The folks who today obsess over BFD and behind-armor trauma should read that last part again.
The Navy subsequently utilized Doron in two forms: By sewing Doron panels into pockets on the outside of the Kapok lifejacket, and by sewing Doron panels into the standard-issue Marine Corps utility jacket. Roughly a thousand such jackets were prepared for use in the Battle of Okinawa, but, unfortunately for the development of body armor if not for the men involved, the Marine division outfitted with the armored jackets was not involved in the fighting.
More than anything prior, this glowing evaluation of Doron and nylon armor in Korea cemented body armor's place in the modern soldier's kit.
Given the Navy's interest in Doron vests during WWII, it should come as no surprise that the Marine Corps were early adopters of body armor – and, throughout the course of the Korean war, all Marine Corps frontline personnel were armored in Doron-Nylon flak vests. The Army, at the same time, was still evaluating Doron and nylon vests on a very limited trial basis. As positive feedback from these trials started to come in, and as positive reports from the Marines reached Army HQ, the Army decided that they needed to hurry up and issue body armor to all of their frontline personnel as well, so they requested 13,020 Marine vests on August 11, 1952. By the end of the war, the Army had procured well over 25,000 Marine Corps vests. It should go without saying, therefore, that the Marine vest, the M-1951, was the Korean War's predominant form of body armor. It weighed 7.75 pounds and was a sleeveless vest with a zipper closure in front. It was made of 1050 denier ballistic nylon fabric and hard Doron fiberglass plates. The shoulder girdle area was protected by 12 layers of ballistic nylon, which was flexible and reportedly comfortable to wear; the chest, abdomen, and back were covered in sixteen curved, 3.175mm thick, overlapping Doron plates.
The Army, following further evaluations, ultimately decided to adopt a different design. The Army personnel assigned to the development of armor projects believed that ballistic nylon was just as effective as Doron, but easier to wear on account of its flexibility and ability to drape. Thus the all-nylon M-1952 was issued to troops over the last months of the war, starting in February 1953. Like the M-1951, it was a sleeveless vest with a zipper in front. It had two front and back panels composed of ballistic nylon bonded with laminating resin, but this was still reasonably flexible, and the vest was reportedly comfortable to wear. It weighed 8.25 pounds, so was slightly heavier than the M-1951, but its flexibility made up the difference.
The M-1951 and M-1952 remained essentially unchanged into, and over the entire course of, the Vietnam war. There were minor, mostly cosmetic, upgrades — but the weights and materials did not differ to any meaningful extent. The vest of the Marine Corps in Vietnam was designated the M-1955, which was, like the M-1951 it replaced, made of ballistic nylon with Doron plates. The Army vest, the M-1969, was of all-nylon construction. It was identical to the M-1952, save for the addition of a high collar, which added roughly half a pound to the vest's weight, and which soldiers generally disliked, as it interfered with the wearing of the M-1 helmet.
Unusual-looking chemical solutions of that sort were not often pursued; they were usually considered failed or abortive experiments. Kwolek went on to mention that "I think someone who wasn't thinking very much or just wasn't aware or took less interest in it, would have thrown it out." But she persisted, so the solution was spun on a spinneret, and the mechanical properties of the resulting fibers were tested. It quickly became apparent that this new "aramid" fiber was three times as strong as nylon and possessed a far higher modulus and heat resistance. And, despite its high modulus, even these first fibers were so fine that woven fabrics derived from them were flexible, and were able to drape like nylon.
The military quickly realized the potential of this new material, though they didn't rush to implement it in armor systems and issue it to troops in Vietnam. Military-grade aramid fabrics were first designated as PRD-29, and PRD-49 — and later as Kevlar® 29, which was previously PRD 49-IV, and Kevlar® 49, which was PRD 49-III. Kevlar 29 was judged the superior grade for ballistic protection, and prototype flak vests were made which offered significantly greater protective ability than those made of nylon and Doron, at the same weight.
In June 1978, vests comprised of 13 layers of Kevlar 29 ballistic fabric within an envelope of water-resistant ballistic nylon were issued as the "Body Armor Fragmentation Protective Vest, Ground Troops" for United States soldiers. In the early 80s, this type of vest was standardized as part of the PASGT armor system, which also included a helmet made of resin-bonded laminate Kevlar 29. The PASGT system was quite long-lived — it remained in use by the US military until the mid-2000s, and still remains extremely common worldwide, as it was extensively exported. The PASGT's successor, the Interceptor Body Armor system, was also made of aramid — in this case, the improved KM2 fiber. The most recently fielded body armor system, the Improved Outer Tactical Vests, which are a partial replacement for the Interceptor, still incorporate aramid fibers in their soft armor component.
Yet this is not to say that aramid is the only option, nor should it even imply that aramid is the best option.
Scientists at DSM in the Netherlands discovered ultra-high molecular weight polyethylene (UHMWPE) fibers by accident in 1963, during experiments in fractionating out different polyethylene lengths from a solution. It was immediately noted that these very long-chained polyethylene molecules were incredibly strong, but, initially, only small amounts were produced, and it seemed impossible to produce meaningful quantities. This is on account of the fact that the UHMWPE fibers were nearly impossible to orient in solution, so they'd typically form intractable aggregates and clumps, and only a small fraction of each production batch would result in usable UHMWPE fibers.
Although the development of this clever gel-spinning process enabled the industrial production of UHMWPE fibers, DSM was not an industrial fiber company. It was — and to a large extent remains — a food and agricultural supply company that discovered UHMWPE fiber by accident. The UHMWPE team at DSM was essentially a "skunkworks" crew that did their experiments in spare time and on weekends, with little corporate oversight. In the years since its discovery and the development of a commercial production process, the decision-makers at DSM showed no interest in commercializing UHMWPE fiber, and this was not helped by the fact that the consulting companies they asked to evaluate their potential product did not think very highly of it.
Around that time, in the very early 80s, Allied Signal (now Honeywell) obtained a patent on a very similar UHMWPE fiber product, though they claimed that the melting point of their material was 20-30 degrees higher than that of DSM's fiber. As it turned out, the two UHMWPE fibers were largely identical, the melting point differences were due to an methodological error on Allied Signal's part, and, as the DSM patent had priority, Allied was compelled to purchase a license for the original DSM patent.
With the license in hand, and no potential intellectual property conflicts on the horizon, Allied started marketing their own fiber, Spectra, as a competitor to Dupont's Kevlar. Dupont countered with effective marketing campaigns which showed how Spectra would weaken at moderately high temperatures — from 60-80°C. The military, aided by institutional inertia, essentially said "if it ain't broke, don't fix it," and stuck with aramid armors.
It could be argued, in hindsight, that Allied and DSM didn't do enough to promote their material. Yet, at the same time, the first grades of UHMWPE fiber were quite poor. We have seen continual improvement since those early days, and today's grades of UHMWPE fiber are more than 44% superior to the best grades of Kevlar on an equal-weight basis.
Dyneema and Spectra are presently used in high-end body armors, the very newest models of military helmet, and lightweight ballistic shields. Unlike aramid, moderately thick panels of UHMWPE (2cm+) are capable of stopping lead-cored rifle rounds at high velocity, but invariably fail against steel-cored rifle rounds. In fact, they can fail against steel-core pistol rounds; that the SS190 AP 5.7x28mm pistol round can punch through a UHMWPE Level III plate has been documented.
In any case, there's significant room for improvement in UHMWPE fiber materials, and it's likely that further gains will be made within the next 10-15 years.
E-glass fibres, manufactured from alumino-borosilicate, are the oldest armor fibers in modern use, as their use dates back to WWII's Doron. This grade of fiberglass is infrequently used in modern body armor systems, but, on account of its very low cost, is often encountered as a spall mitigation liner in armored vehicles.
S-glass, of magnesium-aluminosilicate, is a superior grade of fiberglass with much-improved mechanical properties: lower density, higher strength, greater stiffness, and a 20% improved strain-to-failure. However, even the best-performing glass fibers perform only roughly half as well as aramid for ballistic applications.
Aramid is, without doubt, the most ubiquitous ballistic fiber in the world at the time of this writing. It is extensively used in standalone body armor systems, spall liners and backings, ballistic helmets and shields, and virtually every other conceivable application — including "armoring" fiber optic lines for extended stays in harsh environments, and armoring satellites from micrometeorite impact. It has excellent resistance to fire and heat, but is sensitive to UV light (photooxidative degradation) and humidity (hydrolysis), so it is typically sealed or coated prior to use, and its characteristic bright yellow color is infrequently seen.
Broadly speaking, this class of polymer composite offers the best performance-to-weight ratio. More specifically, there are a number of grades available, ranging from low-cost grades with a weight efficacy roughly equal to aramid, to very highly-optimized grades, such as Dyneema SB-117 and Spectra Shield 5143, that are much more effective than aramid on a per-weight basis.
UHMWPE is stable in the presence of UV light, but has a low melting-point that leads to performance degradation at high temperatures. This becomes a serious consideration at temperatures over 70°C.
Note: The antiballistic properties of Dyneema HB212 are significantly better than Spectra 1000, but its mechanical properties have not been made public in a comprehensive way.
Carbon fiber is a structural composite that's rarely used as a ballistic material on account of its brittleness, relatively high density, and lack of ductility. It boasts an extremely high yield strength and flexural modulus, however, and its strength and stiffness make it attractive for certain niche applications in armor. It is also highly resistant to UV light, chemical exposure, and temperature extremes. The very best grades of carbon fiber — Toray's T1100G (ultra-high strength) and M60J (ultra-high stiffness) — represent the current state of the art, and are uncommon, whereas the grades T300 and T800 represent the fibers most frequently used in aerospace and automotive applications. T300, in particular, dominates the carbon fiber industry — 95% of sales are of the "standard modulus" T300 grade.


