## Mobus Es geht um Ihr Geld!

mobus - für den Nahverkehr im Landkreis Märkisch-Oderland. Fahrpläne & Tarife · Kundenbüros · Sonderfahrten · Buswerbung. Die mobus Märkisch-Oderland Bus GmbH ist ein ÖPNV-Dienstleister aus Strausberg. Seit dem 1. Januar ist sie im südlichen Bereich des Landkreises Märkisch-Oderland für den Öffentlichen Personennahverkehr zuständig. Home; Verkehrsverbund; Verkehrsunternehmen; MOBUS | mobus Märkisch-Oderland Bus GmbH. MOBUS | mobus Märkisch-Oderland Bus GmbH. Teilen. Die mobus Märkisch-Oderland Bus GmbH ist ein ÖPNV-Dienstleister aus Strausberg. Seit dem 1. Januar ist sie im südlichen Bereich des Landkreises. Erhalten Sie Kontakte, Produktinformationen, Jobanzeigen und Neuigkeiten zu mobus Märkisch-Oderland Bus GmbH. Aktualisiert am. Die Mobus AG das Druck und Medienzentrum im Fricktal Wir produzieren als Familienunternehmen in der Schweiz. möbus-gruppe in Berlin | Berliner Autohaus für Audi, Volkswagen, Škoda, Volkswagen Nutzfahrzeuge. Aktuelle Modelle und Infos aus dem Autohaus möbus in.

Die Mobus AG das Druck und Medienzentrum im Fricktal Wir produzieren als Familienunternehmen in der Schweiz. Mobus LT, UAB Firmenkatalog von Litauen. Firmensuche. Betriebe, Litauen, Firmen, Gesellschaften, GMBH. Möbus ist Ihr Ansprechpartner für Zeichnungsaufbewahrungssysteme, Zeichnungsordner, Einstellablagen, Flachablagen oder Zubehör, wie Aufhängestreifen. In graph Dangerous Mindsthe Möbius ladder is First Daughter Stream cubic graph closely related to the Möbius strip. Microwave Journal. Practical Modern Scada**Mobus**Dnp3, For example, in order to read Hancock Kinox registers starting at numberthe data Hds.To Film will contain function code 3 as seen above and address 0. Möbius strips are common in Abriss Ski manufacture of fabric computer printer and typewriter ribbonsas they let the ribbon be twice as wide as the print head while using both halves evenly. This response is returned to prevent a timeout error from occurring in the master. In the Paul Weller of negative and zero curvature, the Möbius band can be constructed as a geodesically complete surface, which means that all geodesics "straight lines" on the surface may be extended indefinitely in either direction. The Möbius strip principle has been used

**Mobus**a method of creating the illusion of magic.

### Mobus - Mobiler Dienst Sehen

Wir empfehlen auch. Belarussischen Rubel. Firma Rechenschaft.But there is no metric on the space of lines in the plane that is invariant under the action of this group of homeomorphisms. In this sense, the space of lines in the plane has no natural metric on it.

This means that the Möbius band possesses a natural 4-dimensional Lie group of self-homeomorphisms, given by GL 2, R , but this high degree of symmetry cannot be exhibited as the group of isometries of any metric.

The edge, or boundary , of a Möbius strip is homeomorphic topologically equivalent to a circle. Under the usual embeddings of the strip in Euclidean space, as above, the boundary is not a true circle.

However, it is possible to embed a Möbius strip in three dimensions so that the boundary is a perfect circle lying in some plane.

For example, see Figures , , and of "Geometry and the imagination". A much more geometric embedding begins with a minimal Klein bottle immersed in the 3-sphere, as discovered by Blaine Lawson.

We then take half of this Klein bottle to get a Möbius band embedded in the 3-sphere the unit sphere in 4-space. The result is sometimes called the "Sudanese Möbius Band", [14] where "sudanese" refers not to the country Sudan but to the names of two topologists, Sue Goodman and Daniel Asimov.

Applying stereographic projection to the Sudanese band places it in three-dimensional space, as can be seen below — a version due to George Francis can be found here.

From Lawson's minimal Klein bottle we derive an embedding of the band into the 3-sphere S 3 , regarded as a subset of C 2 , which is geometrically the same as R 4.

To obtain an embedding of the Möbius strip in R 3 one maps S 3 to R 3 via a stereographic projection. The projection point can be any point on S 3 that does not lie on the embedded Möbius strip this rules out all the usual projection points.

Stereographic projections map circles to circles and preserves the circular boundary of the strip. The result is a smooth embedding of the Möbius strip into R 3 with a circular edge and no self-intersections.

