Generalized digital (k0,k1)-homeomorphism

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Generalized digital (k0,k1)-homeomorphism

This invention relates generally to parallel mechanisms, and relates in particular to methods and apparatus for controlling mechanical devices comprising two platforms connected together, through a special geometry, by a plurality of legs acting in-parallel.

Recently, there has been an increasing interest in direct applications of parallel mechanisms to real-world industrial problems. In situations where the needs for accuracy and sturdiness dominate the requirement of a large workspace, parallel mechanisms present themselves as viable alternatives to their serial counterparts.

Parallel mechanisms generally comprise two platforms which are connected by a plurality of prismatic joints or legs acting in-parallel. The most common configuration comprises six legs, and the legs are linear actuators such as hydraulic cylinders.

One of the platforms is defined as the "movable platform," which has six degrees of freedom relative to the other platform, which is the "base.

When the locations of the connection points of the prismatic legs are known for both platforms, and when a means to change and sense the lengths of the six prismatic legs is provided, then closed-loop control of the position and orientation of the movable platform relative to the base platform is possible and depends on the solutions to two geometrical computations. First, when a desired position and orientation of the movable platform is known, then the corresponding desired lengths of the six legs are determined via a so-called "reverse displacement analysis.

On the other hand, when the actual leg lengths are known, the determination of the actual position and orientation of the movable platform is accomplished via a so-called "forward displacement analysis.

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Because of the complexities of such parallel devices, the present inventors believe that for the closed-loop control of the position and orientation of the movable platform, the prior art only successfully utilizes an iterative forward displacement analysis together with the simpler reverse displacement analysis.

An iterative methodology for accomplishing the forward displacement analysis has many drawbacks. First, the solution is not obtained in a prescribed fixed amount of time. Iterative solutions to the mathematics of devices of this type typically are conducted with multidimensional searches, which are extremely time consuming and have no constant search time. For those that study closed-loop control systems, it is well known that timing is critical.

Second, an iterative solution depends on good initial guesses of the position and orientation of the movable platform.

generalized digital (k0,k1)-homeomorphism

To combat this, it is customary to use the last known actual position and orientation as an initial guess to ascertain the "new" actual position and orientation.

However when using this technique, it is possible that the mechanism can "run away" from the iterative algorithm. Whenever the legs are able to move faster than the iterative algorithm can manage, the algorithm will have difficulty reporting the actual position and orientation of the movable platform. Third, an iterative solution has no way of determining regions of mechanism singularities, which are regions where the movable platform cannot be fully constrained no matter what the forces in the legs may be.

Singularities such as these cause static instabilities in parallel mechanisms. Multiple closures can exist in these regions.

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This will cause numerical problems in the iterative algorithm, because the algorithm can actually report the mechanism to be in a wrong closure. Stated in other words, there is there is no mathematical way of determining closures in an iterative algorithm. One prior art parallel mechanism is known as a "Stewart" platform.

Understanding Cryptography

This configuration was introduced in for use in an aircraft simulator. Since then, numerous parallel mechanisms containing prismatic joints have been called Stewart platforms, although D. Stewart originally suggested only two different arrangements. Stewart's two suggested arrangements were a platform see FIGS.Understanding Cryptography.

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Cloud Cryptography Cloud computing is the emerging trend in today's world. Cloud computing is not a separate technology, it is platform which provides platform as a service, Infrastructure as a service and Software as a service. The most important thing with cloud is t. Department of Computer Science. Cryptography Engineering Preface to Cryptography Engineering xxiii.

History xxiv. Example Syllabi xxiv. Additional Information xxvi. Preface to Practical Cryptography the 1 st Edition xxvii. Neural Cryptography Two neural networks which are trained on their mutual output bits show a Braid Group Cryptography.The generalized universal lifting property plays an important role in classical topology. In digital topology we also have its digital version [5, 6, 14].

More precisely, the paper [6] established the concept of a digital covering see also [11, 17]. It has substantially contributed to the calculation of digital fundamental groups of some digital spaces, the classification of digital spaces and so forth.

The paper [6] also established the unique lifting property of a digital covering which plays an important role in studying both digital covering and digital homotopy theory. Motivated by the unique lifting property, the paper develops a pseudocovering which is weaker than a digital covering and investigates its various properties.

Furthermore, the paper proves that a pseudocovering with some hypothesis has the unique pseudolifting property which is weaker than the unique lifting property in digital covering theory. Keywords: digital topology, digital image, weakly local k0,k1 -isomorphism, unique lifting property, pseudocovering, digital covering, pseudolifting property.