text:
\section{Introduction}

Forty years have elapsed since Freund and Rubin\cite{Freund} opened the way for the study of the seven-dimensional coset compact manifold that occurs in the descent of the eleven-dimensional supergravity to four dimensions.

Can one find traces of this coset manifold  in the Standard Model? To any  group-inclined theorist, a compact seven-dimensional manifold is the domain of  the continuous group $G_2$, the smallest exceptional Lie group  well known as the automorphism group of Cayley numbers.

Spurred by  eleven-dimensional physics, manifolds of $G_2$ holonomy  have been studied ever since the Freund-Rubin paper. These works concern themselves with continuous $G_2$. While (continuous) $SU_3$  is a subgroup of $G_2$, its discrete subgroups have not received the same attention.

The search for an organizing pattern that explains the triplication of Standard Model's chiral families, their mixings and masses  initially suggested  the continuous family  symmetry $SU_3$. The  discovery of neutrino oscillations with  two large lepton mixing angles  pointed to  an underlying {\em Yukawa Crystallography} described by  a discrete family symmetry -- ergo a plethora of models\cite{Review,FlavorReviews} some with triplet representations of discrete subgroups of  $SU_3$.

 This author's research has concentrated on the discrete family symmetries generated by $\m T_7$, the  Frobenius group with 21 elements, and more recently{\cite{ramond1}  on $\m T_{13}$, the $39$-element  Frobenius group. The original physics motivation: both are $SU_3$ subgroups with triplet representations,  can unify quark and lepton flavor models.

The mathematical literature, offers an alternate {\em raison d'\^etre}  for $\m T_7$ as the maximal subgroup of  the simple group $ \m P\m S\m L_2(7)$ of order 168;

Similarly, $\m T_{13}\times \m Z_2$ is the maximal subgroup of another simple group,  $\m P\m S\m L_2(13)$ of order 1092.

 Interestingly both  $\m P\m S\m L_2(7)$ and $\m P\m S\m L_2(13)$ are discrete subgroups of continuous $G_2$; both have seven-dimensional representations embedded in the septet of the  Lie algebra\cite{Slansky}  $G_2$.

 This paper    summarizes  well-known mathematical facts which may offer a discrete path from the Standard Model  to the Freund-Rubin $G_2$ manifold.

\section{Some Frobenius Groups and Progenitors}
We begin with a description of the essentials of the Frobenius groups or order 21 and 39 and 78.
\vskip .5cm
 \noindent $\bullet$  $ \m T_7^{}=\m Z_7^{}\rtimes Z_3^{}$
 \vskip .5cm
\noindent  This 21-element Frobenius group   has two generators which satisfy the presentation
 $$<S,\,T\,|\,S^3=T^7=e,~~S\,T\,S^2=T^2\,>$$
 It contains  five  conjugacy classes,

 $$
 C_1^{(1)}=\{\,e\,\},~ C_7^{(2)}=\{\,T\,\},~ C_7^{(3)}=\{\,S^2\,T\,S\,T^2\,\},
 \, C_7^{(4)}=\{\,T\,S^2\,\},~
  C_7^{(5)}=\{\,S\,\},
  $$
 with $(1,\,3,\,3,\,7,\,7)$ elements of order $(1,\,7,\,7,\,3,\,3)$,  respectively.

 Its five representations break into  three singlets representations:

 $${\bf 1}:~~~T=S=1,\quad {\bf 1'}:~~~T=1,\, S=\omega,\quad {\bf 1''}={\bf \bar 1'}:~~~T=1,\, S=\omega^2,\quad \omega^3=1,$$
 and one complex triplet representation with   conjugate:

$$S=\begin{pmatrix}0&1&0\\0&0&1\\ 1&0&0\end{pmatrix}\quad {\bf 3}:~T=\begin{pmatrix}\eta&0&0\\0&\eta^2&0\\0&0&\eta^4\end{pmatrix},\,~
{\bf \bar 3}:~T=\begin{pmatrix}\eta^6&0&0\\0&\eta^5&0\\0&0&\eta^3\end{pmatrix},
$$
where $\eta^7=1$.

 \vskip 1cm
  \noindent $\bullet$ $ \m T_{13}^{}=\m Z_{13}^{}\rtimes Z_3^{}$
 \vskip .5cm
 \noindent The 39-element Frobenius group  has  two generators with a similar presentation

 $$<S,\,T\,|\,S^3=T^{13}=1,~~S\,T\,S^2=T^3\,>$$
 It contains seven conjugacy classes and  irreps ($n=0,1,\dots 12$):

 \begin{eqnarray*}
 C_1^{(1)}&=&\{\,e\,\},\quad C^{(2)}=\{\,S\,T^n\,\},\quad C^{(3)}=\{\,S^2\,T^n\,\}\quad C^{(4)}=\{\,T,\,T^3,\,T^9\,\},\\
  C^{(5)}&=&\{\,T^2,\,T^5,\,T^6\,\},\quad C^{(6)}=\{\,T^4,\,T^{10},\,T^{12}\,\},\quad C^{(7)}=\{\,T^7,\,T^8,\,T^{11}\,\}
 \end{eqnarray*}
 with $(1,\,13,\,13,\,3,\,3,\,3,\,3)$ elements of order $(1,\,3,\,3,\,13,\,13,\,13,\,13)$ , respectively.

