Geometric Structures of Stable Time-Variant State Feedback Systems

A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.

Information Geometric Structures for the Thermodynamic Manifold

In view of information geometry,the state space S of thermodynamic parameters is investigated.First a Riemannian metric for S is defined and then the α-geometric structures of S is given.Some of results obtained by other authors are extended.

Photonic graphene with reconfigurable geometric structures in coherent atomic ensembles

Photonic graphene,possesses a honeycomb-like geometric structure,provides a superior platform for simulating photonic bandgap,Dirac physics,and topological photonics.Here,the photonic graphene with reconfigurable geometric structures is demonstrated in a 5S_(1/2)–5P_(3/2)–5D_(5/2) cascade-type 85Rb atomic ensembles.A strong hexagonal-coupling field,formed by the interference of three identical coupling beams,is responsible for optically inducing photonic graphene in atomic vapor.The incident weak probe beam experiences discrete diffraction,and the observed pattern at the output plane of vapor cell exhibits a clear hexagonal intensity distribution.The complete photonic graphene geometries from transversely stretched to longitudinally stretched are conveniently constructed by varying the spatial arrangement of three coupling beams,and the corresponding diffraction patterns are implemented theoretically and experimentally to map these distorted geometric structures.Moreover,the distribution of lattice sites intensity in photonic graphene is further dynamically adjusted by two-photon detuning and the coupling beams power.This work paves the way for further investigation of light transport and graphene dynamics.

(AuAg)_(44)(SPhtBu)_(26) versus(AuAg)_(44)(SPhF_(2))_(30):Tailoring the Geometric Structures and Optical Properties of Nanocluster Analogues

Monolayer-protected nanoclusters are ideal models for understanding the correlations between structures and properties of inorganic nanoparticles,especially for those molecules with identical sizes but comparable structures.Here,we controllably prepared and structurally determined a valence-neutral Au_(24+x)Ag_(20-x)(SPhtBu)_(26)(0<x<4)nanocluster with comparable structure features to a well-known Au_(12)Ag_(32)(SPhF_(2))_(30) cluster.The Au_(24+x)Ag_(20-x)(SPhtBu)_(26) cluster contained a hollow Au_(12)@M_(20) metallic kernel(M=Au/Ag),12 Au_(1)(SR)_(2) staples,and two bridging SR molecules,and its average molecular formula was determined to be Au_(26.3)Ag_(17.7)(SPhtBu)_(26),as evidenced by X-ray crystallography and electrospray ionization mass spectrometry.Because of the ligand effect and the asymmetrical arrangement of the Au dopants in the dodecahedral cage,the Au_(24+x)Ag_(20-x)(SPhtBu)_(26) nanocluster exhibited lower molecular symmetry relative to Au_(12)Ag_(32)(SPhF_(2))_(30) in terms of the dodecahedral kernel and motif shell structures.Besides,the strong π-π interaction in Au2_(4+x)Ag_(20-x)(SPhtBu)_(26) contributed to its enhanced photoluminescence intensity compared with Au_(12)Ag_(32)(SPhF_(2))_(30).The study,herein,extends the 44-metal-atom cluster family,thereby enabling us to better understand the correlations between their structures and properties at the atomic level.

An Original Didactic of the Standard Model “The Particle’s Geometric Model” (Nucleons and K-Mesons)

This paper shows a didactic model (PGM), and not only, but representative of the Hadrons described in the Standard Model (SM). In this model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (IQuO). By the properties of IQuO one can define the electric charge and that of color of quarks. Showing the “aurea” (golden) triangular shape of all quarks, we manage to represent the geometric combinations of the nucleons, light mesons, and K-mesons. By the geometric shape of W-bosons, we represent the weak decay of pions and charged Kaons and neutral, highlighting in geometric terms the possibilities of decay in two and three pions of neutral Kaon and the transition to anti-Kaon. In conclusion, from this didactic representation, an in-depth and exhaustive phenomenology of hadrons emerges, which even manages to resolve some problematic aspects of the SM.

