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The paper deals with the use of tripositive ion Eu3+ as a luminescent probe for the evaluation of the local site symmetry in coordination compounds with europium(III) content. The energy levels of the Eu3+ multiplets in the ligand matrix may be split by the crystal field into a maximum number of 2J+1 components, depending on the site symmetry of the Eu3+ion. Analysis of photoluminescence spectra provides information on the local site symmetry of the compound. The topic is discussed with reference to literature data as well as own experimental results obtained in the Laboratory of Optoelectronics "A. Andries" of the Institute of Applied Physics. This work gives a deeper insight into the spectral characteristics of Eu3+ ions in ligand matrices and can be a guiding support for investigation of photoluminescence in Eu(III) complexes.

In this paper, we study conformally flat almost Kenmotsu 3-manifolds such that tr h 2 is a constant and ∇ ξ h = - 2 α h φ for some constant α . Moreover, we classify conformally flat H-almost Kenmotsu 3-manifolds. [ABSTRACT FROM AUTHOR]

Investigation of the VO2+ ions in a single crystal of glycine zinc sulphate (GZS) using electron paramagnetic resonance (EPR) spectroscopy is done at ambient temperature. The single crystal was formed using a solution growth process that slowly evaporated at room temperature. EPR spectrum has been recorded for three mutually orthogonal crystal planes of the prepared GZS single crystal. In the present research work, two identical distinguishable VO2+ ion sites have been followed and analyzed. According to the calculated g-principle values, the examination of the hyperfine line positions for all three planes explains why the impurity ion occupies rhombic crystal field symmetry with the surrounding ligands. Additionally, it is revealed that both sites occupy as a substitutional position in the crystal lattice site by taking the place of the zinc ion site, since the effect of spin–orbital motion coupling is dependent on the distinct nature of the paramagnetic ion environment. The optical absorption spectrum of vanadyl ions-doped glycine zinc sulphate was measured in the UV–Vis–NIR range. Comparing Spin Hamiltonian parameters and optical absorption studies, the molecular orbital coefficient values, such as β1*2, β2*2, eπ*2, K, (1 − α2), and (1 − γ2), were calculated. From the above data, the ionic bonding nature and contribution of σ, π bonding were found out which decide the different behaviors of electrons affecting the crystal properties. These results indicate that the GZS-VO2+ single crystal system could serve as a suitable material for the NLO device application. [ABSTRACT FROM AUTHOR]

In this paper, we study the semi-symmetry and pseudo-symmetry of almost cosymplectic 3 -manifolds. First, we prove that an H -almost cosymplectic 3 -manifold M is semi-symmetric if and only if it is cosymplectic. Here by an H -almost cosymplectic 3 -manifold, we mean an almost cosymplectic 3 -manifold whose characteristic vector field ξ is a harmonic unit vector field. If an almost cosymplectic 3 -manifold M whose fundamental endomorphism field h is parallel in the direction of the characteristic vector field ξ ( ∇ ξ h = 0), then it is H -almost cosymplectic. In particular, an almost cosymplectic 3 -manifold M satisfying ∇ ξ h = 0 is semi-symmetric if and only if it is cosymplectic. Next, we prove that pseudo-symmetric H -almost cosymplectic 3 -manifolds are certain generalized almost cosymplectic (κ , μ , ν) -spaces. [ABSTRACT FROM AUTHOR]

The paper presents a new algorithm for reflection symmetry detection, which is specialized to detect maximal symmetric patterns in an Earth observation (EO) dataset. First, we stress the particularities that make symmetry detection in EO data different from detection in other geometric sets. The EO data acquisition cannot provide exact pairs of symmetric elements and, therefore, the approximate symmetry must be addressed, which is accomplished by voxelization. Besides this, the EO data symmetric patterns in the top view usually contain the most useful information for further processing and, thus, it suffices to detect symmetries with vertical symmetry planes. The algorithm first extracts the so-called interesting voxels and then finds symmetric pairs of line segments, separately for each horizontal voxel slice. The results with the same symmetry plane are then merged, first in individual slices and then through all the slices. The detected maximal symmetric patterns represent the so-called partial symmetries, which can be further processed to identify global and local symmetries. LiDAR datasets of six urban and natural attractions in Slovenia of different scales and in different voxel resolutions were analyzed in this paper, demonstrating high detection speed and quality of solutions. [ABSTRACT FROM AUTHOR]

