Thus for each i, as t increases the value of \phi(t,i) eventually becomes constant and equals \omega(i). As with the case of computable real numbers, it is not possible to effectively move between the two representations of limit computable reals.
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This region is called the hydrodynamically fully developed region. But this is not the fully developed fluid flow until the normalized temperature profile also becomes constant. In case of laminar flow, the velocity profile in the fully developed region is parabolic but in the case of turbulent flow it gets a little flatter due to vigorous mixing in radial direction and eddy motion. The velocity profile remains unchanged in the fully developed region.
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A ring is called Noetherian (in honor of Emmy Noether, who developed this concept) if every ascending chain of ideals :0 ⊆ I0 ⊆ I1 ... ⊆ In ⊆ In + 1 ⊆ ... becomes stationary, i.e. becomes constant beyond some index n. Equivalently, any ideal is generated by finitely many elements, or, yet equivalent, submodules of finitely generated modules are finitely generated. Being Noetherian is a highly important finiteness condition, and the condition is preserved under many operations that occur frequently in geometry.
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Water flows from the header at the top of each of the ten spirals as smooth, accelerating supercritical flow. When maximum velocity for the 1 in 16 gradient and roughness coefficient has been reached, the flow becomes constant and is therefore critical, a condition of least possible stability.Froude number = 1.0 In this unstable condition water is easily sculpted by minor external forces. The weir configuration and drag disturbance from the sides of the spiral create waves which travel downstream.
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In the study of artificial neural networks (ANNs), the neural tangent kernel (NTK) is a kernel which describes the evolution of deep artificial neural networks during their training by gradient descent. It allows ANNs to be studied using theoretical tools from Kernel Methods. For most common neural network architectures, in the limit of large layer width the NTK becomes constant. This enables simple closed form statements to be made about neural network predictions, training dynamics, generalization, and loss surfaces.
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The Avramov fragility parameter α is based on a Kohlraush-type formula of viscosity derived for glasses: strong liquids have α ≈ 1 whereas liquids with higher α values become more fragile. Doremus indicated that practically all melts deviate from the Arrhenius behaviour, e.g. the activation energy of viscosity changes from a high QH at low temperature to a low QL at high temperature. However asymptotically both at low and high temperatures the activation energy of viscosity becomes constant, e.g.
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Several choices of \rho and \psi have been proposed. The two figures below show four \rho functions and their corresponding \psi functions. Image:RhoFunctions.png For squared errors, \rho(x) increases at an accelerating rate, whilst for absolute errors, it increases at a constant rate. When Winsorizing is used, a mixture of these two effects is introduced: for small values of x, \rho increases at the squared rate, but once the chosen threshold is reached (1.5 in this example), the rate of increase becomes constant.
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During the third period the team becomes constant participant in the Bulgarian First division. From 1970, until 1982 „the seamen” begin to enlarge their ambitions to become more than a “provincial team”. In 1975 the club makes its debut in the European Club Competitions – the “Radivoje Korac” cup. In the preliminary round, under the name of “Akademic” – Varna, we eliminate “Karshiaka” from Izmir. In the group we play “Partizan” – Beograd, “Sinudinia” – Bologna and “Bayer tuss 04” – Leverkusen. At that campaign we beat “Partizan” 116-100 in the full “Kongresna” hall.
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A variance-stabilizing transformation aims to remove a variance-on-mean relationship, so that the variance becomes constant relative to the mean. Examples of variance-stabilizing transformations are the Fisher transformation for the sample correlation coefficient, the square root transformation or Anscombe transform for Poisson data (count data), the Box–Cox transformation for regression analysis, and the arcsine square root transformation or angular transformation for proportions (binomial data). While commonly used for statistical analysis of proportional data, the arcsine square root transformation is not recommended because logistic regression or a logit transformation are more appropriate for binomial or non-binomial proportions, respectively, especially due to decreased type-II error.
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A fully developed heat flow in a pipe can be considered in the following situation. If the tube wall of the pipe is constantly heated or cooled so the heat flux from the wall to the fluid via convection is a fixed value, then the bulk temperature of the fluid increases steadily at a fixed rate along the flow direction. An example can be a pipe covered entirely by an electrical heating pad, and the flow is introduced after a uniform heat flux from the pad is achieved. At a distance away from the entrance of the fluid, the fully developed heat flow is achieved when the heat transfer coefficient of the fluid becomes constant, and the temperature profile has the same shape along the flow.
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It is after escaping with the barbarians that the friends realize Goldmoon's desire of traveling to Haven, where she hoped the Seekers, priests who were in search of the old gods but degenerated into a political movement, would be able to teach her about the healing staff. In the following chapters, Weis and Hickman continue to make the female barbarian the main focus of the story, stating that she discovered two constellations were missing from the firmament, and then revisiting when the staff protected Riverwind when the tribe was going to stone him. However, her protagonism fades in the battle sequences that follow, where she is protected by Riverwind, Sturm Brightblade, a Squire of the Knights of Solamnia and Tanis Half-Elven, the leader of the group. This behavior becomes constant throughout the rest of the series.
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It was shown by Herglotz (1911),Herglotz (1911) that a relativistic theory of elasticity can be based on the assumption, that stresses arise when the condition of Born rigidity is broken.Pauli (1921) An example of breaking Born rigidity is the Ehrenfest paradox: Even though the state of uniform circular motion of a body is among the allowed Born rigid motions of class B, a body cannot be brought from any other state of motion into uniform circular motion without breaking the condition of Born rigidity during the phase in which the body undergoes various accelerations. But if this phase is over and the centripetal acceleration becomes constant, the body can be uniformly rotating in agreement with Born rigidity. Likewise, if it is now in uniform circular motion, this state cannot be changed without again breaking the Born rigidity of the body.
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