An epic that starts in the middle. And that's the original! Discusses dimensions of space, early twentieth-century advances, the physics of elementary particles, string theory and branes, and proposals for extra-dimension universes. Warped Minds explores the transformation of psychopathologies into cultural phenomena in the wake of the transition from an epistemological to an ontological approach to psychopathology. A path-breaking journey into the brain, showing how perception, thought, and action are products of "maps" etched into your gray matter--and how technology can use them to read your mind.
This work concerns the computation of various L 2 cohomology theories, where L2 cohomology is an analogue of de Rham cohomology on complete Riemannian manifolds which demands the forms under consideration be square integrable.
These computations take place on a class of manifolds defined herein, which generalize the arithmetic quotients of rank one symmetric spaces. In particular, they are all with the sole exception of the Euclidean line finite volume. Nevertheless, infinite dimensionality problems can still arise for this L 2 cohomology, so the square integrability condition is tightened or loosened by multiplying various exponential weighting functions into the Riemannian measure. This often produces finite dimensional weighted L 2 cohomology groups.
Finally, the manifolds under study are sufficiently close to arithmetic quotients of rank one symmetric spaces that the cohomology of the links of the cusp points at infinity admits a weight space decomposition, allowing the definition of an analogue of the weighted cohomology of [GHM94] on them. This analogue, called warped cohomology, will in fact compute the weighted L2 cohomologies defined above and is defined on many nonarithmetic spaces.
Warped cohomology allows results on such spaces which are similar to the weighted L2 construction of weighted cohomology theorem A derived on arithmetic quotients of symmetric spaces of any rank in [Nai99]. As political tensions rise on Bajor, Security Chief Odo probes a series of murders aboard the station, while Commander Sisko struggles to cope with a new religious faction out to seize control of Bajor and to force the Federation out of the region.
After Stalin's death in , the Soviet Union dismantled the enormous system of terror and torture that he had created. But there has never been any Russian ban on former party functionaries, nor any external authority to dispense justice. Memorials to the Soviet victims are inadequate, and their families have received no significant compensation.
This book's premise is that late Soviet and post-Soviet culture, haunted by its past, has produced a unique set of memorial practices. More than twenty years after the collapse of the Soviet Union, Russia remains "the land of the unburied": the events of the mid-twentieth century are still very much alive, and still contentious.
Alexander Etkind shows how post-Soviet Russia has turned the painful process of mastering the past into an important part of its political present.
When seventeen-year-old Tessa Brody comes into possession of an ancient unicorn tapestry, she is plummeted into sixteenth-century England, where her life is intertwined with that of a handsome nobleman who is desperately trying to escape a terrible fate. A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y.
The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson—Walker models, are warped product manifolds.
The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson—Walker's and Schwarzschild's.
The famous John Nash's embedding theorem published in implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space.
The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Read this scary short fiction story about former college roommates who are gifted a collectible, but warped, vintage Ouija Board. They are warned to fix the warped board before they play the game or bad things will happen.
They fail to honor their promise to fix the warp before they play and encounter the wrath of the Ouija. Skip to content. Warped Passages. Warped Passages Book Review:. Altogether, LIGO and Virgo have observed gravitational waves from dozens of merging black-hole and neutron-star binaries 3.
Fischer, H. Pfeiffer, A. Abbott, B. Article Google Scholar. Abbott, R. X 11 , Google Scholar. Punturo, M. Reitze, D. Amaro-Seoane, P. Baumgarte, T. Press, Pretorius, F. Duez, M. Fischer, N. Ossokine, S. D , Boyle, M. Gamba, R. Tichy, W. Fernando, M. SIAM J. Daszuta, B. Bugner, M. The controller can then communicate a signal to the sensor assembly to project a signal across the surface of the substrate using the transmitter unit 1 16 and to capture the projected signal using the receiver unit 1 In various embodiments, the encoder on the track assembly 1 12 communicates a feedback signal to the controller to inform the controller of the position of the track assembly 1 When the track assembly 1 12 reaches an intended position, the controller communicates a signal to the sensor assembly to cause the sensor assembly to capture a measurement at the intended position.
The sensor assembly communicates a signal representative of the measurement to the controller Figure 5 depicts a graphical representation of plotted measurements of the sensor assembly of a substrate measurement apparatus in accordance with an embodiment of the present principles on a warped substrate. As depicted in Figure 4, the compiled measurement results indicate a flat profile for the substrate under test.
In the embodiment of Figure 4, sensor assembly measurements were taken, as described above, at increments of 10mm across a substrate having a diameter of mm. The plotted sensor measurements result in a baseline profile having a height of pm across the entire measured surface of the substrate of Figure 4. In the embodiment of Figure 5, sensor measurements were again taken at increments of 10mm across a warped substrate having a diameter of mm.
