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We investigate the descriptional complexity of the νi- and αi-products with 0 ≤ i ≤ 2 of two automata, for reset, permutation, permutation-reset, and finite automata in general. This is a continuation of the recent studies on the state complexity of the well-known cascade product undertaken in [7, 8]. Here we show that in almost all cases, except for the direct product (ν0) and the cascade product (α0) for certain types of automata operands, the whole range of state complexities, namely the interval [1,nm], where n is the state complexity of the left operand and m that of the right one, is attainable. To this end we prove a simulation result on products of automata that allows us to reduce the products of automata in question to the ν0, α0, and a double sided α0-product. [ABSTRACT FROM AUTHOR]

The number seven is, since ancient Eastern cultures, the one that most clearly expresses philosophical, religious, astrological and Kabbalistic symbolism. It is considered the symbol of value and balance. This paper aims to reconstruct the vicissitudes of the phraseology underlying the number seven in Italian and its dialects [ABSTRACT FROM AUTHOR]

The binding energy, equilibrium geometry, and vibrational frequencies of small free Nin clusters (n ≤ 20) are calculated using interatomic interaction potentials found within the embedded atom method. Calculations of the energy parameter of stability ΔE2 and dissociation energy show that the most energetically stable clusters are those with the magic numbers of atoms n = 4, 6, 13, and 19. Calculations of atomic vibrations reveal that the dynamic contribution to the stability of clusters is determined by the minimum vibrational frequency, whose extreme values fall on clusters with the magic numbers of atoms n = 4, 6, 13, and 19. The maximum vibrational frequency varies nonmonotonically, and it has unclear extreme values for clusters with n < 19. This result is consistent with the available experimental data on stable structures of small and medium-sized metal clusters. [ABSTRACT FROM AUTHOR]

The Cubic plus Yukawa plus Exponential (CYE) model has been used to study the different decay properties of Superheavy nuclei 298,310114, 306,318122, 308,310124, 310,322126 and compared them with the available theoretical and experimental values. Here, the half-lives of several clusters have been computed that have not yet been detected experimentally. Hopefully, this will assist future research in this area. As a result of comparing the three different decay modes (α-decay, cluster radioactivity and spontaneous fission), it was possible to predict the predominant decay modes of Superheavy nuclei. [ABSTRACT FROM AUTHOR]

Monolayer-protected noble metal clusters, also called nanoclusters, can be produced with the atomic precision and in large-scale quantity and are playing an increasingly important role in the field of nanoscience. To outline the origin and the perspectives of this new field, we overview the main results obtained on free metal clusters produced in gas phase including mainly electronic properties, the giant atom concept, the optical properties, briefly the role of the metal atom (alkali, divalent, noble metal) and finally the atomic structure of clusters. We also discuss the limitations of the free clusters. Then, we describe the field of monolayer-protected metal clusters, the main results, the new offered perspectives, the added complexity, and the role of the ligand beyond the superatom concept. [ABSTRACT FROM AUTHOR]

We investigate the state complexity of languages resulting from the cascade product of two minimal deterministic finite automata with  n and  m states, respectively. More precisely we study the magic number problem of the cascade product operation and show what range of complexities can be produced in case the left automaton is unary, that is, has only a singleton letter alphabet. Here we distinguish the cases when the involved automata are reset automata, permutation automata, permutation-reset automata, or do not have any restriction on their structure. It turns out that the picture on the obtained state complexities of the cascade product is diverse, and for all cases, except where the left automaton is a unary permutation(-reset) or a deterministic finite automaton without structural restrictions, and the right one is a reset automaton or a deterministic finite automaton without structural restrictions, we are able to identify state sizes that cannot be reached — these numbers are called "magic." [ABSTRACT FROM AUTHOR]

ABSTRACTMonolayer-protected noble metal clusters, also called nanoclusters, can be produced with the atomic precision and in large-scale quantity and are playing an increasingly important role in the field of nanoscience. To outline the origin and the perspectives of this new field, we overview the main results obtained on free metal clusters produced in gas phase including mainly electronic properties, the giant atom concept, the optical properties, briefly the role of the metal atom (alkali, divalent, noble metal) and finally the atomic structure of clusters. We also discuss the limitations of the free clusters. Then, we describe the field of monolayer-protected metal clusters, the main results, the new offered perspectives, the added complexity, and the role of the ligand beyond the superatom concept.

