Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition A CD-ROM containing an (...) interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic. (shrink)

Does Aristotle in the Nicomachean Ethics give one consistent answer to the question what life is best or two mutually inconsistent answers? In the First Book he says that we can agree to say that the best life is eudaimonia or eupraxia but must go on to say in what eudaimonia consists. By considering the specific nature of man as a thinking animal he reaches a conclusion: eudaimonia, the human good, is the activity of soul in accordance with virtue, and (...) if there are more than one virtue in accordance with the best and most complete, and in a complete life. Aristotle states that his formula is no more than a sketch or outline, but that a good sketch is important since, if the outline is right, anyone can articulate it and supply details. He seems to be thinking here not just of the rest of his own treatise but of the work of pupils and successors; he speaks, as at the end of the Topics, of progress in a science. (shrink)

Aristotle maintains that every man has, or should have, a single end, a target at which he aims. The doctrine is stated in E.N. I 2. ‘If, then, there is some end of the things we do which we desire for its own sake, and if we do not choose everything for the sake of something else, clearly this must be the good and the chief good. Will not the knowledge of it, then, have a great influence on life? Shall (...) we not, like archers who have a mark to aim t, be more likely to hit upon what is right?’. Aristotle does not here prove, nor need we understand him as claiming to prove, that there is only one end which is desired for itself. He points out correctly that, if there are objects which are desired but not desired for themselves, there must be some object which is desired for itself. The passage further suggests that, if there were one such object and one only, this fact would be important and helpful for the conduct of life. (shrink)

W. F. R. Hardie; X—Aristotle's Doctrine that Virtue is a “Mean”, Proceedings of the Aristotelian Society, Volume 65, Issue 1, 1 June 1965, Pages 183–204, https.

John Conington was a towering figure in Victorian scholarship, not least because of his remarkably sensitive and literate commentaries on Virgil’s _Aeneid. _The three-volume cloth edition of _The Works of Virgil_, begun by Conington in 1852, has been unavailable for over a century, except in rare second-hand sets. Now, for the first time, the whole of Conington’s work is being reissued in a set of six paperback volumes. Each volume includes a new introduction by an established scholar, setting Conington's commentary (...) in context, as well as a general introduction to Conington’s work by Philip Hardie, who offers a fresh appreciation of the work. (shrink)

Mammalian AMP‐activated protein kinase is the central component of a protein kinase cascade which inactivates three key enzymes involved in the synthesis or release of free fatty acids and cholesterol inside the cell. The kinase cascade is activated by elevation of AMP, and perhaps also by fatty acid and cholesterol metabolites. The system may fulfil a protective function, preventing damage caused by depletion of ATP or excessive intracellular release of free lipids, a type of stress response. Recent evidence suggests that (...) it may have been in existence for at least a billion years, since a very similar protein kinase cascade is present in higher plants. This system therefore represents an early eukaryotic protein kinase cascade, which is unique in that it is regulated by intracellular metabolites rather than extracellular signals or cell cycle events. (shrink)

The ancient evidence about the Culex is collected by Miss Jackson in her article in the Classical Quarterly . There seems no reason to doubt that Lucan said ‘et quantum mihi restat ad Culicem!’; and, whatever Lucan meant by it, Statius turned it into a compliment for the poet by making Calliope predict the various works he would produce ‘ante annos Culicis Maroniani’ . In the Neronian age, we may take it, it was not an obscure or conjectural matter, but (...) one of common knowledge or belief, that a certain known poem, the Culex, was the work of Virgil. About the other opuscula there is no evidence as early as that. The Aetna and Moretum are ascribed to him dubiously; the Ciris, Dirae, Epigrammata, Priapea, Catalepton are attributed to him with more confidence, but not so confidently as the Culex. It almost looks as if the belief in the Virgilian authorship spread from the Culex to certain other poems which were in some way or other connected with it. Here there is admittedly a great difficulty for those who are inclined to deny or to doubt that it is Virgil's. Are not the facts most easily explained by supposing that it was Virgil's ? At all events it is in various ways improbable that it was written, and produced as Virgil's, at some time between Virgil's death and the youth of Lucan. It is difficult to imagine who would have a motive for doing such a thing, or who could do it successfully. So it is incumbent upon the sceptic to produce some plausible view of what may have happened. (shrink)

Lvcilivs, fr. 965 :quaenam uox ex te resonans meo gradu remoram facit ?Mr. Housman in the first number of the Classical Quarterly refuted and pulverized the attempt of Marx to emend this passage by writing quoia nam. ‘ Ex tecto ’ and ‘ ex aede’ have been suggested; but it is obvious that if ‘ ex aede’ is to be contemplated, emendation may go on S0009838800019431_inline1—scores of words could be found that would make sense. There is no context. If the (...) passage is to be emended at all, I suggest that Lucilius wrotequaenam uox EXTVOORERESONANS. (shrink)

