In recent years, the research of wavelet frames on the graph has become a hot topic in harmonic analysis. In this paper, we mainly introduce the relevant knowledge of the wavelet frames on the graph, including relevant concepts, construction methods, and related theory. Meanwhile, because the construction of graph tight framelets is closely related to the classical wavelet framelets on ℝ, we give a new construction of tight frames on ℝ. Based on the pseudosplines of type II, we derive an (...) MRA tight wavelet frame with three generators ψ 1, ψ 2, and ψ 3 using the oblique extension principle, which generate a tight wavelet frame in L 2 ℝ. We analyze that three wavelet functions have the highest possible order of vanishing moments, which matches the order of the approximation order of the framelet system provided by the refinable function. Moreover, we introduce the construction of the Haar basis for a chain and analyze the global orthogonal bases on a graph G. Based on the sequence of framelet generators in L 2 ℝ and the Haar basis for a coarse-grained chain, the decimated tight framelets on graphs can be constructed. Finally, we analyze the detailed construction process of the wavelet frame on a graph. (shrink)

In CQ n.s. 26 . 62–84 I argued that the defeat of Sparta in 371 B.C. was not due to the pursuit of unwise policies towards the other Greek states. Unwise policies there had been. Sparta being by no means superior to Athens in the formulation of foreign policy, but these did not affect the position on the eve of Leuctra when, with Thebes politically isolated, and with some of the Boeotians disaffected, Cieombrotus at the head of a numerically superior (...) Spartan and allied army was poised for the, destruction of Theban power; a triumph of policy it must have seemed. Sparta failed for military reasons. Her army was unequal to the military genius of Epaminondas. (shrink)

In 404 Sparta stood supreme, militarily and politically master of Greece, in concord with Persia. By 362, the year at which Xenophon terminated his history on the sad note of ‘even greater confusion and uncertainty’, she was eclipsed militarily, never to win a great battle again; and so far from being master even of the Peloponnese that she would spend the rest of time struggling to recover her own ancestral domain of Messenia, no longer a world power, merely a local (...) wrangler. The reasons for all this which are to seek are of absorbing interest and prime importance for the history of Greece, but it is hard to resist the temptation to connect the change with the policies of Agesilaus whose reign virtually coincided with the period in question. He was king for forty-one years and over thirty of them well before the battle of Leuctra and he had influence in the state unequalled as far as we can tell by any other king. (shrink)

Over sixty years ago, it was written of early Greek tyranny that it ‘had arisen only in towns where an industrial and commercial regime tended to prevail over rural economy, but where an iron hand was needed to mobilize the masses and to launch them in assault on the privileged classes… But tyranny nowhere endured. After it had performed the services which the popular classes expected of it, after it had powerfully contributed to material prosperity and to the development of (...) democracy, it disappeared with an astonishing rapidity… The people regarded tyranny only as an expedient. They used it as a battering ram with which to demolish the citadel of the oligarchs, and when their end had been achieved they hastily abandoned the weapon which wounded their hands.’ Thus Gustav Glotz, whose view found favour with de Ste Croix. He too concluded with appeal to Aristotle, who in a famous passage declared that unlike monarchy, which arises to help ‘the great and good’ against the People, and the monarch who is appointed as one of ‘the great and good’, ‘the tyrant comes from the People and the multitude to confront the men of note and prevent the People being unjustly treated by them. This is clear from what actually happened, for, generally speaking, the majority of the tyrants became tyrants from being demagogues so to speak, having got themselves trusted by their abusive attacks on the men of note.’ Against this view of Aristotle and all his latter-day satellites, this paper is directed. (shrink)

The reader of Demosthenes can hardly avoid the impression that there was something sadly awry with the Athenian naval system in the two decades prior to Chaeronea. The war in the north Aegean was essentially a naval war, and Demosthenes frequently enough blamedAthen's failure on her lack of preparation. ‘Why do you think, Athenians,… that all our expeditionary forces are too late for the critical moments?…In the business of the war and the preparation for it everything is in disorder, unreformed, (...) undefined. So it is that some news arrives, we appoint trierarchs, we give them the opportunity legally to get others to act in their stead, we consider provision of money, then it is decided that the metics and those “living out” should go on the ships, then again you yourselves, then to allow substitutes, and during these delays^the cause for which we would have been sailing is lost before we have sailed] For we spend the time for action on preparations, but the critical moments for action do not last as long as our dilatoriness and cautious procedures’ . This was spoken in 351 and it is much the same a decade later. (shrink)