We consider an N fermion system at low temperature T in which we encounter special particle number values N m exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all N-values but experience sudden jumps at the N m . For a quantum state described by the matrix ρ , its purity is expressed by T r ρ 2 and then the degree of mixture is given by 1 − T r ρ 2 , a quantity that coincides with the entropy S q for q = 2 . Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained. [ABSTRACT FROM AUTHOR]

Applications of configuration-mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new “outposts” are highlighted: 28O, 42Si, 60Ca and 78Ni. Topics include shell gaps, single-particle properties, islands of inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions.

Abstract أعادة رؤية فى إحدى قلادات توت عنخ آمون Ar]] في صندوق على هيئة الخرطوش عُثر عليه في كنز مقبرة الملك توت عنخ آمون KV 62 بطيبة، تم العثور على أروع قلادةمحلاه بشكل القمر وزهور اللوتس متناغمة مع براعمها، وهناك دلالات توضح أن الملك كان يرتديها أثناء حياته، هذا البحث سوف يقدم رؤية جديدة لهذه القلادة ورمزيتها الدينية، وسيكشف القوة السحرية لهذه القلادة. [En] In a cartouche-shaped box found in the treasury of king Tutankhamun’s tomb KV 62 in Thebes, one of the most wonderful moon-shaped necklaces with lotus flowers matching their buds was discovered. Some signs show that the King wore this necklace throughout his lifetime. This research paper presents a revised view of this necklace and its religious symbolism and explores its magic power.

We consider an N fermion system at low temperature T in which we encounter special particle number values Nm exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all N-values but experience sudden jumps at the Nm. For a quantum state described by the matrix ρ, its purity is expressed by Trρ2 and then the degree of mixture is given by 1−Trρ2, a quantity that coincides with the entropy Sq for q=2. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained.

A systematic investigation of superheavy nuclei in the isotopic chains of proton numbers Z=106, 114, 120, and 126 together with isotonic chains of neutron numbers N=162, 172, and 184 is presented in the theoretical framework of relativistic mean-field density functionals based on density-dependent meson-nucleon couplings. Ground-state properties, including binding energy, shape, deformation, density profile, and radius, are estimated to provide compelling evidence of magicity in these even-even nuclei, aligning with the concept of the 'island of stability.' The analysis reveals central depletion in the charge density, indicating a bubble-like structure, primarily attributed to the substantial repulsive Coulomb field and the influence of higher l -states. A thorough examination of potential decay modes, employing various semi-empirical formulas, is presented. The probable α -decay chains are evaluated, demonstrating excellent agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Applications of configuration-mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new "outposts" are highlighted: 28 O, 42 Si, 60 Ca and 78 Ni. Topics include shell gaps, single-particle properties, islands of inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions. [ABSTRACT FROM AUTHOR]

Abstract Hollow nanostructures are at the forefront of many scientific endeavors. These consist of nanoboxes, nanocages, nanoframes, and nanotubes. We examine the mathematics of atomic coordination in nanoboxes. Such structures consist of a hollow box with n shells and t outer layers. The magical formulas we derive depend on both n and t. We find that nanoboxes with t = 2 or 3, or walls with only a few layers generally have bulk coordinated atoms. The benefits of low-coordination in nanostructures is shown to only occur when the wall thickness is much thinner than normally synthesized. The case where t = 1 is unique, and has distinct magic formulas. Such low-coordinated nanoboxes are of interest for a myriad variety of applications, including batteries, fuel cells, plasmonic, catalytic and biomedical uses. Given these formulas, it is possible to determine the surface dispersion of the nanoboxes. We expect these formulas to be useful in understanding how the atomic coordination varies with n and t within a nanobox.