There has been much discussion in recent years regarding the date and authorship of the poems included in the Appendix Vergiliana, and about the Civis and the Culex in particular. Evidence of very various kinds has been brought to bear on the question. My chief aim in this paper is to propound a criterion which as far as I know is new—though it seems to me a fairly conspicuous thing, and I do not know why it has not been investigated (...) —and to examine certain criteria which seem to me to have been treated quite wrongly—treated in a way which could lead to no conclusion—even by so distinguished a scholar as Norden. I propose in a second paper to examine the argument from diction, especially in regard to the Culex, and to try to show that the evidence adduced for Virgilian authorship by Miss Jackson is not so conclusive as it has been supposed to be; and, next, to point out certain features or mannerisms in the Culex which seem to me to be on the whole against authorship by Virgil. I have hardly any doubt that both the Ciris and the Culex were written before 44 B.C., and the Lydia and Dirae only two or three years later; but, while the evidence for the early date of some of the Vergiliana grows stronger on further examination, the evidence for Virgilian authorship seems to me to grow weaker, even in the case of the well-attested Culex. (shrink)

Variations in levels of apolipoprotein E have been tied to the risk and progression of Alzheimer's disease . Our group has previously compared and contrasted the promoters of the mouse and human ApoE gene promoter sequences and found notable similarities and significant differences that suggest the importance of the APOE promoter's role in the human disease. We examine here three specific single-nucleotide polymorphisms within the human APOE promoter region, specifically at -491 , -427 , and at -219 upstream from the (...) +1 transcription start site. The -219 and -491 polymorphic variations have significant association with instance of AD, and -491AA has significant risk even when stratified for the APOEepsilon4 allele. We also show significant effects on reporter gene expression in neuronal cell cultures, and, notably, these effects are modified by species origin of the cells. The -491 and -219 polymorphisms may have an interactive effect in addition to any independent activity. DNA-protein interactions differ between each polymorphic state. We propose SP1 and GATA as candidates for regulatory control of the -491 and -219 polymorphic sites. This work's significance lies in drawing connection among APOE promoter polymorphisms' associations with AD to functional promoter activity differences and specific changes in DNA-protein interactions in cell culture-based assays. Taken together, these results suggest that APOE expression levels are a risk factor for AD irrespective of APOEepsilon4 allele status. (shrink)

‘After it, the philosophy of perception cannot be discussed in ways it usually was discussed before.’ This is said about Sense and Sensibilia by Mr Bernard Williams in an article, ‘J. L. Austin's philosophy’, published in the Oxford Magazine of 6 December 1962. It is not quite clear what Mr Williams means by the remark. It might be understood as an endorsement of Austin's insistence that philosophers have lapsed into crudity and error through their neglect of distinctions marked by the (...) rich variety of linguistic expressions in ordinary use. But Mr Williams himself in his article makes some effective criticisms of Austin's opinion that ordinary language is a reservoir of philosophically significant distinctions, and points out also that Austin's own practice in these lectures did not exhibit any close connection between his survey of the variety of the uses of such words as ‘look’, ‘seem’, ‘appear’, and his criticism of theories of perception. (shrink)

One of the most dynamic areas of plant molecular biology is the investigation of the actions of three classes of herbicides: s‐triazines (atrazine, simazine), glyphosate, and sulfonylureas (chlorsulfuron, sulfometuron methyl) (Figure 1). The results of this work are expected to provide the first significant applications of plant biotechnology: directly, in the genetic engineering of crop plants resistant to specific herbicides and, indirectly, in providing a molecular basis for the rational design of new herbicides for specific biological targets.s‐Triazines affect photosynthesis by (...) inhibiting the binding of quinones to the chloroplast membrane QB protein. An s‐triazine resistant QB protein isolated from weeds in fields consistently treated with the herbicide has a serine in place of a glycine in this highly conserved protein. Glyphosate inhibits 5‐enolpyruvyl‐shikimate‐3‐phosphate synthase (EPSP synthase), an enzyme in the aromatic amino acid biosynthetic pathway. Mutagenized bacteria produce a resistant EPSP synthase with a substitution of serine for proline. Sulfonylureas inhibit the acetolactate synthase (ALS) of bacteria, yeast, and higher plants; this enzyme catalyzes the first step in the synthesis of branched chain amino acids. Resistant ALS has been found in bacteria, yeast and tobacco with a proline substituted by serine in yeast ALS. These findings provide a strong basis for developing projected plant biotechnology applications. (shrink)

The dream related by Ennius in the first book of his Annales, in which the ghost of Homer appeared to him, has been the subject of much discussion. There are various pieces of evidence about it from which inferences can be drawn; sometimes, I think, too much has been inferred, sometimes too little. My chief object in this paper is to consider what exactly was the view held or expounded by Ennius regarding the nature of the soul and the conditions (...) under which a ghost appears. But I propose in the first place to review the evidence and to contemplate the dream as a poetic product, a thing which has its place in the history of poetry and its affinities with similar passages in other authors. (shrink)

The Hercules Oetaeus, whatever be its authorship, is closely related to the other plays, and often has what seem to be reminiscences of them, not always felicitous reminiscences. Often, of course, they are reminiscences of the other Hercules, and may supply a clue to the text of that play. Many of them were pointed out by Leo, but there is room for further investigation.

The words “free will” have uses in ordinary talk as in “free will offering” and, most commonly, in the expression “of my own free will.” We all know what states of affairs make this expression applicable, and its standard use is defined by this application. Yet philosophers discuss, or used to discuss, whether the will is free, libertarians saying that it is and determinists denying this. Are they, or were they, asking whether anyone ever acts of his own free will? (...) If so, the question asked was absurd. (shrink)