An Original Didactic about Standard Model (Geometric Model of Particle: The Quarks)

This work shows a didactic model representative of the quarks described in the Standard Model (SM). In the model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (GMP). From these didactic hypotheses emerges an in-depth phenomenology of particles (quarks) fully compatible with that of SM, showing, besides, that the number of possible quarks is six.

Geometrical Structures of Certain Class of Statistical Manifolds

The geometrical structures of the certain class of statistical manifolds are investigated. The geometwhich includes the original geometrical metrics of S.Amari.

An Initial Research on the Geometric Theory of Quasicrystal Structures

The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .

Boosting Electrochemical Urea Synthesis via Constructing Ordered Pd–Zn Active Pair

Electrochemical co-reduction of nitrate(NO_(3)^(-))and carbon dioxide(CO_(2))has been widely regarded as a promising route to produce urea under ambient conditions,however the yield rate of urea has remained limited.Here,we report an atomically ordered intermetallic pallium-zinc(PdZn)electrocatalyst comprising a high density of PdZn pairs for boosting urea electrosynthesis.It is found that Pd and Zn are responsible for the adsorption and activation of NO_(3)^(-)and CO_(2),respectively,and thus the co-adsorption and co-activation NO_(3)^(-)and CO_(2) are achieved in ordered PdZn pairs.More importantly,the ordered and well-defined PdZn pairs provide a dual-site geometric structure conducive to the key C-N coupling with a low kinetical barrier,as demonstrated on both operando measurements and theoretical calculations.Consequently,the PdZn electrocatalyst displays excellent performance for the co-reduction to generate urea with a maximum urea Faradaic efficiency of 62.78%and a urea yield rate of 1274.42μg mg^(-1) h^(-1),and the latter is 1.5-fold larger than disordered pairs in PdZn alloys.This work paves new pathways to boost urea electrosynthesis via constructing ordered dual-metal pairs.

Geometric effect promoted hydrotalcites catalysts towards aldol condensation reaction

In solid basic catalysis field,how to achieve optimized activity and desired stability through elaborate control over basic site properties remains a challenge.In this work,taking advantage of the structure memory effect of layered double hydroxides(LDHs),rehydrated Ca4 Al1-x Gax-LDHs and Ca4 Al1-x Inx-LDHs catalysts were prepared and applied in aldol condensation reaction that isobutyraldehyde(IBD)reacts with formaldehyde(FA)to obtain hydroxypivalaldehyde(HPA).Notably,the resulting re-Ca4 Al0.90Ga0.10-LDHs exhibits an extraordinarily-high catalytic activity(HPA yield:72%),which is to our best knowledge the highest level in this reaction.The weak Br?nsted basic site,7-coordinated Ca-OH group,which serves as an active site,catalyzes the condensation process and promotes the product desorption.Studies on structure-property correlations demonstrate that Ga as a structural promoter induces a moderate expansion of the laminate lattice,which results in a significant increase in the concentration of weak basic sites in re-Ca4Al0.90Ga0.10-LDHs,accounting for its high catalytic activity.This work illuminates that geometric structure of basic active sites can be tuned via introducing catalyst additive,which leads to a largely improved performance of hydrotalcite solid basic catalysts towards aldol condensation reaction.

The Theoretical Value of Mass of the Light <i>η</i>-Meson via the Quarks’ Geometric Model

Highlighting a golden triangular form in u and d quarks (Quark Geometric Model), we build the geometric structures of light meson η and individualize its decays and spin. By the structure equations describing mesons, we determine a mathematic procedure to calculate the theoretical value of the mass of light mesons η.

The Theoretical Spectrum of Mass of the Light Mesons without Strangeness via the Quarks’ Geometric Model

Using the “Aureum Geometric Model” (AGM) of quarks, we formulate the structure equations describing mesons and, by a mathematic procedure, we calculate the theoretical spectrum of mass values of light mesons without strangeness.

