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19A658 flux of Brzeski, Cohen and 10A206 15P2083 N88-33849[P] Brzeski, Boone and Cohen BROCKMAN, L..Q:

Does there exist a non-trivial homomorphism $\mathbb{Z}\to \mathbb{Z}_{49}\times \mathbb{Z}_{49}$

Does there exist a non-trivial homomorphism $\mathbb{Z}\to \mathbb{Z}_{49}\times \mathbb{Z}_{49}$?
My approach: Since $\mathbb{Z}_{49}\times \mathbb{Z}_{49}$ is a abelian group of order $49^{2}=2401$, then by Cauchy Theorem we know that $\mathbb{Z}_{49}\times \mathbb{Z}_{49}$ is cyclic group. Now let’s look for a minimal generator of $\mathbb{Z}_{49}\times \mathbb{Z}_{49}$,then it is either
$(1,0)$ or $(0,1)$,we can not have $(1,1)$ or $(-1,-1)$ because it will give us a cyclic group of order $8$ or $16$, respectively. Now it will take us to contradiction, because such a minimal generator would not generate the group.
But I am confused when I am faced to a problem where I need to prove a homomorphism is non-trivial(for the solution of the problem, the answer

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Timing Solution Crack Software

All references to the following are hereby incorporated by reference herein:
1) G. Conner, A. F. Turner, S. B. Young and J. P. Hou, “Particle recognition and classification through distortion measurement and characterization,” Journal of Microscopy, vol. 198, pp. 9–29, 1996.
2) S. A. McQuarrie, “Statistical Mechanics,” New York: J. Wiley & Sons, Inc., 1970.
3) J. D. Nohara, “Optimal crack-velocity determination from extended video data,” Appl. Phys. Lett. 56(6), Aug. 24, 1990, pp. 650–652.
4) R. A. Roemer and R. W. Ray, “Cracktip field emission in brittle systems,” Progr. Quant. Electr., vol. 12, pp. 1–49, 1987.
5) G. Schenk and R. D. James, “Detection and Measurement of Crack Velocity,” SPIE Proceedings, vol. 2847, 1997.
6) P. L. Warn, “Some numerical methods for fracture mechanics,” Mater. Res. Soc. Symp. Proc., vol. 37, pp. 435–444, 1989.
7) P. L. Warn, “Finite element methods for fracture mechanics,” pp. 105–118, Proceedings of the 1986 Torino Conference, Politecnico di Torino, Italy, IEEE Press.
8) R. C. Brockman and R. W. Brockman, “Reversible plasticity theory and application to fiberglass and carbon composites,” ASME J. Mech. Design, vol. 124, pp. 74–81, 1992.
9) M. H. Bahrami, P. L. Williams, and J. B. van der Veer, “State-of-the-art in computational modeling of microcrack growth,” Comput. Mater. Sci., vol. 33, pp. 241–261, 2004.
FIG. 1 is a graph 100 that illustrates a distribution of maximum crack extension 100 for a collection of cracks 102 at various locations 104 of a specimen 105 (or plate). For example, the graph 100 can be made by measuring max extents
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