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February 27, 2018News Alert
Ninth Circuit Orders EPA to Update Standards for Lead-Based Paint and Dust Hazards
Beveridge & DiamondMark Duvall, Tim Serie
The Environmental Protection Agency (EPA) must propose an update of its lead-based paint and dust hazard standards by March 27, 2018, according to a court order. The current standards were promulgated in 2001, and have never been updated since then. Title IV to the Toxic Substances Control Act (TSCA) requires EPA to keep these standards updated, since they play critical roles in a number of the lead-based paint programs, including lead hazard disclosure in real estate transactions and lead hazard abatement activities.
The court order came in the form of a mandamus granted by the United States Court of Appeals for the Ninth Circuit on December 27, 2017. Several environmental groups had requested the court to order EPA to update the lead paint and lead dust standards after their administrative petition directed to EPA in 2009 resulted in no rulemaking. The court ordered EPA to propose a rule within 90 days, and to finalize the rule within one year after the promulgation of the proposed rule. EPA can only modify the deadlines if it provides new information to the court to justify an extension.
This alert provides an overview of TSCA Title IV programs and the potential significance of the two standards to be updated. Title IV stakeholders, such as realty agents, the lead hazard assessment and abatement industry, and the home improvement industry, may want to monitor EPA's upcoming lead-related rulemaking activities.
Lead Hazard Standards under TSCA Title IV
Lead-based paint was widely used in the construction industry across the United States in the early decades of the 20th century. In 1971, driven by concerns about lead poisoning, Congress passed the Lead-based Paint Poisoning Prevention Act, which prohibited the use of lead-based paint. The federal government subsequently banned the use of lead-based paint and surface coatings in 1978. However, lead exposure hazards remain a potential concern for properties that were painted prior to the 1978 ban.
Congress addressed the lead hazards in those legacy properties with the Residential Lead-Based Paint Hazard Reduction Act (Paint Hazard Act) in 1992. The Paint Hazard Act added Title IV to TSCA, authorizing EPA to promulgate lead hazard regulations. Congress recognized that three media may contain lead hazards: lead-contaminated paint, lead-contaminated dust, and lead-contaminated soil. Under section 403 of TSCA, Congress directed EPA to identify lead hazards in these media. EPA was required to:
[w]ithin 18 months after the enactment of [Title IV of TSCA] . . . identify, for the purposes of this title, and the Residential Lead-Based Paint Hazard Reduction Act of 1992, lead-based paint hazards, lead-contaminated dust, and lead-contaminated soil.
Congress provided limited instruction regarding how EPA should identify the hazard for these contaminated media, except for a few descriptions of these concepts that are tied to lead contamination and adverse human health impacts. Furthermore, although Congress was silent on the dust-lead and soil-lead hazards, an initial numerical threshold for paint appeared in the definition of "lead-based paint" under TSCA section 401: "1.0 milligrams per centimeter squared or 0.5 percent by weight." Congress authorized EPA and the Department of Housing and Urban Development (HUD), another agency tasked with administering the Paint Hazard Act, to lower this standard within their respective jurisdictions.
Despite the mandatory timeframe, EPA did not promulgate any hazard identification until 2001, when it published the paint, dust, and soil lead hazard standards (2001 Hazard Standards). In the 2001 Hazard Standards, "lead-based paint hazard" refers to: "hazardous lead-based paint, dust-lead hazard or soil-lead hazard as identified in [40 C.F.R.] § 745.65."
EPA designated numerical benchmarks under 40 C.F.R. § 745.65 for both "dust-lead hazard" and "soil-lead hazard." The dust-lead hazard standards, which were later subject to the A Community Voice litigation, are 40 μg/ft2 for floors and 250 μg/ft2 for interior window sills in residential dwellings and child-occupied facilities.
"Paint-lead hazard," in contrast, has several alternative narrative definitions under 40 C.F.R. § 745.65, which are tied to either "lead-based paint" or "lead-based painted surface." Neither term is defined in the 2001 Hazard Standards. During the 2001 rulemaking, EPA explicitly abandoned the proposal to set a threshold level for paint hazards. The paint hazard standard was, as a result, effectively built on the cutoff threshold in the definition of "lead-based paint" that Congress provided in section 401 of TSCA. EPA has not separately lowered the threshold established by Congress in the Paint Hazard Act. It settled on the same values in a few other TSCA Title IV regulations as well.
Rulemaking Petition and Litigation
EPA did not revise the 2001 Hazard Standards after promulgating them. In 2009, citizen groups filed a TSCA section 21 petition requesting EPA to change the dust hazard standards (to 10 μg/ft2 for floors and 100 μg/ft2 for window sills) and lower the threshold for lead-based paint (to 0.06 percent by weight), citing evolving science allegedly showing that the existing hazard standards are insufficient to protect children's health. EPA granted the request for rulemaking in October 2009, but did not issue any further response or propose a new rule. The citizen groups filed a mandamus petition before the court in 2016, arguing that EPA unreasonably delayed the rule's promulgation.
In the A Community Voice decision, the Ninth Circuit held that EPA had a duty to modify the section 403 hazard standards under both TSCA Title IV and the Administrative Procedure Act (APA). The court held that Congress intended the section 403 decision-making to be "an ongoing process" and that EPA under TSCA Title IV should "account for new information, and . . . modify initial standards when necessary to further Congress's intent." Alternatively, the court also held that because EPA granted the petition for rulemaking, it must "enter a final decision subject to judicial review . . . within a reasonable time" under APA. On either ground, EPA could not unreasonably delay the rulemaking process. The court then found that EPA's eight-year delay was not reasonable, and issued a mandamus.
EPA represented in court that it could have a proposed rule by 2021 and a final rule by 2023. The court rejected the timeframe. Instead, the court gave EPA 90 days to propose a new rule and another year to finalize the proposed rule. EPA can only request a judicial modification of these deadlines if it can justify an extension.
The Regulatory Significance of Section 403 Standards and the Ninth Circuit's Decision
The A Community Voice decision is significant because section 403 standards are incorporated into a number of regulations under TSCA Title IV and the Paint Hazard Act. Lower thresholds expand the scope of obligations under these programs.
The Paint Hazard Act and TSCA Title IV delegated the authority to reduce and control lead hazards from legacy properties to multiple governmental agencies. Most notably, EPA must develop programs for:
Proper training and certification of "lead-based paint activities," which are essentially lead assessment and abatement activities (under TSCA section 402) - EPA is also required to promulgate technical standards for lead-based paint activities, including laboratory analysis and characteristics of products used for lead-based paint activities (under TSCA section 405);
Disclosure of lead-based paint hazards, which has two components:
EPA must develop a lead hazard information pamphlet (under TSCA section 406(a)); and
EPA must require disclosure for renovation activities and sales and leases of pre-1978 target housing with the pamphlet (under TSCA section 406(b) and Paint Hazard Act section 1018); and
Renovation and remodeling activities, for which training, certification, and disclosure are all required (under TSCA sections 402(c), 406(b)).
In addition, under section 404 of TSCA, EPA may also authorize state lead hazard programs for sections 402 and 406.
HUD is authorized under the Paint Hazard Act to:
Evaluate and reduce lead-based hazards for pre-1978 federally-assisted or federally-owned housing (under the Paint Hazard Act sections 1012 and 1013);
Develop guidelines for these evaluation and reduction activities (under the Paint Hazard Act section 1017); and
Work with EPA to require disclosure of lead hazards for sales and leases of pre-1978 target housing (under the Paint Hazard Act section 1018).
Both EPA and HUD engaged in rulemaking after the enactment of the Paint Hazard Act. The two agencies first collectively issued the sale and lease disclosure rule, under section 1018 of the Paint Hazard Act, in March 1996. After issuing this rule, the agencies parted and took two separate paths to rulemaking:
EPA promulgated its TSCA section 402 lead abatement rule in August 1996. It also issued a renovation, repair and painting program rule (RRP rule) in 2008 pursuant to TSCA sections 402(c) and 406(b). EPA's disclosure rule, RRP rule, and abatement rule are collectively set forth in 40 C.F.R. Part 745. In addition to the federal regulation, forty-four jurisdictions across the U.S. have received EPA authorization to operate their own state programs (the section 404 jurisdictions).
HUD first developed its Paint Hazard Act section 1017 guideline in 1995 and then replaced it with a second edition in 2012. In 1999, HUD released a comprehensive lead-safe housing rule, which addressed the requirements under sections 1012 and 1013 and incorporated the 1996 EPA-HUD sale and lease disclosure rule. HUD's disclosure rule and the lead-safe housing rule are collectively set forth in 24 C.F.R. Part 35.
TSCA section 403 hazards are referenced in a number of these programs. For example:
Under the Paint Hazard Act section 1018 sale and lease disclosure rule, a seller or lessor of pre-1978 "target housing" must disclose known lead-based paint and lead-based paint hazards with warning statements.
Under the TSCA section 402 rule, most lead-based paint activities must be performed by certified individuals. This includes, "abatement," for example, which refers to "any measure or set of measures designed to permanently eliminate lead-based paint hazards." In the 2001 Hazard Standards, EPA noted that "permanent elimination of lead-based paint, and dust or soil lead would not require the use of certified personnel unless lead-based paint hazards are present in those media." Furthermore, any report produced after a risk assessment under the Section 402 rule must include a description of identified lead-based paint hazards. Any occupant protection plan must also describe measures and procedures to protect the building occupants from exposure to lead-based paint hazards.
In addition, in order to obtain EPA authorization for their section 404 programs, states and Indian tribes must demonstrate that their programs include standards for identifying lead-based paint hazards that are at least as protective as the federal standards.
Therefore, a change in what constitute "lead-based paint hazards" could completely change the scope of obligations in the substantive rules above, and such changes may affect federal and state programs alike.
Changes in these compliance obligations under the lead programs can bring real-world impacts, as EPA does enforce the lead-based paint rules. In both fiscal years 2016 and 2017, EPA completed over 100 enforcement actions under the RRP rule, the disclosure rule, and the abatement rule. EPA imposed over $1 million in penalties in each of these two years. In 2016, EPA settled with a major home improvement company for alleged violations of the RRP rule in renovation projects across several states. The company agreed to pay $400,000 in civil penalties and implement a corporate-wide compliance system. In 2017, a realtor in New York pled guilty to criminal violations of the lead disclosure rule and is facing potential criminal penalties.
Following the A Community Voice decision, EPA will likely initiate the rulemaking process to update the hazard standards. After the citizen groups filed their petition for mandamus, HUD updated its dust-lead hazard and clearance levels in a policy guidance document, effective April 1, 2017, which applies to grantees receiving HUD grants for lead hazard control and reduction. The new HUD dust-lead hazard levels are 10 μg/ft2 for floors and 100 μg/ft2 for window sills, which match the levels requested in the EPA rulemaking petition and Ninth Circuit litigation.
Considering the Ninth Circuit decision and HUD's action, business communities that engage in activities which have potential lead hazard implications, such as lead assessment, abatement, or cleanup, housing improvement or renovation, and realty transactions, should monitor and participate in EPA's rulemaking actions in the coming months.
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Mark N. Duvall
Timothy M. Serie
©2019 Beveridge & Diamond PC
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text:
Q: How to draw orthogonal vectors using TikZ I have the problem, that I want to draw a vector that is decomposed into two orthogonal parts. A short example:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=2pt,fill,label={#1},name=#1,color=red},
  extended line/.style={shorten >=-#1,shorten <=-#1},
  extended line/.default=1cm,scale=2]
\begin{scope}[rotate=30]
  \node [dot=A] at (1,4) {};
  \node [dot=B] at (2,2) {};
  \node [dot=P] at (4,4) {};
  \draw [->] (A) -- (B);
  \draw [->] (A) -- (P -| B);
  \draw [->] (A) -- ($(B) - (P-|B) + (A)$);
\end{scope}
\end{tikzpicture}
\end{document}

