Low cycle fatigue experiment of a dissimilar metal weld of steel and Ni-base alloy with different strain **amplitudes** at room temperature were carried out, then the curve of strain-life and characteristics of cycle response were obtained. Based on the experimental results of cyclic **stress**-strain hysteresis loop in fatigue progress at different levels of strain **amplitudes**, the variation laws of the **stress** **amplitudes** and cyclic elastic modulus with respected to the fatigue cycle were analyzed. The effect of the static elastic modulus and dynamic elastic modulus on the low cycle fatigue parameters was investigated. The results showed that the specimen of the weld joint during the progress of fatigue exhibited cyclic hardening at the beginning of 10 cycles, and then exhibited cyclic softening until fractured. The cyclic elastic modulus was decreased with increased number of cycles, and then remained almost stable and decreased dramatically near the end of the life. Finally, the fatigue life curve was concluded, which can be recommended as reference when assessing the integrity of Inconel weld. The static elastic modulus and dynamic elastic modulus showed little different effects on the strain amplitude-life curve.

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Different bar samples were prepared for cross-sectional observation in the longitudinal direction with EBSD analysis, as shown in Figs. 5(a) 5(c). The fractions of different misorientation angle grain boundaries were counted and recorded from observations on different fractured samples that tested at 240 and 390400 MPa **stress** **amplitudes**, as shown in Fig. 6. There was an increase in the fractions of high angle grain boundaries (HAGBs) in the fatigue-fractured anodized/sealed samples and an increase in the fractions of low angle grain boundaries (LAGBs) in the fatigue-fractured bare sample.

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components of the drive train in vehicles. The num- bers of load cycles in these applications can be very high which explains the interest in the very high cycle fatigue (VHCF) properties of these materials. Ishii et al. [1] performed ultrasonic fatigue tests at load ratio R = -1 with four 18Ni maraging steels with about 1870 MPa tensile strength containing inclu- sions of different sizes. A transition of crack initiation from the surface to the interior at Ti(N,C)-inclusions was observed when the number of cycles to failure increased beyond 10 7 . Mean lifetimes in the regime of 10 9 cycles were found at **stress** **amplitudes** between 300 and 400 MPa, where the materials with smaller inclusions showed higher cyclic strengths. Wang et al. [2] tested maraging steel with a tensile strength of 2800 MPa at load ratio R = 0.1. They observed a change from surface crack initiation to preferential initiation at interior inclusions as lifetimes increased beyond 10 6 cycles. A mean lifetime of about 10 7 cy- cles was found at a **stress** amplitude of 470 MPa. The relatively low cyclic strength in relation to the very high static strength was attributed to cyclic softening and growth of precipitates during cyclic deformation. Moriyama et al. [3] and Kawagoishi et al. [4] studied the influence of shot peening on the fatigue strength of 18Ni maraging steel. Rotating bending fatigue tests showed that the S–N curve measured with shot- peened specimens was shifted towards higher **stress** **amplitudes** compared with the untreated material due to the beneficial influence of surface compression stresses. Surface crack initiation in the HCF regime and interior crack initiation at inclusions in the VHCF regime was observed for the shot-peened material [3, 4].

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Although Sanjuro et al. [18] clearly state, that the surface finishing accompanied with the removal of surface **stress** raisers contributes mostly to the enhanced corrosion fatigue behavior (whereas residual **stress** only accounts for 10%), one possible explanation of this surface dependent fatigue behavior is that at **stress** **amplitudes** above 275 MPa the surfaces of turned specimen (technical surface) underwent microstructural hardening processes during machining due to plastic deformation resulting in residual **stress**. That is: turning implements compressive **stress** surpassing the increased surface roughness.

