The synthesis and structural characterization of a new triangular Cu3-3OH pyrazolato complex of formula, [Cu3(μ3-OH)(pz)3(Hpz)3][BF4]2 (1-Cu3), Hpz = pyrazole, is presented. The triangular unit forms a quasi-isosceles triangle with Cu-Cu distances of 3.3739(9), 3.3571(9), and 3.370(1) Å. This complex is isostructural to the hexanuclear complex [Cu3(μ3-OH)(pz)3(Hpz)3](ClO4)2]2 (QOPJIP). A comparative structural analysis with other reported triangular Cu3-3OH pyrazolato complexes has been done, showing that, depending on the pyrazolato derivative, auxiliary ligand or counter-anion can affect the nuclearity and/or the dimensionality of the system. The magnetic properties of 1-Cu3 are analyzed by experimental data and DFT calculation. A detailed analysis is done on the magnetic properties comparing experimental and theoretical data of other molecular triangular Cu3-3OH complexes, showing that the displacement of the μ3-OH- from the Cu3 plane, together with the type of organic ligands, influences the nature of the magnetic exchange interaction between the spin-carrier centers, since it affects the overlap of the magnetic orbitals involved in the exchange pathways. Finally, a detailed comparison of the magnetic properties of 1-Cu3 and QOPJIP was done, which allowed us to understand the differences in their magnetic properties.

We summarize the results on electron transport in hybrid superconducting S/B/S' mesa-structure consisted of the oxide epitaxial S/B heterostructures, where S is the cuprate YBa2Cu3O 7-x superconductor, B – an interlayer with the spin dependent characteristics, and S’ is the Nb top superconductor. Josephson effect was observed manifested in appearance of oscillating Shapiro steps amplitudes with microwave signal power due to synchronization of junction self-generation of electromagnetic radiation and the external microwave probe signal. Triplet component of superconducting correlations emerged when the interlayer comprised two magnetic materials SrRuO3 and La0.7Sr0.3MnO3 with non-collinear magnetizations as well in the case of antiferromagnetic insulator Sr2IrO4 characterized by strong spin-orbit interaction. Thickness of the interlayer in the both cases considerably exceeded the coherence length of the magnetic spin active interlayer hinting on appearance of long-range proximity effect and spin-triplet superconducting current. Magnetic field dependences measured at dc, and the existence of the second harmonic in superconducting current–phase relation revealed by measurements at microwave frequencies will be discussed.

In the article, the fireball formed in the collision of relativistic nuclei is considered as a quantum object. Based on this, an attempt is made to explain the difference in the measurements of hyperon yields in the two experiments - NA49 and NA57. Using the basic principles of quantum mechanics, it was shown that a fireball can have two quantum states - with and without ignited Quark-Gluon Plasma (QGP). With an increase of the collision energy of heavy ions, the probability of QGP ignition increases. At the same time, the probability of the formation of fireball without QGP ignition also remains nonzero even at nuclear collision energies that are much higher than the threshold QGP formation energy, which may be erroneously considered to be fixed and which is intensively sought in modern heavy ion accelerators. Thus, at SPS energy of heavy ion collisions \sqrt{s_{NN}} = 17.3 GeV, which is much higher than the assumed threshold energy of QGP formation in the region around or slightly above of \sqrt{s_{NN}} = 3 GeV, only half of the central collisions of heavy ions bring to the formation of a fireball consisted of deconfined matter (quarks and gluons), the remaining half of the collisions lead to the formation of a fireball from only hadronic matter (mesons, nucleons, hyperons etc.).

Abstract: Scavenging of electrogenerated superoxide radical anion (O2•−) by pyrogallol (PyH3) was investigated on the basis of cyclic voltammetry and in situ electrolytic electron spin resonance spectrum in N,N-dimethylformamide with the aid of density functional theory (DFT) calculations. Quasi-reversible dioxygen/O2•− redox coupe was modified by the presence of PyH3, suggesting that O2•− was scavenged by PyH3 through proton-coupled electron transfer (PCET) involving two proton transfer and one electron transfer. The DFT calculation suggested that the formation of hydrogen bond (HB) complex and the subsequent concerted-two-proton coupled electron transfer (2PCET) characterized by catechol moiety in PyH3 is plausible mechanism which embodies the superior kinetics of the O2•− scavenging by PyH3 as shown in the electrochemical results. Furthermore, it was clarified that three hydroxyl groups of PyH3 promote the formation of prereactive HB complex, in comparative analyses using related compounds, resulting the promotion of the O2•− scavenging.

