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Journal articles on the topic 'Fract'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Luethy, Magdalena Laura, Andreas Schötzau, and Anja Palmowski-Wolfe. "Establishing Prediction Intervals for the SpeedWheel Acuity Test in Adults and Children." Klinische Monatsblätter für Augenheilkunde 238, no. 04 (April 2021): 488–92. http://dx.doi.org/10.1055/a-1403-2218.

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Abstract Background The SpeedWheel (SW) test is an objective test of visual acuity (VA) using suppression of the optokinetic nystagmus (OKN). Here, we established prediction intervals of the SW measures compared to Snellen acuity in adults and children. Subjects and Methods In this prospective, single center study, subjects aged at least 4 years underwent testing of VA with SW, Landolt-C, and Tumbling-E symbols (Freiburg acuity test: FrACT-C, FrACT-E). Prediction intervals were established for SW compared to FrACT-C or -E and for FrACT-E compared to FrACT-C. Mixed linear effect models were applied for statistical analysis. Results From 241 subjects, 471 eyes were included: median age 36 years, range 4 – 88 years, 43.6% male, 56.4% female. Eyes included were either healthy or had various underlying ophthalmic conditions. Prediction intervals for SW to estimate FrACT-C or -E acuity showed a similar range compared to the prediction interval of FrACT-C for the estimation of FrACT-E acuity. For each acuity step, there was no influence of age. Up to an SW acuity of 0.7 logMAR, 80% of the subjects had a FrACT-C acuity that was at most 1.6 logMAR lines below, and for an SW acuity of 1.0 logMAR, FrACT-C acuity was not worse than 4 logMAR lines. Prediction intervals for eyes with refractive error, cataract, visual field loss and retinal disease did not differ significantly from healthy eyes in contrast to eyes with amblyopia or multiple ophthalmic disorders. SW correlated well to FrACT tests and results of a previous study fell within our prediction estimates. Conclusion Our prediction intervals for SW acuity may be used to estimate Snellen acuity (FrACT-C and -E) in the clinic in adults and children unable to cooperate in other acuity testing.

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2

LUTTON, EVELYNE. "EVOLUTION OF FRACTAL SHAPES FOR ARTISTS AND DESIGNERS." International Journal on Artificial Intelligence Tools 15, no. 04 (August 2006): 651–72. http://dx.doi.org/10.1142/s0218213006002850.

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We analyse in this paper the way randomness is considered and used in ArtiE-Fract. ArtiE-Fract is an interactive software, that allows the user (artist or designer) to explore the space of fractal 2D shapes with help of an interactive genetic programming scheme. The basic components of ArtiE-Fract are first described, then we focus on its use by two artists, illustrated by samples of their works. These "real life" tests have led us to implement additional components in the software. It seems obvious for the people who use ArtiE-Fract that this system is a versatile tool for creation, especially regarding the specific use of controlled random components.

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3

Fractal and Fractional Editorial Office. "Acknowledgement to Reviewers of Fractal Fract in 2019." Fractal and Fractional 4, no. 1 (January 23, 2020): 4. http://dx.doi.org/10.3390/fractalfract4010004.

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The editorial team greatly appreciates the reviewers who have dedicated their considerable time and expertise to the journal’s rigorous editorial process over the past 12 months, regardless of whether the papers are finally published or not [...]

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4

Roscani, Sabrina, and Domingo Tarzia. "An integral relationship for a fractional one-phase Stefan problem." Fractional Calculus and Applied Analysis 21, no. 4 (August 28, 2018): 901–18. http://dx.doi.org/10.1515/fca-2018-0049.

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Abstract A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered by using the Riemann–Liouville derivative. This formulation is more convenient than the one given in Roscani and Santillan (Fract. Calc. Appl. Anal., 16, No 4 (2013), 802–815) and Tarzia and Ceretani (Fract. Calc. Appl. Anal., 20, No 2 (2017), 399–421), because it allows us to work with Green’s identities (which does not apply when Caputo derivatives are considered). As a main result, an integral relationship between the temperature and the free boundary is obtained which is equivalent to the fractional Stefan condition. Moreover, an exact solution of similarity type expressed in terms of Wright functions is also given.