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Fatigue assessments by the more robust strain-based approach demand the determination of the local strain history from nominal stresses. For notched members, a cyclic constitutive relation, the **stress** concentration factor SCF and a strain concentration rule are used with this aim in some approximate solutions. The plastic part of the cyclic constitutive relations for many materials is well adjusted by a Ramberg-Osgood RO type equation. The parameters in the RO equation are the cyclic strength coefficient and exponent H’ and n’ respectively. These parameters can be experimentally determined or estimated from the condition of strain compatibility between the RO and the Coffin-Manson-Basquin CMB equations. The present paper discusses the influence that the use of both types of parameters, independent or experimentally determined and compatible or estimated , has on the numerical **stress**-life curves of the AISI 4340 Aircraft Quality steel. By numerical **stress**-life curves we mean the **stress** **amplitudes** and the fatigue-life that result from the numerical solution of both, the strain-life CMB and the **stress**-strain RO relations, for the same strain amplitude. This would be equivalent to using a linear strain concentration rule notched members with two RO equations, one with independent parameters and the other with compatible parameters, for **stress** and life calculations. The effects of the **stress** state are also accounted for in the present investigation since both, **stress**-life and **stress**- strain equations are modified in accordance with the total deformation theory of plasticity and through the introduction of a plane **stress** biaxial ratio. The principal finding of the present paper is that, for the studied material, the numerical **stress**-life curves that result from the use of compatible and independent parameters are indistinguishable for the same **stress** state. Consequently, there are no important implications on life time calculations when the cyclic **stress**-strain curve is estimated in such a way that compatibility conditions for the AISI 4340 aircraft quality steel are ensured.

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°'RH = Normal stress stress amplitudes Fraction of damage; and planes in a cylinder on a maximum shear on planes at failure stress of maximum shear on the maximum shear stress normal lon[r]

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This chapter takes a step back, and considers the anomalies themselves. Section 1.2 discussed how naive BRST arguments indicate that A-model topological string **amplitudes** are independent of anti-holomorphic K¨ahler moduli, as well as all complex structure mod- uli; and B-model **amplitudes** are independent of anti-holomorphic complex structure moduli, and all K¨ahler moduli. The BCOV holomorphic anomaly equations capture the anomalous dependence of A- and B-model **amplitudes** on their anti-holomorphic but still “right” moduli (that is, K¨ahler for A-model, and complex structure for B-model), but confirmed indepen- dence from “wrong” moduli — thus showing decoupling of two models. Walcher [13] recently proposed an extension of the BCOV holomorphic anomaly equations to the open topological string case (that is, in the presence of D-branes), under the additional assumptions that open string moduli do not contribute to factorisations in open string channels, and that disk one-point functions (closed string states terminating on a boundary) vanish.

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on 25 October 2013 and 1 April 2014, respectively (Figs. 7 and 8), produced relatively good estimates of wave ampli- tudes and arrival times when compared with the recorded signals from DART ® stations. These two cases indicate that the expeditious strategy involving Okada-like modeling of the tsunami initial condition and numerical modeling of the tsunami propagation can produce correct results. Neverthe- less, the lack of precise source information (dimension and slip) and detailed bathymetric models leads to some differ- ences between these signals. Figures 7b, c and 8b–d high- light these limitations, especially regarding the estimates of the wave periods and the **amplitudes** of the second waves. This is particularly due to the use of empirical scaling law to estimate the earthquake fault parameters (dimension and slip) as well as adopting a uniform slip distribution along the fault plane. Appropriate methods to constrain the fault slip distribution model require inversion of tsunami data (Fujii et al., 2011; Wei et al., 2013; Satake et al., 2013).

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In Fig. 4.-8. force components are displayed for different eccentricities and different angular velocities. Values are periodically changing. Values of positive and negative **amplitudes** of forces in x axis direction are almost same. That does not apply to **amplitudes** of forces in y axis direction as well. Positive force **amplitudes** in y axis direction are almost constant for one value of angular velocity, but negative values are different.

For low genus, this can be done more or less directly, because the structure of the **amplitudes** are so simple. However for g ≥ 3 the story gets more complicated. In such cases we have found a modified version of the harmonicity equation of [3] for which the boundary contributions cancel, and are strong enough to yield the genus g partition function up to an overall constant. Specialized to g = 1, 2 this result agrees with explicit computations of the **amplitudes**. This is somewhat analogous to the method used in [4] to compute the topological N = 2 string **amplitudes**, with the replacement of holomorphic anomaly with harmonicity equation.