Epaminondas the soldier has been much admired. His two great battles rank as masterpieces of the military art. Epaminondas himself perhaps regarded them as his greatest achievements, to judge by his last words as reported by Diodorus . He had been carried from the battlefield of Mantinea with a spear stuck in his chest. The doctors declared that when the spear was removed he would die. After hearing that his own shield was safe and that the Boeotians had won, he (...) ordered that the spear be removed. One of his friends said to him ‘But you die without a son.’ He answered ‘I do, by God, but I leave two daughters, my victory of Leuctra and my victory of Mantinea’, and then he died. Nor were his ‘daughters’ unadmired. By remarkable chance the future Philip II of Macedon was hostage at Thebes at the very time of Epaminondas' pre-eminence and did not fail to learn, as Chaeronea was to show. (shrink)

The Twenty-fifth Congress of the CPSU emphasized that under present-day conditions, problems of ideological struggle and conflict between the two social systems are assuming increasing importance. In this connection, particularly significant for us are questions pertaining to the deepening confrontation of socialism and capitalism in the realm of social philosophy, which, with the relaxation of international tensions and strengthening of scientific and cultural contacts, is in many respects acquiring new sharpness and assuming new forms. It is precisely in the sphere (...) of the theory of social philosophy that bourgeois and revisionist thought strives the most for some kind of "infiltration of ideas," because this sphere is falsely regarded as "remote" from politics and the class struggle going on in the world. In this sphere attempts are being made to find new methods of struggle against Marxism-Leninism, but in fact these are often only modernized variants of the old ones, which have become decrepit and obsolete in the extreme. Of particular significance under present conditions is criticism of bourgeois Marxology as one of the basic and principal trends in the theoretical struggle of capitalism-oriented philosophy against Marxism. To reveal all this convincingly it is necessary to turn to history. (shrink)

In 346 the Athenians were sadly deceived by Philip. The long war for Amphipolis had taken its toll and the people wanted relief, but the real motive of those who wanted peace in 346, both Philocrates with his principal abettor Demosthenes, and Eubulus and Aeschines, was to try to keep Philip out of Greece itself.2 In Elaphebolion the only debate was about means, whether, as Aeschines wanted, to try to get Phocis included in a Common Peace, or, as Demosthenes with (...) a clearer view of what Philip would accept urged, to make a separate peace and alliance and leave the salvation of Phocis to the future: he probably thought that, if Philip should afterwards attack Phocis, Athens could choose between her allies and, as in 352, rush to the aid of Phocis. (shrink)

It is perhaps worth briefly discussing a subject on which Demosthenes has so much to say and on which there is so little satisfactory evidence. In every speech which he delivered after 346 he referred, in greater or less detail, to breaches of the Peace of Philocrates, and this insistence on Philip's may mislead us. The case of Cardia is suggestive. In 341, in the speech On the Chersonese, he sought to create the impression that Philip was acting in breach (...) of the peace by sending troops to help defend Cardia against Diopeithes. (shrink)

In the course of Demosthenes' lifetime, indeed within a mere decade, the whole balance of power in the Greek world was destroyed. By 338 the city states were completely overshadowed by the national state of Macedon, and it is the concern of all students of Demosthenes to analyse this dramatic change. The task is not easy. The evidence is most unsatisfactory. None of the great historians of the age has survived in other than a few precious fragments, and in the (...) absence of Ephorus, Anaximenes, Theopompus, and the Atthidographers the pale reflections of some of them in Book XVI of Diodorus are poor consolation. It is on the Athenian orators that we have to rely, the very men most concerned in the politics of Athens, in the act of glossing over and denying their own share in the disaster and of misrepresenting that of their opponents. Memories were no longer then than they are today. In 343 both Demosthenes and Aeschines in discussing the events of a mere three years past denied all responsibility for the making of the Peace of Philocrates; one, at least, was lying, confidently. The formal documents were, generally speaking, merely heard, and only in part at that, and the orators were well practised in exploiting such material. If Aeschines and Demosthenes could lie so freely within three years of the events, what they had to say at a longer interval must be much more suspect. (shrink)

