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Register a new userOn Bifurcated supertasks and related questions
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Antonio Leon
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Bifurcated supertasks entail the actual infinite division of time (accelerated system of reference) as well as the existence of half-curves of infinite length (supertask system of reference). This paper analyzes both issues from a critique perspective. It also analyzes a conflictive case of hypercomputation performed by means of a bifurcated supertask. The results of these analyzes suggest the convenience of reviewing certain foundational aspects of infinitist theories.
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We obtain explicit lower bounds on multiplicative order of elements that have more general form than finite field Gauss period. In a partial case of Gauss period this bound improves the previous bound of O.Ahmadi, I.E.Shparlinski and J.F.Voloch
The concept of graceful labels was proposed by Rosa, scholars began to study graceful labels of various graphs and obtained relevant results.Let the graph is a bipartite graceful graph, we have proved some graphs are graceful labeling in this paper.
We present a new necessary and sufficient condition to determine the entanglement status of an arbitrary N-qubit quantum state (maybe pure or mixed) represented by a density matrix. A necessary condition satisfied by separable bipartite quantum states was obtained by A. Peres, [1]. A. Peres showed that if a bipartite state represented by the density matrix is separable then its partial transpose is positive semidefinite and has no negative eigenvalues. In other words, if the partial transpose is not positive semidefinite and so one or more of its eigenvalues are negative then the state represented by the corresponding density matrix is entangled. It was then shown by M. Horodecki et.al, [2], that this necessary condition is also sufficient for two-by-two and two-by-three dimensional systems. However, in other dimensions, it was shown by P. Horodecki, [3], that the criterion due to A. Peres is not sufficient. In this paper, we develop a new approach and a new criterion for deciding the entanglement status of the states represented by the density matrices corresponding to N-qubit systems. We begin with a 2-qubit case and then show that these results for 2-qubit systems can be extended to N-qubit systems by proceeding along similar lines. We discuss few examples to illustrate the method proposed in this paper for testing the entanglement status of few density matrices.
The yielding of disordered materials is a complex transition involving significant changes of the materials microstructure and dynamics. After yielding, many soft materials recover their quiescent properties over time as they age. There remains, however, a lack of understanding of the nature of this recovery. Here, we elucidate the mechanisms by which fibrillar networks restore their ability to support stress after yielding. Crucially, we observe that the aging response bifurcates around a critical stress $sigma_mathrm{c}$, which is equivalent to the material yield stress. After an initial yielding event, fibrillar networks subsequently yield faster and at lower magnitudes of stress. For stresses $sigma<sigma_mathrm{c}$, the time to yielding increases with waiting time $t_mathrm{w}$ and diverges once the network has restored sufficient entanglement density to support the stress. When $sigma > sigma_mathrm{c}$, the yield time instead plateaus at a finite value because the developed network density is insufficient to support the applied stress. We quantitatively relate the yielding and aging behavior of the network to the competition between stress-induced disentanglement and dynamic fluctuations of the fibrils rebuilding the network. The bifurcation in the material response around $sigma_c$ provides a new possibility to more rigorously localize the yield stress in disordered materials with time-dependent behavior.
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule and Laplace transform. It is analytically shown that the commonly used Leibniz rule cannot be applied for Caputo derivative. Similarly, the well-known Laplace transform of Riemann-Liouville derivative is doubtful for n-th continuously differentiable function. By the aid of this series representation, the exact formula of Caputo Leibniz rule and the explanation of Riemann-Liouville Laplace transform are presented. Finally, three illustrative examples are revisited to confirm the obtained results.
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