Lifting Theory Research Articles

Best N-Simultaneous Approximation in Lp(μ,X)

Let X be a Banach space. Let 1≤p<∞ and denote by Lp(μ,X) the Banach space of all X-valued Bochner p-integrable functions on a certain positive complete σ-finite measure space (Ω,Σ,μ), endowed with the usual p-norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset W of X, the set Lp(μ,W) is N-simultaneously proximinal in Lp(μ,X) for any arbitrary monotonous norm N in Rn.

Vortex-Lift Mechanism in Axial Turbomachinery with Periodically Pitched Stators

Conventional aerodynamic theory of lift is based on the Kutta–Joukowski condition, in which the lift and drag coefficients are predicted based on the assumption that flow is attached and steady-state. Recent research on insect flight indicates, however, that the unsteady motion of a wing can generate much higher unsteady aerodynamic force through the flow induced by the shedding vortices. In the present work, therefore, we propose a novel type of stage consisting of rotor and periodically pitched stator to take advantage of unsteady vortex lift. The numerical results suggest that the flowfield around the leading and trailing edges of the blades are substantially modified by the interactions between the rotor and pitching stator. Several transient lift peaks can be generated for each period. If an appropriate pitching phase is chosen for the stator, stage performance can be improved through unsteady lift mechanism effects.

Comparison of the Goryachkin Theory to Soil Flow on a Sweep

The Goryachkin trihedral wedge theories describe soil flow over a surface resembling the wing of a sweep. The current study tested the Goryachkin crushing and lifting theories’ prediction of soil flow across a sweep by comparing with measurements from observed soil flow. Treatments included sweeps with three different rake angles (13.5, 16, and 44°) operated at three speeds (5, 7, and 9 km/h) and at two depths (50 and 100 mm). Flow direction was determined from scratch marks on the sweep surface.

Nonlinear lifting theory for unsteady WIG in proximity to incident water waves. Part 2: Three-dimension

The present article presents a nonlinear analysis for determining the three-dimensional unsteady potential-flow characteristics about a wing subject to wing-in-ground effect (WIG) operating above progressive water waves. By means of the time-domain Green's function for the three-dimensional dipole moving above the free surface satisfying the dynamic and kinematic boundary conditions on the mean free surface, the influence of the free surface on the vortex ring is considered. Then, the nonlinear unsteady lifting surface theory is developed to study the lifting problem for a three-dimensional wing operating above progressive water waves. Furthermore, the roll-up shed from the wing in the presence of a free surface and water waves is taken into account. With the computed results, the non-dimensional force coefficients (including the lift coefficient, induced drag coefficient and lift-to-drag ratio) are presented with the variation of different geometry and water wave parameters. The data reported in the literature are presented to validate the present approach.

Nonlinear lifting theory for unsteady WIG in proximity to incident water waves. Part 1: Two-dimension

A nonlinear analysis is made for determining the two-dimensional unsteady potential-flow characteristics about a wing subject to wing-in-ground effect (WIG) operating above progressive water waves. The dynamic boundary condition requiring the constant pressure and the kinematic boundary condition prescribing the continuity in the vertical velocity are satisfied on the undisturbed free surface. The boundary conditions imposed on the free surface are linear, but the kinematic boundary condition satisfied on the foil surface is nonlinear. Through the derivation and evaluation of the time-domain Green's functions for two-dimensional singularities above a free surface, the influence of water waves on the lift performance of the two-dimensional WIG is addressed using the discrete vortex method. Furthermore, the roll-up of the wake vorticity is considered. The comparison of present work with other numerical results available in the literature shows the validation of the present approach.

Why airplanes fly: The Strong Programme and the theory of lift

When the Wright brothers made their first controlled flight in 1903, no scientific theory could explain why their airplane should fly. In technical terms, the phenomena that needed explanation was lift, the upward vertical forces on an airplane in steady flight. Existing theories of fluid motion either predicted no lift at all or values for lift that were far lower than those achieved in practice. This scientific anomaly became an embarrassment after 1908, when the Wright brothers demonstrated their improved Flyer throughout Europe. With the Wrights’ demonstrations and Louis Bleriot’s 1909 flight across the English Channel, European militaries began investing heavily in aviation research and experimentation, highlighting the inadequacy of existing theories of lift. This is the ‘‘enigma of the airfoil’’ that Bloor seeks to explain in his book. To do so he gives his readers a detailed technical history of the development of airfoil theory, a central achievement of modern aerodynamics. But the enigma he seeks to explain goes beyond the theory of lift itself. Bloor also provides a careful comparative analysis of the two main schools of aerodynamic theory in the early 20th century, one British and the other German. The puzzle he examines here is well known in the history of aerodynamics, the British ‘‘failure’’ to embrace the circulation theory of lift pioneered by German-speaking academic engineers. As a founder of the Strong Programme in the sociology of scientific knowledge, Bloor rejects using social factors to explain only the British failure and not the German success. In doing so, he provides penetrating insights into different modes of reasoning involved in the application of mathematical theory to technological practice.

