Ring Inversion Research Articles

Characterizations and representations of w-core inverses in rings

Let R be an associate ring with involution and let a,w ? R. The notion of EI along an element is introduced. An element w is called EI along a if w?a exists and w?aw = ww?a. Its several characterizations are given by w-core inverses. Several necessary and sufficient conditions such that a #O w aw and wa#O w a are projections are derived. In particular, it is shown that a #O waw is a projection if and only if aw is Moore-Penrose invertible with (aw)? = a #O w if and only if aw is group invertible with (aw)# = a #O w . Also, wa#O w a is a projection if and only if a is Moore-Penrose invertible with a? = wa#O w. Then, we describe the existence of w-core inverse of a by the existence of (the unique) projection p ? R and idempotent q ? R satisfying pR = aR = awR = qR and Rq = Raw.

On forward-order law for core inverse in rings

This article establishes a few sufficient conditions of the forward-order law for the core inverse of elements in rings with involution. It also presents the forward-order law for the weighted core inverse and the triple forward-order law for the core inverse. Additionally, we discuss the hybrid forward-order law involving different generalized inverses like the Moore–Penrose inverse, the group inverse, and the core inverse.

Left and right-Drazin inverses in rings and operator algebras

The paper introduces the left and right versions of the large class of Drazin inverses in terms of the left and right annihilators in a ring, which are called left-Drazin and right-Drazin inverses. We characterize some basic properties of these one-sided Drazin inverses, and discuss Jacobson’s lemma for them. In addition, the relation between the Drazin inverses and these two one-sided inverses is given by means of the spectrum and the operator decomposition. As an application, the left-Drazin and right-Drazin invertibilities in the Calkin algebra are investigated.

Aromatic ring flips in differently packed ubiquitin protein crystals from MAS NMR and MD

Probing the dynamics of aromatic side chains provides important insights into the behavior of a protein because flips of aromatic rings in a protein’s hydrophobic core report on breathing motion involving a large part of the protein. Inherently invisible to crystallography, aromatic motions have been primarily studied by solution NMR. The question how packing of proteins in crystals affects ring flips has, thus, remained largely unexplored. Here we apply magic-angle spinning NMR, advanced phenylalanine 1H-13C/2H isotope labeling and MD simulation to a protein in three different crystal packing environments to shed light onto possible impact of packing on ring flips. The flips of the two Phe residues in ubiquitin, both surface exposed, appear remarkably conserved in the different crystal forms, even though the intermolecular packing is quite different: Phe4 flips on a ca. 10–20 ns time scale, and Phe45 are broadened in all crystals, presumably due to µs motion. Our findings suggest that intramolecular influences are more important for ring flips than intermolecular (packing) effects.

A new class of generalized inverses in semigroups and rings with involution

Let S be a -semigroup and let . The initial goal of this work is to introduce two new classes of generalized inverses, called the w-core inverse and the dual v-core inverse in S. An element is w-core invertible if there exists some such that , xawa = a and . Such an x is called a w-core inverse of a. It is shown that the core inverse and the pseudo core inverse can be characterized in terms of the w-core inverse. Several characterizations of the w-core inverse of a are derived, and the expression is given by the inverse of w along a and {1, 3}-inverses of a in S. Also, the connections between the w-core inverse and other generalized inverses are given. In particular, when S is a -ring, the criterion for the w-core inverse is given by units. The dual v-core inverse of a is defined by the existence of satisfying , avay = a and . Dual results for the dual v-core inverse also hold. Communicated by Pace Nielsen

Enhanced self-healing driving force in polymer materials by regulating molecular structure

For self-healing polymers, obtaining excellent healing ability and mechanical properties usually need complex chemical structure, external healing conditions, and high manufacturing difficulty. Therefore, self-healing efficiency and rate, mechanical strength, and simple structure design as well as no additional healing conditions of the material are contradictory properties and are difficult to optimize simultaneously. Herein, self-healable thermoplastic poly (urethane urea) elastomers driven by surface energy were fabricated by the introduction of asymmetric alicyclic structures and the healing properties in polymers were optimized by regulating surface energy. The results showed that with the increasing of isophorone diamine contents, the surface energy driving force increased from 36 kPa to 149 kPa, the healing time decreased from 30d to 5d, and healing efficiency, and tensile strength reached 100.9% and 4.04 MPa at room temperature. At the same time, polymers also obtained a high healing efficiency under high-temperature healing conditions. The healing mechanism is that asymmetric alicyclic structures with steric hindrance and ring flip promote the dissociation of hydrogen bonds, provide sufficient chain mobility, decrease the junction density, and improve the surface energy as well as the dissociation and reconstruction of hydrogen bonds. Energetic polymer composites using thermoplastic poly (urethane urea) elastomers as matrix obtained excellent healing properties. This study will offer a novel healing approach for developing advanced self-healing polymer materials.