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To turn the generic amplitude into a classes or particles amplitude, all generic objects must be replaced by their concrete values at the particular level. This replacement is specified by the rules ➇. For example, for the first (and in this simple example only) classes diagram, Mass[S[Gen3]] becomes MW. In general, one generic amplitude will of course fan out into several derived classes or particles **amplitudes**, so the Insertions function will have several entries.

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The modern treatment of kaon interactions with nucleons at low energies is based on e ff ective field theory, the chiral perturbation theory (χPT), combined with coupled channels techniques used to deal with divergencies that thwart the convergence of the χPT expansion. We employ a chirally motivated separable potential model [5], [4] that matches the e ff ective meson–baryon potentials to the chiral meson–baryon **amplitudes** obtained up to the second order in the χPT expansion in meson momenta and quark masses. The model parameters (chiral Lagrangian couplings, the low energy constants, and the inverse ranges that define the off-shell form factors) are standardly fitted to the K − p low energy cross sections, to the K − p threshold branching ratios and to the 1s level characteristics of kaonic hy-

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greatly reduced, and they are comparatively difficult to locate. At stimulus **amplitudes** above approximately 100μm, afferent fibers are known to fire twice within a single stimulus cycle, but as they reportedly occur in a "disorganized" manner (Talbot et al., 1968), and the activity of afferent fibers is not known to significantly change with time, they are unlikely result in such a differential effect. Instead, as it has been shown that neuron entrainment improves over the first few hundred milliseconds of stimulation at this frequency (Whitsel et al., 2003), the spike is likely indicative of a period before which the mechanisms that power cortical entrainment have taken significant effect. As with the startle response, this pre-entrainment peak suggests that the activity of cortical neurons is modulated through mechanisms that require some period of time or previous level of activity to take effect.

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I confirm that I have been explained that I have been given the option of undergoing testing to determine ocular pulse **amplitudes** by dynamic contour tonometry. I have understood the risks and complications of this study and have had the opportunity to ask the investigators any questions I may have had. I understand that my participation in the study is voluntary and that I can leave the study at any given time, without having my medical care or legal rights being affected. I agree that the investigators and their team have the access to all the data that I may provide them. I accept to share the data obtained during analysis in the faith that it will be used only for scientific purposes. I accept that my identity will not be revealed if the data be published or sent to a third party. I agree not to restrict the scientific use of any of the data or results that may arise from this study.

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In chapter 2, we discuss some of the methods that have been used to obtain dispersion relations for Feynman integrals, and to obtain the thresholds and weight functions in these dispersion relations. We also discuss a method of obtaining the weight functions in approximate dispersion relations for scattering **amplitudes** and vertex functions. In this method, a dispersion relation is obtained, for a particular amplitude, by making assumptions about the analytic properties and behaviour of the amplitude at infinity. The weight function is then obtained by using the unitarity relation (discussed in sects. 2-3, 3-2 and 4-2). Approximations to the **amplitudes** on the right hand side of the unitarity relation are made, and in this way an approximation to the imaginary part of the amplitude (weight function) is obtained.

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The time domain signal recorded for the 0° case was subtracted from each subsequent time domain data set that was captured. This process removed any unwanted signals, such as remaining oscillations due to the impulse cutting off abruptly, or reﬂections off the back edge. The process is perfect, in that it completely re- moves the unwanted signals without changing the signal of inter- est (the reﬂection from the curved section) at all. Such an ideal removal is possible in a simulation due to the conditions leading to the unwanted signals being absolutely identical in each case (the back edge and transducer positions are exactly the same), due to the complete absence of conventional noise, and due to the simulation being totally linear, such that the presence of a wave in no way changes the propagation of any other wave. The re- ﬂected signals were extracted from the simulation data using sim- ple time-gating; no frequency ﬁltering was necessary as simulated data has no conventional noise source. Fig. 4 compares a signal re- ﬂected from an edge (Fig. 4a), the case where there is no further medium into which to propagate, with the signals reﬂected from a 90° curve (Fig. 4b). Note that the **amplitudes** have been norma- lised, so that the peak-to-peak amplitude of the edge reﬂection is unity. There is a clear signal reﬂected in each case, although for the large radius curvature cases, the signal becomes very small.

