arXiv subjects

Mohammad Arab

Publications and source records attributed to Mohammad Arab.

6 recordsLinked to original sources

arXiv2026

Cosmological perturbations and clustering mechanisms in multifield dark energy

We investigate the cosmological signatures of two-field dark energy with curved field-space geometry. We numerically solve the background and linear perturbation equations and assess the validity of the effective single-field description. We examine three distinct dark-energy clustering mechanisms: effective sound-speed suppression, dynamical excitation of the heavy mode, and tachyonic instabilities induced by field-space curvature, and explore their possible imprints on the matter power spectrum and cosmic microwave background anisotropies. Our analysis establishes multifield dark energy as a rich and testable extension of quintessence, with observable clustering signatures relevant to current and future cosmological surveys.

astro-ph.CO↗

arXiv2021

Creative proofs in combinations

In this article, we present four issues and provide a creative and concise proof for each of them. The four issues are: 1- Inequality $\frac{1}{\sqrt{n\pi+\frac{\pi}{2}}}<\frac{\binom{2n}{n}}{2^{2n}}<\frac{1}{\sqrt{n\pi}}$ 2- A special case of Jonathan Wilde's problem 3- Combination series 4- A feature of powerful numbers.

math.CO↗

arXiv2021

Providing an Approach to Predicting Customer Quality in E-Commerce Social Networks Based on Big Data and Unsupervised Learning Method

One of the goals of every business enterprise is to increase customer loyalty. The degree of customer loyalty is called customer quality which its forecasting will affect strategic marketing practices. The purpose of this study is to predict the quality of customers of large e-commerce social networks by big data algorithms and unsupervised learning. For this purpose, a graph-based social network analysis framework was used for community detection in the Stanford Network Analysis Platform (SNAP). Then in the found communities, the quality of customers was predicted. The results showed that various visits with an impact of 37.13% can have the greatest impact on customer quality and the order of impact of other parameters were from highest to lowest: number of frequent customer visits (28.56%), role in social networks (28.37%), Indirect transactions (26.74%), activity days (25.62%) and customer social network size (25.06%).

cs.SI↗

arXiv2021

Well-defined Erd\"{o}s-Straus equations and L.C.M

The Erd\"{o}s-Straus conjecture states that the equation $\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ has positive integer solutions $x, y, z$ for every postive integers $n\ge 2$. We generalize the Erd\"{o}s-Straus equation, state several methods for obtaining well-defined equations, and some features of well-defined equations. Using well-defined equations, we explain the inefficiency of the solutions that did not lead to a complete proof of the problem. Finally, we prove that this conjecture cannot be completely proven by the methods expressed in various articles. For this reason, we express conjectures equivalent to the Erd\"{o}s-Straus conjecture and make the concept of conjecture clearer. The well-defined equations of Erd\"{o}s-Straus have a lot to do with the concept of the least common multiple and the greatest common divisor, and in the last section, we will independently express the functions and features based on the subject of the least common multiple.

math.NT↗

arXiv2021

Quasi-matter Bounce Cosmology in Light of Planck

We study quasi-matter bounce cosmology in light of Planck cosmic microwave background (CMB) angular anisotropy measurements along with the BICEP2/Keck Array data. We propose a new primordial scalar power spectrum by considering a linear approximation of the equation of state $w\cong w_0+\kappa(\eta-\eta_0)$ for quasi-matter field in the contracting phase of the universe. Using this new primordial scalar power spectrum, we constrain the zeroth-order approximation of the equation of state $w_0= -\,0.00340\pm 0.00044$ and first-order correction $10^{4} \zeta= -1.67^{+1.50}_{-0.83}$ at the $1\sigma$ confidence level by Planck temperature and polarization in combination with the BICEP2/Keck Array data in which $\zeta = 12\kappa/k_*$ with pivot scale $k_*$. The spectral index of scalar perturbations is determined to be $n_{\rm Bs}=0.9623\pm0.0055$ which lies 7$\sigma$ away from the scale-invariant primordial spectrum. We find scale dependency for $n_{\rm s}$ at the $1\sigma$ confidence level and a tighter constraint on the running of the spectral index compared to $\Lambda$CDM+$\alpha_s$ cosmology. The running of the spectral index in quasi-matter bounce cosmology is $\alpha_{\rm Bs}= \pi \zeta /2 c_{\rm s} = -\hspace{.5mm}0.0021 \pm 0.0016$ which is nonzero at the $1.3\sigma$ level, whereas in $\Lambda$CDM+$\alpha_{\rm s}$ it is nonzero at the $0.8\sigma$ level for Planck temperature and polarization data. The sound speed of density fluctuations of the quasi-matter field at the crossing time is $c_{\rm s} = 0.097^{+0.037}_{-0.023}$, which is not a very small value in the contracting phase.

astro-ph.CO↗

arXiv2019

Alternative approach to the critical behavior and microscopic structure of the power-Maxwell black holes

Employing a new approach toward thermodynamic phase space, we investigate the phase transition, critical behavior and microscopic structure of higher dimensional black holes in an Anti-de Sitter (AdS) background and in the presence of Power-Maxwell field. In contrast to the usual extended $P-V$ phase space where the cosmological constant (pressure) is treated as a thermodynamic variable, we fix the cosmological constant and treat the charge of the black hole (or more precisely $Q^s$) as a thermodynamic variable. Based on this new standpoint, we develop the resemblance between higher dimensional nonlinear black hole and Van der Waals liquid-gas system. We write down the equation of state as $% Q^s=Q^s(T,\psi)$, where $\psi$ is the conjugate of $Q^s$, and construct a Smarr relation based on this new phase space as $M=M(S,P,Q^s)$, while $% s=2p/(2p-1)$ and $p$ is the power parameter of the Power-Maxwell Lagrangian. We obtain the Gibbs free energy of the system and find a swallowtail behaviour in Gibbs diagrams, which is a characteristic of first-order phase transition and express the analogy between our system and van der Waals fluid-gas system. Moreover, we calculate the critical exponents and show that they are independent of the model parameters and are the same as those of Van der Waals system which is predicted by the mean field theory. Finally , we successfully explain the microscopic behavior of the black hole by using thermodynamic geometry. We observe a gap in the scalar curvature $R$ occurs between small and large black hole. The maximum amount of the gap increases as the number of dimensions increases. We finally find that character of the interaction among the internal constituents of the black hole thermodynamic system is intrinsically a strong repulsive interaction.

physics.gen-ph↗