Value Of Nf Research Articles

Focusing properties and focal shift of vortex Hermite-cosh-Gaussian beams

In this work, we investigate the focusing properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) passing through a converging lens system. The analytical propagation equation as well as the beam width expression of a focused vHChGB is derived based on the Huygens-Fresnel diffraction principle. From the obtained formulae, the effects of the Gaussian Fresnel number NF and the initial beam parameters, namely the beam order, the decentered parameter b, and the vortex charge number m, on the structure of the light intensity distribution and the beam spot size in the focal region are analyzed numerically. It is shown that the focal shift, which is determined from the minimum beam spot width criterion, is strongly dependent on the Fresnel number NF. And it is affected by the parameter b and the vortex charge m but is nearly insensitive to the beam order n. For a fixed value of NF, the focal shift is smaller when b or m is larger. The focal shift decreases monotonously with the increase of NF until it vanishes asymptotically for large values of NF. The obtained results may be useful for the applications of vHChGB in beam shaping and beam focusing.

Fatigue and damage properties of non-consecutive jointed mudstone samples subjected to cyclic triaxial loading

Non-consecutive jointed mudstone samples with dip angles (0° is the horizontal axis) of 15°, 30°, and 45° were subjected to a series of cyclic triaxial loading tests at various frequencies, with the aim of evaluating the fatigue and damage properties of jointed mudstone samples, including the ultimate cycle number, maximum axial strain, damage evolution, and failure behavior. The results from the tests indicate the following: (i) the higher the frequency, the greater the maximum axial strain difference and the higher the value of Eavl (average Young’s modulus during loading) and Eavu (average Young’s modulus during unloading), and (ii) compared with triaxial compressive loading, additional cracks are found in the samples subjected to cyclic loading, and the propagation of cracks initiates from the joint tip toward the two ends of the sample. Meanwhile, under the condition of a lower frequency, additional cracks occur after failure. Based on the experimental data, a new indicator (RS), considering the effect of the amplitude, peak deviatoric stress, and valley deviatoric stress, was proposed to indicate the stress level. At the same RS and dip angle, there is a positive correlation between frequency and lgNf (Nf is the number of cycles before the failure of the rock samples, and lgNf is the logarithmic value of Nf). Furthermore, a newly proposed damage variable based on shear strain is used to describe the damage evolution of jointed mudstone subjected to cyclic triaxial loading.

Durability of Concrete Under the Combined Action of Carbonization and Fatigue Loading of Vehicles

Natural factors such as environments gradually cause the aging of structural materials of concrete bridges and mechanical properties of the components are constantly degraded. When highway bridge structures are under the combined with vehicle loading and environmental diversities, the degradation of structural performance is further aggravated. In this study, according to the deterioration trend of concrete durability in atmospheric environment, durability tests for concrete under the combined action of fatigue loading of vehicles and carbonization were performed by artificial climate simulation. A bending fatigue test for concrete under vehicle loading was carried out, and the trend of fatigue life change with vehicle loading level and the trend of fatigue strain development were obtained. The results show that the fatigue life increases with the decrease in fatigue loading level of vehicles, and the logarithmic value of fatigue life Nf is linear with the fatigue stress level S. Fast carbonization tests for concrete were performed with respect to the fatigue damage degree D of 0, 0.2, 0.4, 0.6, and 0.8. It was found that the carbonization trend of fatigue damaged concrete under vehicle loading follows the Fick first law. The carbonization depth increases with the increase in carbonization time, relatively fast at the initial stage and then slowly at the later stage. When the fatigue damage degree D is less than 0.4, the effects of fatigue damage on carbonization is relatively small. When D is more than 0.4, the effect of fatigue damage on carbonization is relatively significant. The extension of interior micro-cracks and micropores caused by fatigue damage is a significant factor affecting the carbonization performance of fatigue damaged concrete. The change trend of carbonization depth of damaged concrete with time was fitted and analyzed. An influencing factor of fatigue damage was introduced, and a durability prediction model for concrete under the combined action of carbonization and fatigue loading of vehicles was established.

