Complex Symmetry Research Articles

On the Jahn-Teller Effect in Silver Complexes of Dimethyl Amino Phenyl Substituted Phthalocyanine.

The structures of Ag complexes with dimethyl amino phenyl substituted phthalocyanine m[dmaphPcAg]q of various charges q and in the two lowest spin states m were optimized using the B3LYP method within the D4h symmetry group and its subgroups. The most stable reaction intermediate in the supposed photoinitiation reaction is 3[dmaphPcAg]-. Group-theoretical analysis of the optimized structures and of their electron states reveals two symmetry-descent mechanisms. The stable structures of maximal symmetry of complexes 1[dmaphPcAg]+, 3[dmaphPcAg]+, 2[dmaphPcAg]0, and 4[dmaphPcAg]2- correspond to the D4 group as a consequence of the pseudo-Jahn-Teller effect within unstable D4h structure. Complexes 4[dmaphPcAg]0, 1[dmaphPcAg]-, 3[dmaphPcAg]-, and 2[dmaphPcAg]2- with double degenerate electron ground states in D4h symmetry structures undergo a symmetry descent to stable structures corresponding to maximal D2 symmetry, not because of a simple Jahn-Teller effect but due to a hidden pseudo-Jahn-Teller effect (strong vibronic interaction between excited electron states). The reduction of the neutral photoinitiator causes symmetry descent to its anionic intermediate because of vibronic interactions that must significantly affect the polymerization reactions.

Comparative Analysis of T4SS Molecular Architectures.

The recently published high-resolution R388 T4SS structure provides exciting new details about the complete complex of T4SS, including the components making up the stalk and arches, numerous symmetry mismatches between regions of the complex, and an intriguing interpretation of the closed stalk and radial symmetry of the inner membrane complex, which is related to pilus biogenesis assembly. However, there are a few unidentified densities in the electron microscopy map and portions of the identified component sequences for which the structure is not yet known. It is also unclear how well this minimized DNA-transporting T4SS predicts the structure of other T4SSs, such as expanded systems and those that transport proteins rather than DNA. In this review, we evaluate what can be inferred from the recent high-resolution structure of the R388 T4SS with respect to the Cag and Dot/Icm systems. These systems were selected because, given what is currently known about these systems, we expect them to present most structural differences compared to the R388 T4SS structure. Furthermore, we discuss bacterial physiology and diversity, the T4SS structures and their variations between different bacterial species. These insights may prove beneficial for researchers who elucidate the structure and functions of T4SS in different bacterial species.

Light- and Chemical-Doping-Induced Magnetic Behavior of Eu Molecular Systems.

Variable temperature electron paramagnetic resonance (VT-EPR) was used to investigate the role of the environment and oxidation states of several coordinated Eu compounds. We find that while Eu(III) chelating complexes are diamagnetic, simple chemical reduction results in the formation of paramagnetic species. In agreement with the distorted D3h symmetry of Eu molecular complexes investigated in this study, the EPR spectrum of reduced complexes showed axially symmetric signals (g⊥ = 2.001 and g∥ = 1.994) that were successfully simulated with two Eu isotopes with nuclear spin 5/2 (151Eu and 153Eu with 48% and 52% natural abundance, respectively) and nuclear g-factors 151Eu/153Eu = 2.27. Illumination of water-soluble complex Eu(dipic)3 at 4 K led to the ligand-to-metal charge transfer (LMCT) that resulted in the formation of Eu(II) in a rhombic environment (gx = 2.006, gy = 1.995, gz = 1.988). The existence of LMCT affects the luminescence of Eu(dipic)3, and pre-reduction of the complex to Eu(II)(dipic)3 reversibly reduces red luminescence with the appearance of a weak CT blue luminescence. Furthermore, encapsulation of a large portion of the dipic ligand with Cucurbit[7]uril, a pumpkin-shaped macrocycle, inhibited ligand-to-metal charge transfer, preventing the formation of Eu(II) upon illumination.

Real symmetric, unitary, and complex symmetric weighted composition operators on Bergman spaces of polydisk

In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators are not assumed to be bounded. The properties of weighted composition operators such as real symmetry, unitariness, complex symmetry, are characterized fully in simple algebraic terms, involving their symbols. As it turns out, a weighted composition operator having a symmetric structure must be bounded. We also obtain the interesting consequence that real symmetric weighted composition operators are complex symmetric corresponding an adapted and highly relevant conjugation.