Conformer Ring Flip Enhances Mechanochromic Performance of ansa-Donor-Acceptor-Donor Mechanochromic Torsional Springs.

Mechanochromophores based on conformational changes of donor-acceptor-donor (DAD) springs allow sensing of forces acting on polymer chains by monotonic changes of absorbance or photoluminescence (PL) wavelength. Here, we identify a series of thiophene (D)-flanked quinoxalines (A) as molecular torsional springs for force sensing in bulk polymers at room temperature. The mode of DAD linkage to the polymer matrix and linker rigidity are key parameters that influence the efficacy of force transduction to the DAD spring and thus mechanochromic response, as probed by in situ PL spectroscopy of bulk films during stress-strain experiments. The largest shift of the PL maximum, and thus the highest sensitivity, is obtained from an ansa-DAD spring exhibiting bridged D units and a stiff A linker. Using detailed spectroscopy and density functional theory calculations, we reveal conformer redistribution in the form of a thiophene ring flip as the major part of the overall mechanochromic response. At forces as low as 27 pN at early stages of deformation, the ring flip precedes mechanically induced planarization of the ansa-DAD spring, the latter process producing a PL shift of 21 nm nN-1. Within the stress-strain diagram, the thiophene ring flip and DAD planarization are thus two separated processes that also cause irreversible and reversible mechanochromic responses, respectively, upon sample failure. As the thiophene ring flip requires much smaller forces than planarization of the DAD spring, such micromechanical motion gives access to sensing of tiny forces and expands both sensitivity and the force range of conformational mechanochromophores.

113. Optical Genome Mapping: Clinical validation and diagnostic utility for cytogenomic analysis of Hematological Neoplasms

Hematological neoplasms are predominantly defined by chromosomal aberrations that includes structural variants (SVs) and copy number variations (CNVs). The current standard-of-care (SOC) methods [karyotyping, fluorescence in-situ hybridization (FISH), and chromosomal microarrays (CMA)] employed for the detection of SVs and CNVs are labor intensive, time and cost-prohibitive, and often does not reveal the genetic complexity of the tumor. Optical genome mapping (OGM) is an emerging technology that can detect all classes of SVs in a single assay. We report the results from our clinical validation (in a CLIA setting) of the OGM technique for hematological neoplasms. The study included 94 sample runs (including replicates) using 71 well characterized unique samples (61 hematological neoplasms and 10 controls). The analytical performance showed a sensitivity of 98.7%, specificity of 100%, accuracy of 98.7%, PPV of 100% and NPV of 98%, that included the detection of 61 aneuploidies, 35 deletions, 28 translocations, 11 duplications/amplifications, 15 insertions/additional material not identified with karyotyping, 12 marker chromosomes, 1 each of ring chromosome, inversion and isochromosome. OGM showed high (robust) technical and analytical reproducibility with a limit of detection of 5% allele fraction for the variant classes evaluated in the study. In addition, OGM demonstrated higher resolution to refine breakpoints, identify the additional material, marker and ring chromosomes. This first CLIA validation report demonstrates the technical and analytical advantages of OGM compared to the current SOC methods used for chromosomal characterization, and we recommend OGM as a potential first-tier cytogenetic test for the evaluation of hematological neoplasms. Hematological neoplasms are predominantly defined by chromosomal aberrations that includes structural variants (SVs) and copy number variations (CNVs). The current standard-of-care (SOC) methods [karyotyping, fluorescence in-situ hybridization (FISH), and chromosomal microarrays (CMA)] employed for the detection of SVs and CNVs are labor intensive, time and cost-prohibitive, and often does not reveal the genetic complexity of the tumor. Optical genome mapping (OGM) is an emerging technology that can detect all classes of SVs in a single assay. We report the results from our clinical validation (in a CLIA setting) of the OGM technique for hematological neoplasms. The study included 94 sample runs (including replicates) using 71 well characterized unique samples (61 hematological neoplasms and 10 controls). The analytical performance showed a sensitivity of 98.7%, specificity of 100%, accuracy of 98.7%, PPV of 100% and NPV of 98%, that included the detection of 61 aneuploidies, 35 deletions, 28 translocations, 11 duplications/amplifications, 15 insertions/additional material not identified with karyotyping, 12 marker chromosomes, 1 each of ring chromosome, inversion and isochromosome. OGM showed high (robust) technical and analytical reproducibility with a limit of detection of 5% allele fraction for the variant classes evaluated in the study. In addition, OGM demonstrated higher resolution to refine breakpoints, identify the additional material, marker and ring chromosomes. This first CLIA validation report demonstrates the technical and analytical advantages of OGM compared to the current SOC methods used for chromosomal characterization, and we recommend OGM as a potential first-tier cytogenetic test for the evaluation of hematological neoplasms.

