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At least 793 records · Page 44

$c$-functions in flows across dimensions

We explore the notion of c-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic c-function and thereby establish a holographic c-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate c-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d N =4 SYM and compactifications of 6d N = (2, 0) theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Amidoxime-functionalized materials and their use in extracting metal ions from liquid solutions

A method of producing a functionalized material that extracts metal ions from solution, the method comprising: (i) providing a precursor material having nitrile groups appended to its surface; and (ii) reacting said nitrile groups with hydroxylamine or a derivative thereof in the presence of a polar aprotic solvent at a temperature of 60-80° C. for at least 1 hour, to convert at least a portion of said nitrile groups to amidoxime and imide dioxime groups, followed by reaction with a base capable of hydrolyzing any remaining nitrile groups to carboxylic acid groups; wherein said functionalized material has a higher uranium absorption capacity than a functionalized material produced under same conditions except that the nitrile groups are reacted with hydroxylamine in only a protic solvent. The invention is also directed to functionalized materials produced by the above-described method, and methods for using the functionalized material for extracting metal ions from metal-containing solutions.

36 MATERIALS SCIENCE↗

Amidoxime-functionalized materials and their use in extracting metal ions from liquid solutions

A method of producing a functionalized material that extracts metal ions from solution, the method comprising: (i) providing a precursor material having nitrile groups appended to its surface; and (ii) reacting said nitrile groups with hydroxylamine or a derivative thereof in the presence of a polar aprotic solvent at a temperature of 60-80° C. for at least 1 hour, to convert at least a portion of said nitrile groups to amidoxime and imide dioxime groups, followed by reaction with a base capable of hydrolyzing any remaining nitrile groups to carboxylic acid groups; wherein said functionalized material has a higher uranium absorption capacity than a functionalized material produced under same conditions except that the nitrile groups are reacted with hydroxylamine in only a protic solvent. The invention is also directed to functionalized materials produced by the above-described method, and methods for using the functionalized material for extracting metal ions from metal-containing solutions.

Janke, Christopher J.↗

Generating Bright Emissive States by Modulating the Bandgap of Monolayer Tungsten Diselenide

Transition metal dichalcogenides (TMDs) are essential due to their fascinating electronic and optical properties, strong exciton binding energy, and layer-dependent bandgap. They can be tuned to function as a single-photon emitter, but the quantum yield of photoluminescence of single-layer WSe 2 is low. There is some evidence that a bright emissive state can be produced by introducing local defects through functionalization. In this paper we use spin-polarized periodic density functional theory (DFT) to study the effect of functionalization for the specific case of cyclic carbenes. We find that the simplest of these molecules, cyclopentadiene carbene (Cyc), binds to the surface by a covalent bond leading to a substantial change in the bandgap (1.24 eV compared to 1.64 eV for the pristine surface). Moreover, there are semiflat bands below the Fermi level that originate from σ bonding and the interaction between the lone-pair p orbitals on the carbon of Cyc that bonds with Se on the TMD. Cyc is found to form a Type IIa heterojunction before and after contact with the surface, where the “a” refers to ordering of the energy levels where the TMD levels have the larger splitting and “b” to the reverse. The effect of various electron-withdrawing and electron-donating groups on Cyc is investigated, and it is found that the direct bandgap and heterointerfaces can be chemically tuned with covalently bound functional groups. With an electron-withdrawing group (EWG) such as –CHO, –COCl, and –CN attached to Cyc, a Type III//Type IIa interface is formed, whereas all other EWGs used in this study form a Type IIa junction, before and after contact to the surface. The electron-donating groups (EDG) form Type Ib//Type Ia junctions, and in particular, we find that the system WSe 2 + Cyc-Me band structure consists of semiflat bands at valence band maxima localized on Cyc-Me and the conduction band minimum is coupled between the surface and functional group with a direct bandgap of 0.88 eV. Hence, we predict that the Cyc-Me-functionalized monolayer WSe 2 will produce a red-shifted bright emissive state. Furthermore, we also find that carbenes with the Cyc all-carbon ring have (1) a triplet ground state and (2) form covalent bonds to WSe 2 , while heterocyclic carbenes (1) have a singlet ground state and (2) do not form covalent bonds to WSe 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Gray matter volume drives the brain age gap in schizophrenia: a SHAP study