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5

Jammal, Alessandro A., Bruna G. Ferreira, Camila S. Zangalli, Jayme R. Vianna, Atalie C. Thompson, Paul H. Artes, Vital P. Costa, and Alexandre S. C. Reis. "Evaluation of contrast sensitivity in patients with advanced glaucoma: comparison of two tests." British Journal of Ophthalmology 104, no. 10 (January 23, 2020): 1418–22. http://dx.doi.org/10.1136/bjophthalmol-2019-315273.

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AimsTo evaluate contrast sensitivity (CS) in patients with advanced glaucomatous visual field damage, and to compare two clinical CS tests.MethodsThis was a cross-sectional test–retest study. Twenty-eight patients with open-angle glaucoma, visual acuity (VA) better than 20/40 and visual field mean deviation (MD) worse than −15 dB were enrolled. Patients underwent VA, visual field and CS testing with the Pelli-Robson (PR) chart and the Freiburg Visual Acuity and Contrast Test (FrACT). Retest measurements were obtained within 1 week to 1 month.ResultsMedian (IQR) age and MD were 61.5 (55.5 to 69.2) years and −27.7 (−29.7 to −22.7) dB, respectively. Median (IQR) VA was 0.08 logarithm minimum angle of resolution (0.02 to 0.16), corresponding to 20/25 (20/20 to 20/30). Median (IQR) CS was 1.35 (1.11 to 1.51) log units with the PR chart and 1.39 (1.24 to 1.64) log units with FrACT. VA explained less than 40% of the variance in CS (adjusted R2=0.36). CS estimates of both tests were closely related (rho=0.88, p=0.001), but CS was 0.09 log units higher with FrACT compared with the PR chart, and the 95% repeatability intervals (Bland-Altman) were 46% tighter with the PR chart.ConclusionsDespite near-normal VA, almost all patients showed moderate to profound deficits in CS. CS measurement provides additional information on central visual function in patients with advanced glaucoma.

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6

Reutskiy, Sergiy, and Zhuo-Jia Fu. "A semi-analytic method for fractional-order ordinary differential equations: Testing results." Fractional Calculus and Applied Analysis 21, no. 6 (December 19, 2018): 1598–618. http://dx.doi.org/10.1515/fca-2018-0084.

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Abstract The paper presents the testing results of a semi-analytic collocation method, using five benchmark problems published in a paper by Xue and Bai in Fract. Calc. Appl. Anal., Vol. 20, No 5 (2017), pp. 1305–1312, DOI: 10.1515/fca-2017-0068.

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7

Zheng, Xiaowei, Guanghua Xu, Yongcheng Wu, Yuhui Du, Renghao Liang, Sicong Zhang, and Kai Zhang. "Rapid, precise and objective visual acuity assessment method by combining FrACT and SSMVEPs." Journal of Vision 20, no. 11 (October 20, 2020): 989. http://dx.doi.org/10.1167/jov.20.11.989.

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8

Paris, Richard. "Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function." Mathematics 8, no. 3 (March 16, 2020): 428. http://dx.doi.org/10.3390/math8030428.

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We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [Fract. Calc. Appl. Anal. 21 (2018) 1156–1169]. We extend the definition of this function using the two-parameter Mittag-Leffler function. The expansions of the similarly extended sine and cosine integrals are also discussed. Numerical examples are presented to illustrate the accuracy of each type of expansion obtained.

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9

Mainardi, Francesco, and Enrico Masina. "Erratum: On modifications of the exponential integral with the Mittag-Leffler function." Fractional Calculus and Applied Analysis 23, no. 2 (April 28, 2020): 600–603. http://dx.doi.org/10.1515/fca-2020-0030.

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AbstractSome plots of the authors’ paper “On modifications of the exponential integral with the Mittag-Leffler function” (Fract. Calc. Appl. Anal. 21, No 5 (2018), pp. 1156–1169) were wrong. This note provides the correct plots contained in Fig. 4 concerning the generalized sine and cosine integrals.Figure 4The generalized sine integral (left) and the generalized cosine integral (right) versus x ∈ [0, 10] for ν = 0.25, 0.50, 0.75, 1

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10

Baraka, Abdelhak, Mohammed Matallah, Mustapha Djafour, and Mokhtar Bouazza. "Caractérisation des effets régissant le comportement dynamique du béton." Matériaux & Techniques 106, no. 5 (2018): 502. http://dx.doi.org/10.1051/mattech/2018043.

