We present a calculational method for inverting programs by inverting the components separately. This is made possible by using assertions as commands and by permitting constructs that exhibit angelic nondeterminism. Rules are given for transforming inverted programs so that the angelic constructs are removed. A simple example illustrates the method.

We study a type of third-order linear differential equations with variable and unbounded coefficients, which are defined in an infinite interval. also consider non-linear generalization coefficients that depends on unknown function. establish sufficient conditions for the correctness this equation maximal regularity estimate their solution. Using these results, we prove solvability nonlinear no...

the use of unbounded tendons is common in prestressed concrete structures and evaluation of the stress increase in unbonded tendons at ultimate flexural strength of such structure has posed a great challenge over the years. based on the bending experiment for two-span continuous post-tension beams with unbounded tendons and externally applied cfrp sheets, the monitoring of the stress increment ...

The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differential equation has a zero in a given interval of real numbers. This is a fundamental reachability problem for continuous linear dynamical systems, such as linear hybrid automata and continuoustime Markov chains. Decidability of the problem is currently open; indeed decidability is open even for the sub-...

The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differential equation has a zero in a given interval of real numbers. This is a fundamental reachability problem for continuous linear dynamical systems, such as linear hybrid automata and continuoustime Markov chains. Decidability of the problem is currently open—indeed decidability is open even for the sub-p...

A novel way for addressing one-sided hypothesis tests for the mean of unable to observe real random variables from which we have information provided in terms of interval data is proposed. For this purpose, a measure of similarity between intervals is considered and the classical one-sided hypothesis test to check whether the similarity between the expectation of a random interval and a subset ...

Animals learn the timing between consecutive events very easily. Their precision is usually proportional to the interval to time (Weber’s law for timing). Most current timing models either require a central clock and unbounded accumulator or whole pre-defined populations of delay lines, decaying traces or oscillators to represent elapsing time. Current adaptive recurrent neural networks fail at...

Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metric, this Ricci flow always exists for all time and converges (after scaling b...

The existence of unbounded nonnegative solutions of a boundary value problem for nth-order differential equations defined on an infinite interval is obtained by means of the M ¨ onch fixed-point theorem. An example is then presented to demonstrate the application of our results.