Conferences Books

First published in 1972, it is remarkable that this book is still in print, and this fact attests to the current interest in singularity theorems in general relativity. The author of course is well-known for his contributions in this area, and he has written these series of lectures primarily for the mathematician whose speciality is differential topology, and who is curious about its applications to general relativity. The author thinks in pictures in this book, and so it is well-suited for the physicist reader also. Detailed proofs are omitted for the singularity theorems, but references are given. Much work and discussion has taken place since this book was published, but it can still serve as an introduction to modern developments.

Section 1 sets the mathematical definitions and conventions used in the later sections. Spacetime is defined as a real, four-dimensional connected smooth Hausdorff manifold on which is defined a global smooth nondegenerate Lorentzian metric. In addition, it is assumed that spacetime is time-orientable, which is not too big a restriction since as the author remarks, one can always find a time-orientable twofold covering of spacetime. Jacobi fields are introduced also, with the goal of eventually using them to study maximal geodesics. Known to physicists as the equation of geodesic deviation, the author derives the Jacobi equation, the solutions of which form an 8-dimensional vector space of Jacobi fields.

In section 2, the author gives definitions that allow one to discuss causality and time ordering for curves on spacetime. Special types of non-smooth curves, called trips, which (piecewise) are future-oriented timelike geodesics, are used to define a chronological ordering of points on spacetime. Causal trips are more restrictive, in that the curves are causal geodesics. The chronological ordering is shown to imply causal ordering, and both orderings are shown to be transitive. This allows the partitioning of spacetime into chronological future and past, and causal future and past. The topological properties of these sets are studied, and conditions are given in terms of null geodesics and timelike curves for causal and chronological ordering.

The next section considers the properties of future and past sets. A future (past) set is one that is equal to the chronological future (past) of some set in spacetime. In addition, subsets of spacetime that do not contain any points that are chronologically related, called achronal sets, and subsets that are boundaries are considered. It is shown that spacetime can be written as the disjoint union of an achronal boundary, and a unique past and future set. It is also shown that achronal boundaries are fairly well-behaved objects: they are 3-dimensional topological manifolds.

In order to rule out "pathological" spacetimes that contain closed trips or closed causal trips, the author studies global causality conditions in section 4. Thus the author defines a spacetime to be future (past)-distinguishing if for any two distinct points, their chronological future (past) sets are unequal. He then defines a spacetime to be strongly causal if every point in it has arbitrarily small causally convex neighborhoods (causally convex meaning that it does not intersect a trip in a disconnected set). The author offers examples to show that local violations of causal convexity can be avoided, and so violations of strong causality at a point are due to the global structure of the spacetime. He shows that a spacetime which is strongly causal at a point must be future and past distinguishing at the point. The converse is not true, and the author gives a counterexample. The Alexandrov topology for spacetime is defined in this section also. Given two points in spacetime, a basis for the open sets for this topology is given by the intersection of the chronological future set of one point with the chronological past set of the other. The author shows that spacetime is strongly causal iff the Alexandrov topology equals the manifold topology iff the Alexandrov topology is Hausdorff. Defining a vicious point to be one through which passes a closed trip, and concentrating attention on the set of all vicious points, the author gives five conditions for strong causality to fail at a point, these conditions involving the boundary of the set of vicious points. He concludes the section by showing that if spacetime is compact, it must contain a closed trip.

Motivated by the notion of an initial value set from physicial considerations, the author defines in the next section domains of dependence for achronal subsets of spacetime, along with the future, past, or total Cauchy horizon for closed achronal subsets. These are related to the familiar Cauchy hypersurfaces from the theory of partial differential equations. It is proven that spacetime is globally hyperbolic iff a Cauchy hypersurface exists for it.

The space of causal curves is defined in the next section, on which is defined the C0-topology. It is shown to be compact under certain conditions. The study of geodesics as curves of maximal length is taken up in section 7. This entails matters of a more purely differential geometric point of view. The important inequality involving the Ricci curvature and an element of volume (or area) on a hypersurface. The author discusses briefly the importance of this inequality in the singularity theorems.

The last section is (unfortunately) very brief, wherein the author discusses the applications of the preceeding sections in singularity theorems. Referring to S. Hawking for the full proof, he gives a general argument and discusses the conditions as to when spacetime will have a past-endless geodesic in M which has a finite length. He defines a future-trapped set as one where the "future horizon" of the set, defined as the difference between its causal and chronological future, is compact. He then outlines a proof of the result that no spacetime can have the property that it contain no closed trips, have endless causal geodesics containing a pair of conjugate points, and contain a future-trapped set.

In this small work Aryeh Kaplan explains the significant of the commandment to put on Tefillin each day. As with so much in life many who put on Tefillin do not eem to have a sense of its real meaning. This work explains why this Mitzvah is so important.

P. K. Sen is one of the pioneering researchers in nonparametric statistic. The topic oof sequential analysis is getting more and more attention fue to advances in group sequential methods and adaptive designs. However you reaely see a nonparametric approach to the problem. This is a nice monograph to introduce you to the topic. If you want complete details Sen has a full-length book on the subject also.

...an epic tale of twists and turns, it makes you laugh, it makes you cry. Peppered throughout with dramatic and colorful characters, "Thermosense XVII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications," is the story of a host of adventurers who travel to Orlando to relay to each other their fantastic adventures and experiments. This is a must read for any fans of Louis L'Amour, Joseph Conrad, Herman Melville, and Richard Hoover. Bravo!!!

