On the Group of Units for the Ring of Linear Transformations

In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of the result in [3].

ON THE DECOMPOSITION OF COMPLEX VECTOR SPACES AND THE JORDAN CANONICAL FORM OF COMPLEX LINEAR TRANSFORMATIONS

New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.

From Translation to Linear and Linear Canonical Transformations

In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called dual couple in this work, is valuable for any other dual couple, so that from the known translation operator exp(a∂x) one may obtain the explicit form and properties of a category of linear and linear canonical transformations in 2N-phase spaces. Moreover, other forms of LCTs are also obtained in this work as so as the transforms by them of functions by integrations as so as by derivations. In this way, different kinds of LCTs such as Fast Fourier, Fourier, Laplace, Xin Ma and Rhodes, Baker-Campbell-Haussdorf, Bargman transforms are found again.

Linearization of Emden Differential Equation via the Generalized Sundman Transformations

The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.

Classical and Quantum Behavior of Generalized Oscillators in Terms of Linear Canonical Transformations

The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.

IMPLEMENTATION OF THE HYBRID GMRES ALGORITHM USING HOUSEHOLDER TRANSFORMATIONS

The standard implementation of the hybrid GMRES algorithm for solving large nonsymmetric linear systems involves a Gram-Schmidt process which is a potential source of significant numerical error. An alternative implementation is outlined here in which orthogonalization by Householder transformations replaces the Gram-Schmidt process. Numerical experiments show that the new implementation is more stable.

A Multi-Gap Multi-Channel Gas Switch for the Linear Transformer Driver

A multi-gap and multi-channel gas switch with convexo-convex discal planet electrodes was designed and investigated. Eight gaps are formed in series by a trigger electrode, six intermediate electrodes and two high voltage electrodes with a uniform gap length of 5 ram. The self breakdown and triggered breakdown performance of the switch are reported. Both the delay time and jitter decrease with the increase in the trigger voltage, switching coefficient and the decrease in the trigger isolating resistor. The delay time of the switch is about 40 ns, and the jitter is less than 2 ns when charged with 4-85 kV and triggered by a voltage pule of -75 kV. The inductance of the switch is about 30 nH.

Numerical Analysis of the Output-Pulse Shaping Capability of Linear Transformer Drivers

Output-pulse shaping capability of a linear transformer driver （LTD） module under different conditions is studied, by conducting the whole circuit model simulation by using the PSPICE code. Results indicate that a higher impedance profile of the internal transmission line would lead to a wider adjustment range for the output current rise time and a narrower adjustment range for the current peak. The number of cavities in series has a positive effect on the output- pulse shaping capability of LTD. Such an improvement in the output-pulse shaping capability can primarily be ascribed to the increment in the axial electric length of LTD. For a triggering time interval longer than the time taken by a pulse to propagate through the length of one cavity, the output parameters of LTD could be improved significantly. The present insulating capability of gas switches and other elements in the LTD cavities may only tolerate a slightly longer deviation in the triggering time interval. It is feasible for the LTD module to reduce the output current rise time, though it is not useful to improve the peak power effectively.

Influences of Switching Jitter on the Operational Performances of Linear Transformer Drivers-Based Drivers

A whole circuit model of a linear transformer drivers （LTD） module composed of 60 cavities in series was developed in the software PSPICE to study the influence of switching jitter on the operational performances of LTDs. In the model, each brick in each cavity is capable of operating with jitter in its switch. Additionally, the manner of triggering cables entering into cavities was considered. The performances of the LTD module operating with three typical cavity-triggering sequences were simulated and the simulation results indicate that switching jitter affects slightly the peak and starting time of the output current pulse. However, the enhancement in switching jitter would significantly lengthen the rise time of the output current pulse. Without considering other factors, a jitter lower than 10 ns may be necessary for the switches in the LTD module to provide output current parameters with an acceptable deviation.

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

Linear Complementary Method for Moving Boundary Problems with Phase Transformation

In this paper, the linear complementary method for moving boundary problems with phase transformation is presented, in which a pair of unknown vectors of heat source with phase transforming and the temperature field can be solved exactly, and a large amount of iterative calculations can be avoided.

Optical Diagnostics of Multi-Gap Gas Switches for Linear Transformer Drivers

The trigger characteristics of a multi-gap gas switch with double insulating layers,a square-groove electrode supporter and a UV pre-ionizing structure are investigated aided by a high sensitivity fiber-bundle array detector, a UV fiber detector, and a framing camera, in addition to standard electrical diagnostics. The fiber-bundle-array detector is used to track the turn-on sequence of each electrode gap at a timing precision of 0.6 ns. Each fiber bundle, including five fibers with different azimuth angles, aims at the whole emitting area of each electrode gap and is fed to a photomultiplier tube. The UV fiber detector with a spectrum response of 260-320 nm,including a fused-quartz fiber of 200 μm in diameter and a solar-blinded photomultiplier tube, is adopted to study the effect of UV pre-ionizing on trigger characteristics. The framing camera,with a capacity of 4 frames per shot and an exposure time of 5 ns, is employed to capture the evolution of channel arcs. Based on the turn-on light signal of each electrode gap, the breakdown delay is divided into statistical delay and formative delay. A decrease in both of them, a smaller switch jitter and more channel arcs are observed with lower gas pressure. An increase in trigger voltage can reduce the statistical delay and its jitter, while higher trigger voltage has a relatively small influence on the formative delay and the number of channel arcs. With the UV pre-ionizing structure at 0.24 MPa gas pressure and 60 kV trigger voltage, the statistical delay and its jitter can be reduced by 1.8 ns and 0.67 ns, while the formative delay and its jitter can only be reduced by 0.5 ns and 0.25 ns.