Complex symmetry of differential operators on generalized Fock spaces

In this paper, we classify the family of entire functions [Formula: see text] such that the induced weighted composition map [Formula: see text], is a conjugation namely [Formula: see text], where [Formula: see text] is an arbitrary complex number and [Formula: see text] is a real number such that [Formula: see text]. In the last section, we characterize the [Formula: see text]-symmetric maximal differential operators on the Fock space [Formula: see text].

Антропометричні особливості обличчя у дітей з уродженими дефектами коміркового відростка верхньої щелепи до хірургічного втручання

The purpose of the study was to investigate the anthropometric parameters of the nasolabial complex in patients with different sizes of the congenital defect of the alveolar process before surgical intervention. Materials and methods. To achieve the goal, a clinical assessment of the nasolabial complex was carried out in 54 children with clefts of upper lip and palate (aged 10 to 19 years). The next indicators were included: the length of the nasal wing, the width of the bottom in the nostril, the vertical displacement of the nasal wing and their ratios. The children were divided into three subgroups, depending on the size of the bone defect, which involved the planning of a different type of surgical intervention: 1 (n=13) – recovery of the defect without osteoplasty, 2 (n=11) – osteoplasty using the mandibular symphysis tissue, 3 (n=30) – osteoplasty using an autograft from tibia. Results and discussion. Clefts of upper lip and palate are accompanied by numerous anatomical and functional disorders in the maxillofacial system. Reconstruction of the maxilla alveolar processes on the cleft side is a necessary stage of the complex rehabilitation of the patient. The degree of severity of functional disorders in cases of clefts of upper lip and palate depends on many factors and conditions – the form and size of the cleft, the patient's age, concomitant local and general somatic pathology, as well as the success of the performed complex treatment. Fixation of the patient's rehabilitation process by photography and analysis of clinical photos are important components of evaluation of treatment results. The volume of the congenital (residual) defect of the alveolar process on maxilla directly affects the level of facial asymmetry which is reflected in changes in the ratios on the affected and healthy side – the length of the nasal wing, the width of the nostril, the angles of the base of the nasal wing. Such anthropometric data may be crucial points in the selection of surgical intervention methods and the use of different autologous transplants. The obtained results are consistent with similar studies by Ajami S., 2020, which established pronounced differences in the structure of the nasolabial complex even under the conditions of full and timely rehabilitation of children with congenital cleft of the upper lip and palate, compared to the ethnic anthropometric norm of healthy patients. And the sooner the integrity of the upper lip is restored, the better the symmetry of the nasolabial complex is achieved. Alveolar process plasty significantly equalizes the symmetry of the nose and upper lip in patients with congenital cleft of the upper lip and palate, which was shown by three-dimensional anthropometric studies in a number of clinics around the world. Conclusion. Anthropometry (photogrammometry) of the nasolabial complex on the face is an additional method in diagnostic that is necessary to make the correct clinical decisions during the planning of reconstructive interventions on the maxilla in case of clefts of lip and palate

Complex symmetric generalized weighted composition operators on Hilbert spaces of analytic functions

We investigate complex symmetry of a generalized weighted composition operator Dn,v,ψ on the reproducing kernel Hilbert space Hγ of analytic functions on the unit disk D. We first characterize a class of anti-linear weighted composition operators that are conjugations with a new approach. Then we obtain necessary and sufficient conditions for Dn,v,ψ to be complex symmetric with respect to these conjugations. Our results not only generalize and unify the ones in the literature, but also provide an affirmative answer to a question from a paper of Lim and Khoi (2018) [16]. The classes of self-adjoint, normal, unitary generalized weighted composition operators on Hγ and their relations with the property of complex symmetry are also studied.

