Invertibility of Infinite-Dimensional Hamiltonian Operators and Its Application to Plate Bending Equation

The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.

Motion-Blurred Image Restoration Based on Joint Invertibility of PSFs

To implement restoration in a single motion blurred image,the PSF(Point Spread Function)is difficult to estimate and the image deconvolution is ill-posed as a result that a good recovery effect cannot be obtained.Considering that several different PSFs can get joint invertibility to make restoration wellposed,we proposed a motion-blurred image restoration method based on joint invertibility of PSFs by means of computational photography.Firstly,we designed a set of observation device which composed by multiple cameras with the same parameters to shoot the moving target in the same field of view continuously to obtain the target images with the same background.The target images have the same brightness,but different exposure time and different motion blur length.It is easy to estimate the blur PSFs of the target images make use of the sequence frames obtained by one camera.According to the motion blur superposition feature of the target and its background,the complete blurred target images can be extracted from the observed images respectively.Finally,for the same target images with different PSFs,the iterative restoration is solved by joint solution of multiple images in spatial domain.The experiments showed that the moving target observation device designed by this method had lower requirements on hardware conditions,and the observed images are more convenient to use joint-PSF solution for image restoration,and the restoration results maintained details well and had lower signal noise ratio(SNR).

Strong Invertibility of Nonlinear Systems and Its Application

From the point of mathematical mapping, this paper discusses the invertibility of nonlinear systems, and presents definition, equivalence theorem, sufficient and necessary conditions of strong invertibility for single input single output systems. Then it analyzes the feasibility of inverse system control method, and yields some conclusions on feasibility.

On Invertibility of Functional Operators with Shift in Weighted Holder Spaces

In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.

Weak invertibility of linear finite automata (I)——Classification and enumeration of transfer functions

Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.

Linear Maps Preserving Invertibility or Related Spectral Properties

We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.

Constructing Finite Automata with Invertibility bytransformation Method

Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse andfor weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automatasatisfying one of these sufficient conditions were also given. This paper extends theconcepts, methods and results to general finite automata, in which states consist offinite input history, finite output history and finite 'inner state' history.

Additive Maps on Matrix Algebras Preserving Invertibility or Singularity

We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.

Weak invertibility of linear finite automata over rings——Classification and enumeration

The weak invertibility problem of finite automata (FAs) has received continuous considerations. The weak invertibility theory has applications in cryptography, both conventional cryptosystems and public key cryptosystems. Given a finite commutative ring (?) with identity, it is known, that the weak invertibility of a linear finite automaton(LFA) over (?) depends only on its transfer function matrix. Let H be the set of all possible transfer function matrices which weakly invertible LFAs over (?) can have. Our

Bijections Preserving Invertibility of Differences of Matrices on H_n

We characterise bijections on the space of hermitian matrices preserving the invertibility of differences of matrix pairs in both directions.

The stationarity and invertibility of a class of nonlinear ARMA models

We investigate some probabilistic properties of a new class of nonlinear time series models. A sufficient condition for the existence of a unique causal, strictly and weakly stationary solution is derived. To understand the proposed models better, we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants, which can also be used for identification purpose. A sufficient condition for invertibility is also provided.

The Invertibility of Rational Univariate Representations

In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is given.It is shown that the rational univariate representations,obtained by both Rouillier’s approach and Wu’s method,are invertible.Moreover,the ideal created by a given rational univariate representation is defined.Some results on invertible rational univariate representations and created ideals are established.Based on these results,a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.

Drazin Invertibility of Operators AB and BA

In this note an alternative proof of the equivalence of Drazin invertibility of operators AB and BA is given. As an application, we will prove that σD(AB) = σD(BA) and σD(A) = σD(A), where σD(M) and ■ denote the Drazin spectrum and the Aluthge transform of an operator M ∈ B(H), respectively.

Grid-Connected/Islanded Switching Control Strategy for Photovoltaic Storage Hybrid Inverters Based on Modified Chimpanzee Optimization Algorithm

Uneven power distribution,transient voltage,and frequency deviations are observed in the photovoltaic storage hybrid inverter during the switching between grid-connected and island modes.In response to these issues,this paper proposes a grid-connected/island switching control strategy for photovoltaic storage hybrid inverters based on the modified chimpanzee optimization algorithm.The proposed strategy incorporates coupling compensation and power differentiation elements based on the traditional droop control.Then,it combines the angular frequency and voltage amplitude adjustments provided by the phase-locked loop-free pre-synchronization control strategy.Precise pre-synchronization is achieved by regulating the virtual current to zero and aligning the photovoltaic storage hybrid inverter with the grid voltage.Additionally,two novel operators,learning and emotional behaviors are introduced to enhance the optimization precision of the chimpanzee algorithm.These operators ensure high-precision and high-reliability optimization of the droop control parameters for photovoltaic storage hybrid inverters.A Simulink model was constructed for simulation analysis,which validated the optimized control strategy’s ability to evenly distribute power under load transients.This strategy effectively mitigated transient voltage and current surges during mode transitions.Consequently,seamless and efficient switching between gridconnected and island modes was achieved for the photovoltaic storage hybrid inverter.The enhanced energy utilization efficiency,in turn,offers robust technical support for grid stability.

