Multiple attribute decision-making method based on projection model for dual hesitant fuzzy set

Fuzzy Optimization and Decision Making - In the decision-making process, retaining the original data information has become a most crucial step. Dual hesitant fuzzy sets (DHFS), which can reflect...     

Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formed by $b$ and $T_θ$ are established. Also we study related problems about two-weight, weak type inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give some results.     

Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.     

On Bahadur asymptotic efficiency in a semiparametric regression model

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Scanning tomographic acoustic microscopy

The scanning tomographic acoustic microscope (STAM) was proposed in 1982 as a method of improving the resolution capability of the scanning laser acoustic microscope (SLAM) based on the principles of tomography. By modifying the SLAM with a quadrature detector, tomographic projections that contain both the amplitude and phase information of the scattered wavefield can be acquired. Subsequently, multiple projections acquired with different incident waves are combined using the "back-and-forth" propagation algorithm to form the tomographic reconstruction. The first STAM reconstructions have been obtained to experimentally demonstrate the superior resolution capability of the STAM over the SLAM. In this paper, the implementation of the STAM is described, and experimental reconstructions of multiple-layer specimens are demonstrated.     

Artificial convolution neural network techniques and applications for lung nodule detection

We have developed a double-matching method and an artificial visual neural network technique for lung nodule detection. This neural network technique is generally applicable to the recognition of medical image pattern in gray scale imaging. The structure of the artificial neural net is a simplified network structure of human vision. The fundamental operation of the artificial neural network is local two-dimensional convolution rather than full connection with weighted multiplication. Weighting coefficients of the convolution kernels are formed by the neural network through backpropagated training. In addition, we modeled radiologists' reading procedures in order to instruct the artificial neural network to recognize the image patterns predefined and those of interest to experts in radiology. We have tested this method for lung nodule detection. The performance studies have shown the potential use of this technique in a clinical setting. This program first performed an initial nodule search with high sensitivity in detecting round objects using a sphere template double-matching technique. The artificial convolution neural network acted as a final classifier to determine whether the suspected image block contains a lung nodule. The total processing time for the automatic detection of lung nodules using both prescan and convolution neural network evaluation was about 15 seconds in a DEC Alpha workstation.     

Fractal drums and then-dimensional modified Weyl-Berry conjecture

In this paper, we study the spectrum of the Dirichlet Laplacian in a bounded (or, more generally, of finite volume) open set R ⁿ (n1) with fractal boundary of interior Minkowski dimension (n–1,n]. By means of the technique of tessellation of domains, we give the exact second term of the asymptotic expansion of the counting functionN() (i.e. the number of positive eigenvalues less than ) as +, which is of the form ^/2 times a negative, bounded and left-continuous function of . This explains the reason why the modified Weyl-Berry conjecture does not hold generally forn2. In addition, we also obtain explicit upper and lower bounds on the second term ofN().     

Level surfaces of non-degenerate functions inR n+1

We study level surfaces of non-degenerate functions inR ⁿ⁺¹. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field for level surfaces of a non-degenerate function and give certain characterizations of when is transversal, by the shape operatorS, the transversal connection , and consider the difference between and the affine normal.     

An identification of the connections of Quillen and Beilinson-Schechtman

Given a family of Riemann surfaces and a holomorphic vector bundle Beilinson and Schechtman construct a canonical connection on the associated determinant bundle. We prove the conjecture which states that their connection coincides with the Quillen connection. This is done by reducing to the case where along fibers are invertible. Both connection forms become more accessible in this case.Supported in part by N.S.F. Grant No. DMS-9201022Supported in part by National Science Council of Republic of China Grant No. NSC 82-0208-M-002-125-T, and NSERC of Canada Grant No. OGP 0121883