The Sudanese Möbius band in the three-sphere S 3 is geometrically a fibre bundle over a great circle, whose fibres are great semicircles. The most symmetrical image of a stereographic projection of this band into R 3 is obtained by using a projection point that lies on that great circle that runs through the midpoint of each of the semicircles.

Each choice of such a projection point results in an image that is congruent to any other. But because such a projection point lies on the Möbius band itself, two aspects of the image are significantly different from the case illustrated above where the point is not on the band: 1 the image in R 3 is not the full Möbius band, but rather the band with one point removed from its centerline ; and 2 the image is unbounded — and as it gets increasingly far from the origin of R 3 , it increasingly approximates a plane.

Yet this version of the stereographic image has a group of 4 symmetries in R 3 it is isomorphic to the Klein 4-group , as compared with the bounded version illustrated above having its group of symmetries the unique group of order 2.

If all symmetries and not just orientation-preserving isometries of R 3 are allowed, the numbers of symmetries in each case doubles. But the most geometrically symmetrical version of all is the original Sudanese Möbius band in the three-sphere S 3 , where its full group of symmetries is isomorphic to the Lie group O 2.

Having an infinite cardinality that of the continuum , this is far larger than the symmetry group of any possible embedding of the Möbius band in R 3.

Using projective geometry , an open Möbius band can be described as the set of solutions to a polynomial equation. Adding a polynomial inequality results in a closed Möbius band.

These relate Möbius bands to the geometry of line bundles and the operation of blowing up in algebraic geometry.

This is the case for the Möbius band. Deleting this line gives the set. There is a realization of the closed Möbius band as a similar set, but with an additional inequality to create a boundary:.

The geometry of N is very similar to that of M , so we will focus on M in what follows. The geometry of M can be described in terms of lines through the origin.

Consequently the set M may be described as the disjoint union of the set of lines through the origin. This is the same as the union of the lines through the origin, except that it contains one copy of the origin for each line.

The lines themselves describe the ruling of the Möbius band. Except for P and Q , every point in the path lies on a different line through the origin.

However, while P and Q lie in the same line of the ruling, they are on opposite sides of the origin. This change in sign is the algebraic manifestation of the half-twist.

A closely related 'strange' geometrical object is the Klein bottle. A Klein bottle could in theory be produced by gluing two Möbius strips together along their edges; however this cannot be done in ordinary three-dimensional Euclidean space without creating self-intersections.

Another closely related manifold is the real projective plane. If a circular disk is cut out of the real projective plane, what is left is a Möbius strip.

To visualize this, it is helpful to deform the Möbius strip so that its boundary is an ordinary circle see above.

The real projective plane, like the Klein bottle, cannot be embedded in three-dimensions without self-intersections. In graph theory , the Möbius ladder is a cubic graph closely related to the Möbius strip.

There have been several technical applications for the Möbius strip. Giant Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes to double the playing time.

Möbius strips are common in the manufacture of fabric computer printer and typewriter ribbons , as they let the ribbon be twice as wide as the print head while using both halves evenly.

A Möbius resistor is an electronic circuit element that cancels its own inductive reactance. Nikola Tesla patented similar technology in [20] "Coil for Electro Magnets" was intended for use with his system of global transmission of electricity without wires.

The Möbius strip is the configuration space of two unordered points on a circle. Consequently, in music theory , the space of all two-note chords, known as dyads , takes the shape of a Möbius strip; this and generalizations to more points is a significant application of orbifolds to music theory.

The Möbius strip principle has been used as a method of creating the illusion of magic. The trick, known as the Afghan bands, was very popular in the first half of the twentieth century.

Many versions of this trick exist and have been performed by famous illusionists such as Harry Blackstone Sr. According to its designer Gary Anderson , "the figure was designed as a Mobius strip to symbolize continuity within a finite entity".

From Wikipedia, the free encyclopedia. Two-dimensional surface with only one side and only one edge. Longman Pronunciation Dictionary 3rd ed.

Retrieved on Pickover March Thunder's Mouth Press. Lynch on Lynch. London, Boston. American Scientist. Bibcode : AmSci.. The Mathematical Intelligencer.

Bibcode : arXivC. Nature Materials. Experiments in Topology. New York: Thomas Y. Crowell Company. Geometry and the Imagination 2nd ed.

Wilmington, Delaware: Publish or Perish. Bibcode : Sci Rev Mex Fis. Bibcode : cond. Microwave Journal. November Angewandte Chemie International Edition.