Here I have the vector AB. I want one of the component vecors to be in the direction of AP. The other should be orthogonal (as seen).
In the example I solved it using -| but this works only if the desired vectors are parallel to the actual axes. I need it for arbitrary points A, B and P.
Can you give me a hint, how to draw it?

A: Here are two styles that do what you want. You have to specify the direction AP as an argument of the style, as shown in my example.
\documentclass{minimal}

\usepackage{xcolor}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.pathreplacing}

\tikzstyle{ortho proj}=[decorate,decoration={show path construction,
lineto code={
    \draw let
    \p{O} = (\tikzinputsegmentfirst),
    \p{A} = (\tikzinputsegmentlast),
    \p{OA} = ($(\p{A})-(\p{O})$),
    \p{w} = #1,
    \n{dot} =  {\x{w}*\x{OA}+\y{w}*\y{OA}},
    \p{proj} = ($\n{dot}/(veclen(\x{w},\y{w}))^2*(\p{w})$)
    in
    (\p{O}) -- ++(\p{proj});}}]

\tikzstyle{perp proj}=[decorate,decoration={show path construction,
lineto code={
    \draw let
    \p{O} = (\tikzinputsegmentfirst),
    \p{A} = (\tikzinputsegmentlast),
    \p{OA} = ($(\p{A})-(\p{O})$),
    \p{w} = #1,
    \n{dot} =  {\x{w}*\x{OA}+\y{w}*\y{OA}},
    \p{proj} = ($\n{dot}/(veclen(\x{w},\y{w}))^2*(\p{w})$),
    \p{perp} = ($(\p{OA}) - (\p{proj})$)
    in
    (\p{O}) -- ++(\p{perp});}}]

\begin{document}

\begin{tikzpicture}

\draw[->] (0,0) -- (2,2);
\draw[ortho proj={(1.5,1)},->] (0,0) -- (2,2);
\draw[perp proj={(1.5,1)},->] (0,0) -- (2,2);

\end{tikzpicture}

\end{document}

The result is

A: I use the following sort of solution (taken from this wonderful answer):
\documentclass{minimal}
\usepackage{tikz}
\begin{document}
\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine}
\def\tikz@AngleOfLine(#1)(#2)#3{%
  \pgfmathanglebetweenpoints{%
    \pgfpointanchor{#1}{center}}{%
    \pgfpointanchor{#2}{center}}
  \pgfmathsetmacro{#3}{\pgfmathresult}%
}
\begin{tikzpicture}
 \coordinate (a) at (0.2,0.3);
 \coordinate (b) at (1.3,2.4);
 \draw[->] (a) -- (b) ;
 \tikzAngleOfLine(a)(b){\angle};
\draw[blue,->] (a) -- ++(\angle+90:2);
\draw[green,->] (a) -- ++(\angle-90:2);
\end{tikzpicture}
\end{document}

Maybe will be useful for others.

A: The projection syntax from the calc library also takes an optional angle: ($(A)!(P)!90:(B)$) is the projection of point (P) on the line from (A) to (B) after that line has been rotated 90 degrees around point (A). This makes it easy to draw the vector components:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[
    dot/.style={
        circle,
        inner sep=2pt,
        fill,
        label={#1},
        name=#1,
        color=red
    },
    scale=2]
\begin{scope}
  \node [dot=A,gray] at (1,4) {};
  \node [dot=B,gray] at (2,2) {};
  \node [dot=P] at (4,3) {};
  \node [dot=P2,cyan] at (3,2.5) {};
  \draw [->] (A) -- (B);
  \draw [->,red] (A) -- ($(A)!(B)!(P)$);
  \draw [->,red] (A) -- ($(A)!(B)!90:(P)$);
  \draw [->,cyan] (A) -- ($(A)!(B)!(P2)$);
  \draw [->,cyan] (A) -- ($(A)!(B)!90:(P2)$);
\end{scope}
\end{tikzpicture}
\end{document}

redpajama_set_name: RedPajamaStackExchange


text:
Kai-Uwe von Hassel, né le  à Gare (région du Tanga) en Afrique orientale allemande, devenue Tanzanie et mort le  à Aix-la-Chapelle en Allemagne, est un homme d'État allemand membre de l'Union chrétienne-démocrate d'Allemagne (CDU).

Né en Afrique orientale allemande, il est expulsé après la Première Guerre mondiale et devient en 1935 vendeur. Il retourne alors au Tanganyika pour y exercer son métier. Il est de nouveau expulsé en 1940 et prend part à la Seconde Guerre mondiale, en tant qu'officier du renseignement militaire.

Il adhère à la CDU en 1946. En 1954, à l'âge de 41 ans, il devient ministre-président de Schleswig-Holstein. Il occupe ce poste huit ans, à la tête de coalitions de droite, devenant le premier à exercer plusieurs mandats.

À la suite de l'affaire du Spiegel, Konrad Adenauer le choisit en 1963 comme nouveau ministre fédéral de la Défense. Maintenu en poste par Ludwig Erhard, il est nommé ministre fédéral des Expulsés par Kurt Georg Kiesinger, en 1966.