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La description du comportement du béton sous chargements dynamiques (explosions, collisions, séismes…) fait actuellement l’objet de nombreux travaux de recherches. Bien que la modélisation reste complexe pour ce matériau à cause de la présence simultanée de plusieurs phénomènes (l’endommagement, les effets d’inertie et de viscosité, la fissuration…), un bon nombre d’approches ont été proposé en associant ces phénomènes (endommagement (Pedersen et al., Eng. Fract. Mech. 75, 3782 (2008) [1]), viscosité (Bazant et al., J. Eng. Mech. ASCE 126(9), 971 (2000a); Bazant et al., J. Eng. Mech. ASCE 126(9), 962 (2000b) [2,3])…, effet d’inertie (Reinhardt & Weerheijm, Int. J. Fract. 51, 31 (1991) [4])). Avec une loi d’endommagement, ce travail formule une description du comportement dynamique du béton en traction et en compression. Fondée sur des concepts physiques (la rigidité non linéaire endommageable associée à la déformation, la viscosité, l’inertie associée à l’accélération et la rupture par résonance), cette loi décrit l’évolution de ces différents effets intervenants lors d’un chargement dynamique du matériau. Enfin, sous la lumière des résultats, l’article propose une interprétation physique à la rupture par écaillage qui apparaît dans le béton surtout sous des charges impulsionnelles en traction (un plan de rupture droit, qui passe parfois à travers les granulats).

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11

Heriot, Wilson J. "Discussion by Wilson J. Heriot, FRACO, FRACS." Ophthalmology 106, no. 10 (October 1999): 1906–7. http://dx.doi.org/10.1016/s0161-6420(99)90435-9.

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12

Molloy, H. F. "Dr Adrian M.Johnson, CBE, FRACP, FRACR, FACD." British Journal of Dermatology 121, no. 1 (July 1989): 139–41. http://dx.doi.org/10.1111/j.1365-2133.1989.tb01411.x.

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13

Constable, Ian. "David Jeremiah McAuliffe frcse, frcs, fracs, fraco." Australian and New Zealand Journal of Ophthalmology 18, no. 1 (February 1990): 115. http://dx.doi.org/10.1111/j.1442-9071.1990.tb00598.x.

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14

Donoghue, Michael F., and Brian H. R. Hill. "ADRIAN MACKEY JOHNSON CMC FRACP, FRACR, FACD." Australasian Journal of Dermatology 30, no. 1 (April 1989): 57–59. http://dx.doi.org/10.1111/j.1440-0960.1989.tb00413.x.

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15

Verco, Christopher J. "Peter Willis Verco MD, FRACP, FRCR, FRACR, DDU." Medical Journal of Australia 173, no. 4 (August 2000): 207. http://dx.doi.org/10.5694/j.1326-5377.2000.tb125603.x.

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16

Mulhearn, Richard J. "James Stewart Rogers MBBS, DO, DTM, FRACO, FRACS." Medical Journal of Australia 168, no. 4 (February 1998): 184. http://dx.doi.org/10.5694/j.1326-5377.1998.tb126781.x.

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17

Ragab, A. R., S. N. Samy, and Ch A. R. Saleh. "Prediction of Central Bursting in Drawing and Extrusion of Metals." Journal of Manufacturing Science and Engineering 127, no. 3 (June 23, 2004): 698–702. http://dx.doi.org/10.1115/1.1961982.

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In this work central bursting in drawing and extrusion of metals is investigated. The analysis is based on a modified stress distribution within the die zone due to Shield (Shield, R. T., 1955, J. Mech. Phys. Solids, 3, pp. 246–258) together with Gurson–Tvergaard’s yield function (Tvergaard, V., 1981, Int. J. Fract., 17, pp. 389–407) and its associated flow rule for voided solids. The effects of hardening and evolution of void shape on void growth are considered. Various fracture criteria are employed to predict the process conditions at which central bursting occurs. The first criterion is due to Avitzur (Avitzur, B., 1968, ASME J. Eng. Ind., 90, pp. 79–91 and Avitzur, B., and Choi, J. C., 1986, ASME J. Eng. Ind., 108, pp. 317–321), the second and simplest criterion is based on vanishing mean stress while a suggested third criterion depends on the current value of the void volume fraction. Two other criteria which are basically due to Thomason’s internal necking condition (Thomason, P. F., 1990, Ductile Fracture of Metals, Pergamon, Oxford) as well as McClintock’s shear band formation criterion are applied (McClintock, F. A., Kaplan, S. M., and Berg, C. S., 1966, Int. J. Fract. Mech., 2, p. 614, and McClintock, F. A., 1968, in Ductility, ASM, Metals, Park, OH). The critical process conditions are predicted and compared with the available experimental data. Comparison showed that predictions based on the vanishing mean stress and the current void volume fraction criteria are closer to experiments than those based on Thomason’s internal necking and McClintock criteria.