Theta lifts and local Maass forms

The first two authors and Kohnen have recently introduced a new class of modular objects called locally harmonic Maass forms, which are annihilated almost everywhere by the hyperbolic Laplacian operator. In this paper, we realize these locally harmonic Maass forms as theta lifts of harmonic weak Maass forms. Using the theory of theta lifts, we then construct examples of (non-harmonic) local Maass forms, which are instead eigenfunctions of the hyperbolic Laplacian almost everywhere.

Generating controllable velocity fluctuations using twin oscillating hydrofoils

AbstractAn experiment apparatus has been previously developed with the ability to independently control the instantaneous flow velocity in a water flume. This configuration, which uses two pitching hydrofoils to generate the flow fluctuations, allows the unsteady response of submerged structures to be studied over a wide range of driving frequencies and conditions. Linear unsteady lift theory has been used to calculate the instantaneous circulation about two pitching hydrofoils in uniform flow. A vortex model is then used to describe the circulation in the wakes that determine the velocity perturbations at the centreline between the foils. This paper introduces how the vortex model can be discretized to allow the inverse problem to be solved, such that the foil motions required to recreate a desired velocity time series can be determined. The results of this model are presented for the simplified cases of oscillatory velocity fluctuations in the vertical and stream-wise directions separately, and also simultaneously. The more general case of two-dimensional aperiodic velocity fluctuations is also presented, which demonstrates the capability of configuration between the suggested frequency limits of $0. 06\leq k\leq 1. 9$.

An analytical investigation of two-dimensional and three-dimensional biplanes operating in the vicinity of a free surface

In the present article, the classical two- and three-dimensional lifting theories are generalized to the biplane operating in proximity to a free surface. The singularity distribution method is employed to calculate the lifting force for a two-dimensional biplane subjected to wing-in-ground effect in the vicinity of a free surface, and the three-dimensional correction is carried out by the aid of the Prandtl lifting line theory. The essential techniques lie in finding the three-dimensional Green’s function for the system of horseshoe vortices operating above a free surface and ensuring numerical implementation. Extensive numerical examples are carried out to show the lift coefficient for the two- and three-dimensional biplanes in the vicinity of a free surface with the variation of the clearance-to-chord ratio and the height-to-chord ratio. Incidentally, the induced (inviscid) drag coefficients as well as the lift-to-drag ratio for a three-dimensional biplane are also computed. Good agreement can be found among results obtained from this study and the experiment.

Weakly compact sets in [formula omitted

Using the theory of liftings, we give simple new proofs of the characterizations of the relatively weakly compact subsets and weak Cauchy sequences of L∞(E). Also a different proof, of a deep result of J. Diestel, W. Ruess, W. Schachermayer about weak compactness in L1(E), is given.

A lifting line theory for a three-dimensional hydrofoil

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

Applications of $${\Phi}$$ -Operators to Hypercomplex Geometry

The main aim of this paper is to study relations between \({\Phi}\) -operators, hyperholomorphic functions and the theory of lifts in tensor bundles. Model of lifts of affinor fields was found by using of \({\Phi}\) -operators. After that, hyperholomorphic properties of pure cross-sections were investigated by the help of this model.

Inductive pairs and lifts in solvable groups

The Fong-Swan theorem showed that for each irreducible Brauer character φ of a finite solvable group, there exists at least one ordinary irreducible character χ that lifts φ. Recently there has been some progress toward understanding the set of lifts of a given Brauer character, by constructing certain canonical sets of lifts and studying their properties. In this paper we develop the theory of lifts of Brauer characters that are induced from inductive pairs. This leads to a lower bound on the number of “well-behaved” lifts of a given Brauer character in terms of the inductive pair. Moreover, it is shown that given a “wellbehaved” lift, the vertices for the lift (a generalization of the vertices of the corresponding Brauer character) are unique up to conjugacy.

On Classical and Quantum Liftings

We analyze the procedure of lifting in classical stochastic and quantum systems. It enables one to 'lift' a state of a system into a state of 'system + reservoir'. This procedure is important both in quantum information theory and the theory of open systems. We illustrate the general theory of liftings by a particular class related to so-called circulant states.

Special cycles on unitary Shimura varieties I. Unramified local theory

The supersingular locus in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n−1) over ℚ is uniformized by a formal scheme $\mathcal{N}$ . In the case when p is an inert prime, we define special cycles ${\mathcal{Z}}({\bold x})$ in $\mathcal{N}$ , associated to collections ${\bold x}$ of m ‘special homomorphisms’ with fundamental matrix T∈Herm m (O k ). When m=n and T is nonsingular, we show that the cycle ${\mathcal{Z}}({\bold x})$ is either empty or is a union of components of the Ekedahl-Oort stratification, and we give a necessary and sufficient condition, in terms of T, for ${\mathcal{Z}}({\bold x})$ to be irreducible. When ${\mathcal{Z}}({\bold x})$ is zero dimensional—in which case it reduces to a single point—we determine the length of the corresponding local ring by using a variant of the theory of quasi-canonical liftings. We show that this length coincides with the derivative of a representation density for hermitian forms.