Background. The root-mean-square charge radii are the important characteristics of atomic nuclei which might be measured experimentally. In this research, we study the experimental data on the root-mean-square charge radii of the spherical nuclei available in the literature. The purpose of this analysis is to establish what is the manifestation of the neutron shells in the considered observable and to find regularities in the behavior of the charge radii when a shell is crossed. Materials and methods. The present analysis is performed by means of calculation of the relative charge radius for a given element x = x (N, Nsh , Z ). This value is equal to the charge radius of an isotope with neutron number N over the charge radius of the isotope t with the closed neutron shell N = Nsh . Results. As the result, we have found manifestation of the shells Nsh = 8, 28, 50 and 82. It turns out that the well-known shells with the neutron numbers 20 and 126 do not show up. Conclusions. It is shown that the values of relative charge radius form groups corresponding to different values of Nsh . On the basis of the revealed regularity, the charge radius is predicted for isotope 30 S which is absent among the experimental data.

Abstract We correct magic formulas for body centered cubic (bcc) structures. The logical rational for this is further corroborated by calculations of the radial distribution function (RDF) for several crystal structures. We add results for truncated cubes which may be found in nature.

In nuclear theory, there is always a quest for possible extensions of the nuclear landscape and extending our knowledge to the limits of nuclear existence. In this study, we examine the stability and structural properties of a wide range of nuclei in super- and ultra-heavy region in a phenomenological semi-microscopic approach. we calculated the shell correlation energy, residual pairing correction energy, two-nucleon separation energy and two-nucleon energy gap for 3670 even–even nuclei along β -stability line and two-neutron driplines in the ranges 7 0 ≤ Z ≤ 2 7 4 with 8 0 ≤ N ≤ 5 4 8 and 7 0 ≤ Z ≤ 2 1 2 with 1 2 6 ≤ N ≤ 5 4 8 , respectively. To assure reliability and confidence of the new results in the ultra-heavy region, we extended the search space to include heavy and super-heavy nuclei. We report 83 double magic nuclei and address the predominance of proton and neutron magic numbers. Our calculations reproduced known results on nuclear magicity and present strong evidences on islands of stability and magic numbers in super- and ultra-heavy regions. We also address shifts in nuclear magicity along the nuclear landscape close to the β -stability line and close to the neutron rich regions. [ABSTRACT FROM AUTHOR]

Hollow nanostructures are at the forefront of many scientific endeavors. These consist of nanoboxes, nanocages, nanoframes, and nanotubes. We examine the mathematics of atomic coordination in nanoboxes. Such structures consist of a hollow box with n shells and t outer layers. The magical formulas we derive depend on both n and t. We find that nanoboxes with t = 2 or 3, or walls with only a few layers generally have bulk coordinated atoms. The benefits of low-coordination in nanostructures is shown to only occur when the wall thickness is much thinner than normally synthesized. The case where t = 1 is unique, and has distinct magic formulas. Such low-coordinated nanoboxes are of interest for a myriad variety of applications, including batteries, fuel cells, plasmonic, catalytic and biomedical uses. Given these formulas, it is possible to determine the surface dispersion of the nanoboxes. We expect these formulas to be useful in understanding how the atomic coordination varies with n and t within a nanobox. [ABSTRACT FROM AUTHOR]

The evolution of the traditional nuclear magic numbers away from the valley of stability is an active field of research. Experimental efforts focus on providing key spectroscopic information that will shed light into the structure of exotic nuclei and understanding the driving mechanism behind the shell evolution. In this work, we investigate the Z=6 spin-orbit shell gap towards the neutron dripline. To do so, we employed NA(p,2p)CA−1 quasi-free scattering reactions to measure the proton component of the 21+ state of 16,18,20C. The experimental findings support the notion of a moderate reduction of the proton 1p1/2−1p3/2 spin-orbit splitting, at variance to recent claims for a prevalent Z=6 magic number towards the neutron dripline.