Uncertainty Principle for the Quaternion Linear Canonical Transform in Terms of Covariance

An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.

基于高效Transformer的图像去雾研究

随着Transformer技术发展使其在计算机视觉(CV)领域中大放异彩,其构建全局依赖关系能力是卷积神经网络(CNN)所不具备的,而Transformer对图像尺寸变化敏感与处理图像位置信息方面却不如CNN,因此,近几年基于Transformer与CNN的网络结构在CV领域是研究热点。图像去雾技术可用于车载避让系统、遥感系统以及物联网设备被设为公共领域的热点问题,因此,本文提出基于Transformer的网络结构实现图像去雾。结合Transformer与UNet构建网络框架,针对Self-Attention因二次判别导致高计算复杂度的问题,我们使用聚焦线性注意力替换Softmax函数,将二次计算复杂度降为O(n),并且为了解决使用线性注意力引起性能下降的问题,使用恢复模块增加输出特征的多样性,实现性能的恢复。经实验表明,与现有的去雾霾网络相比,文章提出的方法在公开数据集RESIDE上获得了更好的实验结果以及更愉悦的去雾效果。

Some New Applications of Elzaki Transform for Solution of Linear Volterra Type Integral Equations

Volterra type integral equations have diverse applications in scientific and other fields. Modelling physical phenomena by employing integral equations is not a new concept. Similarly, extensive research is underway to find accurate and efficient solution methods for integral equations. Some of noteworthy methods include Adomian Decomposition Method (ADM), Variational Iteration Method (VIM), Method of Successive Approximation (MSA), Galerkin method, Laplace transform method, etc. This research is focused on demonstrating Elzaki transform application for solution of linear Volterra integral equations which include convolution type equations as well as one system of equations. The selected problems are available in literature and have been solved using various analytical, semi-analytical and numerical techniques. Results obtained after application of Elzaki transform have been compared with solutions obtained through other prominent semi-analytic methods i.e. ADM and MSA (limited to first four iterations). The results substantiate that Elzaki transform method is not only a compatible alternate approach to other analytic methods like Laplace transform method but also simple in application once compared with methods ADM and MSA.

THE BLUE AND MINQUE IN GAUSS-MARKOFF MODEL WITH LINEAR TRANSFORMATION OF THE OBSERVABLE VARIABLES

For a singular linear model A = （y, Xβ, σ2 V） and its transformed model MF = （Fy, FXβ, σ 2FVF＇）, where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala （1981） are strengthened and consequences in Puntanen and Nurhonen （1992）, and Puntanen （1996） are extended.

Predicting Nonlinear Wave Trough Distributions Utilizing A Transformed Linear Simulation Method

This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a secondorder nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.

基于Transformer-LSTM网络的轴承寿命预测

轴承是旋转机械设备中的重要部件,由于工况、材质、加工方式等原因,轴承寿命时长相差许多。传统的并行或串行神经网络预测方式,对数据集有一定要求。因此,需要一种能够适用于不同数据长短的轴承剩余使用寿命预测网络。为此提出了一种能够预测不同寿命时长的Transformer-LSTM串并行神经网络预测模型。通过将Transformer解码层进行重构,并与长短期记忆时序神经网络(long short-term memory,LSTM)网络结构融合,实现轴承寿命数据的串并行预测处理。试验结果表明Transformer-LSTM神经网络能够精准预测长、中、短不同寿命时长的轴承失效时间,具有较强的模型泛化能力,提升轴承寿命预测精度与模型的泛化能力。

NOVEL LINEAR TRANSFORMATION SWITCHED-CAPACITOR FILTER DESIGN

This paper presents a novel method that is applied to realize the Linear Transformation(LT)Switched-Capacitor Filter(SCF).It adopts the Voltage Control Voltage Source(VCVS)equalized transfor-mation to revise the original LC ladder filter and induce it into 16 basic sections and then extend the princi-ple of the LT in order to fit active and 3 port networks and give out switched-capacitor circuits corre-sponding to the 16 basic sections,which can realize all four kinds of filters——LP,HP,BP,BS filters.De-signed examples are given here.An Nth order filter only requires N amplifiers and the circuit is insensitive toparasitic capacitances.The experimental results of a 3rd order elliptic LP and a 6th order elliptic BP are giv-en and agree with the theory.

A DECOMPOSITION DEPENDED ON DIRECTIONS FOR NONSINGULAR LINEAR TRANSFORMATION

In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.