There have been many advances in treatment with X-Rays and radioactive su stances. This is an account of those recently adopted and those to be used in futu in the Radiotherapy Department at Bristol. t There are two great difficulties in using Deep X-Rays for the treatment of maligna disease. First, " Deep " X-Rays do not penetrate really deeply. Their effective rafl& is a few centimetres deepe...

The topic of this thesis is approximation algorithms for optimization versions of NP-complete decision problems. No exact algorithms with sub-exponential running times are known for these problems, and therefore approximation algorithms with polynomial running times are studied. An approximation algorithm does not necessarily nd the optimal solution, but it leaves a guarantee of how far from th...

Some new Hilbert-Pachpatte discrete inequalities and their integral analogues are established in this paper. Other inequalities are also given in remarks.

The reconstruction conjecture claims that every graph on at least three vertices is uniquely determined by its collection of vertex deleted subgraphs. Even though it is one of the foremost unsolved problems in Graph Theory, work on it has slowed down, may be due to the general feeling that existing techniques are not likely to lead to a complete solution. Here we give the results that have appe...

Set systems of finite VC dimension are frequently used in applications relating to machine learning theory and statistics. Two simple types of VC classes which have been widely studied are the maximum classes (those which are extremal with respect to Sauer’s lemma) and so-called Dudley classes, which arise as sets of positivity for linearly parameterized functions. These two types of VC class w...

Keeping in the view the non-probabilistic nature of experiment, we introduced some new generalized exponential fuzzy entropy involving one or more real parameters and to check their authenticity, the essential properties of these measures have been studied. Introduced fuzzy entropies contain several other existing parametric and non-parametric measures of fuzzy entropies defined by De Luca and ...

We propose public-key cryptosystems with public key a system of polynomial equations and private key an ideal.

Kinetic transition networks can now be calculated for small proteins using geometry optimisation to characterise minima, transition states and pathways, and unimolecular rate theory to supply rate constants corresponding to each transition state. The networks can be visualised by constructing disconnectivity graphs, revealing striking differences between good structure-seeking systems and a mod...

Abstract: Let  q d k n , , code be a linear code of length n, dimension k and minimum Hamming distance d over GF (q). One of the most important problems in coding theory is to construct codes with best possible minimum distances. In this paper new one-generator quasi-cyclic (QC) codes over GF (3) are presented. Some of the results are received by construction X.