一类树的邻接矩阵的Moore-Penrose广义逆

根据矩阵结构性质,利用分块矩阵技巧给出任意点数、任意长直径的毛毛虫树邻接矩阵的Moore-Penrose广义逆的具体形式,为进一步研究毛毛虫树的代数性质提供理论支撑.

用新激活函数加快新ZNN模型求解时变矩阵Moore-Penrose逆

基于梯度的神经网络(GNN)和张神经网络(ZNN)是两种可用于求解时变矩阵Moore-Penrose逆问题的递归神经网络。与GNN相比,ZNN的计算精度更高。此外,本文提出了一种新的ZNN模型。因此,本文主要利用带有新优化激活函数的ZNN模型来求解时变行满秩(或列满秩)矩阵Moore-Penrose逆问题。这种带有新优化激活函数的ZNN模型可以在有限时间内加速求解时变矩阵的Moore-Penrose逆。通过Lyapunov理论分析,得到了收敛时间的上限。仿真结果进一步证实了理论分析,并证明了采用新优化的激活函数的ZNN模型在求解时变矩阵Moore-Penrose逆时的有效性。

The Reverse Order Law for Moore-Penrose Inverse of Closed Operators

In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].

一个2×2块矩阵的Moore-Penrose逆的显式公式

The representation for the Moore-Penrose inverse of the matrix[AC BD]is derived by using the solvability theory of linear equations,where A∈C^(m×n),B∈C^(m×p),C∈C^(q×n)and D∈C^(q×p),with which some special cases are discussed.

实方阵的Moore-Penrose广义逆的MCG算法探究

证明了矩阵Moore-Penrose逆的唯一性以及建立了求矩阵Moore-Penrose逆的算法。首先将求矩阵的Moore-Penrose逆转为求解含有三个矩阵变量的矩阵方程组,其次建立求该矩阵方程组的修正共轭梯度算法(MCG算法),给出了MCG算法的性质和收敛性证明,对于任意给定的初始矩阵该算法能在有限步迭代计算后得到矩阵的Moore-Penrose逆。最后给出数值算例,证明MCG算法在求解矩阵Moore-Penrose逆中具有很高的计算效率。

Giant reversible barocaloric effects with high thermal cycle stability in epoxybonded(MnCoGe)_(0.96)(CuCoSn)_(0.04) composite

Hexagonal MnMX-based(M=Co or Ni,X=Si or Ge)alloys exhibit giant reversible barocaloric effects.However,giant volume expansion would result in the as-cast MnMX ingots fragmenting into powders,and inevitably bring the deterioration of mechanical properties and formability.Grain fragmentation can bring degradation of structural transformation entropy change during cyclic application and removal of pressure.In this paper,giant reversible barocaloric effects with high thermal cycle stability can be achieved in the epoxy bonded(MnCoGe)0.96(CuCoSn)0.04 composite.Giant reversible isothermal entropy change of 43.0 J·kg^(−1)·K^(−1) and adiabatic temperature change from barocaloric effects(ΔT_(BCE))of 15.6 K can be obtained within a wide temperature span of 30 K at 360 MPa,which is mainly attributed to the integration of the change in the transition temperature driven by pressure of−101 K·GPa^(−1) and suitable thermal hysteresis of 11.1 K.Further,the variation of reversibleΔ_(TBCE) against the applied hydrostatic pressure reaches up to 43 K·GPa^(−1),which is at the highest level among the other reported giant barocaloric compounds.More importantly,after 60 thermal cycles,the composite does not break and the calorimetric curves coincide well,demonstrating good thermal cycle stability.