In addition to being a typical red light emitting center, Eu3+ can also be used to study the evolution of lattice symmetry due to its unique electric dipole leap (5D 0 -7F 2) sensitivity to the lattice environment. Here, we synthesized a series of Ba 1-x Sr x La 0.9 LiWO 6 : 0.10Eu3+ (x = 0.0–1.0) phosphors and used the leap properties to establish a link between the evolution of the lattice environment and the luminescence properties. The introduction of Sr2+ does not affect the lattice type avoiding the effect of phase transition on the luminescence intensity. The lattice symmetry reaches a minimum at Sr2+ concentration of 0.8, which corresponds exactly to the peak of the luminescence intensity. It demonstrated the feasibility of adjusting the occupancy symmetry of Eu3+ to achieve luminescence enhancement. The covalent effect on the luminescence properties in this system is weak compared to the environmental changes by analyzing the attraction of the cations to O2− in the luminescence center neighbors. At the optimal doping concentration, Ba 0.2 Sr 0.8 La 0.6 LiWO 6 : 0.40Eu3+ phosphor has excellent internal quantum efficiency 95.3%, good color purity 94.79%, and extremely standard color coordinates (0.667, 0.332). In addition, it still has 80.6% emission intensity at 200°C compared to room temperature, which means it has good thermal stability. The good comprehensive performance has laid an important foundation for its application in WLED. [ABSTRACT FROM AUTHOR]

Due to the extrinsic contribution of domain wall motions to electro-strains, the incompatibility of the large electro-strain with a low hysteresis in piezoelectric ceramics is a stumbling block for designing high-performance piezoelectrical actuators. Herein, we report a critical state in relaxor ferroelectric systems enables to enhance the electro-strain and to reduce the hysteresis simultaneously. A room temperature ergodic relaxor state dominated by nanodomains with different local symmetries can be obtained by introducing Bi(Zn1/2Ti1/2)TiO3 into 0.73 Pb(Mg1/3Nb2/3)O3-0.27PbTiO3 matrix. Like the morphotropic phase boundary (MPB) in ferroelectrics, the coexistence of different local symmetries is capable of facilitating the transition from the ergodic relaxor state to the ferroelectric under the applied field due to the ease of polarization rotation, thereby leading to a giant electro-stain (0.24%) under an electric field of 50 kV/cm. Furthermore, the field-induced ferroelectric state with the long-range ferroelectric order can spontaneously reverse back to the initial ergodic relaxor state during unloading the electric field, which contributes to a low hysteresis (15.4%). The present work not only introduces a solid solution system with excellent electro-strain properties but also affords a guidance for manipulating the electro-strain behavior by modulating phase structures and domain configurations of piezoelectric ceramics.

Local graph symmetry groups act in a non-identical fashion on just a proper (local) subset of a graph's vertices, and consequent theorems for adjacency matrices simplify eigen-solutions. These theorems give a way to deal with a hierarchy of local sub-symmetries, such as are manifested by so-called "dendrimers", which are (highly) branched polymers obtainable at a given generation number r from the polymer at the preceding generation number (r − 1) by connecting d copies of new branching monomer units to each end-unit of this preceding tree-like dendrimer, the initial generation number r = 1 consisting of a single monomer unit connected to d others. Our local symmetry methodology leads to an (essentially) analytic eigen-solution for the Bethe tree case, with the branching units just single sites—but further there result novel (qualitatively distinctive) features: eigenvector localization and eigenvalue clumping. Moreover, these novel characteristics persist for more general "dendrimers", here considered and illustrated in the context of electronic structure of conjugated-carbon π-networks. The overall view here is of a systematic development and characterization for such dendrimer polymers paralleling some aspects of the standard development and characteristics for linear-chain benzenoid polymers—for instance, that of plotting eigen-energies as a function of symmetry. Clumping of eigen-spectra, and localization features in dendrimer eigenfunctions occur and are examined. [ABSTRACT FROM AUTHOR]

