Sharif Digital Repository

Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully label graphs. In this paper, first a new approach based on the mathematical programming technique is presented to model the graceful labeling problem. Then a “branching method” is developed to solve the problem for special classes of graphs. Computational results show the efficiency of the proposed algorithm for different classes of graphs. One of the interesting results of our model is in the class of trees. The largest tree known to be graceful has at most 27 vertices... 

Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully label graphs. In this paper, first a new approach based on the mathematical programming technique is presented to model the graceful labeling problem. Then a “branching method” is developed to solve the problem for special classes of graphs. Computational results show the efficiency of the proposed algorithm for different classes of graphs. One of the interesting results of our model is in the class of trees. The largest tree known to be graceful has at most 27 vertices... 

We investigate short-term non-linearity of solar irradiance fluctuations using the multifractal detrended fluctuation analysis (MFDFA). The MFDFA shows that time series of solar irradiance have a long range correlation function with a multifractal behavior. We apply this method to solar irradiance time series from several regions around the world with resolutions of seconds and minutes. The obtained generalized Hurst and Renyi exponents h(q) and τ(q) suggest the non-linear and non-stationary essence of measured irradiance time series. Also, we analyze shuffled, random phase, and rank-wised surrogated data to reveal the nature of the multifractality and conclude that linear and non-linear... 

Abstract: Parkinson has remained as one of the most difficult diseases to diagnose, as there are no biomarkers to be measured, and this requires one patient to do neurological and physical examinations. As Parkinson is a progressive disease, accurate detection of its symptoms is a crucial factor for therapeutic reasons. In this study, we perform Multifractal Detrended Fluctuation Analysis (MFDFA) on measured keystroke time series for three different categories of subjects: healthy, early-PD, and De-Novo patients. We have observed different scaling behavior in terms of multifractality of the measured time series, which can be used as a practical tool for diagnosis purposes. Additionally, the... 

There are mathematical errors in eqn (17) and (19) in the original article and within the text. The corrected equations and text are as given below: (formula presented) where z is the dynamic exponent and F is a scaling function. Additionally, the exponential function on the fifth page of the article, line 43 should read: The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.. © 2021 Royal Society of Chemistry. All rights reserved  

Owing to the local/heterogeneous structures in supercooled liquids, after several decades of research, it is now clear that supercooled liquids are structurally different from their conventional liquid counterparts. Accordingly, an approach based on a local probe should provide a better understanding about the local mechanical properties as well as heterogeneous structures. Recently, the superiority of active microrheology over global rheology has been demonstrated [Yu et al., Sci. Adv., 2020, 6, 8766]. Here, we elaborate this new avenue of research and provide more evidence for such superiority. We report on the results of an extensive molecular dynamics simulation of active microrheology...