Surviving winter on the Qinghai-Xizang Plateau:Extensive reversible protein phosphorylation plays a dominant role in regulating hypometabolism in hibernating Nanorana parkeri

Changes in protein abundance and reversible protein phosphorylation(RPP)play important roles in regulating hypometabolism but have never been documented in overwintering frogs at high altitudes.To test the hypothesis that protein abundance and phosphorylation change in response to winter hibernation,we conducted a comprehensive and quantitative proteomic and phosphoproteomic analysis of the liver of the Xizang plateau frog,Nanorana parkeri,living on the Qinghai-Xizang Plateau.In total,5170 proteins and 5695 phosphorylation sites in 1938 proteins were quantified.Based on proteomic analysis,674 differentially expressed proteins(438 up-regulated,236 down-regulated)were screened in hibernating N.parkeri versus summer individuals.Functional enrichment analysis revealed that higher expressed proteins in winter were significantly enriched in immune-related signaling pathways,whereas lower expressed proteins were mainly involved in metabolic processes.A total of 4251 modified sites(4147 up-regulated,104 down-regulated)belonging to 1638 phosphoproteins(1555 up-regulated,83 down-regulated)were significantly changed in the liver.During hibernation,RPP regulated a diverse array of proteins involved in multiple functions,including metabolic enzymatic activity,ion transport,protein turnover,signal transduction,and alternative splicing.These changes contribute to enhancing protection,suppressing energy-consuming processes,and inducing metabolic depression.Moreover,the activities of phosphofructokinase,glutamate dehydrogenase,and ATPase were all significantly lower in winter compared to summer.In conclusion,our results support the hypothesis and demonstrate the importance of RPP as a regulatory mechanism when animals transition into a hypometabolic state.

Triple reverse order law for the Drazin inverse

In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.

Numerical analysis for the free-boundary current reversal equilibrium in the AC plasma current operation in a tokamak

In recent decades, tokamak discharges with zero total toroidal current have been reported in tokamak experiments, and this is one of the key problems in alternating current(AC) operations.An efficient free-boundary equilibrium code is developed to investigate such advanced tokamak discharges with current reversal equilibrium configuration. The calculation results show that the reversal current equilibrium can maintain finite pressure and also has considerable effects on the position of the X-point and the magnetic separatrix shape, and hence also on the position of the strike point on the divertor plates, which is extremely useful for magnetic design, MHD stability analysis, and experimental data analysis etc. for the AC plasma current operation on tokamaks.

Preliminary compact torus injection experiments on the Keda Torus eXperiment reversed field pinch

A new compact torus injector(KTX-CTI)has been built for injection experiments on the Keda Torus eXperiment(KTX)reversed field pinch(RFP).The aim is to study the fundamental physics governing the compact torus(CT)central fueling processes.In experiments conducted under the sole influence of a 0.1 T toroidal magnetic field,the injected CT successfully penetrated the entire toroidal magnetic field,reaching the inner wall of the KTX vacuum vessel.Upon reaching the inner wall,the CT diffused both radially outward and toroidally within the vessel at a discernible diffusion speed.Moreover,the inherent helicity within the CT induced a modest KTX plasma current of 200 A,consistent with predictions based on helicity conservation.CT injection demonstrated the capability to initiate KTX discharges at low loop voltages,suggesting its potential as a pre-ionization and current startup technique.During RFP discharges featuring CT injection,the central plasma density was found to exceed the Greenwald density limit,with more peaked density profiles,indicating the predominant confinement of CT plasma within the core region of the KTX bulk plasma.

A numerical survey of parameters to reach ignition condition for axial compression of a large-sized field reversed configuration

Field reversed configuration(FRC)is widely considered as an ideal target plasma for magnetoinertial fusion.However,its confinement and stability,both proportional to the radius,will deteriorate inevitably during radial compression.Hence,we propose a new fusion approach based on axial compression of a large-sized FRC.The axial compression can be made by plasma jets or plasmoids converging onto the axial ends of the FRC.The parameter space that can reach the ignition condition while preserving the FRC's overall quality is studied using a numerical model based on different FRC confinement scalings.It is found that ignition is possible for a large FRC that can be achieved with the current FRC formation techniques if compression ratio is greater than 50.A more realistic compression is to combine axial with moderate radial compression,which is also presented and calculated in this work.