Neuroimaging-based brain age is a biomarker that is generated by machine learning (ML) predictions. The brain age gap (BAG) is typically defined as the difference between the predicted brain age and chronological age. Studies have consistently reported a positive BAG in individuals with schizophrenia (SCZ). However, there is little understanding of which specific factors drive the ML-based brain age predictions, leading to limited biological interpretations of the BAG. We gathered data from three publicly available databases - COBRE, MCIC, and UCLA - and an additional dataset (TOPSY) of early-stage schizophrenia (82.5% untreated first-episode sample) and calculated brain age with pre-trained gradient-boosted trees. Then, we applied SHapley Additive Explanations (SHAP) to identify which brain features influence brain age predictions. We investigated the interaction between the SHAP score for each feature and group as a function of the BAG. These analyses identified total gray matter volume (group × SHAP interaction term β = 1.71 [0.53; 3.23]; p corr < 0.03) as the feature that influences the BAG observed in SCZ among the brain features that are most predictive of brain age. Other brain features also presented differences in SHAP values between SCZ and HC, but they were not significantly associated with the BAG. We compared the findings with a non-psychotic depression dataset (CAN-BIND), where the interaction was not significant. This study has important implications for the understanding of brain age prediction models and the BAG in SCZ and, potentially, in other psychiatric disorders.

60 APPLIED LIFE SCIENCES↗

Local Coordination Environment of Lanthanides Adsorbed onto Cr- and Zr-based Metal–Organic Frameworks

Separating individual lanthanide (Ln) elements in aqueous mixtures is challenging. Ion-selective capture by porous materials, such as metal–organic frameworks (MOFs), is a promising approach. To design ion-selective MOFs, molecular details of the Ln adsorption complexes within the MOFs must be understood. We determine the local coordination environment of lanthanides Nd(III), Gd(III), and Lu(III) adsorbed onto Cr(III)-based terephthalate MOF (Cr-MIL-101) and Zr(IV)-based Universitet in Oslo MOFs (UiO-66 and UiO-68) and their derivatives. In the Cr(III)- and Zr(IV)-based MOFs, Ln adsorb as inner-sphere complexes at the metal oxo clusters, regardless of whether the organic linkers are decorated with amino groups. Missing linkers result in favorable Ln binding sites at oxo clusters; however, Ln can coordinate to metal sites even with linkers in place. Further, MOF functionalization with phosphonate groups led to Ln chemisorption onto these groups, which out-compete metal cluster sites. Ln form monodentate and bidentate and mononuclear and binuclear surface complexes. We conclude that MOFs for ion-selective Ln capture can be designed by a combination of (1) maximizing metal-lanthanide interactions via shared O atoms at the metal oxo cluster sites, where mixed oxo clusters can lead to ion-selective Ln adsorption, and (2) functionalizing MOFs with Ln-selective groups capable of out-completing the metal oxo cluster sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The 1 → 3 massive splitting functions from QCD factorization and SCET

Splitting functions are universal functions describing the collinear dynamics of gauge theories, and as such are crucial ingredients for a wide variety of calculations in perturbative QCD. We present analytic results for the triple collinear splitting functions in QCD with a single massive parton. We derive the splitting functions using two distinct methods; first by expanding the squared matrix elements in the collinear limit, and secondly by using soft-collinear effective theory with massive quarks. We find agreement between these two approaches, providing a strong check of our results. Additionally, we also check all iterated and soft limits of our results, finding agreement with predictions from factorization. Our results provide an important ingredient for higher order perturbative calculations involving massive partons, and for the description of the collinear dynamics of heavy flavor jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Synthesis and Exploratory Catalysis of 3d Metals: Atom and Group-Transfer Reactions and the Activation and Functionalization of Small Molecules Including Greenhouse Gases

