Function space topologies between the uniform topology and the Whitney topology

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topologizing homeomorphism groups

This paper surveys topologies, called admissible group topologies, of the full group of self-homeomorphisms of a Tychonoff space , which yield continuity of both the group operations and at the same time provide continuity of the evaluation function or, in other words, make the evaluation function a group action of on . By means of a compact extension procedure, beyond local compactness and in two essentially different cases of rim-compactness, we show that the complete upper-semilattice of all admissible group topologies on admits a least element, that can be described simply as a set-open topology and contemporaneously as a uniform topology. But, then, carrying on another efficient way to produce admissible group topologies in substitution of, or in parallel with, the compact extension procedure, we show that rim-compactness is not a necessary condition for the existence of the least admissible group topology. Finally, we give necessary and sufficient conditions for the topology of uniform convergence on the bounded sets of a local proximity space to be an admissible group topology. Also, we cite that local compactness of is not a necessary condition for the compact-open topology to be an admissible group topology of

Proximal convergence

Suppose X is a topological space and Y a proximity space , fn L C f (Leader Convergence) iff for each A in X, B in Y, f(A) near B implies eventually fn (A) is near B. L.C. is a generalization of U. C. (Uniform Convergence). In this paper we study L. C. and various generalizations and prove analogues of the classical results of Arzelà, Dini and others

Active vibration control of a mounting bracket for automotive gearboxes

The aim of this paper is to investigate the use of active vibration control in automotive gearboxes mounting brackets to reduce tonal disturbances. A combination of piezoelectric accelerometers and an internally preloaded piezo stack actuator is used to counteract their unbalanced caused vibrations. Initially, a numerical modal analysis was carried out to identify the normal modes in the frequency range of interest. The piezo stack was simulated by a ROD element and its effect numerically characterized. The upper and lower faces of the stack were mechanically coupled with the bracket structure, whereas the active control strategy involved the relative displacement of two opposite points of the bracket. To this aim, dedicated interfaces were designed to integrate the stack into the mounting bracket. In order to control the vibrations in correspondence of the second bending mode (1599.4Hz), the primary disturbance, simulated by a shaker, was modelled in the frequency domain using a white noise signal. A narrow window of 20Hz was initially selected as the control system domain. Then, this frequency range has been made gradually wider around the resonance peak, in order to optimize the control effect, and then extended up to 80 Hz when undesired effects occurred. Primary and secondary control plants were firstly numerically fitted from the measured responses and excitations using system identification techniques, and then used for the active controller design and simulations

Feasibility study for a tonal vibration control system of a mounting bracket for automotive gearboxes

A conceptual design of an active device able to attenuate the tonal vibrations of a mounting bracket for automotive gearboxes is addressed in this paper. A preloaded piezo stack actuator is used to counteract the unbalanced vibrations of the component by monitoring its operational deformations. Firstly, a numerical modal analysis is carried out to characterize the normal modes in the frequency range of interest. The piezo stack is simulated by a rod element and its effect is numerically characterized. The upper and lower faces of the stack are mechanically coupled with the bracket structure, whereas the active control deals with the relative displacement of two points of the bracket. The primary disturbance was simulated by a shaker to control the vibrations in correspondence of the second bending mode (around 1.6 kHz). A 20 Hz narrow band was additionally selected as the control window. Then, this frequency range was enlarged around the resonance peak in order to optimize the control effect, till 80 Hz to investigate the resulting effects. Finally, focus is given to the structural damping by assessing its impact on the control forces and phases to cancel the deformation along the contact direction. The description of the experimental results concludes this work by generally confirming the numerical expectations

Study on the Influence of Chirality in the Threading of Calix[6]arene Hosts with Dialkylammonium Axles

The influence of chirality in calixarene threading has been studied by exploiting the “superweak anion approach”. In particular, the formation of chiral pseudo[2]rotaxanes bearing a classical stereogenic center in their axle and/or wheel components has been considered. Two kind of pseudo[2]rotaxane stereoadducts, the “endo-chiral” and “exo-chiral” ones, having the stereogenic center of a cationic axle inside or outside, respectively, the calix-cavity of a chiral calixarene were preferentially formed with specifically designed chiral axles by a fine exploitation of the so-called “endo-alkyl rule” and a newly defined “endo-α-methyl-benzyl rule” (threading of a hexaalkoxycalix[6]arene with a directional (α-methyl-benzyl)benzylammonium axle occurs with an endo-α-methyl-benzyl preference). The obtained pseudorotaxanes were studied in solution by 1D and 2D NMR, and in the gas-phase by means of the enantiomer-labeled (EL) mass spectrometry method, by combining enantiopure hosts with pseudoracemates of one deuterated and one unlabeled chiral axle enantiomer. In both instances, there was not a clear enantiodiscrimination in the threading process with the studied host/guest systems. Possible rationales are given to explain the scarce reciprocal influence between the guest and host chiral centers