Transactional memoryIn computer science and engineering, transactional memory attempts to simplify concurrent programming by allowing a group of load and store instructions to execute in an atomic way. It is a concurrency control mechanism analogous to database transactions for controlling access to shared memory in concurrent computing. Transactional memory systems provide high-level abstraction as an alternative to low-level thread synchronization. This abstraction allows for coordination between concurrent reads and writes of shared data in parallel systems.
Partition function (number theory)In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. No closed-form expression for the partition function is known, but it has both asymptotic expansions that accurately approximate it and recurrence relations by which it can be calculated exactly. It grows as an exponential function of the square root of its argument.
Rank of a partitionIn mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer associated with the partition. In fact at least two different definitions of rank appear in the literature. The first definition, with which most of this article is concerned, is that the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition.
Quantum mechanics of time travelUntil recently, most studies on time travel are based upon classical general relativity. Coming up with a quantum version of time travel requires physicists to figure out the time evolution equations for density states in the presence of closed timelike curves (CTC). Novikov had conjectured that once quantum mechanics is taken into account, self-consistent solutions always exist for all time machine configurations, and initial conditions. However, it has been noted such solutions are not unique in general, in violation of determinism, unitarity and linearity.
Pentagonal number theoremIn mathematics, the pentagonal number theorem, originally due to Euler, relates the product and series representations of the Euler function. It states that In other words, The exponents 1, 2, 5, 7, 12, ... on the right hand side are given by the formula gk = k(3k − 1)/2 for k = 1, −1, 2, −2, 3, ... and are called (generalized) pentagonal numbers . (The constant term 1 corresponds to .) This holds as an identity of convergent power series for , and also as an identity of formal power series.
Kashmir conflictThe Kashmir conflict is a territorial conflict over the Kashmir region, primarily between India and Pakistan, and also between China and India in the northeastern portion of the region. The conflict started after the partition of India in 1947 as both India and Pakistan claimed the entirety of the former princely state of Jammu and Kashmir. It is a dispute over the region that escalated into three wars between India and Pakistan and several other armed skirmishes.