Citation export Email this article.Recent attempts to enric Furthermore, the recursivity of the notion of n-surface is essential to demonstrate n-dimensional properties. This is the notion of surface upon whi Recently, the notion of k- or k0, k1 -homotopy equivalence in DTC was firstly introduced in [8] see also [5, 11, 14, 26, 28] and has often used in classifying digital images from the viewpoint o Documents: Advanced Search Include Citations.

In this paper we present a data structure improving region segmentation of 2D images. This data structure provides an efficient access to the set of pixel of one region. It also provides topological informations like the frontier of a region, the neighbours of a region or the set of regions included Abstract - Cited by 39 7 self - Add to MetaCart In this paper we present a data structure improving region segmentation of 2D images.

It also provides topological informations like the frontier of a region, the neighbours of a region or the set of regions included in one region. Thanks to this data structure different segmentation algorithms can be combined to perform the segmentation of an image.

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Interactive refinement or merge of regions can also be performed efficiently. Keywords Segmentation, inter-pixel boundary, topological map.

It quickly appeared that this problem cannot be solved without an priori knowledge of the objects to be recognized. Segmentation algorithms can thus be categorized in two classes: domain-dependent algorithms which attempt to recognize specific objects in a scene -- for instance tumors in chest radi The relations wi The relations with other notions directly or indirectly connected with generalized closed sets are investigated. The notion of TGO-connectedness is introduced. Citation Context Many applications require the extraction of an object boundary from a discrete image.

In most cases, the result of such a process is expected to be, topologically, a surface, and this property might be required in subsequent operations. However, only through careful design can such a guarantee be Abstract - Cited by 9 2 self - Add to MetaCart Many applications require the extraction of an object boundary from a discrete image.

However, only through careful design can such a guarantee be provided. In the present article we will focus on partially ordered sets and the notion of n-surfaces introduced by Evako et al. Partially ordered sets are topological spaces that can represent the topology of a wide range of discrete spaces, including abstract simplicial complexes and regular grids.We show that it is exactly quantized for a time reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect.

This topological order parameter can be applied to both interacting and disordered systems, and used for determining their phase diagrams. PACS numbers: Recently, topological insulators TI have attracted great attention in condensed matter physics[1—3]. Historically, the concept of the time reversal T invariant TI has been developed along two independent routes[1].

It is now understood that this state is the fundamental T -invariant TI state, from which both the three and the two dimensional T -invariant TIs can be derived[6—8]. Using the simple procedure of dimensional reduction, the TFT for three and two dimensional T -invariant TIs has been constructed[6]. Independently, the topological band theory TBT was first developed starting from the pioneering work of Kane and Mele[9], who first proposed a Z2 topological invariant within the non-interacting band theory.

This non-interacting Z2 topological invariant has been generalized to the three dimensional TIs[10—12].

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The TFT is generally valid for systems with interactions and disorder; recently, it has been shown that the TFT reduces exactly to the the TBT in the non-interacting limit[13]. The TFT has been further developed recently[14— 17]. TIs are widely believed to be a new state of quantum matter. Since all states of matter in Nature, including band insulators, are necessarily interacting, it is important to formulate a general definition of TIs which is valid for general interactions and disorder.

This is especially important since an explicit counter-example in one dimension has been constructed where a non-interacting topological state becomes unstable against interactions[18]. After the theoretical prediction and experimental discoveries of the weakly interacting TIs[1—3], it would be most interesting to investigate topological Mott insulators where the interaction plays an essential role[19—26].

In the case where strong electronic correlations play a crucial role, it is essential to define a general topological order parameter which can determine the phase diagram of these systems.

The TFT approach defines the generally interacting TI in terms of a topological term in the effective electromagnetic action. In this work, we give an explicit formula of P3 which can be evaluated in a generally interacting system. Our explicit formula for the topological order parameter P3 satisfies the following general criteria: 1 It is well defined in the presence of interaction and disorder.

The TBT is based on the single particle band states, and can not be easily generalized to interacting systems. On the other hand, the TFT is valid for systems with general interactions and disroder, and the quantized magneto-electric polarization can be directly measured experimentally[6, 14, 27, 28].A compatibility problem exists when two-channel program material is played over loudspeaker layouts with more than two front loudspeakers.

Two-channel music recordings, when used either as cinema sound tracks or played on a typical home theater setup, are examples, as are older quadraphonic and related recordings played over a 5. The theory of generalized head-related stereophony of Cooper and Bauck applies to this problem, indicating an infinite number of solutions. A few solutions are examined in detail, resulting in several remedial network specifications. These solutions are incorporated into a simulation and a signal-based error function, essentially a plot of the sweet spot is plotted for each and compared to errors which arise from conventional methods.

