Meyer sets, topological eigenvalues, and Cantor fiber bundles

We introduce two new characterizations of Meyer sets. A repetitive Delone set in $\R^d$ with finite local complexity is topologically conjugate to a Meyer set if and only if it has $d$ linearly independent topological eigenvalues, which is if and only if it is topologically conjugate to a bundle over a $d$-torus with totally disconnected compact fiber and expansive canonical action. "Conjugate to" is a non-trivial condition, as we show that there exist sets that are topologically conjugate to Meyer sets but are not themselves Meyer. We also exhibit a diffractive set that is not Meyer, answering in the negative a question posed by Lagarias, and exhibit a Meyer set for which the measurable and topological eigenvalues are different.Comment: minor errors corrected, references added. To appear in the Journal of the LM

Special Interrogation Report: Brigadefuhrer Kurt Meyer Command, 12th SS Panzer Division (6 June-25 August 1944)

Brigadefuhrer Kurt Meyer remains a controversial figure in Canadian military history. As a commander of Waffen-SS troops in Normandy, he fought the Canadians in the days and weeks after the Allied landings and allegedly ordered the killing of prisoners of war. A Canadian military court at Aurich in occupied Germany tried and convicted Meyer on charges of war crimes. Although sentenced to death, Meyer received commutation to life imprisonment from the convening authority, Major-General Chris Vokes. Meyer was imprisoned in New Brunswick and West Germany until his release in 1954. Several significant political, legal, public opinion, diplomatic, and military factors worked together to turn Meyer into Canada\u27s most notorious war criminal. His trial raised delicate issues of command responsibility for the first time, while Meyer and his formation, the 12th SS Panzer Division, became almost household names in some parts of Canada. Some Canadians may have genuinely hated the man and his ideals, but Meyer garnered curiosity and respect for his abilities as a fighting officer. A combat veteran of campaigns in Poland, the West, the Balkans, and the Eastern Front, Meyer felt most comfortable at the front of his troops. The inclination was borne from years of experience in the reconnaissance role and a personal disregard for danger. Meyer was among the best-regarded silver foxes of the Waffen-SS, the combat arm of Heinrich Himmler\u27s Schutzstaffel. Meyer likely did not believe that he would survive the war; this fact may have played some part in his complicity in the killing of Canadian prisoners of war behind the lines. Winning the battle or to die trying in a heroic fashion was always his first concern. After being captured alive, Meyer became the subject of several interrogations to further investigations for his eventual war crimes prosecution and to assess Canadian and German battlefield performance during the Normandy campaign. The following document gives good insights into Meyer’s background, his unwavering adherence to the Nazi cause, the obvious pride in his formation’s conduct, and the tactical battles against the Canadians in Normandy. This interview was conducted by the G Intelligence officer at the HQ of Canadian Forces in the Netherlands on 24 August 1945. In terms of operational details on the battlefield, Meyer demonstrated a remarkable memory, which proved less forthcoming on other matters during his war crimes trial. Meyer obviously inflated his own role and that of the troops under his command in operations. Canadian interrogators, on the other hand, added their own analysis of Meyer’s claims. While furnishing an important perspective from the enemy’s side, this interrogation report must be used with the standard checks for bias and reliability in any primary source

On the Bragg Diffraction Spectra of a Meyer Set

Meyer sets have a relatively dense set of Bragg peaks and for this reason they may be considered as basic mathematical examples of (aperiodic) crystals. In this paper we investigate the pure point part of the diffraction of Meyer sets in more detail. The results are of two kinds. First we show that given a Meyer set and any intensity a less than the maximum intensity of its Bragg peaks, the set of Bragg peaks whose intensity exceeds a is itself a Meyer set (in the Fourier space). Second we show that if a Meyer set is modified by addition and removal of points in such a way that its density is not altered too much (the allowable amount being given explicitly as a proportion of the original density) then the newly obtained set still has a relatively dense set of Bragg peaks.Comment: 32 page

Deforming Meyer sets

A linear deformation of a Meyer set $M$ in \RR^d is the image of $M$ under a group homomorphism of the group $[M]$ generated by $M$ into \RR^d. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In the case that the deformation is a Meyer set and the deformation is injective, the deformation is pure point diffractive if the orginal set $M$ is pure point diffractive.Comment: 6 page

"The German Influence on the Origin of U.S. Federal Financial Rescues"

While federal financial rescues have become a common response to crises, federal provision of finance was not one of the original powers of the federal government. One man, Eugene Meyer, is largely responsible for the origin of federal financial rescues, through both the War Finance Corporation and Reconstruction Finance Corporation. Meyer learned laissez faire economics from William Graham Sumner at Yale. However, German economist Adolph Wagner’s state-socialism philosophy heavily influenced Meyer’s thinking, and Meyer developed an interventionist philosophy. Serving in key government positions, Meyer put his beliefs into practice. These channels of influence and the resulting policies are examined.Financial rescues; War Finance Corporation; Reconstruction Finance Corporation.