WEYL TRANSFORMATIONS ON MANIFOLDS Ⅱ. Generalized Trace and Inverse Mapping Formula

The two gate formula for a diffusion X_t in R^n is considered.The formula gives an expressionof the density function of X_t in terms of the path integral of the Brownian bridge starting from xand ending on y at time t.

COHERENT STATES, INVERSE MAPPING FORMULA FOR WEYL TRANSFORMATIONS AND APPLICATION TO EQUATIONS OF KdV TYPE

In this paper, we consider the trace of generalized operators and inverse Weyl transformation.First of all we repeat the definition of test operators and generalized operators given in [18],denoting L~2(R) by H.

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.

Use of Local Region Maps on Convolutional LSTM for Single-Image HDR Reconstruction

Low dynamic range(LDR)images captured by consumer cameras have a limited luminance range.As the conventional method for generating high dynamic range(HDR)images involves merging multiple-exposure LDR images of the same scene(assuming a stationary scene),we introduce a learning-based model for single-image HDR reconstruction.An input LDR image is sequentially segmented into the local region maps based on the cumulative histogram of the input brightness distribution.Using the local region maps,SParam-Net estimates the parameters of an inverse tone mapping function to generate a pseudo-HDR image.We process the segmented region maps as the input sequences on long short-term memory.Finally,a fast super-resolution convolutional neural network is used for HDR image reconstruction.The proposed method was trained and tested on datasets including HDR-Real,LDR-HDR-pair,and HDR-Eye.The experimental results revealed that HDR images can be generated more reliably than using contemporary end-to-end approaches.

Neural Network Inversion for Multilayer Quaternion Neural Networks

Recently, solutions to inverse problems have been required in various engineering fields. The neural network inversion method has been studied as one of the neural network-based solutions. On the other hand, the extension of the neural network to a higher-dimensional domain, e.g., complex-value or quaternion, has been proposed, and a number of higher-dimensional neural network models have been proposed. Using the quatemion, we have the advantage of expressing 3D （three-dimensional） object attitudes easily. In the quaternion domain, we can define inverse problems where the cause and the result are expressed by the quaternion. In this paper, we extend the neural network inversion method to the quatemion domain. Further, we provide the results of the computer experiments to demonstrate the process and effectiveness of our method.

Robust lane recognition for structured road based on monocular vision

A robust lane detection and tracking system based on monocular vision is presented in this paper. First, the lane detection algorithm can transform raw images into top view images by inverse perspective mapping （ IPM）, and detect both inner sides of the lane accurately from the top view im- ages. Then the system will turn to lane tracking procedures to extract the lane according to the infor- mation of last frame. If it fails to track the lane, lane detection will be triggered again until the true lane is found. In this system, 0-oriented Hough transform is applied to extract candidate lane mark- ers, and a geometrical analysis of the lane candidates is proposed to remove the outliers. Additional- ly, vanishing point and region of interest（ROI） dynamically planning are used to enhance the accura- cy and efficiency. The system was tested under various road conditions, and the result turned out to be robust and reliable.

Hybrid projection method for generalized mixed equilibrium problems,variational inequality problems,and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.

THE FUZZY NUMERICAL VALUE SIMULATION OF NANOMETER ELECTRO-THERMAL IN HOT-WORKING

The fuzzy numerical value analysis method is adopted for the first time, which solves the problem of nanometer electro-thermal in filming process, The key technique is embodied by controlling the time distribution, temperature and press in the filming process. The concrete technique of filming is showed by establishing the fuzzy mumbership function of above three indexes, which improves the precision of the materials of nanometer electro-thermal in hot-working. At the same time, the principles of the fuzzy relationship mapping inversion （FRMI） is put forward, Therefore, the standardization and continuity can be met.

The Factor Decomposition Theorem of Bounded Generalized Inverse Modules and Their Topological Continuity

In this paper we obtain a Douglas type factor decomposition theorem about certain important bounded module maps. Thus, we come to the discussion of the topological continuity of bounded generalized inverse module maps. Let X be a topological space, x →Tx ： X→L（E） be a continuous map, and each R（Tx） be a closed submodule in E, for every fixed x C X. Then the map x→ Tx^＋： X→L（E） is continuous if and only if ｜｜Tx^＋｜｜ is locally bounded, where Tx^＋ is the bounded generalized inverse module map of Tx. Furthermore, this is equivalent to the following statement： For each x0 in X, there exists a neighborhood ∪0 at x0 and a positive number λ such that （0, λ^2）lohtatn in ∩x∈∪0C／σ（Tx^＋Tx）, where a（T） denotes the spectrum of operator T.

Reconstruction of convection coefficients of an elliptic equation in the plane by Dirichlet to Neumann map

The inverse problem of determining two convection coefficients of an elliptic partial differential equation by Dirichlet to Neumann map is discussed.It is well known that this is a severely ill-posed problem with high nonlinearity.By the inverse scattering technique for first order elliptic system in the plane and the theory of generalized analytic functions,we give a constructive method for this inverse problem.

A new grid deformation technology with high quality and robustness based on quaternion

Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation＇＇ is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation（TFI） technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation＇＇ improves the efficiency and quality of the basic quaternion deformation method significantly.