FMRI neurofeedback in emotion regulation: A literature review

Emotion regulation is one of the most prevalent objectives for real-time fMRI neurofeedback (rt-fMRI-NF) studies. The existing studies differ in a number of methodological parameters. This study provides a literature review of the main parameters and results of studies using rt-fMRI-NF for emotion regulation enhancement. A search of the Web of Science database up through November 8, 2018, identified 144 articles written in English, 89 of which were excluded as irrelevant for this study. The remaining 51 original studies and four secondary analyses of previously published original studies were included in the literature review. The selection of target brain areas, target populations, emotion regulation protocols, NF presentation, control group types, and emotion regulation instructions were examined in relation to achieved brain regulation and changes in cognitive or clinical outcomes. Study results were evaluated in terms of their statistical robustness. The results show that healthy people are able to regulate their brain activity in the presence of rt-fMRI-NF from various brain regions related to emotion regulation, including the amygdala, anterior insula, and anterior cingulate cortex. The regulation of brain activity using rt-fMRI-NF from prefrontal-limbic connectivity or from individually navigated brain areas is feasible as well. Most studies that used a control group show that rt-fMRI-NF actually induces some effects on brain regulation, cognitive variables, and clinical variables. Generally, the success of ROI regulation during NF training is related to the combination of target brain region, the type of emotion regulation task, and the population undergoing the training. In terms of patient groups, the strongest support for the beneficial effects of rt-fMRI-NF has been shown in increased positive emotion experiencing in patients with depression and in decreased anxiety in patients with anxiety disorders. Symptom reduction following NF training has been also reported in patients with PTSD, BPD, and schizophrenia, but direct comparisons with control groups in these studies makes it impossible to evaluate the added value of NF. Studies often do not report all the relevant analyses for evaluating NF success and many studies lack statistical robustness. Overall, rt-fMRI-NF seems a promising tool for emotion regulation enhancement with the potential to induce long-term symptom reduction in patients with various mental disorders. Preplanning of statistical analyses, careful interpretations of the results, and evaluations of the NF effect on symptom reduction in patient groups is recommended.

Diagnostic Performance of Neurofilaments in Chinese Patients With Amyotrophic Lateral Sclerosis: A Prospective Study.

Several studies have attempted to reduce diagnostic delay and identify biomarkers for drug development in amyotrophic lateral sclerosis (ALS). In this study, we aimed to evaluate the diagnostic accuracy for ALS of cerebrospinal fluid (CSF) neurofilament (Nf), Tau protein, and inflammatory factors such as interleukin (IL)-2, IL-6, IL-10, IL-15, and granulocyte-macrophage colony-stimulating factor (GMCSF) in Chinese patients. Our prospective study measured the concentration of phosphorylated Nf heavy chain (pNfH), Nf light chain (NfL), Tau, pTau, and inflammatory factors in the CSF of 85 patients. Detailed clinical data and laboratory, neuroimaging, and neurophysiological findings were recorded. The concentrations of pNfH and NfL were higher in the ALS group than in the control group. At the 1104 pg/mL pNfH cutoff, the specificity was 68.8%, the sensitivity 100%, and the area under the curve (AUC) 0.907. At the 1,139 pg/mL NfL cutoff, the specificity was 56.3%, the sensitivity 96.2%, and the AUC 0.775. There was no significant difference in the concentrations of Tau, pTau, IL-2, IL-6, IL-10, IL-15, and GMCSF between the ALS and control groups (p > 0.05). In the ALS group, the concentration of pNfH in the CSF was correlated with disease duration (r = −0.475, p < 0.001). This is the first prospective study to confirm the diagnostic value of Nf for ALS in Chinese patients.

Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions

We study SU(N ) Quantum Chromodynamics (QCD) in 3+1 dimensions with Nf degenerate fundamental quarks with mass m and a θ-parameter. For generic m and θ the theory has a single gapped vacuum. However, as θ is varied through θ = π for large m there is a first order transition. For Nf = 1 the first order transition line ends at a point with a massless η′ particle (for all N ) and for Nf> 1 the first order transition ends at m = 0, where, depending on the value of Nf , the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4d bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3d phases. These turn out to be the phases of the recently studied 3d Chern-Simons matter theories, thus relating the dynamics of QCD4 and QCD3, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4d theory has an SU(Nf ) sigma model, the domain wall theory at low (nonzero) mass supports a 3d massless mathbb{C}{mathrm{mathbb{P}}}^{N_f-1} nonlinear σ-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.