Abstract: Elimination of superoxide radical anion (O2•−) by tocopherols (TOH), and related compounds was investigated on the basis of cyclic voltammetry and in situ electrolytic electron spin resonance spectral measurements in N,N-dimethylformamide (DMF) with the aid of density functional theory (DFT) calculations. Quasi-reversible O2/O2•− redox was modified by the presence of TOHs, suggesting that the electrogenerated O2•− was eliminated by α-, β-, γ-TOH through proton-coupled electron transfer (PCET), but not by δ-TOH. The structure–activity correlation of α-, β-, γ-, and δ-TOH characterized by methyl group on the 6-chromanol ring was experimentally confirmed, where the methyl group promotes the PCET mechanism. Furthermore, comparative analyses using some related chemical analogues suggested that methoxyl group of the 6-chromanol ring is required for a successful electron transfer (ET) to O2•− through the PCET. The electrochemical and DFT results in dehydrated DMF suggested that the PCET mechanism involves preceding proton transfer (PT) forming hydroperoxyl radical followed by a concerted PCET (ET–PT). The O2•− elimination by TOH proceeds efficiently along the net PCET mechanism involving one ET and two PTs.

The elimination of superoxide radical anions (O2•−) by 5-amino-2-hydroxybenzoic acid (mesalazine, 5-ASA), 4-amino-2-hydroxybenzoic acid (4-ASA), and related compounds used for ulcerative colitis treatment was investigated using cyclic voltammetry and electron spin resonance (ESR) analyses aided by density functional theory (DFT) calculations. Quasi-reversible O2/O2•− redox was found to be modified by the compounds, suggesting that an acid-base reaction in which a hydroperoxyl radical (HO2•) is formed from O2•− occurs. However, the deprotonated 5-ASA anion can eliminate O2•− through proton-coupled electron transfer (PCET), forming a radical product. This electron transfer (ET) was confirmed by ESR analysis. The 4-aminophenol moiety in 5-ASA plays an important role in the PCET involving two proton transfers and one ET based on -conjugation. The electrochemical and DFT results indicated that O2•− elimination by 5-ASA proceeds efficiently viathrough the PCET mechanism after deprotonation of the 1-carboxyl group. Thus, 5-ASA may act as an anti-inflammatory agent in the alkali intestine through PCET-based O2•− elimination.

Low-frequency electron paramagnetic resonance (EPR) is used to extract the EPR parameter A-mid and support the approximate X-band value of g-mid for Ba(Co_yZn_1/3-yTa_2/3)O₃. Although cobalt hyperfine structure for the [+/−1/2> state is often unresolved at X-band or S-band, it is resolved in measurements on this compound. This allows for detailed analysis of the molecular orbital for the [+/−1/2> state, which is often the ground state. Moreover, this work shows that the EPR parameters for Co substituted into Zn compounds gives important insight into the properties of zinc binding sites.

By expressing the Schrödinger wave function in the form $\psi =R{e}^{iS/\hslash }$ , where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, viz., $V_Q=-\frac{{\hslash }^2}{2m}\frac{{\nabla }^{2}R}{R}$ , we have obtained a spin potential $V_S=-\frac{S{\nabla }^{2}S}{m}$ that depends on S which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass $m{c}^2$ with an internal frequency of $2m{c}^2/\hslash$ , satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. On the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighboring space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

Spin dependent quantum transport properties in twisted carbon nanotube and stretched carbon nanotube are calculated using density functional theory (DFT) and non-equilibrium green’s function (NEGF) formulation. Twisting and stretching have no effect on spin transport in CNTs at low bias voltages. However, at high bias voltages the effects are significant. Stretching restricts any spin-up current in antiparallel configuration (APC) which results in higher magneto resistance (MR). Twisting allows spin-up current almost equivalent to the pristine CNT case resulting in lower MR. High spin filtration is observed in PC and APC for pristine, stretched and twisted structures at all applied voltages. In APC, at low voltages spin filtration in stretched CNT is higher than in pristine and twisted ones with pristine giving higher spin filtration than twisted CNT.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.

