Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays.

Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning

Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.

Highly ordered crystallization of α-FAPbl_(3) films via homogeneous seeds for efficient perovskite solar cells

Formamidine lead triiodide(FAPbI_(3))perovskites have become the most promising photovoltaic materials for perovskite solar cells with record power conversion efficiency(PCE).However,random nucleation,phase transition,and lattice defects are still the key challenges limiting the quality of FAPbI_(3) films.Previous studies show that the introduction or adding of seeds in the precursor is effective to promote the nucleation and crystallization of perovskite films.Nevertheless,the seed-assisted approach focuses on heterogeneous seeds or hetero-composites,which inevitably induce a lattice-mismatch,the genera-tion of strain or defects,and the phase segregation in the perovskite films.Herein,we first demonstrate that high-quality perovskite films are controllably prepared using α-and δ-phases mixed FAPbI_(3) micro-crystal as the homogeneous seeds with the one-step antisolvent method.The partially dissolved seeds with suitable sizes improve the crystallinity of the perovskite flm with preferable orientation,improved carrier lifetime,and increased carrier mobility.More importantly,the α-phase-containing seeds promote the formation of α-phase FAPbI_(3) films,leading to the reduction of residual lattice strain and the suppres-sion of I-ion migration.Besides,the adding of dimethyl 2,6-pyridine dicarboxylate(DPD)into the pre-cursor further suppresses the generation of defects,contributing to the PCE of devices prepared in air ambient being significantly improved to 23.75%,among the highest PCEs for fully air-processed FAPbI_(3) solar cells.The unpackaged target devices possess a high stability,maintaining 80%of the initial PCE under simulated solar illumination exceeding 800 h.

Adaptive detection of range-spread targets in homogeneous and partially homogeneous clutter plus subspace interference

Adaptive detection of range-spread targets is considered in the presence of subspace interference plus Gaussian clutter with unknown covariance matrix.The target signal and interference are supposed to lie in two linearly independent subspaces with deterministic but unknown coordinates.Relying on the two-step criteria,two adaptive detectors based on Gradient tests are proposed,in homogeneous and partially homogeneous clutter plus subspace interference,respectively.Both of the proposed detectors exhibit theoretically constant false alarm rate property against unknown clutter covariance matrix as well as the power level.Numerical results show that,the proposed detectors have better performance than their existing counterparts,especially for mismatches in the signal steering vectors.

On Enforcing Dyadic-type Homogeneous Binary Function Product Constraints in MatBase

Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.

Homogeneous distributed natural pyrite-derived composite induced by modified graphite as high-performance lithium-ion batteries anode

Natural minerals-based energy materials have attracted enormous attention because of the advantages of good materials consistency,high production,environmental friendliness,and low cost.The uniform distribution of grains can effectively inhibit the aggregation of active materials,improving lithium storage performance.In this work,natural graphite is modified by polyvinylpyrrolidone to obtain modified graphite with reduced size and better dispersion.Natural pyrite composite polyvinylpyrrolidone-modified graphite(pyrite/PG)material with uniform particle distribution is obtained by the ball milling process.The subsequent calcination process converts pyrite/PG into Fe_(1-x)Scompounded with polyvinylpyrrolidone-modified graphite(Fe_(1-x)S/PG).The homogeneous grain distributions of active material can facilitate the faster transfer of electrons and promote the efficient utilization of active materials.The as-prepared Fe_(1-x)S/PG electrode exhibits a remarkably reversible specific capacity of 613.0 mAh·g^(-1)at 0.2 A·g^(-1)after 80 cycles and an excellent rate capability of 523.0 mAh·g^(-1)at 5 A·g^(-1).Even at a higher current density of 10 A·g^(-1),it can deliver a specific capacity of 348.0 mAh·g^(-1).Moreover,the dominant pseudocapacitance in redox reactions accounts for the impressive rate and cycling stability.This work provides a low-cost and facile method to fabricate natural mineral-based anode materials and apprise readers about the impact of uniform particle distribution on lithium storage performance.