Branching rules obtained from explicit correspondences of automorphic representations

In this paper, we show how one can use the theory of lifting of automorphic forms in order to obtain formulas of branching rules in complex groups. We also use this technique to give formulas for certain functionals which are defined on unramified representations.

Lifting inequalities: a framework for generating strong cuts for nonlinear programs

In this paper, we introduce the first generic lifting techniques for deriving strong globally valid cuts for nonlinear programs. The theory is geometric and provides insights into lifting-based cut generation procedures, yielding short proofs of earlier results in mixed-integer programming. Using convex extensions, we obtain conditions that allow for sequence-independent lifting in nonlinear settings, paving a way for efficient cut-generation procedures for nonlinear programs. This sequence-independent lifting framework also subsumes the superadditive lifting theory that has been used to generate many general-purpose, strong cuts for integer programs. We specialize our lifting results to derive facet-defining inequalities for mixed-integer bilinear knapsack sets. Finally, we demonstrate the strength of nonlinear lifting by showing that these inequalities cannot be obtained using a single round of traditional integer programming cut-generation techniques applied on a tight reformulation of the problem.

Mechanism of membrane fouling control by suspended carriers in a submerged membrane bioreactor

In an attempt to alleviate membrane fouling, a kind of cylindrical rigid suspended carrier was added in a submerged membrane bioreactor (SMBR) treating synthetic domestic wastewater. Its effect was investigated at different mixed liquor suspended solid (MLSS) concentrations and carrier doses. It was found that the suspended carriers added in the SMBR had two effects on membrane fouling: first was the positive effect by mechanically scouring membrane surface, thereby mitigating cake layer fouling; the second was the negative effect by breaking up sludge flocs that caused an increase in the amount of small particles and supernatant total organic carbon and thus accelerated membrane fouling. The whole effect of suspended carriers on membrane fouling depended on the relative intensity of these two effects. Based on the experimental results of all runs and the inertial lift theory, therefore, it was concluded that there existed an effective carrier dose range for mitigating membrane fouling on the whole. When MLSS concentrations were 5 g/L, 8 g/L, and 11 g/L, then the effective carrier doses (carrier volume vs. total volume) were about less than 4.4%, 7.3%, and 9.5%, respectively.

TWISTED CHARACTER OF A SMALL REPRESENTATION OF GL(4)

We compute by a purely local method the (elliptic) θ-twisted character χπY of the representation πY = I(3, 1)(13 × χY) of G = GL (4, F), where F is a p-adic field, p ≠ 2, and Y is an unramified quadratic extension of F; χY is the nontrivial character of F×/NY/FY×. The representation πY is normalizedly induced from [Formula: see text], mi ∈ GL (i, F), on the maximal parabolic subgroup of type (3, 1); θ is the "transpose-inverse" involution of G. We show that the twisted character χπY of πY is an unstable function: its value at a twisted regular elliptic conjugacy class with norm in CY = CY(F)="( GL (2, Y)/F×)F" is minus its value at the other class within the twisted stable conjugacy class. It is 0 at the classes without norm in CY. Moreover πY is the endoscopic lift of the trivial representation of CY. We deal only with unramified Y/F, as globally this case occurs almost everywhere. The case of ramified Y/F would require another paper. Our CY = "( R Y/F GL (2)/ GL (1))F" has Y-points CY(Y) = {(g, g′) ∈ GL (2, Y) × GL (2, Y); det (g) = det (g′)}/Y× (Y× embeds diagonally); σ(≠ 1) in Gal (Y/F) acts by σ(g, g′) = (σg′, σg). It is a θ-twisted elliptic endoscopic group of GL(4). Naturally this computation plays a role in the theory of lifting of CY and GSp(2) to GL(4) using the trace formula, to be discussed elsewhere. Our work extends — to the context of nontrivial central characters — the work of [7], where representations of PGL (4, F) are studied. In [7] we develop a 4-dimensional analogue of the model of the small representation of PGL (3, F) introduced by the first author and Kazhdan in [5] in a 3-dimensional case, and we extend the local method of computation introduced in [6]. As in [7] we use here the classification of twisted (stable) regular conjugacy classes in GL (4, F) of [4], motivated by Weissauer [13].

Propagation of CR extendibility along complex tangent directions

We discuss the propagation along CR curves of extendibility of CR functions in the framework of the theory of partial lifts of CR curves and of analytic discs introduced by the authors in (Baracco, L. and Zampieri, G., 2001, Analytic discs and extension of CR functions. Compositio Mathematica, 127, 289–295) and (Baracco, L. and Zampieri, G., 2002, Tangent discs and extension of CR functions to wedges of . J. Geom. Analysis, 12(1), 1–7).