Il quitte l'exécutif en 1969, ayant été élu président du Bundestag. Il conserve ce poste jusqu'aux élections de 1972, puis exerce les fonctions de vice-président de l'assemblée. À l'occasion des élections européennes de 1979, il rejoint le Parlement européen.

Il se retire de la vie politique à l'issue de son mandat de cinq ans, à l'âge de 71 ans.

Biographie

Une jeunesse entre Afrique et Allemagne
Il est le fils de Theodor von Hassel, officier de la troupe de protection de l'Afrique orientale. En 1919, la famille est expulsée par les nouvelles autorités britanniques et décide de s'installer à Glücksburg, juste en face du Danemark.

Il passe avec succès son Abitur en 1933, puis suit pendant deux ans un apprentissage de vendeur de produits agricoles. En 1935, il retourne s'installer au Tanganyika et y exerce son métier.

La Seconde Guerre mondiale
Il est interné en 1939 à Dar-es-Salaam et de nouveau expulsé en Allemagne l'année suivante. Il s'engage alors dans la Wehrmacht et participe à la Seconde Guerre mondiale. En 1943, il est recruté par le service de renseignements de l'État-major en tant qu'interprète. Fait prisonnier de guerre en 1945, il est rapidement relâché.

Débuts en politique
Alors qu'il est devenu fonctionnaire territorial de l'arrondissement de Flensbourg, il décide de s'engager en politique et rejoint l'Union chrétienne-démocrate d'Allemagne en 1946. En 1947, il met fin à sa carrière professionnelle et se fait élire au conseil municipal de Glücksburg, devenant bourgmestre de la ville pour quatre ans. Il entre l'année d'après, en 1948, à l'assemblée d'arrondissement.

Ascension
À l'occasion des élections du , il est élu député au Landtag du Schleswig-Holstein au scrutin uninominal. Son résultat de 34,8 % est le deuxième plus mauvais de la CDU. Cette même année, il est nommé vice-président de la CDU du Land, sous la présidence de Carl Schröter.

Le , il est nommé représentant parlementaire du ministre de l'Intérieur Paul Pagel, alors que le ministre-président chrétien-démocrate Friedrich-Wilhelm Lübke vient de former son second cabinet. Il est ensuite reconduit par Lübke, successeur de Schröter, dans ses fonctions à la CDU régionale.

À l'occasion des élections fédérales du 6 septembre 1953, il se présente dans la  fédérale. Il totalise 51,4 % des voix, ce qui garantit son élection au Bundestag. Il est ensuite réélu pour un nouveau mandat au Landtag le , de nouveau avec le deuxième plus mauvais résultat des chrétiens-démocrates, à savoir 30,6 %.

Ministre-président du Schleswig-Holstein
Victime de graves problèmes de santé, Lübke renonce à se succéder. Kai-Uwe von Hassel, 41 ans, négocie la constitution d'une alliance de droite réunissant la CDU, le Bloc pan-allemand/Fédération des expulsés et réfugiés (GB/BHE) et le Parti libéral-démocrate (FDP), qui compte 40 députés sur 69.

Il est officiellement investi par le Landtag le  et démissionne du Bundestag le  suivant. Il est ensuite porté à la présidence de la CDU du Land. Le , il prend pour un an la présidence tournante du Conseil fédéral. Il décide cette même année de quitter son mandat d'élu d'arrondissement.

À l'occasion du  fédéral du parti, qui se réunit à Stuttgart, il est élu vice-président fédéral le , sous la présidence du chancelier fédéral Konrad Adenauer.

Lors des élections régionales du , il établit la domination chrétienne-démocrate sur le Land du nord de l'Allemagne de l'Ouest. Sa formation remporte 44,4 % des voix, soit 33 députés sur 69. Lui-même est réélu avec 35,5 %, soit le pire résultat d'un candidat de la CDU. Il décide d'assurer la reconduction de sa coalition, qui compte désormais 41 élus. Le GB/BHE se retire en 1959, sans mettre en danger la majorité, à la suite du passage de deux de ses membres à la CDU.

Candidat pour un troisième mandat exécutif au scrutin du , il confirme la première place de sa formation, qui obtient 45 % des voix et 34 sièges, ratant d'une voix la majorité absolue. Avec 36 % des voix dans sa circonscription, il est de nouveau le député le plus mal élu de son parti. Il envisage alors de maintenir son alliance avec les libéraux, mais ceux-ci préfèrent essayer de s'associer avec les sociaux-démocrates et le parti danois, qui refuse. Le , une semaine avant l'ouverture de la législature, les ministres FDP démissionnent et le gouvernement se retrouve chargé des affaires courantes.

Ministre fédéral
Finalement, le , Kai-Uwe von Hassel est choisi, à 49 ans, comme nouveau ministre fédéral de la Défense par Adenauer ; il prend alors la suite de Franz-Josef Strauß, compromis dans l'affaire du Spiegel, et cède le pouvoir à Kiel à Helmut Lemke, qui parvient à constituer une « coalition noire-jaune » avec les libéraux. Il quitte alors son mandat de conseiller municipal. En 1964, il laisse la présidence régionale du parti à Lemke, dont il devient vice-président. Son mandat est marqué par la mise en service, en 1965, des chars d'assaut Leopard 1 dans la Bundeswehr. Le  suivant, le nouveau chancelier fédéral Ludwig Erhard le reconduit à son poste.

Cette même année, aux élections fédérales du 3 octobre, il se présente une nouvelle fois au Bundestag, dans la nouvelle  fédérale. Il conquiert un nouveau mandat de député avec 52,2 % des suffrages, et démissionne du Landtag. Il est maintenu dans ses fonctions au sein du cabinet Erhard II, constitué le . Il autorise par la suite les soldats à avoir une activité syndicale.

Le , le ministre-président du Bade-Wurtemberg Kurt Georg Kiesinger prend la suite d'Erhard et forme une « grande coalition ». Hassel cède ses fonctions à Gerhard Schröder et prend le poste de ministre fédéral des Expulsés, des Réfugiés et des Blessés de guerre.

Cadre du Bundestag

À la suite de la démission d'Eugen Gerstenmaier le , Kai-Uwe von Hassel est choisi par le groupe CDU/CSU au Bundestag pour prendre la présidence de l'assemblée parlementaire fédérale.

Il est élu le , par 252 voix sur 456 et quitte immédiatement le gouvernement. Il est alors le premier et seul homme politique allemand à avoir présidé les deux chambres parlementaires. Les élections fédérales du 28 septembre 1969 conduisent à un changement de majorité, mais les chrétiens-démocrates conservent le premier groupe parlementaire. En conséquence, le , il est réélu président du Bundestag, par 411 suffrages sur 517. Le , alors que Rainer Barzel prend la présidence fédérale de la CDU, il n'est pas reconduit dans ses fonctions de vice-président, mais continue de siéger au bureau en tant que membre de droit.

Les élections anticipées du 19 décembre 1972 donnent au groupe SPD au Bundestag le statut de première force parlementaire. À l'ouverture de la législature, le , il est donc désigné vice-président de l'assemblée, cédant son poste à la sociale-démocrate Annemarie Renger.

De l'Europe à la fin de carrière
L'année 1975 marque le début de la fin de son parcours politique, avec son abandon de la vice-présidence de la CDU du Schleswig-Holstein. À la suite du scrutin parlementaire de 1976, ses fonctions de vice-président du Bundestag reviennent au chrétien-social Richard Stücklen.

À l'occasion des premières élections européennes directes, en 1979, il se fait élire député au Parlement européen. Il siège tout au long de son mandat au sein de la commission politique. Ne s'étant pas représenté au scrutin fédéral de 1980, il quitte la vie politique à l'issue de la législature, en 1984.

Vie privée
Il a été marié deux fois, et a été père de deux fils et d'une fille. Son fils Joachim, de son premier mariage, s'est tué dans le crash de son Lockheed F-104 Starfighter en 1970. Le , il est victime d'une crise cardiaque lors de la remise du prix international Charlemagne d'Aix-la-Chapelle et meurt à l'âge de 84 ans. Il est enterré à Bad Godesberg, dans la ville de Bonn.