Under several types of input signals, the new processor exhibits substantially better performance than conventional methods, yet it is simple and economical to implement. Click to purchase paper as a non-member or login as an AES member.

generalized digital (k0,k1)-homeomorphism

If your company or school subscribes to the E-Library then switch to the institutional version. Start a discussion about this paper! AES E-Library.The present invention relates to a method of measuring the thickness of a transparent thin film formed on a substrate and, more particularly, to a technique of measuring the film thickness optically with high accuracy. Conventionally, various methods have been proposed for optically measuring the thickness of a silicon oxide film formed on a silicon substrate, for example, in an inspection step of semiconductor manufacturing process.

The conventional methods are classified into three types according to the principles thereof, which will be referred to as "a polarization analysis method", "a reflected light energy measuring method" and "a reflectance measuring method". In the polarization analysis method, light is irradiated obliquely to an objective sample, and the thickness of a transparent thin film formed on a substrate in the sample is determined on the basis of change of the polarization state of the reflected light thereof.

The change of the polarization state has two meanings, one of which is the change of relative phase shifts between a P-wave component having electric field vector parallel to the plane of incidence and an S-wave component vertical thereto, and the other is the change of amplitude ratio of the both waves.

The polarization analysis method employes a device which is called an ellipsometer, and is an excellent technique capable of measuring a film thickness of even 10 nm or less accurately. However, since it is difficult in this method to measure the film thickness by specifying a minute area as a region to be measured on a sample, the reflected light energy measuring method is adopted in place thereof for such measurement of the film thickness.

In the reflected light energy measuring method, the film thickness is measured on the basis of the characteristic that the energy of the light reflected from the objective sample varies in accordance with the thickness of the transparent thin film.

The variation of the light energy is caused by the phenomenon that the light reflected from the surface of the transparent thin film and that reflected from the interface between the transparent thin film and the substrate interfere with each other. More particularly, this method is conducted as follows. After obtaining correlation data between the reflected light energy and the film thicknesses of the transparent thin films in reference samples having the same optical constants of the transparent thin film and the substrate as the objective sample, the reflected light energy of the objective sample is measured.

The correlation data is searched for a film thickness approximately corresponding to the reflected light energy measured.

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The value of the film thickness thus found is taken as the film thickness of the transparent thin film in the objective sample. The correlation data is searched for a film thickness dx approxiamtely corresponding to the measured reflectance Rs.

The value of the film thickness dx thus found is taken as the film thickness dx of the transparent thin film in the objective sample.

As described above, in the reflected light energy measuring method, since the film thickness is measured on the basis of the correlation data between the reflected light energy and the film thicknesses, it is essential to obtain the correlation data in advance.

However, it is not easy to obtain it, as described below. A measured value of the reflected light energy includes influences of the characteristics peculiar to a device used for the measurement, for example, a photoelectric transfer efficiency of photoelectric converter for detecting light source energy and reflected light energy. Hence, the measured value must obtained experientially as follows:.

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First of all, a number of reference samples having respectively known different film thicknesses of the transparent thin films and the same optical constants of the transparent thin films and substrates as the objective sample are prepared. The respective reflected light energy of the reference samples is measured with the same device as that of the objective sample.

The measured results are used as correlation data between the reflected light energy and the film thicknesses. Since the correlation data cannot attain sufficient accuracy in measuring the film thickness without collecting data to some extent in detail, a large number of reference samples must be prepared.

Accordingly, a large amount of work is necessary for measuring the reflected light energy of the reference samples. Besides, it is not easy but requires a large amount of work to prepare a large number of reference samples. As aforementioned, the conventional reflected light energy measuring method has a problem in that a large amount of work is necessary for preparation process because the correlation data between the reflected light energy and the film thicknesses must be obtained experientially in advance with the device which is actually used for measuring the objective sample.

Contrary to the energy measuring method, the reflectance measuring method does not have the aforementioned problem, because it is based on the correlation data between the reflectance Rs and the film thickness dx. The value of the reflectance Rs does not include influences of the characteristics peculiar to a device used for measurement.

Correlation data between the reflectance Rs and the film thickness dx published in various references are usable.

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They do not need experiential determination as seen in the case of the correlation data between the reflected light energy Es and the film thickness dx which is employed in the reflected light energy measuring method.

However, it is not easy to measure the reflectance Rs of the objective sample. The present invention is directed to a method of measuring a thickness dx of a transparent film provided in an objective sample, wherein the film is formed on a substrate and the objective sample has a known correlation between the thickness dx and a reflectance Rs for light. Preferably, the method further comprises the step of: f arranging the correlation in a form of a table and storing the table in a memory means.


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