Spreading dynamics of superposed liquid drops on a spinning disk

We have experimentally studied simultaneous spreading of superposed drops of two Newtonian liquids on top of a horizontal spinning disk using the flow visualization technique. An inner drop of high surface tension liquid is placed centrally on the disk followed by a drop of outer liquid (lower surface tension) placed exactly above that. The disk is then rotated at a desired speed for a range of volume ratios of two liquids. Such an arrangement of two superposed liquid drops does not affect the spreading behavior of the outer liquid but influences that of the inner liquid significantly. The drop spreads to a larger extent and breaks into more fingers (Nf) as compared to the case where the same liquid is spreading in the absence of outer liquid. The experimentally observed number of fingers is compared with the prediction using available theory for single liquid. It is found that the theory over-predicts the value of Nf for the inner liquid while it is covered by an outer liquid. We provide a theoretical justification for this observation using linear stability analysis. Our analysis demonstrates that for small but finite surface tension ratio of the two liquids, the presence of the outer interface reduces the value of the most unstable wave number which is equivalent to the decrease in the number of fingers observed experimentally. Finally, sustained rotation of the disk leads to the formation of droplets at the tip of the fingers traveling outwards.

Scaling dimensions in QED3 from the \u03f5-expansion

We study the fixed point that controls the IR dynamics of QED in d = 4 − 2ϵ dimensions. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in the ϵ-expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to d = 3 to estimate their value at the IR fixed point of QED3 as function of the number of fermions Nf . The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of Nf , which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, the ϵ-expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of Nf .

Adsorption Study on Moringa Oleifera Seeds and Musa Cavendish as Natural Water Purification Agents for Removal of Lead, Nickel and Cadmium from Drinking Water

The effectiveness of plant based materials Moringa oleifera (Moringa) seeds and Musa cavendish (banana peel) for removing heavy metals namely lead (Pb), nickel (Ni) and cadmium (Cd) from contaminated groundwater was studied. Tests were carried out with individual and combined biomass at neutral pH condition on synthetic groundwater samples. The optimum biomass doses were determined as 200 mg/L for single biomass and 400 mg/L (in the ratio of 200 mg/L: 200 mg/L) for combined biomasses and used for adsorption isotherm studies with contact time of 30 minutes. Results showed that combined biomasses was able to met the Pb, Ni and Cd WHO standards from higher Pb, Ni and Cd initial concentrations which were up to 40 µg/L, 50 µg/L 9 µg/L, respectively compared to individual biomass of Moringa seed and banana peel. Moringa seeds exhibited the highest removal of Pb (81%) while the combined biomasses was most effective in removing Ni (74%) and Cd (97%) over wider their initial concentration ranges. The experimental data were linearized with Langmuir and Freundlich adsorption isotherm models. Freundlich model described the Pb adsorption better than the Langmuir model for all the tested biomasses. However, the Langmuir model fit better with the experimental data of Ni adsorption by Moringa seeds. Both models showed negligible differences in the coefficient of determination (R2) when applied for Ni and Cd adsorption on banana peel and combined biomasses, suggesting that there were multiple layers on the biomass interacting with the metals. Chemisorption is suggested to be involved in Pb adsorption for all tested biomasses as the value of nF calculated was lower than one. This type of adsorption could explain the phenomenon of different behavior of Pb removal and the higher Pb adsorption capacity (represented by KF values) compared to Ni and Cd. The study demonstrates that Moringa seeds, banana peel and their combination have the potential to be used as a natural alternative to the other water treatment agents for removing the Pb, Ni and Cd from drinking water.

