ON INVERSES AND ALGEBRAIC LOOPS OF CO-H-SPACES

In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.

LEFT INVERSES AND RIGHT INVERSES OF A STRONG ENDOMORPHISM OF A GRAPH

In this paper, we characterize left inverses and right inverses of a strong endomorphism of a graph under some certain Green's equivalence conditions. In addition, the number of them is also given.

A CHARACTERIZATION OF THE GENERALIZED INVERSES OVER DIVISION RINGS

Peal[2] shows that a sufficient and necessary condition on the existence of theMoore-Penrose inverse over any fields.Zhuang [3] generalize the result to any divisionrings.In this section we give another sufficient and necessary condition on the existence ofthe Moore-Penrose inverse over any division rings.Our result can be regarded as an im-provement of Theorem lin[1].As a medium result,we also show a characterization ofthe{1,2}-inverse.

CONTINUITY OF GENERALIZED INVERSES OF LINEAR OPERATORS IN BANACH SPACES AND ITS APPLICATIONS

The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses were independent of the choice of the generalized inverse. Based on this result, two sufficient and necessary conditions for the lower semi-continuity of generalized inverses as the set-valued mappings are given.

The SMW Formula for Bounded Homogeneous Generalized Inverses with Applications

In this paper, we present an extension of the so-called classical Sherman-Morrison-Woodbury (for short SMW) formula for bounded homogeneous generalized inverse in Banach spaces. Some particular cases and applications will be also considered. Our results generalize the results of many authors for finite dimensional matrices and Hilbert space operators in the literature.

Commuting Outer Inverses

The group, Drazin and Koliha-Drazin inverses are particular classes of commuting outer inverses. In this note, we use the inverse along an element to study some spectral conditions related to these inverses in the case of bounded linear operators on a Banach space.

Generalized Inverses and Units in a Unitary Ring

Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units.As applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,and the existence and expression of the inverse along a product of two regular elements are obtained,which generalizes the main result of Mary and Patricio(2016)about the group inverse of a product.

Weighted Moore-Penrose Inverses and Weighted Core Inverses in Rings with Involution

In this paper,the authors derive the existence criteria and the formulae of the weighted Moore-Penrose inverse,the e-core inverse and the f-dual core inverse in rings.Also,new characterizations between weighted Moore-Penrose inverses and one-sided inverses along an element are given.

Jacobson's Lemma for Generalized Drazin–Riesz Inverses

For bounded linear operators A,B,C and D on a Banach space X,we show that if BAC=BDB and CDB=CAC then I-AC is generalized Drazin-Riesz invertible if and only if I-BD is generalized Drazin-Riesz invertible,which gives a positive answer to Question 4.9 in Yan,Zeng and Zhu[Complex Anal.Oper.Theory 14,Paper No.12(2020)].In particular,we show that Jacobson’s lemma holds for generalized Drazin-Riesz inverses.

New Identities for Moore-Penrose Inverses of Some Operator Products and Their Reverse-order Laws

We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville's inclusions are made into equalities.

The MW5.5 earthquake on August 6,2023,in Pingyuan,Shandong,China:A rupture on a buried fault

On August 6,2023,a magnitude MW5.5 earthquake struck Pingyuan County,Dezhou City,Shandong Province,China.This event was significant as no large earthquakes had been recorded in the region for over a century,and no active fault had been previously identified.This study collects 1309 P-wave arrival times and 866 S-wave arrival times from 74 seismic stations less than 200 km to the epicenter to constrain the spatial distribution of the mainshock and its 125 early aftershocks by the double difference earthquake relocation method,and selects 864 P-waveforms from 288 stations located within 800 km of the epicenter to constrain the focal mechanism solution of the mainshock through centroid moment tensor inversion.The relocation and the inversion indicate,the Pingyuan MW5.5 earthquake was caused by a rupture on a buried fault,likely an extensive segment of the Gaotang fault.This buried fault exhibited a dip of approximately 75°to the northwest,with a strike of 222°,similar to the Gaotang fault.The rupture initiated at the depth of 18.6 km and propagated upward and northeastward.However,the ground surface was not broken.The total duration of the rupture was~6.0 s,releasing the scalar moment of 2.5895×1017 N·m,equivalent to MW5.54.The moment rate reached the maximum only 1.4 seconds after the rupture initiation,and the 90%scalar moment was released in the first 4.6 s.In the first 1.4 seconds of the rupture process,the rupture velocity was estimated to be 2.6 km/s,slower than the local S-wave velocity.As the rupture neared its end,the rupture velocity decreased significantly.This study provides valuable insights into the seismic characteristics of the Pingyuan MW5.5 earthquake,shedding light on the previously unidentified buried fault responsible for the seismic activity in the region.Understanding the behavior of such faults is crucial for assessing seismic hazards and enhancing earthquake preparedness in the future.

Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

Layer-Valley Hall Effect under Inversion and Time-Reversal Symmetries

Hall effects have been the central paradigms in modern physics,materials science and practical applications,and have led to many exciting breakthroughs,including the discovery of topological Chern invariants and the revolution of metrological resistance standard.To date,the Hall effects have mainly focused on a single degree of freedom(Do F),and most of them require the breaking of spatial-inversion and/or time-reversal symmetries.Here we demonstrate a new type of Hall effect,i.e.,layer-valley Hall effect,based on a combined layer-valley Do F characterized by the product of layer and valley indices.The layer-valley Hall effect has a quantum origin arising from the layer-valley contrasting Berry curvature,and can occur in nonmagnetic centrosymmetric crystals with both spatial-inversion and time-reversal symmetries,transcending the symmetry constraints of single Do F Hall effect based on the constituent layer or valley index.Moreover,the layer-valley Hall effect is highly tunable and shows a W-shaped pattern in response to the out-of-plane electric fields.Additionally,we discuss the potential detection approaches and material-specific design principles of layer-valley Hall effect.Our results demonstrate novel Hall physics and open up exotic paradigms for new research direction of layer-valleytronics that exploits the quantum nature of the coupled layer-valley DoF.

Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming

Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

Sliding and damming properties of granular debris with different geometric configurations and grain size distributions

Granular debris plays a significant role in determining damming deposit characteristics. An indepth understanding of how variations in grain size distribution(GSD) and geometric configurations impact the behavior of granular debris during the occurrence of granular debris is essential for precise assessment and effective mitigation of landslide hazards in mountainous terrains. This research aims to investigate the impact of GSD and geometric configurations on sliding and damming properties through laboratory experiments. The geometric configurations were categorized into three categories based on the spatial distribution of maximum volume: located at the front(Type Ⅰ), middle(Type Ⅱ), and rear(Type Ⅲ) of the granular debris. Our experimental findings highlight that the sliding and damming processes primarily depend on the interaction among the geometric configuration, grain size, and GSD in granular debris. Different sliding and damming mechanisms across various geometric configurations induce variability in motion parameters and deposition patterns. For Type Ⅰ configurations, the front debris functions as the critical and primary driving component, with energy dissipation primarily occurring through inter-grain interactions. In contrast, Type Ⅱ configurations feature the middle debris as the dominant driving component, experiencing hindrance from the front debris and propulsion from the rear, leading to complex alterations in sliding motion. Here, energy dissipation arises from a combination of inter-grain and grain-substrate interactions. Lastly, in Type Ⅲ configurations, both the middle and rear debris serve as the main driving components, with the rear sliding debris impeded by the front. In this case, energy dissipation predominantly results from grainsubstrate interaction. Moreover, we have quantitatively demonstrated that the inverse grading in damming deposits, where coarse grain moves upward and fine grain moves downward, is primarily caused by grain sorting due to collisions among the grains and between the grain and the base. The impact of grain on the horizontal channel further aids grain sorting and contributes to inverse grading. The proposed classification of three geometric configurations in our study enhances the understanding of damming properties from the view of mechanism, which provides valuable insights for related study about damming granular debris.