 \noindent  Its seven representations break into  three singlets representations:

 $${\bf 1}:~~~T=S=1,\quad {\bf 1'}:~~~T=1,\, S=\omega,\quad {\bf 1''}={\bf \bar 1'}:~~~T=1,\, S=\omega^2,\quad \omega^3=1,$$
 and two  inequivalent triplet representations  and their conjugates ($\rho^{13}=1$):

 \begin{eqnarray*}
 S=\begin{pmatrix}0&1&0\\0&0&1\\ 1&0&0\end{pmatrix}\quad {\bf 3}_1:~T&=&\begin{pmatrix}\rho&0&0\\0&\rho^3&0\\0&0&\rho^9\end{pmatrix},\,~
{\bf \bar 3}_1:~T=\begin{pmatrix}\rho^{12}&0&0\\0&\rho^{10}&0\\0&0&\rho^4\end{pmatrix},\\
{\bf 3}_2:~T&=&\begin{pmatrix}\rho^2&0&0\\0&\rho^6&0\\0&0&\rho^5\end{pmatrix},\,
{\bf \bar 3}_2:~T=\begin{pmatrix}\rho^{11}&0&0\\0&\rho^7&0\\0&0&\rho^8\end{pmatrix}.
\end{eqnarray*}

 \vskip .5cm
 \noindent Their embeddings into continuous $SU_3$ are straightforward

 $$
 SU_3^{}\subset \m T^{}_7:\qquad {\bf 3}={\bf 3},\qquad {\bf 8}={\bf 1'}+{\bf \bar 1'}+{\bf 3}+{\bf \bar 3}
 $$
and two equivalent embeddings for $\m T_{13}$,
$$
SU_3^{}\supset \m T^{}_{13} :\qquad
\begin{cases} {\bf 3}={\bf 3}_1,\quad {\bf 8}={\bf 1'}+{\bf \bar 1'}+{\bf 3_2}+{\bf \bar 3_2},\cr
  {\bf 3}={\bf 3}_2, \quad {\bf 8}={\bf 1'}+{\bf \bar 1'}+{\bf 3_1}+{\bf \bar 3_1}
 \end{cases}.$$

 \section{Frobenius groups and Spin Lattices}
 Textures based on Frobenius groups such as $\m T_7$ and $\m T_{13}$ can be viewed as  mappings between the world of data (Standard Model parameters) and a   potential $V(\varphi)$, depending on   local familons fields  $\varphi(x,\alpha)$, with only family charges (no gauged quantum numbers).  The familon potential is  invariant the family texture group.

They are labelled by  $x$  the space-time coordinate, and $\alpha$  the family symmetry index. From  the Freund-Rubin perspective, these two labels should unify into those of an eleven-dimensional manifold.

Familons develop vacuum values which can be mapped backwards to the Standard Model and explain/predict its experimental consequences. This is the Familons's {\em ``Standard Model Portal"}. One may ask if there exist other  portals  into different physical systems, with the same  family symmetry expressed in terms of different physical variables, without the gauge {\em accoutrement}  of the Standard Model.
 \vskip .5cm

In 1981, it was noted\cite{Wyler}  that  nonAbelian discrete symmetries expressed as semi-direct products of cyclic Abelian groups, emerge  from spin lattice models with specialized couplings.
\vskip .5cm
 \noindent Consider a square  lattice  with each lattice site labelled by ${\bf n}$. There  sits a ``spin" which can assume one of $p$ values where $p$ is prime  (for the groups discussed above $p=7, 13$), described by the Abelian $\m Z_p$ symmetry, a cyclic group with  $p$ one-dimensional representations with characters,

 $$\chi^{}_r=\exp\Big[\frac{2\pi i}{p}\,r\Big]\qquad r=0,1,...,p-1.$$
The state of the spin at each  lattice point ${\bf n}$ is labelled by the integers $\sigma_{\bf n}=\{0,1,2,...,p-1\}$.

Their interactions  between two lattice points ${\bf n}$ and ${\bf m}$, are determined by the Lagrangian,

$$L(\sigma_{\bf n},\sigma_{\bf m})=L(\sigma_{\bf n}-\sigma_{\bf m}),$$
which preserve global translation invariance over the whole  lattice. For simplicity interaction occurs only between nearest neighbors, with the Action

 $$S=\sum_{<{\bf n}\,{\bf m}>} \, L(\sigma_{\bf n}-\sigma_{\bf m}).$$
Consider the transformations

$$\sigma_{\bf n}~\rightarrow ~\sigma_{\bf n}'=g(\sigma_{\bf n}),$$
 generated by the automorphism group of $\m Z_p$, which  maps the spins into themselves at each site. Global invariance  is achieved whenever

 $$
 L(\sigma_{\bf n}-\sigma_{\bf m})~\rightarrow~L(g(\sigma_{\bf n})-g(\sigma_{\bf m})=L(\sigma_{\bf n}-\sigma_{\bf m}).
 $$
 When $p$  is an odd prime, the automorphism group of $\ Z_p$ is $\m Z_{p-1}$;   Its elements are powers of  generator(s) so that

 $$g(\sigma_{\bf n})=v^m\sigma_{\bf n}\qquad \text{mod}(p)$$

\vskip .5cm

 The other symmetry is the global translation (affine) symmetry under which

 $$\sigma_{\bf n}~\rightarrow ~\sigma_{\bf n}+\tau\qquad \text{mod}(p)
 $$
 at all lattice sites, where $\tau$ is a fixed element of $\m Z_p$.
 When combined, these two symmetries generate a nonAbelian discrete symmetry,   the semi-direct product of the two cyclic symmetries.

The generic  Action is then

$$S(\{y_0,y_1,...,y_{p-1}\})=\sum_{<\bf n\,m>}\,\sum_{r=0}^{p-1}y_r^{}\exp\Big[\frac{2\pi i}{p}r(\sigma_{\bf n}-\sigma_{\bf m})\Big].
$$
The  global symmetry acts on the coupling constants  $y_0,y_1,...y_{p-1}$ which values determined by the desired symmetry.

\vskip .5cm

$\bullet$ Consider the case $p=7$ where the automorphism group is   $\m Z_6=\m Z_2\times \m Z_3$. Our construction yields three non-Abelian groups, ,  $\m Z_7\rtimes \m Z_3=\m T_7$, $\m Z_7\rtimes \m Z_2$, and $\m Z_7\rtimes \m Z_6$.
\vskip .3cm
For  $\m T_7$, let $v$ generate the homomorphic subgroup $\m Z_3$. The general action on the spins at each site is then

$$\sigma_{\bf n}~\rightarrow~v^m\sigma_{\bf n}+\tau, \qquad \text{mod}(7).$$
The integer $v$ is determined by the requirement

$$v^3=1 \quad \text{mod}(7)~~\rightarrow~~\qquad \begin{cases} v=2: 2^3=8=1 \quad  \text{mod}(7)\\ v=4: 4^3=64=1 \quad  \text{mod}(7)\end{cases}
.$$
This symmetry is realized only for special values of the coupling constants, determined by the  $\m T_7$ representations, that is  $y_1=y_2=y_4$ and/or $y_3=y_5=y_6$.
 \vskip .3cm
 The same construction with the full automorphism group yields $\m Z_7\rtimes \m Z_6=\m T_7\times \m Z_2$ which is realized only if all six coupling constants are equal.
\vskip .5cm

 $\bullet$ If we take   $p=13$ the $\m X_{13}$ automorphism group is $\m Z_{12}=\m Z_6\times \m Z_2=\m Z_3\times \m Z_2\times \m Z_2$. The construction of the nonAbelian symmetries proceeds in the same way. The Action depends on thirteen coupling constants $y_0,y_1,...,y_{12}$.

 $\m T_{13}$ is constructed  by considering $\m Z_3$ as the automorphism group. Its generator $w$ is determined by requiring that

 $$w^3=1, \qquad \text{mod}(13)~~\rightarrow~~\qquad \begin{cases} w=3: 3^3=27=1 \quad  \text{mod}(13)\\ w=4: 9^3=729=1 \quad  \text{mod}(13)\end{cases}
.$$
Global invariance under $\m T_{13}$, is obtained whenever the twelve couplings  assemble themselves in four groups of triplets corresponding to $\bf 3_1$, $\bf 3_2$ and their conjugates.
 \vskip .3cm
By choosing   $\m Z_6$ as  the automorphism group, the same construction realizes the  $\m T_{13}\times \m Z_2$ symmetry by grouping  the couplings into groups of six with equal values, reflecting its two sextet representations.