Cryptographic algorithms installed on Internet of Things (IoT) devices suffer many attacks. Some of these attacks include the differential linear attack (DL). The DL attack depends on the computation of the probability of differential-linear characteristics, which yields a Differential-Linear Connectivity Table (DLCT). The DLCT is a probability table that provides an attacker many possibilities of guessing the cryptographic keys of any algorithm such as Serpent. In essence, the attacker firstly constructs a DLCT by using building blocks such as Substitution Boxes (S-Boxes) found in many algorithms’ architectures. In depth, this study focuses on securing IoT devices against DL attacks used on Serpent algorithms by using three magic numbers mapped on a newly developed mathematical function called Blocker, which will be added on Serpent’s infrastructure before being installed in IoT devices. The new S-Boxes with 32-bit output were generated to replace the original Serpent’s S-Boxes with 4-bit output. The new S-Boxes were also inserted in Serpent’s architecture. This novel approach of using magic numbers and the Blocker Function worked successfully in this study. The results demonstrated an algorithm for which its S-Box is composed of a 4-bit-output that is more vulnerable to being attacked than an algorithm in which its S-Box comprises 32-bit outputs. The novel approach of using a Blocker, developed by three magic numbers and 32-bits output S-Boxes, successfully blocked the construction of DLCT and DL attacks. This approach managed to secure the Serpent algorithm installed on IoT devices against DL attacks.

There has been plenty of empirical evidence which shows that the single-particle picture holds to a good approximation in atomic nuclei. In this picture, protons and neutrons move independently inside a mean-field potential generated by an interaction among the nucleons. This leads to the concept of nuclear shells, similar to the electronic shells in atoms. In particular, the magic numbers due to closures of the nucleonic shells, corresponding to noble gases in elements, have been known to play an important role in nuclear physics. Here we propose a periodic table for atomic nuclei, in which the elements are arranged according to the known nucleonic shells. The nuclear periodic table clearly indicates that nuclei in the vicinity of the magic numbers can be understood in terms of a shell closure with one or two additional nucleons or nucleon holes, while nuclei far from the magic numbers are characterized by nuclear deformation. [ABSTRACT FROM AUTHOR]

The alpha decay chain properties of Z = 122 isotope in the mass range 298? A 350, even-even nuclei, are studied using a fission-like model with an effective combination of the cubic plus proximity potential in the pre and post-scission regions, wherein the decay rates are calculated using improved transfer matrix method, and the results are in good agreement with other phenomenological formulae such as Universal decay law, Viola-Seaborg, Royer, etc. The nuclear ground-state masses are taken from WS4 mass model. The next minimum in the half-life curves of the decay chain obtained at N=186,178 & 164 suggest the shell closure at N=184, 176 & 162 which coincides well with the predictions of two-centre shell model approach. This study also unveils that the isotopes 298-300, 302, 304-306, 308-310, 312,314122 show 7α, 5α, 4α, 3α, 2α and 1α decay chain, respectively. All the other isotopes from A = 316 to 350 may undergo spontaneous fission since the obtained SF half -lives are comparatively less. The predictions in the present study may have an impact in the experimental synthesis and detection of the new isotopes in near future. [ABSTRACT FROM AUTHOR]

The absence of magic numbers in bosonic 4He clusters predicted by all theories since 1984 has been challenged by high-resolution matter-wave diffraction experiments. The observed magic numbers were explained in terms of enhanced growth rates of specific cluster sizes for which an additional excitation level calculated by diffusion Monte Carlo is stabilized. The present theoretical study provides an alternative explanation based on a simple independent particle model of the He clusters. Collisions between cluster atoms in excited states within the cluster lead to selective evaporation via an Auger process. The calculated magic numbers as well as the shape of the number distributions are in quite reasonable agreement with the experiments.

