The exceptional points (EPs) of non-Hermitian systems, where n different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian ...systems. In particular, the ϵ 1 n dependence of the energy level splitting on a perturbative parameter ϵ near an nth order EP stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility dϵ1/n/dϵ diverges at the EP. Here we theoretically study the sensitivity of parameter estimation near the EPs, using the exact formalism of quantum Fisher information (QFI). The QFI formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the EP bears no dramatic enhancement of the sensitivity. Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter.
The normalized Laplacian makes a great contribution on analyzing the structure properties of nonregular graphs. Let On be a linear octagonal‐quadrilateral network. In this article, we first concern ...the normalized Laplacian spectrum of On based on the decomposition theorem for the corresponding matrices. Then we derive the closed‐term formulas of the degree‐Kirchhoff index and the number of spanning trees of linear octagonal‐quadrilateral networks on the basis of the relations between the roots and coefficients, respectively.
The degree‐Kirchhoff index and complexity are the important parameters to explore the structural properties of a given network. The normalized Laplacian plays a key role on studying the structure properties of nonregular graphs. The formulas of the degree‐Kirchhoff index and the exactly complexity of the linear octagonal‐quadrilateral graphs are given in terms of the normalized Laplacian.
A molecular network can be characterized by several different ways, like a matrix, a polynomial, a drawing or a topological descriptor. A topological descriptor is a numeric quantity associated with ...a network or a graph that characterizes its whole structural properties. Analyzing and determining the topological indices and structural properties of a network or a graph have been a worthy studied topic in the field of chemistry, networks analysis, etc. In this paper, we consider several types of the generalized Sierpiński networks and investigate the explicit expressions of some well-known valency-based topological indices. Taking into account the other structural property of the generalized Sierpiński networks, the average degree is determined.
Quantum coherence control usually requires low temperature environments. Even for nitrogen-vacancy center spins in diamond, a remarkable exception, the coherence signal is limited to about 700 K due ...to the quench of the spin-dependent fluorescence at a higher temperature. Here we overcome this limit and demonstrate quantum coherence control of the electron spins of nitrogen-vacancy centers in nanodiamonds at temperatures near 1000 K. The scheme is based on initialization and readout of the spins at room temperature and control at high temperature, which is enabled by pulse laser heating and rapid diffusion cooling of nanodiamonds on amorphous carbon films. Using the diamond magnetometry based on optically detected magnetic resonance up to 800 K, we observe the magnetic phase transition of a single nickel nanoparticle at about 615 K. This work enables nano-thermometry and nano-magnetometry in the high-temperature regime.
The Cartesian product and join are two classical operations in graphs. Let dL(G)(e) be the degree of a vertex e in line graph L(G) of a graph G. The edge versions of atom-bond connectivity (ABCe) and ...geometric arithmetic (GAe) indices of
are defined as ∑ef∈E(L(G))dL(G)(e)+dL(G)(f)-2dL(G)(e)×dL(G)(f) and ∑ef∈E(L(G))2dL(G)(e)×dL(G)(f)dL(G)(e)+dL(G)(f), respectively. In this paper, ABCe and GAe indices for certain Cartesian product graphs (such as Pn□Pm, Pn□Cm and Pn□Sm) are obtained. In addition, ABCe and GAe indices of certain join graphs (such as Cm+Pn+Sr, Pm+Pn+Pr, Cm+Cn+Cr and Sm+Sn+Sr) are deduced. Our results enrich and revise some known results.
•ZIF-8 nanoparticles have been fabricated via a facile method at room temperature.•The ZIF-8 nanoparticles show high adsorption capacity for arsenic removal at neutral and basic ...conditions.•Electrostatic attraction and hydroxyl and amine groups play key roles in the adsorption process.
