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text:
• Colorado • Denver • Hiking
Hankins Pass Trail No. 630
Pike & San Isabel National Forests Cimarron & Comanche National Grasslands
19316 Goddard Ranch Ct.
Morrison, CO 80465
Trailhead Elevation:
Elevation Range:
8200 feet to 10000 feet
Elevation Change:
Summer to Fall
From the Goose Creek Trailhead, hike downhill to a footbridge across Hankins Gulch. Just across the creek the Hankins Pass Trail heads west, while the Goose Creek Trail goes east (right). Climbing at first up through a forested valley, the trail eventually reaches a series of open meadows surrounded by aspen groves. The trail from here to the pass is very gorgeous in late September when the aspen leaves are changing color. At the top of Hankins Pass is a junction with the Lake Park Trail. That trail heads north (right) toward Lake Park, while the Hankins Pass Trail begins it's descent to the west.
The grade on the west side of the pass is quite a bit steeper than the gradual rise up to the pass from the east. After a short descent, the trail reaches the wilderness boundary and the junction with the Lizard Rock Trail. The Lizard Rock Trail leads south to the Spruce Grove Campground, while the Hankins Pass Trail continues down in a northwesterly direction to its end at the junction with the Brookside-McCurdy Trail. If you head south from this junction on Brookside-McCurdy Trail you will reach the Twin Eagles Trailhead.
8200 feet to 10000
The Hankins Pass Trail is the southernmost trail in the Lost Creek Wilderness. From the east, the trail gives the hiker a gradually rising climb up Hankins Gulch through dense forest to pleasant open meadows and aspen groves. From the junction with the Lake Park Trail at the top of Hankins Pass, the trail drops down the west side of the Tarryall Mountains to a junction with the Lizard Rock Trail coming up from the Spruce Grove Trailhead, and then continues to descend to meet the Brookside-McCurdy Trail.
The trail is easy to follow and heads in a general westerly direction. There are horse corrals near the Goose Creek Trailhead that are available for public use. There are a number of campsites between the trailhead and Hankins Pass. However, there are few areas suitable for camping west of the pass due to the steep gradient of the trail. Because the trail is entirely in designated wilderness, Wilderness regulations apply.

redpajama_set_name: RedPajamaCommonCrawl


Home Page / Home / Comedy News / Steve Harvey Announces Retirement From Stand Up!
Steve Harvey Announces Retirement From Stand Up!
In a news item that we meant to post yesterday, comedian and radio show host Steve Harvey announced on his radio show that he would be retiring from doing stand up. He stated that his last performance would be at the next Hoodie Awards, (annually held in Las Vegas) and that he would bless the stage one last time.
This really comes as no surprise as Harvey has taken on many gigs, from hosting his radio show to also hosting the new season of Family Feud. We still stand by our prediction that when the day time talk show he is in preproduction on begins to air that he will retire from his radio gig.
See JB Smoove & Method Man In 'The Sitter'!
DL Hughley Disappears From New York Radio Station Kiss-FM!
Comedic Actress & Host Niecy Nash Gets Married!


text:
Sara Davis Buechner
Get FREE Tickets
Sunday March 3, 2019 @ 3PM
Sunday, March 3, 2019 @ 3PM
FREE Bronx Piano Sundays
Virtuoso pianist and transgender shero!
Noted for her musical command, cosmopolitan artistry, and visionary independence, Sara Davis Buechner is one of the most original concert pianists of our time. Lauded for her "intelligence, integrity and all-encompassing technical prowess" (New York Times), "thoughtful artistry in the full service of music" (Washington Post), and "astounding virtuosity" (Philippine Star). A standout afternoon concert program will feature music by New Orleans composer Louis Moreau Gottschalk (1829-1869), Cuban-Spanish composer Joaquín María Nin-Culmell (1908-2004), Sara's own music, plus Danzas of the beloved Puerto Rican composer Juan Morel Campos (1857-1896). The artist wishes to dedicate her concert to the ongoing recovery of all artists in Puerto Rico — donations to Pregones/PRTT's #MásPorPuertoRico are encouraged!
FREE CONCERT — Seating is limited, RESERVE NOW!
In her twenties Ms. Buechner earned a bouquet of top prizes at the world's premiere international piano competitions — Queen Elisabeth (Brussels), Leeds, Mozart (Salzburg), Beethoven (Vienna), and Sydney. She was a Bronze Medalist of the 1986 Tschaikowsky Competition in Moscow and the Gold Medalist of the 1984 Gina Bachauer International Piano Competition.
Ms. Buechner has performed in every state and province of North America — as recitalist, chamber musician and soloist with top orchestras like the New York Philharmonic, San Francisco Symphony and Philadelphia Orchestra; and in venues such as Carnegie Hall, the Kennedy Center and the Hollywood Bowl. She has toured throughout Latin and South America and Europe; and she enjoys a special following in Asia, where she has been a featured soloist with the Sydney Symphony, New Zealand Philharmonic, New Japan Philharmonic and Shanghai Philharmonic, among many others.
She has commissioned and premiered important contemporary scores by composers such as Michael Brown, John Corigliano, Ray Green, Dick Hyman, Vitězslavá Kaprálová, Jared Miller, Joaquín Nin-Culmell, and Yukiko Nishimura. Ms. Buechner's performance versatility extends to unique collaborations with film and dance (including tours with the Mark Morris Dance Group, and Japanese kabuki-mime-mask dancer Yayoi Hirano).
Ms. Buechner has released numerous acclaimed recordings of rare piano music by composers such as Rudolf Friml ("a revelation" — The New York Times), Dana Suesse, Joseph Lamb, Joaquín Turina, Miklós Rózsa, and Ferruccio Busoni (including the world première recording of the Bach-Busoni "Goldberg" Variations). Stereophile magazine selected her Gershwin CD as "Recording of the Month," and her interpretation of Hollywood Piano Concertos won Germany's coveted Deutsches Schauplatten Preis. Most recently her recorded traversal of the score to Carl Dreiser's silent movie classic Master of the House (1925) may be heard on Criterion Collection DVD.
Sara Davis Buechner joined the faculty of Temple University's Boyer College of Music and Dance in 2016, after previously teaching at the Manhattan School of Music, New York University and the University of British Columbia. She has presented masterclasses and workshops at major pedagogic venues worldwide, adjudicated important international piano competitions, and is also a contributing editor for Dover Publications International. In 2017 Ms. Buechner marked her 30th year as a dedicated Yamaha Artist.
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text:
\section{Introductory remarks}
\label{sec:intro}
\noindent

For a finite set $V$ let   $\mathrm{Sym}(V)$ and  $\mathrm{Alt}(V)$
denote the corresponding symmetric group
and alternating group on $V$. (Of course, if $|V|=n$ the
standard notations $S_n$, $A_n$ apply.)
Let $G\le \mathrm{Sym}(V)$ be a permutation group acting on a set $V$.
Two elements $g,h\in G$
are said to be {\em intersecting} if $g(v) = h(v)$ for some $v \in V$.
Furthermore, a subset ${\cal F}$ of $G$ is an {\em intersecting set}
if every pair of elements of ${\cal F}$ is intersecting.
The {\em intersection density} $\rho({\cal F})$ of the intersecting set ${\cal F}$
is defined to be the quotient
$$
\rho({\cal F})=\frac{|{\cal F}|}{\max_{v\in V}|G_v|},
$$
and the {\em intersection density} $\rho(G)$ of a group $G$,
 first defined by Li, Song and Pantangi in \cite{LSP},
is the maximum value of
$\rho({\cal F})$ where ${\cal F}$ runs over all intersecting sets in
$G$, that is,
$$
\rho(G)=\max\{\rho({\cal F})\colon {\cal F}\subseteq G, {\cal F} \textrm{ is intersecting}\} = \frac{\max\{|{\cal F}| \colon {\cal F}\subset G\textrm{ is intersecting}\}}{\max_{v\in V}|G_v|}.
$$
Observe that, since $G_v$ is an intersecting set in $G$,
we have $\rho(G)\ge 1$.
Observe also that for  a transitive group $G$
acting on a set $V$ we have $\rho(G)= 1$
if and only if
the maximum cardinality of the intersecting set is $|G|/|V|$, in which case
we say that $G$ has the {\em Erd\"os-Ko-Rado property} or
{\em EKR-property} in short.
Moreover, $G$ has the {\em strict-EKR-property} if
the canonical intersecting sets are the only maximum intersecting sets of $G$,
where a {\em canonical} intersecting set is an intersecting set of the form
$gG_v$, $v\in V$ and $g\in G$.

Following \cite{MRS21} we define ${\cal I}_n$ to be the set
of all intersection densities of transitive permutation groups
of degree $n$, that is,
$$
{\cal I}_n=\{\rho(G) \mid G\textrm{ transitive of degree } n\},
$$
and we let $I(n)$ to be the maximum value in ${\cal I}_n$.

Motivation for this paper comes from \cite[Conjectures~6.(3) and {\color{red}6.}(4)]{MRS21}
and \cite[Question~7.1]{R21}.

\begin{conjecture}
\label{conj:pk} {\rm\cite[Conjecture~6.6(3)]{MRS21}}
 If $n$ is a prime power, then $I(n)=1$.
\end{conjecture}

\begin{conjecture}
\label{conj:2p} {\rm\cite[Conjecture~6.6(4)]{MRS21}}
 If $n=2p$ where $p$ is a prime, then $I(n)=2$.
\end{conjecture}

Conjecture~\ref{conj:2p} is settled in \cite{R21},
where an additional  problem regarding the possible values of
intersection densities in ${\cal I}_{2p}$ was posed.

\begin{question}
\label{que:2p}
{\rm \cite[Question~6.1]{R21}}
Does there exist an odd prime $p$ and a transitive group $G$ of degree $2p$
such that $\rho(G)$ is not an integer?
\end{question}

In this paper we settle Conjecture~\ref{conj:pk} and
give a negative answer
to Question~\ref{que:2p} by obtaining
a complete classification of intersection densities of transitive groups
of degree twice a prime.

\begin{theorem}
\label{the:main2}
For a transitive permutation group $G$ of prime power degree
the intersection density $\rho(G)$ is equal to $1$.
\end{theorem}

\begin{theorem}
\label{the:main3}
Let $G$ be a transitive permutation group of degree $2p$, where $p$ is a prime.
Then the intersection density $\rho(G)$ is  either  $1$ or $2$. More precisely, $\rho(G)=2$ if and only if either
\begin{enumerate}[(i)]
\itemsep=0pt
\item $G\cong K\rtimes H$ acting on a set $V=\{x_i\colon i\in\mathbb{Z}_p\}\cup\{y_i\colon i\in\mathbb{Z}_p\}$
where $K\le E\cap \mathrm{Alt}(V)$,
$E\cong\mathbb{Z}_2^p$ is an elementary abelian $2$-group
generated by the involutions $\epsilon_i=(x_i\ y_i)$, $i\in\mathbb{Z}_p$,
and $H=\langle (x_0\ x_1\ \ldots \ x_{p-1})(y_0\ y_1\ \ldots\  y_{p-1}) \rangle\cong\mathbb{Z}_p$,
or
\item $G\cong A_5$ acting on a $10$-element set of pairs
of $\{1,2,3,4,5\}$.
\end{enumerate}
\end{theorem}

\section{Preliminaries}
\label{sec:pre}
\noindent

\subsection{(Im)primitivity of transitive permutation groups}
\label{ssec:definition}
\noindent

Let $G$ be a
transitive permutation group $G$ acting on a set $V$.
A partition ${\cal{B}}$ of $V$ is called $G$-{\em invariant}
if the elements of $G$ permute the parts, the so called
{\em blocks} of ${\cal{B}}$, setwise.
If the trivial partitions $\{V\}$ and $\{\{v\}: v \in V\}$
are the only
$G$-invariant partitions of $V$, then $G$ is {\em primitive},
and is {\em imprimitive} otherwise.
In the latter case the corresponding
$G$-invariant partition will be referred to as the
{\em complete imprimitivity block system} of $G$.
We say that $G$ is {\em doubly transitive} if given any two ordered pairs
$(u,v)$ and $(u',v')$ of  elements $u,v,u',v'\in V$, such that $u\ne v$ and $u'\ne v'$,
there exists an element  $g\in G$ such that $g(u,v)=(u',v')$.
Note that a doubly transitive group is primitive.
A primitive group which is not doubly transitive is called {\em simply primitive}.

