This paper gives a general view of a recently developed thermodynamic model of the thermoelastic rnartensitic transformation. Unlike existing empirical, mathematical or thermodynamic models, this generalised thermodynamic model can be used to understand and describe quantitatively the overall thermomechanical behaviour of polycrystalline shape memory alloys. Important points of difference betwe...

We have investigated the relationship between sexual isolation and DNA sequence divergence in the transformation (at locus rpoB) of a naturally competent strain of Bacillus subtilis. Using both genomic DNA and a PCR-amplified segment of gene rpoB as donor, we found that the extent of sexual isolation at locus rpoB was closely predicted, over three orders of magnitude, as a log-linear function o...

It is shown that every ray transfer matrix, often called the ABCD matrix, can be written as a similarity transformation of one of the Wigner matrices that dictate the internal space-time symmetries of relativistic particles, while the transformation matrix is a rotation preceded by a squeeze. The implementation of this mathematical procedure is described, and how it facilitates the calculations...

This paper is an introduction to the mathematical estimation of the crystallographic texture and microstructure resulting from the displacive transformation of austenite in steels, under the influence of an externally applied system of stresses. It begins with an introduction to the problem, a description of the phenomenological theory of martensite crystallography, and the application of this ...

This paper discusses a simple application of the wavelet transformation to analyse nerve cell impulse patterns. The action potentials converted into delta, or Dirac, functions were convoluted in the time domain with a modified Gauss (the negative of the second derivative of Gauss) function, varying in width between 0.6 and 384 ms. The width of the Gauss function was varied in 640 steps. Some pa...

Scientific computing involves both creativity on the part of the human scientist and a great deal of mechanical drudgery that can and should he automated. In the domain of mathematical modeling, problems can be specified naturally and concisely in terms of the mathematics and physics of the application. Our goal is to minimize the time required for scientists and engineers to implement these ma...

Idealized scientific representations result from employing claims that we take to be false. It is not surprising, then, that idealizations are a prime example of allegedly inconsistent scientific representations. I argue that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the ...

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by extracting a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of...

Mathematical approaches refer to make quantitative descriptions, deductions and calculations through the use of mathematics concepts, approaches and techniques, then draw some new conclusions and foresee by mathematical analysis and judgement. In recent years, Compressed Sensing theory (CS) provides solutions in alleviating the huge amount of information demand in the pressure of signal samplin...

We give a precise de nition of evolving algebras as nondeterminis tic mathematical machines All proofs in the paper are based on this de nition First we de ne constant propagation as a transformation on evolving algebras Then we extend evolving algebras by macro de nitions and de ne folding and unfolding transformations for macros Next we introduce a simple transformation to atten transition ru...