The Immense Impact of Reverse Edges on Large Hierarchical Networks

Hierarchical networks are frequently encountered in animal groups,gene networks,and artificial engineering systems such as multiple robots,unmanned vehicle systems,smart grids,wind farm networks,and so forth.The structure of a large directed hierarchical network is often strongly influenced by reverse edges from lower-to higher-level nodes,such as lagging birds’howl in a flock or the opinions of lowerlevel individuals feeding back to higher-level ones in a social group.This study reveals that,for most large-scale real hierarchical networks,the majority of the reverse edges do not affect the synchronization process of the entire network;the synchronization process is influenced only by a small part of these reverse edges along specific paths.More surprisingly,a single effective reverse edge can slow down the synchronization of a huge hierarchical network by over 60%.The effect of such edges depends not on the network size but only on the average in-degree of the involved subnetwork.The overwhelming majority of active reverse edges turn out to have some kind of“bunching”effect on the information flows of hierarchical networks,which slows down synchronization processes.This finding refines the current understanding of the role of reverse edges in many natural,social,and engineering hierarchical networks,which might be beneficial for precisely tuning the synchronization rhythms of these networks.Our study also proposes an effective way to attack a hierarchical network by adding a malicious reverse edge to it and provides some guidance for protecting a network by screening out the specific small proportion of vulnerable nodes.

A Reverse Path Planning Approach for Enhanced Performance of Multi-Degree-of-Freedom Industrial Manipulators

In the domain of autonomous industrial manipulators,precise positioning and appropriate posture selection in path planning are pivotal for tasks involving obstacle avoidance,such as handling,heat sealing,and stacking.While Multi-Degree-of-Freedom(MDOF)manipulators offer kinematic redundancy,aiding in the derivation of optimal inverse kinematic solutions to meet position and posture requisites,their path planning entails intricate multiobjective optimization,encompassing path,posture,and joint motion optimization.Achieving satisfactory results in practical scenarios remains challenging.In response,this study introduces a novel Reverse Path Planning(RPP)methodology tailored for industrial manipulators.The approach commences by conceptualizing the manipulator’s end-effector as an agent within a reinforcement learning(RL)framework,wherein the state space,action set,and reward function are precisely defined to expedite the search for an initial collision-free path.To enhance convergence speed,the Q-learning algorithm in RL is augmented with Dyna-Q.Additionally,we formulate the cylindrical bounding box of the manipulator based on its Denavit-Hartenberg(DH)parameters and propose a swift collision detection technique.Furthermore,the motion performance of the end-effector is refined through a bidirectional search,and joint weighting coefficients are introduced to mitigate motion in high-power joints.The efficacy of the proposed RPP methodology is rigorously examined through extensive simulations conducted on a six-degree-of-freedom(6-DOF)manipulator encountering two distinct obstacle configurations and target positions.Experimental results substantiate that the RPP method adeptly orchestrates the computation of the shortest collision-free path while adhering to specific posture constraints at the target point.Moreover,itminimizes both posture angle deviations and joint motion,showcasing its prowess in enhancing the operational performance of MDOF industrial manipulators.

Dialectical Thermodynamics’Solution to the Conceptual Imbroglio That Is the Reversible Path

According to the second law of thermodynamics, as currently understood, any given transit of a system along the reversible path proceeds with a total entropy change equal to zero. The fact that this condition is also the identifier of thermodynamic equilibrium, makes each and every point along the reversible path a state of equilibrium, and the reversible path, as expressed by a noted thermodynamic author, “a dense succession of equilibrium states”. The difficulties with these notions are plural. The fact, for example, that systems need to be forced out of equilibrium via the expenditure of work, would make any spontaneous reversible process a consumer of work, this in opposition to common thermodynamic wisdom that makes spontaneous reversible processes the most efficient transformers of work-producing-potential into actual work. The solution to this and other related impasses is provided by Dialectical Thermodynamics via its previously proved notion assigning a negative entropy change to the energy upgrading process represented by the transformation of heat into work. The said solution is here exemplified with the ideal-gas phase isomerization of butane into isobutane.