 \section{The Road to $G_2$}
 Searching  for a theoretical origin of these Frobenius symmetries is tantamount to finding   their progenitor simple groups\cite{ATLAS}. We begin with some mathematical factoids:
\vskip .5cm

- $\m T^{}_7$ is the largest  maximal subgroup of $ \m P\m S\m L_2(7)$:
 \vskip .3cm
 $$\m P\m S\m L_2(7)\supset \m T^{}_7. $$
 \vskip .5cm

- $\m T^{}_{13}$ is naturally embedded into the $78$-element Frobenius group $\m Z_{13}^{}\rtimes Z_6^{}$, itself embedded into   $ \m P\m S\m L_2(13)$, the  simple group of order $1092$:
\vskip .3cm
$$ \m P\m S\m L_2(13)~\supset~\m Z_{13}^{}\rtimes Z^{}_6~\supset~\m T^{}_{13}$$

\vskip .5cm
\noindent These two simple groups have a common feature:  real seven-dimensional representations, which suggests that they are embeddable into continuous $G_2$.
\vskip .5cm
 \noindent This is indeed the case, as shown by various authors\cite{Wales,Meurman,Wybourne}

\noindent  A list of $G_2$'s  seven irreducible  discrete subgroup can be be found in\cite{EvansPugh,He}; as expected, all  have real septet representations.

To begin, note that  the $G_2$ Kronecker product of two fundamentals

$$
{\bf 7}\times{\bf 7}=\big[{\bf 7}+{\bf 14}\big]_a+\big[{\bf 1}+{\bf 27}\big]_s
$$
 contains the septet in its antisymmetric product.   Therefore a necessary condition for a good embedding is that the Kronecker product of the subgroup representations must satisfy this requirement, thus limiting  the possible embeddings. The rest of the decomposition  in the antisymmetric product then expresses  the  $G_2$ adjoint in terms of the subgroup's representations.

We now summarize  from  Evans and Pughs\cite{EvansPugh}  the specific embeddings for each of the seven cases.

\vskip .75cm

$\bullet$   {\large $ G_2~\supset~ \m P\m S\m L_2(7)$}
\vskip .5cm
\noindent Order 168. Irreps: ${\bf 1},{\bf 3},{\bf  \bar 3}, {\bf 6},{\bf 7},{\bf 8}$.
\vskip .3cm
\noindent Kronecker products:

${\bf 7}\times {\bf 7}=({\bf 7}+{\bf 3}+{\bf \bar 3}+{\bf 8})_a+({\bf 1}+{\bf 6}+{\bf 6}+{\bf7}+{\bf 8})_s$

$
({\bf 1}+{\bf 3}+{\bf \bar 3})\times({\bf 1}+{\bf 3}+{\bf \bar 3})=({\bf 1}+{\bf 3}+{\bf \bar 3}+{\bf 3}+{\bf \bar 3}+{\bf 8})_a+
({\bf 1}+{\bf 6}+{\bf 6}+{\bf 7}+{\bf 8})_s$

\vskip .3cm
\noindent Two  embedding:

${\bf 7}={\bf 7},\qquad {\bf 14}={\bf 3}+{\bf \bar 3}+{\bf 8}$

${\bf 7}={\bf 1}+{\bf 3}+{\bf \bar 3},\qquad {\bf 14}={\bf 3}+{\bf \bar 3}+{\bf 8}$
\newpage
$\bullet$   {\large $G_2~\supset~ \m P\m G\m L_2(7)$}
\vskip .5cm
\noindent Order 336. Irreps: ${\bf 1},{\bf 1}_1,{\bf 6}_1,{\bf   6}_2, {\bf 6}_3,{\bf 7}_1,{\bf 7}_2,{\bf 8}_1,{\bf 8}_2$.
\vskip .3cm
\noindent Kronecker product:

${\bf 7_2}\times {\bf 7}_2=({\bf 7_2}+...)_a+({\bf 1}+\cdots )_s$

$({\bf 1}_1+{\bf 6}_1)\times ({\bf 1}_1+{\bf 6}_1)=(({\bf 1}_1+{\bf 6}_1)+{\bf 1}'+{\bf 6}_1+{\bf 8}_1)_a+({\bf 1}+{\bf 6}_1+{\bf 6}_2+{\bf 6}_3+{\bf 8}_2)_s$
\vskip .3cm
\noindent Two embeddings:

${\bf 7}={\bf 7}_2, \qquad {\bf 14}={\bf 6}_1+{\bf 8}_1$

${\bf 7}={\bf 1}_1+{\bf 6}_1,\qquad {\bf 14}=....$
\vskip .75cm

$\bullet$   {\large$G_2~\supset~ \m P\m S\m L_2(7)\rtimes(\m Z_2\times\m Z_2\times\m Z_2)$}
\vskip .5cm

\noindent Order 1344. Irreps: ${\bf 1},{\bf 3},{\bf  \bar 3}, {\bf 6},{\bf 7}_1,{\bf 7}_2,{\bf 7}_3,{\bf 8},{\bf 14},{\bf 21}_1,{\bf 21}_2$.
\vskip .3cm
\noindent Kronecker product: ${\bf 7_1}\times{\bf 7}_1=({\bf 7_1}+{\bf 14})_a+({\bf 1}+{\bf 6}+{\bf 21})_s$
\vskip .3cm
\noindent Two embeddings: ${\bf 7}={\bf 7}_1, \quad \text{ and} \quad {\bf 7}={\bf 7}_2 $

\vskip .75cm

$\bullet$   {\large $G_2~\supset~ \m P\m S\m L_2(8)$}
\vskip .5cm
\noindent Order 504. Irreps: ${\bf 1},{\bf  7}_1, {\bf 7}_2,{\bf 7}_3,{\bf 7}_4,{\bf 8},{\bf 9}_1,{\bf 9}_2,{\bf 9}_3$.
 \vskip .3cm
\noindent Kronecker product: ${\bf 7_1}\times{\bf 7}_1={\bf 7_2}\times{\bf 7}_2=({\bf 7_1}+{\bf 7}_2+{\bf 7}_3)_a+({\bf 1}+{\bf 9}_1+{\bf 9}_2+{\bf 9}_3)_s$

\vskip .3cm
\noindent Two embeddings: ${\bf 7}={\bf 7}_1, \quad {\bf 14}={\bf 14}_1 $  or  ${\bf 7}={\bf 7}_2, \quad {\bf 14}={\bf 14}_1  $

 \vskip .75cm

$\bullet$   {\large $G_2~\supset~ \m P\m S\m L_2(13)$}
\vskip .3cm
 \noindent Order 1092. Irreps: ${\bf 1},{\bf  7}_1, {\bf 7}_2,{\bf 12}_1,{\bf 12}_2,{\bf 12}_3,{\bf 13},{\bf 14}_1,{\bf 14}_2$.
  \vskip .5cm
\noindent Kronecker product:

${\bf 7_1}\times{\bf 7}_1=({\bf 7_1}+{\bf 14}_1)_a+({\bf 1}+{\bf 13}+{\bf 14_2})_s$

${\bf 7_2}\times{\bf 7}_2=({\bf 7_2}+{\bf 14}_1)_a+({\bf 1}+{\bf 13}+{\bf 14_2})_s$
\vskip .3cm
\noindent Two embeddings: ${\bf 7}={\bf 7}_1, \qquad {\bf 14}={\bf 14}_1$   or ${\bf 7}={\bf 7}_2, \qquad {\bf 14}={\bf 14}_1$
  \vskip .75cm
$\bullet$   {\large $G_2~\supset~ PU(3;3)$}
\vskip .5cm
\noindent Order: 6048. Irreps: ${\bf 1},{\bf 6},{\bf  7}_1, {\bf 7},{\bf \bar 7},{\bf 14},{\bf 21}_1,{\bf 21},{\bf \overline {21}},{\bf 27},{\bf 28},{\bf \overline {28}},{\bf 32},{\bf \overline { 32}}$.
 \vskip .3cm
\noindent Kronecker product: ${\bf 7}\times{\bf 7}=({\bf 7}+{\bf 14})_a+({\bf 1}+{\bf 27})_s$
\vskip .1cm
\noindent  One  embedding: ${\bf 7}={\bf 7}$

\vskip 1cm

$\bullet$   {\large$G_2~\supset~ G_2(\m {Z}_2)$}
\vskip .3cm
  \noindent Order: 12096. Irreps:  ${\bf 1},{\bf 1}_1,{\bf 1}_2,{\bf 6},{\bf \bar 6},{\bf 7}_1,{\bf 7}_2,{\bf  14}_1, {\bf 14}_2,{\bf 14}_3,{\bf 21}_1,{\bf 21}_2,{\bf 27}_1,{\bf 27}_2,{\bf 42},{\bf 56},{\bf 64}$.