Determining ways to convert natural gas, with zero emissions, and to more value-added materials such as olefins is one of the main goals in my research group. Over this funding period, we explored the chemistry of early-transition metals with metal-nitrogen multiple bonds, specifically titanium and zirconium nitrides, and explored their redox properties, basicity and reactivity with small molecules including greenhouses gases such as carbon dioxide. Some of these work serve as inspiration for the chemistry of important materials such as uranium nitride along with its unprecedented basicity and ability to activate C-H bonds. Using robust chelating templates we also examined rare examples of trivalent group 4 transition metal ions, and studied these spectroscopically. Using early transition metal ions we also explored synthetic routes to new phosphide based products using the phosphaethynolate salt. In addition, we also explored the chemistry of ferrous systems, and redox active ligand that can allow us to reversibly break and make C-S as well as N-N bonds, activate dinitrogen forming unusual MNNM topologies. Our final component describes how we activate methane and dehydrocouple if with a carbene source to form ethylene. Using this information, we also discovered a simple to make iridium catalyst that activate and functionalize methane with 9:1 selectivity for mono-functionalization. We have established a pathway that leads to poisoning of the catalyst and have found optimal conditions for higher selectivity and with over 170 Turnovers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Poisson hurdle model-based method for clustering microbiome features

Abstract Motivation High-throughput sequencing technologies have greatly facilitated microbiome research and have generated a large volume of microbiome data with the potential to answer key questions regarding microbiome assembly, structure and function. Cluster analysis aims to group features that behave similarly across treatments, and such grouping helps to highlight the functional relationships among features and may provide biological insights into microbiome networks. However, clustering microbiome data are challenging due to the sparsity and high dimensionality. Results We propose a model-based clustering method based on Poisson hurdle models for sparse microbiome count data. We describe an expectation–maximization algorithm and a modified version using simulated annealing to conduct the cluster analysis. Moreover, we provide algorithms for initialization and choosing the number of clusters. Simulation results demonstrate that our proposed methods provide better clustering results than alternative methods under a variety of settings. We also apply the proposed method to a sorghum rhizosphere microbiome dataset that results in interesting biological findings. Availability and implementation R package is freely available for download at https://cran.r-project.org/package=PHclust. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

Selective CO 2 Reduction by Bis(bipyridine)cobalt(II) Catalysts: The Role of Pendant Pyridine as a Proton Acceptor

Electrochemical CO 2 reduction reaction (CO 2 RR) catalyzed by molecular earth-abundant metal catalysts is a promising strategy to convert CO 2 into value-added products. One recent trend in this field has been focusing on the rational design of catalysts by incorporating redox-active ligands and modifying the secondary coordination sphere (SCS) to achieve efficient and selective CO 2 RR. Herein, we report a series of Co bis­(bipyridine) catalysts featuring various dangling groups, such as pyridine, tertiary amine, or butyl, in the secondary coordination sphere (Co-PyMe, Co-Py, Co-PrN, and Co-Bu). Efficient, selective electrocatalytic CO 2 RR was achieved by the complexes after the generation of triply reduced intermediate consisting of a Co I center and a dianionic ligand, producing CO as the major product and trace amount of H 2 . Strong correlations with the identity of dangling groups and turnover frequency (TOF) have been observed, in which Co-PyMe displayed the highest TOF (1086 s –1 in MeCN/H 2 O). Mechanistic studies indicated that the acceleration of CO 2 RR with pyridine-functionalized catalysts were derived from the protonation of pyridine dangling groups which participated as weak acids in the H-bonding network with exogenous proton sources, stabilizing CO 2 -bound intermediates and facilitating proton transfer. In addition, precatalytic CO 2 binding and activation at the third reduction (−2.1 V) was revealed by CV and SEC-IR studies. The resultant doubly reduced CO-bound species acted as a trapping state which inhibited CO 2 RR electrocatalysis. Regeneration of active species was accessed via reductive dissociation of CO at a more negative potential. In conclusion, this study highlights the combined effects of redox-active ligands and pyridine/pyridinium as SCS groups on CO 2 RR catalysis and provides design principles for future development of CO 2 RR catalysts utilizing pyridine/pyridiniums as SCS functional groups to fine-tune the catalytic activity.