Notes et références

Annexes

Bibliographie

Articles connexes
 Politique de l'Allemagne
 Schleswig-Holstein
 Cabinet von Hassel I et II
 Cabinet Adenauer V
 Cabinet Erhard I et II
 Cabinet Kiesinger

Liens externes

  Biographie sur le site du ministère fédéral de la Défense
  Liste et biographies des présidents du Bundestag

Ministre-président du Schleswig-Holstein
Ministre de la Défense de la République fédérale d'Allemagne
Ministre des Expulsés de la République fédérale d'Allemagne
Président du Bundestag
Député de la deuxième législature du Bundestag
Député de la cinquième législature du Bundestag
Député de la sixième législature du Bundestag
Député de la septième législature du Bundestag
Député de la huitième législature du Bundestag
Député européen élu en Allemagne 1979-1984
Personnalité de l'Union chrétienne-démocrate d'Allemagne
Grand-croix de l'ordre du Mérite de la République fédérale d'Allemagne
Chevalier grand-croix de l'ordre du Mérite de la République italienne
Grand-croix de l'ordre du Christ
Commandeur de l'ordre de Saint-Sylvestre
Naissance en avril 1913
Décès en mai 1997
Décès à Aix-la-Chapelle
Décès à 84 ans
Président du Bundesrat (Allemagne)

redpajama_set_name: RedPajamaWikipedia


text:
Field & Game Australia
Home News Going hunting and fishing
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Bryce Johnson is a fierce advocate of hunting, fishing and the environment. In his 37 years as head of Fish & Game New Zealand. he's been unafraid to tackle big issues and even bigger opponents.
After announcing his retirement three months ago, Bryce Johnson has kept busy while his replacement is recruited by continuing a campaign against the powerful dairy industry.
Some years ago, Fish & Game NZ started a controversial campaign calling out 'Dirty Dairying' and the threat poor agricultural practices posed to clean waterways and the environment.
"We are not anti-dairy farming. We are anti-environmentally unsustainable dairy farming; a subtle but significant difference," Bryce told delegates at a Federated Farmers Council meeting in February.
Bryce Johnson
Bryce's appearance at this and other dairy industry gatherings in the past year is testament to his tenacity and his ability to engage opponents in solving problems.
"At the time when we started it I'm sure my photo went up in a lot of cow sheds and had cow shit thrown at it every milking," he said.
Fish & Game NZ is a high-profile organisation, which is not viewed through the narrow lens of hunting and fishing: it has a much broader public role as an advocate for the natural landscape, clean water flowing rivers, access to the outdoors for all purposes.
"We have an understanding that we don't worry about whether you look at a duck through binoculars or down a shotgun barrel; we worry about the duck, the habitat and the environment," Bryce said.
"We are not out there defending wetlands we hunt on, we are defending the environment. We took a lot of hits over the dirty dairy campaign at the time and a lot of threats, but we took it up on behalf of the public, people who want clean water to swim in and to fish and hunt in."
Bryce's journey has been easier because of Fish & Game's structure.
In 1980, Bryce led Acclimatisation Societies, a hangover from early English settlers.
"These societies were set up to create a 'little bit of England' and they introduced familiar game species from the early 1800s," he said.
While similar societies in Australia had long since vanished, in New Zealand they survived (with recognition from Parliament) until 1990.
When the government of the day decided to untangle a mess of quasi-autonomous non-government organisations, Bryce Johnson saw an opportunity.
"It terrified them that they would be axed and many were. We put our hand up and said we want a review, we want to strengthen our hand in the law."
There was a seamless transition to Fish and Game Councils with a strengthened statutory mandate.
"As long as we discharge our functions to the best of our ability, the government is not in a position to tell us how to do our job," he said.
"The regional councils set the limits upon themselves but it is very much a science based process."
Hunting and fishing are culturally significant in New Zealand, and for many families, a key source of food. Anti-hunting activism is not an issue that diverts resources away from core activities.
"It has always amazed me that the Australian situation hasn't crossed the Tasman," Bryce said.
In New Zealand, too many people are still close to nature and many rely on hunting and fishing as nature's supermarket."
Bryce isn't from a hunting family although his father was a keen salt water fisherman.
"It was a godfather who introduced me to hunting with an old .22, which I inherited when he died. I was also introduced to trout fishing."
At university, in the midst of rising meat prices, Bryce saw an opportunity to fund his education.
"The meat price got a bit high for deer so I spent every weekend stalking deer and selling the meat to fund my university studies," he said.
After university, Bryce worked for the Agriculture Minister and did research on the Chukar partridge, an introduced bird that ranges high in the alps.
"I've had chances to leave and do other stuff, including enter Parliament, but I've stayed because I love it," he said.
"Clubs are for people who want to talk about fishing, Fish & Game membership is for those who want to protect habitat and maintain, manage and enhance fishing and hunting.
"Anglers and hunters have the strongest of motives to make the right decisions and people take great pride in being on their local Fish & Game Council. I admire those people who do it, that's why I've stayed here so long."
Retirement means fishing, hunting and raising a few cattle but Bryce will still be a voice for change.
"What will be great is being able do one thing at a time," he said.
August shoot results
Branch: Port Phillip Day & Date: Saturday 5th August 2017 Shoot Type: (As per Shoot Book) 75 target simulated Sponsor: Number of Shooters: 89 Weather: Very windy and cold. High Gun: Mark DuRose 70 AA: Adam DuRose 67; Gary Dimidis 67; Daryl...
June shoot results
Day & Date: Saturday 3rd June 2017 Shoot Type: (As per Shoot Book) 100 target Sporting Pairs Sponsor: Number of Shooters: 100 Weather: Fine but cool High Gun: Gary Dimidis 84 AA: Jason Barclay 80; Daryl Snowdon 80; Stuart Smith 80 A: Shaun...
March shoot results
Port Phillip - Saturday 4th March 2017 Shoot Type: 75 target simulated Number of Shooters: 67 Weather: Clear skies and windy High Gun: Daryl Snowdon 63 AA: Doug McLeod 63; Matthew Spencer 63; Andrew Opie 62 A: Ves Dubocanin 60; Nigel Loughridge 58...

redpajama_set_name: RedPajamaCommonCrawl


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Bizarre, Criminal law May 9, 2016 May 9, 2016
Massachusetts Chemist Admits To Using Drugs From Police Samples And Using Lab To Make Crack Cocaine
Sonja Farak, who worked for an Amherst laboratory which tested drug samples for police, was a popular witness in criminal trials. She however had more insight than most judges and attorneys knew. Recently, it was revealed that she not only was a drug addict but was often high on drugs, including during appearances in court. Now as many of 30,000 cases might have to be reexamined for before new trials or hearings.
Reports states that Farak was high almost every day that she worked on drug testing. She was a virtual laboratory herself of drug use — taking methamphetamines, ketamine, cocaine, LSD and other drugs. It is amazing that no one knew or took action despite her work on tens of thousands of cases from 2005-2013.
This is just the latest such scandal for the state. Roughly 40,000 cases have to be reviewed due to the actions of Annie Dookhan, who worked at a state drug lab in Boston. Dookhan was sentenced to at least three years in prison in 2013 after pleading guilty to faking test results in criminal cases.
For a drug addict, Farak, 37, hit the jackpot in a lab with a steady stream of drug samples or "standards" submitted the police. She admitted that she regularly took the drug herself.
Farak has admitted ingesting lab "standards" – drug samples used as benchmarks to test against substances submitted by police for testing. She even smoked crack before a 2012 state police accreditation inspection on the lab. She also used the lab to manufacture crack cocaine.
Farak pleaded guilty to tampering with evidence, stealing cocaine from the lab and unlawful possession in January 2014 and was sentenced to 18 months in prison.
Tourist Takes Selfie In Portugal With "Dom Sebastian" By Climbing On Ornate Arch . . . And Shatters Historic Statue
Penn Professor Thrown Off Plane After Woman Sees Him Doing Strange Notations . . . That Turn Out To Be Math Calculations
9 thoughts on "Massachusetts Chemist Admits To Using Drugs From Police Samples And Using Lab To Make Crack Cocaine"
Elmer Fudd says:
The whole story kind of cracks me up. No pun intended.
bam bam says:
I believe that the article mentioned that she used the lab to manufacture crack cocaine, as opposed to meth–regardless, I don't understand how there was a total lack of oversight, for years, where no one noticed that any drugs were going missing or that crack cocaine was being manufactured in the facility. I would be willing to bet that there are more people, as of yet, unnamed, involved in this saga.
Was she working alone in that lab? How is it that she was capable of actually manufacturing crack cocaine in the lab and no one noticed–supervisors, co-workers, police officers, etc.? Was there no oversight in these facilities? After samples are tested, who is responsible for returning these samples to the evidence room? Aren't items weighed (cocaine) and/or counted (pills) prior to and directing following these tests? Somehow, I doubt that she was a one-man-band and the only one involved in these activities.
Paul Schulte says:
bam bam – cooking meth can have explosive effects. If you can do it in a small camper trailer, you could do it in a lab, but the downside is you might blow up the lab.
Lars Vegan says:
High on Cocaine!
Casey Jones better…
Watch your speed.
Trouble ahead.
Trouble behind.
And I've got that notion that you have..
Just lost your mind.
Next witness.
Walter White never sampled the product. Just finished that incredible series[Breaking Bad] for the second time. Like all great shows, it's better the second time.
Oh, that war on drugs is working so well.
Don de Drain says:
Police first suspected her of wrongdoing when she said: "Don't meth around with me. "
I think she was high in her mug shot. She looks like a very happy camper! I foresee a lot of plea bargaining by the state.


