Synchronization tracking in pulse position modulation receiver

A clock pulse generator for decoding pulse position modulation in an optical communication receiver is synchronized by a delay tracking loop which multiplies impulses of a data pulse by the square wave clock pulses from the generator to produce positive impulses when the clock pulse is of one level, and negative impulses when the clock pulse is of another level. A delay tracking loop integrates the impulses and produces an error signal that adjusts the delay so the clock pulses will be synchronized with data pulses. A dead-time tau sub d is provided between data pulses of an interval tau sub p in the data pulse period tau. When synchronized, the average number of positive impulses integrated will equal the average number of negative impulses over the continuous stream of data pulses

On invariants and homology of spaces of knots in arbitrary manifolds

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to well-defined knot invariants are identified as 1-dimensional cohomology classes of generalized loop spaces of the manifold. Unlike the case of the 3-sphere, these obstructions can be non-trivial and provide invariants of the manifold itself. The corresponding algebraic machinery allows us to obtain on the level of the ``abstract nonsense'' some of results and problems of the theory, and to extract from other the essential topological part

Homology of spaces of homogeneous polynomials in R2R^2 without multiple zeros

For any natural $d \ge k \ge 2$ we calculate the cohomology groups of the space of homogeneous polynomials $R^2 \to R$ of degree $d$, which do not vanish with multiplicity $\ge k$ on real lines. For $k=2$ this problem provides the simplest example of the situation, when the "finite degree" invariants of nonsingular objects are not a complete system of invariants

Letter Written by Victor A. Speert to Edith Speert Dated November 28, 1944

[Transcription begins] 28 November 1944 Somewheres in Germany My beloved darling, I’m a very sad boy today for I received no packages and no letters. Nevertheless I remain undaunted and ready to go forth with my letter writing. Nothing new or eventful happened today aside from our usual hum-drum existence [sic]. We’ve still got our elegant set-up and good food—yessiree, we’re sitting on the top of the world. Boy, we’re sure getting sufficient PX supplies these days. Today we made another distribution of cigarettes, chocolate, soap, etc. That’s the one advantage of being in combat, you get your share of rations. The weather is starting to get a bit nasty outdoors. Today it showered frequently and it’s beginning to get colder. As I am writing this letter Shelton is frying bacon over one of our stoves. You know, the bacon comes in cans and is already sliced. Makes it so handy to get that evening snack. Hm! It smells good! Sweetheart, I still can smell those good Sunday breakfasts that you used to make. When you used to stuff food into me as though you were fattening a turkey. Come to think of it, it’s been quite a period that [sic] I’ve fried eggs—I just haven’t bothered to ask the Dutch civilian people for eggs. But, I do get to eat their butter, which is delicious, or to quote you, “out of this world.” We took some snapshots of “our pin-up board” last night. Our pinup board consists of pictures of nudes which Shelton cut out of some of the German art magazines found around here. By the way, the so-called “Kulten Art” is based wholly on the portrayal of nudes (male & female). In addition he has pictures of girls (naturally) from the Yank Magazine (no doubt you’ve seen many of them). Among some of the junk we’ve collected so far is an old muzzle loaded gun used in the 1700’s [sic]—perhaps it may even have antique value. Honey, as you can see I don’t have a heck of a lot to say except that I miss you madly, love you completely and can’t wait until I have you in my arms again. Good night, dear, your lover, Vic [Transcription ends