Characterizing Fast Conformational Exchange of Aromatic Rings Using Residual Dipolar Couplings: Distinguishing Jumplike Flips from Other Exchange Mechanisms.

Aromatic ring flips are a hallmark of protein dynamics. They are experimentally studied by NMR spectroscopy, where recent advances have led to improved characterization across a wide range of time scales. Results on different proteins have been interpreted as continuous diffusive ring rotations or jumplike flips, leading to diverging views of the protein interior as being fluidlike or solidlike, respectively. It is challenging to distinguish between these mechanisms and other types of conformational exchange because chemical-shift-mediated line broadening provides only conclusive evidence for ring flips only if the system can be moved from the slow- to intermediate/fast-exchange regime. Moreover, whenever the chemical shift difference between the two symmetry-related sites is close to zero, it is not generally possible to determine the exchange time scale. Here we resolve these issues by measuring residual dipolar coupling (RDC)-mediated exchange contributions using NMR relaxation dispersion experiments on proteins dissolved in dilute liquid crystalline media. Excellent agreement is found between the experimental difference in RDC between the two symmetry-related sites and the value calculated from high-resolution X-ray structures, demonstrating that dynamics measured for F52 in the B1 domain of protein G reports on distinct, jumplike flips rather than other types of conformational exchange.

C7 Epimerization of Benzylidene-Protected β-d-Idopyranosides Brings Structural Insights into Idose Conformational Flexibility.

Idose is unique among other aldohexoses because of its high conformational flexibility in solution. We herein show that benzylidene acetal-protected 3-O-acyl-β-d-idopyranosides undergo Lewis acid-catalyzed C7 epimerization with concomitant 4C1 to 1C4 ring inversion. The reaction conditions and structural parameters for this transformation to occur have been thoroughly investigated through an extensive glycosylation study combined with NMR analyses, X-ray diffraction, and quantum molecular modeling. In addition to reporting a direct, β-stereoselective idosylation approach, our work brings fundamental structural insights into the conformational flexibility of idose.

A-value revisited: ring flip energy of chair structures in halogenated cyclohexanes by quantum chemical methods

A-value is conventionally defined as the ring flip Gibbs energy of chair conformers in monosubstituted cyclohexanes. It is well accepted in organic chemistry as one of the proxies of steric hindrance of a substituent group with respect to hydrogen. In this paper, the ring flip energy of mono– and dihalogenated cyclohexanes was investigated by high-level quantum chemical methods. Satisfactory agreements between calculated values and published experimental values from NMR were established before extending the concept to ring flip energies of polyhalogenated cyclohexanes. We assessed the qualitative and quantitative accuracy of prediction of ring flip energies by A-values in two models: a simple and intuitive model based on linear combinations of A-values and a proposed extension of this model to include geminal substituent interactions. The simple model results in poor predictions of ring flip energy in polyhalogenated cyclohexanes, and the extended model provides only slight improvement. Our data suggests that simple linear combination of traditional or extended A-values may not be appropriate for the energy prediction of systems in this study.

Characterizations of weighted core inverses in rings with involution

Let [Formula: see text] be a unital ring with involution. The author investigates the characterizations and representations of weighted core inverse of an element in [Formula: see text] by idempotents and units. Let [Formula: see text], [Formula: see text] be an invertible Hermitian element and [Formula: see text]. We prove that [Formula: see text] is [Formula: see text]-core invertible if and only if there exists an element (or an idempotent) [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text] (or [Formula: see text]) is invertible. As a consequence, for two invertible Hermitian elements [Formula: see text] and [Formula: see text] in [Formula: see text], [Formula: see text] is weighted-[Formula: see text] with respect to [Formula: see text] if and only if there exists an element (or an idempotent) [Formula: see text] such that [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] (or [Formula: see text]) is invertible. These results generalize and improve conclusions in [T. T. Li and J. L. Chen, Characterizations of core and dual core inverses in rings with involution, Linear Multilinear Algebra 66 (2018) 717–730].