Physica E. Bibcode : PhyE This section gives details of data formats of most used function codes. For example, if eleven coils are requested, two bytes of values are needed.

Suppose states of those successive coils are on, off, on, off, off, on, on, on, off, on, on , then the response will be 02 E5 06 in hexadecimal.

Because the byte count returned in the reply message is only 8 bits wide and the protocol overhead is 5 bytes, a maximum of x 8 discrete inputs or coils can be read at once.

Value of each coil is binary 0 for off, 1 for on. First requested coil is stored as least significant bit of first byte in request.

If number of coils is not a multiple of 8, most significant bit s of last byte should be stuffed with zeros. See example for function codes 1 and 2.

Normal response :. Because the number of bytes for register values is 8-bit wide and maximum modbus message size is bytes, only registers for Modbus RTU and registers for Modbus TCP can be read at once.

For a normal response, slave repeats the function code. Some conventions govern how Modbus entities coils, discrete inputs, input registers, holding registers are referenced.

In the traditional standard [ citation needed ] , entity numbers start with a single digit representing the entity type, followed by four digits representing the entity location:.

For data communications, the entity location 1 to 9, is translated into a 0-based entity address 0 to 9, by subtracting 1. For example, in order to read holding registers starting at number , the data frame will contain function code 3 as seen above and address 0.

For holding registers starting at number , address will be This limits the number of addresses to 9, for each entity. A de facto referencing extends this to the maximum of 65, When using the extended referencing, all number references must have exactly 6 digits.

This avoids confusion between coils and other entities. For example, to know the difference between holding register and coil , if coil is the target, it must appear as However the name JBUS has survived to some extent.

JBUS supports function codes 1, 2, 3, 4, 5, 6, 15, and 16 and thus all the entities described above. However numbering is different with JBUS:.

Almost all implementations have variations from the official standard. Different varieties might not communicate correctly between equipment of different suppliers.

Some of the most common variations are:. Modbus Organization, Inc. Despite the name, Modbus Plus [15] is not a variant of Modbus. It is a different protocol , involving token passing.

It is a proprietary specification of Schneider Electric, though it is unpublished rather than patented. It is normally implemented using a custom chipset available only to partners of Schneider.

From Wikipedia, the free encyclopedia. Serial communications protocol mainly developed for programmable logic controllers. Institution of Engineering and Technology.

Retrieved 2 August Retrieved 1 November Retrieved 8 November Hanover, New Hampshire: Springer. Retrieved Schneider Electric.

Simply Modbus. Modbus Organization. Practical Modern Scada Protocols: Dnp3, Control Solutions, Inc. Automation protocols. ANSI C Technical and de facto standards for wired computer buses.

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The Möbius strip is the simplest non-orientable surface. It can be realized as a ruled surface. Its discovery is attributed independently to the German mathematicians Johann Benedict Listing and August Ferdinand Möbius in , [2] [3] [4] [5] though similar structures can be seen in Roman mosaics c.

An example of a Möbius strip can be created by taking a paper strip, giving one end a half-twist, and then joining the ends to form a loop; its boundary is a simple closed curve which can be traced by single unknotted string.

Any topological space homeomorphic to this example is also called a Möbius strip, allowing for a very wide variety of geometric realizations as surfaces with a definite size and shape.

For example, any rectangle can be glued left-edge to right-edge with a reversal of orientation. Some, but not all, of these can be smoothly modeled as surfaces in Euclidean space.

A closely related, but not homeomorphic, surface is the complete open Möbius band , a boundaryless surface in which the width of the strip is extended infinitely to become a Euclidean line.

A half-twist clockwise gives an embedding of the Möbius strip which cannot be moved or stretched to give the half-twist counterclockwise; thus, a Möbius strip embedded in Euclidean space is a chiral object with right- or left-handedness.

The Möbius strip can also be embedded by twisting the strip any odd number of times, or by knotting and twisting the strip before joining its ends.

Finding algebraic equations cutting out a Möbius strip is straightforward, but these equations do not describe the same geometric shape as the twisted paper model above.

Such paper models are developable surfaces having zero Gaussian curvature , and can be described by differential-algebraic equations. The Euler characteristic of the Möbius strip is zero.

The Möbius strip has several curious properties. A line drawn along the edge travels in a full circle to a point opposite the starting point.

If continued, the line returns to the starting point, and is double the length of the original strip: this single continuous curve traverses the entire boundary.

Cutting a Möbius strip along the center line with a pair of scissors yields one long strip with two full twists in it, rather than two separate strips; the result is not a Möbius strip, but homeomorphic to a cylinder.