Nothing about Xenophon's Hellenica is more outrageous than his treatment of the relations of Persia and the Greeks. It was orthodoxy in the circle of Agesilaus that Theban medizing, barbarismos, had sabotaged the plans for a glorious anabasis and recalled him to the defence of his city . Not until the Thebans woo and win the fickle favour of the King , does anything like detail emerge. In the regrettable interlude, the less said the better. If the third speech of (...) Andocides had not survived, there would have been some tangled theorizing about a note in Didymus , especially as regards ‘the ambassadors who in Sparta consented’, but sober historical judgement would never have transgressed so far from the text of Xenophon as to postulate a Peace Congress in Sparta as well as in Sardis in 392. Likewise, the merest chance of epigraphic survival assures us that the oaths, which the ‘Athenians and the Spartans and the other Greeks’ swore in 387/6, ‘the King swore’ — and so on. If we did not have the reflection of Ephorus in Diodorus, albeit a mirror cracked and blemished, we would be sadly astray in 375 and 371. When, however, the despicable Thebans become the King's favoured power, disgraceful scenes unfold. ‘Pelopidas very much had things his own way with the Persian; he could say that the Thebans alone of the Greeks had fought on the King's side at Plataea, that they had never afterwards campaigned against him, that the Spartans were at war with them because they would not join Agesilaus…etc.’ . A Persian is found at Thebes reading out the contents of a Royal Rescript, after displaying the Royal seal ; at Sparta twenty years before, such details had been left to the imagination. The cause of Xenophon's method in this matter is not for the moment under discussion, but rather the consequence, viz. our uncertainty about what precisely the King's Peace said. There was a document, inscribed on stone pillars and displayed in the national shrines . If ever a copy turns up, what can we expect to find? The measure of our uncertainty was provided by Wilcken, who produced a curious hypothesis which found little sympathy; that he could do so shows the state of the evidence. Some effort of the imagination is needed, and those who gravely disapprove of conjectures of what might have been the case need read no further. At the end one can be sure of very little. Conjectures, however, have been uttered, en passant, elsewhere. What may prove to be a chorus of disdain has begun. A formal confession may be welcome. (shrink)

It is commonly supposed that in the eighth century B.c. there was a ‘population explosion’ in Greece which moved the Greeks to send out colonies. A. J. Graham in the Cambridge Ancient History iii, 3 is typical: ‘The basic active cause of the colonizing movement was overpopulation’; ‘at the very time when the Archaic colonising movement began, in the second half of the eighth century, there was a marked increase in population in Greece’ . The presumed connection between overpopulation and (...) colonisation is not immediately obvious. The evidence for the population explosion is found in the increased number of burials in Attica and the Argolid, but Athens sent out no colony before the very end of the seventh century and Argos probably none at all, certainly none in this period. So special explanations have to be formulated for Athens' and Argos' lack of colonies while their postulated ‘population explosion’ is presumed for Greece as a whole and called in to explain the burst of colonising in the eighth century. The hypothesis is not used for seventh-century colonisation when the number of burials declines. (shrink)

In the first book of his History Thucydides shows ‘the Spartans and the Allies’, to give the Peloponnesian League its formal title, making the decision that Athens had broken the Thirty Years Peace. After receiving the complaints of various allies, the Spartans discussed in the assembly the conduct of Athens and what should be done about it and ended by voting that the treaty had been broken and that the Athenians were in the wrong . This decision they communicated to (...) the allies who had come complaining, and declared that they wished to summon all the allies and submit it to the vote, ‘in order that after general consultation they might make war, should it so seem good“ . Then, after the Excursus on the Pentekontaetia, Thucydides records the congress of the League in which the Spartans put to the vote whether it was necessary to go to war and the majority voted for war . Thus Sparta proposed and the allies disposed. (shrink)