Thirty Minutes of Senate History is a collection of short vignettes of Senate history as presented by Senate Historian Richard A. Baker to weekly meetings of the Senate Democratic Conference in 1997. I was a little uncomfortable when I realized that this publication originated with the Democrats (I daresay this is the only thing I own with a foreword by Tom Daschle), but this is actually a pretty interesting little collection. Certainly, Democrats figure more prominently than Republicans in these historical anecdotes, but it's really not a partisan publication (and the most recent "event" mentioned was way back in 1969). There really are some fascinating facts lurking in these pages.

Naturally, it begins with some of the formative moments of Senate history, including its somewhat inauspicious move to Washington, D.C. (to a then-unfinished building). Many might be interested to learn that Senators came within one vote of establishing no salary whatsoever for themselves (Benjamin Franklin endorsed the idea of no salary because he thought it would help ensure that senators came from and represented the wealthy - folks still assume old B.F. was the consummate democrat, despite this and other proof). Always fractious, the Senate had a spirited debate over the purchase of Thomas Jefferson's library to replace the books the British used to help burn down the Capitol in 1814 (it seems Jefferson had a few foreign books in his collection). Did you know that one U.S. Senator has been killed in battle? Senator Edward Dickinson Baker died at The Battle of Ball's Bluff in the early days of the War Between the States. Perhaps the most fascinating story included here is that of the arrest of a reporter - by the Senate - in 1848 for failing to name the official who leaked a copy of the treaty with Mexico. Held within Senate chambers and treated to dinner and a bed by the sergeant at arms each night, the reporter lived the life of Riley (and kept right on working - at double his salary) for the one month of his Senate imprisonment.

Not surprisingly, some of the Senate stalwarts earned special mention among the 30 short presentations here - men such as Daniel Webster and John C. Calhoun (but not, surprisingly, Henry Clay), as well as some powerful men basically forgotten over the years. Of course, the caning of Senator Charles Sumner by Representative Preston Books earns an entry - and it actually talks about the incendiary and personally nasty Sumner speech that led to that tragedy. Among all of the fascinating facts mentioned in these pages, however, is the description of California Senator Clair Engle, unable to speak because of a brain tumor, lifting a frail arm and pointing to his eye to indicate his Aye vote to help end the marathon Civil Rights filibuster of 1964 (following a fourteen and a half hour opposition speech by Robert Byrd).

Everyone experinces in their life moments of truth. It is in these times we come to understand and realize the ultimate reality and grounding for ourselves and everything around us. Though not very long, Merton's journal entries spill out the sacramental truth he saw in Alaska. God spoke to Merton through everything around him during his stay in Alaska - the people, trees, water, mountains, etc. And in turn it pours back out of Merton in his talks and conferences. Very few things in this world we can be sure of. But the truth is never wrong and never changes - this book reveals a little slice of the Great Center which we all seek to draw near to.

Yes, as this article says, the 9/11/2001 attacks came from out of the sky but not from out of the blue.

These attacks came less than 48 hours after the end of the infamous Durban Conference which Cooper and Brackman spend seven pages discussing here. The arbitrary and racist acts of the participants at this "Racism" conference are simply amazing.

As the authors explain, the NGO Forum at Durban adopted an "action program" which called for:

1) dismantling "Israeli colonies"

2) a "right of return" of Arabs to Israel

3) reinstitution of the UN resolution equating Zionism with racism

4) the repeal of Israel's Law of Return for Jews to Israel

5) preparation of "educational packets" by the UN describing "the Israeli racist apartheid system"

6) establishment of a special UN Special Committee on Israeli apartheid

7) development of UN programs to counter "propaganda" that portrays Levantine Arabs as violent terrorists

8) launching by the UN of an international anti-Israel apartheid movement

9) convening of a War Crimes tribunal to prosecute Israel's leaders

10) demanding that the international community completely isolate Israel

11) condemning all states supporting, aiding, and abetting Israel

Decent people tended to notice that the tenor of all this was strikingly similar to some of the worst antisemitic literature of the twentieth century.

In my opinion, the Durban Conference is, so far, the greatest diplomatic disaster of this century. It basically advocated a total overthrow of human rights. It mocked truth and justice. Let's hope that, at the very least, it will remain the worst diplomatic disaster of this century through 2100.

I was shocked by what happened at Durban. I recommend this article, and think that everyone ought to be aware of how bad it was so they can do something to prevent it being repeated.

This volume consists of papers prsented at an EBRD-sponsored conference on central and east European trade policy issues held at the European Bank's London office on 26 and 27 March 1992. The papers deal with three main areas:

* international trade and payment systems required to sustain intraregional trade;
* EC trade policy toward central and eastern Europe; and
* trade policy and long-term adjustment in the region.
--- excerpt from books Introduction

Excellent conference proceeding: top contributors, varied important current topics and new ideas. Professional level, or interested and somewhat knowledgable amateur.

The Treaty of Versailles was a treaty with which almost no one was satisfied. The United States threatedned to withdraw from the process, failed to ratify the treaty and eventually came to a separate peace with Germany. France considered it too lenient. Britain thought that the economic descruction of Germany would be the result. Germany considered it not a treaty but a dictated peace.

France's field marshall Ferdinand Foch said, 'this is not peace, it is an armistice for twenty years.' He was right, almost exactly to the minute. Nguyen That Thanh, a young Vietnamese waiter attempted to attract the attention of the leaders. He was rejected, returned to Viet Nam and changed his name to Ho Chi Minh.

This small book gives an excellent introduction to the famous treaty and it's failures.