Jacobson's lemma for the generalized \(n\)-strong Drazin inverses in rings and in operator algebras

In this paper, we extend Jacobson's lemma for Drazin inverses to the generalized \(n\)-strong Drazin inverses in a ring, and prove that \(1-ac\) is generalized \(n\)-strong Drazin invertible if and only if \(1-ba\) is generalized \(n\)-strong Drazin invertible, provided that \(a(ba)^{2}=abaca=acaba=(ac)^{2}a\). In addition, Jacobson's lemma for the left and right Fredholm operators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.

Polymorphic transition due to grinding: the case of 3-[1-(tert-butoxycarbonyl)azetidin-3-yl]-1,2-oxazole-4-carboxylic acid.

A polymorphic transition as a result of grinding was found for 3-[1-(tert-butoxycarbonyl)azetidin-3-yl]-1,2-oxazole-4-carboxylic acid. The thorough study of polymorphic structures before and after crystal structure transformation has revealed some pre-conditions for a polymorphic transition and regularities of changes in molecular and crystal structure. In metastable polymorph 1a, the conformationally flexible molecule adopts a conformation with the higher energy and forms a less preferable linear supramolecular synthon. Additional energy imparted to a crystal structure during the grinding process proved to be enough to overcome low energy barriers for the nitrogen inversion and rotation of the oxazole ring around the sp3-sp2 single bond. As a result, polymorph 1b with a molecule adopting conformation with lower energy and forming a more preferable centrosymmetric supramolecular synthon was obtained. The study of pairwise interaction energies in the two polymorphs has shown that metastable polymorph 1a is organized by molecular building units and has a columnar-layered structure. A centrosymmetric dimer should be recognized as a complex building unit in more stable polymorph 1b, which has a layered structure.

Effect of Sulfation on the Conformational Dynamics of Dermatan Sulfate Glycosaminoglycan: A Gaussian Accelerated Molecular Dynamics Study.

Glycosaminoglycans (GAGs) are anionic biopolymers present on cell surfaces as a part of proteoglycans. The biological activities of GAGs depend on the sulfation pattern. In our study, we have considered three octadecasaccharide dermatan sulfate (DS) chains with increasing order of sulfation (dp6s, dp7s, and dp12s) to illuminate the role of sulfation on the GAG units and its chain conformation through 10 μs-long Gaussian accelerated molecular dynamics simulations. DS is composed of repeating disaccharide units of iduronic acid (IdoA) and N-acetylgalactosamine (N-GalNAc). Here, N-GalNAc is linked to IdoA via β(1-4), while IdoA is linked to N-GalNAc through α(1-3). With the increase in sulfation, the DS structure becomes more rigid and linear, as is evident from the distribution of root-mean-square deviations (RMSDs) and end-to-end distances. The tetrasaccharide linker region of the main chain shows a rigid conformation in terms of the glycosidic linkage. We have observed that upon sulfation (i.e., dp12s), the ring flip between two chair forms vanished for IdoA. The dynamic cross-correlation analysis reveals that the anticorrelation motions in dp12s are reduced significantly compared to dp6s or dp7s. An increase in sulfation generates relatively more stable hydrogen-bond networks, including water bridging with the neighboring monosaccharides. Despite the favorable linear structures of the GAG chains, our study also predicts few significant bendings related to the different puckering states, which may play a notable role in the function of the DS. The relation between the global conformation with the micro-level parameters such as puckering and water-mediated hydrogen bonds shapes the overall conformational space of GAGs. Overall, atomistic details of the DS chain provided in this study will help understand their functional and mechanical roles, besides developing new biomaterials.

NMR spectroscopic and theoretical study on the isomerism of dimethyl benzodiazepine(diylidene)diacetates.

The isomerism of dimethyl 2,2'-(7,8-dichloro-1H-benzo[b][1,4]diazepine-2,4-(3H,5H)diylidene)diacetate (1a) and dimethyl 2,2'-(7,8-dichloro-3-methyl-1H-benzo[b][1,4]diazepine-2,4-(3H,5H)diylidene)diacetate (1b) was investigated by 1 H, 13 C and 15 N nuclear magnetic resonance (NMR) spectroscopy. In CDCl3 solution, inversion of the diazepine ring was observed, whereas in (D6 )DMSO and (D7 )DMF solution, besides the ring inversion, a partial cleavage of one chelate ring appeared connected with (E/Z) isomerization about one of the exocyclic C=C bonds. Gibbs free energies (ΔG) and free activation energies (ΔG≠ ) were calculated based on B3PW91-SCRF/ZVP DFT computations. Agreement between NMR data and density functional theory (DFT) computations was found.

