R eferences [1] S. Asawasamrit, KK-isomorphism and its properties , Int. J. Pure Appl. Math. 78 (2012) 65–73. [2] J. Hao and C.X. Li, On ideals of an ideal in a BCI-algebra , Sci. Math. Jpn. (in Editione Electronica) 10 (2004) 493–500. [3] Q.P. Hu and X. Li, On BCH-algebras , Math. Semin. Notes, Kobe Univ. 11 (1983) 313–320. [4] A. Iampan, A new branch of the logical algebra: UP-algebras , J. Algebra Relat. Top. 5 (2017) 35–54. doi:10.22124/JART.2017.2403 [5] A. Iampan, Introducing fully UP-semigroups , Discuss. Math

### Aiyared Iampan

R eferences [1] S.S. Ahn and Y.H. Kim, On BE-semigroups , Int. J. Math. Math. Sci. (2011) Article ID 676020, 2011. doi:10.1155/2011/676020 [2] J.C. Endam and J.P. Vilela, On JB-semigroups , Appl. Math. Sci. 9 (2015) 2901–2911. doi:10.12988/ams.2015.46427 [3] A. Iampan, A new branch of the logical algebra: UP-algebras , J. Algebra Relat. Top. 5 (2017) 35–54. doi:10.22124/JART.2017.2403 [4] Y.B. Jun, S.M. Hong and E.H. Roh, BCI-semigroups , Honam Math. J. 15 (1993) 59–64. [5] Y.B. Jun, E.H. Roh and X.L. Xin, I

### Óscar J. Falcón, Raúl M. Falcón, Juan Núñez, Ana M. Pacheco and M. Trinidad Villar

del IV Encuentro Andaluz de Matemfiatica Discreta (2005), 99-104. [4] A. Carriazo, L.M. Fernfiandez and J. Núñez, Combinatorial structures associated with Lie algebras of finite dimension, Linear Algebra and its Applications 389 (2004), 43-61. [5] S. Cicalò, W. de Graaf and C. Schneider, Six-dimensional nilpotent Lie algebras, Linear Algebra Appl. 436:1 (2012), 163-189. [6] O. J. Falcón, R. M. Falcón and J. Núñez, Isomorphism and isotopism classes of filiform Lie algebras of dimension up to seven, Submitted, 2015

### Nataša Janjić, Darko Kapor, Dragan Doder and Igor Savić

for drag effect, wind effect and velocity included. In our approach, we used the polynomial model for the distance vs time combined with the solutions of the algebraic cubic equation. Time effect of the wind influence implies that the wind blowing during the race into sprinters’ back (tail wind) contributes to a decrease, and in the case of a frontal blow (head wind), to an increase of the final time t f of the run. The increase of the final time for the head wind is larger than the corresponding decrease of the final time in the case of the tail wind. In

### Arkadiusz Gąsecki

References [1]ALBRECHT. M.-CID, C.: Algebraic techniques in differential cryptanalysis, IACR Cryptology ePrint Archive, Report 2008/177. [2]GASECKI. A.- MISZTAL, M.: Application of algebraic techniques in differential crypt- analysis aganst block cipher DES, MUT Bulletin, Warsaw, 2011. [3]BIHAM, E.-SHAMIR, A.: Differential cryptanalysis of DES-like cryptosystems, in: Ad- vances in Cryptology-CRYPTO '90 (A. Menezes et al., eds.), Santa Barbara, USA, 1990, Lecture Notes in Comput. Sci., Vol. 537, Springer

### Michel Goze, Paola Piu and Elisabeth Remm

References 1. Bahtürin, Y.; Goze, M. - Z2 x Z 2-symmetric spaces, Pacific J. Math., 236 (2008), 1-21. 10.2140/pjm.2008.236.1 2. BahtüRIN, Y.; Goze, M.; Remm, E. - Group gradings on Lie Algebras and Applications to Geometry: II. Chapter 1, Developments and Retrospectives in Lie theory, Developments in Mathematics, 37, G. Mason and al. editors, Springer International Publishing, 2014, DOI 10.1007/978 - 3 - 319 - 09934 - 7-1. 3. Calvaruso, G. - Homogeneous structures on three-dimensional Lorentzian manifolds, J. Geom. Phys., 57 (2007), 1279-1291. 10

### István Szöllősi

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### Paweł Kapusta, Michał Majchrowicz, Dominik Sankowski and Robert Banasiak

, Corsica, France, 2011 [9] J.W. Ruge, K. St uben, Algebraic Multigrid, Multigrid Methods (Frontier in Applied Mathematics), Society for industrial Mathematics, Ch. 4, pp. 73 -130, 1994 [10] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical recipses in C++, Second Edition, The Press Syndicate of the University of Cambridge, 1992 [11] D. Michels, Sparse-Matrix-CG-Solver in CUDA, Proceedings of CESCG 2011: The 15th Central European Seminar on Computer Graphics, 2011 [12] B.D. Kirk

### Lothar Seybold, Marcin Witczak, Paweł Majdzik and Ralf Stetter

References Abrams, M., Doraswamy, N. and Mathur, A. (1992). Chitra: Visual analysis of parallel and distributed programs in the time, event, and frequency domains, IEEE Transactions on Parallel and Distributed Systems 3 (6): 672–685. Baccelli, F., Cohen, G., Olsder, G.J. and Quadrat, J.-P. (1992). Synchronization and Linearity: An Algebra for Discrete Event Systems , John Wiley & Sons Ltd., Chichester. Blanke, M., Schröder, J., Kinnaert, M., Lunze, J. and Staroswiecki, M. (2006). Diagnosis and Fault-Tolerant Control , Springer, Berlin

### Cristina Almeida Magalhães, Perrin Smith Neto, Pedro Américo Almeida Magalhães Júnior and Clovis Sperb de Barcellos

## Abstract

Digital photoelasticity is an important optical metrology follow-up for stress and strain analysis using full-field digital photographic images. Advances in digital image processing, data acquisition, procedures for pattern recognition and storage capacity enable the use of the computer-aided technique in automation and facilitate improvement of the digital photoelastic technique. The objective of this research is to find new equations for a novel phase-shifting method in digital photoelasticity. Some innovations are proposed. In terms of phaseshifting, only the analyzer is rotated, and the other equations are deduced by applying a new numerical technique instead of the usual algebraic techniques. This approach can be used to calculate a larger sequence of images. Each image represents a pattern and a measurement of the stresses present in the object. A decrease in the mean errors was obtained by increasing the number of observations. A reduction in the difference between the theoretical and experimental values of stresses was obtained by increasing the number of images in the equations for calculating phase. Every photographic image has errors and random noise, but the uncertainties due to these effects can be reduced with a larger number of observations. The proposed method with many images and high accuracy is a good alternative to the photoelastic techniques.