Fatigue Characteristics of Selected Light Metal Alloys

The paper addresses results of fatigue testing of light metal alloys used in the automotive as well as aerospace and aviation industries, among others. The material subject to testing comprised hot-worked rods made of the AZ31 alloy, the Ti-6Al-4V two-phase titanium alloy and the 2017A (T451) aluminium alloy. Both low- and high-cycle fatigue tests were conducted at room temperature on the cycle asymmetry ratio of R=-1. The low-cycle fatigue tests were performed using the MTS-810 machine on two levels of total strain, i.e.Δεc= 1.0% and 1.2%. The high-cycle fatigue tests, on the other hand, were performed using a machine from VEB Werkstoffprufmaschinen-Leipzig under conditions of rotary bending. Based on the results thus obtained, one could develop fatigue life characteristics of the materials examined (expressed as the number of cycles until failure of sample Nf) as well as characteristics of cyclic material strain σa=f(N) under the conditions of low-cycle fatigue testing. The Ti-6Al-4V titanium alloy was found to be characterised by the highest value of fatigue life Nf, both in lowand high-cycle tests. The lowest fatigue life, on the other hand, was established for the aluminium alloys examined. Under the high-cycle fatigue tests, the life of the 2017A aluminium and the AZ31 magnesium alloy studied was determined by the value of stress amplitude σa. With the stress exceeding 150 MPa, it was the aluminium alloy which displayed higher fatigue life, whereas the magnesium alloy proved better on lower stress.

Dynamic AdS/QCD and the spectrum of walking gauge theories

We present a simple AdS/QCD model in which the formation of the chiral condensate is dynamically determined. The gauge dynamics is input through the running of the quark bilinear's anomalous dimension, gamma. The condensate provides a dynamically generated infra-red wall in the computation of mesonic bound state masses and decay constants. As an example, we use the model, with perturbative computations of the running of gamma, to study SU(3) gauge theory with a continuous number of quark flavours, Nf. We follow the behaviour of the spectrum as we approach the conformal window through a walking gauge theory regime. We show such walking theories display a BKT phase transition, with Miransky scaling, as one approaches the edge of the conformal window at the critical value of Nf. We show that these walking theories possess an enhanced quark condensate, a light Higgs like excitation and argue that the non-perturbative contribution to S falls to zero. We also study the deformation of the BKT transition when the quarks have a current mass which may be of use for understanding lattice simulations of walking theories.

Investigation of Transformer Turns Ratio Between Feed and Slot of Aperture Coupled Slot Antenna by Using $S_{11}$ Parameter

This communication presents a simplified design approach to obtain the turns ratio nf which models the coupling between the microstrip feed and slot line of an aperture coupled slot antenna by using the S11 parameter. Equations are derived using S11 parameter to determine nf and simulations are carried out at 2 GHz using substrates of PCB FR4, Duroid 5870, and Duroid 6010. Results indicate nf is proportional to the slot length from 0 to 20 mm increasing rapidly with length. Over 20 mm slot length, the trend reduces and the value of nf tends towards 1. In addition, nf varies with the height of substrate but is little affected by dielectric constant of substrate which could therefore be ignored to simplify the design procedure. Measured results show good agreement with the theoretical model.

Influence of the Torsion Angle in 3,3′-Dimethyl-2,2′-bipyridine on the Intermediate Valence of Yb in (C5Me5)2Yb(3,3′-Me2-bipy)

The synthesis and X-ray crystal structures of Cp*2Yb(3,3′-Me2bipy) and [Cp*2Yb(3,3′-Me2bipy)][Cp*2YbCl1.6I0.4]*CH2Cl2 are described. In both complexes, the NCCN torsion angles are approximately 40°. The temperature-independent value of nf of 0.17 shows that the valence of ytterbium in the neutral adduct is multiconfigurational, in reasonable agreement with a CASSCF calculation that yields a nf value of 0.27; that is, the two configurations in the wave function are f13(π*1)1 and f14(π*1)0 in a ratio of 0.27:0.73, respectively, and the open-shell singlet lies 0.28 eV below the triplet state (nf accounts for f-hole occupancy; that is, nf = 1 when the configuration is f13 and nf = 0 when the configuration is f14). A correlation is outlined between the value of nf and the individual ytterbocene and bipyridine fragments such that, as the reduction potentials of the ytterbocene cation and the free x,x′-R2-bipy ligands approach each other, the value of nf and therefore the f13:f14 ratio reaches a maximum; conversely, the ratio is minimized as the disparity increases.

