Carathéodory's existence theoremIn mathematics, Carathéodory's existence theorem says that an ordinary differential equation has a solution under relatively mild conditions. It is a generalization of Peano's existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows existence of solutions (in a more general sense) for some discontinuous equations. The theorem is named after Constantin Carathéodory.
Asymptotic expansionIn mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. Investigations by revealed that the divergent part of an asymptotic expansion is latently meaningful, i.e. contains information about the exact value of the expanded function.
Homogeneous functionIn mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the degree; that is, if k is an integer, a function f of n variables is homogeneous of degree k if for every and For example, a homogeneous polynomial of degree k defines a homogeneous function of degree k.
Exponential backoffExponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate. These algorithms find usage in a wide range of systems and processes, with radio networks and computer networks being particularly notable. An exponential backoff algorithm is a form of closed-loop control system that reduces the rate of a controlled process in response to adverse events.
Ad hoc hypothesisIn science and philosophy, an ad hoc hypothesis is a hypothesis added to a theory in order to save it from being falsified. Often, ad hoc hypothesizing is employed to compensate for anomalies not anticipated by the theory in its unmodified form. Scientists are often skeptical of theories that rely on frequent, unsupported adjustments to sustain them. This is because, if a theorist so chooses, there is no limit to the number of ad hoc hypotheses that they could add. Thus the theory becomes more and more complex, but is never falsified.
Point at infinityIn geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line. In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring. In the real case, a point at infinity completes a line into a topologically closed curve.
SpinlockIn software engineering, a spinlock is a lock that causes a thread trying to acquire it to simply wait in a loop ("spin") while repeatedly checking whether the lock is available. Since the thread remains active but is not performing a useful task, the use of such a lock is a kind of busy waiting. Once acquired, spinlocks will usually be held until they are explicitly released, although in some implementations they may be automatically released if the thread being waited on (the one that holds the lock) blocks or "goes to sleep".