Research Progress of Fabrics with Different Geometric Structures for Triboelectric Nanogenerators in Flexible and Wearable Electronics

Widespread reliance on fossil fuels,and the resulting imbalance between energy supply and demand have emerged as significant obstacles to achieving sustainable development.Triboelectric nanogenerators(TENGs)offer a viable solution to this problem.Among the various materials used in TENGs,fabrics with geometric structures have attracted considerable interest because of their advantageous properties,such as their light weight,breathable structures,favorable softness,and excellent breathability.This review provides a comprehensive introduction to fabric geometric(fabric structure with yarn as the basic unit,including woven fabrics formed by warp and weft yarns and knitted fabrics formed by yarn coils,etc.)TENGs,including their definition,working principle,and mechanisms,and explores the recent progress in TENGs based on one-,two-,and three-dimensional structures,classifying them into woven and knitted fabrics according to the fabrication method.We summarize the advantages and disadvantages of TENGs with different dimensions.Considering the intrinsically limited conductivity of the fiber and fabric,progress in improving the comprehensive output performance of TENGs via combination with other conductive materials and surface modification is discussed.Finally,this review concludes with a discussion of the challenges,opportunities,and potential applications related to TENGs based on fabric geometric structures.This study is expected to provide readers with new strategies and conceptual ideas to improve the performance of TENGs constructed with fabrics,particularly through the optimization of their structures.

A Density Functional Theory Study of the Geometric and Electronic Structure of MgF_2 (110) Surface

Abstract＂ Ab initio density functional theory （DFT） was employed to study geometric and electronic structure of MgF2 （110） surface. Three different clean surface models have been considered. The results show that the surface terminated with one-layer F has the smallest relaxation and the lowest surface energy, which indicates this model is the most energetically favorable structure of MgF2（110） surface. Furthermore, the electronic properties are also discussed from the point of density of states and charge density. Analysis of electronic structure shows that the band gap of the surface is significantly narrowed with respect to the bulk. The electrons of the surface exhibit strong locality and larger effective mass.

Quantum Chemical Calculation on the Structures and Electronic Properties of Phosphonate Ester as Rare Earth Extractants

Molecular mechanics, molecular dynamics and semi empirical quantum chemical method have been used to study the geometric and electronic structures of six phosphonate ester as rare earth extractants. The results show that the phosphorus atom exhibits sp 3 hybridization. The structures of the extractants are determined by the repulsion of the hydrocarbon groups. In the extractants that have two 2 ethyl hexyl groups, one 2 ethyl hexyl extends straight, and the other extends twistily. When the number of oxygen atom decreases, the negative charge of the phosphoryl oxygen atom increases, but the negative charge of oxygen atom and the positive charge of hydrogen of the hydroxyl group decreases, and the energies of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital(LUMO) increase. The energies of the occupied frontier orbitals are close to each other.

First principles study on geometric and electronic properties of two-dimensional Nb_(2)CT_(x) MXenes

MXenes are a new type of two-dimensional carbides with rich physical and chemical properties. The physics of MXenes, and thus the applications, are dominated by surface functional groups. Herein, the effects of different terminations(O,S, Se, Te) on the geometric and electronic properties of Nb_(2)C MXenes were studied via density functional theory(DFT)calculations. Three adsorption sites were examined to determine the most stable configurations. The results showed that both the types and the positions of surface functional groups influence the geometric stability and physical characters of Nb_(2)C. The S and Se terminations make the Nb_(2)C MXenes to be semiconductor, while Nb_(2)C MXenes with other terminations(O, Te) are conductor. The electron location function, density of states, Bader charge distribution, and the projected crystal orbital Hamilton population were conducted to explain the origin of adsorption stability and electronic nature difference. Our results provide a fundamental understanding about the effects of surface terminations on the intrinsic stability and electronic properties of Nb_(2)C MXenes.

