In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one interesting and still open problems Diophantine analysis. We search for positive integer solutions equation case where right-hand side Mersenne numbers. By using definition numbers, appropriate inequalities parameters prime factorization $n!$ show that there no solution to equation. Thus, obtain result de...

On March 3, 1998, the centenary of Emil Artin was celebrated at the Universiteit van Amsterdam. This paper is based on the two morning lectures, enti-tled`Artin reciprocity and quadratic reciprocity' and`Class eld theory in practice', which were delivered by the authors. It provides an elementary introduction to Artin reciprocity and illustrates its practical use by establishing a recently obse...

We propose a novel acceleration scheme for Monte Carlo based statistical static timing analysis (MC-SSTA). MC-SSTA, which repeatedly executes ordinary STA using a set of randomly generated gate delay samples, is widely accepted as an accuracy reference. A large number of random samples, however, should be processed to obtain accurate delay distributions, and software implementation of MC-SSTA, ...

In this paper we will be concerned with certain patterns where semantically equivalent English and German sentences differ in terms of constituents. We will present these patterns, select three for more detailed analysis, and then show how transformation from the English source to the German target is implemented in the Logos MT system.

We propose a pseudorandom number generator specialized to generate double precision floating point numbers. It generates 52-bit pseudorandom patterns supplemented by a constant most significant 12 bits (sign and exponent), so that the concatenated 64 bits represents a floating point number obeying the IEEE 754 format. To keep the constant part, we adopt an affine transition function instead of ...

We exhibit ten new primitive trinomials over GF(2) of record degrees 24 036 583, 25 964 951, 30 402 457, and 32 582 657. This completes the search for the currently known Mersenne prime exponents. Primitive trinomials of degree up to 6 972 593 were previously known [4]. We have completed a search for all known Mersenne prime exponents [7]. Ten new primitive trinomials were found. Our results ar...

In this paper we describe the application of a movementbased design process for digital musical instruments (DMIs) which led to the development of a prototype DMI named the Twister. The development is described in two parts. Firstly, we consider the design of the interface or physical controller. Following this we describe the development of a specific sonic character, mapping approach and perf...

Abstract Specialized hardware implemented on field programmable gate array (FPGA) is used to simulate critical 2D Ising lattices up 4096 2 . Four mainstream, high-quality pseudorandom number generators (PRNGs) including Xorshift , Mersenne Twister Xorwow and ALFG are tested this system, three of them found misbehave with different degree confidence levels. It observed that PRNGs quality issues ...