The following result about normalizers of Sylow $p$-subgroups
in doubly transitive groups of prime degree will be needed
in the proof of Theorem~\ref{the:main3}.

\begin{lemma}\label{lem:prime}
Let $G$ be a doubly transitive group of prime degree $p$.
Then a Sylow $p$-subgroup $P$ of $G$
is strictly contained in its normalizer $N_G(P)$.
\end{lemma}

\begin{proof}
Let $G$ be a doubly transitive group of prime degree $p$
acting on a set $V$.
Consider the action of $G$ on the set $\cal{P}$ of all Sylow $p$-subgroups
of $G$ by conjugation. By Sylow theorems this action is transitive
with $N=N_G(P)$ as the corresponding stabilizer of $P$.
If $N=P$ then the intersection of any two stabilizers
of this action is trivial, and so $G$  acts on $\cal{P}$ as Frobenius group.
It follows that $G$ contains a regular normal subgroup $T$ of order
$|{\cal P}|\equiv {1\pmod p}$.
Now consider the action of $T$ on the set $V$. Since $T$ is a normal
subgroup of a transitive group $G$ of prime degree it follows that $T$
is transitive on $V$, a contradiction since $|T|$ is not divisible by $p$.
\end{proof}

\subsection{Derangement  graphs}
\noindent

The intersection density of a permutation group can be studied via
{\em derangements}, that is,  fixed-point-free elements of
$G$.
Let ${\cal D}$ be the set of all derangements
of a permutation group $G$. Then following \cite{MRS21}
we define the {\em derangement graph} of $G$
to be the graph $\Gamma_G=\hbox{{\rm Cay}}(G,{\cal D})$ with vertex set $G$
and edge set consisting of all pairs $(g,h)\in G\times G$ such that
$gh^{-1}\in {\cal D}$. Therefore $\Gamma_G$ is the Cayley graph of $G$
with connection set ${\cal D}$, which is a loop-less simple graph
since ${\cal D}$
does not contain the identity element of $G$ and
${\cal D}$ is inverse-closed. In the terminology of the
derangement graph an intersecting set of $G$ is an
independent set or a coclique of $\Gamma_G$.
Since, by a classical theorem of Jordan \cite[Th\'eor$\grave{e}$me~I]{J72},
a transitive permutation group $G$ on a finite set $V$
of cardinality at least $2$
contains   derangements, we have $\rho(G)<|V|$.
(Note also, that by a theorem of Fein, Kantor and Schacher \cite[Theorem 1]{FKS81}, every transitive permutation group contains a derangement of prime power order.)

The following classical upper bound on the size of the largest coclique in vertex-transitive graphs turns out to be very useful when considering the intersection densities of  permutation groups. Namely,
the derangement graph $\Gamma_G$ of a permutation group $G$
is always vertex-transitive.

\begin{proposition}
\label{pro:coclique}
{\rm \cite{GM16}}
Let $\Gamma$ be a vertex-transitive graph.
Then the largest coclique in $\Gamma$ is of size  $\alpha(\Gamma)$
bounded by
$$
\alpha(\Gamma)\le\frac{|V(\Gamma)|}{\omega(\Gamma)},
$$
where $\omega(\Gamma)$ is the size of a maximum clique in $\Gamma$.
\end{proposition}

\subsection{Intersection density of transitive groups}
\noindent

\begin{proposition}
\label{pro:1}
Let $G$ be a transitive permutation group  and ${\cal{F}}$ an intersecting
set of $G$. Then there exists an intersecting
set ${\cal{F}}'$ suh that $|{\cal{F}}|=|{\cal{F}}'|$ and $1\in {\cal{F}}'$.
\end{proposition}

\begin{proof}
Take an element $f\in {\cal{F}}$ and let ${\cal{F}}'=f^{-1}{\cal{F}}$.
Then $1\in{\cal{F}}'$ and since for $g_1,g_2\in{\cal{F}}$ the element
$f^{-1}g_1(f^{-1}g_2)^{-1}=f^{-1}g_1g_2^{-1}f$
is not a derangement (as it is a conjugate of a non-derangement)
we can conclude that ${\cal{F}}'$ is an intersecting set of $G$.
\end{proof}

The following observation regarding intersection density of doubly transitive permutation groups was made in \cite{MRS21}.

\begin{proposition}
\label{pro:2-transitive}
{\rm \cite[Lemma~2.1(3)]{MRS21}}
If $G$ is doubly transitive permutation group then $\rho(G)=1$.
\end{proposition}

The following result proved in \cite{MRS21} shows that it suffices to consider
minimal transitive subgroups when searching for the maximum value of ${\cal I}_n$.

\begin{proposition}
\label{pro:minimal}
{\rm \cite[Lemma~6.5]{MRS21}}
If $H\le G$ are transitive permutation groups then
$\rho(G)\le \rho(H)$.
\end{proposition}

\begin{proposition}
\label{pro:semiregular}
Let $G$ be a transitive permutation group acting on a set $V$
and containing a semiregular subgroup $H$
with $k$ orbits on $V$. Then $\rho(G)\le k$.
In particular, if $H$ is regular then $\rho(G)=1$.
\end{proposition}

\begin{proof}
Since $H$ is semiregular it follows that
for any two different elements $g,h\in H$
the element $gh^{-1}\in H$ is semiregular.
This implies that $H\subseteq V(\Gamma_G)$
induces a clique in $\Gamma_G$ of size $|H|$. Consequently,
Proposition~\ref{pro:coclique} implies that
$$
\alpha(\Gamma_G)\le\frac{|V(\Gamma_G)|}{|H|}=\frac{|G|}{|H|},
\ \
\textrm{ and so }
\ \
\rho(G)=\frac{\alpha(\Gamma_G)}{|G_v|}\le \frac{|G|}{|H||G_v|}=\frac{|V|}{|H|}=k.
$$
If $H$ is regular (that is, if $k=1$) then the above inequality
gives $\rho(G)\le 1$. But as observed in the introduction the intersection
density is at least $1$ for any permutation group, and so
we conclude that in this case $\rho(G)=1$.
\end{proof}

By the above proposition every transitive permutation group
admitting a regular subgroup has EKR-property.
Trivial examples of permutation groups with the
strict-EKR-property are  regular permutation groups.
Observe  that a
transitive permutation group $G$ admitting a regular subgroup
of index $2$ also has the strict-EKR-property.
Namely, if ${\cal{F}}$ is a maximal intersecting set of $G$  containing $1$
and $f\in {\cal{F}}\setminus\{1\}$, then $f$ fixes a point $v$, and therefore $\{1,f\}=G_v$
(since stabilizers have order $2$).
This shows that every generalized dihedral group has the strict-EKR-property.
The same idea cannot be generalized to cases where $G$ has a regular subgroup of index greater than 2. For example, consider $G=A_4$ acting on $\{1,2,3,4\}$. Then $G$ has the EKR-property, as it admits a regular subgroup $\{id,(1\,2)(3\,4),(1\,3)(2\,4),(1\,4)(2\,3)\}\cong\mathbb{Z}_2\times\mathbb{Z}_2$ of index 3. However, $G$ does not have the strict-EKR-property since $\{id,(1\,3\,2),(1\,4\,2)\}$ is a maximum non-canonical intersecting set.

In the example below we show that the action of $S_4$ on $2$-element subsets of $\{1,2,3,4\}$ has the EKR-property but not the strict-EKR-property, while the action of $A_4$ on the same set does not have the EKR-property.

\begin{example}\label{ex:EKR}
{\rm
Let $G=S_4$ acting on the set of all $2$-element subsets of $\{1,2,3,4\}$. Observe that $B=\{\{1,2\},\{3,4\}\}$ is a block of size $2$ for $G$ that induces a complete imprimitivity block system ${\cal{B}}$ with $3$ blocks of size $2$. The kernel of the action of $G$ on ${\cal{B}}$ is $K=\{id,(1\,2)(3\,4),(1\,3)(2\,4),(1\,4)(2\,3)\}$. Observe that $\{id,(1\, 2\, 3\, 4), (1\, 3\, 2), (1\, 4\, 2), (1\, 2\, 4\, 3)\}$ is a clique of size 5 in the derangement graph $\Gamma_G$.
It follows that $\alpha(\Gamma_G)\leq |V(\Gamma_G)|/\omega(\Gamma_G)\leq 24/5$, and since $\alpha(\Gamma_G)$ is an integer, we have
$\alpha(\Gamma_G)\leq 4=|G_v|$. This shows that $G$ has the EKR-property, that is, $\rho(G)=1$. Observe that $K$ is an intersecting set of size $4$ which is not canonical, and so $G$ does not have the strict-EKR-property.

Also, since $K\le A_4$ it follows that
the action of $H=A_4$ on the set of all $2$-element subsets of $\{1,2,3,4\}$
has an intersecting set of size $4$, and so $H$
does not have the EKR-property. In fact $\rho(H)=2$.

}
\end{example}

\section{Transitive groups of prime power degree $p^k$}
\label{sec:2p}
\noindent

The next lemma about intersection densities of transitive permutation groups
admitting imprimitivity block systems arising from semiregular subgroups will be used in the proofs of the main results of this paper.

\begin{lemma}\label{lem:semiq}
Let $G$ be a transitive permutation group
admitting a semiregular subgroup $H$ whose orbits form
a $G$-invariant partition
${\cal{B}}$, and  let ${\overline{G}}$ be the permutation group
induced by the action of $G$ on ${\cal{B}}$.
Then $\rho(G)\leq \rho({\overline{G}})$.
\end{lemma}

\begin{proof}
Let $G$ be a transitive permutation group acting on a set $V$.
Let $K=\textrm{Ker}(G\to {\overline{G}})$ be the kernel of the action of $G$ on ${\cal{B}}$,
and let ${\cal{F}}$ be an intersecting set of $G$.
We claim that
\begin{eqnarray}
\label{eq:p}
|{\cal{F}} \cap gH| \leq 1 \textrm{ for every $g\in G$}.
\end{eqnarray}
Let $x,y\in {\cal{F}} \cap gH$. Then $x=gh_1$ and $y=gh_2$
for some $h_1,h_2 \in H$, and $xy^{-1}=g(h_1h_2^{-1})g^{-1}$. Since $x,y\in {\cal{F}}$, it follows that $xy^{-1}$ fixes a point. On the other hand, $xy^{-1}$ is a conjugate of an element $h_1h_2^{-1}\in H$,
and thus since $H$ is semiregular, it follows that $h_1=h_2$, implying that $x=y$, proving (\ref{eq:p}).

We now show that $\overline{{\cal{F}}}=\{\overline{f}\mid f \in F\}$ is an intersecting set of ${\overline{G}}$.  Let $f,g\in {\cal{F}}$. Then $fg^{-1}$ fixes a point $v$, and hence $\overline{fg^{-1}}=\overline{f} \overline{g}^{-1}$ fixes the block of ${\cal{B}}$ that contains $v$, and so $\overline{{\cal{F}}}$ is indeed
an intersecting set of ${\overline{G}}$.