The luminescence center energy transfer, crystal field strength, and covalency are limited by the crystal structure of the host and subsequently affect the luminescence efficiency, color, and intensity. Here, we report an excellent red phosphor BaLaLiWO 6 :0.40Eu3+ and the dependence between symmetry and luminous performance. A model for changing symmetry is drawn by analyzing the Coulomb potential and structure for the application of a double-perovskite phosphor BLLWO: Dy3+, Eu3+ in white light LEDs. The addition of Dy3+/Eu3+ makes the W-O bond formed by the B-site and oxygen ion longer and the Li-O bond shorter, and the difference between the eight octahedral around the A-site is reduced, increasing the symmetry of the A-site. Local symmetry was successfully modulated by changing the Eu3+ concentration to control the Y/B ratio of Dy3+ and the R/O ratio of Eu3+ and smoothly achieved (0.382, 0.373) warm white light color coordinate. The phosphor has excellent thermal stability and still has 92.3% intensity at 475 K. The above results show that the wavelength composition of the luminescence is tunable by changing the symmetry of the environment in which the doped ions are located. It applies to single hosts for the regulation of white light emission. [ABSTRACT FROM AUTHOR]

We are interested in the possibility of using Brandt groupoids in physical chemistry. They can, in particular, describe local symmetry and spatially limited motion of particles, in which the latter can move only a limited distance from their initial position. As an illustrative example, we consider the mutual exchange of the positions of the ligands in the coordination compounds. [ABSTRACT FROM AUTHOR]

In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we generalize the results of H. Liu and J. Li [2], and add some further facts, such as an optimal system of Lie symmetry subalgebras and two local symmetries.

Classification theorems of locally symmetric, second-order locally symmetric, Ricci symmetric, semi-symmetric and Ricci semi-symmetric generalized Robertson-Walker (in short, GRW) spacetime I f × N are given. Some implications for these symmetries of GRW space-times are considered. A summary of sufficient conditions on the warping function f and the fibre manifold N is given to verify each symmetry. [ABSTRACT FROM AUTHOR]

Newton's rings serve a crucial role in interferogram analysis for estimating physical parameters, including the radius of curvature of lenses and the centre of the rings. The fractional Fourier transform (FRFT), traditionally employed for extracting physical parameters from Newton's rings, is characterised by its time-intensive nature. This study identified the local symmetry of maximum amplitude within FRFT domains across varying rotation angles associated with Newton's rings. Utilising this local symmetry, an optimisation approach utilising triangle shrinkage was introduced, enhancing the efficiency of FRFT in determining physical parameters from Newton's rings. This innovation significantly reduces the time required for parameter estimation while maintaining the accuracy levels of the FRFT and non-uniform order searching (NOS) methods. Experimental outcomes confirm that our proposed method effectively addresses diverse scenarios and yields superior results. Notably, the method processes 1080 × 1080 pixel images within approximately 3.3 s, significantly faster than both the FRFT and NOS methods, by factors of approximately 1/800 and 1/2, respectively. • The paper discloses the local symmetry of the maximum magnitude in the FRFT domains. • The triangle shrinkage method is proposed. • The validity of the method is suitable for practical measurements. [ABSTRACT FROM AUTHOR]

Preparation and structural analysis of BaLaGa 3 O 7 :Eu3+ red phosphor Theoretical design and successful introduction of Dy3+ to smooth the color coordinates to the white light color coordinate range; modeling the crystal model to verify the interaction of symmetry and luminescence features. [Display omitted] Melilite structured phosphor is a significant luminescent material, but limited by its structure and luminescent properties, its luminescence intensity and spectral composition cannot satisfy the application requirements. To solve this issue, we look into the connection for the first time between the amount of rare-earth elements added and the symmetry of structure in melilite phosphors. We got the results by looking at the PL spectral data and J-O parameters of the melilite phosphor BaLa 1−x−y Ga 3 O 7 :xDy3+,yEu3+. Dy3+ was located in the low symmetry site, resulting in the local asymmetry being successfully enhanced to obtain warm-white color coordinates (0.398, 0.393) by adjusting the concentration of Eu3+ to vary the Y/B ratio of Dy3+ and the R/O ratio of Eu3+. Meanwhile, in the way that energy is transferred with an electric quadrupole-electric quadrupole between phosphor dopant ions. The energy transfer efficiency of Dy3+-Eu3+ is up to 81.99 %. At 475 K, the phosphor maintains an intensity of 81.1 % and exhibits reliable thermal stability. The color purity and EQE of BLGO:0.40Eu3+ are 49.7 % and 38.56 %, respectively. These results reveal that modifying the local symmetry surrounding the doped ions allows for adjusting the luminescence's wavelength composition. This approach can be applied to phosphors generated for warm white light-emitting diodes (WLEDs) with a single matrix. [ABSTRACT FROM AUTHOR]