Chiral Hierarchical Architecture Induced by Confinement-Assisted Living Supramolecular Polymerization of Simple Achiral Molecules

Chiral supramolecular assembly (CSA) based on achiral molecules has provided important clues to understand the origin of biological chirality. However, a simple achiral monomer faces the challenge of chiral stacking with the absence of a chiral resource. The difficulty is that simple achiral monomer lacks steric repulsion to provide asymmetry during hierarchical assembly, which is a prerequisite for chiral stacking with an angle. Moreover, during chiral stacking of achiral molecules or units, the right-handed and left-handed chiral supramolecular isomers (CSIs) are equally formed due to the mirror-imaged conformation, which leads to chirality silence. Here, with the benefit of two-dimensional confinement space of layered double hydroxide (LDH), simple achiral molecules can be arranged to staggered bilayer arrays by imprinting the topological structure of LDH. Once LDH is removed, these staggered arrays can form asymmetric living seeds, which can further elongate to living units with the advantage of living supramolecular polymerization (LSP) by following off-pathway. Due to the asymmetry of living units, the possible chiral stacking outcomes, CSIs, are not mirror-imaged. With the increase of the molecular number in living units, the energy difference between CSIs can be amplified by self-replication of LSP, leading to handedness preference. Thus, the detectable CSA is mainly derived from the CSI with energetically favored hierarchical structure. Thus, our strategy breaks the stereotype that the complex molecular structure and symmetry breaking mechanism are necessary for the formation of detectable CSA by achiral molecules.

Structured ground states of randomly interacting bosons

Bosonic degrees of freedom and their emergence as part of complex quantum many-body dynamics, symmetries, collective behavior, clustering, and phase transitions play an important role in modern studies of quantum systems. In this paper, we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.

Spin‐Decoupled Beam Steering with Active Optical Chirality Based on Terahertz Liquid Crystal Chiral Metadevice

AbstractBroadband terahertz (THz) chirality and wavefront manipulation play important roles in wireless communication, imaging, and radar systems. In this work, by integrating liquid crystal (LC) into a dielectric metasurface, the gradient phase distribution from the Si metasurface and the tunable birefringent phase shift from LC are engineered to perform an active spin‐decoupled beam steering with the strong spin asymmetric transmission. By using geometric symmetry analysis, the relationships between the symmetry breaking and the optical chirality of the metadevice are revealed under different LC orientations, and both the simulations and experiments further verify the dependence of this chirality on spin‐decoupled beam steering with different spin states. The results show that with the orientation changes of the LC by driving the different magnetic fields, the circular dichroism of the device at the 0° deflection angle is ≈100% dynamically modulated and even flipped in the broadband range of 0.8–1.3 THz. With these changes in THz chirality, a tunable spin‐decoupled beam steering occurs in the range of 25°‐45°. This work shows that tunable LC anisotropy leads to more complex symmetry breaking in this structure, and results in more functions than conventional spin‐decoupled wavefront manipulations, which expands the scope of THz chiral metadevice and its applications.

Complex symmetric Toeplitz operators on the unit polydisk

In this paper, we study the complex symmetry of Toeplitz operators on the weighted Bergman spaces over the unit polydisk. First, we completely characterize when anti-linear weighted composition operators [Formula: see text] are conjugations. We then give a sufficient and necessary condition for Toeplitz operators to be complex symmetric with respect to these conjugations. As a consequence, some interesting higher-dimensional complex symmetric phenomena appear on the unit polydisk such as the monomial Toeplitz operators [Formula: see text] with [Formula: see text] for some symmetric permutation matrix [Formula: see text]. Surprisingly, these operators [Formula: see text] are the only ones that are complex symmetric monomial Toeplitz operators on the unit bidisk.

Prevalence and Pattern of Stylohyoid Chain Complex on Panoramic Radiographs: A Retrospective Study

Objective: The elongated styloid process (SP) and calcified stylohyoid ligament can be evaluated radiologically and are associated with some symptoms and syndromes. This study aimed to define the incidence of different stylohyoid chain patterns and classify them.
 Methods: Digital panoramic radiographs of 1217 patients were included in the study. The styloid chain patterns were analyzed according to MacDonald-Jankowski’s study. Data analysis was performed using the IBM SPSS Statistics 21.0 (Statistical Package for Social Sciences) program. 
 Descriptive values were analyzed by using descriptive statistics. The data were assessed by using Chi-squared tests. A probability level of less than .05 (p ˂ .05) was considered significant.
 Results: The prevalence of the stylohyoid chain complex patterns was higher for normal SP (86.5%), followed by elongated SP (7.1%), calcified stylohyoid ligament (2.2%), and absent stylohyoid chain (2.8%). Unclassified SP was detected in twenty individuals on the left (1.6%) and fourteen on the right (1.2%). In view of symmetry of the stylohyoid chain complex, 979 (80.4%) were symmetric, 238 (19.6%) were asymmetric and 14 (1.15%) of the asymmetrical ones were unilateral. There was no significant difference in gender for the type of stylohyoid chain complex pattern (p > .05). There was statistically significant difference between the stylohyoid complex pattern and age groups for the right and left 
 sides (p < .05).
 Conclusion: The authors believe that this study provides additional information about the frequency of the elongated styloid process and provides valuable knowledge of the anatomical variations of the SP. Current findings should be correlated with clinical symptoms in future studies