Let $\overline{f}\in \overline{{\cal{F}}}$ and let $[\overline{f}]=\{g\in {\cal{F}} \mid \overline{g}=\overline{f}\}$ be the set of all those elements in ${\cal{F}}$ whose
image under the homomorphism $G\to{\overline{G}}$ is equal to $\overline{f}$.
Of course, $[\overline{f}]\subseteq fK$. Writing $fK$ as a union of $|K\colon H|$ cosets of $H$, and using (\ref{eq:p}), it follows that $[\overline{f}]$ contains at most one element from each of the cosets of $H$, that is, $|[\overline{f}]|\leq |K|/|H|$. Since
$$
{\cal{F}}=\bigcup_{\overline{f}\in \overline{{\cal{F}}}} [\overline{f}]
\textrm{ it follows that }
|{\cal{F}}| \leq \frac{|K||\overline{{\cal{F}}}|}{|H|}.
$$

Now $\overline{{\cal{F}}}$ being  an intersecting set of ${\overline{G}}$, implies that
$|\overline{{\cal{F}}}| \leq \rho({\overline{G}}) \cdot |{\overline{G}}_B|$ for  $B\in {\cal{B}}$.
Since ${\overline{G}}$ is a transitive permutation group of degree $\frac{|V|}{|H|}$
we have that $|{\overline{G}}_B|=\frac{|{\overline{G}}||H|}{|V|}$, and so
$$
|{\cal{F}}| \leq \frac{|K|}{|H|}\cdot|\overline{{\cal{F}}}| \leq  \frac{|K|}{|H|}\cdot \rho({\overline{G}})
\cdot|{\overline{G}}_B|=\frac{|K|}{|H|}\cdot \rho({\overline{G}}) \cdot \frac{|{\overline{G}}||H|}{|V|}=\rho({\overline{G}})\cdot  \frac{|K||{\overline{G}}|}{|V|}=\rho({\overline{G}})\cdot |G_v|.
$$
Hence $|{\cal{F}}|/|G_v|\le \rho({\overline{G}})$, and
since ${\cal{F}}$ is an arbitrary intersecting set of $G$, it follows that $\rho(G)\leq \rho({\overline{G}})$.
\end{proof}

\begin{proofT2}
Let $G$ be transitive permutation group of degree $p^k$, where $p$ is
a prime and $k\ge 1$, acting on a set $V$.
Let $P$ be a Sylow $p$-subgroup of $G$ of order  $|P|=p^m$.
Then, by \cite[Theorem~3.4]{W64}, $P$ is transitive on $V$.
In view of Proposition~\ref{pro:minimal} we only need to show that
$\rho(P)= 1$.

The proof will be by  induction on $|P|=p^m$. If $m=1$, it follows that $P$ is regular, hence $\rho(P)=1$ by Proposition~\ref{pro:semiregular}. Suppose that $m>1$, and that intersection density of every transitive $p$-group of order less than $p^m$ is equal to 1.
By a well-known result on $p$-groups,
the center $Z=Z(P)$ of  $P$ is non-trivial.
Observe that,  since $G$ acts faithfully on $V$, the group
$Z$ is semiregular on $V$. Moreover, $Z$ is a normal subgroup of $P$, hence the orbits of $Z$ form a $P$-invariant partition. Let $Q$ be the permutation group induced by the action of $P$ on the orbits of $Z$. Then $Q$ is a transitive $p$-group of order less than $|P|$, hence by the induction hypothesis $\rho(Q)=1$. Applying Lemma~\ref{lem:semiq} it follows that $\rho(P)\leq \rho(Q)=1$, hence $\rho(P)=1$.
\end{proofT2}

\section{Transitive groups of degree $2p$}
\label{sec:2p}
\noindent

The intersection density of transitive permutation groups of
degree $2p$, $p$ a prime, has first been addressed in \cite{MRS21},
with the partial answer that this density is at most $2$
given in \cite{R21} (see Proposition~\ref{pro:AMC}).
Its proof
relies on the fact that a transitive permutation group of degree $2p$,
$p$ prime, is either doubly transitive, in which case
Proposition~\ref{pro:2-transitive} implies that  its
intersection density equals 1, or it contains a derangement
of order $p$, in which case the corresponding derangement graph
contains a clique of size $p$, and so
Proposition~\ref{pro:coclique} applies
to get that its intersection density is at most $2$.

\begin{proposition}
\label{pro:AMC}
{\rm \cite[Theorem~1.10]{R21}
Let $G$ be transitive permutation group of degree $2p$,
$p$ a prime, then $\rho(G)\le 2$.}
\end{proposition}

Transitive permutation groups of degree $2p$, $p$ a prime,
have received a considerable attention over the
last decades, mostly within the context of vertex-transitive graphs
(see  \cite{I1,I2,I3,I4,DM81,S72,W56}).
Such a group is doubly transitive, simply primitive or it admits a
complete imprimitivity block system consisting of blocks of size $2$ or $p$.
By Proposition~\ref{pro:2-transitive}  the intersection density of
doubly transitive permutation groups is equal to $1$.
By the classification of finite simple groups (CFSG)
the only simply primitive groups of degree twice a prime
are the groups
$A_5$ and $S_5$ acting on the set of pairs of a $5$-element set,
see \cite{LS}.
(It would be of interest to produce a CFSG-free proof of this fact.)

Whereas simply primitive groups and groups admitting a
complete imprimitivity block system consisting of blocks of size $p$
are dealt with directly in the proof of Theorem~\ref{the:main3}, some
preliminary observations are needed for groups admitting a
complete imprimitivity block system with
blocks of size $2$.
So let $G$ be a transitive permutation group acting on the set
$V=\{x_0,\ldots,x_{p-1},y_0,\ldots,y_{p-1}\}$ with
complete imprimitivity block system ${\cal{B}}$ with blocks $\{x_i,y_i\}$ of size $2$.
We denote by ${\overline{G}}=G/{{\cal{B}}}$ the permutation group induced by the
action of $ G$  on ${\cal{B}}$,
that is, for each $g\in G$ its induced action on ${\cal{B}}$ is denoted by
$\overline{g}$.
In this induced action the block $\{x_i,y_i\}$ is identified
with $i$ for each $i\in \mathbb{Z}_p$.

\begin{lemma}
\label{lem:blocks of size 2 induced action solvable}
Let $p$ be a prime and
$G$ be a transitive permutation group of degree $2p$
acting on a set $V$ and having a
complete imprimitivity block system ${\cal{B}}$  with blocks
of size $2$ such that
the kernel $K=\textrm{Ker}(G\to {\overline{G}})\ne 1$
and  the induced action ${\overline{G}}=G/{{\cal{B}}}$ is not doubly transitive.
Then $\rho(G)=1$ unless
${\overline{G}}$ is cyclic and $K\le\textrm{Alt}(V)$,
in which case $\rho(G)=2$.
\end{lemma}

\begin{proof}
Let $K=\textrm{Ker}(G\to {\overline{G}})$. If $K$ contains an odd permutation
then it is easy to see that $G$ contains a cyclic regular subgroup.
It follows that $\rho(G)=1$ by Proposition~\ref{pro:semiregular}.
We may therefore assume that $K\le \textrm{Alt}(V)$.

Suppose first that ${\overline{G}}$ is cyclic. Then $|G|=|K||{\overline{G}}|=p|K|$.
Since $K\le \textrm{Alt}(V)$, $K$ contains no derangement,
and so $K$ is an intersecting set.
Since $|K|=2|G_v|$ it follows  that $\rho(G)\geq 2$,
and so, by Proposition~\ref{pro:AMC}, $\rho(G)=2$.

Suppose now that ${\overline{G}}$ is not cyclic. Since ${\overline{G}}$ is not doubly transitive group
of degree $p$, it follows that ${\overline{G}}= \langle a \rangle \rtimes \langle b \rangle \cong \mathbb{Z}_p\rtimes \mathbb{Z}_d$ for some divisor $d\geq 2$ of $p-1$, where
we assume that $b$ fixes $0$ and has all other cycles
of length $d$ in its cycle decomposition.
Let ${\cal{F}}$ be an intersecting set of $G$. By Proposition~\ref{pro:1}
we may assume that $1\in {\cal{F}}$, and so no element of ${\cal{F}}$ is a derangement.
In particular, every element of ${\cal{F}}$ must fix at least one block in ${\cal{B}}$, and so we can express ${\cal{F}}$ as a union of disjoint sets
$$
{\cal{F}}=({\cal{F}} \cap K) \cup {\cal{F}}_0 \cup {\cal{F}}_1 \cup \ldots \cup {\cal{F}}_{p-1},
$$
where ${\cal{F}}_i=\{f\in {\cal{F}}\mid  fix(\overline{f})=\{i\}\}$. Namely,
for $k\in K$ we have $fix(\overline{k})=\mathbb{Z}_p$, whereas
a non-identity element of
${\overline{G}}\cong \mathbb{Z}_p\rtimes \mathbb{Z}_d$ can have at most one fixed point.
Consequently an element of $G$ can belong to at most one of the sets ${\cal{F}}_i$.

Suppose that ${\cal{F}}_i\neq \emptyset$, for some $i\in \mathbb{Z}_p$.
Since no element of ${\cal{F}}$ is a derangement
it follows that for each $f\in{\cal{F}}_i$ we have $fix(f)=\{x_i,y_i\}$.
Let $\sigma\in G$ be such that $\overline{\sigma}=b$.
In particular,  $\sigma\notin K$, and $\overline{\sigma}$ fixes only the block
$\{x_0,y_0\}$ and is of order $d$.
Consequently, either $fix(\sigma)=\emptyset$ or $fix(\sigma)=\{x_0,y_0\}$.
We may  assume that $fix(\sigma)=\{x_0,y_0\}$ for
if $fix(\sigma)=\emptyset$ we can multiply $\sigma$ with an element of $k\in K$ interchanging $x_0$ and $y_0$
(such an element exists since $K\neq 1$), and so $\overline{\sigma k}=b$
and $fix(\sigma k)=\{x_0,y_0\}$.
Choose  $\pi\in G$ in such a way that $\overline{\pi}=a$, and let
$f_i=\pi^i \sigma \pi^{-i}$.
Then $fix(f_i)=\{x_i,y_i\}$ and $fix(\overline{f_i})=\{i\}$. Let $K_i=\{k\in K\mid x_i,y_i \in fix(k)\}$.

\medskip
\noindent
{\sc Claim 1:} ${\cal{F}}_i\subseteq f_iK_i\cup f_i^2K_i \cup \ldots \cup f_i^{d-1}K_i$, for every $i\in \mathbb{Z}_p$.
\medskip

\noindent
Let $f\in {\cal{F}}_i$ be arbitrary. Then $fix(\overline{f})=\{i\}$, which
 together with the fact that ${\overline{G}}\cong \mathbb{Z}_p\rtimes \mathbb{Z}_d$
implies that $\overline{f}\in \langle \overline{f_i} \rangle$.
Therefore $\overline{f}=\overline{f_i}^t$ for some $t\in \mathbb{Z}_d$, and so
$\overline{f_i^{-t}f}=1$ in ${\overline{G}}$. Hence
$f_i^{-t}f \in K$, and so $f\in f_i^tK$.
Since $f$ is not contained in $K$ we therefore have
$f=f_i^tk$ for $t\ne 0$ and  $k\in K$.
Observe that $f$ as an element of ${\cal{F}}_i$ must have
a fixed point, and so $fix(f)=\{x_i,y_i\}$. Consequently, since
 $fix(f_i)=\{x_i,y_i\}$ it follows that
$k$ must also fix $x_i$ and $y_i$. This implies that
$f=f_i^tk\in f_i^tK_i$, completing the proof of Claim 1.