In functional materials, the local environment around active species that may contain just a few nearest‐neighboring atomic shells often changes in response to external conditions. Strong disorder in the local environment poses a challenge to commonly used extended X‐ray absorption fine structure (EXAFS) analysis. Furthermore, the dilute concentrations of absorbing atoms, small sample size and the constraints of the experimental setup often limit the utility of EXAFS for structural analysis. X‐ray absorption near‐edge structure (XANES) has been established as a good alternative method to provide local electronic and geometric information of materials. The pre‐edge region in the XANES spectra of metal compounds is a useful but relatively under‐utilized resource of information of the chemical composition and structural disorder in nano‐materials. This study explores two examples of materials in which the transition metal environment is either relatively symmetric or strongly asymmetric. In the former case, EXAFS results agree with those obtained from the pre‐edge XANES analysis, whereas in the latter case they are in a seeming contradiction. The two observations are reconciled by revisiting the limitations of EXAFS in the case of a strong, asymmetric bond length disorder, expected for mixed‐valence oxides, and emphasize the utility of the pre‐edge XANES analysis for detecting local heterogeneities in structural and compositional motifs. [ABSTRACT FROM AUTHOR]

Four biradical‐Ln complexes with different transition metal ions, namely [LnM(hfac)5(NITPh‐PyPzbis)] (MII=MnII and LnIII=Gd 1, Dy 2; MII=NiII and LnIII=Tb 3, Dy 4), were prepared by the reaction of Ln(hfac)3 ⋅ 2H2O, Mn(hfac)2 ⋅ 2H2O or Ni(hfac)2 ⋅ 2H2O with NITPh‐PyPzbis biradical (hfac=hexafluoroacetylacetonate, NITPh‐PyPzbis=5‐(3‐(2‐pyridinyl)‐1H‐pyrazol‐1‐yl)‐1,3‐bis(1'‐oxyl‐3'‐oxido‐ 4',4',5',5'‐tetramethyl‐4,5‐hydro‐1H‐imidazol‐2‐yl)benzene). In complexes 1–4, the NITPh‐PyPzbis biradical chelates one LnIII ion by means of its aminoxyl moieties and the transition metal ion is introduced through the two N donors from the pyridyl pyrazolyl moiety. Magnetic investigations indicate that complex 4 displays visible maxima in frequency/temperature‐dependent χ′′ signals with two‐step relaxation processes, but complex 2 exhibits no slow magnetization relaxation. The comparison of structure parameters of both Dy complexes indicates that the symmetries of coordination spheres of two Dy ions are D2d for 2 and C2v for 4, which thus probably results in different magnetic relaxation behaviors. This work provides new insight for improving properties of Ln‐biradical based SMMs. [ABSTRACT FROM AUTHOR]

Despite the high energy density of Ni‐rich layered‐oxide electrodes, their real‐world implementation in batteries is hindered by the substantial voltage decay on cycling, which mainly originates from bulk and surface structural degradation. Here, in operando observation of cation disorder, a major origin of structural degradation, reveals the voltage decay mechanism in Ni‐rich cathode. Viewed along [1 1–0] and [110] orientations by scanning transmission electron microscopy, it is demonstrated that transition metal (TM) migration gives rise to the drastic fluctuation of interlamellar spacing and NiO bond length, but almost exerts no influence on atom site in ab plane. Density functional theory calculations reveal that the fluctuation of the NiO bond length triggers voltage decay via lifting the energy level of the antibonding (3dz2‐2p)* orbits. Broadening bands by a shorter NiO bond increase the voltage slope of battery, which will reduce the accessible Li capacity within the stable voltage range of the electrolyte. Furthermore, a collaborative path of TM migration triggered by oxygen vacancy is verified to account for the TM migration. The finding provides insights into new chemistry to be explored for developing high‐capacity layered electrodes that evade voltage decay. [ABSTRACT FROM AUTHOR]