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ED Publishes New Clery Handbook
The Jeanne Clery Act, a consumer protection law passed in 1990 amending the Higher Education Act (HEA), requires all colleges and universities that receive federal funding to share information about crime on campus and their efforts to improve campus safety with the Department of Education and the public.
In late June, the Department of Education published a revision to The Handbook for Campus Safety and Security Reporting, which provides interpretations and guidance to assist institutions in understanding and meeting the various HEA requirements. This is the first update to the handbook since 2011. Staff with Clery responsibilities are encouraged to review the handbook in its entirety.
While the handbook provides updates on previous Clery reporting elements, the most notable change is the addition of new requirements included in the Violence Against Women Act (VAWA), which includes many requirements related to dating violence, domestic violence, sexual assault, and stalking. Specifically, the changes to Clery by VAWA include:
Disclosure of statistics of the number of dating violence, domestic violence, sexual assault, and stalking incidents.
Disclosure of statistics of new categories of hate crimes.
Implementation by institutions and disclosure of programs to prevent dating violence, domestic violence, sexual assault, and stalking.
Disclosure of procedures victims should follow if one of the crimes listed above occurs.
Implementation by institutions and disclosure of procedures for institutional disciplinary action in cases of those crimes.
On July 7, The Clery Center for Security on Campus held a webinar highlighting key points in the new handbook. A recording of the webinar is available on YouTube.
Bryan Dickson
Assistant Director, Advocacy and Student Financial Services
Higher Education Community Weighs In on Proposed Title IX Overhaul
The Department of Education's recent proposal to revamp investigations of campus sexual assault is one of the most controversial that has been put forth by the Trump administration to date. NACUBO joined 60 other higher education associations to support comments submitted to the department by the American Council on Education that highlighted the proposed rule's positive aspects and areas of concern.
Title IX Senate Hearing Adds to National Discussion
As lawmakers discuss a potential new way forward in the handling of campus sexual assault, the Department of Education faces ongoing litigation and its own complex rulemaking process as it attempts to redefine Title IX rules.
What Did I Miss in Washington? April 2-15, 2019
In this edition: Congress holds hearings on HEA priorities, the FTC proposes new IT security requirements, and more.


text:
\section{Abelian Groups}

If $G$ is abelian, then no Sylow $p$-subgroup can be cyclic.  This means that if $G$ is
not a $p$-group, then it has at least $p+1$ subgroups of order $p$ and $q+1$ subgroups of
order $q$ for some distinct primes $p$ and $q$ and so at least $(p+1)(q+1) \geq 12$ non-trivial
subgroups.  So, $G$ must be a non-cyclic $p$-group.

If $G$ contains $Z_p \times Z_p \times Z_p$ then it has at least $2p^2 + 2p +4 \geq 16$ subgroups.
Consequently, $G = Z_{p^r} \times Z_{p^s}$ with $r \geq s \geq 1$.

Now, $Z_{p^2} \times Z_{p^2}$ has $p^2 + 3p + 5 \geq 15$ subgroups, so we must have $s = 1$.
Furthermore, $Z_{p^4} \times Z_p$ has $4p + 6 \geq 14$ subgroups, so $r \leq 3$.

Hence, the abelian groups with $G = \widetilde{G}$ and at most 12 subgroups are:

$r = 1$: ($p + 3$ subgroups) p = 2, 3, 5, 7

$r = 2$: ($2p + 4$ subgroups) p = 2, 3

$r = 3$: ($3p + 5$ subgroups) p = 2

\section{Non-Abelian Groups}

Now we consider non-abelian $G$.  Let $q$ be any prime dividing $|G|$.  If Sylow $q$ is not normal, there
are at least $q+1$ Sylow $q$-subgroups.  If Sylow $q$ is normal, there is a $q$-complement.  If the complement
is normal, then the Sylow $q$ cannot be cyclic (else $G \neq \widetilde{G}$) and so has at least $q+1$ maximal
subgroups. Finally, if the complement is not normal, then we have at least $q$ complements and 1 Sylow $q$.
So, in every case, with the trival subgroup and $G$, the number of subgroups is at least $q+3$.  This implies
$q \leq 9$.

??? Can $|G|$ be div by all of 2, 3, 5, and 7 ???  As below, at least 2 must be normal  and their
product has a complement with 2 primes that can have at most 3 subgroups $\Rightarrow\Leftarrow$ impossible.

Suppose $|G|$ is divisible by 3 distinct primes $p, q, r$.

If none of the Sylows are normal, we have at least $(p + 1) + (q + 1) + (r + 1) \geq 13$ subgroups,
so at least one is normal. Call it an $r$-subgroup $N$. Complementing $N$, we have a two prime group $H$ in $G$
and every subgroup of $H$ gives rise to at least two subgroups of $G$ (itself and itself times $N$).  So, $H$ has at most 6 subgroups.

???Must we have $H = \widetilde{H}$???  NO: $Z_6$ on $Z_7$.

\begin{lemma} A group $H$ divisible by 2 primes with at most 6 subgroups is either $Z_p \times Z_q,
Z_p \times Z_{q^2}$, or $S_3$.
\end{lemma}
\noindent
\begin{proof}
If $H$ is abelian, one sylow has 2 subgroups, the other 2 or 3 subgroups, so
$H = Z_p \times Z_q$ or $Z_p \times Z_{q^2}$.  If $H$ has a non-abelian sylow, the sylow has
at least 3 maximal subgroups, 1 prime order, 1 triv, 1 whole subgrp, plus the other sylow $\Rightarrow \geq 7$
subgrps, which is too many.  So both sylows of $H$ are abelian and so at least one is not normal.
Assume WLOG $p < q$.  Then there are at least p+1 non-normal sylows, one other sylow, the whole
group, and trivial $\Rightarrow \geq p+4$ subgroups.  So we must have equality on our estimate which
means, $p = 2$,  sylow 2 is not normal, $p+1$ divides $|G|$, so $q = 3$, sylow 3 is normal, sylows
have no non-trivial subgroups $\Rightarrow H = S_3$.
\end{proof}

\vspace{0.2in}
If $H$ is abelian with cyclic sylows, then neither Sylow can act trivially on $N$ or it would be
central cyclic in $G$.  Therefore $N$ cannot normalize the sylows or $H$ and so the number of
conjugates of each is at least $r$.  This gives at least $3r$ subgroups of $G$.  Furthermore we
have $G$, $N$, 1, and $N H_p$ and $N H_q$, so at least $3r + 5$ subgroups.  Consequently,
we must have $r = 2$.

Our list of subgroups includes only $N$ and 1 from subgroups of $N$.  So, if $N$ has at least 4
subgroups, then $G$ will have at least 13 subgroups.  Therefore, $N$ is cyclic of order 2 or 4.
But odd primes cannot act non-trivially on a cyclic group of order 2 or 4, so this situation is
impossible.

Last, we consider the case of $H = S_3$.  In this case, $r \geq 5$.
If $H$ acts trivially on $N$, then $N$ cannot be cyclic and so has at least 8 subgroups.  Since
$S_3$ has 6 subgroups, $G$ will have at least 48 subgroups.  So, $H$ acts non-trivially on
$N$ and a sylow 2, $H_2$, must also act non-trivally on $N$.  In particular, $N$ does not normalize $H$
or $H_2$ and, as above, this gives us at least $2r$ subgroups of $G$.  We also have $G$, $N$, and 1.
Since $r$ is at least 5, this implies $G$ has more than 12 subgroups.

Consequently, $|G|$ must be divisible by at most two primes.

\section{Groups with two primes in the order}

Suppose $|G| = p^a q^b$, $p < q$ primes and $G$ is non-abelian.