In the course of Demosthenes' lifetime, indeed within a mere decade, the whole balance of power in the Greek world was destroyed. By 338 the city states were completely overshadowed by the national state of Macedon, and it is the concern of all students of Demosthenes to analyse this dramatic change. The task is not easy. The evidence is most unsatisfactory. None of the great historians of the age has survived in other than a few precious fragments, and in the (...) absence of Ephorus, Anaximenes, Theopompus, and the Atthidographers the pale reflections of some of them in Book XVI of Diodorus are poor consolation. It is on the Athenian orators that we have to rely, the very men most concerned in the politics of Athens, in the act of glossing over and denying their own share in the disaster and of misrepresenting that of their opponents. Memories were no longer then than they are today. In 343 both Demosthenes and Aeschines in discussing the events of a mere three years past denied all responsibility for the making of the Peace of Philocrates; one, at least, was lying, confidently. The formal documents were, generally speaking, merely heard, and only in part at that, and the orators were well practised in exploiting such material. If Aeschines and Demosthenes could lie so freely within three years of the events, what they had to say at a longer interval must be much more suspect. (shrink)

Demosthenes prophesied1 that, unless Athens stopped Philip in the north, she would have to deal with him in Greece itself, and the events of 346 proved him right. Right in this much, he has been presumed right in general, and the policies of those he opposed have received only scant consideration before being dismissed as the selfish pursuit of peace by the rich, who were so blinded by their material interests that they could not see the real issues involved. It (...) is the purpose of this article to question, from a purely military standpoint, the soundness of Demosthenes' policy. (shrink)

In REG 73 and 75 I discussed various points connected with the Peace of Philocrates, a number of which have been assailed by M. M. Markle in CQ N.S. 24 in an article entitled ‘The Strategy of Philip in 346 B.C.’. Time passes, and, although de Ste. Croix in his Origins of the Peloponnesian War , p.105, felt able to declare that ‘a book shortly to be published by M. M. Markle makes a valuable and original contribution to our understanding (...) of the Peace of Philocrates’, and Markle himself confirms that a book is indeed forthcoming, some comment on his preliminary comments may be permitted. (shrink)

In recent years, three ancient manuscripts relating to the _Yi jin_g (_I Ching_), or _Classic of Changes_, have been discovered. The earliest--the Shanghai Museum Zhou Yi--dates to about 300 B.C.E. and shows evidence of the text's original circulation. The _Guicang_, or _Returning to Be Stored_, reflects another ancient Chinese divination tradition based on hexagrams similar to those of the _Yi jing_. In 1993, two manuscripts were found in a third-century B.C.E. tomb at Wangjiatai that contain almost exact parallels to (...) the _Guicang_'s early quotations, supplying new information on the performance of early Chinese divination. Finally, the Fuyang_ Zhou Y_i was excavated from the tomb of Xia Hou Zao, lord of Ruyin, who died in 165 B.C.E. Each line of this classic is followed by one or more generic prognostications similar to phrases found in the_ Yi jing_, indicating exciting new ways the text was produced and used in the interpretation of divinations. _Unearthing the Changes_ details the discovery and significance of the Shanghai Museum _Zhou Yi_, the Wangjiatai _Guicang_, and the Fuyang _Zhou Yi_, including full translations of the texts and additional evidence constructing a new narrative of the _Yi jing_'s writing and transmission in the first millennium B.C.E. An introduction situates the role of archaeology in the modern attempt to understand the Classic of Changes. By showing how the text emerged out of a popular tradition of divination, these newly unearthed manuscripts reveal an important religious dimension to its evolution. (shrink)

Don Carlos de Sigüenza y sor Juana Inés de la Cruz no solo se encuentran en la encrucijada del paso de la edad media a la moderna, y del viejo al nuevo mundo, sino de la vieja a la nueva vía de reflexión y de la vieja a la nueva ciencia. Es lo que se intenta mostrar en estas páginas.