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Topology

While geometry is primarily concerned with the mathematical properties of spatial objects, topology is concerned with the mathematical properties of those objects under continuous deformations. Please post all questions about topological subjects like homeomorphisms, manifolds, convergence, and connectedness, as well as their broad applications in computing, physics, and graph theory, into this category.

1,087 Questions

Why is it difficult to trace fault in ring topology?

In a ring topology, data travels in a circular path, making it challenging to isolate a fault because the entire network is interconnected. If a fault occurs, it can disrupt the entire network, and finding the exact location of the fault can be tricky without the right tools or monitoring systems in place.

How do you calculate diameter bearing from reaction force?

To calculate the diameter of a bearing required to withstand a given reaction force, you need to consider factors such as the material properties, bearing design, and load distribution. It involves calculating the stress on the bearing and ensuring it stays within the allowable stress limit for the material used. It is recommended to consult engineering handbooks or software for specific calculations tailored to the bearing and loading conditions.

What is mesh powder?

Mesh powder refers to finely ground particles that have been sieved and classified according to their size using a mesh screen. This classification allows for a more uniform and consistent particle size distribution, making mesh powder suitable for various applications such as in manufacturing, pharmaceuticals, and construction materials.

Is it true that in an active topology each node participates in moving data through the network?

Yes, in an active topology, each node participates in moving data through the network by actively sending, receiving, and processing data packets. This type of topology allows for a more dynamic and efficient flow of information compared to passive topologies where nodes only passively relay data.

What happens to packet when corrupted on bus topology?

When a packet is corrupted on a bus topology network, the receiving device will detect the corruption using error-checking mechanisms such as CRC (Cyclic Redundancy Check). The corrupted packet will be discarded by the receiving device, and the sender will need to retransmit the packet. This process adds latency to the communication but ensures data integrity.

What is difference between a logical network and physical?

A physical network is different from a logical network. Logical networks are defined at the Network layer by the arrangement of the hierarchical addressing scheme. Physical networks represent the interconnection of devices on a common media. Sometimes, a physical network is also referred to as a network segment

Who invented algebra and topology?

The word algebra is a Latin variant of the Arabic word al-jabr. This came from the title of a book, "Hidab al-jabr wal-muqubala", written in Baghdad about 825 A.D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi. The words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to designate two basic operations in solving equations. Jabrwas to transpose subtracted terms to the other side of the equation. Muqubalah was to cancel like terms on opposite sides of the equation. In fact, the title has been translated to mean "science of restoration (or reunion) and opposition" or "science of transposition and cancellation" and "The Book of Completion and Cancellation" or "The Book of Restoration and Balancing." Jabr is used in the step where x - 2 = 12 becomes x = 14. The left-side of the first equation, where x is lessened by 2, is "restored" or "completed" back to x in the second equation. Muqabalah takes us from x + y = y + 7 to x = 7 by "cancelling" or "balancing" the two sides of the equation. Eventually the muqabalah was left behind, and this type of math became known as algebra in many languages.

What does a negative mesh current imply?

A negative mesh current simply indicates that the actual current direction is opposite to the assumed direction in the circuit analysis. This does not alter the magnitude of the current, only its direction. Negative mesh currents are common in network analysis and are used to correctly represent the current flow in a circuit.

What is the theory of continuity?

first discovered by Atchley in 1989. This was discovered following the contraversy that came with the dis-engagement theory.

It is the theory that as we grow older we maintain who we were; personality's, values, beliefs, etc. The theory states that we can still stay social an build social relationships - only it will be with a smaller network of people (e.g. neighbours, family, close friends, etc.) but we may leave behind other friends such as work friends because of retirement.

What is lateral continuity?

The law of original lateral continuity states sedimentary material extends laterally in all directions. This extension continues until it is terminated against the edges of their original basin of deposition.

Which of the following topologies is susceptible to bounce?

Any technology with the possible exception to token ring may be susceptible to signal bounce when one of the cable segment is disconnected or there is a short in the wire segment. An unterminated end of a wire segment will cause signal bounce because there is no termination at one of the ends to absorb the signal, preventing it from bouncing back into the cable.

What is an example of a simple borel measurable function?

One example of a simple Borel measurable function is the indicator function of a Borel set. This function takes the value 1 on the set and 0 outside the set, making it easy to determine its measurability with respect to the Borel sigma algebra.

What is the physics theory of the fifth dimension?

The physics theory of the fifth dimension, as proposed in some string theory models, suggests that there may be extra spatial dimensions beyond the familiar three dimensions of space and one dimension of time. These extra dimensions are compactified or curled up at a very small scale, making them difficult to detect with current technology. The existence of these extra dimensions could help explain the fundamental forces of nature and unify the laws of physics.

What are the applications of DNA topology?