The behavior of lithium donors in bulk single-crystal isotopically pure Si1 –xGex alloys (x = 0.0039–0.05) enriched in spinless 28Si and 72Ge isotopes (99.998 and 99.984%, respectively) is investigated by electron spin resonance. The fine structure of the spectrum of electrons localized at Li donors is studied at temperatures of T = 3.5–30 K in the expectation that, much like with pure silicon, enriching Si1 –xGex alloys in spinless isotopes (28SiisoGe, where iso = 70, 72, 74, 76) makes it possible to attain a higher resolution in the spectra of electron spin resonance. The results demonstrate that, despite the irregular arrangement of Ge atoms in the lattice of the 28Si1 –x72Gex alloy, the presence of local distortions in their vicinity, and the broadening of the electron-spin-resonance lines of donor electrons due to random strains, the lines of Li donors observed in the spectra of isotopically pure 28Si1 –x72Gex single crystals with x = 0.39, 1.2, and 2.9 at. % are narrower than the corresponding lines in the spectra of similar crystals with the natural composition of silicon and germanium isotopes. Similarly to the case of silicon crystals, this allowed us to study for the first time the angular dependences of the line positions in the electron-spin-resonance spectra of lithium in Si1 –xGex for different values of x. [ABSTRACT FROM AUTHOR]

For square contingency tables with nominal categories, a local symmetry model which indicates the symmetric structure of probabilities for only one pair of symmetric cells is proposed. For ordinal square tables, the present paper proposes (1) another local symmetry model for cumulative probabilities from the upper-right and lower-left corners of the table, and (2) a measure to represent the degree of departure from the proposed model. The measure has the form of a weighted harmonic mean of the diversity index, which includes the Shannon entropy as a special case. Examples are given in which the proposed method is applied to square table data on decayed teeth in Japanese women patients. [ABSTRACT FROM AUTHOR]

The fully nonlinear notion of resonance − geometrical resonance − in the general context of dissipative systems subjected to spatially periodic phase-modulated potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system's energy when the potential is stationary. The geometrical resonance solutions represent a local symmetry whose critical breaking leads to a new analytical criterion for the onset of chaotic instabilities. This physical criterion is deduced in the co-moving frame from the local energy conservation over the shortest significant timescale. Remarkably, the new physical criterion for the onset of chaotic instabilities is shown to be valid over large regions of parameter space, thus being useful beyond the scope of current mathematical techniques. More importantly, the present theory helps to understand the unreasonable effectiveness of the Melnikov's method beyond the perturbative regime. • A theory of geometrical resonance in dissipative systems subjected to spatially periodic phase-modulated potentials has been presented. • The present physical theory suggests understanding the onset of homoclinic chaotic instabilities as being coincident with a critical breaking of the geometrical resonance local symmetry , specifically, as coinciding with a critical breaking of the local conservation of the separatrix's energy. • The present theory helps to understand the unreasonable effectiveness of the predictions of the Melnikov's method beyond the perturbative regime. [ABSTRACT FROM AUTHOR]

W ,κ µ-spaces with κ< are locally -symmetric.e define complex locally -symmetric spaces. As an example we prove that complex -spaces with κ

A solvent effect towards the performance of two single-molecule magnets (SMMs) was observed. The tetrahydrofuran and toluene solvents can switch the equatorial coordinated 4-Phenylpyridine (4-PhPy) molecules from five to four, respectively, in [Dy(OtBu)2(4-PhPy)5]BPh41 and Na{[Dy(OtBu)2(4-PhPy)4][BPh4]2}∙2thf∙hex 2. This alternation significantly changes the local coordination symmetry of the Dy(III) center from D5h to D4h for 1 and 2, seperately. Magnetic studies show that the magnetic anisotropy energy barrier of 2 is higher than that of 1, while the relation of blocking temperature is just on the contrary due to the symmetry effect. The calculations of the electrostatic potential successfully explained the driving force of solvents for the molecular structure change, confirming the feasibility of adjusting the performance of SMMs via diverse solvents.