\medskip
\noindent
{\sc Claim 2:} If ${\cal{F}}\cap f_i^tK_i \neq \emptyset$ (with $i\in\mathbb{Z}_p$ and $t\in \mathbb{Z}_d\setminus\{0\}$), then ${\cal{F}}\cap f_j^tK_j = \emptyset$ for  $j\in \mathbb{Z}_p\setminus\{i\}$.
\medskip

\noindent
Let $f=f_i^tk_i\in {\cal{F}}\cap f_i^tK_i$ for some $k_i\in K_i$, and let
$g=f_j^tk_j\in {\cal{F}}\cap f_j^tK_j$ for some $j\in \mathbb{Z}_p$ and $k_j\in K_j$. Since ${\cal{F}}$ is an intersecting set, it follows that $fg^{-1}$ has a fixed point.
Since $K$ is normal in $G$ we have
that $fg^{-1}=f_i^tk_ik_j^{-1}f_j^{-t}=f_i^tf_j^{-t}k$ for some $k\in K$.
Consequently, $\overline{fg^{-1}}=\overline{f_i^tf_j^{-t}}$. Observe that $f_i^tf_j^{-t}= (\pi^i f_0^t \pi^{-i})(\pi^j f_0^{-t} \pi^{-j})=(\pi^i f_0^t \pi^{-i}) \pi^{j-i}(\pi^i f_0^{-t}\pi^{-i})\pi^{i-j}$, which implies that
$\overline{f_i^tf_j^{-t}}$ belongs
to the commutator subgroup $[{\overline{G}},{\overline{G}}]$ of ${\overline{G}}$. But
$[{\overline{G}},{\overline{G}}]=\langle \overline{\pi} \rangle=\langle a \rangle$.
By assumption $fg^{-1}$ is not a derangement, and so
it follows that $\overline{fg^{-1}}=1$, that is, $\overline{f}=\overline{g}$.
Recall that $fix(\overline{f})=fix(\overline{f_i^t})=\{i\}$ and $fix(\overline{g}))=fix(\overline{f_j^t})=\{j\}$.
It follows that $i=j$, completing the proof of Claim 2.

\medskip
\noindent
{\sc Claim 3:} If exactly $m$ of the sets ${\cal{F}}_i$ are non-empty, then $|{\cal{F}}\cap K|\leq \frac{|K|}{2^m}$.
\medskip

\noindent
Let $W=\{i\in \mathbb{Z}_p\mid {\cal{F}}_i\neq \emptyset\}$ and let $|W|=m$.
Let $f\in {\cal{F}}\cap K$ be arbitrary and take  $g\in {\cal{F}}_i$, $i\in W$.
Since $g$ is not a derangement we have that $fix(g)=\{x_i,y_i\}$.
But by assumption $gf^{-1}$ must fix a point, and so $fix(gf^{-1})=\{x_i,y_i\}$. Consequently, $f$ must also fix $x_i$ and $y_i$.
This shows that ${\cal{F}}\cap K\leq K_i$ for every $i\in W$.
It follows that ${\cal{F}} \cap K \leq \cap_{i\in W}K_i=K_{(W)}$,
where $K_{(W)}=\{k\in K\mid k(x_i)=x_i \textrm{ for  every } i\in W\}$.
It is easy to see that $|K_{(W)}|=\frac{|K|}{2^m}$, and so
$|{\cal{F}}\cap K|\leq \frac{|K|}{2^m}$, proving Claim 3.

\medskip

In the rest of the proof we  distinguishing two cases.
If ${\cal{F}}_i=\emptyset$ for every $i\in \mathbb{Z}_p$ then
${\cal{F}}\subseteq K$, and so $|{\cal{F}}|\leq |K|\leq \frac{|K|\cdot d}{2}=|G_v|$,
where the second inequality holds since $d\geq 2$.
We conclude that $\rho(G)=1$.

Suppose now that
${\cal{F}}_i\neq \emptyset$ for some $i\in \mathbb{Z}_p$.
Recall that ${\cal{F}}=({\cal{F}} \cap K) \cup {\cal{F}}_0 \cup {\cal{F}}_1 \cup \ldots \cup {\cal{F}}_{p-1}$.
By Claim 1 it follows that
\begin{eqnarray*}
{\cal{F}}\subseteq ({\cal{F}}\cap K) &\cup &  ({\cal{F}} \cap (f_0K_0\cup f_1K_1\cup \ldots \cup f_{p-1}K_{p-1}))\\
&\cup & ({\cal{F}} \cap  (f_0^2K_0\cup f_1^2K_1\cup \ldots \cup f_{p-1}^2K_{p-1}))\\
&\ldots & \\
&\cup & ({\cal{F}} \cap  (f_0^{d-1}K_0\cup f_1^{d-1}K_1\cup \ldots \cup f_{p-1}^{d-1}K_{p-1})).
\end{eqnarray*}
Claim 2 implies that $|{\cal{F}} \cap  (f_0^tK_0\cup f_1^tK_1\cup \ldots \cup f_{p-1}^tK_{p-1})|\leq |f_i^tK_i|=|K_i|=|K|/2$.
Therefore $|{\cal{F}}|\leq |{\cal{F}}\cap K|+(|K|/2)(d-1)$.
Since  at least one of the sets ${\cal{F}}_i$ is non-empty, Claim 3 implies
that $|{\cal{F}}\cap K|\leq \frac{|K|}{2}$. Consequently,
$|{\cal{F}}|\leq \frac{|K|}{2}\cdot d=|G_v|$, and so $\rho(G)=1$. Completing the proof of Lemma~\ref{lem:blocks of size 2 induced action solvable}.
\end{proof}

\begin{corollary}\label{cor:strict-EKR}
Let $G$ be a transitive group
of degree $2p$ acting on a set $V$ that admits a
complete imprimitivity block system ${\cal{B}}$  with blocks
of size $2$ such that
the kernel $K=\textrm{Ker}(G\to {\overline{G}})\ne 1$
and  ${\overline{G}}=G/{{\cal{B}}}\cong \mathbb{Z}_p\rtimes \mathbb{Z}_d$ is not doubly transitive.
If $K\le Alt(V)$ then $G$ has EKR-property if and only if $d>1$ and $G$ has the strict-EKR-property if and only if $d>2$.
\end{corollary}

\begin{proof}
The claim regarding EKR-property follows directly from Lemma~\ref{lem:blocks of size 2 induced action solvable}, since $G$ has EKR-property if and only if $\rho(G)=1$.
If $d=2$ then $F=K$ is a maximum intersecting set which is not canonical, implying that $G$ does not have the strict-EKR-property.

Suppose that $d>2$. Then $|K|<|G_v|$, hence a maximum intersecting set cannot be contained in $K$. From the proof of Lemma~\ref{lem:blocks of size 2 induced action solvable}, it follows that the size of an intersecting set ${\cal{F}}$ is at most $\frac{|K|}{2^m}+\frac{|K|}{2}(d-1)$, where $m$ is the number of sets ${\cal{F}}_i$ (defined in the proof of Lemma~\ref{lem:blocks of size 2 induced action solvable}) that are non-empty.
Observe that $\frac{|K|}{2^m}+\frac{|K|}{2}(d-1)=\frac{d|K|}{2}=|G_v|$ if and only if $m=1$.
It follows that a maximum intersecting set ${\cal{F}}$ equals $K_i\cup f_iK_i \cup \ldots \cup f_i^{d-1}K_i=G_{x_i}$, implying that $G$ has the strict-EKR-property.
\end{proof}

\begin{remark}
\label{remark:strong-EKR}
{\rm
Note that Example~\ref{ex:EKR} is the special case of the situation described in Corollary~\ref{cor:strict-EKR} with
$p=3$, $d=2$, $|K|=4$ for $S_4$ and $p=3$, $d=1$, $|K|=4$ for $A_4$.
}
\end{remark}

The following result, which can be extracted from
\cite[Theorem~6.2]{DM81}
and \cite[Lemma~3.4]{MP01}, will be needed in the proof
of Theorem~\ref{the:main3}.

\begin{proposition} \label{pro:DM2}
{\rm \cite[Lemma~3.4]{MP01}}
Let $G$ be a transitive permutation group of degree
$2p$, $p$ a prime, admitting  a complete imprimitivity block system ${\cal{B}}$
with blocks of size $2$. Then either $G$ also admits blocks of size $p$,
or for any pair $B,B'\in{\cal{B}}$ there exists
$g\in K=\textrm{Ker}(G\to {\overline{G}})$ fixing $B$ pointwise and $B'$ setwise but not pointwise.
\end{proposition}

We are now ready to prove the main result of this paper.

\medskip

\begin{proofT3}
Let $p$ be an odd prime, $V$ a set of cardinality $2p$ and
$G$ a transitive permutation
group acting on $V$.
Since every transitive permutation group
of degree $mp$, where $m\le p$,
contains an $(m,p)$-semiregular element (see, for example,
 \cite[Theorem~3.6]{DM81}) it follows that $G$ contains a
$(2,p)$-semiregular automorphism $\pi$.
Let $P=\langle\pi\rangle$ and let $O$ and $O'$ be the two orbits of $P$.
Applying Proposition~\ref{pro:semiregular} for
the semiregular subgroup $P$ we
conclude that $\rho(G)\le 2$ (see also Proposition~\ref{pro:AMC}).

Suppose first that $G$ is primitive.
Then by CFSG either $G$ is doubly transitive
or $p=5$ and $G$ is isomorphic to $A_5$ or $S_5$
acting on a $10$-element set of pairs of $\{1,2,3,4,5\}$.
In the first
case $\rho(G)=1$ by Proposition~\ref{pro:2-transitive}.
As for the second
case it was calculated in \cite{R21} that $\rho(G)=2$ if $G=A_5$
and   $\rho(G)=1$ if $G=S_5$. In fact it can be seen
that for $G=A_5$
every subgroup $A_4\le A_5$ gives rise to an intersecting set
of cardinality $12$, forcing $\rho(G)=2$.
On the other hand, if $G=S_5$ then in the associated derangement graph
a clique of size $10$ is obtained from the union of a Sylow $5$-subgroup
and the coset of this subgroup containing an element of order $4$
normalizing this subgroup (see also the more general argument
in the next paragraph).

Suppose now that $G$ is imprimitive with ${\cal{B}}$ as the corresponding
complete imprimitivity block system.
Clearly, ${\cal{B}}$ either consists of two blocks of size $p$ or
$p$ blocks of size $2$.
In the first case ${\cal{B}}=\{O,O'\}$,
and Lemma~\ref{lem:semiq} implies that
$\rho(G)\le \rho({\overline{G}})=1$ where ${\overline{G}}\cong S_2$ is the
induced action of $G$ on ${\cal{B}}$.

