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Discontinuities in mathematics refer to points on a function where there is a break in the graph. They can occur when the function is not defined at a particular point or when the function approaches different values from the left and right sides of the point. Common types of discontinuities include jump discontinuities, infinite discontinuities, and removable discontinuities.
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What is fault earth science?
Faults in earth science are fractures or discontinuities in the Earth's crust where there has been movement. This movement can be vertical, horizontal, or diagonal, and is caused by stress within the Earth's lithosphere. Faults are classified by the direction of movement as either normal (extensional), reverse (compressional), or strike-slip (lateral).
What are the two layers of discontinuity that are part of the interior structure of earth?
The two layers of discontinuity in Earth's interior are the Mohorovičić discontinuity (Moho) that separates the Earth's crust from the underlying mantle, and the Gutenberg discontinuity that marks the boundary between the mantle and the outer core. These discontinuities are characterized by changes in seismic wave velocity and composition.
A common cause of gap in rock layers is what?
A common cause of a gap in rock layers is erosion. This can occur due to natural processes such as wind, water, or glaciers removing layers of rock over time. As a result, gaps can form in the sequence of rock layers, creating discontinuities in the geological record.
What is a crack in crustal rock called?
Cracks in rocks of the crust are known broadly as discontinuities. If there is relative movement of the rocks on the two sides of the crack, then it is known as a fault. If there is not then it is known as a joint.
How can ground water cause caves and sinkholes?
Groundwater can dissolve rock material such as limestone over long periods of time, creating cavities underground. These cavities can eventually collapse, forming sinkholes. The process is known as karst topography and is common in areas with soluble rock layers.
Where are stringer discontinuities found?
Does sheet metal have stringer discontinuties
Discontinuities of first and second kind?
A discontinuity of the first kind occurs when a function's limit does not exist at a specific point, while a discontinuity of the second kind happens when the function's value at a particular point is undefined or infinite. Discontinuities of the first kind can be classified as removable, jump, or infinite discontinuities, based on the behavior of the limit.
Is every measurable functions continuous?
No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
What are the discontinuities of the function f(x) the quantity of x squared plus 5 x plus 6 all over 2 x plus 16.?
This is a rational function; such functions have discontinuities when their DENOMINATOR (the bottom part) is equal to zero. Therefore, to find the discontinuities, simply solve the equation:Denominator = 0 Or specifically in this case: 2x + 16 = 0
What is the difference between Riemann and Lebesgue integral?
The Lebesgue integral covers a wider variety of cases. Specifically, the definition of hte Riemann integral permits a finite number of discontinuities; the Lebesgue integral permits a countable infinity of discontinuities.
How do you find the discontinuities of 2x-3?
y=2x-3 has no discontinuities because no matter what you plug into x the function will be continuous.THEOREM 2.7.2Polynomials are continuous functionsIf P is polynomial and c is any real number thenlimx → c p(x) = p(c)
Explain the basic principle of magnetic particle testing?
By changing the permiability of ferromagnetic meterials, surface and near surface discontinuities are traced, is the principle of magnetic particle testing. By changing the permiability of ferromagnetic meterials, surface and near surface discontinuities are traced, is the principle of magnetic particle testing.
What function is integrable but not continuous?
A function may have a finite number of discontinuities and still be integrable according to Riemann (i.e., the Riemann integral exists); it may even have a countable infinite number of discontinuities and still be integrable according to Lebesgue. Any function with a finite amount of discontinuities (that satisfies other requirements, such as being bounded) can serve as an example; an example of a specific function would be the function defined as: f(x) = 1, for x < 10 f(x) = 2, otherwise
Whereare the major seismic discontinuites found?
Major seismic discontinuities are found within the Earth's interior, such as the Mohorovičić discontinuity (Moho) between the crust and mantle, and the Gutenberg discontinuity between the mantle and outer core. These discontinuities are detected by changes in seismic waves' speed and behavior as they pass through different layers of the Earth.
Can a discontinuous function be developed in a Fourier series?
Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
What is curvelet transform?
multiscale and multidirectional transform just like Fourier and wavelet but more sparse and redundant....useful in representing 2-D discontinuities in image
How thick is the upper mantle by itself?
The thickness of upper mantle discontinuities (at depths around 410 km and 660 km) provides a critical clue to our understanding of deep earth. Since the amplitude of reflected or S‐P converted waves is controlled by the thickness of discontinuities, short‐period studies of such waves may give a fine constraint on the thickness of upper mantle discontinuities. In this study, we analysed short‐period and vertical waveform data from 14 deep events in the Fiji‐Tonga region. The data were obtained from J‐Array, a short‐period and large‐aperture seismic array in Japan. With slant stack analyses of these data, we detected short‐period reflections or S‐to‐P conversions from 410 km and 660 km discontinuities near sources, which implies that both discontinuities are quite sharp. To directly measure the frequency content of these waves, linear slant stacks were made with various frequency pass‐bands (0.2-0.5, 0.5-1.0 and 1.0-2.0 Hz). Synthetic traces were generated for the models with various thicknesses of the 410 km and the 660 km discontinuities. Comparison of slant stacks with synthetic traces indicates that the thickness of both discontinuities is at most 5 km.