The argument for two primes is more complicated than I would like.  I'll use indentation to organize
assumptions (like in computer code).
\begin{description}
\item[If neither sylow is cyclic,] then we have $(p+1)+(q+1)$ maximals in the sylows, the two sylows and the
whole group and trivial.  That is, the number of subgroups is at least $p + q + 6$.  This can only be less
than or equal to 12 when $p = 2, q = 3$.  Furthermore, the close estimate means each sylow must be normal
and prime squared order.  That forces $G$ to be abelian $\Rightarrow\Leftarrow$.

\item[If sylow $p$ is cyclic,]\quad \\

	\begin{description}
	\item[If sylow $p$ is normal,] then the sylow $q$ cannot act non-trivially and so the sylow $p$ is cyclic
and central $\Rightarrow\Leftarrow$.
	\item[else sylow $p$ is not normal,] then the number of sylow $p$ is $\geq q$.  \\
		\begin{description}
		\item[If sylow $q$ not cyclic,] we have at least $q+1$ maximals and so at least $2q+4$ subgroups.
Again the estimate forces sylow $q$ to be $Z_3 \times Z_3$ and $p = 2$, at least 10 subgroups.
Furthermore, we cannot have 9 sylow 2's, so there is a central subgroup of order 3.
Counting again, we have whole, trivial, one 9, four 3's, three sylow 2's, three sylow 2 times central 3 $\Rightarrow \geq 13$ subgroups. $\Rightarrow\Leftarrow$
		\item[else sylow $q$ is cyclic,] then $G$ must be supersolvable since both sylows are cyclic and it follows the sylow $q$
must be normal.  Sylow $p$ must act non-trivially on $q$, so $(p,q) = (2,3), (2,5), (2,7)$, or $(3,7)$.\\
The only case where the action is not that of an element of order $p$ is when $p=2, q=5$ when $Z_4$ acts
faithfully on $Z_5$.  In this case, $G$ will have a quotient group of order 20 isomorphic to $Z_4$ acting
faithfully on $Z_5$.  Since this group has 14 subgroups, we do not need to consider such $G$.
		Therefore, we can assume the sylow $p$ acts as an element of order $p$.  The sylow $p$ fixes only the identity in sylow $q$ (only possible non-triv
action).  This means the sylow $p$ is self-normalizing and so the number of sylow $p$ subgroups is $q^b$.  Now the
subgroup of order $p^{a-1}$ centralizes the sylow $q$ and so is the intersection of the sylow $p$'s.  Hence the non-triv
$p$-subgroups are order $p, \ldots, p^{a-1}$, and $q^b$ subgroups order $p^a$.  There are $b$ non-triv $q$-subgroups
and $(a-1)\cdot b$ proper abelian subgroups divisible by $pq$.  Furthermore, for each non-triv, proper $q$-subgroup, order $q^c$, we can multiply that by the sylow $p$'s to get subgroups of order $p^a q^c$.  There will be $q^c$ different sylow $p$'s
giving the same subgroup of order $p^a q^c$ and so a total of $q^{b-c}$ such subgroups.
Consequently, the number of (non-abelian) proper subgroups
divisible by $p^a q$ will be $q + q^2 + \cdots + q^{b-1} = (q^b - q)/(q-1)$.
Including trivial and whole group, the number of subgroups is:
$$
(a-1 + q^b) + b + (a-1)b + \frac{q^b - q}{q-1} + 2 = q^b + \frac{q^b - q}{q-1} + a(b + 1) + 1.
$$
The corresponding values are shown in the following tables.

\qquad\begin{tabular}{|c c|c|c|}
\hline
\multicolumn{4}{|c|}{$q = 3$}\\
\hline
&\multicolumn{3}{c|}{$b$}\\
& &1&2\\
\cline{2-4}
&1&6&16\\
\cline{2-4}
$a$&2&8&19\\
\cline{2-4}
&3&10&22\\
\cline{2-4}
&4&12&25\\
\cline{2-4}
&5&14&28\\
\hline
\end{tabular}
\begin{tabular}{|c c|c|c|}
\hline
\multicolumn{4}{|c|}{$q = 5$}\\
\hline
&\multicolumn{3}{c|}{$b$}\\
& &1&2\\
\cline{2-4}
&1&8&34\\
\cline{2-4}
$a$&2&10&37\\
\cline{2-4}
&3&12&40\\
\cline{2-4}
&4&14&43\\
\hline
\end{tabular}
\begin{tabular}{|c c|c|c|}
\hline
\multicolumn{4}{|c|}{$q = 7$}\\
\hline
&\multicolumn{3}{c|}{$b$}\\
& &1&2\\
\cline{2-4}
&1&10&60\\
\cline{2-4}
$a$&2&12&63\\
\cline{2-4}
&3&14&66\\
\hline
\end{tabular}

Since the $q = 7$ table applies to both $p = 2$ and $p = 3$ we see there are 11 groups with at most 12
subgroups in this case.\\

		\end{description}

	\end{description}
	\item[else sylow $p$ is not cyclic,] and so sylow $q$ must be cyclic and not central.

	\begin{description}
	\item[If neither sylow is normal,] then number of sylow $p$ is at least $q$ and the
number of sylow $q$ is at least $q+1$.  Including trivial and whole, we have at least
$2q + 3$ subgroups, which means $q < 5$ and so we have $q = 3, p = 2$.
We have at least three sylow 2's and at least four sylow 3's, triv, whole, and one
sylow 2 will contain three subgroups of order 2.  However, that's already 12 subgroups
and we have more order 2 subgroups in the other sylow 2's. $\Rightarrow\Leftarrow$
	\item[If sylow $p$ is normal,] then it cannot be cyclic, else it would be central.  Furthermore,
$Z_p \times Z_p \times Z_p$ has too many subgroups, so the sylow $p$ must be a two-generator
group.  So, the sylow $p$ has $p+1$ maximal subgroups, there are at least $q+1$ sylow $q$'s
and with sylow $p$ itself, triv, and whole, we have at least $p + q + 5$ subgroups.  If $p \geq 3$,
this is too many, so we must have $p = 2$.  If $q \geq 5$, then our count gives at least 12 subgroups.
The only way to avoid going over 12 would be to have the sylow $p$ be $Z_2 \times Z_2$, sylow
$q$ be $Z_5$.  But $Z_5$ has no non-trivial action on $Z_2 \times Z_2$, and so we are left
only with the case $p = 2, q = 3$, and at least 10 subgroups.  Now, the alternating group
$A_4$ satisfies these conditions and has 10 subgroups.  If sylow 3 has order larger than 3, then
there will be a central 3-subgroup whose product with the various 2-subgroups will give more
than 12 subgroups.  So, the sylow 3 must be order 3.  If sylow 2 has order larger than 4, then
the frattini subgroup of the sylow 2 and the frattini subgroup times the various sylow 3-subgroups give more
than 12 subgroups.  So, $A_4$ is the only group in this case.
	\item[If sylow $q$ is normal,] we are already assuming the sylow $q$ is cyclic.
Furthermore, the sylow $p$ is not normal and not cyclic.  So we have at least $q$ sylow $p$'s and
the sylow $p$'s have at least $p+1$ maximal subgroups.
		\begin{description}
		\item[If two sylow $p$'s have a common maximal subgroup, $M$,] then the normalizer of $M$ will contain
at least two sylow $p$-subgroups of $G$ and so must be divisible by $q$.  Thus the intersection of the normalizer with
the sylow $q$-subgroup is a non-trivial central $q$ subgroup.
Therefore, our subgroups include $q$ sylow $p$'s, $q$ sylow $p$'s times the central $q$, at least $p+1$ maximal
subgroups of sylow $p$, each of those $p+1$ times the central $q$,
the sylow $q$, the central $q$, triv, and whole for at least $2q +2p + 6 \geq 16$ subgroups. $\Rightarrow\Leftarrow$
		\item[else no shared maximal subgroups,] which means we have at least $q(p+1)$ maximal subgroups of sylow $p$'s
altogether.  Therefore we have at least  these $q(p+1)$ subgroups, $q$ sylow $p$-subgroups, one sylow $q$, triv, and whole.
That is, $qp +2q + 3 \geq 15$ subgroups. $\Rightarrow\Leftarrow$

		\end{description}

	\end{description}
\end{description}

Hence, the non-abelian groups with $G = \widetilde{G}$, $|G|$ divisible by at least two primes, and at most 12 subgroups are:

$Z_p \ltimes Z_q$: ($q+3$ subgroups) $(p, q)$ = (2, 3), (2, 5), (2, 7), or (3, 7)

$Z_{p^2} \ltimes Z_q$ with action of order $p$: ($q+5$ subgroups) $(p, q)$ = (2, 3), (2, 5), (2, 7), or (3, 7)

$Z_8 \ltimes Z_q$ with action of order 2: ($q+7$ subgroups) $q$ = 3 or 5

$Z_{16} \ltimes Z_3$ with action of order 2: (12 subgroups)

$A_4$: (10 subgroups)

\section{$p$-Groups}

Finally, we have the case of $G$ a non-abelian $p$-group, $|G| = p^n$.

