of I-spaces, for a definition see [2, p. 276], contains the usual category of Hausdorff fc-spaces (= compactly generated spaces = Kelley spaces) as a subcategory.

Lagally’s Theorem and the Lifting Body Problem

A review is presented on the use of Lagally's Theorem to determine forces and moments on bodies moving through an ideal fluid, including the extension to unsteady flows by Cummins and the evaluation of the virtual moment by Landweber and Yih for the case of sources and doublets. The latter is generalized to cover any type of singularity. Applications thus far have been restricted to distributions of singularities which lie entirely within the body. This paper considers the lifting body problem in which a vortex or doublet sheet cuts through the body. It is shown that direct application of the final Lagally equations to such a problem yields erroneous results. An approach is presented in which the Lagally integrals are correctly evaluated for this type of singularity distribution.

A reduction of the strong lifting problem

A reduction of the strong lifting problem

A numerical method for the calculation of nonlinear, unsteady lifting potential flow problems

A numerical method is developed for attacking lifting problems of a general three-dimensional wing executing an arbitrary motion in a potential flow. The formulation of the problem is exact in the sense that the boundary conditions are satisfied on the surface of the wing and the geometry of the time-dependent wake is predicted. The problem is then governed by a Fredholm integral equation of the first kind which relates the velocity potential doublet distribution to the normal velocity on the surface of the wing, subject to the Kutta condition of smooth flow off the trailing edge and the condition that the wake cannot sustain any pressure difference. The solution of the integral equation is obtained in a step-by-step fashion, and the appearing surface integrals are evaluated by employing a discrete set of approximate surface elements and an assumption of the doublet distribution over the element which is based on a formal expansion of the velocity influence coefficient. Verification of the method is made by comparison with solutions of classical problems. To demonstrate its utility, the method is applied to obtain the airloads due to transient motion of wings with simple planforms. The nonlinear effects due to the wake, aspect ratio, and thickness are discussed. Results of these calculations indicate that the present method can be applied to treat more complicated geometries and motion to obtain accurate and efficient prediction of the airloads.

Performance of the Lower Pawelek Reservoir, Falls City Field, Karnes County, Texas

Abstract This paper presents the initial results of a pressure maintenance by waterreturn project in the Lower Pawelek reservoir of the Falls City Field, KarnesCounty, Southwest Texas. Production is from the Lower Wilcox section at anaverage depth of 6,030'Ft on the downthrown side of a "down to thecoast" fault. Of particular interest is that the reservoir oil is highgravity and low viscosity but far undersaturated with gas at the originalreservoir pressure and temperature. The early pressure and production historyindicated only a partial or limited water drive, and this fact, coupled withthe characteristics of the reservoir fluid and artificial lifting problems, made advisable the water injection program to maintain reservoirpressure. The paper includes a description of the reservoir and reservoir fluids, thepressure and production history, a description of the water injectionfacilities, and the results of reservoir calculations involving Hurst'sunsteady state flow and the material balance equations for calculation of waterinflux and prediction of the pressure-production relationship at various ratesof withdrawal. The reservoir calculations and initial field results indicate that reservoirpressures in excess of 85 per cent of original pressure can be maintained bycontrol of water injection even at very high rates of production. Introduction The purpose of this paper is to report the initial results of a pressuremaintenance by water return program in the Lower Pawelek reservoir, Falls CityField, Karnes County, Texas, and to calculate an empirical relationship betweenpressure and production in this limited or partial water drive reservoir. Discussion Location The Falls City Field (Fig. 1) is located two miles north of the town of FallsCity in Karnes County, Texas, and is approximately 50 miles south-southeast ofSan Antonio on U. S. Highway 181. Discovery and Development The initial block of leases was taken after a surface geological surveyidentified a major east-west fault and closure on the south or downthrownsection. The discovery well, Southern Minerals Corporation's Joe F. Bartosch 1, was completed at 4,650'Ft in the Lower Bartosch sand in December, 1944.Drilling was continuous until December, 1946, and resulted in the discovery of12 oil reservoirs between 4,600 and 6,050'Ft in the Middle and Lower Wilcoxformations. T.P. 2937