A Composite Ansatz for Calculation of Dynamical Structure Factor

We propose an ansatz without adjustable parameters for the calculation of a dynamical structure factor.The ansatz combines the quasi-particle Green’s function,especially the contribution from the renormalization factor,and the exchange-correlation kernel from time-dependent density functional theory together,verified for typical metals and semiconductors from a plasmon excitation regime to the Compton scattering regime.It has the capability to reconcile both small-angle and large-angle inelastic x-ray scattering(IXS)signals with muchimproved accuracy,which can be used as the theoretical base model,in inversely inferring electronic structures of condensed matter from IXS experimental signals directly.It may also be used to diagnose thermal parameters,such as temperature and density,of dense plasmas in x-ray Thomson scattering experiments.

A VGGNet-based correction for satellite altimetry-derived gravity anomalies to improve the accuracy of bathymetry to depths of 6500 m

Understanding the topographic patterns of the seafloor is a very important part of understanding our planet.Although the science involved in bathymetric surveying has advanced much over the decades,less than 20%of the seafloor has been precisely modeled to date,and there is an urgent need to improve the accuracy and reduce the uncertainty of underwater survey data.In this study,we introduce a pretrained visual geometry group network(VGGNet)method based on deep learning.To apply this method,we input gravity anomaly data derived from ship measurements and satellite altimetry into the model and correct the latter,which has a larger spatial coverage,based on the former,which is considered the true value and is more accurate.After obtaining the corrected high-precision gravity model,it is inverted to the corresponding bathymetric model by applying the gravity-depth correlation.We choose four data pairs collected from different environments,i.e.,the Southern Ocean,Pacific Ocean,Atlantic Ocean and Caribbean Sea,to evaluate the topographic correction results of the model.The experiments show that the coefficient of determination(R~2)reaches 0.834 among the results of the four experimental groups,signifying a high correlation.The standard deviation and normalized root mean square error are also evaluated,and the accuracy of their performance improved by up to 24.2%compared with similar research done in recent years.The evaluation of the R^(2) values at different water depths shows that our model can achieve performance results above 0.90 at certain water depths and can also significantly improve results from mid-water depths when compared to previous research.Finally,the bathymetry corrected by our model is able to show an accuracy improvement level of more than 21%within 1%of the total water depths,which is sufficient to prove that the VGGNet-based method has the ability to perform a gravity-bathymetry correction and achieve outstanding results.

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

Nonlinear robust adaptive control for bidirectional stabilization system of all-electric tank with unknown actuator backlash compensation and disturbance estimation

Since backlash nonlinearity is inevitably existing in actuators for bidirectional stabilization system of allelectric tank,it behaves more drastically in high maneuvering environments.In this work,the accurate tracking control for bidirectional stabilization system of moving all-electric tank with actuator backlash and unmodeled disturbance is solved.By utilizing the smooth adaptive backlash inverse model,a nonlinear robust adaptive feedback control scheme is presented.The unknown parameters and unmodelled disturbance are addressed separately through the derived parametric adaptive function and the continuous nonlinear robust term.Because the unknown backlash parameters are updated via adaptive function and the backlash effect can be suppressed successfully by inverse operation,which ensures the system stability.Meanwhile,the system disturbance in the high maneuverable environment can be estimated with the constructed adaptive law online improving the engineering practicality.Finally,Lyapunov-based analysis proves that the developed controller can ensure the tracking error asymptotically converges to zero even with unmodeled disturbance and unknown actuator backlash.Contrast co-simulations and experiments illustrate the advantages of the proposed approach.

Crashworthiness Design and Multi-Objective Optimization of Bionic Thin-Walled Hybrid Tube Structures

Thin-walled structures are widely used in cars due to their lightweight construction and energy-absorbing properties.However,issues such as high initial stress and lowenergy-absorbing efficiency arise.This study proposes a novel energy-absorbing structure inwhich a straight tube is combinedwith a conical tube and a bamboo-inspired bulkhead structure is introduced.This configuration allows the conical tube to flip outward first and then fold together with the straight tube.This deformation mode absorbs more energy and less peak force than the conical tube sinking and flipping inward.Through finite element numerical simulation,the specific energy absorption capacity of the structure is increased by 26%compared to that of a regular circular cross-section tube.Finally,the impact resistance of the bionic straight tapered tube structure is further improved through multi-objective optimization,promoting the engineering application and lightweight design of hybrid cross-section tubes.