A systematic application of the MP procedure [Baggio (2019). Acta Cryst. C75, 837–850] to a subset of Z′ = 4 structures in the literature revealed a number of suggestive properties in many of the cases analysed, which allowed us to conclude that: (i) very few of those structures showed no pseudosymmetry (PS) whatsoever linking any of the possible moiety pairs in the asymmetric unit (AU), the vast majority disclosing, instead, at least two (and frequently more) molecules linked by these PS operations; (ii) on occasion, two pairs of molecules were related, each by the same PS element, enabling the resulting pair of dimers to be viewed locally as a Z′ = 2 rather than a Z′ = 4 case; (iii) sometimes all four moieties in the AU appeared interrelated by PS relationships, closely suggesting a distribution of symmetry operations as found in real space groups; (iv) in many cases, this resemblance was of a superior quality, leading to surprising local replicas of real space groups in the reduced realm of the AU, thus locally reducing the description to a Z′ = 1 one. Through a systematic application of the MP procedure, we analyze in this article a number of these latter cases, which proved to be surprisingly common, far beyond any original expectation, and leaving open the question about the eventual reasons for the phenomenon, which would certainly merit appropriate theoretical attention. [ABSTRACT FROM AUTHOR]

Blue and green turquoise–planerite species from Carico Lake Valley in Nevada have the formulae □0.69(Na0.01K0.01Cu0.20Ca0.06Mg0.02Ba0.01 Zn0.01)(Al5.97V0.04 Fe0.03)[PO4]4 (OH)8·4H2O and □0.66(K0.01Cu0.24Ca0.05Mg0.02Ba0.01Zn0.01)(Al5.87Fe0.13)[PO4]4(OH)8·4H2O, respectively. The content of Al3+ and Fe3+ at the B‐site together with slight differences in Cu amount at the A‐site is the main factors that differentiate these two species. Green planerite shows higher crystallinity and contains less water in its structure. The blue species is more porous with a lower degree of structural order and higher water enrichment. The Cu/Fe ratio together with local symmetry around chromophore ions in the structure seem to be responsible for the specific colouration of both phosphates. The species are inhomogeneous and contain a wealth of mineral (goethite, barite, quartz, kaolinite, chloritoid, destinezite, and some vanadate) and organic inclusions (bituminous matter and aliphatic hydrocarbons). Raman microspectroscopy with the application of different exciting radiation, that is, laser lines of 514.5 nm (green) and 442 nm (blue) for blue and green turquoise–planerite species revealed further differences between these two coloured species: (a) various positions of the most intensive band attributed to ν3 (PO4)3‐, (b) shift of ν3 four component bands, (c) various intensity ratios and integral intensity ratios of ν3 component bands, and (d) some diagnostic bands coming from Fe‐O (green species) and Cu‐O vibrations (blue species) obtained with principal component analysis (PCA). [ABSTRACT FROM AUTHOR]

The crystallographic analysis of the structures of [Hg7As4](AgI3)2 (I), [Hg6As4Br3](SnBr3) (II), and [Hg11As4](GaBr4)4 (III) treated as host-guest structures is performed. It is shown that the spatial basis ("skeleton") of the structures is formed by crystallographic planes densely occupied by mercury and halogen atoms. The cubic symmetry of the first two structures is initiated by the local symmetry of the ([As2]Hg6) building block. The C2/m symmetry of the third structure is initiated by the 2/m local symmetry of the blocks with linear groups containing [Hg2] and [Hg3] fragments. [ABSTRACT FROM AUTHOR]

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern consisting of disjoint congruent symmetric motifs. The pattern has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of , a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of , the symmetry of that is both a global and local symmetry, effects the same permutation of the colors used to color and the corresponding motif, respectively. [ABSTRACT FROM AUTHOR]

We study a Markovian agent-based model (MABM) in this paper. Each agent is endowed with a local state that changes over time as the agent interacts with its neighbours. The neighbourhood structure is given by a graph. Recently, Simon, Taylor, and Kiss [40] used the automorphisms of the underlying graph to generate a lumpable partition of the joint state space, ensuring Markovianness of the lumped process for binary dynamics. However, many large random graphs tend to become asymmetric, rendering the automorphism-based lumping approach ineffective as a tool of model reduction. In order to mitigate this problem, we propose a lumping method based on a notion of local symmetry, which compares only local neighbourhoods of vertices. Since local symmetry only ensures approximate lumpability, we quantify the approximation error by means of the Kullback–Leibler divergence rate between the original Markov chain and a lifted Markov chain. We prove the approximation error decreases monotonically. The connections to fibrations of graphs are also discussed. [ABSTRACT FROM AUTHOR]