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18

Wang, G. S. "Erratum to “The interaction of doubly periodic cracks” [Theoret. Appl. Fract. Mech. 42 (2004) 249–294]." Theoretical and Applied Fracture Mechanics 43, no. 1 (March 2005): 1–3. http://dx.doi.org/10.1016/j.tafmec.2004.12.001.

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19

Purohit, S. D. "Solutions of Fractional Partial Differential Equations of Quantum Mechanics." Advances in Applied Mathematics and Mechanics 5, no. 05 (October 2013): 639–51. http://dx.doi.org/10.4208/aamm.12-m1298.

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AbstractThe aim of this article is to investigate the solutions of generalized fractional partial differential equations involving Hilfer time fractional derivative and the space fractional generalized Laplace operators, occurring in quantum mechanics. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms, in terms of the Fox’sH-function. Several special cases as solutions of one dimensional non-homogeneous fractional equations occurring in the quantum mechanics are presented. The results given earlier by Saxena et al. [Fract. Calc. Appl. Anal., 13(2) (2010), pp. 177–190] and Purohit and Kalla [J. Phys. A Math. Theor., 44 (4) (2011), 045202] follow as special cases of our findings.

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20

Lazopoulos, Konstantinos A., and Anastasios K. Lazopoulos. "Fractional vector calculus and fluid mechanics." Journal of the Mechanical Behavior of Materials 26, no. 1-2 (April 25, 2017): 43–54. http://dx.doi.org/10.1515/jmbm-2017-0012.

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AbstractBasic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85–104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy’s flow in porous media is studied.

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21

Ferreira, Rui A. C. "Addendum to “Some Discrete Fractional Lyapunov-type inequalities” [Fract. Differ. Calc. 5 (2015), no. 1, 87-92]." Fractional Differential Calculus, no. 2 (2018): 357–59. http://dx.doi.org/10.7153/fdc-2018-08-22.

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22

Lange, C., N. Feltgen, B. Junker, K. Schulze-Bonsel, and M. Bach. "Resolving the clinical acuity categories “hand motion” and “counting fingers” using the Freiburg Visual Acuity Test (FrACT)." Graefe's Archive for Clinical and Experimental Ophthalmology 247, no. 1 (September 3, 2008): 137–42. http://dx.doi.org/10.1007/s00417-008-0926-0.

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23

Kennedy, Stephen K., and Wei-Hsiung Lin. "Fract—A fortran subroutine to calculate the variables necessary to determine the fractal dimension of closed forms." Computers & Geosciences 12, no. 5 (January 1986): 705–12. http://dx.doi.org/10.1016/0098-3004(86)90046-4.

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24

Weng, Xiaowei, Dimitry Chuprakov, Olga Kresse, Romain Prioul, and Haotian Wang. "Hydraulic fracture-height containment by permeable weak bedding interfaces." GEOPHYSICS 83, no. 3 (May 1, 2018): MR137—MR152. http://dx.doi.org/10.1190/geo2017-0048.1.