Adrenaline in pulp capping treatment of reversible pulpitis

BACKGROUND The role of epinephrine in the treatment of pulp capping in patients with reversible pulpitis is not clear.AIM To explore the role of epinephrine in the treatment of pulp capping in patients with reversible pulpitis.METHODS A total of 100 patients with reversible pulpitis who were treated in Anhui Jieshou People's Hospital from January 2020 to December 2021 were included in the study.They were categorized into an observation group(n=50;treatment with adrenaline)and a control group(n=50;treatment with zinc oxide eugenol paste).The 24-h postoperative pain,regression time of gingival congestion and redness,clinical efficacy,and incidence of adverse reactions were compared between the groups.Patients were further categorized into the ineffective and effective treatment groups based on clinical efficacy.Logistic multiple regression analysis explored factors affecting the efficacy of pulp capping treatment.RESULTS A significant difference in 24-h postoperative pain was observed between the groups(P<0.05),with a higher proportion of grade I pain noted in the observation group than in the control group(P<0.01).The regression time of gingival congestion and swelling was lower in the observation group(2.61±1.44 d and 2.73±1.36 d,respectively)than in the control group(3.85±1.47 d and 4.28±1.61 d,respectively)(P<0.05).The 2-wk postoperative total effective rate was lower in the control group(80.00%)than in the observation group(94.00%)(P<0.05).The incidence of adverse reactions was not significantly different between the control(14.00%)and observation(12.00%)groups(P>0.05).The proportion of adrenaline usage was lower(P<0.05)and that of anaerobic digestion by Streptococcus and Fusobacterium nucleatum was higher in the ineffective treatment group than in the effective treatment group(P<0.05).Logistic multiple regression analysis revealed adrenaline as a protective factor(P<0.05)and anaerobic digestion by Streptococcus and F.nucleatum as risk factors for pulp capping in reversible pulpitis(P<0.05).CONCLUSION Adrenaline demonstrated therapeutic efficacy in pulp capping treatment for reversible pulpitis,reducing pain and improving clinical symptoms safely.It is a protective factor for pulp capping,whereas Streptococcus and F.nucleatum are risk factors.Targeted measures can be implemented to improve clinical efficacy.

Improvement effect of reversible solid solutions Mg_(2)Ni(Cu)/Mg_(2)Ni(Cu)H_(4)on hydrogen storage performance of MgH_(2)

The hydrogen absorption/desorption kinetic properties of MgH_(2)can be effectively enhanced by doping specific catalysts.In this work,MOFs-derived NiCu@C nanoparticles(~15 nm)with regular core-shell structure were successfully prepared and introduced into MgH_(2)(denoted as MgH_(2)-NiCu@C).The onset and peak temperatures of hydrogen desorption of MgH_(2)-11 wt.%NiCu@C are 175.0℃and282.2℃,respectively.The apparent activation energy of dehydrogenated reaction is 77.2±4.5 kJ/mol for MgH_(2)-11 wt.%NiCu@C,which is lower than half of that of the as-milled MgH_(2).Moreover,MgH_(2)-11 wt.%NiCu@C displays great cyclic stability.The strengthening"hydrogen pumping"effect of reversible solid solutions Mg_(2)Ni(Cu)/Mg_(2)Ni(Cu)H_(4)is proposed to explain the remarkable improvement in hydrogen absorption/desorption kinetic properties of MgH_(2).This work offers a novel perspective for the design of bimetallic nanoparticles and beyond for application in hydrogen storage and other energy related fields.

Critical Solvation Structures Arrested Active Molecules for Reversible Zn Electrochemistry

Aqueous Zn-ion batteries(AZIBs)have attracted increasing attention in next-generation energy storage systems due to their high safety and economic.Unfortunately,the side reactions,dendrites and hydrogen evolution effects at the zinc anode interface in aqueous electrolytes seriously hinder the application of aqueous zinc-ion batteries.Here,we report a critical solvation strategy to achieve reversible zinc electrochemistry by introducing a small polar molecule acetonitrile to form a“catcher”to arrest active molecules(bound water molecules).The stable solvation structure of[Zn(H_(2)O)_(6)]^(2+)is capable of maintaining and completely inhibiting free water molecules.When[Zn(H_(2)O)_(6)]^(2+)is partially desolvated in the Helmholtz outer layer,the separated active molecules will be arrested by the“catcher”formed by the strong hydrogen bond N-H bond,ensuring the stable desolvation of Zn^(2+).The Zn||Zn symmetric battery can stably cycle for 2250 h at 1 mAh cm^(-2),Zn||V_(6)O_(13) full battery achieved a capacity retention rate of 99.2%after 10,000 cycles at 10 A g^(-1).This paper proposes a novel critical solvation strategy that paves the route for the construction of high-performance AZIBs.