Empirical drops in ground-state nuclear polarizabilities indicate deviations from the effect of giant dipole resonances and may reveal the presence of shell effects in semi-magic nuclei with neutron magic numbers N = 50 , 82 and 126. Similar drops of polarizability in the quasi-continuum of nuclei with, or close to, magic numbers N = 28 , 50 and 82, could reflect the continuing influence of shell closures up to the nucleon separation energy. These findings open a new avenue to investigating magic numbers at high-excitation energies and strongly support recent large-scale shell-model calculations in the quasi-continuum region, which describe the origin of the low-energy enhancement of the photon strength function as induced paramagnetism. The nuclear-structure dependence of the photon-strength function asserts the generalized Brink-Axel hypothesis as more universal than originally expected. [ABSTRACT FROM AUTHOR]

Abstract In this work, we report DFT calculations of the energy formation and stability of multi-vacancies in a unit of Zeolite Template Carbon (C 39 H 9). We label as V n the respective vacancy where n carbon atoms have been removed from the pristine C 39 H 9 structure. The results show that V 2 , V 4 , V 6 and V 9 are the most stable vacancies on the ZTC structure. This result agrees with many other studies. Besides, the most stable vacancy of ZTC structure is when nine carbon atoms are removed (V 9) from the ZTC structure. The formation of pentagon rings in the reconstruction of the ZTC vacancy give drastic effect on the energetics stability. Therefore, the formation of pentagon rings eliminates the dangling bonds thus lowering the energy formation. It is also carried out the decoration of ZTC vacancy with Lithium and Calcium atoms, this is the way to use de ZTC vacancy decorated as a medium for hydrogen storage. The results show that the ZTC vacancy decorated with 3 Lithium atoms can adsorb a maximum of nine hydrogen molecules (3 hydrogen molecules per Lithium atom). This gives a gravimetric storage capacity of 4.44 wt percent (wt. %), which is not enough for meeting DOE gravimetric target. On the other hand, to reach DOE gravimetric target, the study of ZTC vacancy decorated with 3 Calcium atoms is carried out, which can adsorb maximum of fifteen hydrogen molecules (5 hydrogen molecules per Calcium atom), this gives gravimetric storage capacity of 5.81 wt %, which meet DOE gravimetric targets, besides the binding energy of hydrogen molecules on ZTC vacancy decorated with 3 Calcium is calculated. These energies are in the range 0.2453–0.2053 eV/H 2 , which are desirable energies for hydrogen adsorption. This is demonstrated by building isotherm adsorption path. The results show that forming vacancies on ZTC structure decorated with three Calcium atoms (3Ca C 30 H 9) is good candidate as medium for hydrogen storage. Highlights • Creation of vacancy in ZTC structure (C 39 H 9) using DFT calculations. • Decoration of ZTC vacancy with metallic atoms (Ca and Li) using DFT theory. • Adsorption energies of H 2 molecules on 3Ca C 30 H 9 are in range 0.2453–0.2053 eV/H. • Maximum storage capacity of H 2 molecules on 3Ca C 30 H 9 system is 5.81 wt %. • Equilibrium pressure is 20–25 MPa for the 3Ca C 30 H 9 nH 2 system. [ABSTRACT FROM AUTHOR]

A new systematic formula is suggested to evaluate the (n, p) reaction cross sections at neutron energy of 14.5 MeV based upon the reaction's Q-value dependence, explicit symmetry breaking, and shell effects. The measured data for the (n, p) reaction cross sections have been gathered from the available literature, and then, it was analyzed for isotopes having 3 ≤ Z ≤ 83. It has been noted that the plot of σ(n,p) against Z/A3/2, N-Z+1/A4/3 and N/Z·A2/3 is more efficient in determining the (n, p) reaction cross sections, as the reaction Q-value is related to values of σ(n,p) too, which has been adequately represented and compared to other terms such as Sp, Sn, and Sα separation energies. The odd-even effects investigated in the cross sections of odd-mass nuclei are higher than those of their neighboring even-even nuclei close to magic numbers. The estimates of the current formula are compared with the experimental data gathered from the literature, and they are found to be in good agreement. [ABSTRACT FROM AUTHOR]

• The density functional theory is used to study electronic structure of quantum dots in magnetic field. • The Kohn-Sham equations for two-dimensional electrons are solved numerically. • The new series of magic numbers for the total angular momentum of electrons are found. • The influence of a charged impurity on the electronic structure of quantum dots has been studied. Density-functional theory is used to study the electronic structure of quantum dots in magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is obtained. The effect of a charged impurity on the electronic structure of a quantum dot has been studied. [ABSTRACT FROM AUTHOR]

