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By using first-order approximations of the feasible set corresponding constraint qualifications are developed.

Degradation rate constants and half-life times were calculated from fifth-generation batches by using first-order kinetics.

The global tumor heterogeneity may be described by using first order histogram-based features; the second-order GLCM-features that quantify local heterogeneity at the scale of a voxel; the features derived from high-order which quantify regional heterogeneity based on the neighborhood, the respective sizes and intensities of groups of voxels (Sollini et al. 2017).

Based on these eigenderivatives, and by using first and second order Taylor expansions, an approximate method is presented for simultaneous modification of natural frequencies and buckling loads.

This paper examines the potential of relevance vector machine (RVM) for slope reliability by using first order second moment method (FOSM).

With well established equations of motion taken as a starting point, the real and imaginary parts of the natural frequencies are calculated by using first and second order perturbation theory.

This system is studied first by using an "exact" time domain method and then by using first order harmonic balance.

The required probability values are evaluated by using first order reliability method.

The second monocular static cue for depth structure, texture, has been investigated predominantly by using first order gradients of texture.

The classification using first-order features and second-order features are explained here.

The governing partial differential equations (PDEs) are solved by using first- and second-order numerical methods.

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