SP3 Hybridized Carbon Atom Dependent Redox Activity and Charge Storage of Quinonoid Main Chain Polymers

Uncontrolled stereochemical flipping of the substituents indirectly affects the redox chemistry of benzoquinone. With this assumption, herein we prepared three different polymers, quinone rings directly bonded (DHBP), quinone rings boned through a methylene bridge (DHB), and phenyl rings substituted methylene bridge (DADC). The substitution of phenyl ring generates the stereo-centered sp3 hybridized carbon center which inhibits ring flipping and uncontrolled stereochemistry. It also affects the electrochemical properties and charge storage ability of the polymer. The polymer with a stereo-centered carbon center (DADC) exhibited 245.4 mAhg−1 specific capacity at 100 mAg−1 current density in an aqueous zinc ion battery. It is far better than the polymers without the stereo-centered polymer, even it is better than the reported quinone cathodes. The outperformance in the charge storage ability was explained in detail based on the stabilization of quinonoid radicals and/or quinonoid anions by the stereochemically restricted carbon center with a bulky phenyl group. The cycling stability was evaluated in galvanostatic charging/discharging over 3000 cycles at 100 mAg−1 current density. The specific capacity was found to be 250.1 mAhg−1 with 91.2% capacity retention and 89.6% coulombic efficiency suggesting the importance of stereo-centered carbon in designing new redox-active organic molecules for energy storage applications.

Perturbation results and forward order law for the Moore–Penrose inverse in rings with involution

Abstract We investigate perturbations of the Moore–Penrose inverse and forward order law for the Moore–Penrose inverse in rings with involution, and thus we extend some results of Castro–Gonzalez and Hartwig to more general settings.

Photoelectron Circular Dichroism as a Signature of Subtle Conformational Changes: The Case of Ring Inversion in 1-Indanol.

Chirality plays a fundamental role in the molecular recognition processes. Molecular flexibility is also crucial in molecular recognition, allowing the interacting molecules to adjust their structures and hence optimize the interaction. Methods probing simultaneously chirality and molecular conformation are therefore crucially needed. Taking advantage of a possible control in the gas phase of the conformational distribution between the equatorial and axial conformers resulting from a ring inversion in jet-cooled 1-indanol, we demonstrate here the sensitivity of valence-shell photoelectron circular dichroism (PECD) to both chirality and subtle conformational changes, in a case where the photoelectron spectra of the two conformers are identical. For the highest occupied orbital, we observe a dramatic inversion of the PECD-induced photoelectron asymmetries, while the photoionization cross-section and usual anisotropy (β) parameter are completely insensitive to conformational isomerism. Such a sensitivity is a major asset for the ongoing developments of PECD-based techniques as a sensitive chiral (bio)chemical analytical tool in the gas phase.

A β-NMR study of the depth, temperature, and molecular-weight dependence of secondary dynamics in polystyrene: Entropy-enthalpy compensation and dynamic gradients near the free surface.

We investigated the depth, temperature, and molecular-weight (MW) dependence of the γ-relaxation in polystyrene glasses using implanted 8Li+ and β-detected nuclear magnetic resonance. Measurements were performed on thin films with MW ranging from 1.1 to 641 kg/mol. The temperature dependence of the average 8Li spin-lattice relaxation time (T1 avg) was measured near the free surface and in the bulk. Spin-lattice relaxation is caused by phenyl ring flips, which involve transitions between local minima over free-energy barriers with enthalpic and entropic contributions. We used transition state theory to model the temperature dependence of the γ-relaxation, and hence T1 avg. There is no clear correlation of the average entropy of activation (Δ‡S̄) and enthalpy of activation (Δ‡H̄) with MW, but there is a clear correlation between Δ‡S̄ and Δ‡H̄, i.e., entropy-enthalpy compensation. This results in the average Gibbs energy of activation, Δ‡Ḡ, being approximately independent of MW. Measurements of the temperature dependence of T1 avg as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to Δ‡H̄ = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in Δ‡Ḡ near the free surface being lower than the bulk. Combining these observations results in a model where the average fluctuation rate of the γ-relaxation has a "double-exponential" depth dependence. This model can explain the depth dependence of 1/T1 avg in polystyrene films. The characteristic length of enhanced dynamics is ∼6nm and approximately independent of MW near room temperature.