 \vskip .5cm
\noindent Kronecker product: ${\bf 7}\times{\bf 7}=({\bf 7}+{\bf 14})_a+({\bf 1}+{\bf 27})_s$

\vskip .3cm
\noindent  One embedding: ${\bf 7}={\bf 7},\quad {\bf 14}={\bf 14}$
\vskip .5cm

\noindent The interested reader can find more information in\cite{EvansPugh}, especially on the McKay graphs which provide a graphical rendion of the Kronecker products.

\vskip .3cm

\noindent We mention for completeness the embeddings of $\m Z_{13}^{}\rtimes Z^{}_6$,  with two real sextuplet representations into  $ \m P\m S\m L_2(13)$,
\vskip .2cm
${\bf 7}_1={\bf 1}+{\bf 6_1}={\bf 1}+{\bf 3}_1+{\bf \bar 3}_1;\qquad {\bf 7}_2={\bf 1}+{\bf 6_2}={\bf 1}+{\bf 3}_2+{\bf \bar 3}_2$
\vskip .3cm
It is not clear if any of these mathematical connections will prove relevant to an understanding of the roots of the Standard Model. It is nevertheless helpful to gather some of the information in on place which perhaps will bear fruit.

\section{Englert Fluxes and $ \m P\m S\m L_2(7)$}
I have to  mention the work of Pietro Fr\'e and collaborators\cite{Fre}  who compactify eleven-dimention supergravity to
 a four-dimensional space-time with   M-2 branes. Their Freund-Rubin manifold is  generalized to a kind of squashed sphere of the type introduced by Englert\cite{Englert}, where the three form satisfies a complicated equations.

 They construct solutions for the three-form on  a seven-dimensiona' manifold modded out by a ``crystallographic lattice" which they take to be $ \m P\m S\m L_2(7)$. They find a supersymmetric solution  with the Frobenius symmetry $\m T_7$.

 Their work provides  yet another example where these nonAbelian discrete symmetries arise.  In fact they believe that it can shed light on M-theory.

 It would be very interesting if their construction generalizes to $\m T_{13}$, or to any of the finite subgroups of $G_2$ described above.

 \section{A personal note}
 I met Peter in person soon after arriving at FermiLab (then NAL). My early recollection  was at a seminar by  Nambu-Sensei:   received in silence by an attentive audience desperately trying to understand the wisdom of the master, until a booming voice arose ``Yoichiro Yoichiro, no, no,no ...", and rushing to the blackboard to explain; I do not remember the rest. My friend  Lou Clavelli who had been a student at Chicago told me, this is Peter Freund.

This stentorian  voice belonged to an extremely friendly and inquisitive person, who knew an amazing amount of physics,  mathematics, and  not least stories! A font of knowledge on many fronts.

 The last time I saw Peter was at the Nambu memorial in Osaka, where we shared a few days which  I very much enjoyed in his civilized  company.

 I am honored by writing this paper on one of his fundamental contributions to physics.
 \vskip 1cm

 \noindent I  thank my collaborators for useful discussion with my students,  Moinul Rahat and Bin Xu, and  acknowledge partial support from the U.S. Department of Energy under award number DE-SC0010296.

redpajama_set_name: RedPajamaArXiv


text:
El Carbó o Es Carbó és una platja del terme de ses Salines, a l'extrem sud-oriental de Mallorca. De vegades s'anomena impròpiament Cala Carbó, ja que no és una cala.

El Carbó és una platja extensa, d'uns 1400 metres de llargada i 45 d'amplada, que s'estén entre la platja des delfí i la punta de na Tianeta. A la platja s'hi poden distingir dos sectors: un primer sector comprès entre la platja des delfí i la Punta de s'Alfàbia, orientat cap a ponent, i un segon sector, entre aquesta punta i la punta de na Tianeta, orientat cap a llebeig, que al seu extrem es tanca altre cop cap a ponent per tancar la petita badia, al fons de la qual hi ha la platja. El primer sector és es Carbó pròpiament dit. El segon és també conegut amb el nom de sa platja de ses Roquetes.

La platja és d'arena blanca i molt fina, tot i que no tan fina com a les platges veïnes d'es Trenc i sa Ràpita, ja dins el terme de Campos. Les aigües són completament cristal·lines. La punta de s'Alfàbia és al mig de la platja i és completament arenosa, constituïda per una duna d'una alçada considerable, d'uns 6 o 7 metres, orientada cap a llebeig.

La platja és completament verge i una de les més ben conservades de Mallorca. Només és freqüentada al mes d'agost per nombroses embarcacions, però així i tot, l'arena està molt poc ocupada per banyistes. Tota la platja es troba dins l'emblemàtica possessió de sa Vall, i per això l'accés des de l'interior està fortament restringit: només hi poden accedir els que puguin acreditar que estan empadronats a ses Salines. L'única alternativa per accedir-hi des de terra és, doncs, caminar bordejant la costa des del nucli turístic de sa Colònia de Sant Jordi, a uns dos quilòmetres de distància.

A la zona hi abunden els illots, entre els quals destaquen na Guardis, on es conserven restes púniques, i especialment na Moltona, just davant es Carbó, separada de la costa per un braç de mar poc profund d'uns 300 metres, i on hi viu una espècie endèmica de sargantana. El conjunt d'illots i la platja són d'un valor paisatgístic espectacular. Davant la platja, a més de l'illot de na Moltona, també n'hi ha d'altres de menor interès, com na Pelada, l'illot gros de na Moltona, l'illot petit de na Moltona i l'illot de ses Roquetes. Aquests tres darrers es poden considerar, però, simples esculls.

La platja és poc profunda i no és perillosa per als banyistes, tot i que no està vigilada i no disposa de cap servei. És una platja resguardada i no s'hi produeixen corrents perillosos.

Referències

Platges de ses Salines

redpajama_set_name: RedPajamaWikipedia


text:
'use strict';

var express = require('express');

var Router = function(controllers, options) {
  var router = express.Router();
  var i;

  for (i = 0; i < controllers.length; i++) {
    controllers[i].routerOptions = options;
    controllers[i].addRoutes(router, options);
  }

  return router;
};

module.exports = Router;

redpajama_set_name: RedPajamaGithub


text:
NoVo Foundation Makes Respectful $90M Investment in Girls and Women of Color
Shafaq Hasan
March 23, 2016; Associated Press
Known for its innovative and pioneering work to empower girls and young women, the NoVo Foundation announced an unprecedented $90 million investment to address the barriers perpetuating inequality and preventing girls and young women of color from finding the same success as some of their peers. The seven-year effort is meant to build and deepen the foundation's previous commitment supporting girls and women with a national focus.
According to the foundation, which is run by Warren Buffett's youngest son, Peter, and his wife Jennifer, the initiative's first part involves going into communities to speak directly with girls and young women of color and hear their perspectives to better understand what their needs are and how they can be addressed. Peter Buffett, as readers may remember, has been challenging of traditional philanthropy, calling it a "perpetual poverty machine."
The project will travel both to big cities as well as more remote areas of the country to listen to those who are supposed to benefit in order to shape the grant initiative. After the initial exploratory phase, the foundation will meet in early 2017 and begin the grantmaking process.
"At the foundation, we believe that we always start with listening—that's a core belief," said NoVo executive director Pamela Shifman in an interview with NPQ. "And we know that girls and young women of color are experts on their own lives. They must lead the way."
While the concept for this project has been in the works since 2014, the need to focus on empowering girls and young women of color has been gaining momentum within the greater philanthropic world has grown in recent years. With black, Hispanic, and Native American girls all less likely to graduate from high school than their white counterparts and significantly more likely to live in poverty, missed educational opportunities and economic impediments propagate further inequality as the girls reach adulthood.
"It was clear to us from the very beginning that we needed to focus on girls. […] What we know is that girls of color in the U.S. face unique and deep-seated structural challenges, including barriers to completing school and living free from all forms of violence, state violence and interpersonal violence," said Shifman.
As noted by the Associated Press, along with the NoVo Foundation, other initiatives have also invested in the cause, like Black Girls Rock! and The Latina A.R.M.Y. Having grown up as a minority myself and experienced some barriers, though certainly not to the extent many other young minority girls have, I can appreciate that finding role models and mentors of color who girls and women can relate to is an important goal the philanthropic world is still trying to address.
For example, nonprofit sector projects, including NoVo's new initiative, may want to turn their attention to ensuring that schools have a diverse pool of teachers and counselors. After graduating from high school and college, in 16 years, I never had a single teacher who was Middle Eastern. Having a black teacher or a Native American teacher who would inherently understand the stumbling blocks their students face, having experienced them themselves, would undoubtedly resonate with girls and young women. Not only could it improve academic performance among girls and young women, but it might more effectively address girls' needs in school.
As the philanthropic world gets on board with the variety of ways they can help young women and girls of color, Shifman is adamant that although NoVo may be a leader in addressing inequality among girls and young women, their efforts are rooted in activism from the past decades and the wisdom of today's young women of color.
"We really take so much guidance from women of color who have been leading a movement for years, for decades to highlight the disparities facing girls and young women of color in this country. Thanks to their efforts disparities facing girls and young women of color have finally become impossible for the rest of the country to ignore."—Shafaq Hasan
Shafaq Hasan is a Community Builder at NPQ. She is a graduate of Brandeis University where she majored in Art History and spent most of her time working in the office of the student newspaper as the Opinions editor, and later, as an Associate editor. As an undergraduate, she was also a research assistant for the Justice Brandeis Law Project at the Schuster Institute for Investigative Journalism from 2011 to 2014.
More about: race-based inequality representative leadershipInequalityNonprofit NewsPhilanthropy
Linking Our Fights to Win: On Combatting Elite Capture
Kitana Ananda and Olúfemi O. Táíwò