Conjugated singlet ground state diradicals have received remarkable attention owing to their potential applications in optoelectronic devices. A distinctive character of these systems is the location of the double exciton state, a low lying excited state dominated by the doubly excited H,H→L,L configuration, which may influence optical and other photophysical properties. In this contribution we investigate this specific excited state, for a series of recently synthesized conjugated diradicals, employing time dependent density functional theory based on the unrestricted parallel spin reference configuration in the spin-flip formulation (SF-TDDFT) and standard TD calculations based on the unrestricted antiparallel spin reference configuration (TDUDFT). The quality of the computed results is assessed considering diradical and multiradical descriptors and the excited state wavefunction composition.

We summarize structural instabilities exhibited by the one dimensional (1D) (arene)2X family of organic conductors in relation with their electronic and magnetic properties. With a charge transfer of one electron to each anion X these salts exhibit a quarter-filled (hole) conduction band located on the donor stacks. Compounds built with donors such as fluorenthene and perylene derivatives and anions X such PF6 or AsF6 exhibit a high temperature (TP~170K) conventional Peierls transition which is announced by a sizeable regime of 1D 2kF charge density wave fluctuations (kF is the Fermi wave vector of the 1D electron gas located on Per stacks). Surprisingly, and probably because of the presence of a multi-sheet warped Fermi surface, the Peierls transition is considerably reduced in the perylene series α-(Per)2[M(mnt)2] where X is the dithiolate molecule with M=Au, Cu, Co and Fe. A special attention is devoted in this paper to physical properties of α-(Per)2[M(mnt)2] salts which with M=Pt, Pd and Ni incorporate segregated S=1/2 1D antiferromagnetic (AF) dithiolate stacks with 1D metallic Per stacks. We analyse conjointly the structural and magnetic properties of these salts in relation with the 1D spin-Peierls (SP) instability located on the dithiolate stacks. We show that the SP instability of the Pd and Ni derivatives occurs in the classical (adiabatic limit) while the SP instability of the Pt derivative occurs in the quantum (anti-adiabatic limit). Furthermore we show that in the Pd and Ni derivatives frustrated 1st neighbour direct and 2nd neighbour indirect (through a fine tuning with the mediated 2kF RKKY coupling interaction on Per stacks) AF interactions add their contribution to the SP instability to open a singlet-triplet gap. Our analysis of the data show unambiguously that magnetic α-(Per)2[M(mnt)2] salts are a typical realization of the physics predicted for two chain 1D Kondo lattices.

The minimum energy structures of the Si3C5 and Si4C8 clusters are planar and contain planar tetracoordinate carbons (ptCs). These species have been classified, qualitatively, as global () and local () aromatics according to the adaptive natural density partitioning (AdNDP) method, which is an orbital localization method. This work evaluates these species' aromaticity, focusing on confirming and quantifying their global and local aromatic character. For this purpose, we use an orbital localization method based on the partitioning of the molecular space according to the topology of the electronic localization function (LOC-ELF). In addition, the magnetically induced current density is analyzed. The LOC-ELF-based analysis coincides with the AdNDP study (double aromaticity, global and local). Besides, the current density analysis detects global and local ring currents. The strength of the global and local current circuit is significant, involving 4n+2 - and -electrons, respectively. The latter implicates the Si-ptC-Si fragment, which would be related to the 3c-2e -bond detected by the orbital localization methods in this fragment.