Seawater desalination and salt production in a hybrid membrane-thermal process

Several hybrid systems, which are developed now, namely NF-MSF, NF-RO-MSF, NF-RO-MD and others offer promising performance. An integrated system for complete usage of components in seawater is also being considered. In all the aforementioned systems NF as water pre-treatment method is applied and a considerable decrease in scale forming components is achieved. Higher recovery may be then reached when desalting in comparison to traditionally treated water. Very compact NF membranes are applied which results in a very high rejection of divalent ions and relatively high rejection of sodium chloride. A simultaneous decrease of NaCl concentration in NF process is then obtained which causes an increase in the RO recovery since the osmotic pressure value of NF permeate is diminished. IfNF-MSF (or NF followed by any thermal method) system is considered a NaCl concentration decrease in the pre-treatment is however not essential for the NF step. The salt concentration influence on thermal method performance is very weak in comparison to RO. Furthermore the highly concentrated MSF brine might be used as a possible by-product, e.g. for obtaining salt. A dual-purpose desalination-salt production system may be then suggested. Two arrangements are presented, namely: UF-NF-MSF-crystallisation and UF-NF-RO-MSF-crystallisation systems. The high rate of water recovery is accompanied by salt obtainment in these systems. If $30/ton of salt is assumed the water cost is equal to $0.71/m3 in UF-NF-MSF-crystallisation system and $0.43/m3 in UF-NF-RO-MSF-crystallisation system. The above data demonstrate that these water costs are competitive compared to those of potable water produced in thermal or RO seawater plants.

On the Thermal Instability in a Contracting Cloud and Formation of a Bound Cluster

We perform linear analysis of thermal instability in a contracting large cloud filled with warm H I gas and investigate the effect of metallicity and radiation flux. When the cloud reaches critical density nf, the cloud fragments into cool, dense condensations because of thermal instability. For a lower metallicity gas cloud, the value of nf is high. Collision between condensations will produce self-gravitating clumps and stars thereafter. From the result of the calculations, we suggest that high star formation efficiency and bound cluster formation are realized in low-metallicity and/or strong-radiation environments.

Light Environment, Nitrogen Content, and Carbon Balance of Basal Leaves of Sunflower Canopies

A good association between leaf N and photosynthetic photon flux density (PPFD) canopy distribution profiles has often been found. However, it is not clear whether N export from basal leaves anticipates the reduction in basal leaf PPFD that occurs as the canopy develops; our first objective was to examine this issue. We documented the dynamics of the light environment and specific leaf nitrogen (Nf) for target leaves at a single level of insertion under sunflower (Helianthus annuus L.) canopies grown at 0.47, 1.18, and 4.76 plants m−2 and contrasted observed Nf with the estimated value of Nf required to maximize net carbon exchange (NCE) for the actual PPFD impinging on target leaves. The second objective of this work was to define the relationships between Nf and PPFD and between Nf and the spectral composition of light impinging on basal leaves. Paired (red and farred) photodiode sensors placed on the adaxial leaf surface were used to document light quality dynamics of basal leaves. Measured Nf was greater than or similar to that required to maximize NCE for 79% of the observations made between achievement of maximum target leaf area and senescence of these leaves. Nf showed a strong association with both red/far‐red ratio of light impinging on target leaves and PPFD, but the association was stronger for the former variable. We conclude that N export from basal leaves does not precede PPFD reduction and that the red/far‐red ratio is a better predictor of Nf gradients within the canopy than PPFD.

Etching rate characterization of SiO2 and Si using ion energy flux and atomic fluorine density in a CF4/O2/Ar electron cyclotron resonance plasma

SiO2 and Si etching in a CF4/O2/Ar plasma has been carried out in an electron cyclotron resonance etcher over a wide range of conditions. The etch rate has been compared with the ion energy flux to the wafer surface, JiEi, and the atomic fluorine density in the gas phase, nF. It is found that the etch rate can be divided into two regimes by a critical value of nF/(JiEi), the ratio of the atomic fluorine density to the ion energy flux. The critical value can be determined from a contour plot of the etch rate as a function of the ion energy flux and the atomic fluorine density. The critical value of nF/(JiEi) for Si is higher than that for SiO2. For nF/(JiEi) higher than the critical value, the SiO2 etch rate linearly increases with the ion energy flux, and the Si etch rate shows a nonlinear increase with the ion energy flux. For nF/(JiEi) lower than the critical value, both SiO2 and Si etch rates linearly increase with the atomic fluorine density.

