On Products and Diagonals of Mappings in Generalized Topological Spaces

Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].

Missing Value Imputation for Radar-Derived Time-Series Tracks of Aerial Targets Based on Improved Self-Attention-Based Network

The frequent missing values in radar-derived time-series tracks of aerial targets(RTT-AT)lead to significant challenges in subsequent data-driven tasks.However,the majority of imputation research focuses on random missing(RM)that differs significantly from common missing patterns of RTT-AT.The method for solving the RM may experience performance degradation or failure when applied to RTT-AT imputation.Conventional autoregressive deep learning methods are prone to error accumulation and long-term dependency loss.In this paper,a non-autoregressive imputation model that addresses the issue of missing value imputation for two common missing patterns in RTT-AT is proposed.Our model consists of two probabilistic sparse diagonal masking self-attention(PSDMSA)units and a weight fusion unit.It learns missing values by combining the representations outputted by the two units,aiming to minimize the difference between the missing values and their actual values.The PSDMSA units effectively capture temporal dependencies and attribute correlations between time steps,improving imputation quality.The weight fusion unit automatically updates the weights of the output representations from the two units to obtain a more accurate final representation.The experimental results indicate that,despite varying missing rates in the two missing patterns,our model consistently outperforms other methods in imputation performance and exhibits a low frequency of deviations in estimates for specific missing entries.Compared to the state-of-the-art autoregressive deep learning imputation model Bidirectional Recurrent Imputation for Time Series(BRITS),our proposed model reduces mean absolute error(MAE)by 31%~50%.Additionally,the model attains a training speed that is 4 to 8 times faster when compared to both BRITS and a standard Transformer model when trained on the same dataset.Finally,the findings from the ablation experiments demonstrate that the PSDMSA,the weight fusion unit,cascade network design,and imputation loss enhance imputation performance and confirm the efficacy of our design.

A color image encryption scheme based on a 2D coupled chaotic system and diagonal scrambling algorithm

A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.

Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

Criteria Condition for Generalized Diagonally Dominant Matrices

In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.

The Distribution of Eigenvance of Product Diagonal Dominance Matrix

Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.

Diagonal街区的理念

介绍了Diagonal街区的理论 ,阐述了Diagonal属于主要大街的一部分 ,指出在Diagonal街区的建筑不仅服务于一个目标 ,而且包含着多样的城市功能和办公空间及住宅 ,组成一个完整的街区。

NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.

Quantization and Squeezed State of Two L-C Circuits with Mutual-Inductance

It is pointed out that the quantum mechanical Hamiltonian of two L-C circuits with mutual-inductance is equivalent to a pair of harmonic oscillators with a kinetic coupling term.We then diagonalize the Hamiltonian.It is shown that instantaneously switching on the external sources may result in a two-mode squeezed state of the system,which actually arises from the effect of mutual-inductance.The quantum fluctuation for the case of l_(1)c_(1)=l_(2)c_(2 ) is analysed and it is found that the current fluctuation in the circuits increases with the increment of the mutual-inductance.

Diagonally loaded SMI algorithm based on inverse matrix recursion

The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.

Stability of mine ventilation system based on multiple regression analysis

In order to overcome the disadvantages of diagonal connection structures that are complex and for which it is difficult to derive the discriminant of the airflow directions of airways, we have applied a multiple regression method to analyze the effect, of changing the rules of mine airflows, on the stability of a mine ventilation system. The amount of air （ Qj ） is determined for the major airway and an optimum regression equation was derived for Qi as a function of the independent variable （ Ri ）, i.e., the venti- lation resistance between different airways. Therefore, corresponding countermeasures are proposed according to the changes in airflows. The calculated results agree very well with our practical situation, indicating that multiple regression analysis is simple, quick and practical and is therefore an effective method to analyze the stability of mine ventilation systems.

GEAR CRACK EARLY DIAGNOSIS USING BISPECTRUM DIAGONAL SLICE

A study of bispectral analysis in gearbox condition monitoring is presented.The theory of bispectrum and quadratic phase coupling (QPC) is first introduced, and then equationsfor computing bispectrum slices are obtained. To meet the needs of online monitoring, a simplifiedmethod of computing bispectrum diagonal slice is adopted. Industrial gearbox vibration signalsmeasured from normal and tooth cracked conditions are analyzed using the above method. Experimentsresults indicate that bispectrum can effectively suppress the additive Gaussian noise andchracterize the QPC phenomenon. It is also shown that the 1-D bispectrum diagonal slice can capturethe non-Gaussian and nonlinear feature of gearbox vibration when crack occurred, hence, this methodcan be employed to gearbox real time monitoring and early diagnosis.