Ferrocenium (Fc+) inherits a number of molecular/electronic properties from the neutral counterparts’ ferrocene (Fc) including the high symmetry. Both Fc+ and Fc prefer the eclipsed structure (D5h) over the staggered structure (D5d) by an energy of 0.36 kcal·mol-1. The present study using the recently developed excess orbital energy spectrum (EOES) shows that the open shell Fc+ cation exhibits similar conformer dependent configurational changes to the neutral Fc conformer pair. A further energy decomposition analysis (EDA) discloses that the reasons for the preferred structures are different between Fc+ and Fc. The dominant differentiating energy between the Fc+ conformers is the electrostatic energy (EEstat), whereas in neutral Fc, it is the quantum mechanical Pauli repulsive energy (EPauli). Within the D5h conformer of Fc+, the EOES reveals that the -electrons of Fc+ experience more substantial conformer dependent energy changes than the -electrons (assumed the hole is in a β orbital).

We changed the symmetry of the Weak Force from SU(2) to the quaternion group $Q_8$, and found that spin spacetime separates into two complementary spaces: a spin polarization spacetime of even parity states, and a spin coherence space, in the $S^3$ hypersphere, of odd parity coherent states. Under the quaternion group, spin is a boson of spin 1 in free flight and a fermion of spin $\frac{1}{2}$ when measured. It immediately follows that neutrinos are not needed to balance spin and conserve energy in beta decay. Additionally, we find the boson electrons emitted in beta decay are odd to parity, leading to parity conservation even though the observed beta distribution is asymmetrical.

Block copolymers are a class of materials particularly interesting for their ability to self-assemble into ordered structures. In this context, the coupling between environment and dynamics is particularly relevant, given that movements at the molecular level influence various properties of macromolecules. Mixing the polymer with a second macromolecule appears to be an easy way to study these relationships. In this work, we studied a system based on two diblock copolymers of methyl methacrylate as first block and 3-methyl-4-[6-(methylacryloyloxy)-hexyloxy]-4’-pentyloxy azobenzene as second block and their blends with PMMA. The relaxational properties of these systems were investigated by electron spin resonance (ESR) spectroscopy sensitive to nanometric length-scales. The results of the study on the blends were related to the dynamic behavior of the copolymer. The study evidenced the presence of fast and slow molecular sites for the molecular reorientation at nanoscale, modulated by the ability of block copolymer to form supramolecular structures. For blends, the heterogeneities at nanoscale are still detected. However it was found that the presence of the PMMA as the major component of the blends modified their dynamic behaviour.

The interaction between spinors and gravity is the most complicated and subtle interaction in the universe, which involves the basic problem to unified quantum theory and general relativity. By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of Dirac equation, the energy momentum tensor of spinors and so on. To split spinor connection into Keller connection $\Upsilon_\mu\in\Lambda^1$ and pseudo-vector potential $\Omega_\mu\in\Lambda^3$ by Clifford algebra not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Keller connection only corresponds to geometric calculations, but the potential $\Omega_\mu$ has dynamical effects, which couples with the spin of a spinor and may be the origin of the celestial magnetic field. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton's second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields. However, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table $S^{\mu\nu}_{ab}$, which plays an important role in the interaction between spinor and gravity. From this paper we find that, Clifford algebra has irreplaceable advantages in the study of geometry and physics.

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

The total enthalpies of the 16 different spin configurations that can be realized in the unit cell of the archetype spin crossover complex [Fe(phen)₂(NCS)₂] (phen=1,2-phenanthroline) were calculated applying periodic density functional theory combined with the Hubbard model and the Grimme-D2 dispersion correction (DFT+U/D2). The obtained enthalpy differences between the individual spin configurations were used to determine spin couplings of an Ising-like model and subsequent Monte Carlo simulations for this model allowed to estimate the phenomenological interaction parameter Г of the Slichter-Drickamer model, which is commonly used to describe the cooperativity of the spin transition. The calculational procedure described here, which led to an estimate of about 3 kJ/mol⁻¹ for Г, in good agreement with experiment, may be used to predict from first principles how modifications of spin crossover complexes can change the character of the spin transition from gradual to abrupt and vice versa.