We may therefore assume that ${\cal{B}}$ consists of blocks of size $2$
and that, furthermore, $G$ admits no blocks of size $p$.
Then, by Proposition~\ref{pro:DM2},
the kernel $ K=\textrm{Ker}(G\to {\overline{G}})$ is non-trivial.
If ${\overline{G}}$ is not doubly transitive, the result follows
by Lemma~\ref{lem:blocks of size 2 induced action solvable}.
Namely,  in this case the condition that
${\overline{G}}$ is cyclic and that $K\le \textrm{Alt}(V)$ is equivalent
to part (i) of Theorem~\ref{the:main3}.
If ${\overline{G}}$ is doubly transitive then,
by Lemma~\ref{lem:prime},
a Sylow $p$-subgroup $\bar{P}$
of ${\overline{G}}$ is strictly contained in $N=N_{{\overline{G}}}(\bar{P})$.
Consequently, the  preimage $H$ of $N$ under the homomorphism
$G\to {\overline{G}}$ is a transitive permutation group of degree $2p$
satisfying the assumptions of Lemma~\ref{lem:blocks of size 2 induced action solvable}. Since $\overline{H}=N$ is not cyclic it follows that
$\rho(H)=1$.
Now Proposition~\ref{pro:minimal} implies that $\rho(G)=1$, too,
completing the proof of Theorem~\ref{the:main3}.
\end{proofT3}

redpajama_set_name: RedPajamaArXiv


A method for preventing overheating of a diesel particulate filter during regeneration when an engine is idling may include using an electric machine to apply a load to the engine and compensating for the increase in applied load by increasing an engine torque set point to reduce the concentration of Oxygen in the exhaust gas flowing to the diesel particulate filter. Increased engine torque may be provided by adjusting air-fuel ratio by enriching an air-fuel mixture supplied to the engine and the diesel particulate filter. The control may be initiated in response to entering an idle mode during regeneration or in response to a measured or estimated temperature of the diesel particular filter exceeding a threshold or limit. Estimated temperature may be predicted using a soot combustion model.
1. A method of controlling a vehicle having an electric machine and a diesel particulate filter (DPF) coupled to an engine, comprising: in response to a DPF temperature exceeding a threshold during regeneration of the DPF while the engine is in idle mode, operating, by a controller, the electric machine in a generator mode to increase engine load and adjusting fueling to the engine to compensate for the engine load increase.
2. The method of claim 1 wherein adjusting the fueling to the engine comprises reducing an air-fuel ratio to increase richness of an air-fuel mixture supplied to the DPF.
3. The method of claim 1 further comprising checking engine speed to confirm that the engine is operating in the idle mode.
4. The method of claim 1 further comprising using a soot combustion model to predict the DPF temperature within the DPF.
5. The method of claim 1 further comprising measuring the DPF temperature using a temperature sensor to measure one of a temperature within the DPF and a temperature of exhaust gas exiting the DPF.
6. The method of claim 1 wherein the electric machine comprises an integrated starter-generator.
7. A vehicle comprising: a diesel engine; an electric machine connected to the engine; a battery connected to the electric machine; a diesel particulate filter (DPF) arranged to receive engine exhaust gas; and a controller programmed to control the engine and the electric machine to reduce oxygen content of the engine exhaust gas in response to a DPF temperature exceeding a threshold during DPF regeneration while the engine is idling.
8. The vehicle of claim 7 wherein the controller is further programmed to increase engine torque and maintain engine speed by operating the electric machine as a generator to charge the battery.
9. The vehicle of claim 7 wherein the controller is further programmed to adjust engine fueling to reduce the oxygen content of the engine exhaust gas.
10. The vehicle of claim 7 wherein the electric machine comprises an integrated starter-generator.
11. The vehicle of claim 7 further comprising a temperature sensor in communication with the controller to measure the DPF temperature.
12. The vehicle of claim 11 wherein the temperature sensor is arranged to measure temperature of exhaust downstream of the DPF.
13. The vehicle of claim 7 wherein the controller is programmed to predict the DPF temperature using a soot combustion model.
14. The vehicle of claim 7 wherein the controller is programmed to reduce an engine air-fuel ratio to increase richness of a mixture supplied to the diesel particulate filter.
15. A method for controlling a vehicle having an electric machine, an engine, and a diesel particulate filter (DPF), comprising: by a controller, in response to the engine entering an idle mode during regeneration of the DPF, operating the electric machine to increase engine load and increasing engine torque in response to the engine load increase to reduce oxygen content of exhaust gas entering the DPF.
16. The method of claim 15 wherein operating the electric machine comprises operating the electric machine as a generator to charge a battery.
17. The method of claim 15 further comprising adjusting an air-fuel ratio of the engine to increase engine torque.
18. The method of claim 17 wherein adjusting the air-fuel ratio comprises adjusting engine fueling.
19. The method of claim 15 wherein the electric machine comprises an integrated starter-generator.
20. The method of claim 15 further comprising controlling engine speed to maintain idle speed while operating the electric machine to increase engine load.
 This application claims foreign priority benefits under 35 U.S.C. .sctn.119(a)-(d) to GB 1514120.3 filed Aug. 11, 2015, which is hereby incorporated by reference in its entirety.
 This disclosure relates to a diesel particulate filter arranged to receive exhaust gas from an engine of a motor vehicle and protecting the diesel particulate filter from overheating during a regeneration event when the engine is idling.
 A diesel particulate filter (DPF) can be damaged during what is known as a `drop to idle` scenario. This is the worst case thermal scenario for a DPF. If an engine of a vehicle drops to idle when the soot combustion process (regeneration process) has just commenced, the maximum potential energy in the form of soot exists in the DPF with the maximum oxygen content seen during engine running but also with the lowest exhaust mass flow to transfer the heat out of the DPF. Additionally, because the vehicle is not moving there is minimal external airflow for cooling the exhaust system from the outside.
 Under these conditions the temperature within the DPF can rise to more than 1000.degree. C. and it is possible to crack the DPF, melt the DPF substrate or degrade the catalyst washcoat which is present to aid the removal of other regulated emissions (HC, CO or NOx). In an extreme case this overheating condition can result in the DPF material combusting which can lead to thermal damage of surrounding components.
 A temperature that is likely to result in damage to the diesel particulate filer is an unacceptably high temperature and the diesel particulate filter can be considered to be overheating when subject to such a temperature.
 According to one embodiment, a method of preventing overheating of a diesel particulate filter during a regeneration event when an engine of a motor vehicle to which the diesel particulate filter is connected is in an idle mode of operation includes, when regeneration of the diesel particulate filter is occurring, the engine is idling and one of a prediction of temperature and a sensed temperature indicates that the temperature within the diesel particulate filter is one of predicted and sensed to be unacceptably high, operating an electric machine drivingly connected to the engine in a generator mode and adjusting the fueling to the engine to compensate for the additional load applied to the engine by the electric machine.
 Adjusting the fueling to the engine may comprise reducing an air-fuel ratio to increase the richness of the mixture supplied to the diesel particulate filter.
 The method may further comprise checking the speed of the engine to confirm that the engine is operating in an idle mode.
 The method may further comprise using a soot combustion model to predict the temperature within the diesel particulate filter and using the predicted temperature to determine whether the temperature of the diesel particulate filter is predicted to be unacceptably high.
 Alternatively, the method may further comprise using a temperature sensor to measure one of the temperature within the diesel particulate filter and the temperature of the exhaust gas exiting the diesel particulate filter and using the measured temperature to determine whether the temperature within the diesel particulate filter is sensed to be unacceptably high. The temperature may be unacceptably high if it is above a predefined temperature limit.
 In one embodiment, a motor vehicle includes a diesel engine, an electric machine drivingly connected to the engine, an electrical energy storage device connected to the electric machine, a diesel particulate filter arranged to receive exhaust gas from the engine and an electronic controller arranged to control the engine and the electric machine. When the engine is operating in an idle mode, regeneration of the diesel particulate filter is occurring, and the temperature within the diesel particulate filter is one of predicted and sensed to be unacceptably high, the electronic controller is arranged to operate the electric machine in a generator mode and adjust the fueling to the engine to compensate for the additional load applied to the engine by the electric machine.
 Adjusting the fueling to the engine may comprise reducing an air-fuel ratio to increase the richness of (or enrich) the mixture supplied to the diesel particulate filter.
 The vehicle may further comprise an engine speed sensor and the electronic controller may be further arranged to use an output from the engine speed sensor to establish whether the engine is operating in the idle mode.
 The vehicle may further comprise a temperature sensor used to measure one of the temperature within the diesel particulate filter and the temperature of the exhaust gas exiting the diesel particulate filter and the electronic controller may be arranged to use the measured temperature to determine whether the temperature within the diesel particulate filter is sensed to be unacceptably high.
 The electronic controller may include a soot combustion model for predicting the temperature within the diesel particulate filter and the electronic controller may be arranged to use the temperature predicted by the soot combustion model to determine whether the temperature within the diesel particulate filter is predicted to be unacceptably high. The temperature may be unacceptably high if it is above a predefined temperature limit.
 In various embodiments, the electric machine may be an integrated starter-generator (ISG) and the vehicle may be a hybrid vehicle.
 FIG. 4 is a composite chart showing a relationship between temperature and time for a DPF during a regeneration event when an engine is idling in accordance with embodiments of the disclosure and the relationship between Oxygen concentration and time for the same event.
 As required, detailed embodiments are disclosed herein; however, it is to be understood that the disclosed embodiments are merely representative and may be embodied in various and alternative forms. The figures are not necessarily to scale; some features may be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the claimed subject matter.
 With reference to FIG. 1, a hybrid motor vehicle 5 includes four road wheels 6, a diesel engine 10 and an electronic controller 20. Control logic, functions, algorithms, or methods performed by controller 20 may be represented by flow charts or similar diagrams in one or more figures. These figures provide representative control strategies and/or logic that may be implemented using one or more processing strategies such as event-driven, interrupt-driven, multi-tasking, multi-threading, and the like. As such, various steps or functions illustrated may be performed in the sequence illustrated, in parallel, or in some cases omitted. Although not always explicitly illustrated, one of ordinary skill in the art will recognize that one or more of the illustrated steps or functions may be repeatedly performed depending upon the particular processing strategy being used. Similarly, the order of processing is not necessarily required to achieve the features and advantages described herein, but is provided for ease of illustration and description. The control logic may be implemented primarily in software executed by a microprocessor-based vehicle, engine, and/or powertrain controller, such as controller 20. Of course, the control logic may be implemented in software, hardware, or a combination of software and hardware in one or more controllers depending upon the particular application. When implemented in software, the control logic may be provided in one or more non-transitory computer-readable storage devices or media having stored data representing code or instructions executed by a computer to control the vehicle or its subsystems. The computer-readable storage devices or media may include one or more of a number of known physical devices which utilize electric, magnetic, and/or optical storage to keep executable instructions and associated calibration information, operating variables, and the like.
 The engine 10 is arranged to receive air through an inlet 11 and in some embodiments the flow of air will be compressed by a supercharger or a turbocharger before it flows into the engine 10 to improve the efficiency of the engine 10.
 Exhaust gas from the engine 10 flows through a first or upstream portion 12 of an exhaust system to a diesel particulate filter (DPF) 15 and after passing through the DPF 15, the exhaust gas flows out to atmosphere via a second or downstream portion 13 of the exhaust system. It will be appreciated that other emission control devices or noise suppression devices may be present in the gas flow path from the engine 10 to the position where it exits to atmosphere.
 An electric machine is drivingly connected to the engine 10. In the case of this example the electric machine is an integrated starter-generator (ISG) 16 that can be used to generate electricity or generate torque depending upon the mode in which it is operating. A battery 17 is connected to the integrated starter-generator 16 along with associated control electronics (not shown). When the integrated starter-generator 16 is operating as a generator it charges the battery 17 and, when the integrated starter-generator 16 is operating as a motor, the battery 17 is arranged to supply electrical energy to the integrated starter-generator 16.
 The integrated starter-generator 16 is used to start the engine 10 and in the case of this example is also able to provide a limited torque boost to the engine 10 during acceleration of the vehicle 5.
 The electronic controller 20 receives inputs from a number of sensors such as a mass airflow sensor 21 used to measure the mass of air flowing into the engine 10, an engine speed sensor 22, a Lambda/Oxygen sensor 24 to measure the air-fuel ratio/Oxygen content of the exhaust gas exiting the engine 10, a vehicle speed sensor 25 to measure the speed of the vehicle 5, a NOx sensor 26 to measure the level of NOx in the exhaust gas from the engine 10 and a temperature sensor 28 to measure the temperature of the exhaust gas exiting the DPF 15.
 The electronic controller 20 is operable to control the operation of the engine 10 and the operating state of the integrated starter-generator 16. It will be appreciated that the electronic controller 20 could be formed of several separate electronic units electrically connected together and need not be in the form of a single unit as shown in FIG. 1.
 The electronic controller 20 is arranged to prevent overheating of the DPF 15 during a regeneration event when the engine 10 is in an idle mode of operation. In the idle mode of operation the engine 10 is rotating at a relatively low rotational speed and there is no torque demand from a driver of the vehicle 5. The fact that the engine is in the idle mode can be sensed by using the sensors associated with the engine 10 such as the engine speed sensor 22 or, if the electronic controller 20 includes an idle speed controller, the fact that idle speed control is active can be used to indicate that the engine 10 is idling.
 Because the electronic controller 20 is arranged to operate the engine 10 in order to carry out a regeneration of the DPF 15 it is able to recognize when the engine 10 has entered the idle mode during such a period of regeneration.
 The electronic controller 20 can then act immediately to control the temperature within the DPF 15 or can delay this temperature controlling function until the signal received by the electronic controller 20 from the exhaust gas temperature sensor 28 located downstream from the DPF 15 indicates that the temperature of the exhaust gas exiting the DPF 15 is excessive. That is to say, if the temperature of the exhaust gas measured by the temperature sensor 28 exceeds a predefined temperature limit (T.sub.Lim), the electronic controller 20 acts to control the temperature within the DPF 15 but if the temperature of the exhaust gas exiting the DPF 15 is below this predefined temperature limit it takes no action but instead allows the regeneration of the DPF 15 to continue. The predefined temperature limit T.sub.Lim may be set to a temperature above which damage may occur such as, for example and without limitation, circa 850.degree. C. It will be appreciated that the temperature sensed by the downstream temperature sensor 28 is not a measurement of the actual temperature within the DPF 15 but that the temperature within the DPF 15 can be inferred from this temperature measurement. The temperature within the DPF 15 is likely to be higher than this measured or modelled temperature.
 It will be appreciated that instead of the downstream temperature sensor 28 a temperature sensor able to measure the temperature within the DPF 15 could be used and, in such a case, the predefined temperature limit could be set higher than 850.degree. C. such as, for example, 950.degree. C.
 Assuming that the determination of the electronic controller 20 is that the temperature within the DPF 15 is excessive and requires controlling, the electronic controller 20 is arranged to use the integrated starter-generator 16 to apply a load to the engine 10 by operating it as a generator. This would normally result in the speed of the engine 10 dropping due to the additional load applied to it by the integrated starter-generator 16. However, to counteract this drop in speed, the engine torque set point for the engine 10 is increased by the electronic controller 20 in order to maintain the required idle speed. If an idle speed controller is present then this action may be an automatic response by the idle speed controller to a drop in engine speed.
 Increasing the engine torque set point will result in the engine running richer than normal and so the quantity of Oxygen flowing to the DPF 15 will drop. For example under normal idle mode conditions the oxygen content of the exhaust gas entering the DPF 15 is typically in the range of 6 to 15% but by the application of the load from the integrated starter-generator 16 this may be reduced to 3 to 5%. This reduction in Oxygen level in the exhaust gas entering the DPF 15 will slow the rate of soot combustion within the DPF 15 and so the temperature of the DPF 15 will be reduced.
 With reference to FIG. 2 there is shown a method 100 for protecting a diesel particulate filter when an engine from which exhaust gas is received by the diesel particulate filter is idling. The method starts in box 110 with the engine 10 running and then in box 120 it is checked whether the engine 10 is idling.
 If the engine 10 is not idling the method returns to box 110 and, if the engine 10 is idling, the method advances from box 120 to box 130 where it is checked whether the DPF 15 is overheating. As previously described this can be achieved by using a temperature sensor 28 to measure the temperature of the exhaust gas exiting the DPF 15.
 However, as an alternative to this approach the temperature within the diesel particulate filter can be modelled or to be more precise a model of the soot combustion process can be used to estimate the temperate within the DPF 15. The use of such a soot combustion model has the advantage that there will be no delay between the time the temperature in the DPF 15 is predicted to be excessive and the start of temperature controlling by the electronic controller 20 whereas there is a delay when the increase is sensed by the downstream temperature sensor 28 because the temperature of the exhaust gas has to increase before its increase can be sensed and so the system then acts reactively. If a soot combustion model such as that disclosed in US Patent Application 2012/0031080 is used then the increase in temperature can be predicted so the system can act proactively resulting in the steps to control the temperature being taken sooner. As before, if the prediction indicates that the temperature within the DPF 15 is likely to be unacceptably high that is to say, above a predefined limit, then the DPF 15 may be overheating.
 If the result of the check in box 130 is that the DPF 15 is not currently overheating, the method returns to box 110 and will then proceed as previously described unless a vehicle key-off event occurs whereupon it ends.
 However, if when checked in box 130 the result is that the DPF 15 is overheating or, if a soot combustion model is used, that DPF overheating is imminent then the method advances to box 140.
 In box 140 the electric machine which in this case is the integrated starter-generator 16 driven by the engine 10 is switched into a battery charging mode. This will cause a load in the form of torque to be applied to the engine 10.
 This would normally cause the engine speed to reduce but, due to an idle speed control system that is formed in this case as part of the electronic controller 20, the result of the application of the applied torque in box 140 is for the engine torque set point to be increased as indicated in box 150 to maintain the idle speed at the desired speed. The effect of increasing the engine torque set point is to increase the torque output from the engine 10 by injecting more fuel in the engine 10. That is to say, the air-fuel ratio (represented by Lambda) is reduced making the composition of the exhaust gas flow richer and reducing the amount of Oxygen in the exhaust gas flow to the DPF 15 as indicated in box 160.
 From box 160 the method advances to box 170 to check whether DPF regeneration has ended. If DPF regeneration has ended then the method advances to box 180 where the integrated starter-generator 16 is returned to normal operation and the engine torque set point is restored to normal and the method then returns to box 110 and all subsequent steps are repeated unless a key-off event has occurred whereupon it ends.
 However, if when checked in box 170, DPF regeneration has not ended, the method returns to boxes 140 and 150 and the reduction of Oxygen supply to the engine 10 continues.
 The effect of carrying out a method in accordance with various embodiments can be seen by comparing the prior art situation shown in FIG. 3 with the situation when the method 100 is used as shown in FIG. 4.
 In the prior art case of FIG. 3, idling of the engine results in an Oxygen concentration in the exhaust gas of circa 15% as indicated by the line (O.sub.2) resulting in a rapid increase in temperature (T) within a DPF due to the availability of Oxygen to fuel combustion of the soot.
 In the case of one embodiment using temperature sensor control as illustrated in FIG. 4, engine idling initially produces an Oxygen concentration (O.sub.2) of circa 15% resulting in a sudden increase in DPF temperature until, at time `t`, temperature control is initiated. That is to say, the temperature of the exhaust gas exiting the DPF 15 has reached the predefined temperature limit T.sub.lim which in this case is set at 850.degree. C.
 Therefore, at the time `t`, torque is applied by the integrated starter-generator 16 to the engine 10 and the engine torque set point correction is made. After making these changes the Oxygen concentration falls to circa 5% resulting in a reduction in the increase in temperature (T) within the DPF 15 due to the limited availability of Oxygen to fuel combustion of the soot in the DPF 15.
 Although embodiments have been described with reference to a hybrid vehicle having an integrated starter-generator, it will be appreciated that it could be applied with benefit to other vehicles having an electric machine with sufficient generating capacity to produce the required load to force an increase in engine output torque to maintain a stable idle speed and the consequential reduction in the Oxygen concentration of the exhaust gas flowing to the diesel particulate filter.
 It will be appreciated by those skilled in the art that although the claimed subject matter has been described by way of example with reference to one or more embodiments it is not limited to the disclosed embodiments and that alternative embodiments could be constructed without departing from the scope of the disclosure as defined by the appended claims.
 While representative embodiments are described above, it is not intended that these embodiments describe all possible forms of the claimed subject matter. Rather, the words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the disclosure. Additionally, the features of various implementing embodiments may be combined to form further embodiments that are not explicitly described or illustrated. While various embodiments may have been described as providing advantages or being preferred over other embodiments or prior art implementations with respect to one or more desired characteristics, as one of ordinary skill in the art is aware, one or more features or characteristics may be compromised to achieve desired overall system attributes, which depend on the specific application and implementation. These attributes include, but are not limited to: cost, strength, durability, life cycle cost, marketability, appearance, packaging, size, serviceability, weight, manufacturability, ease of assembly, etc. Embodiments described as less desirable than other embodiments or prior art implementations with respect to one or more characteristics are not necessarily outside the scope of the disclosure and may be desirable for particular applications.