DNA topology is the focus of an interdiscipline between molecular biology and mathematics and as a term refers to DNA supercoiling, knotting and catenation. More simply put, DNA topology studies the shape and path of the DNA helix in three dimensional space. The topology of DNA topoisomers is important to replication, transcription and recombination, including the recombination events important to the life cycles of many viruses. Topoisomerases are enzymes that change the topology of DNA. DNA Topology starts with a basic account of DNA structure before going on to cover DNA supercoiling, the definitions and physical meanings of linking number, twist, and writhe, and the free energy associated with supercoiling. It then considers the rather more complex description of DNA lying on a curved surface and its application to the nucleosome, followed by the phenomena of DNA knotting and catenation

What are the types of topology?

whatarethetypeoftopology

Network topology is a layout which shows that how a connectivity communicates and the flow takes place in a network. types of topology are 1. BUS topology,2. Star topology,3. ring topology.

What is the driest place or thing?

Death Valley California is the hottest, sunniest and driest place in the us. Summer temperatures reach 130 degrees and it is drier than winter. It once went with no precipitation for 2 and a half years.

How do isotonic and isometric contraction differ?

Isotonic contractions involve a change in muscle length and joint movement, while isometric contractions do not result in joint movement or change in muscle length. Isotonic contractions are further classified into concentric (muscle shortens) and eccentric (muscle lengthens) contractions. Isometric contractions involve the muscle producing tension without changing its length.

Explain how anemometers are useful today?

Anemometers are useful today for measuring wind speed and direction, which is valuable for a range of applications including weather forecasting, aviation, and assessing environmental conditions for activities like wind energy generation. They provide real-time data that helps in making informed decisions related to safety, operations, and planning.

Difference between spectrophotometry and differential spectrophotometry?

Differential spectrophotometry is a spectrophotometric analytical technique in which a solution of the sample's major component is placed in the reference cell and the recorded spectrum represents the difference between the sample cell and the reference cell...basically it uses major component of system as reference and NOT solvent ..for example if a enzyme ligand system is to be assayed ..enzyme + solvent is reference and enzyme + ligand + solvent is test sample..its for quantitative detection.

What direction is 206 degree azimuth?

Zero/360 degrees is North; 90 is East; 180 is South; 270 is West.

{each is 90 degrees from the next}

225 is Southwest. 45 degrees or half way between south and west. 210 is South-southwest Is that close enough for you? ;-)

What is the equation of continuity?

The Equation of Continuity is the four dimensional derivative of a four dimensional variable set to zero. This is also called the limit equation and the Boundary equation, and the Homeostasis Equation. The Continuity Equation is also called the Invariant Equation or Condition. The most famous equation that is in fact a continuity Equation is Maxwell's Electromagnetic equations.

(d/dR + Del)(Br + Bv) = (dBr/dR -Del.Bv) + (dBv/dR + DelxBv + Del Br) = 0

This gives two equations the real Continuity Equation:

0=(dBr/dR - Del.Bv)

and the vector Continuity Equation:

0=(dBv/dR + Del Br)

This Equation will be more familiar when R=ct and dR=cdt and cB = E then

0=(dBr/dt - Del.Ev) and

0=(dBv/dt + Del Er)

The Continuity Equation says the sum of the derivatives is zero. The four dimensional variable has two parts a real part Br and a vector part Bv. The Continuity Equation is the sum of the real derivatives is zero and the sum of the vector derivatives is zero.

The term DelxBv is zero at Continuity because this term is perpendicular to both the other two terms and makes it impossible geometrically for the vectors to sum to zero unless it is zero.

Only if the DelxBv=0 can the vectors sum to zero. This situation occurs when the other two terms are parallel or anti-parallel. If anti-parallel then dBv/Dr is equal and opposite to Del Br and the vectors sum to zero.

This is Newton's Equal and Opposite statement in his 3rd Law and is a geometrical necessity for the vectors to sum to zero..

Many Equations of Physics have misrepresented the Continuity Equation and others have not recognized the continuity Equation as in Maxwell's Equations.

The Continuity Equation is probably the most important equation in science!

The Four dimensional space of science is a quaternion non-commutative (non-parallel) space defined by William Rowan Hamilton in 1843, (i,j,k and 1), with rules i^2=j^2=k^2=-1.

20BAR what is this measurement aquatic?

You question is not clear, but I think you mean to ask how deep in water is a pressure of 20 Bars. A bar is one atmosphere pressure which is about 10 meters of water depth. Since water is incompressible, the relationship is linear. 20 Bars is 200 meters depth.

What is a simple solar collector and how does it function?

A simple solar collector is typically a device that absorbs sunlight and converts it into heat, often used for heating water or air. It usually consists of a dark, absorptive surface enclosed in a transparent cover to trap solar radiation. When sunlight strikes the collector, the absorptive surface heats up and transfers that heat to a fluid circulating through the collector, which can then be used for various applications.

What are the properties of an octagonal prism?

An octagonal prism has 10 faces (8 lateral faces and 2 bases), 16 vertices, and 24 edges. It has 8 congruent sides that are octagons and 8 rectangular lateral faces. The cross-section of an octagonal prism is an octagon.