Fragmentation of elongated cylindrical clouds. I - Isothermal clouds

view Abstract Citations (70) References (29) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Fragmentation of Elongated Cylindrical Clouds. I. Isothermal Clouds Bastien, Pierre ; Arcoragi, Jean-Pierre ; Benz, Willy ; Bonnell, Ian ; Martel, Hugo Abstract A numerical study is presented of fragmentation in its simplest possible form: that of elongated, isothermal, axially symmetric clouds. Results have been obtained for different ratios of length to diameter, L/D, and initial Jeans numbers, J0 (ratio of gravitational to thermal energies). Initial density perturbations are introduced on the axis of otherwise uniformly dense cylinders, and the maximum number of fragments Nf(max) that can form and grow for combinations of L/D and J0 is determined. The value of Nf(max) increases with J0 at small J0, then saturates at a finite value Nf(max) about 2L/D at large J0. That results contradicts analytical predictions based on a linear stability analysis for infinite cylinders or the ratio of the total mass to the Jeans mass. The results are directly applicable to observations of the cores of dark molecular clouds which are found to be mostly prolate. These cores are then expected to fragment and form stars in multiple systems or in small groups, as frequently observed in star-forming regions. Publication: The Astrophysical Journal Pub Date: September 1991 DOI: 10.1086/170424 Bibcode: 1991ApJ...378..255B Keywords: Molecular Clouds; Nebulae; Star Formation; Cylindrical Bodies; Finite Difference Theory; Hydrodynamics; Poisson Equation; Astrophysics; HYDRODYNAMICS; NEBULAE: GENERAL; NUMERICAL METHODS; STARS: FORMATION full text sources ADS | Related Materials (5) Part 2: 1991ApJ...380..476A Part 3: 1991ApJ...377..553B Part 4: 1992ApJ...400..579B Part 5: 1992ApJ...401..654B Part 6: 1993ApJ...406..614B

Electron content over Tucuman

The first morphological study of electron content (NF) over Tucumán (26.9° S, 65.4° W) (dipole geomagnetic coordinates: Latitude, −15.62°, Longitude, 4.64°, L = 1.08) using ATS 3 and GOES 3 geosynchronous satellite signals has been done, for the period April 1982 through March 1983 near the maximum of the second highest solar cycle. The NF over Tucumán is characterized by a day to day temporal variability, by semiannual variation, by equatorial anomaly influence, by different behaviors during magnetic storms and by occasional postsunset second maximum. Data of Tucumán and other stations were used for a comparative study. The maximum value of NF occurs later at Tucumán and has a similar order of magnitude in comparison to that observed at other stations. The winter anomaly is only present at northern hemisphere stations.

高速度工具鋼の引張・圧縮疲労強度に関する研究 ＩＩＩ フィッシュアイを伴う丸棒試験片のき裂進展挙動

The behavior of crack propagation in the complete reversed tensile and compressive fatigue test piece of circular section with Fish eye of the heat treated high-speed steel was investigated by using an acoustic emission technique. Moreover, the property of crack propagation in the 1/2CT test piece was investigated.The results obtained are summerized as follows;(1) The number of stress cycles NAE for crack initiation and propagation and the number of stress cycles Nf for fracture were accurately estimated by measuring continuously AE total ringdown counts during the fatigue process.(2) The fatigue life was good accord with the value of Nf estimated by the acoustic emission technique. The life of fatigue crack propagation (Nf-NAE)Lab. was 25-50% of the fatigue life Nf and decreased with decreasing stress amplitude.(3) The life of fatigue crack propagation (Nf-NAE)cal. calculated from the property of crack propagation in the 1/2CT test piece showed good agreement with the value of (Nf-NAE)Lab. obtained by the acoustic emission technique.(4) The behavior of crack propagation in the complete reversed tensile and compressive fatigue test piece of circular section showed good corrrelation with the behavior of crack propagation in the 1/2CT test piece, so that it is suggested that the initiative mechanism of residual stress on the fracture surface with Fish eye can be discussed by using the 1/2CT test piece.