Laboratory investigation on damping characteristics of homogeneous and stratified soil-ash system

In this study,the damping responses of uniform soil,equi-proportional fly ash,and local soil as a single unit were investigated.The large-strain cyclic triaxial tests were performed for the specimen compacted at the desired density(95%e99%of maximum dry density).The compacted specimens were tested under the loading frequency of 0.3e1 Hz with medium confinement of 70e100 kPa.Also,the unsymmetrical behavior of the hysteresis loop was analyzed using three different damping estimation approaches,i.e.symmetric hysteresis loop(SHL),asymmetric hysteresis loop(ASHL),and the modified American Society for Testing and Materials(ASTM)method.The outcome of the study shows for fly ash,local soil,and layered soil-ash,the ASHL technique has the highest damping value,followed by ASTM and then the SHL approach.The specimens prepared under high density and subjected to high confinement show low damping values.However,the specimens tested at high frequency exhibits high damping behavior.Similarly,the damping value of fly ash determined using the SHL and ASHL methods has a similar profile and reaches a maximum at 1%shear strain value before decreasing.The composite stratified deposit exhibits more dependency on relative compaction,confining pressure,and less on loading frequency.Based on the results,it is highly recommended to use the ASHL approach,especially under large strain conditions irrespective of soil type.The maximum damping ratio of stratified deposits is always in between the damping ratio of local soil and fly ash.The damping ratio of stratified soil and local soil is slightly larger than that of the other soils,although the damping ratio of fly ash is equivalent to that of the sand and clayey soil.These results may be helpful in the accurate determination of the damping properties of the layered soil-ash system that is required in the seismic response analysis.

Realization of homogeneous dielectric barrier discharge in atmospheric pressure argon and the effect of beads on its characteristics

This paper describes the realization of a homogeneous dielectric barrier discharge(DBD)in argon at atmospheric pressure.The effect of the morphology of the dielectric surface(especially the dielectric surface covered by hollow ceramic beads(99%Al_(2)O_(3))with different diameters)on discharge is investigated.With different dielectrics,the argon DBD presents two discharge modes:a filamentary mode and a homogeneous mode.Fast photography shows that the filamentary mode operates in a streamer discharge,and the homogeneous mode operates in a Townsend discharge regime.It is found that a homogeneous discharge can be generated within a certain voltage range.The voltage amplitude range decreases,and the breakdown voltage increases with the increase in the mean diameter of the ceramic beads.Waveforms of the total current and optical emission signal present stochastic pulses per half voltage cycle for the filamentary mode,whereas there is one single hump per half voltage cycle for the homogeneous mode.In the homogeneous mode,the intensity of the optical emission decreases with the mean diameter of the ceramic beads.The optical emission spectrum is mainly composed of atomic lines of argon and the second positive system of molecular nitrogen.It reveals that the electron density decreases with the increasing mean diameter of the ceramic beads.The vibrational temperature increases with the increasing mean diameter of the ceramic beads.It is believed that a large number of microdischarges are formed,and smaller ceramic beads have a larger activation surface area and more point discharge.Electrons liberated in the shallow well and electrons generated from microdischarges can increase the secondary electron emission coefficient of the cathode and provide initial electrons for discharge continuously.Therefore,the breakdown electric field is reduced,which contributes to easier generation of homogeneous discharge.This is confirmed by the simulation results.

A homogeneous atmospheric pressure air plasma in a 10 mm gap based on a three-electrode configuration

Generation of atmospheric pressure homogeneous air plasma in a large gap(>4 mm)is a challenge.In this study,an atmospheric pressure homogeneous air plasma generated in a gap up to 10 mm is reported,which is based on a three-electrode configuration,where a high-voltage(HV)electrode and a middle electrode form a surface dielectric barrier discharge(S-DBD),and together with the ground electrode form the main volume discharge.High-speed photographs confirm that the discharge in the main gap is homogeneous.The gas temperature of the plasma estimated from the N_(2)(C^(3)∏_(u)-B^(3)∏_(g))(Δv=-2)emission is about 320 K,which is close to room temperature.A detailed analysis shows that the discharge ignited between the HV electrode and the middle electrode is serving as an electron source,and the electrons deposited on the dielectric plate are due to the S-DBD along with the applied voltage generating a driving force,which results in a high concentration of seed electrons in the main gap and induces the homogeneous plasma.Further analysis shows that the electric field in the main gap is only about18.45 k V·cm^(-1),which is much lower than the typical breakdown electric field of 30 k V·cm^(-1)for atmospheric pressure air discharge.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES

In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.