In this study, zeolitic imidazolate framework-8 (ZIF-8) nanosorbent was successfully synthesized via a facile method at room temperature. The ZIF-8 nanoparticles were characterized by nitrogen sorption, powder X-ray diffraction, field emission scanning electron microscope, transmission electron microscopy and Zeta potential. The synthesized ZIF-8 nanoparticles exhibited a high surface area of 1063.5m2/g and were of 200–400nm in particle size. The kinetic and isotherm data of arsenic adsorption on ZIF-8 were well fitted by pseudo-second-order and Langmuir models, respectively. The maximal adsorption capacities of As(III) and As(V) were of 49.49 and 60.03mg/g, respectively, at T=25°C and pH 7.0. The ZIP-8 nanoparticles were stable at neutral and basic conditions. However, large amounts of Zn2+ were released into water from the sorbent at acidic condition, which dramatically hindered the adsorption of arsenic. SO42− and NO3− had no significant effect on the arsenic adsorption while the adsorption was significantly inhibited by PO43− and CO32−. X-ray photoelectron spectroscopy and Fourier transform infrared spectroscopy analysis revealed that electrostatic attraction and hydroxyl and amine groups on ZIF-8 surface played vital roles in the adsorption process.
In this article, we present an efficient computer‐based computational technique to compute the energy and Estrada index of graphs. It is shown that our computational method is more efficient and ...bears less computational and algorithmic complexity. We use our method to show the main result of this article, which asserts that the Estrada index correlates with the π‐electronic energies of lower benzenoid hydrocarbons with correlation coefficient 0.9993. This enhances the practical applicability of the Estrada index and warrants its further usage in quantitative structure activity relationships. We further apply our computational technique in computing the energy and Estrada index of two infinite families of boron triangular nanotubes. We perform simulation based on certain computer software packages to study the graph‐theoretic behavior of the obtained results. Our results help to correlate certain physicochemical properties of underlying chemical structures of these nanotubes.
Scatter plot between the Estrada index and π‐electronic energies for 30 lower polycyclic aromatic hydrocarbons. The data shows a strong correlation between the Estrada index and π‐electronic energies having correlation coefficient 0.993. This enhances the practical applicability of the Estrada index and warrants its further usage in in quantitative structure activity relationships.
The entire world is struggling to control the spread of coronavirus (COVID‐19) as there are no proper drugs for treating the disease. Under clinical trials, some of the repurposed antiviral drugs ...have been applied to COVID‐19 patients and reported the efficacy of the drugs with the diverse inferences. Molecular topology has been developed in recent years as an influential approach for drug design and discovery in which molecules that are structurally related show similar pharmacological properties. It permits a purely mathematical description of the molecular structure so that in the development of identification of new drugs can be found through adequate topological indices. In this paper, we study the structural properties of the several antiviral drugs such as chloroquine, hydroxychloroquine, lopinavir, ritonavir, remdesivir, theaflavin, nafamostat, camostat, umifenovir and bevacizumab by considering the distance and bond measures of chemical compounds. Our quantitative values of the topological indices are extremely useful in the recent development of designing new drugs for COVID‐19.
The primary results of the paper include distance‐based and bond additive topological descriptors of antiviral medications for the treatment of COVID‐19 like chloroquine, hydroxychloroquine, lopinavir, ritonavir, remdesivir, theaflavin, nafamostat, camostat, umifenovir, and bevacizumab by graph‐theoretic technique, in particular, strength‐weighted quotient graph.
In this study, the compact third‐order filter with wide stopband is proposed, and it is based on the folded substrate integrated waveguide (FSIW)‐patch resonator. The embedded semicircular patch with ...two etched slots is integrated into the closed dual‐mode FSIW, so the miniaturized single‐cavity triple‐mode resonator with electromagnetic (EM) shielding and high quality can be achieved. In addition, the slots can reduce transverse electricity (TE)101 and TE201 on FSIW, while the other higher‐order modes of FSIW remain unchanged, then the wide stopband can be realized, and the stopband can be further widened by designing the feeding position to suppress higher‐order modes. Then, this filter based on hybrid FSIW modes has compact size, wide stopband, and good EM shielding. Finally, a prototype with 3‐dB fractional bandwidth of 8.4% is designed at 5.87 GHz (f0), and its insertion loss is only 1.16 dB. The upper‐stopband attenuation is better than 23 dB extended to 3.08f0. It occupies only 0.18λg2, where λg is the guided wavelength at f0.
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