Some new characterizations of a space curve due to a modified frame N⃗,C⃗,W⃗$\left\{ \overrightarrow {N},\; \overrightarrow {C},\; \overrightarrow {W}\right\}$ in Euclidean 3-space

In our paper, we computed some new characterizations due to an alternative modified frame N ⃗ , C ⃗ , W ⃗ $\left\{ \overrightarrow {N}, \overrightarrow {C}, \overrightarrow {W}\right\}$ in Euclidean 3-space and we get general differential equation characterizations of a space curve due to the vectors N ⃗ , C ⃗ , W ⃗ $ \overrightarrow {N}, \overrightarrow {C}, \overrightarrow {W}$ . Furthermore, we investigated some differential equations characterizations of the harmonic and harmonic 1-type curves.

Global existence of positive periodic solutions of a general differential equation with neutral type

In this paper, the dynamics of a general differential equation with neutral type are investigated. Under certain assumptions, the stability of positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of eigenvalues. And global existence of positive periodic solutions is established by using the global Hopf bifurcation result of Krawcewicz et al. Finally, by taking neutral Nicholson’s blowflies model and neutral Mackey–Glass model as two examples, some numerical simulations are carried out to illustrate the analytical results.

Novel Modeling of the Work-Hardening Curve

The paper aims at a critical analysis of the existent description of plastic strengthening/work-hardening curve. The adequate description of the curve, having a physical sense, has been proposed. The description begins from the very source which is the primary, general differential equation. That source was used to formulate the characteristics of the studied system. Then the analytical solution of the dependence between the yield stress and the relative deformation is provided. The description of the work-hardening curve has been developed to further form a proper dependence of the yield force on the absolute yield strain. Other functional characteristics, namely the coefficient of the plastic rigidity, yield work, and the plastic potentials, have also been formed.