GEOMETRIC STRUCTURE OF ETHYLENOXIDE ADSORBED ON Cu(110) SURFACE

The binding energies of ethylene oxide (Et-O) adsorbed on Cu(110) surface for different adsorption sites and orientations are calculated with an atom superposition and electron delocalization molecular orbital (ASED-MO) using cluster models. It shows that the top site of Cu(110) surface is preferable for Et-O adsorption and the orientation of C-C bond of Et-O is parallel to the [110] direction of the substratc. The distance of an oxygen of Et-O to the Cu atom is approximately 1.5817(?). It is different from the supposition of C. Benndorf et al., in which the oxygen was proposed on the short bridge site with C-C bond orientating to [110] direction of Cu(110)

Structures, stabilities, and electronic properties of F-doped Sin （n=1～12） clusters：Density functional theory investigation

The geometries, stabilities, and electronic properties of FSin （n=1～12） clusters are systematically investigated by using first-principles calculations based on the hybrid density-functional theory at the B3LYP/6-311G level. The geometries are found to undergo a structural change from two-dimensional to three-dimensional structure when the cluster size n equals 3. On the basis of the obtained lowest-energy geometries, the size dependencies of cluster properties, such as averaged binding energy, fragmentation energy, second-order energy difference, HOMO–LUMO （highest occupied molecular orbital–lowest unoccupied molecular orbital） gap and chemical hardness, are discussed. In addition, natural population analysis indicates that the F atom in the most stable FSin cluster is recorded as being negative and the charges always transfer from Si atoms to the F atom in the FSin clusters.

Geometric Structure and Tectonic Activities of Wanquan Fault,Hebei Province

Based on detailed investigations and prospecting,this paper describes the geometrical characteristics and tectonic activities of Wanquan fault in northwest of Beijing. This fault strikes mainly northeast or northeast to north,dipping southeast,and extends over a length of 15km. It is a major geological and geomorphological margin,controlling the neotectonic movement in this region. On the southeast side of Wanquan fault are the Late Quaternary unconsolidated deposits,forming a basin or deposition; but on the other side is Mesozoic volcano debris,forming lower-mountains and hills. Wanquan fault is a mid- to-high-angle normal fault dipping southeast. This fault was more active in the Quaternary. Since the middle-late part of the alate Pleistocene,the average rate with vertical slip of a single fault is over 0. 03 ～ 0. 3mm /a,but the fault has multiple slipping surfaces,and a total rate with vertical slip will be estimated.

In situ confined vertical growth of Co_(2.5)Ni_(0.5)Si_(2)O_(5)(OH)_(4)nanoarrays on rGO for an efficient oxygen evolution reaction

Rational design of oxygen evolution reaction(OER)catalysts at low cost would greatly benefit the economy.Taking advantage of earth-abundant elements Si,Co and Ni,we produce a unique-structure where cobalt-nickel silicate hydroxide[Co_(2.5)Ni_(0.5)Si_(2)O_(5)(OH)_(4)]is vertically grown on a reduced graphene oxide(rGO)support(CNS@rGO).This is developed as a low-cost and prospective OER catalyst.Compared to cobalt or nickel silicate hydroxide@rGO(CS@rGO and NS@rGO,respectively)nanoarrays,the bimetal CNS@rGO nanoarray exhibits impressive OER performance with an overpotential of 307 mV@10 mA cm^(-2).This value is higher than that of CS@rGO and NS@rGO.The CNS@rGO nanoarray has an overpotential of 446 mV@100 mA cm^(-2),about 1.4 times that of the commercial RuO_(2)electrocatalyst.The achieved OER activity is superior to the state-of-the-art metal oxides/hydroxides and their derivatives.The vertically grown nanostructure and optimized metal-support electronic interactions play an indispensable role for OER performance improvement,including a fast electron transfer pathway,short proton/electron diffusion distance,more active metal centers,as well as optimized dualatomic electron density.Taking advantage of interlay chemical regulation and the in-situ growth method,the advanced-structural CNS@rGO nanoarrays provide a new horizon to the rational and flexible design of efficient and promising OER electrocatalysts.