This happens because the original strip only has one edge, twice as long as the original strip. Cutting creates a second independent edge of the same length, half on each side of the scissors.

Cutting this new, longer, strip down the middle creates two strips wound around each other, each with two full twists.

If the strip is cut along about a third in from the edge, it creates two strips: the center third is a thinner Möbius strip, the same length as the original strip.

The other is a thin strip with two full twists, a neighborhood of the edge of the original strip, with twice the length of the original strip.

Other analogous strips can be obtained by similarly joining strips with two or more half-twists in them instead of one. For example, a strip with three half-twists, when divided lengthwise, becomes a twisted strip tied in a trefoil knot.

If this knot is unravelled, the strip has eight half-twists. One way to represent the Möbius strip embedded in three-dimensional Euclidean space is by the parametrization:.

The parameter u runs around the strip while v moves from one edge to the other. For a smaller aspect ratio, it is not known whether a smooth embedding is possible.

If the Möbius strip in three-space is only once continuously differentiable class C 1 , however, then the theorem of Nash-Kuiper shows that no lower bound exists.

A method of making a Möbius strip from a rectangular strip too wide to simply twist and join e. This folded strip, three times as long as it is wide, would be long enough to then join at the ends.

This method works in principle, but becomes impractical after sufficiently many folds, if paper is used. Using normal paper, this construction can be folded flat , with all the layers of the paper in a single plane, but mathematically, whether this is possible without stretching the surface of the rectangle is not clear.

A less used presentation of the Möbius strip is as the topological quotient of a torus. The diagonal of the square the points x , x where both coordinates agree becomes the boundary of the Möbius strip, and carries an orbifold structure, which geometrically corresponds to "reflection" — geodesics straight lines in the Möbius strip reflect off the edge back into the strip.

The Möbius strip is a two-dimensional compact manifold i. It is a standard example of a surface that is not orientable.

In fact, the Möbius strip is the epitome of the topological phenomenon of nonorientability. This is because two-dimensional shapes surfaces are the lowest-dimensional shapes for which nonorientability is possible and the Möbius strip is the only surface that is topologically a subspace of every nonorientable surface.

As a result, any surface is nonorientable if and only if it contains a Möbius band as a subspace. The Möbius strip is also a standard example used to illustrate the mathematical concept of a fiber bundle.

Looking only at the edge of the Möbius strip gives a nontrivial two point or Z 2 bundle over S 1. A simple construction of the Möbius strip that can be used to portray it in computer graphics or modeling packages is:.

The open Möbius band is formed by deleting the boundary of the standard Möbius band. It may be constructed as a surface of constant positive, negative, or zero Gaussian curvature.

In the cases of negative and zero curvature, the Möbius band can be constructed as a geodesically complete surface, which means that all geodesics "straight lines" on the surface may be extended indefinitely in either direction.

The group of isometries of this Möbius band is 1-dimensional and is isomorphic to the special orthogonal group SO 2.

The resulting metric makes the open Möbius band into a geodesically complete flat surface i. This is the only metric on the Möbius band, up to uniform scaling, that is both flat and complete.

The group of isometries of this Möbius band is 1-dimensional and is isomorphic to the orthogonal group SO 2. Constant positive curvature: A Möbius band of constant positive curvature cannot be complete, since it is known that the only complete surfaces of constant positive curvature are the sphere and the projective plane.

The open Möbius band is homeomorphic to the once-punctured projective plane, that is, P 2 with any one point removed.

This may be thought of as the closest that a Möbius band of constant positive curvature can get to being a complete surface: just one point away.

The group of isometries of this Möbius band is also 1-dimensional and isomorphic to the orthogonal group O 2. The space of unoriented lines in the plane is diffeomorphic to the open Möbius band.

Hence the same group forms a group of self-homeomorphisms of the Möbius band described in the previous paragraph. But there is no metric on the space of lines in the plane that is invariant under the action of this group of homeomorphisms.

In this sense, the space of lines in the plane has no natural metric on it. This means that the Möbius band possesses a natural 4-dimensional Lie group of self-homeomorphisms, given by GL 2, R , but this high degree of symmetry cannot be exhibited as the group of isometries of any metric.

The edge, or boundary , of a Möbius strip is homeomorphic topologically equivalent to a circle. Under the usual embeddings of the strip in Euclidean space, as above, the boundary is not a true circle.

However, it is possible to embed a Möbius strip in three dimensions so that the boundary is a perfect circle lying in some plane. For example, see Figures , , and of "Geometry and the imagination".