CO2 reduction↗

Efficient Iridium Catalysts for Formic Acid Dehydrogenation: Investigating the Electronic Effect on the Elementary β-Hydride Elimination and Hydrogen Formation Steps

We report herein a series of Cp*Ir complexes containing a rigid 8-aminoquinolinesulfonamide moiety as highly efficient catalysts for the dehydrogenation of formic acid (FA). The complex [Cp*Ir(L)Cl] (HL = N-(quinolin-8-yl)benzenesulfonamide) displayed a high turnover frequency (TOF) of 2.97 × 10 4 h –1 and a good stability (>100 h) at 60 °C. Comparative studies of [Cp*Ir(L)Cl] with the rigid ligand and [Cp*Ir(L')Cl] (HL' = N-propylpypridine-2-sulfonamide) without the rigid aminoquinoline moiety demonstrated that the 8-aminoquinoline moiety could dramatically enhance the stability of the catalyst. The electron-donating ability of the N,N'-chelating ligand was tuned by functionalizing the phenyl group of the L ligand with OMe, Cl, and CF 3 to have a systematical perturbation of the electronic structure of [Cp*Ir(L)Cl]. Experimental kinetic studies and density functional theory (DFT) calculations on this series of Cp*Ir complexes revealed that (i) the electron-donating groups enhance the hydrogen formation step while slowing down the β-hydride elimination and (ii) the electron-withdrawing groups display the opposite effect on these reaction steps, which in turn leads to lower optimum pH for catalytic activity compared to the electron-donating groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Group transfer polymerization for the production of functional monomers

The present invention provides efficient processes for preparing brush polymers. In general, the process comprises three distinct reaction steps utilizing two separate catalysts. In the first step, the initiating compound comprising norbornene is contacted with a silane in the presence of a catalyst, thereby forming a silated intermediate. This silated intermediate is then contacted with a monomer in the presence of a catalyst via Group Transfer Polymerization (GTP). The resulting compound from GTP is contacted with a ring opening metathesis polymerization (ROMP) catalyst to prepare the brush polymer. Surprisingly, the brush polymers obtained from the above process are accessed in an efficient and rapid GTP methodology as compared to prior methods.

Miyake, Garret↗

Cellulose synthesis complexes are homo-oligomeric and hetero-oligomeric in Physcomitrium patens

The common ancestor of seed plants and mosses contained homo-oligomeric cellulose synthesis complexes (CSCs) composed of identical subunits encoded by a single CELLULOSE SYNTHASE (CESA) gene. Seed plants use different CESA isoforms for primary and secondary cell wall deposition. Both primary and secondary CESAs form hetero-oligomeric CSCs that assemble and function in planta only when all the required isoforms are present. The moss Physcomitrium (Physcomitrella) patens has seven CESA genes that can be grouped into two functionally and phylogenetically distinct classes. Previously, we showed that PpCESA3 and/or PpCESA8 (class A) together with PpCESA6 and/or PpCESA7 (class B) form obligate hetero-oligomeric complexes required for normal secondary cell wall deposition. Here, we show that gametophore morphogenesis requires a member of class A, PpCESA5, and is sustained in the absence of other PpCESA isoforms. Further, PpCESA5 also differs from the other class A PpCESAs as it is able to self-interact and does not co-immunoprecipitate with other PpCESA isoforms. These results are consistent with the hypothesis that homo-oligomeric CSCs containing only PpCESA5 subunits synthesize cellulose required for gametophore morphogenesis. Analysis of mutant phenotypes also revealed that, like secondary cell wall deposition, normal protonemal tip growth requires class B isoforms (PpCESA4 or PpCESA10), along with a class A partner (PpCESA3, PpCESA5, or PpCESA8). Thus, P. patens contains both homo-oligomeric and hetero-oligomeric CSCs.