Stresses in the Scapular Fossa Do Not Exceed the Yield Stress When Elevated up to 135 Degrees of Abduction after Reverse Shoulder Arthroplasty

Reverse shoulder arthroplasty (RSA) is an effective treatment for rotator cuff tears. Despite its advantages, complications occur at a high rate. Complications requiring revision include a high rate of base plate failure, 38% of which are due to instability. The primary stability the base plate ensures is a crucial factor and, thus, is the subject of much debate in clinical studies and biomechanical research. This study is aimed to provide data that will contribute to the base plate’s pri-mary stability and glenoid longevity by clarifying the stresses at the scapular fossa and base plate interface associated with elevation after RSA. A 3D finite element model was created from the DICOM data for the scapulohumeral joint and SMR shoulder system. For loading conditions, 30 N was applied for each posi-tion with abduction angles of 0, 45, 90, and 135 degrees. A three-dimensional fi-nite element analysis was performed using the static implicit method with LS-DYNA. The von Mises stresses in the scapular fossa were found not to exceed the yield stress on the bone even after elevation to an abduction angle of 135 de-grees after RSA. It is rough to uniformly compare the yield stress and the von Mises stress, but it was inferred that the possibility of fracture is low unless a large external force is applied. A maximum von Mises stress showed 0 degrees of abduction, suggesting that the lowered position is in a more severe condition than the elevated position. If better improvement is desired, it may be necessary to devise ways to reduce the stress on the upper screw. .

Rational Design of Ruddlesden-Popper Perovskite Ferrites as Air Electrode for Highly Active and Durable Reversible Protonic Ceramic Cells

Reversible protonic ceramic cells(RePCCs)hold promise for efficient energy storage,but their practicality is hindered by a lack of high-performance air electrode materials.Ruddlesden-Popper perovskite Sr_(3)Fe_(2)O_(7−δ)(SF)exhibits superior proton uptake and rapid ionic conduction,boosting activity.However,excessive proton uptake during RePCC operation degrades SF’s crystal structure,impacting durability.This study introduces a novel A/B-sites co-substitution strategy for modifying air electrodes,incorporating Sr-deficiency and Nb-substitution to create Sr_(2.8)Fe_(1.8)Nb_(0.2)O_(7−δ)(D-SFN).Nb stabilizes SF’s crystal,curbing excessive phase formation,and Sr-deficiency boosts oxygen vacancy concentration,optimizing oxygen transport.The D-SFN electrode demonstrates outstanding activity and durability,achieving a peak power density of 596 mW cm^(−2)in fuel cell mode and a current density of−1.19 A cm^(−2)in electrolysis mode at 1.3 V,650℃,with excellent cycling durability.This approach holds the potential for advancing robust and efficient air electrodes in RePCCs for renewable energy storage.

Honeymoon phase in type 1 diabetes mellitus: A window of opportunity for diabetes reversal?

The knowledge of the pathogenesis of type 1 diabetes mellitus(T1DM)continues to rapidly evolve.The natural course of the disease can be described in four clinical stages based on the autoimmune markers and glycemic status.Not all individuals of T1DM progress in that specific sequence.We hereby present a case of T1DM with a classical third phase(honeymoon phase)and discuss the intri-cacies of this interesting phase along with a possible future promise of“cure”with the use of immunotherapies.We now know that the course of T1DM may not be in only one direction towards further progression;rather the disease may have a waxing and waning course with even reversal of type 1 diabetes concept being discussed.The third phase popularly called the“honeymoon phase”,is of special interest as this phase is complex in its pathogenesis.The honeymoon phase of T1DM seems to provide the best window of opportunity for using targeted therapies using various immunomodulatory agents leading to the possibility of achieving the elusive“diabetes reversal”in T1DM.Identifying this phase is therefore the key,with a lot of varying criteria having been proposed.