The group $Z_p \times Z_p \times Z_p$ has  at least 16 subgroups, so $G$ must be a two-generator group.
Consequently, we have $G$, $p+1$ maximals, the Frattini subgroup, and triv $\Rightarrow \geq p+4$ subgroups.

When $p$ is odd we will have at least $p+1$ order $p$, one of which might be the Frattini, so we'd have
at least $2p+4 \Rightarrow p$ = 2 or 3.

Assume $|G'| = p$ and $Z(G)$ cyclic.  Then $G' \subset Z(G)$ and for $x,y \in G$, $[x^p,y] = [x,y]^p = 1$
so $x^p$ is central and $\Phi(G) \subset Z(G)$.  Now $|G: \Phi(G)| = p^2$ and so we must have $\Phi(G) = Z(G)$
is cyclic order $p^{n-2}$.

If $G$ has a single subgroup of order $p$, then $p = 2$ and $G$ is generalized quaternion.  Now, each generalized
quaternion 2-group contains the next smaller as a subgroup.  So, we can just check: $Q_8$ has 6 subgroups,
$Q_{16}$ has 11 subgroups, and $Q_{32}$ has 20.  That is, $G$ must be $Q_8$ or $Q_{16}$.

Otherwise, $G$ has more than one subgroup of order $p$ and so we can choose $S \subset G$ with $S$ order p and
not in the center.  Then $M = S Z(G)$ is an abelian subgroup isomorphic to $Z_p \times Z_{p^{n-2}}$.  From the
abelian case above, we see that the number of subgroups of $M$ is given in the following table.

\qquad\begin{tabular}{|c c|c|c|c|}
\hline
&\multicolumn{4}{c|}{$n$}\\
& &3&4&5\\
\cline{2-5}
$p$&2&5&8&11\\
\cline{2-5}
&3&6&10&14\\
\hline
\end{tabular}

In addition to the subgroups in $M$, $G$ also has $p$ other maximal subgroups, and $G$ itself.  So, increasing
each table entry by $p+1$ we see the only possibilities for at most 12 subgroups are $|G|$ = 8, 16, or 27.

By brute force check we find for order 8 the dihedral group $D_8$ with 10 subgroups, for order 16 a group with presentation $\langle a, b|a^2, b^8, b^a = b^5 \rangle$
having 11 subgroups, and
for order 27 the extraspecial group of exponent 9 with 10 subgroups.

Thus we have found five groups with $|G'| = p$ and cyclic center.  Now any non-abelian finite $p$-group will
have such a group as a homomorphic image.

Note that no generalized quaternion group can have a smaller generalized quaternion group as a homomorphic image.
One easy way to see this is to note that $Q_n/Z(Q_n) = D_{n/2}$ and any non-abelian image of a dihedral group will have more
than one involution.  We will use this fact several times below.

Suppose $|G| = 3^5$ and choose $K$ maximal such that $\overline{G} = G/K$ is non-abelian.  It follows that
$\overline{G}$ will have $|\overline{G}'| = 3$ and $Z(\overline{G})$ cyclic.  If $|K| \leq 3$, it follows from
above that $\overline{G}$, and so $G$, will have more than 12 subgroups.  If $|K| = 3^2$, then $|\overline{G}| = 3^3$
and so must be the extraspecial group of exponent $3^2$.  Thus, $\overline{G}$ has 10 subgroups.  The only way
we could have at most 12 subgroups in $G$ is if $K$ is cyclic and every subgroup either contains $K$ or is order 3
or 1 in $K$.  However, this implies that $G$ has only one subgroup of order 3, which is impossible.  Consequently, no
non-abelian 3-group of order at least $3^5$ can have at most 12 subgroups.  We know from above that there is
only one such group of order $3^3$ and a computer check shows that there are no examples of order $3^4$ (these
groups have at least 14 subgroups).

Now suppose $|G| = 2^6$ and choose $K$ maximal such that $\overline{G} = G/K$ is non-abelian.  As above,
$\overline{G}$ will have $|\overline{G}'| = 2$ and $Z(\overline{G})$ cyclic.  If $|K| \leq 2$, it follows from
above that $\overline{G}$, and so $G$, will have more than 12 subgroups.
  If $|K| = 2^2$, then $|\overline{G}| = 2^4$
and so we see from above that $\overline{G}$ is one of two groups each of which have 11 subgroups.  Since $K$
has at least 2 proper subgroups, $G$ must have 13 or more subgroups.  Finally, consider $|K| = 2^3$.  Then $\overline{G}$
must be $D_8$ or $Q_8$ with 10 or 6 subgroups respectively.  Since $K$ has at least 3 proper subgroups, $\overline{G}$ cannot be $D_8$ and so must be $Q_8$ with 6 subgroups.  Even if all of the subgroups of $G$ either contained $K$ or were
contained in $K$, then $K$ would have to have at most 7 subgroups (6 proper).  However, the only groups of order $2^3$
with 7 or fewer subgroups are $Z_8$ and $Q_8$.  Since each of these have a single subgroup of order 2, our
assumption would force $G$ to be generalized quaternion, which it clearly is not.  Thus we see that no non-abelian 2-group
of order at least $2^6$ can have number of subgroups less than or equal to 12.  A computer check shows there are
no examples of order $2^5$ (these groups have at least 14 subgroups) and only the two groups mentioned above for
order $2^4$.

Hence, the non-abelian $p$-groups with $G = \widetilde{G}$ and at most 12 subgroups are:

$D_8$: (10 subgroups)

$Q_8$: (6 subgroups)

$Q_{16}$: (11 subgroups)

$Z_2 \ltimes Z_8$: (11 subgroups)

$E_{27}$ extraspecial order 27, exponent 9: (10 subgroups)

\section{Conclusion}

Collecting all of our results, we have:

\qquad\begin{tabular}{c|l}
$n$&Groups with $G = \widetilde{G}$ and $n$ subgroups\\
\hline
1&Trivial group\\
2&\\
3&\\
4&\\
5&$Z_2 \times Z_2$\\
6&$Z_3 \times Z_3$, $S_3$, $Q_8$\\
7&\\
8&$Z_2 \times Z_4$, $Z_5 \times Z_5$, $D_{10}$, $Z_4 \ltimes Z_3$\\
9&\\
10&$Z_3 \times Z_9$, $Z_7 \times Z_7$, $D_{14}$, $A_4$, $Z_3 \ltimes Z_7$, $Z_4 \ltimes Z_5$, $Z_8 \ltimes Z_3$, $E_{27}$\\
11&$Z_2 \times Z_8$, $Q_{16}$, $Z_2 \ltimes Z_8$\\
12&$Z_4 \ltimes Z_7$, $Z_9 \ltimes Z_7$, $Z_8 \ltimes Z_5$, $Z_{16} \ltimes Z_3$\\
\end{tabular}

In particular the sequence of the number of groups with $G = \widetilde{G}$ and $n$ subgroups would be:
$$
1, 0, 0, 0, 1, 3, 0, 4, 0, 8, 3, 4, \ldots
$$

Forming the direct product with a coprime, cyclic group of order $p^k$ will multiply the number of subgroups by $k+1$.
Thus we find groups with $n$ subgroups corresponding to various factorizations of $n$.