Complexes of triply positive europium ion with organic ligands are popular objects for studying photophysical properties. This is related not only to the bright red emission of this 4f element, but also to some spectroscopic peculiarities of its luminescence: the first excited spin-orbit level (7F1) lies only about 300 cm−1 above the ground state (7F0), so that at room temperature its population is around 25–30%. However, such electronic structure of Eu(III) provides its paramagnetism under ordinary conditions. This fact is often ignored by researchers, which is shortsighted from the materials science point of view. A comprehensive and systematic study of the magnetic behavior for the Eu(III) molecular coordination compounds is a challenging task for the development of new polyfunctional materials. The present work presents synthesis, single crystal XRD analysis results, and a magnetic study for the firstly prepared europium(III) complexes with two neutral scorpionate ligands: trispyrazolylmethane (HCPz3) and its methylated analog, tris(3,5-dimethyl-1-pyrazolyl)methane (HC(PzMe2)3). The values of the spin-orbit coupling parameter obtained for Eu-trication by a theoretical approximation of the experimental magnetic susceptibility data are compared with those known for the scarce amount of the magnetically studied molecular compounds.

The screen-printed carbon nanofibers electrodes (SPCNFE) represent an alternative with great acceptance due to their results, as well as their low impact for the environment. In order to improve their performance, in the present work they were modified with silver nanoparticles (Ag-NPs) and electrochemically characterized by using anodic stripping voltammetry. From the Ag-NPs synthesis, silver seeds (Ag-NS) and silver nanoprisms (Ag-NPr) were obtained. The Ag-NPs formation was confirmed by micrographs where Ag-NPs with diameters of 12.20±0.04 nm for Ag-NS, and 20.40±0.09 nm for Ag-NPr were observed. The electrodes were modified by using three different deposition methods: drop-casting, spin-coating and in-situ approaches. It was observed that the last methodology showed a low amount of Ag-NS deposited on the electrode surface and a deep alteration of this surface. Those facts suggested that the in situ synthesis methodology were not appropriate for the determination of heavy metals and it was discarded. The incorporation of the nanoparticles by spin-coating and drop-casting strategies showed different spatial distribution on the electrode surface as proved by scanning electron microscopy. The electrodes modified by these strategies, were evaluated for the cadmium(II) and lead(II) detection using differential pulse anodic stripping voltammetry, obtaining detection limit values of 2.1 and 2.8 µg L^-1, respectively. The overall results showed that the incorporation route does not change directly the electrocatalytic effect of the nanoparticles, but the shape of these nanoparticles (spherical for seeds and triangular for prisms) has a preferential electrocatalytical enhancement over Cd(II) or Pb(II).

Starting from Thomas Friedrich’s work “Weak Spin(9) structures on 16-dimensional Riemannian manifolds”, we review several interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical 8-form and its analogies with quaternionic geometry, the role of Spin(9) both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel Spin(9) manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley-Rosenfeld planes and to three series of Grassmannians.

Surgical navigation has evolved as a vital tool in maxillofacial surgery, offering precise and patient-specific data. This study explores the clinical applications and accuracy of intraoperative tool tracking in maxillofacial surgery. The research includes 37 patients with various pathologies who underwent surgery assisted by a surgical navigation system using tracked instruments. The study showcases two representative cases: one involving coronoid hyperplasia with mouth opening deficit and another addressing nose-orbital-ethmoidal-frontal ossifying fibroma resection. The results indicate that surgical navigation with tracked instruments provides high precision (<1.5 mm error), reduced surgical time, and less invasive approaches. The study highlights the potential for reproducible outcomes and increased safety, especially in complex cases. Despite some limitations, the synergy between surgical navigation and tracked instruments offers a promising approach in maxillofacial surgery, expanding its applications beyond current practices.

The bipartite entanglement is comprehensively investigated in the mononuclear molecular complex (Et3NH)[Ni(hfac)2L], where HL denotes 2-(2-hydroxy-3-methoxy-5-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-3-oxide-1-oxyl and hfacH stands for hexafluoroacetylacetone. From the magnetic point of view, the molecular compound (Et3NH)[Ni(hfac)2L] consists of an exchange-coupled spin-1 Ni2+ magnetic ion and a spin-12 nitronyl-nitroxide radical substituted nitrophenol. The nickel-radical molecular complex affords an experimental realization of a mixed spin-(12, 1) Heisenberg dimer with a strong antiferromagnetic exchange coupling J/kB= 505 K and two distinct g-factors gRad=2.005 and gNi=2.275. By adopting this set of magnetic parameters we demonstrate that the Zeeman splitting of a quantum ferrimagnetic ground-state doublet due to a weak magnetic field may substantially reinforce the strength of bipartite entanglement at low temperatures. The molecular compound (Et3NH)[Ni(hfac)2L] maintains sufficiently strong thermal entanglement even at room temperature, vanishing only above 546 K. Specifically, the thermal entanglement in the nickel-radical molecular complex retains approximately 40% of the maximum value corresponding to perfectly entangled Bell states at room temperature, which implies that this magnetic compound provides suitable platform of a molecular qubit with potential implications for room-temperature quantum computation and quantum information processing.