redpajama_set_name: RedPajamaCommonCrawl


Finally, for the first time an application that lets you categorize and record guests and their responses for an event!
Guest List RSVP is a very simple to use application that helps you organize the information about who is going to be coming to your event in an easy to read chronological format.
Our app creates a tab delimited file that can be used to be exported/imported into any spreadsheet computer software.
With this application your guests are categorized by important or optional guest for the event depending on its relevance and closeness. For each family or guest you have the option to enter the amount of people that will be attending, when they replied and their names. Furthermore, you can select from a simple scroll down menu if they will be joining you, have not replied or will not be able to attend. After you enter the information, it appears summarized in a list format as soon as you load the application.
For your convenience we added the option to quickly send the information about guests to anyone interested such as the party planner or even yourself with the tap of the envelope icon. Also, in the target section you can enter the minimum and maximum amount of guests you intend to host, your budget and how much you want the cost per guest to be.
Business meetings, weddings, birthday parties and family reunions among others will definitely be easier to plan with "Guest List"; since it is a great way to keep organized all the guest information in just one application!
We are constantly working on improving this and our other applications; please feel free to share with us any ideas or suggestions you may have! Also, if you feel like there is an application missing for your lifestyle on the iPhone, please let us know; we are always looking for new ideas to develop in order to simplify life with your iPhone!
Keywords: Corporate, graduation, school, college, meetings, events, Wedding, Bar mitzvah, Business, engagement,Baptism, Bridal, Shower, Baby, birthday, house warming, bachelorette, bachelor, invitation, married, marriage, and more!


In our study of the General Epistles this year, we have tried to keep in mind the original context in which the letters were written in order that we might be faithful to the intent of the writer. As we have mentioned several times already, several of these letters deal with the rise of false teaching and the impact of false teachers upon the original audience. In the case of 1 John, these teachers espoused a proto-Gnostic heresy that denied the reality of the incarnation as well as the importance of love for the brethren and personal holiness.
The original audience of 1 John, however, did not follow these teachers but successfully resisted them. We know that their resistance was successful from places like today's passage, which tells us that the audience had overcome the spirit of the antichrist lying behind any denial of the incarnation (4:4; see vv. 2–3).
Though the audience had resisted these teachers, the disruption they caused had resulted in many of the orthodox doubting their salvation. However, the fact they had overcome this false teaching should have assured them of the reality of their redemption. For they were only able to resist this false teaching because of the One in them who is greater than the one in the world (v. 4).
This One is the Holy Spirit who dwells within all believers (3:24; 1 Cor. 6:19–20). As Christians we enjoy the subjective testimony of His presence as He moves our own spirit to cry out "Abba, Father!" (Gal. 4:6). Yet the presence of the Spirit, we have seen, manifests itself in objective ways, particularly by having us hold firmly to the orthodox teachings of the apostles. He gives us faith to confess the incarnation (1 John 4:2) as well as every other essential doctrine, and by making this confession we prove that we have the Spirit and are enabled to resist falsehood just as John's original audience did.
False teaching is overcome by the truth, and we will only know the truth if we submit ourselves to the Spirit of truth Himself. Therefore, we must surrender ourselves daily to Him, asking Him to illumine the Word of God and empower us for service. Without His guidance, we will not overcome the world (Gal. 5:16–26).
Many of the greatest Reformed theologians in history, including John Calvin and John Owen, are well-known for their understanding of the person and work of the Holy Spirit. Unfortunately, for a variety of reasons, the Spirit today is sometimes called the forgotten person of the Trinity. Do you treasure the work of the Spirit in your life? Do you ask Him to guide your study of Scripture and inflame you with passion for God and His people? Ask Him to do these things today.