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In laminated formations, the vertical height growth of a hydraulic fracture can be strongly influenced by the interaction of the fracture tip with the bedding interfaces it crosses. A weak interface may fail in shear and then slip, depending on the strength and frictional properties, the effective vertical stress at the interface, and the net pressure. Shear failure and slippage at the interface can retard the height growth or even stop it completely. A 2D analytical model called the FracT model has been developed that examines the shear slippage along the bedding interface adjacent to the fracture tip and the resulting blunting of the fracture tip at the interface, as well as the stress condition on the face opposite from the hydraulic fracture tip for possible fracture nucleation that leads to fracture crossing. The growth of the shear slippage along the interface with time is coupled with the fluid flow into the permeable interface. A parametric study has been carried out to investigate the key formation parameters that influence the crossing/arrest of the fracture at the bedding interface and the shear slippage and depth of fluid penetration into the interface. The study suggests that the interfacial coefficient of friction and the ratio of the vertical to minimum horizontal stress are two of the most influential parameters governing fracture arrest by a weak interface. For the fracture tip to be arrested at the interface, the vertical stress acting on the interface must be close to the minimum horizontal stress or the interfacial coefficient of friction must be very small. The FracT model has also been integrated into a pseudo-3D-based complex hydraulic fracture model. This quantitative mechanistic model that incorporates a bedding-plane slip-driven mechanism is a necessary step to understand and bridge the characterization (sonic) and monitoring (microseismic) observations.

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25

Thomson, John R. "Kenneth George Howsam MB BS, DO, FRACS, FRACO, FRACMA, FACO." Medical Journal of Australia 189, no. 7 (October 2008): 401. http://dx.doi.org/10.5694/j.1326-5377.2008.tb02090.x.

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26

Donovan, John W. "Gwyn Howells CB, MB BS, MD, FRC P, FRACP, FRACM." Medical Journal of Australia 168, no. 9 (May 1998): 457. http://dx.doi.org/10.5694/j.1326-5377.1998.tb139028.x.

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27

Gomez, Florence. "Saint-Gobain r�fract� dans les Trente Glorieuses. Images d�une soci�t� prise entre identit� et modernisation." Revue fran�aise d'histoire �conomique N�6, no. 2 (2016): 56. http://dx.doi.org/10.3917/rfhe.006.0056.

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28

Ferro, G., J. M. Tulliani, A. Lopez, and P. Jagdale. "Corrigendum to “New cementitious composite building material with enhanced toughness” [Theor. Appl. Fract. Mech. 76 (2015) 67–74]." Theoretical and Applied Fracture Mechanics 80 (December 2015): 267. http://dx.doi.org/10.1016/j.tafmec.2015.07.008.

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29

Cao, Jian, H. M. Srivastava, and Zhi-Guo Liu. "Some iterated fractional q-integrals and their applications." Fractional Calculus and Applied Analysis 21, no. 3 (June 26, 2018): 672–95. http://dx.doi.org/10.1515/fca-2018-0036.

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Abstract Motivated by the fact that fractional q-integrals play important roles in numerous areas of mathematical, physical and engineering sciences, it is natural to consider the corresponding iterated fractional q-integrals. The main object of this paper is to define these iterated fractional q-integrals, to build the relations between iterated fractional q-integrals and certain families of generating functions for q-polynomials and to generalize two fractional q-identities which are given in a recent work [Fract. Calc. Appl. Anal. 10 (2007), 359–373]. As applications of the main results presented here, we deduce several bilinear generating functions, Srivastava-Agarwal type generating functions, multilinear generating functions and U(n + 1) type generating functions for the Rajković-Marinković-Stanković polynomials.

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30

Anderson, Fred. "Adrian Mackey Johnson CBE, MB BS, OTR, OOM, FRACR, FRACP, FACO." Medical Journal of Australia 154, no. 4 (February 1991): 289. http://dx.doi.org/10.5694/j.1326-5377.1991.tb121097.x.

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Hansen-Dörr, Arne Claus, Franz Dammaß, René de Borst, and Markus Kästner. "Erratum to “Phase-field modeling of crack branching and deflection in heterogeneous media” [Eng. Fract. Mech. 232 (2020) 107004]." Engineering Fracture Mechanics 241 (January 2021): 107449. http://dx.doi.org/10.1016/j.engfracmech.2020.107449.

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32

Giglio, M., S. Beretta, D. Colombo, U. Mariani, and G. Ratti. "Corrigendum to ‘‘Defect tolerance assessment of a helicopter component subjected to multiaxial load’’ [Eng. Fract. Mech. 77 (2010) 2479–2490]." Engineering Fracture Mechanics 78, no. 9 (June 2011): 2095. http://dx.doi.org/10.1016/j.engfracmech.2011.04.001.