Baby food is expensive. Trust me, I know because I bought it for a few weeks. It didn't take long for me to come to my senses and realize there really was no need to pay someone else to make food for my baby. I was cooking dinner every night for myself, so why not for her?
Now don't get me wrong, I wasn't a huge organic baby food making machine, but I do know I saved tons of money by not buying baby food. And I also knew exactly what my daughter was eating because I made it.
All the parts are dishwasher-safe.
There are different blades to make baby food for different stages.
The storage cups come with date stamps so you never have to guess when you made something.
Buy the best kids' eating utensils in our buying guides.


Debbie Butler joined Cumberland Trust in 2005. As Senior Vice President and Trust Officer in the Distinctive Care Division, Debbie leads the administration team servicing Cumberland Trust's client relationships with special care and senior care needs. Debbie has worked in the financial services and banking industry since 1991. Her previous experience includes working in SunTrust Bank's Trust Services division and with First American Bank in their retail banking division.
Debbie is a graduate of the three-year Trust School program with Cannon Financial Institute.


[ ] Completed Zoning Application (Development Permit Application). Mark "Other" on the Zoning Application and be sure to indicate what use you wish to convert from and to.
File the permit for your conversion by clicking the button below and printing the zoning application. Submit the application along with your property survey and architectural plans and a business check, money order or cashier's check for $20.00 to the Plainfield Building Division. No cash, cards or personal checks are accepted. Sorry :( .


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Q: Edit queue available to heavy editors across all sites I don't like the decision for basing the ability to have more 'power' in editing with higher rep users -- just 'cause you have 10k rep doesn't mean you can pwn me (~2.5k rep) at editing. But that's another story.
Technically, someone could make something that would go through all the recent suggested edits. All they need to do is search the most recent suggested edits, and filter out the ones rejected or approved.
http://stackoverflow.com/suggested-edits/ INSERT HIGH NUMBER.

So what's the point of having the editing queue available to only 10k users? I have made over a thousand edits on SE, and I think I can tell the difference between an edit to approve and an edit to reject. (Notice I didn't say "good/bad edit".)
StackExchange is suppposed to be like Wikipedia, right? So give the good editors more privileges across sites, regardless of whether they have enough rep or not!
In fact: I propose an integrated edit queue on StackExchange. You can look at the edit queue for sites/tags you indicate.

TL;DR

*

*Editing privileges based on number of quality edits (Wikipedia style).

*Editing privileges are sustained across different SE sites.