The apparent shape of the black hole shadow provides a full description of the spin, the inclination angle and the charge of a Kerr black hole, without any astrophysical process or underlying theory in the astrophysical process.

The magnetic field of the earth plays an important role in the ecosystem, and the magnetic field of celestial bodies is also important in the formation of cosmic large-scale structures, but the origin and evolution of the celestial magnetic field is still an unresolved mystery. Many hypotheses to explain the origin have been proposed, but there are some insurmountable difficulties for each one. At present, the theory widely accepted in scientific society is the dynamo model, it says that, the movement of magnetofluid inside celestial bodies, which can overcome the Ohmic dissipative effect and generate persistent weak electric current and macroscopic magnetic field. However, this model needs an initial seed magnetic field, and the true values of many physical parameters inside the celestial body are difficult to obtain, and there is no stable solution to the large range of fluid motion. These are all difficulties for the dynamo model. Furthermore, it is difficult for the dynamo to explain the correlation between the dipole magnetic field and angular momentum of a celestial body. In this paper, by calculating the interaction between spin of particles and gravity of celestial body according to Clifford algebra, we find that a rotational celestial body provides a field $\Omega^\alpha$ for spins, which is similar to the magnetic field of a dipole, and the spins of charged particles within the celestial body are arranged along the flux line of $\Omega^\alpha$, then a macroscopic magnetic field is induced. The calculation shows that the strength of $\Omega^\alpha$ is proportional to the angular momentum of the celestial body, which explains the correlation between the magnetic intensity and angular momentum. The results of this paper suggest that further study of the effects of internal variables such as density, velocity, pressure and temperature of a celestial body on $\Omega^\alpha$ may provide some new insights into the origin and evolution of celestial magnetic field.

Accumulation of proteins in filter membranes limits the efficiently of filtering technologies for cleaning wastewater. Efforts are ongoing to coat commercial filters with different materials (such as titanium-dioxide, TiO2) in order to reduce the fouling of the membrane. Beyond monitoring the desired effect of retention of biomolecules, it is demanding to understand what are the biophysical changes in water-soluble proteins caused by interacting with the new coated filter membranes, an aspect that has received little attention so far. Using spin label electron paramagnetic resonance (EPR), aided with native fluorescent spectroscopy and dynamic light scattering (DLS), here we report the changes in the structure and dynamics of bovine serum albumin (BSA) exposed to TiO2 (P25) nanoparticles or passing through commercial polyvinylidene fluoride (PVDF) membranes coated with the same nanoparticles. We have found that the filtering process and prolongued exposure to TiO2 nanoparticles had significant effects on different regions of BSA, and denaturation of the protein was not observed, neither with TiO2 nanoparticles nor by pressing through TiO2-coated filter membranes.

We propose a phenomenological theory of spin behavior in a magnetic field, which explains from the point of view of classical physics the two-valued result of the Stern-Gerlach experiment. The behavior of the spin and intrinsic magnetic moment of an electron wave of an atom in an external magnetic field is considered. We show that in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector. Within the framework of classical electrodynamics, the calculation of the motion of an atomic beam in an inhomogeneous magnetic field is carried out, which reproduces the results of the Stern-Gerlach experiment.