The phase transition of E‐vanillyl oxime {1‐[(E)‐(hydroxyimino)methyl]‐4‐hydroxy‐3‐methoxybenzene, C8H9NO3} has been analysed by single‐crystal and powder X‐ray diffraction. The high‐temperature (HT) phase (P21/a, Z′ = 1) transforms into the low‐temperature (LT) phase (threefold superstructure, , Z′ = 6) at ca 190 K. The point operations lost on cooling, {m[010], 2[010]}, are retained as twin operations and constitute the twin law. The screw rotations and glide reflections are retained in the LT phase as partial operations acting on a subset of Euclidean space. The full symmetry of the LT phase, including partial operations, is described by a disconnected space groupoid which is built of three connected components. [ABSTRACT FROM AUTHOR]

An intuitive method is presented for detecting pseudosymmetries in Z′ > 1 cases as a complement to well‐proven strategies already available in the literature. It is based in the simple idea that the mid‐points between equivalent atoms in symmetrically related molecules are disposed according to simple well‐known patterns, which are easily recognizable by optical inspection. A number of Z′ = 4 cases in the literature are analyzed, which allows some of the potentialities of the method to be revealed. [ABSTRACT FROM AUTHOR]

This paper describes a systematic study of the spectra and local structures of lanthanide (Ln) L‐edge XANES. We found that Ln L1 and L3‐edge XANES spectra exhibit characteristic features correlated to their local symmetry through experimental and theoretical simulations. We also propose a simple local structure index criterion for a combination of XANES study and theoretical simulation. Possible solutions of intrinsic problems such as low resolution of characteristic features in the Ln L‐edge XANES and site distributions are also discussed. [ABSTRACT FROM AUTHOR]

We consider the unit tangent sphere bundle of Riemannian manifold (M, g) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of (M, g) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficient for the g-natural metric G̃ to be locally symmetric. [ABSTRACT FROM AUTHOR]

Highlights • Ni doped SnO 2 thin films were deposited on Si substrate (001) by PLD technique. • NEXAFS at Ni L 3,2 edges confirmed that the Ni ions exist in high spin divalent ground state. • The UHV assisted growth condition created a favorable condition for oxygen non-stoichiometry. • A significant modification have be observed in the surface morphology. • Magnetic behavior seems to be more relevant to the formation of VO2+ at the surfaces. Abstract We have investigated the ferromagnetic behavior, electronic states and local geometrical structure of Ni (2 and 10 at %) doped SnO 2 thin films. The films were successfully fabricated with the help of pulsed laser deposition (PLD) technique on Si (100) substrate under ultrahigh vacuum (UHV) condition. X-ray diffraction (XRD) results revealed the single phase character of SnO 2 rutile lattice structure with P4 2 /mnm space group. The inclusion of Ni ions into SnO 2 matrix induced oxygen vacancy (Vo), enhanced the distortion in octahedral local symmetry and reduced the oxidation state of the host Sn4+ (SnO 2) to Sn3+ (Sn 2 O 3), these details have been estimated by Raman scattering, Near edge X-ray absorption fine structure (NEXAFS) spectra at Ni L 3,2 and O K edges. Further quantitative details on the local geometrical structure around Ni ions were obtained via fitting the experimental Fourier transforms EXAFS spectra |X(R)| with FEFF6 code. The magnetization measurements performed at room temperature (RT) infers that Ni doped SnO 2 films displayed ferromagnetic (FM) signal, and there was no significant difference in the saturation moments even with increase in the Ni content. Hence, the similarity in the observed magnetic behavior of the films seems relevant to the same crystal growth condition (UHV) and might not be limited directly to the Ni dopant concentrations. The FM signal and the role of surface defects have been discussed in the light of spin-split impurity band percolation mechanism. [ABSTRACT FROM AUTHOR]