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Negi, Alok, and Sachin Kumar. "Corrigendum to “Localizing gradient damage model with smoothed stress based anisotropic nonlocal interactions” [Eng. Fract. Mech. 214 (2019) 21–39]." Engineering Fracture Mechanics 230 (May 2020): 106976. http://dx.doi.org/10.1016/j.engfracmech.2020.106976.

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34

Martínez, J. H., P. Ariza, M. Zanin, D. Papo, F. Maestú, J. M. Pastor, R. Bajo, Stefano Boccaletti, and J. M. Buldú. "Corrigendum to “Anomalous Consistency in Mild Cognitive Impairment: A complex networks approach” [Chaos Solitons Fract. J. 70 (2014) 144–155]." Chaos, Solitons & Fractals 73 (April 2015): 202. http://dx.doi.org/10.1016/j.chaos.2015.01.008.

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Anton, Alexandra, Daniel Böhringer, Michael Bach, Thomas Reinhard, and Florian Birnbaum. "Contrast sensitivity with bifocal intraocular lenses is halved, as measured with the Freiburg Vision Test (FrACT), yet patients are happy." Graefe's Archive for Clinical and Experimental Ophthalmology 252, no. 3 (January 17, 2014): 539–44. http://dx.doi.org/10.1007/s00417-014-2565-y.

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36

Meyers, Derek. "John Llewellyn Colvin AM, RFD, MB BS, DO, FRCS(Edin), FRACS, FRACO." Medical Journal of Australia 184, no. 4 (February 2006): 184. http://dx.doi.org/10.5694/j.1326-5377.2006.tb00183.x.

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37

Jones, M. K., M. F. Horstemeyer, and A. D. Belvin. "A Multiscale Analysis of Void Coalescence in Nickel." Journal of Engineering Materials and Technology 129, no. 1 (June 9, 2006): 94–104. http://dx.doi.org/10.1115/1.2400265.

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An internal state variable void coalescence equation developed by Horstemeyer, Lathrop, Gokhale, and Dighe (2000, Theor. Appl. Fract. Mech., 33(1), pp. 31–47) that comprises void impingement and void sheet mechanisms is updated based on three-dimensional micromechanical simulations and novel experiments. This macroscale coalescence equation, developed originally from two-dimensional finite element simulations, was formulated to enhance void growth. In this study, three-dimensional micromechanical finite element simulations were employed using cylindrical and spherical void geometries in nickel that were validated by experiments. The number of voids, void orientation, and void spacing were all varied and tested and simulated under uniaxial loading conditions. The micromechanical results showed excellent agreement with experiments in terms of void volume fractions versus strain and local void geometry images. Perhaps more importantly, the macroscale internal state variable void coalescence equation did not require a functional form change but just a coefficient value modification.

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38

Chen, Chao-Ping, and Feng Qi. "Completely monotonic function associated with the Gamma functions and proof of Wallis' inequality." Tamkang Journal of Mathematics 36, no. 4 (December 31, 2005): 303–7. http://dx.doi.org/10.5556/j.tkjm.36.2005.101.

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We prove: (i) A logarithmically completely monotonic function is completely monotonic. (ii) For $ x>0 $ and $ n=0, 1, 2, \ldots $, then$$ (-1)^{n}\left(\ln \frac{x \Gamma(x)}{\sqrt{x+1/4}\,\Gamma(x+1/2)}\right)^{(n)}>0. $$(iii) For all natural numbers $ n $, then$$ \frac1{\sqrt{\pi(n+4/ \pi-1)}}\leq \frac{(2n-1)!!}{(2n)!!}

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39

Kilambi, Sreelatha, and Steven M. Tipton. "Corrigendum to “Algorithm to estimate notch root strain in tension using numerical analysis”. [Theor. Appl. Fract. Mech. 77 (2015) 1–13]." Theoretical and Applied Fracture Mechanics 85 (October 2016): 457. http://dx.doi.org/10.1016/j.tafmec.2016.04.005.

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40

"Fract-ED." Choice Reviews Online 36, no. 03 (November 1, 1998): 36–1615. http://dx.doi.org/10.5860/choice.36-1615.

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41

Chica, Edwin L., Antolín L. Ibán, José M. G. Terán, and Pablo M. López-Reyes. "Influence of Ductile Damage Evolution on the Collapse Load of Frames." Journal of Applied Mechanics 77, no. 3 (February 4, 2010). http://dx.doi.org/10.1115/1.4000427.