[Display omitted] Electronic, structural, and magnetic properties of small Fe n aggregates with n < 15 atoms were investigated in the framework of the density functional theory (DFT). Our results indicate that spin–orbit coupling has little effect on the structural properties. The magnetic moment of each atom in the cluster is greater than the magnetic moment of their bulk material and the average binding energy value rises monotonically with the size of the cluster and approaches the bulk value. As well as Fe 7 and Fe 13 are the two first magic numbers in good agreement with experimental reports. We studied the adsorption of diatomic SO, CO, O 2 , and N 2 molecules on the Fe 7 and Fe 13 nanoclusters. The most stable adsorption sites, binding energies, and the effect of adsorption on the electronic properties of the Fe clusters were studied. The different aspects of the adsorption mechanism were also investigated. The interaction intensity order is SO, O 2 , CO, and N 2 , and the bond length of the molecules increased after adsorption. X@Fe 13 (X = SO, O 2 , CO, and N 2) systems represent higher magnetization compared to the X@Fe 7 systems. The maximum effect of absorption on the magnetization of the Fe 13 cluster was about 2.4% and on the Fe 7 cluster was about 9.6%. These results provide insights into the application of iron-based catalysts and the understanding of the real reactions and experimental reports. [ABSTRACT FROM AUTHOR]

Graphical abstract A pronounced blue-shift of the maximum of the anion yield of negatively charged gold clusters with increasing cluster size is observed and attributed to the need to evaporate helium from the clusters for their observation in the nascent state. Highlights • Size distributions of Au n ± complexes from doped Helium droplets are measured. • Similar magic numbers and structures compared to other methods are observed. • Optimal energy for cation formation shifts downwards with increasing cluster size. • The maximum of the anion formation efficiency shows the opposite behaviour. Abstract We report the mass spectrometric detection of positive and negative cluster ions of gold atoms formed by the pickup of gold by helium nanodroplets (HNDs) near zero K and subsequent exposure to electron impact. Both singly and doubly charged positive cluster ions were observed. Ionization is initiated by the helium ions He+ and He*−, metastable helium atoms He* as well as electron attachment. We focus on the size distributions of the ions, electron energy dependence of ion yield, patterns of stability and the presence of "magic" clusters. As reported previously by others using a variety of other methodologies, a clear oscillation in the intensity of (Au) n +/- is seen, especially for n <21, with odd-numbered clusters being more intense than even-numbered clusters. The distributions peak early around n = 8. There is a suggestion of magic numbers at n = 35 and 58. Efficiencies of formation of the gold cluster anions were monitored as a function of the energy of the electrons; the measured intensity distributions exhibit a shift to higher energies with increasing cluster size that is attributed to the need to evaporate helium from the clusters for their observation in the nascent state. [ABSTRACT FROM AUTHOR]

We formalized the nuclear mass problem in the inverse problem framework. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The inverse problem was formulated for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker. It was solved in a step-by-step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than 2.6MeV, starting from the number of protons and number of neutrons equal to 1. The explicit form of unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified least procedure, that realized in the algorithms which were developed by Lubomir Aleksandrov to solve the nonlinear systems of equations via the Gauss-Newton method, lets us to choose the better one between two functions with same . In the obtained generalized model, the corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers as well on the asymptotic boundaries of their influence. The obtained results were compared with the predictions of other models. [ABSTRACT FROM AUTHOR]

Inspired by the experimental discovery of magic numbers we present a first study using density functional theory for the structure and properties of neutral and cationic Bi6Cu3 and Bi5Cu2 clusters. Our results confirm predictions based on Wade's rules. The closed electron shells, characteristic of cationic clusters help impose enhanced stability, while also complying with Wade's rules. Charge distribution analysis, as well as electrostatic potential maps show that in almost all cases, Bi atoms donate charges to Cu atoms. According to the analysis of condensed Fukui indices, Cu atoms inside both clusters are not reactive. Contrastingly, Bi atoms are reactive and may be targeted by different types of attack. This study of the electronic properties may thus help to determine experimental strategies with the capacity to enhance the synthesis of catalysts. [ABSTRACT FROM AUTHOR]