Finding affordable and stylish clothes for men can be a bit tricky. So many brands and retailers produce cookie-cutter styles that will quickly assimilate your individuality into a look that is largely homogeneous. In other words, you'll waste a lot of time, energy, and money only to look like everyone else.
If you're currently stuck in the world of Old Navy, Gap, Banana Republic, American Eagle, Express, Abercrombie & Fitch, or Hollister, then this guide is written especially for you: it's time to break away from the herd. Those brands are alright for young adults up to the age of 19 or so but once you officially exit your teens, you need to start dressing like an adult.
Here are the top 15 retailers that offer some of the most affordable, stylish fashions available to men: BlueFly, Bonobos, Century 21, Club Monaco, Gilt Groupe, H&M, Jack Threads, Saks Off 5th, Top Man, Uniqlo, Vineyard Vines, YesStyle, Yoox, Zappos, and Zara.
Gilt is an online retailer that offers an exclusive, invitation-only program that gives you access to scheduled sales of all sorts of hand-selected luxury fashions for men. You may get a savings of up to 60% off retail. I also love that they feature a number of the smaller boutique brands.
Quantities are very limited on their sales, but you do have an opportunity to preview the items prior to the sale launch; this is helpful because if you find a must-have item, you can put the sale on your calendar and return to the website to order once the sale begins.
If you are obsessed with designer labels but want authentic apparel at discounted prices, then look no further than BlueFly. The fashion buyers there source brand new clothes from over 350 retailers at discounts of 20% to 75%. Personally, I have spent quite a bit at BlueFly to update my business attire, so I can attest to the value and savings. If you're looking for name brand at a discount, then this is the place to shop.
Bonobos is one of my favorite men's clothing retailers. The company started out tackling the problem of poor-fitting men's pants when they completely redesigned the cut of men's pants to be better-fitting and more flattering to the body. With that same principle of making good fitting clothes, Bonobos produces a full line of men's clothing including shorts, jackets, shirts, and more.
Unless you live in the New York City metropolitan area, you've probably never heard of Century 21, but if you ever have a chance to visit one of their 10 locations, you should.
Century 21 is unlike any discount retailer I've ever seen. It's sort of like a massive warehouse with floor after floor of discounted high-end fashions. Imagine Filene's basement (before going of business) but on steroids--that's what Century 21 is like.
You can shop Century 21 online, however they don't have anywhere near the designers online as they do in the store as there are many one-of-kind pieces in the store.
Club Monaco may appear in a shopping mall in the a clot of uninspiring fashion retailers like Banana Republic or Express, but don't be fooled, it's quite different. Founded in Toronto, Club Monaco offers chic fashions that appeal to the creative consumer and they truly embody the concept of affordable luxury.
Club Monaco also does something you won't see at any other fashion retailer–they offer 20% discount to college students. You just need to show your ID.
H&M is a Swedish-based company with the goal to provide good fashion and quality at the best price. Similar to Uniqlo (see below), H&M does an excellent job at keeping tabs on the market trends and runway looks, and new concepts are planned almost a year in advance.
The men's collections include everything from tailored and modern to basics, leisurewear, and seasonal fashions. Plus, they also produce matching accessories, underwear, and shoes.
H&M clothes cannot be purchased online, but they do have 2,200 stores in 40 markets–you're bound to find them in most big cities.
Jack Threads is a members-only shopping club that posts new sales around noon each day; it's very similar to Gilt, but they focus on a totally different customer. At Jack Threads, you're only going to find contemporary fashions like street, skate, and surf wear.
For the hip and cool kids, it's the perfect place to find top-tier but deeply discounted fashions.
Saks Off 5th is a clearinghouse for Saks Fifth Avenue stores. Here you will find some pretty incredible deals and mark-downs. Saks has developed the Off 5th brand into its own store concept so while it does have markdowns, it also carries merchandise for its house brand.
Some of the best deals you'll find at Off 5th are with the private label Saks brand products, especially the men's dress shirts. This is my go-to store for dress shirts; the cotton is fine, soft, and available at an incredible value.
I think Saks Off 5th is a great place for the budding young professional to find stellar business attire.
A counterpart to the famous TOPSHOP brand, TOPMAN is a leading men's fashion retailer in the UK with a number of retail stores, but also online (with international shipping). TOPMAN is leading the revolution in men's fashion on the British High Street with their in-house designed fashions and styles.
Uniqlo is Japan's leading clothing retailer of casual wear and operates over 800 retail stores across the globe. Its clothing designs are produced up to a year in advance by an in-house team that continuously monitors the latest fashion trends and styles.
Like H&M, you cannot purchase clothes from Uniqlo online at this time. Their only store in the USA is in New York City.
Vinyard Vines, inspired by life on Martha's Vineyard, is a colorful, preppy fashion brand with a full assortment of clothing that exudes personality.
YesStyle is the first online retailer to globally distribute a huge selection of men's clothes from Asia. They offer customers the latest trends along with thousands of fashion items from designers across Asia. For men seeking the most progressive styles in men's fashion, you need not look any further than YesStyle–it's a treasure trove of some of the most exotic and sensational clothes you'll ever find.
Yoox is one of the leading multi-brand fashion and design retailers online. Of all the retailers I've reviewed, Yoox probably has one of the largest selections of hard-to-find pieces from some of the most prestigious designers. You could easily spend hours surfing through the inventory on their website (and they have an amazing iPad app as well).
Zappos is widely known as a discounted retailer of name brand shoes, but they also carry a wide selection of designer clothing and accessories.
In fact, there are designers on Zappos that I don't see carried anywhere else online at a discount (e.g. Alexander McQueen). What makes Zappos so special is their customer service and returns policy–it's truly a hassle-free experience.
Zara is a Spain-based fashion retailer that operates hundreds of stores in over 70 countries. Unlike H&M and Uniqlo that both traditionally need 6 months to a year to introduce new fashions into their stores, Zara is able to do this in about two weeks. In other words, Zara is able to respond to the latest trends more quickly than its competitors, providing you an opportunity to seize the latest and greatest fashions for your wardrobe.
Which brand do you like the best?
Lol this Article lost all credibility when he put H&M on the list but stores like Express and Banana Republic are for 19 year olds. H&M is part of this new craze where you buy nice looking clothes in the worst possible quality. Might as well put Forever21 on this list as well.
I think ZARA have some very good offers.
Where do you go to buy cheap second hand designers clothes?
You can't forget http://www.threadsandshirts.com Great online site for custom shirts, suits and much more affordable than some of the sites already mentioned. They are pretty good from a men's fashion point of view.
Nice stores here! Thanks for showing me a few new ones. And for all the guys griping about the prices, go check the retail price on some of these designers. I think they are all a great deal and we'll deserved of the title affordable.
I typed in "affordable mens clothes" in google and here I am, now being referred to 'discounted' websites selling me socks at $100+. The average twenty-something has no way to afford this.
Or, Jacob, you could write an article titled "Top 15 Most Affordable, Stylish Places to Buy Men's Clothes" in which you actually list 15 affordable places. Instead of stores like Vineyard Vines, where a v-neck sweater sells for $145.00.
I've taken a lot of heat on this article. I'm trying to provide discounted retail options (that yes, aren't the cheapest), but cheaper than full retail and still provide good fashion. If you want the cheapest, then stroll on over to Walmart and JC Penny.
Are you serious? Besides H&M and Zara, NONE of these are affordable.
Jacob, if this is your own personal article, I think you should remove the word affordable from everywhere it's written. If this is just content you were paid to write, then the company who paid you is just dumb..
Great hub and great clothes. I am especially a fan of men's leather clothing. What are your thoughts on men's leather jackets, leather pants?
"Seriously, I don't understand how you figure this is affordable. H&M is the only store that fits the bill." Ditto.
Do you have any suggestion as to where I could find leather jackets and pants that are not too expensive?
Seriously, I don't understand how you figure this is affordable. H&M is the only store that fits the bill.
Really awesome places to buy clothes.
True, really stylish way of getting clothes.
All are best shopping places for men.
This person must be a trust fund baby, some of these websites have $200 shoes as there cheapest pair.


Don't let the limited capabilities of your hotel or B&B keep you from your fitness habits while vacationing in St Augustine. We have the package built for travelers with the most versatile offering in St Augustine to fit your need.
Passes include access to all amenities and group exercise classes. Personal Training and Team Training are available with additional charge.


Did you know that broadband Internet is up to 73 times faster than dialup and that it is always on.
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Theories and methods involved in environment and health research from a medical geographical perspective. "Environment" includes urban, social, political, cultural and physical environments. "Health" includes complete social, physical, and emotional well-being. Current issues in environment and health will be placed within a wider social/community context.
All of GEOG 101A, GEOG 211, GEOG 218.