59 BASIC BIOLOGICAL SCIENCES↗

ToF-SIMS imaging reveals that p -hydroxybenzoate groups specifically decorate the lignin of fibres in the xylem of poplar and willow

Esterified phenolics occur as γ-linked lignin acylations in many plant taxa but little is known about the distribution or function of such groups. In the family Salicaceae, p-hydroxybenzoate groups are present in the lignin of poplars (Populus spp.) and willows (Salix spp.). In this study, the distribution of cell wall-bound p-hydroxybenzoate was examined in different tissue and cell types of poplar and willow trees. This analysis showed that p-hydroxybenzoate groups were most prevalent in juvenile stems, and were elevated in tension wood and following nitrogen fertilisation. Closer examination of stem cross-sections using time-of-flight secondary-ion mass spectrometry (ToF-SIMS) directly showed that p-hydroxybenzoate groups occur predominantly in the cell walls of fibres and are largely absent from vessel elements. Furthermore, these results point to a role for ester-linked groups in modifying the syringyl-rich lignin of fibres, perhaps to strengthen the cell walls of these structural elements or to increase lignification rates.

59 BASIC BIOLOGICAL SCIENCES↗

Spontaneous rearrangement of acetylated xylan on hydrophilic cellulose surfaces

The interaction of xylan, an abundant plant polysaccharide, with cellulose microfibrils is essential for secondary cell wall strength. A deeper understanding of these interactions is crucial both to improve our understanding of plant cell wall architecture and to design alternate strategies to overcome cellulose recalcitrance for the production of biofuels and sustainable biomaterials. Naturally occurring acetate or glucuronic acid substitutions on xylan have been shown to influence xylan-cellulose interactions. In this work, we use unrestrained molecular dynamics simulations to determine the interactions with the (110) hydrophilic face of cellulose fibers of four different xylans. In the absence of cellulose, all xylans, independent of the substitution pattern, adopt a highly flexible threefold helical screw conformation. However, when xylan is spatially close to a cellulose surface 1,2 linked acetyl xylans (2AcX) adopt rigid twofold helical screw conformations. The 2AcX conformations are primarily stabilized by interactions between the acetylated oxygen and the glycosidic linkage with C-O6 of cellulose. In contrast, the glycosidic oxygens and acetyl decorations for 1,3 linked acetyl groups (3AcX) are oriented away from the cellulose surface and the 3AcX xylans maintain threefold helical screw conformations on the cellulose surface. Our results show that evenly spaced chemical functionalization (with acetyl groups) and the position of substitution (1,2) on xylan backbone play key roles in tuning the xylan-cellulose interactions to stabilize the twofold helical screw conformations of xylan on the cellulose surface. A comparison with previous experimental findings further suggests that 1,2 substitutions induce twofold helical screw conformations of xylan on the cellulose surface irrespective of the chemical nature of the substituent, while 1,3 substitutions primarily bind lignin in threefold helical screw conformations rather than cellulose in plant cell walls.

1,2 Ac↗

Distinguishing Leptothrix and Sphaerotilus genera by an integrated genomic-phenotypic analysis supported by new Leptothrix genomes

The Sphaerotilus-Leptothrix group of bacteria includes one of the first described microorganisms, Leptothrix ochracea, an uncultured type strain, plus isolates of Leptothrix and Sphaerotilus. This group is unified by the ability to form sheaths and oxidize metals, although L. ochracea exhibits obvious ecological, morphological, and functional differences from the rest of Sphaerotilus-Leptothrix. Recently, there have been calls to combine the group into one genus, Sphaerotilus; however, these studies lacked adequate genomic representation of L. ochracea. Here, we present a comprehensive comparative genomic analysis of the Sphaerotilus-Leptothrix group, including expanded representation of L. ochracea, a closely related novel species, Leptothrix toolikensis, and two new isolates (Leptothrix mechoopdaensis). Analysis of 38 genomes resolves three phylogenetic and functional groups: the ochracea-type Leptothrix (Group 1), the mobilis-type Leptothrix (Group 2), and Sphaerotilus (Group 3). Group 1 genomes form a separate genus based on average nucleotide identity and alignment fraction. The genomes clearly diverge from the rest of Sphaerotilus-Leptothrix in phylogeny, size, and metabolic potential. Group 1 genomes are much smaller (2.59–3.04 Mb) than those of Groups 2 (4.55–6.06 Mb) and 3 (3.94–5.07 Mb), while encoding more metal oxidases and fewer carbohydrate-active enzymes. Group 2 clusters with Group 3 phylogenetically and is similar in organic carbon metabolisms but maintains more metal oxidation genes. Group 2 members lack homogeneity in phenotype and genotype, suggesting that additional isolates and genomes are needed for confident classification. However, Group 1 genomes (L. ochracea and L. toolikensis) show clear divergence, precluding their inclusion in Sphaerotilus and supporting the retention of the genus Leptothrix.