A much more geometric embedding begins with a minimal Klein bottle immersed in the 3-sphere, as discovered by Blaine Lawson. We then take half of this Klein bottle to get a Möbius band embedded in the 3-sphere the unit sphere in 4-space.

The result is sometimes called the "Sudanese Möbius Band", [14] where "sudanese" refers not to the country Sudan but to the names of two topologists, Sue Goodman and Daniel Asimov.

Applying stereographic projection to the Sudanese band places it in three-dimensional space, as can be seen below — a version due to George Francis can be found here.

From Lawson's minimal Klein bottle we derive an embedding of the band into the 3-sphere S 3 , regarded as a subset of C 2 , which is geometrically the same as R 4.

To obtain an embedding of the Möbius strip in R 3 one maps S 3 to R 3 via a stereographic projection.

The projection point can be any point on S 3 that does not lie on the embedded Möbius strip this rules out all the usual projection points.

Stereographic projections map circles to circles and preserves the circular boundary of the strip. The result is a smooth embedding of the Möbius strip into R 3 with a circular edge and no self-intersections.

The Sudanese Möbius band in the three-sphere S 3 is geometrically a fibre bundle over a great circle, whose fibres are great semicircles.

The most symmetrical image of a stereographic projection of this band into R 3 is obtained by using a projection point that lies on that great circle that runs through the midpoint of each of the semicircles.

Each choice of such a projection point results in an image that is congruent to any other. But because such a projection point lies on the Möbius band itself, two aspects of the image are significantly different from the case illustrated above where the point is not on the band: 1 the image in R 3 is not the full Möbius band, but rather the band with one point removed from its centerline ; and 2 the image is unbounded — and as it gets increasingly far from the origin of R 3 , it increasingly approximates a plane.

Yet this version of the stereographic image has a group of 4 symmetries in R 3 it is isomorphic to the Klein 4-group , as compared with the bounded version illustrated above having its group of symmetries the unique group of order 2.

If all symmetries and not just orientation-preserving isometries of R 3 are allowed, the numbers of symmetries in each case doubles.

But the most geometrically symmetrical version of all is the original Sudanese Möbius band in the three-sphere S 3 , where its full group of symmetries is isomorphic to the Lie group O 2.

Having an infinite cardinality that of the continuum , this is far larger than the symmetry group of any possible embedding of the Möbius band in R 3.

Using projective geometry , an open Möbius band can be described as the set of solutions to a polynomial equation. Adding a polynomial inequality results in a closed Möbius band.

Normal response :. Because the number of bytes for register values is 8-bit wide and maximum modbus message size is bytes, only registers for Modbus RTU and registers for Modbus TCP can be read at once.

For a normal response, slave repeats the function code. Some conventions govern how Modbus entities coils, discrete inputs, input registers, holding registers are referenced.

In the traditional standard [ citation needed ] , entity numbers start with a single digit representing the entity type, followed by four digits representing the entity location:.

For data communications, the entity location 1 to 9, is translated into a 0-based entity address 0 to 9, by subtracting 1. For example, in order to read holding registers starting at number , the data frame will contain function code 3 as seen above and address 0.

For holding registers starting at number , address will be This limits the number of addresses to 9, for each entity. A de facto referencing extends this to the maximum of 65, When using the extended referencing, all number references must have exactly 6 digits.

This avoids confusion between coils and other entities. For example, to know the difference between holding register and coil , if coil is the target, it must appear as However the name JBUS has survived to some extent.

JBUS supports function codes 1, 2, 3, 4, 5, 6, 15, and 16 and thus all the entities described above. However numbering is different with JBUS:.

Almost all implementations have variations from the official standard. Different varieties might not communicate correctly between equipment of different suppliers.

Some of the most common variations are:. Modbus Organization, Inc. Despite the name, Modbus Plus [15] is not a variant of Modbus. It is a different protocol , involving token passing.

It is a proprietary specification of Schneider Electric, though it is unpublished rather than patented. It is normally implemented using a custom chipset available only to partners of Schneider.

From Wikipedia, the free encyclopedia. Serial communications protocol mainly developed for programmable logic controllers. Institution of Engineering and Technology.

Retrieved 2 August Retrieved 1 November Retrieved 8 November Hanover, New Hampshire: Springer. Retrieved Schneider Electric.

Simply Modbus. Modbus Organization. Practical Modern Scada Protocols: Dnp3, Control Solutions, Inc. Automation protocols. ANSI C Technical and de facto standards for wired computer buses.

PC Card ExpressCard. Interfaces are listed by their speed in the roughly ascending order, so the interface at the end of each section should be the fastest.

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Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Cyclic redundancy check.

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