Characterizations of realized homogeneous Besov and Triebel-Lizorkin spaces via differences

Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense.

Variation principle of piezothermoelastic bodies,canonical equation and homogeneous equation

Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.

GENERALIZED HOMOGENEOUS FUNCTIONS AND THE TWO-BODY PROBLEM

A generalization of the homogeneous function concept is studied.An application is done with a solution of the two-body problem.

Application of Fractional Calculus to a Linear Third Order (Nonhomogeneous and Homogeneous) Ordinary Differential Equation

In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.

ARITHMETIC SUM OF TWO HOMOGENEOUS CANTOR SETS

In this note, an example of two homogeneous Cantor sets whose arithmetic sum is a homogeneous Cantor set with a positive Lebesgue measure is given.

Homogeneous Degradation of Cellulose in Its Aqueous Solution at Mild Temperature under Atmospheric Pressure

Degradation of cellulose to chemicals is one of major routes for biomass conversion. Here, a new simple and two-step method has been developed to convert cellulose in its homogeneously alkaline solution to organic acids under atmospheric pressure at mild temperature. At first, cellulose was degraded to smM1 molecular intermediates at 110 ℃ for 3 h under atmospheric pressure, and then it was oxidized with H202 at 50 ℃ for 4 h. Under the optimal condition, 73.5% conversion of cellulose could be achieved, and the yield of organic acids was 32.8% （formic acid）, 11.6% （lactic acid）, and 2.3% （oxalic acid）, respectively. It is noteworthy that the new strategy reduces energy consumption in the process of reaction, unlike the hydrothermal reaction under high temperature and high pressure.

Synthesis of Ce:YAG Phosphor via Homogeneous Precipitation under Microwave Irradiation

Ultra-fine Ce:YAG phosphors were prepared by homogeneous precipitation under microwave irradiation method . The formation of Ce: YAG was investigated by means of XRD and DTA/TG. The purified YAG crystallized phase was obtained at a lower temperature (1100℃). Basically spherical Ce:YAG powders were indicated from TEM images, and the size of the particles is about 80 nm. Two peaks of 436 and 473 nm can be seen from the excitation spectrum in the range of 402 -510 nm. A broad emission band located at 480 ~ 630 nm shows the phosphors prepared by this method have good emission properties.

Homogeneous bottom-growth of lithium metal anode enabled by double-gradient lithiophilic skeleton

Lithium(Li) metal is considered as the most promising anode material for the next-generation high performance Li batteries.However,the uncontrollable dendritic growth impedes its commercial application.Herein,we design a 3 D Si@carbon nanofibers(CNFs)@ZnO-ZnO-Cu skeleton(SCZ) for guiding the homogeneous bottom-growth of Li metal.The top LixSi@CNFs and bottom LiyZn@CNFs layers could form conductivity and overpotential gradient to avoid the "top-growth" of Li metal.Moreover,the top lithiophilic LixSi@CNFs layer could regulate the nucleation and deposition of Li-ions even if the lithium dendrites grow out of the skeleton under high capacity Li deposition(30 mAh cm^(-2)).As a result,the SCZ-Li||LiFePO_(4) full cell delivers a high capacity of ~104 mAh g^(-1)(~94.82% capacity retention) after 2000 cycles at 5 C, elucidating the potential application of the 3 D double-gradient Li metal composite anode.

Homogeneous Acetylation of Cellulose at Relatively High Concentrations in an Ionic Liquid

At relatively high cellulose mass concentrations(8%,10%,and 12%),homogeneous acetylation of cellulose was carried out in an ionic liquid,1-allyl-3-methylimidazolium chloride(AmimCl).Without using any catalyst,cellulose acetates(CAs)with the degree of substitution(DS)in a range from 0.4 to 3.0 were synthesized in one-step.The effects of reaction time,temperature and molar ratio of acetic anhydride/anhydroglucose unit(AGU) in cellulose on DS value of CAs were investigated.The synthesized CAs were characterized by means of FT-IR, NMR,and solubility,mechanical and thermal tests.After the acetylation,the used ionic liquid AmimCl was easily recycled and reused.This study shows the potential of the homogeneous acetylation of cellulose at relatively high concentrations in ionic liquids in future industrial applications.