Narrow Results

In this paper, we get the nuclear mass-density parameter of known mass and known charge radius by using the AME2020 nuclear mass database and the CR2013 nuclear charge radius database. For the nuclei with $N\ge 21$, we obtained an empirical formula of the constant parameter equal to 0 for the difference of nuclear mass-density parameter between two neighboring isotope. That is, the nuclear mass-density parameter of the two neighboring isotopes was equal. By using this empirical formula combined with AME2020 and CR2013 databases, the calculated value of 625 nuclear charge radii was obtained. The root-mean-square deviation (RMSD) of nuclear charge radius that we have successfully obtained is $\sigma =0.011$fm. In addition, one of the corrections is the neutron factor. This correction is the key improvement which reduces the RMSD to 0.0077fm. Considering the neutron shell effect, the different shell ranges were divided into two categories for correction, and the RMSD was reduced to 0.0056fm. Based on the revised empirical formula combined with the AME2020 database, the calculated and predicted values of nuclear charge radius were obtained with high accuracy. Some of these predictions are also very consistent with experimental values measured in recent years. In addition, we use BP neural network to study the difference of nuclear mass-density parameter on the basis of two categories. The RMSDs obtained are 0.0028fm and 0.0038fm, respectively. It can be seen that such a division has a certain degree of reliability and feasibility. These results show that the new relation proposed in this paper has simplicity and reliability, which can be compared with other local nuclear charge radius relations.

In this paper, we have successfully obtained the mean mass-density parameter (${\rho }_m$) using the nuclear masses AME2020 database and nuclear charge radius (CR) CR2013 database. The empirical formula is derived based on the relationship between ${\rho }_m$ and $N∕Z$ (the ratio of the number of neutrons to protons). Subsequently, we obtained an empirical formula for the difference in ${\rho }_m$ between two neighboring isotopes. By utilizing this empirical formula along with the AME2020 and CR2013 databases, we then calculated 625 charge radii for nuclei with $N\ge 21$. The root-mean-square deviation (RMSD) between the calculated values and the experimental values in the CR2013 database is 0.0075fm. The predicted nuclear CR values are comparable to those of other researches, which some predictions closely matching the experimental values measured in recent years. Additionally, this work used the Back Propagation (BP) neural network to establish a model for describing and predicting the difference in the mean mass-density parameter between two neighboring isotopes. The RMSD between the calculated and experimental values obtained using this model is 0.0039fm. Some of our predicted values have good accuracy and compared well with experimental values. Both of the above methods indicate that the nuclear CR relationship proposed in this paper based on the difference in mean mass-density parameter has simplicity and reliability.

An approach for information storage employs tetrapyrrole macrocycles as charge-storage elements attached to a (semi)conductor in hybrid chips. Anti-counterfeiting measures must cohere with the tiny amounts of such electroactive material and strict constraints on composition in chips; accordingly, the incorporation of typical anti-counterfeiting taggants or microcarriers is precluded. The provenance of the tetrapyrroles can be established through the use of isotopic substitution integral to the macrocycle. The isotopic substitution can be achieved by rational site-specific incorporation or by combinatorial procedures. The formation of a mixture of such macrocycles with various isotopic composition (isotopically unmodified, isotopologues, isotopomers) provides the molecular equivalent of an indelible printed watermark. Resonance Raman spectroscopic examination can reveal the watermark, but not the underlying molecular and isotopic composition; imaging mass spectrometry can reveal the presence of isotopologues but cannot discriminate among isotopomers. Hence, deciphering the code that encrypts the watermark in an attempt at forgery is expected to be prohibitive. A brief overview is provided of strategies for incorporating isotopes in meso-substituted tetrapyrrole macrocycles.

It is proved that every finite-dimensional algebra is embeddable in a simple finite-dimensional algebra (a suitable isotope of a matrix algebra). An isotope of the 2nd order matrix algebra over an infinite extension of the ground field may contain a trivial ideal.

Every one-sided isotope of a simple unital alternative or Jordan algebra is a simple algebra. Besides, any isotope of a central simple non-Lie Maltsev algebra of characteristic other than 2 and 3 is a simple algebra. But an isotope of a simple Jordan algebra of the symmetric bilinear form on the infinite dimensional space may contain a trivial ideal.