\begin{tabular}{c|l}
$n$&Similarity class representatives with $n$ subgroups\\
\hline
1&Trivial group\\
2&$Z_2$\\
3&$Z_{2^2}$\\
4&$Z_{2^3}$, $Z_2 \times Z_3$\\
5&$Z_{2^4}$, $Z_2 \times Z_2$\\
6&$Z_{2^5}$, $Z_2 \times Z_{3^2}$, $Z_3 \times Z_3$, $S_3$, $Q_8$\\
7&$Z_{2^6}$\\
8&$Z_{2^7}$, $Z_2 \times Z_{3^3}$, $Z_2 \times Z_3 \times Z_5$, $Z_2 \times Z_4$, $Z_5 \times Z_5$, $D_{10}$, $Z_4 \ltimes Z_3$\\
9&$Z_{2^8}$, $Z_{2^2} \times Z_{3^2}$\\
10&$Z_{2^9}$, $Z_2 \times Z_{3^4}$, $Z_2 \times Z_2 \times Z_3$, $Z_3 \times Z_9$, $Z_7 \times Z_7$, $D_{14}$, $A_4$, $Z_3 \ltimes Z_7$, $Z_4 \ltimes Z_5$, $Z_8 \ltimes Z_3$, $E_{27}$\\
11&$Z_{2^{10}}$, $Z_2 \times Z_8$, $Q_{16}$, $Z_2 \ltimes Z_8$\\
12&$Z_{2^{11}}$, $Z_2 \times Z_{3^5}$, $Z_3 \times Z_3 \times Z_2$, $S_3 \times Z_5$, $Q_8 \times Z_3$,
$Z_{2^2} \times Z_{3^3}$, $Z_2 \times Z_3 \times Z_{5^2}$, $Z_4 \ltimes Z_7$,\\
&\qquad $Z_9 \ltimes Z_7$, $Z_8 \ltimes Z_5$, $Z_{16} \ltimes Z_3$\\
\end{tabular}

In the following version of the previous table we represent classes using $p, q, r$ to represent primes which do not
occur anywhere else in the group order.  This makes it a bit easier to recognize the infinite classes.

\begin{tabular}{c|l}
$n$&Similarity classes with $n$ subgroups\\
\hline
1&Trivial group\\
2&$Z_p$\\
3&$Z_{p^2}$\\
4&$Z_{p^3}$, $Z_p \times Z_q$\\
5&$Z_{p^4}$, $Z_2 \times Z_2$\\
6&$Z_{p^5}$, $Z_p \times Z_{q^2}$, $Z_3 \times Z_3$, $S_3$, $Q_8$\\
7&$Z_{p^6}$\\
8&$Z_{p^7}$, $Z_p \times Z_{q^3}$, $Z_p \times Z_q \times Z_r$, $Z_2 \times Z_4$, $Z_5 \times Z_5$, $D_{10}$, $Z_4 \ltimes Z_3$\\
9&$Z_{p^8}$, $Z_{p^2} \times Z_{q^2}$\\
10&$Z_{p^9}$, $Z_p \times Z_{q^4}$, $Z_2 \times Z_2 \times Z_p$, $Z_3 \times Z_9$, $Z_7 \times Z_7$, $D_{14}$, $A_4$, $Z_3 \ltimes Z_7$, $Z_4 \ltimes Z_5$, $Z_8 \ltimes Z_3$, $E_{27}$\\
11&$Z_{p^{10}}$, $Z_2 \times Z_8$, $Q_{16}$, $Z_2 \ltimes Z_8$\\
12&$Z_{p^{11}}$, $Z_p \times Z_{q^5}$, $Z_3 \times Z_3 \times Z_p$, $S_3 \times Z_p$, $Q_8 \times Z_p$,
$Z_{p^2} \times Z_{q^3}$, $Z_p \times Z_q \times Z_{r^2}$, $Z_4 \ltimes Z_7$,\\
&\qquad $Z_9 \ltimes Z_7$, $Z_8 \ltimes Z_5$, $Z_{16} \ltimes Z_3$\\
\end{tabular}

In conclusion, the sequence of number of similarity classes with a given number of subgroups begins:
$$
1, 1, 1, 2, 2, 5, 1, 7, 2, 11, 4, 11, \ldots
$$

Note: In \cite{Miller}, Miller lists the groups with specified number of subgroups where the number of subgroups runs from 1 through 9.  His lists agree with ours.

\begin {thebibliography}{9}
\bibitem{Miller}
G.A. Miller, Groups having a small number of subgroups,
\textit{Proc. Natl. Acad. Sci. U S A},
 vol. 25 (1939) 367--371.

\bibitem {Slat}
M.C. Slattery, On a property motivated by groups with a specified number of subgroups, \textit{Amer. Math. Monthly}, vol. 123 (2016) 78--81.

\bibitem {Slat2}
M.C. Slattery, Editor's End Notes, \textit{Amer. Math. Monthly}, vol. 123 (2016) 515.

\bibitem{OEIS}
N.J.A. Sloane, The on-line encyclopedia of integer sequences, \texttt{http://oeis.org}.
\end {thebibliography}

\end{document}

redpajama_set_name: RedPajamaArXiv


Gallhammer was born in 2002 in the Vivian Slaughter's mind, who wanted to form a band based in the atmosphere and darknes of Hellhammer.
The remaining components, Reaper and Mika joined Vivian in 2003, even they didn't know how to play their instruments, as both had been vocalists in their former bands.
Vivian was the vocalist in a grindcore act and had played the saxophone in a noise band. Risa sang in a group of Avant-garde, and Mika sang in a rock band. In March 2003, Gallhammer had already recorded a tape, whith only 30 copies given as gifts in their debut gig at Koiwa Death Fest. In these first concerts Gallhammer included in the setlist Hellhammer and Amebix songs, the main influences of the trio.
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After traveling around Tokyo in 2005, in 2006 finally came the contract with Peaceville Records. With the contract it came "The Dawn Of .." a compilation that included a DVD with a show in Okayama and several home videos of gigs in Tokyo.
The debut album in Peaceville, "Ill Innocence", was released in the middle of 2007, after which Gallhammer went to tour Europe. As a result, it was released a DVD entitled "Ruin Of A Church," recorded at Colchester Arts Center, a venue located in a church in ruins.


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text:
Q: Web2Py: Not track changes between modules I have two modules that work together.
For example, I have user.py and email.py. user.py have a function to verify a register and email.py have a function to send a email of confirmation. I import in controller user.py, and user.py import email.py.
with:
from gluon.custom_import import track_changes
track_changes(True)

I detect changes in user.py, but not in email.py. I tried to put track_changes also in user.py and it doesn't work.
Are there something that I can do without restart server/web2py?
Web2Py: 2.16.1-stable+timestamp.2017.11.14.05.54.25 (I try with *.exe and *.py)
OS: Windows 10 Pro
Thanks!

A: web2py uses a custom importer that first attempts to import a module via the standard Python built-in method and then looks in the application's /modules folder only if the built-in method fails. Only modules found via this custom import process are trackable.
Because user.py has already been imported and email.py is in the same folder as user.py, the Python built-in import method knows to look in the same folder for the email module when it encounters import email within the user.py file. As a result, the web2py custom import process does not kick in, and the module is therefore not tracked.
I suppose this behavior could be changed, but for now, that's how it works, so your second import will not be tracked.

A: I had a lot of problems with Modules not being reimported after I had made changes. track_changes never worked for me. In the end i added this to my db.py file.
import importlib
import sys
# Now import all your modules
import Common
importlib.reload(sys.modules['Common'])

This has worked well for me. I understand it should be removed when it goes to production.


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text:
'Stumptown' Spotlights Female Veterans And Indigenous Women; Cobie Smulders Addresses Character's Bisexuality – Comic-Con
'Mulaney' Order Trimmed To 13 Episodes
Fox has trimmed the order for new comedy series Mulaney by three episodes, from 16 to 13. The network made the call after two airings, as the series just wrapped filming Episode 13 and was about to go into production on Episode 14.
The multi-camera Mulaney had an unusual 16-episode order as Fox originally picked up 6 episodes last October and then ordered additional 10 in May when the net opted not not to pick up any of its comedy pilots to series. While no 2014 Fox comedy pilots went to series, the network has four straight-to-series half-hour shows for this season, Mulaney as well as live-action Last Man on Earth and Weird Loners and animated Bordertown.
Related: 'Mulaney' Off To Weak Start: Ratings Rat Race
Mulaney garnered mixed reviews and got off to a slow star in the ratings, opening to a 1.0 among adults 18-49 in Live+Same Day. The comedy posted a rare Week 2 growth, inching up by 10% to a 1.1 rating despite its lead-in slipping from a 1.9 for an original Family Guy to a 1.7 for a repeat last week. While the 1.1 rating is still on the low side, that is higher than another Fox series, returning The Mindy Project (1.0), logged the last two weeks. It has a 15-episode third season order.
If Mulaney had opened big, Fox would've likely accommodated a larger order. Faced with a limited inventory for midseason with three more comedies in the can, Fox opted to stick with the amount of Mulaney episodes it needs. The series will continue to air in its regular Sunday 9:30 PM slot.
Mulaney