Labelling techniques such as electron paramagnetic resonance spectroscopy and single-molecule fluorescence resonance energy transfer, allow access to distances in the range of tens of angstroms, corresponding to the size of proteins and small to medium-sized protein complexes. Such measurements do not require long-range ordering and are therefore applicable to systems with partial disorder. Data from spin-label-based measurements can be processed into distance distributions that provide information about the extent of such disorder. Using such information in modelling presents several challenges, including a small number of restraints, the influence of the label itself on the measured distance and distribution width, and balancing the fitting quality of the long-range restraints with the fitting quality of other restraint subsets. Starting with general considerations about integrative and hybrid structural modelling, this review provides an overview of recent approaches to these problems and identifies where further progress is needed.

The X-ray induced spin crossover transition of an Fe(II) molecular thin film in the presence and absence of a magnetic field has been investigated. The thermal activation energy barrier in the soft X-ray activation of the spin crossover transition for [Fe{H2B(pz)2}2(bipy)] molecular thin films is reduced in the presence of an applied magnetic field, as measured through X-ray absorption spectroscopy at various temperatures. The influence of a 1.8 T magnetic field is sufficient to cause deviations from the expected exponential spin state transition behavior that is measured in the field free case. We find that orbital moment diminishes with increasing temperature, relative to the spin moment in the vicinity of room temperature.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

We examine here characteristics of electromagnetic waves that propagate through an unbounded space filled with a homogeneous isotropic chiral medium. Resulting characters are compared to those of the electromagnetic waves propagating through an achiral free space. To this goal, we form energy conservation laws for key bilinear parameters in a chiral case. Due to a nonzero medium chirality, conservation laws turn out to contain extra terms that are linked to the spin-orbit coupling, which is absent for an achiral case. As an example, we take a plane wave for achiral case to evaluate those bilinear parameters. Resultantly, the conservation laws for a chiral case are found to reveal inconsistencies among several bilinear parameters that constitute the con-servation laws , thereby prompting us to establish partial remedies for formulating proper wave-propagation problems.

The spin magnetic moments and spin g factors (g_s = -2) of electron, muon and tau are explained based on the electric charges (EC) and lepton charges (LC) in terms of the three-dimensional quantized space model. The spin g factors of electron, muon and tau are g_s = -2 which is the sum of the EC g factor (g_EC = -1) and the LC g factor (g_LC = -1). The spin g factor (g_s = -2) of the electron is predicted by the Dirac’s equation. The orbit g factors of electron, muon and tau are g_L = g_EC = -1 from the EC g factor (g_EC = -1) without the contribution of the LC g factor (g_LC = -1). The spin g factors of the elementary fermions are calculated from the equation of g_s = g_EC + g_LC + g_CC where g_EC = EC/|EC|, g_LC = LC/|LC| and g_CC = CC/|CC|. For example, the spin g factors of the neutrinos and dark matters are g_s = -1. The spin g factors of the u and d quarks are g_s = 0 and g_s = -2, respectively. The g factor problem of neutrinos with the non-zero LC charges are solved by the LC Coulomb force of F_c(LC) ≈0. It is, for the first time, proposed that the binary motion (fluctuations) of the m_EC and m_LC masses for the electron, muon and tau leptons make the anomalous g factor. This binary motion could be originated from the virtual particle processes including the photons. Also, the weak force (beta) decay is closely related to the binary motion of the m_EC and m_LC for the electron, muon and tau leptons.