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In this note we analyze the influence of four damage models on the collapse load of a structure. The models considered here have been developed using the hypothesis based on the concept of effective stress and the principle of strain equivalence and they were proposed by Lemaitre and Chaboche (1990, Mechanics of Solid Materials), Wang (1992, “Unified CDM Model and Local Criterion for Ductile Fracture—I. Unified CDM Model for Ductile Fracture,” Eng. Fract. Mech., 42, pp. 177–183), Chandrakanth and Pandey (1995, “An Isotropic Damage Model for Ductile Material,” Eng. Fract. Mech., 50, pp. 457–465), and Bonora (1997, “A Nonlinear CDM Model for Ductile Failure,” Eng. Fract. Mech., 58, pp. 11–28). The differences between them consist mainly in the form of the dissipative potential from which the kinetic law of damage is derived and also in the assumptions made about some parameters of the material.

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42

"Acknowledgement to Reviewers of Fractal Fract in 2018." Fractal and Fractional 3, no. 1 (January 16, 2019): 2. http://dx.doi.org/10.3390/fractalfract3010002.

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43

"Fatigue crack closureDavidson, D.L. Eng. Fract. Mech. 1991 38, (6), 393–402." International Journal of Fatigue 13, no. 6 (November 1991): 509. http://dx.doi.org/10.1016/0142-1123(91)90589-q.

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44

Samko, Stefan. "Remark to the paper of S. Samko, “A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n”, from FCAA, vol. 16, No 2, 2013." Fractional Calculus and Applied Analysis 17, no. 1 (January 1, 2014). http://dx.doi.org/10.2478/s13540-014-0167-3.

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AbstractWe improve the formulation of the main statement in the paper “Note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n”, published in this journal, Fract. Calc. Appl. Anal., Vol. 16, No 2 (2013), DOI: 10.2478/s13540-013-0023-x; http://link.springer.com/article/10.2478/s13540-013-0023-x.

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45

Fabrizio, Mauro. "Some Remarks on the Fractional Cattaneo-Maxwell Equation for the Heat Propagation." Fractional Calculus and Applied Analysis 18, no. 4 (January 1, 2015). http://dx.doi.org/10.1515/fca-2015-0061.

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AbstractWith this short note, I would like to clarify some of the results contained in our previous paper [5]: M. Fabrizio, Fractional rheological models for thermomechanical systems. Dissipation and free energies. Fract. Calc. Appl. Anal. 17, No 1 (2014), 206-223; DOI: 10.2478/s13540-014-0163-7; http://www.degruyter.com/view/j/fca.2014.17.issue-1/issue-files/fca.2014.17.issue-1.xml, concerning the thermodynamic conditions for fractional models of heat propagation, which generalize the classical Cattaneo-Maxwell and Fourier laws.

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"A fatigue crack growth thresholdMarci, G. Eng. Fract. Mech. Feb. 1992 41, (3), 367–385." International Journal of Fatigue 15, no. 1 (January 1993): 68. http://dx.doi.org/10.1016/0142-1123(93)90137-f.

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"Stochastic models of fatigue crack growthLangley, R.S. Eng. Fract. Mech. 1989 32, (1), 137–145." International Journal of Fatigue 11, no. 4 (July 1989): 283. http://dx.doi.org/10.1016/0142-1123(89)90377-0.

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"A model for high cycle fatigueMazumfar, P.K. Eng Fract Mech (Apr 1992) 416 pp 907–917." International Journal of Fatigue 15, no. 3 (May 1993): 252. http://dx.doi.org/10.1016/0142-1123(93)90220-k.

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"Modelling delay and thickness effects in fatigueClayton, J.Q. Eng. Fract. Mech. 1989 32, (2), 289–308." International Journal of Fatigue 11, no. 4 (July 1989): 286. http://dx.doi.org/10.1016/0142-1123(89)90408-8.

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"Fracture mechanics of delamination in ARALL laminatesYeh, J.R. Eng. Fract. Mech. 1988, 30, (6), 827–837." International Journal of Fatigue 11, no. 3 (May 1989): 204. http://dx.doi.org/10.1016/0142-1123(89)90450-7.

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