Recent developments on applications of sequential loop closing and diagonal dominance control schemes to industrial multivariable system

With a focus on an industrial multivariable system, two subsystems including the flow and the level outputs are analysed and controlled, which have applicability in both real and academic environments. In such a case, at first, each subsystem is distinctively represented by its model, since the outcomes point out that the chosen models have the same behavior as corresponding ones. Then, the industrial multivariable system and its presentation are achieved in line with the integration of these subsystems, since the interaction between them can not actually be ignored. To analyze the interaction presented, the Gershgorin bands need to be acquired, where the results are used to modify the system parameters to appropriate values. Subsequently, in the view of modeling results, the control concept in two different techniques including sequential loop closing control(SLCC) scheme and diagonal dominance control(DDC) schemes is proposed to implement on the system through the Profibus network, as long as the OPC(OLE for process control) server is utilized to communicate between the control schemes presented and the multivariable system. The real test scenarios are carried out and the corresponding outcomes in their present forms are acquired. In the same way, the proposed control schemes results are compared with each other, where the real consequences verify the validity of them in the field of the presented industrial multivariable system control.

Analysis of factors affecting diagonal tension and compression capacity of corner joints in furniture frames fabricated with dovetail key

This study was conducted to analyze the effect of joint type, and numbers and types of dovetail keys on diagonal tension and compression performance of corner joints in a furniture frame. Joint members were cut from white fir lumber. Butted and mitered joints were constructed with one and two dovetail key（s） with butterfly and H shapes. Joints were glued by polyvinyl acetate （PVAc） and cynoacrylate （CA）. Compression capacity of joints was higher than diagonal tension. Mitered joints were stronger than butted ones. Butterfly dovetail keys were superior to H shape keys. Double keys performed better than single key. Experimental joints glued with PVAc were stronger than those glued with CA glue and control specimens. In terms of strength, butterfly dovetailed joints were comparable with doweled joints.

Studyon hardware-in-the-loopsimulation of beer fermentation system

Beer fermentation process is a complex biochemical reaction process.It is the most important to control temperature of the wort in fermentation tank in accordance with the beer fermentation temperature curve so as to ensure the completion of fermentation.The controlled object is characterized by large inertia,long time delay and mutual coupling of three temperature areas.Based on this,a temperature control method for beer fermentation system is designed.Using digital incremental proportion integration differentiation （PID） control algorithm,the controlled quantity is transmitted to the controlled object after diagonal matrix decoupling.This simulation system can be completed in laboratory using VB and Kingview software,so it has the features of good security and low cost.It is very suitable for experimental teaching.

Adaptive diagonal loaded minimum variance beamforming applied to medical ultrasound imaging

In order to enhance the robustness and contrast in the minimum variance(MV) beamformer, adaptive diagonal loading method was proposed. The conventional diagonal loading technique has already been used in the MV beamformer, but has the drawback that its level is specified by predefined parameter and without consideration of input-data. To alleviate this problem, the level of diagonal loading was computed appropriately and automatically from the given data by shrinkage method in the proposed adaptive diagonal loaded beamformer. The performance of the proposed beamformer was tested on the simulated point target and cyst phantom was obtained using Field II. In the point target simulation, it is shown that the proposed method has higher lateral resolution than the conventional delay-and-sum beamformer and could be more robust in estimating the amplitude peak than the MV beamformer when acoustic velocity error exists. In the cyst phantom simulation, the proposed beamformer has shown that it achieves an improvement in contrast ratio and without distorting the edges of cyst.

Tracking multiple targets in MIMO radar via adaptive asymmetric joint diagonalization with deflation

In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.

The theoretical study on diagonal wave interaction with perforated-wall breakwater with rock fill

The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical method is presented to calculate the reflection coefficient and the wave force coefficient of the breakwater. The calculated results of the reflection coefficient for limiting cases are the same to the existing results. The main effect factors of the reflection coefficient and the wave force coefficient are analyzed by numerical examples. With the increasing of thickness of rock fill, the wave force coefficient on the perforated wall generally decreases, while the reflection coefficient increases. With the increasing of the incident angle of the wave, the reflection coefficient of the breakwater first decreases, reaches its minimum, and then increases monotonously.

Ship motion extreme short time prediction of ship pitch based on diagonal recurrent neural network

A DRNN (diagonal recurrent neural network) and its RPE (recurrent prediction error) learning algorithm are proposed in this paper .Using of the simple structure of DRNN can reduce the capacity of calculation. The principle of RPE learning algorithm is to adjust weights along the direction of Gauss-Newton. Meanwhile, it is unnecessary to calculate the second local derivative and the inverse matrixes, whose unbiasedness is proved. With application to the extremely short time prediction of large ship pitch, satisfactory results are obtained. Prediction effect of this algorithm is compared with that of auto-regression and periodical diagram method, and comparison results show that the proposed algorithm is feasible.

Identification of indoor multi-component pollution gas aliasing peak based on JADE

Monitoring indoor harmful gas can obtain the infrared spectra of mixed harmful gases.Since the absorption bands of mixed gases overlap and their qualitative and quantitative analyses are not easy,feature extraction method based on joint approximative diagonalization of eigenmatrix（JADE）is proposed.By fully mining the hidden information of original data and analyzing higher-order statistics information of the data,each substance spectrum in the mixed gas can be accurately distinguished.In addition,a multi-dimensional data quantitative analysis model of the extracted independent source is established by using support vector machine（SVM）based on regular theory.The experimental results show that the correlation coefficients of the components of mixed gases is above 0.999 1by quantitative analysis,which verifies the accuracy of this feature extraction method.