Revisiting superconductivity in the extended one-band Hubbard model: Pairing via spin and charge fluctuations

The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and ${B}_{2g}$ (${d}_{xy}$) pairing dominates in the absence of repulsive longer-range Coulomb interactions ${V}_{\mathrm{NN}}$, the latter induces pairing in other symmetry channels, including, e.g., ${A}_{2g}$ ($g$-wave), nodal ${A}_{1g}$ (extended $s$-wave), or nodal ${E}_{u}$ ($p$-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, ${V}_{\mathrm{NN}}<0$, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts ${E}_{u}$ ($p$-wave) spin-triplet or ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.

Wronskian structures of planar symplectic ensembles

We consider the eigenvalues of non-Hermitian random matrices in the symmetry class of the symplectic Ginibre ensemble, which are known to form a Pfaffian point process in the plane. It was recently discovered that the limiting correlation kernel of the symplectic Ginibre ensemble in the vicinity of the real line can be expressed in a unified form of a Wronskian. We derive scaling limits for variations of the symplectic Ginibre ensemble and obtain such Wronskian structures for the associated universality classes. These include almost-Hermitian bulk/edge scaling limits of the elliptic symplectic Ginibre ensemble and edge scaling limits of the symplectic Ginibre ensemble with boundary confinement. Our proofs follow from the generalised Christoffel–Darboux formula for the former and from the Laplace method for the latter. Based on such a unified integrable structure of Wronskian form, we also provide an intimate relation between the function in the argument of the Wronskian in the symplectic symmetry class and the kernel in the complex symmetry class which form determinantal point processes in the plane.

Anomalous symmetry breaking in the Weyl semimetal CeAlGe

CeAlGe, a proposed type-II Weyl semimetal, orders antiferromagnetically below 5 K. At 2 K, spin-flop and a spin-flip transitions to less than 1 $\mu_B$/Ce are observed in the $M(H)$ data below 30 kOe, ($\bf{H}\|\bf{a}$ and $\bf{b}$, and 4.3 kOe, $\bf{H}\|\langle110\rangle$, respectively, indicating a four-fold symmetry of the $M(H)$ data along the principal directions in the tetragonal $\it{ab}$ plane with $\langle110\rangle$ set of easy directions. However, anomalously robust and complex twofold symmetry is observed in the angular dependence of resistivity and magnetic torque data in the magnetically ordered state once the field is swept in the $\it{ab}$ plane. This twofold symmetry is independent of temperature and field hystereses and suggests a magnetic phase transition that separates two different magnetic structures in the $\it{ab}$ plane. The boundary of this magnetic phase transition and possibly the type of low-field magnetic structure can be tuned by an Al deficiency.

Numerical ranges and complex symmetric operators in semi-inner-product spaces

We introduce the numerical range of a bounded linear operator on a semi-inner-product space. We compute the numerical ranges of some operators on ell _{2}^{p}(mathbb{C})(1le p < infty ) and show that the numerical range of the backward shift on an infinite-dimensional space ell ^{p} is the open unit disc. We define a conjugation and a complex symmetric operator on a semi-inner-product space and discuss complex symmetry in the dual space. We prove some properties of a generalized adjoint of a complex symmetric operator. We also show that the numerical range of the complex conjugation on ell _{n}^{p}(n ge 2) is the closed unit disc. Finally, we discuss the sequentially essential numerical ranges of operators on a semi-inner-product space.

Structure Determination of Binuclear Triple-Decker Phthalocyaninato Complexes by NMR via Paramagnetic Shifts Analysis Using Symmetry Peculiarities.