text:
Rebecca Salter RA, portrait by Geoffrey Winston
Rebecca Salter PRA
Rebecca Salter studied at Bristol Polytechnic and then at Kyoto City University of the Arts in Japan, where she lived for six years. While living in Kyoto, Salter studied traditional Japanese woodblock printing with Professor Kurosaki Akira and has since written two books on the subject. Her interest in printmaking is combined with her main practice in painting. Until 2016 she was Associate Lecturer on the MA Printmaking Course at Camberwell College of Art, University of the Arts, London.
Salter exhibits regularly in London and internationally, and in 2011 she had a major retrospective into the light of things at the Yale Center for British Art, New Haven, Connecticut. A monograph was published to coincide with the show. An accompanying exhibition at Yale University Art Gallery explored links between Western artists and Japan. She has also been artist in residence twice (2003 and 2011) at the Josef and Anni Albers Foundation, Connecticut. Salter has undertaken several architectural commissions including 15 Sackville Street, London W1, St George's Hospital, Tooting and NGS Macmillan Cancer Unit, Chesterfield Royal Hospital. She has work in many private and public collections including Tate, British Museum, Yale Center for British Art and Yale University Art Gallery.
Salter was elected as a Royal Academician to the category of Printmaker in December 2014 and, in June 2017, was elected as the Keeper of the Royal Academy. On 10th December 2019 she was elected the 27th President of the Royal Academy of Arts and became the first female President since the Academy was founded in 1768.
Elected RA: 10 December 2014
President from: 2019
Keeper from: 2017 - 2019
Preferred media: Printmaking, Woodblock prints, Wood engraving, and Painting
Works by Rebecca Salter in the RA Collection
Untitled AG48, 2014
Gouache and pyrography on japanese paper
Works associated with Rebecca Salter in the RA Collection
From: Anne-Katrin Purkiss
Rebecca Salter RA, April 2015
Giclee print. camera: nikon d800
Anne-Katrin Purkiss
Rebecca Salter R.A., April 2015
Silver gelatin print. camera: hasselblad, 400 asa ilford delta film
F.L. Griggs RA
Tattershall Holy Trinity, 1912
The act of drawing is at the heart of everything I do. It is the most intimate of processes, encouraging you to explore and take risks and at its best reveals both the hand and mind of the artist to the viewer.
Rebecca Salter RA
Rebecca Salter RA, Untitled AD30, 2012.
Mixed media on Japanese paper on linen. 160 x 180 cm. © Rebecca Salter.
Rebecca Salter RA, Untitled AH27, 2015.
Mixed media on linen. 160 x 170 cm. Courtesy of the artist.
Mixed media on muslin on linen. 100 x 105 cm. Courtesy of the artist.
Rebecca Salter RA, Untitled AK3, 2017.
Rebecca Salter RA, Untitled AJ14, 2016.
Mixed media on Japanese paper. 92 x 98 cm. Courtesy of the artist.
Watercolour on Somerset paper. 98 x 92 cm. Courtesy of the artist.
Rebecca Salter RA, Grisaille series 1 and 2, 2016.
Editions of 14.
Japanese woodblock on kozo paper. 35.5 x 27 cm, 35.5 x 27 cm. Courtesy of the artist.
Rebecca Salter RA, Rasa, 2017.
Edition of 30.
Japanese woodblock on torinoko paper. 33 x 48 cm. Courtesy of the artist.
Selected CV
Recent solo exhibitions
2016 Paintings, Drawings, Prints, Beardsmore Gallery, London
2015 First Light, Howard Scott Gallery, New York
Along These Lines, Beardsmore Gallery, London
2013 Beyond, Beardsmore Gallery, London
2011 into the light of things: Rebecca Salter 1981-2011, Yale Center for British Art, Connecticut
Solo exhibition, Howard Scott Gallery, New York
Drawn, Beardsmore Gallery, London
2009 Pale Remembered, Beardsmore Gallery, London
2007 The Unquiet Gaze, Howard Scott Gallery, New York
2006 Bliss of Solitude, Beardsmore Gallery, London
2004 Inner Eye, Howard Scott Gallery, New York
The British Museum
The British Council
Government Art Collection
Cambridge Institute for Medical Research
Frechen Kunstverein, Germany
Graphotek, Stadtbucherei, Stuttgart, Germany
Yale Center for British Art, New Haven, USA
Yale University Art Gallery, New Haven, USA
Library of Congress, Washington DC, USA
Rebecca Salter, Japanese Woodblock Printing, 2001
A&C Black/University of Hawaii
Rebecca Salter, Japanese Popular Prints, 2006
ed. Gillian Forrester, Rebecca Salter: into the light of things, 2011
Rebecca Salter PRA: "Do not tell young people they can't do things"
Meet Rebecca Salter PRA – the first female President in the RA's 251-year history. Speaking in 2017 upon her election as Keeper of our Schools, she talks art and the next generation, trying a new culture and swimming in the winter.
249 years of teaching artists in the RA Schools
At the heart of the Royal Academy, you can find Britain's longest-running art school, which has been training artists since 1769. As soon-to-be graduates present their final year show, Skye Sherwin speaks to students and tutors to find out what's changed in the last quarter millennia.
Top picks from the Collection: Rebecca Salter RA
"I've been drawn to works on paper that really show the thought processes of artists and architects", says printmaker, painter, and Keeper of the RA Schools Rebecca Salter, as she gives an audio tour of the online Collection.
< 3 years ago
The best art books for foodies
Rebecca Salter RA brings her artist's palate to matters of taste, in a delicious round-up of the best books on art and food.
How do you get from the "American dream" to the Japanese house?
Sam Phillips finds the dotted line from the British Museum's American prints through to Japanese architecture at the Barbican, in six sizzling spring shows.
> 3 years ago
How I made it, by Rebecca Salter RA
Rebecca Salter RA talks about the "uncharted territory" of working in film for Picture the Light, her collaboration with the musician Max de Wardener.
Making a Japanese woodblock print for the Summer Exhibition
In this video, Rebecca Salter RA explains the traditional tools and techniques used by the Sato Woodblock Workshop in Kyoto when creating her print for the Summer Exhibition 2016.
Rebecca Salter RA on the tradition of Japanese woodblock printing
The Academician has spent her career studying and promoting the threatened art of Japanese woodblock printing. Here, she tells us about her new prints, commissioned for the Summer Exhibition.
Friends Week 2015: The highlights
The inaugural Friends Week at the Royal Academy featured a packed programme of talks and events. If you missed it – don't despair. Here are some of the highlights.
Our pick of this week's art events: 8 – 15 May
From Sarah Lucas's erotic sculptures at the Venice Biennale to Jeff Koons at Norwich Castle Museum & Art Gallery, we guide you through the week's top art events.
10 minutes with… Rebecca Salter RA
Each month, we have a quick chat with one of our Academicians to find out what they're up to and what the RA means to them.


text:
Hank Williams III (* jako Shelton Hank Williams; 12. prosince 1972 Nashville, Tennessee, USA) je americký zpěvák, kytarista, hudební skladatel. Je vnukem Hanka Williamse a jeho otec je Hank Williams, Jr.. Hraje převážně country, ale byl členem i několika heavy metalových a punk rockových skupin, jako jsou Superjoint Ritual, Arson Anthem a Assjack.

Diskografie
 Three Hanks: Men with Broken Hearts (1996)
 Risin' Outlaw (1999)
 Lovesick, Broke and Driftin' (2002)
 Straight to Hell (2006)
 Damn Right, Rebel Proud (2008)
 Rebel Within (2010)
 Hillbilly Joker (2011)
 Ghost to a Ghost/Gutter Town (2011)
 3 Bar Ranch Cattle Callin' (2011)
 Attention Deficit Domination (2011)
 Long Gone Daddy (2012)

Externí odkazy

Narození v roce 1972
Žijící lidé
Američtí zpěváci
Američtí kytaristé
Američtí bubeníci
Američtí baskytaristé
Cowpunk
Muži
Narození 12. prosince
Narození v Nashvillu


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Before before I go into the different sins of content marketing, lets check out this survey done of what the biggest content marketing challenges are.
Do not get Mad: Since promotion on social media takes less time and it is extremely cost effective, marketing professionals are increasingly shifting their attention from traditional SEO techniques. The greed to get more from social media campaigns drive many marketers crazy and they go on submitting almost anything that come their way, be it interesting or boring, into different social media platform in the hope of driving more traffic to their websites. But this is sheer wastage of time and effort.
Stay committed: Do you know what makes the difference between a good marketer and a bad marketer? It is just the commitment. Good marketer works hard to end and he never rests until he attains success, whereas a bad marketer takes things for granted and looks for short cut all the time. But believe me, there is no shortcut to success. You have to write different content for different social media websites and you need to have different marketing strategies if you are to see success at the end.
Do not be Angry: Since the concept of content driven marketing is still in its development stages, you might end up seeing the same rivals promoting their content on all networks. Now, do not get angry at the sight of this. You need to stay calm and never ever try to mock or defame others because if you do so, they will also follow the same path and your online reputation will go busted. Hate only begets hate. Love all and you will be loved by all.
Do Not be jealous: Do not be jealous at the success of others. Think this way – people are successful just because they have worked hard and the only way you can see success is by working honestly. The bottom-line is that unless you have great content, there is very little chance of making it big in the content driven marketing campaign. Another thing, you should not use content of others and promote it as your own, it will just be a clear case of marketing suicide.
Do Not be over Confident: If you think the quality of your content is great, this is good for your company and your marketing mix but there is no need to brag. Mortal people, as we are, we can't help but boast at the slightest sign of doing better than the others. We try to undermine the quality of others and this is where downfall begins. We should stop bragging rather we should takes the gloves off and get ready for making further improvement on the quality. Think like Jobs and not like people standing next to you working 9 to 5 job.
Do Not Be Disappointed: Marketing of content is time consuming and sometimes it takes month to get the results. So, you should not get disappointed if you do not see any sign of success at the initial stage. Stick to what you are doing and you content driven marketing campaign will be able to tap the elusive success at the end.