A necessary condition on invertibility of finite automata

This paper gives a necessary condition for a kind of weakly invertible, invertible, weak inverse or inverse finite automata by linear RaRb transformation sequence. For such finite automata the existence of terminating RaRb transformation sequence is also established.

Invertibility of Bergman Toeplitz operators with harmonic polynomial symbols

Let p be an analytic polynomial on the unit disk.We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when all coefficients of p are real numbers.Furthermore,we establish several necessary and sufficient,easy-to-check conditions for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when some coefficients of p are complex numbers.

Permanent Magnet Temperature Estimation for PMSMs Using Virtual Position-offset Injection

This paper proposes a virtual position-offset injection based permanent magnet temperature estimation approach for permanent magnet synchronous machines(PMSMs). The concept of virtual position-offset injection is mathematically transforming the machine model to a virtual frame with a position-offset. The virtual frame temperature estimation model is derived to calculate the permanent magnet temperature(PMT) directly from the measurements with computation efficiency. The estimation model involves a combined inductance term, which can simplify the establishment of saturation compensation model with less measurements. Moreover, resistance and inverter distorted terms are cancelled in the estimation model, which can improve the robustness to the winding temperature rise and inverter distortion. The proposed approach can achieve simplified computation in temperature estimation and reduced memory usage in saturation compensation. While existing model-based approaches could be affected by either the need of resistance and inverter information or complex saturation compensation. Experiments are conducted on the test machine to verify the proposed approach under various operating conditions.

Comparative analyses of mitogenomes in the social bees with insights into evolution of long inverted repeats in the Meliponini

The insect mitogenome is typically a compact circular molecule with highly conserved gene contents.Nonetheless,mitogenome structural variations have been reported in specific taxa,and gene rearrangements,usually the tRNAs,occur in different lineages.Because synapomorphies of mitogenome organizations can provide information for phylogenetic inferences,comparative analyses of mitogenomes have been given increasing attention.However,most studies use a very few species to represent the whole genus,tribe,family,or even order,overlooking potential variations at lower taxonomic levels,which might lead to some incorrect inferences.To provide new insights into mitogenome organizations and their implications for phylogenetic inference,this study conducted comparative analyses for mitogenomes of three social bee tribes(Meliponini,Bombini,and Apini)based on the phylogenetic framework with denser taxonomic sampling at the species and population levels.Comparative analyses revealed that mitogenomes of Apini and Bombini are the typical type,while those of Meliponini show diverse variations in mitogenome sizes and organizations.Large inverted repeats(IRs)cause significant gene rearrangements of protein coding genes(PCGs)and rRNAs in Indo-Malay/Australian stingless bee species.Molecular evolution analyses showed that the lineage with IRs have lower dN/dS ratios for PCGs than lineages without IRs,indicating potential effects of IRs on the evolution of mitochondrial genes.The finding of IRs and different patterns of gene rearrangements suggested that Meliponini is a hotspot in mitogenome evolution.Unlike conserved PCGs and rRNAs whose rearrangements were found only in the mentioned lineages within Meliponini,tRNA rearrangements are common across all three tribes of social bees,and are significant even at the species level,indicating that comprehensive sampling is needed to fully understand the patterns of tRNA rearrangements,and their implications for phylogenetic inference.

Coordinated Capacitor Voltage Balancing Method for Cascaded H-bridge Inverter with Supercapacitor and DC-DC Stage

Cascaded H-bridge inverter(CHBI) with supercapacitors(SCs) and dc-dc stage shows significant promise for medium to high voltage energy storage applications. This paper investigates the voltage balance of capacitors within the CHBI, including both the dc-link capacitors and SCs. Balance control over the dc-link capacitor voltages is realized by the dcdc stage in each submodule(SM), while a hybrid modulation strategy(HMS) is implemented in the H-bridge to balance the SC voltages among the SMs. Meanwhile, the dc-link voltage fluctuations are analyzed under the HMS. A virtual voltage variable is introduced to coordinate the balancing of dc-link capacitor voltages and SC voltages. Compared to the balancing method that solely considers the SC voltages, the presented method reduces the dc-link voltage fluctuations without affecting the voltage balance of SCs. Finally, both simulation and experimental results verify the effectiveness of the presented method.

Analysis of Progressively Type-Ⅱ Inverted Generalized Gamma Censored Data and Its Engineering Application

A novel inverted generalized gamma(IGG)distribution,proposed for data modelling with an upside-down bathtub hazard rate,is considered.In many real-world practical situations,when a researcher wants to conduct a comparative study of the life testing of items based on cost and duration of testing,censoring strategies are frequently used.From this point of view,in the presence of censored data compiled from the most well-known progressively Type-Ⅱ censoring technique,this study examines different parameters of the IGG distribution.From a classical point of view,the likelihood and product of spacing estimation methods are considered.Observed Fisher information and the deltamethod are used to obtain the approximate confidence intervals for any unknown parametric function of the suggestedmodel.In the Bayesian paradigm,the same traditional inferential approaches are used to estimate all unknown subjects.Markov-Chain with Monte-Carlo steps are considered to approximate all Bayes’findings.Extensive numerical comparisons are presented to examine the performance of the proposed methodologies using various criteria of accuracy.Further,using several optimality criteria,the optimumprogressive censoring design is suggested.To highlight how the proposed estimators can be used in practice and to verify the flexibility of the proposed model,we analyze the failure times of twenty mechanical components of a diesel engine.