Inspired by the experimental discovery of magic numbers we present a first study using density functional theory for the structure and properties of neutral and cationic Bi6Cu3 and Bi5Cu2 clusters. Our results confirm predictions based on Wade's rules. The closed electron shells, characteristic of cationic clusters help impose enhanced stability, while also complying with Wade's rules. Charge distribution analysis, as well as electrostatic potential maps show that in almost all cases, Bi atoms donate charges to Cu atoms. According to the analysis of condensed Fukui indices, Cu atoms inside both clusters are not reactive. Contrastingly, Bi atoms are reactive and may be targeted by different types of attack. This study of the electronic properties may thus help to determine experimental strategies with the capacity to enhance the synthesis of catalysts. [ABSTRACT FROM AUTHOR]

Isothermal molecular dynamics is used to find the magic numbers corresponding to clusters of fcc transition metals: silver and copper. To that end, we use both our own computer program with a tight-binding potential and well-known LAMMPS software whose standard package is designed to model metal systems by the embedded atom method. Regardless of the choice between two relaxation techniques (lowtemperature relaxation at 1 K and the variant involving a gradual temperature decrease with subsequent relaxation at 1 K), magic number 13 is detected that corresponds to the first term of the Chini series. At the same time, other magic numbers are also found that belong and do not belong to this series. [ABSTRACT FROM AUTHOR]

Practitioners may face difficulties in the interpretation of fire codes since they often present so called “magic numbers”, i.e. numbers available in the codes which are listed for providing the design of building fire safety, for which the derivation and justification are not explained. The present paper discusses the need for a transparent regulatory approach, in which legislators publicly justify each of the choices made during the development of the fire codes. This approach has been used for the first time during the development of the Italian Fire Safety Code DM03/08/15, where the process adopted for the development of the code requirements has been publicly released in parallel with the code itself. This is deemed to facilitate the interpretation of the fire code, avoiding mis-use and preventing criticism on lack of transparency. To address this issue, the Italian legislators have conducted a process of reconstructing the assumptions adopted for the definition of magic numbers in other International codes (i.e., British Standard 9999) in order to identify suitable specifications for the national context under consideration. This includes the performance of a series of calculations rather than a mere historical examination of their basis. As a first attempt towards an increased transparency in fire code development at an International level, this paper publicly summarizes the process adopted by the Italian legislators for the development of the new Italian fire code, focusing on the exemplary case of the calculations performed for the definition of the requirements concerning stair design (i.e. vertical evacuation). This is presented by comparing the deemed-to-satisfy provisions of the Italian code with the ones given in the British Standard 9999. The process of developing fire codes is discussed together with the benefits associated with transparency in the assumptions adopted for their definition. [ABSTRACT FROM AUTHOR]

In the last 35 years, a large amount of data on the changes in the mean-square charge radii, δ〈 r 〉, around the lead region has been gathered. Isotopic chains are often normalised and compared to reduce the impact of systematic uncertainties of the extracted δ〈 r 〉 from the isotope shifts. However, this biased picture can obscure other interesting effects that are apparent in absolute scale. In this contribution, we review the extent of the knowledge on the δ〈 r 〉 in the lead region in addition to observations on the absolute scale. [ABSTRACT FROM AUTHOR]

Nuclear level densities of Pb and Y are calculated using the Lipkin-Nogami (LN) method and Bradeen-Cooper-Schrieffer (BCS) model. It is revealed that the calculated nuclear level densities are highly matched with the experimental data of Oslo group. The excitation energy and entropy are calculated for mentioned nuclei. In the case of two studied nuclei the characteristic of being magic for the number of neutrons or protons causes the decrease of the excitation energy and entropy contribution of magic system at low temperatures. [ABSTRACT FROM AUTHOR]