Space-time evolution is briefly explained by using the 3-dimensional quantized space model (TQSM) based on the 4-dimensional (4-D) Euclidean space. The energy (E=cDtDV), charges (|q|= cDt) and absolute time (ct) are newly defined based on the 4-D Euclidean space. The big bang is understood by the space-time evolution of the 4-D Euclidean space but not by the sudden 4-D Minkowski space-time creation. The big bang process created the matter universe with the positive energy and the partner anti-matter universe with the negative energy from the CPT symmetry. Our universe is the matter universe with the negative charges of electric charge (EC), lepton charge (LC) and color charge (CC). This first universe is made of three dark matter -, lepton -, and quark - primary black holes with the huge negative charges which cause the Coulomb repulsive forces much bigger than the gravitational forces. The huge Coulomb forces induce the inflation of the primary black holes, that decay to the super-massive black holes. The dark matter super-massive black holes surrounded by the normal matters and dark matters make the galaxies and galaxy clusters. The spiral arms of galaxies are closely related to the decay of the 3-D charged normal matter black holes to the 1-D charged normal matter black holes. The elementary leptons and quarks are created by the decay of the normal matter charged black holes, that is caused by the Coulomb forces much stronger than the gravitational forces. The Coulomb forces are very weak with the very small Coulomb constants (k₁(EC) = k_dd(EC) ) for the dark matters and very strong with the very big Coulomb constants (k₂(EC) = k_nn(EC)) for the normal matters because of the non-communication of the photons between the dark matters and normal matters. The photons are charge dependent and mass independent. But the dark matters and normal matters have the similar and very weak gravitational forces because of the communication of the gravitons between the dark matters and normal matters. The gravitons are charge independent and mass dependent. Note that the three kinds of charges (EC, LC and CC) and one kind of mass (m) exist in our matter universe. The dark matters, leptons and quarks have the charge configurations of (EC), (EC,LC) and (EC,LC,CC), respectively. Partial masses of elementary fermions are calculated, and the proton spin crisis is explained. The charged black holes are not the singularities.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Changing the symmetry of spin from SU(2) to the quaternion group, $Q_8$, has many ramifications. In this paper we first summarize the properties of Q-spin and then discuss some of those resulting changes.

There are unsolved problems related to inflation, gravity, dark matter, dark energy, missing antimatter, and the birth of the universe. Some of them can be better answered by assuming the existence of aether and hypoatoms. Both were created during the inflation in the very early universe. While aether forms vacuum, hypoatoms, composed of both matter and antimatter and believed to be neutrinos, form all observable matter. In vacuum, aether exists between the particle-antiparticle dark matter form and the dark energy form in a dynamic equilibrium: A + A-bar = gamma + gamma. The same reaction stabilizes hypoatoms and generates a 3-dimensional sink flow of aether that causes gravity. Based on the hypoatom structure, the singularity does not exist inside a black hole; the core of the black hole is a hypoatom star or neutrino star. By gaining enough mass, ca. 3 X 10²² M_sun, to exceed neutrino degeneracy pressure, the black hole collapses or annihilates into the singularity, thus turning itself into a white hole or a Big Bang. The universe is anisotropic. Its center, or where the Big Bang happened, is at 0.66^+0.03_-0.01 times the radius of the observable universe at Galactic coordinates (l, b) = (286⁺¹⁰_-10, -43⁺⁷_-6). If we look from the Local Group to the center of the universe, the universe is rotating clockwise.

We present an overview over eight brightly luminescent Cu(I) dimers of the type Cu2X2(PN)3 with X = Cl, Br, I and P^N = 2-diphenylphosphino-pyridine (Ph2Ppy), 2-diphenylphosphino-pyrimidine (Ph2Ppym), 1-diphenylphosphino-isoquinoline (Ph2Piqn) including three new crystal structures (Cu2Br2(Ph2Ppy)3, 1-Br, Cu2I2(Ph2Ppym)3, 2-I, and Cu2I2(Ph2Piqn)3, 3-I). However, we mainly focus on their photo-luminescence properties. All compounds exhibit combined thermally activated delayed fluorescence (TADF) and phosphorescence at ambient temperature. Emission color, decay time, and quantum yield varies over large ranges. For deeper characterization, we select Cu2I2(Ph2Ppy)3, 1-I, showing a quantum yield of 81 %. DFT and SOC-TDDFT calculations provide insight into the electronic structures of the singlet S1 and triplet T1 states. Both stem from metal+iodide-to-ligand charge transfer transitions. Evaluation of the emission decay dynamics, measured from 1.2 ≤ T ≤ 300 K, gives ∆E(S1-T1) = 380 cm-1 (47 meV), a transition rate of k(S1→S0) = 2.25×106 s-1 (445 ns), T1 zero-field splittings, transition rates from the triplet substates, and spin-lattice relaxation times. We also discuss the interplay of S1-TADF and T1-phosphorescence. The combined emission paths shorten the overall decay time. For OLED applications, utilization of both singlet and triplet harvesting can be highly favorable for improvement of the device performance.

Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.