*An edit queue on stackexchange.com.

A: Firstly, it's not 10k anymore. The edit queue is now shown to 5k users as a partial fulfillment of this feature request. However, I do not support your idea of a network wide edit queue.
I moderate two sites on the network: Gardening & Signal processing and I can tell you from first hand experience that the edit queues in both the site are very different. On gardening, the edits are mostly minor and involve link fixes/grammar corrections/image fixes/overall improvements to the post. These are pretty easy to approve/reject and doesn't require much thinking.
However, on a highly specialized site like signal processing, there were some suggested edits that have stayed in the queue for 5-6 days (days!), because none of the mods (and one user who could see the queue) knew much about the subtopic related to the question. We eventually ended up reading a bit about the subject, discussing the edit made and decided to approve it.
Now I certainly cannot expect a random person who just happens to be an awesome editor on cooking.SE or christianity.SE to approve those edits, nor do I want them to! We don't want madmen correcting /etc/passwd on unix.SE to /etc/password and someone on english.SE approving it!
Now you might say that oh well, a good editor would not approve partial/poor edits. Wrong! Here's a recently approved edit on Stack Overflow. The person who suggested the change missed lt;br&gt several times  (one even right before his edit), a few lower case i's and bungled up the spelling of grammar in his edit reason. This was even approved by 2 users! Can you imagine what would happen if we implemented an SE wide queue, and only 1 user is required to approve?
For these reasons, I strongly oppose any additional edit privileges on one site based on privileges earned on another. If you want to earn the privilege to edit, do it the hard way! Earn 2k rep. (or 1k on betas).

redpajama_set_name: RedPajamaStackExchange


Better handling for off-road and on-road.
Precise adjustments increase the suspension's carrying capacity, and reduce uncontrolled movement on SUVs and light trucks. A more confident steering feel guarantees better control of your vehicle, safer handling and increased traction.


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Explore emerging and overlooked issues as you define the future of policy research, education and practice.
The Doctoral Program prepares scholars and scholar-practitioners for academic and professional careers. Our PhD students are educated to be versatile and, judging from the success of our graduates, can expect to thrive in whatever positions they choose — and in whatever positions choose them — over their full careers.
Public Policy doctoral programs have proliferated and prospered over the last half century. Why? Answers would vary, of course, but here's one that's usefully understood in dissertation context. In more traditional disciplines, especially in the social sciences, doctoral students choose methods and then look for ways to demonstrate mastery of those methods. In Public Policy, ideally, doctoral students choose problems and then master the methods needed to solve those problems. Choosing a problem takes a while. So does composing a research question leading to a problem-solving answer.
The doctoral program requires that students take 8 classes (24 course credits total). Three are specifically required:
Normative Analysis (PLCY 698E)
Quantitative Analysis (PLCY 798R)
Qualitative Analysis (PLCY 798Z)
Five other courses are chosen in consultation with a student's faculty advisor. Choices will reflect past coursework and current research interests but must also be chosen with qualifying examinations in mind.
Our PhD program does admit students intending to study part-time. However, admission is competitive and we have to have a faculty member willing to serve as a research advisor. Additionally, it is important that a student's job be closely aligned with the research topic.
Steps in advancement to candidacy for the PhD
Passing all qualifying examinations Qualifying Exams (also known as Comprehensive Exams or General Exams) are taken right after 4 semesters of coursework or when a student feels prepared and whenever made available by the examining professor or professors. Many students take exams right after finishing the courses most likely to prepare them to pass. Areas examined (in alphabetical order) are: Microeconomic analysis Normative analysis Political analysis Quantitative analysis Specialization(s) This is a single area (or combination of areas) chosen by the student as bearing directly on dissertation intentions. The specialization exam is planned jointly by the student, the student's advisor and, often, one or more professors sharing aspects of the student's research interest. Preparation is lengthy but instructive. The exam's authors — always at least two professors — grade the exam.
Assembling a faculty committee chaired by a student's advisor This committee, once fully formed and successfully nominated, will go on to function as a dissertation examining committee.
Proposing a dissertation research plan (prospectus) to the faculty committee
Defending the proposal at a scheduled public event
Note: Students are required to maintain continuous enrollment, i.e., be registered every semester. If the student has completed all coursework but not yet advanced to candidacy, the student should register for PLCY898-Pre-Candidacy Research in the research advisor's section number.
Steps in the dissertation phase
A student who has advanced to candidacy is automatically enrolled by the UMD Registrar in 6 credits of PLCY 899, Doctoral Dissertation Research. The UMD Graduate School requires a minimum of 12 credits of PLCY 899 before a student is eligible to graduate.
Nominating the fully formed dissertation examining committee, with the candidate's advisor as the chair. The committee's composition must observe Graduate School rules with approval needed for any exceptions. Note that all members of the dissertation examining committee should have earned the degree to be awarded (the PhD) or an equivalent terminal degree (such as the DSc or DPH).
Writing the dissertation
Defending the dissertation at a scheduled public event
Submitting the committee form approved via signature by all members of the committee to the Office of the Registrar and electronically submitting the dissertation through the university's online system. The Registrar will verify the dissertation formatting and clear the student for graduation.
View our frequently asked questions for more information about the PhD program.
Explore dissertations completed by candidates in the School of Public Policy.
View the Graduate School's policies related to the Doctor of Philosophy degree.
View our PhD Candidates
Learn more about R.H. Sprinkle
R.H. Sprinkle
Robert Hunt Sprinkle works at the intersection of politics and the life sciences. He studied history at Dartmouth College and medicine at the University of Cincinnati and trained clinically at the University of Virginia and the University of Texas Southwestern Medical Center, Dallas. He is a diplomate of both the American Board of Family Medicine and the American Board of Pediatrics and a fellow of the respective clinical academies; he maintains current certification in both specialties and medical licensure in four states.
See what financial aid and scholarships are available to help fund your education.


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Home » Arts » New Media » Sam Rosenberg: 'I'm Shmacked' and the dangers of romanticizing college party culture
Posted inArts, New Media
Sam Rosenberg: 'I'm Shmacked' and the dangers of romanticizing college party culture
by Sam Rosenberg February 14, 2017 April 20, 2021
Partying is something that will always be intrinsic to the college experience. For college students, a party represents an opportunity to be independent, and more importantly, it's an excuse to be young, wild and free (yes, I am quoting that Wiz Khalifa & Snoop Dogg song). But while we should embrace certain aspects of a fun college party, we shouldn't be ignoring the potential red flags that idealize the college party experience.
With the widespread growth of social media and advancement in technology, big party colleges have incorporated the "go hard or go home" mentality, prompting competition with other schools to throw large, crazy parties and have them go viral in some way. One of the most pervasive purveyors of this kind of unruly partying comes from "I'm Shmacked," an online entertainment platform that has capitalized on the college party scene through entertaining, albeit provocative and problematic videos.
Created by Arya Toufanian and Jeffrie Ray, "I'm Shmacked" implemented itself as the premier platform for showcasing the "reality" of college parties when it debuted its first video in 2011, taken at a Temple University party. After their online presence proliferated, video crews from "I'm Shmacked" continued to visit universities all around the United States, where they would record the wildest of parties, usually held at fraternities, and edit them into highly stylized, five-minute clips, synced to a blaring, frenetic EDM soundtrack.
Now with 130,000+ likes on Facebook, 449,000 followers on Instagram and 37,000 subscribers on YouTube, "I'm Shmacked" has become a nationwide phenomenon. In order to expand its online empire, "I'm Shmacked" has developed subaccounts for different universities across the country, everything from Indiana University to USC to even here at the University of Michigan. In addition to parties, they promote everything from college fall festivals to spring break trips to sorority recruitment. Toufanian and Ray have also monetized the "I'm Shmacked" brand by booking venues near college campuses and throwing insane parties. "I'm Shmacked" has its own merchandise and it even spawned a few imitator platforms, including the similarly popular TotalFratMove and the unabashedly explicit Old Row. In 2014, it was reportedly valued at $5 million.
What I find particularly dangerous about this platform is not just how it normalizes binge drinking and objectifies college girls, but how it romanticizes party culture. "I'm Shmacked" frames the culture of college parties as a free-for-fall extravaganza, filled with gorgeous girls, toxically masculine guys and a whole lot of alcohol.
Some might argue that one of "I'm Shmacked" 's more beneficial quality is its ability to show prospective students what college parties are like, which can help them determine what school's party scene suits them the most (note: "A new way to scout colleges" is written in their Instagram bio). However, I would counter that by saying that it promotes a negative, misleading and distorted portrait of college party life. A prospective student might watch an "I'm Shmacked" video and think these are what college parties are like — a place to shotgun beers, chugging Four Lokos, watch girls twerk on each other and do stupid shit with no consequences.
In particular, "I'm Shmacked" profits off distributing amateur videos sent by college students of people binge drinking and heavy drinking. However, these videos, which are littered on the platform's Instagram account, neglect to showcase just how dangerous binge drinking can be. According to a 2015 article from the National Institute on Alcohol Abuse and Alcoholism, 37.9 percent of college students ages 18–22 reported binge drinking in the past month compared with 32.6 percent of other persons of the same age. Researchers also estimate that each year 1,825 college students between the ages of 18 and 24 die from alcohol-related unintentional injuries, including motor-vehicle crashes. "I'm Shmacked" may not be directly responsible for these deaths, but they are complicit in perpetuating and glorifying binge drinking as normal and celebratory rather than fatal.
As for objectifying women, "I'm Shmacked" uses college girls, most of whom are white, blonde and scantily clad, to promote their merchandise, spring break events and generally for entertainment.
This is nothing new, of course. Objectifying women and binge drinking have been portrayed in several films and TV shows about college, such as "Blue Mountain State," "Animal House," "American Pie," "Road Trip" and "Old School." But the important distinction to make here is that because our generation has become so acclimated to consuming information and content from social media, "I'm Shmacked" has taken advantage of the virality of social media by reinforcing the stereotypes of college parties through the pictures and videos they post.
Most people in our generation grew up obsessing over this idea that you have to throw the biggest, craziest and largest party in order to have fun. Parties can be fun, and they should be. People should feel like they can drink without having the compulsion to black out. Women should be able to dress in whatever they want at parties without being perceived through the male gaze of Instagram. If the kind of partying in "I'm Shmacked" videos is the "ideal" fun for college students, then maybe there should another platform that portrays college parties — and college life, for that matter — more accurately.
I asked a twelfth year senior to get me excited for college
Is it morally responsible to allow the proliferation of liquor stores on campus?
U.S. versus European degrees. Is the money worth it?