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hibit a limiting amplitude. Noting that this model works with an actual tidal flow over a topography at rest, it seems rea- sonable to argue that the limiting factor is inherent to the tidal forcing. This supports the idea that the forced-MCC-f equations represent an insightful tool for the fully nonlinear framework, where tidally generated solitons may attain limit- ing **amplitudes** with or without reaching a table-shaped form. Another departure from classical theories is that strongly nonlinear tide-generated solitons may exhibit larger maxi- mum **amplitudes** than predicted from eKdV and MCC so- lutions, while soliton phase speeds are always smaller. We attribute these differences to the fact that tide-generated soli- tons ride on internal tides and, hence, their wave properties are not simply the response to a two-fluid layer system as such, as in eKdV and MCC solitons, but are also subjected to the forcing of the system, to a variable background flow, and to interfacial displacements of the internal tide itself. In this context, numerical results also show that solitons propagate freely from the source only when the tidal flow is small (sub- critical flow), while an increase in the tidal forcing (critical and supercritical flow) generates accelerating and decelerat- ing phases of the soliton speed.

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Quantum field theory is a cornerstone of modern theoretical physics, whose conventional approach is to write down a Lagrangian and then derive all struc- tures therein. However, there has been tremendous progress in the modern S-matrix program revealing many symmetries and dualities obscured by the traditional approach. These new structures show up in a wide range of theo- ries, including Yang-Mills (YM), gravity, and effective field theories (EFTs). The initial motivation of the modern S-matrix program is to reduce the com- plexities of the usual method of Feynman diagrams. Feynman diagram calcu- lation introduces off-shell redundancies from gauge invariance and a choice of field basis which appear in intermediate processes but are absent in observ- ables. The modern S-matrix program exploits physical criteria like Lorentz invariance and unitarity to construct scattering **amplitudes** directly and with- out the aid of a Lagrangian. The history can be traced back to the unitarity methods [1, 2] developed in the 90’s for loop-level calculation. The second wave of revolution was led by the celebrated BCFW recursion relations which compute S-matrices in YM without using Feynman diagrams at all [3, 4]. On-shell recursion relations were soon extended to gravity theories [5, 6], su- persymmetric theories [7], and, eventually, all renormalizable and some non- renormalizable theories [8]. In the context of planar N = 4 super Yang-Mills theory, on-shell recursion is even generalized to all-loop order [9]. These de- velopments made traditionally intractable calculations possible, and generated many surprisingly simple formulae of scattering **amplitudes**. Since the devel- opment of on-shell recursion relations, many other alternative formulations of S-matrix have been invented, e.g., on-shell diagrams and positive Grassman- nian [10, 11], Cachazeo-He-Yuan (CHY) formula [12–14], hexagon bootstrap [15, 16], flux tube S-matrix [17, 18], twistor methods [19–27], and amplituhe- dron [28, 29]. We refer readers interested in more detail to the pedagogical review [30].

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Absolute value for the scattering amplitude can be inferred from knowledge of three factors: the waveform of the signal scattered by the flaw, the waveform obtained in a reference experi[r]

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Conclusion: Our analysis suggests that procedures that arrest cells in different stages of the cell cycle differentially affect expression of some cell cycle related genes once the cells are released from arrest. The impact of the cell-arresting method on expression of a cell cycle related gene can be quantitatively estimated from the ratio of two estimated **amplitudes** in two experiments. The ratio can be used to gauge the variation in the phase/peak expression time distribution involved in stochastic transcription and post-transcriptional processes for the gene. Further investigations are needed using normal, unperturbed and synchronized HeLa cells as a reference to compare how many cell cycle related genes are directly and indirectly affected by various cell-arresting methods.

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