This study presents necessary conditions for the existence and sufficient conditions for the stability or instability of the static meniscus (liquid bridge) appearing in the cylindrical bar single crystal growth from the melt, of predetermined sizes, by using the dewetted Bridgman growth method. The cases when the wetting angle \(\theta_c\) and the growth angle \(\alpha_e\) verify the inequality \(\theta_c + \alpha_e < \pi\) or \(\theta_c + \alpha_e > \pi\) are treated separately. Experimentally, only static meniscus (liquid bridge) which verifies the necessary condition of existence and the sufficient conditions of stability can be created; static meniscus (liquid bridge) which does not verify both of these conditions, can exist only in computation because in reality they collapse during experimental creation. The results of this study is significant for the cylindrical bar single crystal growth from the melt, of predetermined sizes, by using the dewetted Bridgman growth method, using prior given specific equipment. That is because the obtained inequalities represent limits for what can and cannot be achieved experimentally. Numerical illustrations are given for GaSb lasser cylindrical bar, and InSb lasser cylindrical bar cylindrical bar.

Decline Curve Analysis (DCA) using an exponential decline model was applied to forecast long-term production performance and estimate the remaining recoverable volume of Well 15/9-F-12 in the Volve Field. Historical production data exhibiting stable decline behavior were used to generate a production forecast for the period from 1 November 2014 to 1 June 2018. The results indicate a continuous decline in oil production rate from 128.896 STB/day at the beginning of the forecast to 9.834 STB/day at the end of the simulation, while cumulative oil production increases asymptotically from 0.406709 MMSTB to 0.467232 MMSTB, reflecting late-life reservoir behavior under boundary-dominated flow conditions. At the reference date, the remaining recoverable volume is estimated at 0.060523 MMSTB. Although producible oil remains, the pronounced decline in production rate progressively constrains economic viability, indicating that well abandonment is primarily governed by economic limits rather than complete reservoir depletion. Overall, the results demonstrate that exponential DCA provides a reliable and physically consistent basis for assessing remaining production potential and supporting late-life reservoir management decisions.

This study presents sufficient conditions for the stability or instability of the static liquid bridge appearing in crystal growth from the melt of micro-fibers, thin plates, and hollow micro-tubes of predetermined sizes using the pulling-down method. The case in which the contact angle and the growth angle verify the inequality ${\alpha }_c>\pi /2-{\alpha }_g$ is considered. Experimentally, only stable static liquid bridges can be created; unstable static liquid bridges exist just in theory, because in reality they collapse. The results of this study are significant for shaped crystal growth from melted materials, with given macroscopic dimensions, and using specific equipment. This is because the obtained inequalities represent limits for what can and cannot be achieved experimentally.

Continuous and discrete Hopfield type neural networks claim to be mathematical descriptions of electrical phenomena appearing in nervous system. We present a set of theoretical results having natural counterpart and another set of theoretical results concerning equilibriums that have no real counterpart at the level of the nervous system. The differentiation criterion of equilibriums is the local exponential asymptotic stability in Liapunov sense of the steady state voltage and the structural stability of the Hopfield system in Smale sense. The believe is that unstable equilibriums in Liapunov sense and equilibriums obtained in case of structurally unstable Hopfield systems, exist only in theory.

This study presents necessary conditions for the existence and sufficient conditions for the stability or instability of the static meniscus (liquid bridge) appearing in the ribbon single crystal growth from the melt, of predetermined sizes, by using the edge-defined-film- fed (EFG) growth method. The cases when the contact angle and the growth angle verify the inequality 0<αc<π2 -αg or π2>αc>π2 -αg are treated separately. Experimentally, only static meniscus (liquid bridges) which verifies the necessary condition of existence and the sufficient conditions of stability can be created; static meniscus (liquid bridges) which does not verify both of these conditions, exist only in theory because in reality they collapses. The results of this study is significant for thin ribbon single crystal growth from melt, with prior given macroscopic dimensions, using prior given specific equipment. That is because the obtained inequalities represent limits for what can and cannot be achieved experimentally.

In case of a discrete-time Hopfield neural network of two neurons with two delays and no self- connections at 23 bifurcation values 23 voltage trajectories appear.Among the 23 voltage trajectories 14 voltage trajectory are not what we call orbits in classic sense. The geometrical aspect of these trajectories suggest that they are fractals. Our conjecture is that the 14 trajectories in discussion are fractals having real couterpart. In case of a discrete-time Hopfield neural network of five neuron with delay and ring architecture at 9 bifurcation values 9 voltage trajectories appear.Among the 9 voltage trajectories we find 5 voltage trajectory which are not what we call orbits in classic sense.The geometrical aspect of these trajectories suggest that they are fractals.Our conjecture is that the 5 trajectories in discussion are fractals having real couterpart.. In case of a discrete-time Hopfield neural network of two neurons with a single delay and self- connections the computed trajectories are what we call orbits in classic sense. In case of a discrete-time Hopfield neural network of two neurons with two delays and self- connections the computed trajectories are what we call orbits in classic sense.