Related papers: Tibetan calendar mathematics
We propose a diagrammatic notation for matrix differentiation. Our new notation enables us to derive formulas for matrix differentiation more easily than the usual matrix (or index) notation. We demonstrate the effectiveness of our notation…
Despite the extensive amount of scholarly work done on Indian mathematics in the last 200 years, the conditions under which it originated and evolved is still not clear. Often, one reads the ancient texts with the present concepts and…
We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing…
We develop a new method of umbral nature to treat blocks of Hermite and of Hermite like polynomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of practical rules allowing significant…
We present a summary of recent and older results on Bessel integrals and their relation with zeta numbers.
Matrix clocks are a generalization of the notion of vector clocks that allows the local representation of causal precedence to reach into an asynchronous distributed computation's past with depth $x$, where $x\ge 1$ is an integer.…
An efficient coordinate-free notation is elucidated for differentiating matrix expressions and other functions between higher-dimensional vector spaces. This method of differentiation is known, but not explained well, in the literature.…
Arithmetic differential equations are analogues of algebraic differential equations in which derivative operators acting on functions are replaced by Fermat quotient operators acting on numbers. Now, various remarkable transcendental…
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically…
We consider a project that consists of activities to be performed in parallel under various temporal constraints, which include start-start, start-finish and finish-start precedence relationships, release times, deadlines, and due dates.…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a…
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Lah numbers and Stirling numbers of the second kind.
We give several different encodings of the step function of a Turing machine in intuitionistic linear logic, and calculate the denotations of these encodings in the Sweedler semantics.
The optimal calculation order of a computational graph can be represented by a set of algebraic expressions. Computational graph and algebraic expression both have close relations and significant differences, this paper looks into these…
Using some new logarithmic formal calculus, we construct a well known vertex algebra, obtaining the Jacobi identity directly, in an essentially self-contained treatment.
We present some lambda calculus with explicit substitutions and named variables. The characteristic feature of this calculus is as follows: renaming of bound variables when performing substitutions is done using special reductions and may…