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Within the framework of three-dimensional (3D) nonlocal elasticity theory, the authors develop an asymptotic theory to investigate the free vibration characteristics of simply supported, single-walled carbon nanotubes (SWCNTs) non-embedded or embedded in an elastic medium using the multiple time scale method. Eringen’s nonlocal constitutive relations are adopted to account for the small length scale effect in the formulation. The interactions between the SWCNT and its surrounding medium are modeled as a two-parameter Pasternak foundation model. After performing a series of mathematical processes, including nondimensionalization, asymptotic expansion, and successive integration, etc., the authors obtain recurrent sets of motion equations for various order problems. The nonlocal classical shell theory (CST) is derived as a first-order approximation of the current 3D nonlocal elasticity problem, and the equations of motion for higher-order problems retain the same differential operators as those of the nonlocal CST, although with different nonhomogeneous terms. The current asymptotic solutions for the natural frequency parameters of non-embedded or embedded SWCNTs and their corresponding through-thickness modal stress and displacement component distributions are obtained to assess the accuracy of various nonlocal shell and beam theories available in the literature.

In conjunction with the Reissner's mixed variational theorem and nonlocal Timoshenko beam theory, we develop a finite element method for the geometrically nonlinear bending analysis of a mu...

An innovative efficient and fast neural networks in which hidden neurons are constructed based on Fourier series expansions (FSNN), half-range cosine (FCSNN) and sine expansions (FSSNN) are proposed and tested for linear and nonlinear regulation problems. The results of numerical examples using FSNN are compared with those obtained from traditional linear regression (LP), nonlinear regression (NLP), backward propagation neural networks (BPANN) and radial basis function neural networks (RBFNN). The results obtained from FSNN agree well with those obtained from LP, NLP, BPANN and RBFNN and show global approximation features to the fitting data. Only a few hidden neurons are required to obtain very good and fast convergence of regression as compared with BPANN and RBFNN.

This paper presents classification of linearly separable and non-separable problems using neural networks in which hidden neurons are constructed based on double Fourier series expansions (FSNN). The results of numerical examples including classification problems of logical AND, logical XOR, cows and wolves, as well as 3-category problem such as IRIS classification. All the FSNN results are compared with those obtained from backward propagation neural networks (BPANN) and radial basis function neural networks (RBFNN). Root mean squared errors (RMSE) of the algorithms during the training process are also compared. The classification results obtained from FSNN agree well with those obtained from BPANN and RBFNN. Only a few hidden neurons in FSNNs are required for very good and fast convergence of training as compared with BPANN and RBFNN.

Epithelial ovarian cancer (EOC) is the seventh most common cancer among women worldwide. The 5-year survival rate for women with EOC is only 30%-50%, which is largely due to the typically late diagnosis of this condition. EOC is difficult to detect in its early stage because of its asymptomatic nature. Recently, near-infrared fluorescent (NIRF) imaging has been developed as a potential tool for detecting EOC at the molecular level. In this study, a NIRF-sensitive probe was designed to detect matrix metalloproteinase (MMP) activity in ovarian cancer cells. A cyanine fluorochrome was conjugated to the amino terminus of a peptide substrate with enzymatic specificity for MMP-3. To analyze the novel MMP-3 probe, an in vivo EOC model was established by subcutaneously implanting SKOV3 cells, a serous-type EOC cell line, in mice. This novel MMP-3-sensitive probe specifically reacted with only the active MMP-3 enzyme, resulting in a significantly enhanced NIRF emission intensity. Histological analysis demonstrated that MMP-3 expression and activity were enhanced in the stromal cells surrounding the ovarian cancer cells. These studies establish a molecular imaging reporter for diagnosing early-stage EOC. Additional studies are required to confirm the early-stage activity of MMP-3 in EOC and its diagnostic and prognostic significance.

On the basis of Reissner’s mixed variational theorem (RMVT), rather than the principle of virtual displacement (PVD), the authors presented a nonlocal Timoshenko beam theory (TBT) for the g...

This paper presents a three-dimensional finite deformation theory for the geometric nonlinear analysis of both the curved and twisted beams using the meshfree method based on the Timoshenko beam hypothesis. The theory presented is simple, but it is capable of solving the stability, postbuckling, snap-through, and large deformation problems effectively. Clear physical meanings will be revealed in derivation of the three-dimensional finite deformation theory. A meshfree method based on the differential reproducing kernel (DRK) approximation collocation method combined with the Newton–Raphson method is employed to solve the strong forms of the geometrically nonlinear problems. Numerical examples are given to illustrate the validity of the method presented.