Leptothrix↗

The Bonding Nature and Adhesion of Polyacrylic Acid Coating on Li-Metal for Li Dendrite Prevention

The success of polyacrylic acid (PAA) to suppress Li dendrite growth suggests that the mechanical properties of polymer-based coatings, including the modulus, toughness, and interfacial adhesion are important design criteria. However, the measurement of the adhesion of thin PAA, as well as other polymer coatings to the reactive Li-metal anode surface is limited experimentally and challenging computationally. In this paper, a strategy was proposed to estimate the adhesion and delamination of the PAA(polymer)/Li interface, based on the bonding nature at the simpler PAA (oligomer)/Li interfaces using density functional theory calculations. It has been shown that the carboxylic acid groups in PAA reacted strongly with metallic Li, which significantly enhances the interfacial adhesion through the Li–O bonds formation, Li ionization and its incorporation into PAA, and –H or –OH termination of Li after decomposition of the COOH functional group. During delamination, it was found that the most likely PAA delamination route involved breaking partial Li–O bonds and lifting some ionized Li atoms from the Li-metal, especially for the Li atoms that showed a charge closer to +1 or are bonded with two O atoms from PAA. Based on the average bonding energies from PAA(oligomer)/Li interface delamination calculations, the work of separation, W sep , of the PAA(polymer)/Li interface was estimated to be ~1.0 (J/m 2 ). The high W sep of PAA (polymer)/Li was comparable with the Li 2 O/Li interface and higher than Li 2 CO 3 /Li and LiF/Li interfaces. This order correlated well with the areal density of Li–O bonds, which can serve as a descriptor for the interfacial adhesion. Furthermore, this computational approach can be applied to other interfaces with polymer-based coatings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Room temperature colossal superparamagnetic order in aminoferrocene–graphene molecular magnets

Intensive studies are published for graphene-based molecular magnets due to their remarkable electric, thermal, and mechanical properties. However, to date, most of all produced molecular magnets are ligand based and subject to challenges regarding the stability of the ligand(s). The lack of long-range coupling limits high operating temperature and leads to a short-range magnetic order. Herein, we introduce an aminoferrocene-based graphene system with room temperature superparamagnetic behavior in the long-range magnetic order that exhibits colossal magnetocrystalline anisotropy of 8 × 10 5 and 3 × 10 7 J/m 3 in aminoferrocene and graphene-based aminoferrocene, respectively. These values are comparable to and even two orders of magnitude larger than pure iron metal. Aminoferrocene [C 10 H 11 FeN] + is synthesized by an electrophilic substitution reaction. It was then reacted with graphene oxide that was prepared by the modified Hammers method. The phase structure and functionalization of surface groups were characterized and confirmed by XRD, FT-IR, and Raman spectroscopy. To model the behavior of the aminoferrocene between two sheets of hydroxylated graphene, we have used density functional theory by placing the aminoferrocene molecule between two highly ordered hydroxylated sheets and allowing the structure to relax. Here, the strong bowing of the isolated graphene sheets suggests that the charge transfer and resulting magnetization could be strongly influenced by pressure effects. In contrast to strategies based on ligands surface attachment, our present work that uses interlayer intercalated aminoferrocene opens routes for future molecular magnets as well as the design of qubit arrays and quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