We teach, work, and live by her profound words!
in 126 countries in 2018!
The artists created their wise feathered Owls using our Paper Palette Process of pre-painted paper. Artists first selected the colors and textures they preferred. They were then given a pre-cut pattern which they traced on the back of the papers. The next step was to cut out the pieces and glue the reconstructed owl on art paper. It was a Hoot! We hope you enjoy them.
…and our artist's families and friends!
We want to extend a very sincere Thank You to Art Paws, Inc.
Art Paws awarded Moments of Memory, Inc. with a very generous Art Grant! We are thrilled to be able to restock our shelves with needed paint, brushes and paper! We are so grateful for their generosity!
Art Paws will again hold their fundraising Artown event at McKinley Art and Culture Center, 925 Riverside Dr., Reno on Sunday, July 21st, 2019.
If you would like to volunteer please contact Michelle McHardy, Art Paws President & Coordinator, artpawsreno.com.
We sincerely THANK the staff and management of the Reno-Tahoe International Airport for their support in the spring of 2018! We received many calls, texts, emails and letters regarding the large display of art we had on display in the depARTures gallery.
Thank you to Ian Carpenter of The Framery for his complimentary matting!
Shirley doesn't remember painting this spectacular watercolor… but you'll remember (I hope) that you contributed to supporting our Mission!
Our goal is to make a difference in people's lives…if only for a moment.
We are sincerely looking forward to receiving your generous donations! We are in need of art supplies to fill the cupboards at all the memory care communities where we teach. You can easily and securely donate here. Thank you in advance!!
Would love your feedback and comments at the bottom. Thank you!
THANK YOU FOR CONSIDERING OUR MISSION TO BRING ART EXPERIENCES TO THOSE LIVING WITH ALZHEIMER'S!
WE ARE ALWAYS IN NEED OF YOUR GENEROUS DONATIONS TO COVER THE WEEKLY COST OF PAPER, PAINTS, PASTELS, BRUSHES AND MORE. A DONATION CAN BE SECURELY AND EASILY MADE HERE.
PS IF YOU'D PREFER TO MAIL IN A CONTRIBUTION A DONATION FORM IS AVAILABLE TO PRINT OUT IN THE MENU BAR AT THE TOP AND MAIL IN.
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Thank you AmazonSmile and to the individual who nominated our organization!
Thank you for considering our mission for your 2019 giving!
To Donate online: Click the first link on the Blogroll on the right.
To mail, go to the Donation Form page, print pages 1-2 and mail.
THANK YOU SO VERY, VERY MUCH FOR YOUR CONSIDERATION AND GENEROSITY!
Moments of Memory, Inc. in Nevada, is an IRS approved (12/15/08) 501 (c)3 tax exempt charity. Our mission is to bring visual art experiences to those living with memory impairment. Your donation, pursuant to NRS 598, may be tax deductible. Please check with your personal accountant.
12 months of new Moments of Memory art!
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Moments of Memory… Art from the Hearts of Alzheimer's Artists.
A non-profit program of visual art expression developed for those living with Alzheimer's and related dementias. With passion and purpose Moments of Memory classes create a safe, supportive environment for social interaction and self-expression resulting in a non-critical and fail-safe experience. Specific techniques enable individuals to focus on a task at hand and experience a sense of accomplishment, counteracting feelings of depression and isolation. Having the opportunity to share the tangible reward of their efforts in a group setting renews self-confidence and trust. Reconnecting with society in a productive community restores a sense of self even in the later stages of the artist's illness.
ART: I've Got Your Back by Babs, created with women's cosmetics!
We would REALLY appreciate your feedback and comments…it takes a village!
Hello Patty, yes all of the framed art is available after April 18th when the gallery comes down. Is there a particular piece you are interested in?…and thank you for asking!
Are any of these works for sale?
Hi Karen, I love Ashland:) Not that I know of…but contact the local Alzheimer's Association and ask them if they have a Memories in the Making program. Also Google Elder Art in Ashland and you might find some weekly classes. Good Luck!
Thank you Karon McDonald for your nice donation…..I'm going to go shopping and buy paper for our art projects!!!
Erica, intern extraordinaire! So great to hear from you. Hoping your travel studies went well. Look forward to seeing you at Stone Valley! Happy New Year!
I am looking through the art gallery now- I love seeing the new projects that are up. The artwork is absolutely beautiful. I hope to see you soon at your new location. You are making a difference and you inspire me!
Lynette, congratulations on the News and Review wins for Best Non Profit AND Best Volunteer. Thanks for all you do for those living with Alzheimer's!
Lisa, I'm so sorry I didn't see your comment, and it so wonderful, Thank You! So happy you liked your card. We haven't had any in stock but will soon and I'll certainly keep you posted, you'll be first on my list! Have a nice memorial day weekend and thank you for contacting me!
I'm greatfully inspired by the work of art created by such beautiful people.
I thankfully recieved one of your cards as a house warming 🎁 when we moved into our new house by our neighbors. I'm really wanting to get some of these cards to share any of my special occasions, with the wonderful sharing of this group/organisation and non profit wonderful for memory. I will continue to look and see if I can find how to buy some of not how do I recieve any or can I?
Just amazing…I am always touched when I see the work you inspire!
Hi! Haven't been on the site forever. Thank God for your talent and your enthusiasm for Moments of Memory. Thanks also for Mom's, Edith's, lovely tribute. She really loved working with you. Keep up the good work.
Thank you everyone for the nice comments! I'm happy you're liking and looking!
Had an awesome time at the car show and I am looking forward to the art auction on October 23rd! This is an amazing organization!
Congratulations on the RGJ award! Very well deserved. Thank you for your dedication Lynette.
Everyday I see the wonderful art that out resident have made and it make me happy knowing how much joy was created along with the beautiful images.
I can't wait for the walk to end Alzheimer's 🙂 loved volunteering last year!
Lynette….Thank you from the bottom of our hearts for such a wonderful event and honoring the love of my life. We all had a great time….moustaches were such a super fun tribute to George!
Beautiful job on the new artwork all! The gentlemen have such talent, it's great to see the "masculinity" in their work. I especially love the bright colored artwork, as you know me! Miss all of the artists and especially YOU!! I am using what you have taught me to enhance the lives of the residents where I now work, although it is not the same without you there to assist me, it DOES work! Love to you my friend and mentor!
Thank you to everyone for all the great comments regarding the NEW art in the Gallery of Art! I do pass on your comments to the artists and they are very touched by your kind words!
We appreciate each and everyone of our supporters, followers and those who "Like" us on FB. Cheers to a New Year of great art experiences for our artists!!!!
Dear Debra, Thank you so very much for the generous calendar order!!!
I sincerely hope you and your clients enjoy them all year long!
I love the site and the new photos put up! I look forward to purchasing a 2014 calendar as well!
I will definitely stop by the Arbors and purchase some of those wonderful greeting cards. I particularly like the pink long legged bird.
So excited about this years Art Auction on April 11. Always love watching the artists enjoy their event. Looking forward to seeing everyone there!
I am so pleased to see this program continue in our area. Thank you to all those who have supported it. Make plans to join us for the event April 11th – you will be inspired beyond belief! See you then!
You have given me great ideas regarding this subject! I was looking for these kinds of posts! Thank you! I am looking forward to more of your posts!
I'm looking forward to the events for Artown! Lynette, you have such imagination! You've inspired all these artists. Fun!
I can't wait for all the events in July! Things are really coming together and I am excited that people are taking note. If everyone will just tell one more person about what we are doing…where the website is…and buy some art – we will be touching sooooo many lives.
Thanks to Lynette for her tremendous dedication in seeing this vision come to reality…many years, tears and fears! Great job!
I think the cards turned out wonderful! thanks to Dynagraphic printing here in Reno who printed them for us at their non profit rate.
What a good deal on these cards. $12 for one set or 2 for $20. I need to buy some more for myself!!
I was wondering if it was possible to get someone into the classes at the Arbors without them being a resident? My mother has moderate dementia from mini-strokes and use to paint a lot. She hasn't done any in at least twenty years but still has her easel and and tool box full of dried up paint and brushes. I would love to see her get back into creating art. We have 5 or 6 of her oils and one water color hanging in the house. Her favorite hangs over her bed, it is a sofa size oil of the Atmospherium Planetarium that she painted shortly after they built it.
Please let me know what help you need for "Anything"!! Especially the upcoming events, you are a wonderful person just by being you! Thank you for helping those in our community with and without Alzheimer's Disease!! As well, thank you for helping me with my dreams of completing college. You are a wonderful mentor to me and I appreciate all of your support!
I just returned home (Omaha, Nebraska) from a trip to Reno and just had to send a note of thanks for your inspirational art display at the airport.
My daughter has severe alcohol dementia and has the capacity of a six year old child. She spends hours coloring, trying to stay within the lines of her coloring book. I am her primary caregiver and am 83 years young. Even with my experience as a lifelong school teacher, her limitations are a challenge for me and I am always looking for ways to expand her abilities. After seeing your art display, I am anxious to integrate some of your techniques. I am grateful that I found your Alzheimer's Moments of Memory. Even though my daughter does not have Alzheimer's, I'm hopeful that we can benefit from trying your ideas. Thank you.
And a downright pleasure to have you as valuable volunteer!
Downright beautiful and inspiring. A pleasure to have participated.
Thank you Kathy we really appreciate your comments!!! If you would like to send me your mother's photo and a story, I'll post it on our "brand new today" Memory Keepers page:o) Speak of her often and keep her memories alive!
As I strolled past the Alzheimer's Art Gallery, I was unashamed by my tears of happiness for those patients who were able to participate in this display and to share their talent with us and by my tears of sadness that my own mother could not have lived to enjoy this type of artistic expression.
My mother died many, many years ago with multiple diseases but her mental condition was a diagnosis of organic brain syndrome (which would now be called Alzheimer's Disease). At the time of her stay in a long term care facility what a disservice to patients that this type of art work was not available.
I applaud this group of Alzheimer's artists, along with the staff who assisted them in putting together this project.
My appreciation is overwhelming. It was such an emotional experience. My thanks to everybody involved. Thank you, Reno Tahoe Airport.
Thank you for the nice comments! We look forward to seeing you at the auction on July 31st! I'll have information available on the website. Keep checking back:)…oh, and there will be more art too!
What an inspiration! While waiting for my aunt to arrive for Easter vacation, my husband and I spent about 30 minutes admiring each piece of art work and reading all the comments. There is certainly a wealth of talent. We will be there for the auction!
I'm 19 and a "wannabe" artist. I cannot tell you how much I enjoyed the art work at the airport.
When I saw the display at the Reno airport, I was brought to tears. My mother is in a nursing home suffering from Alzheimer's. If only the nursing home had this type of art, I know my mom would respond and enjoy.
Very nice site…and I appreciate the information. In California, we have an Adult Day Health Care Center that has a similar program…the art is framed and exhibited within the Center. This is a great way to show the talents of those suffering from the affects of Alzheimer's. thank you so much!
Was able to spend time with your exhibition at the Reno Airport while I waited for my daughter. My mother had alzheimers and I spent a great deal of time with her in her assisted living facility. I so appreciate the reminders your exhibit provided me of that time and experience. The project itself is wonderful, as is the artful result. Thank you to all who participate, directors, volunteers, resident artists, and donating framers.
Congratulations on a WONDERFUL show. I am so impressed! It was fantastic to see the artist's faces as they realized that it was their work on display.
3, 5X7 prints Sun by Alex, Sun by Tommie, and Sun by Edith.
I would also like 1 sets of cards: Sun by Alex.
For a total of $30 plus postage. Please email me with instructions for payment.
I am soooo impressed! Moments of Memory is a wonderful project. You are making a difference in the lives of the residents. I admire your talent, your dedication, your patience, and your ability to make things happen. You are an inspiration and a blessing to those you you give so freely to. Thanks for all you do!
Fabulous! I will bring my children to peruse the wonderful art on display. Is this program is available to dementia patients at other facilities?
Great job Lynette. I admire your dedication and passion!
Fantastic job putting together these events! Can't wait to see the response. You have really done some incredible work in getting Moments of Memory up and rolling. I love that this program is available in our area!
Nicely done Lynette! I hope your group knows how fortunate they are to have you on the team. Thanks for sending the link.
THe disease does make its victims feel depressed and isolated and this program creates such positive results! Bravo Lynni!
Awesome idea! My grandmother suffered from this for many years. In those days they just sat her in a wheel chair and ignored her. With no interaction she just kept getting worse.
Thanks for looking:) I appreciate your feedback. Save the Date..LOL I get it!
Beautiful, and well written….Looking forward to the Evening Gala in July…Save The Date!
Fabulous. Love what you have done with this page.