The detailed knowledge about the structure of multinuclear paramagnetic lanthanide complexes for the targeted design of these compounds with special magnetic, sensory, optical and electronic properties is a very important task. At the same time, establishing the structure of such multinuclear paramagnetic lanthanide complexes in solution, using NMR is a difficult task, since several paramagnetic centers act simultaneously on the resulting chemical shift of a particular nucleus. In this paper, we have demonstrated the possibility of molecular structure determination in solution on the example of binuclear triple-decker lanthanide(III) complexes with tetra-15-crown-5-phthalocyanine Ln2[(15C5)4Pc]3 {where Ln = Tb (1) and Dy (2)} by quantitative analysis of the pseudo-contact lanthanide-induced shifts (LIS). The symmetry of complexes was used for the simplification of the calculation of pseudo-contact shifts on the base of the expression for the magnetic susceptibility tensor in the arbitrary oriented magnetic axis system. Good agreement between the calculated and experimental shifts in the 1H NMR spectra indicates the similarity of the structure for the complexes 1 and 2 in solution of CDCl3 and the structure in the crystalline phase, found from the data of the X-ray structural study of the similar complex Lu2[(15C5)4Pc]3. The described approach can be useful for LIS analysis of other polynuclear symmetric lanthanide complexes.

Complex ellipsoids and complex symmetry

Several characterizations of complex ellipsoids among convex bodies in \({\mathbb {C}}^n\), in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.

Three-dimensional quantification of skeletal midfacial complex symmetry.

Quantification of skeletal symmetry in a healthy population could have a strong impact on the reconstructive surgical procedures where mirroring of the contralateral healthy side acts as a clinical reference for the restoration of unilateral defects. Hence, the aim of this study was to three-dimensionally assess the symmetry of skeletal midfacial complex in skeletal class I patients. A sample of 100 cone beam computed tomography (CBCT) scans (50 males, 50 females; age range: 19-40years) were recruited. Automated segmentation of the skeletal midfacial complex was performed to create a three-dimensional (3D) virtual model using a convolutional neural network (CNN)-based segmentation tool. Thereafter, the segmented model was mirrored and registered to quantify skeletal symmetry using a color-coded conformance mapping based on a surface part comparison analysis. Overall, the mean and root-mean-square (RMS) differences between complete true and mirrored models were 0.14 ± 0.12 and 0.87 ± 0.21mm, respectively. Female patients had a significantly more symmetrical midfacial complex (mean difference: 0.11 ± 0.1mm, RMS: 0.81 ± 0.17mm) compared to male patients (mean difference: 0.16 ± 0.13mm, RMS: 0.94 ± 0.23mm). No significant difference existed between left and right sides irrespective of the patient's gender. The comparison between true and mirrored complete and left/right split midfacial complex showed symmetry within a clinically acceptable range of 1mm, which justifies the applicability of using the mirroring technique. The presented data could act as a reference guide for surgeons during planning of reconstructive surgical procedures and outcome assessment at follow-up.

Cryo-EM structures of light-harvesting 2 complexes from Rhodopseudomonas palustris reveal the molecular origin of absorption tuning

The genomes of some purple photosynthetic bacteria contain a multigene puc family encoding a series of α- and β-polypeptides that together form a heterogeneous antenna of light-harvesting 2 (LH2) complexes. To unravel this complexity, we generated four sets of puc deletion mutants in Rhodopseudomonas palustris, each encoding a single type of pucBA gene pair and enabling the purification of complexes designated as PucA-LH2, PucB-LH2, PucD-LH2, and PucE-LH2. The structures of all four purified LH2 complexes were determined by cryogenic electron microscopy (cryo-EM) at resolutions ranging from 2.7 to 3.6 Å. Uniquely, each of these complexes contains a hitherto unknown polypeptide, γ, that forms an extended undulating ribbon that lies in the plane of the membrane and that encloses six of the nine LH2 αβ-subunits. The γ-subunit, which is located near to the cytoplasmic side of the complex, breaks the C9 symmetry of the LH2 complex and binds six extra bacteriochlorophylls (BChls) that enhance the 800-nm absorption of each complex. The structures show that all four complexes have two complete rings of BChls, conferring absorption bands centered at 800 and 850 nm on the PucA-LH2, PucB-LH2, and PucE-LH2 complexes, but, unusually, the PucD-LH2 antenna has only a single strong near-infared (NIR) absorption peak at 803 nm. Comparison of the cryo-EM structures of these LH2 complexes reveals altered patterns of hydrogen bonds between LH2 αβ-side chains and the bacteriochlorin rings, further emphasizing the major role that H bonds play in spectral tuning of bacterial antenna complexes.