As depicted in Figure 5, the plotted sensor measurements depict an obvious decline in the height of the warped substrate. In Figure 5, an initial sensor measurement indicated a height for the substrate of approximately pm and a final sensor measurement indicated a height for the substrate of approximately pm, with sensor measurements in between the first and last measurement points indicating a steady decline in the height of the substrate between those two points.
Such information can be used to compare the measurements of a measured substrate with tolerances for substrate surface flatness to determine, for example, if a substrate is acceptable for processing or not. If determined, based on the tolerances, that a substrate is not suitable for processing, the substrate can be sent to undergo corrective measures or can be eliminated from a processing routine. The method can proceed to For example and as described above, a receiver unit aligned to receive the signals from the transmitter captures the signal after the signal translates across the surface of the substrate.
For example and as described above, the signals captured by the receiver unit at each respective location, includes a portion of the light column that was not blocked by any rise in the surface of the substrate.
Such information is used, for example, by the controller to determine a surface profile of the substrate. That is, the encoder communicates positional information to the controller of a location of the sensor assembly with respect to the surface of the substrate and the receiver unit communicates signal information to the controller.
Having such information, the controller is able to determine a representation of the surface of the substrate. The method can then be exited. For example, in one embodiment a user is able to input, using an input device such as a keyboard or touch screen of the controller , step increments or positional information as to where on a substrate under test a user would like sensor measurements taken.
A user is also able to input information necessary to run a test as described above and have the controller automatically perform the test procedures. A user can also indicate that a test be run continuously and have the track assembly 1 12 run continuously as the sensor assembly takes continuous measurements. The signal results captured by the receiving unit are communicated to the controller and the positional information from the encoder is communicated to the controller for use by the controller in determining a surface profile for the substrate under test.
Such information can be used to determine if a surface of the substrate is warped and, if so, an amount of the warpage. As described above, such information can be plotted on a graph for example as measurement height versus location on the surface of the substrate at which the measurement was taken, and presented on a display as a surface profile for a substrate under test.
Such information can also be stored in a memory of the controller For example, in one embodiment, the track assembly 1 12, the encoder , the sensor support assembly 1 14 including the transmitter unit 1 16 and the receiver unit 1 18 can be installed into an existing process chamber.
As such, a substrate to be tested can be placed on a support pedestal of the process chamber and the sensor support assembly 1 14 including the transmitter unit 1 16 and receiver unit 1 18, the track assembly 1 12 and encoder can be implemented as described herein to determine a surface profile for a substrate in the existing process chamber to, for example, determine if the substrate is warped.
In other embodiments, a substrate measurement apparatus , or at least portions thereof, can be temporarily positioned, for example as a sub-assembly, in an existing process chamber to determine a surface profile for a substrate in the existing process chamber as described above.
For example, Figure 7 depicts a high level block diagram of the substrate measurement apparatus of Figure 2 including a second track assembly , a second encoder not shown mounted on the second track assembly , a second sensor support assembly and a second sensor assembly including a second transmitter unit and a second receiver unit In the embodiment of Figure 7, the second track assembly , second encoder not shown , second sensor support assembly and second sensor assembly including the second transmitter unit and the second receiver unit are implemented to project and capture a signal in a direction perpendicular to the projected and captured signal described with respect to the substrate measurement apparatus of Figure 2.
As such, in the embodiment of Figure 7, the substrate measurement apparatus is capable of taking measurements of a single point on the surface of the substrate, the single point being defined by where the signals from the first transmitter unit 1 16 and the second transmitter unit cross on the surface of the substrate.
In such embodiments, the first sensor support assembly 1 14 having the first sensor assembly mounted thereon and the second sensor support assembly having the second sensor assembly mounted thereon can be moved independently and at different times or in other embodiments can be moved in unison. Claims: 1. A method for determining a surface profile for a substrate, comprising:. The method of claim 1 , wherein the projected signal comprises a laser beam comprising a vertical laser column.
The method of claim 1 , comprising: plotting representations of the captured signals on a display to present a representation of the surface profile for the substrate. An apparatus for determining a surface profile for a substrate, comprising: a first sensor pair comprising:.
The apparatus of claim 9, comprising a second sensor support assembly to support and locate the second transmitter along the third side of the substrate and to support and locate the second receiver along the fourth side of the substrate, the second support assembly being mounted on the second track assembly and a second guide to guide an end of the second sensor support assembly.
The apparatus of claim 8, comprising a first sensor support assembly to support and locate the first transmitter along the first side of the substrate and to support and locate the first receiver along the second side of the substrate, the first support assembly being mounted on the first track assembly.
The apparatus of claim 1 1 , comprising a first guide to guide an end of the first sensor support assembly. The apparatus of claim 8, wherein the first sensor pair comprises a laser micrometer.
The system of claim 14, wherein the substrate measurement apparatus further comprises:.
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