text:
Not only did political events make a huge impact on fashion trends but also the political figure played a critical role in forecasting the fashion trend. For example, First Lady Jacqueline Kennedy was a fashionable icon of the early 1960s who led formal dressing trend. By wearing a Chanel suit, a structural Givenchy shift dress or a soft color Cassini coat with huge buttons, it created her elegant look and led a delicate trend.[33]
I also loved "copy your competition and then be better"; what sets each person/blog apart is the perspective they write from. We're all unique like snowflakes (how precious) but the reality of it is, how are you showing that uniqueness? In order to be a successful blogger, you need to connect with your audience in a way they want to be connected with. Recycling ideas and putting your unique voice and creativity on them is how you'll connect in a different way than others have. I just bought a book, "Steal like an artist" (by Austin Kleon) that talks about this exact thing!
The fashion industry is seeing how 3D printing technology has influenced designers such as Iris Van Herpen and Kimberly Ovitz. These designers have been heavily experimenting and developing 3D printed couture pieces. As the technology grows, the 3D printers will become more accessible to designers and eventually consumers, which could potentially shape the fashion industry entirely.
2) Converting traffic – Publish a weekly newsletter once a week. Keep it brief and share 1 tip each week. This has worked really well for me to build up a relationship with my readers and drives sales of my online app courses. When people email to thank you for free info shared to your mailing list, and converted to buying paid courses based on this, you are on the right track.
Susie Lau's Style Bubble has been going for over a decade and includes intelligent articles on everything from underground global fashion talent to perfume. She also provides fascinating behind-the-scenes pieces on the real work it takes to create a beautiful Chanel garment. Then there's the tongue-in-cheek Man Repeller run by Leandra Medine and her team. Its smart, witty take on fashion is refreshing. And if over-the-top clothes aren't your thing, we've also found plenty of bloggers with more pared-back styles for the minimalists.
Aiming to "amplify a greater message of unity, inclusion, diversity, and feminism in a fashion space", Mara Hoffman invited the founders of the Women's March on Washington to open her show which featured modern silhouettes of utilitarian wear, described by critics as "Made for a modern warrior" and "Clothing for those who still have work to do".[75] Prabal Gurung debuted his collection of T-shirts featuring slogans such as "The Future is Female", "We Will Not Be Silenced", and "Nevertheless She Persisted", with proceeds going to the ACLU, Planned Parenthood, and Gurung's own charity, "Shikshya Foundation Nepal".[72] Similarly, The Business of Fashion launched the #TiedTogether movement on Social Media, encouraging member of the industry from editors to models, to wear a white bandana advocating for "unity, solidarity, and inclusiveness during fashion week".[76]
These levels consist of many separate but interdependent sectors. These sectors are Textile Design and Production, Fashion Design and Manufacturing, Fashion Retailing, Marketing and Merchandising, Fashion Shows, and Media and Marketing. Each sector is devoted to the goal of satisfying consumer demand for apparel under conditions that enable participants in the industry to operate at a profit.[32]
Great Post, I chose to focus on the crowdfunding niche. It was a 2 billion dollar industry last year and is projected to be a 5 billion dollar industry this year. I recommend using Fiverr to use graphic designers for first time bloggers. I did use the logo designed for five dollars at the top of my site (bottom now) but stopped using it because it didn't look good on mobile.
Why: While Lesego doesn't have a blog per se, she does have a very active Instagram full of gorgeous photography and thoughtful captions (she occasionally dabbles in vlogging too). Be it the latest fashion trends, amazing lingerie or even those tricky to style narrow sunglasses, she's a deft hand at styling and out to destroy any preconceptions of what a curvy girl can and can't wear.
Vogue, founded in the United States in 1892, has been the longest-lasting and most successful of the hundreds of fashion magazines that have come and gone. Increasing affluence after World War II and, most importantly, the advent of cheap color printing in the 1960s, led to a huge boost in its sales and heavy coverage of fashion in mainstream women's magazines, followed by men's magazines in the 1990s. One such example of Vogue's popularity is the younger version, Teen Vogue, which covers clothing and trends that are targeted more toward the "fashionista on a budget". Haute couture designers followed the trend by starting ready-to-wear and perfume lines which are heavily advertised in the magazines and now dwarf their original couture businesses. A recent development within fashion print media is the rise of text-based and critical magazines which aim to prove that fashion is not superficial, by creating a dialogue between fashion academia and the industry. Examples of this trend are: Fashion Theory (1997) and Vestoj (2009). Television coverage began in the 1950s with small fashion features. In the 1960s and 1970s, fashion segments on various entertainment shows became more frequent, and by the 1980s, dedicated fashion shows such as Fashion Television started to appear. FashionTV was the pioneer in this undertaking and has since grown to become the leader in both Fashion Television and new media channels. The Fashion Industry is beginning to promote their styles through Bloggers on social media's. Vogue specified Chiara Ferragni as "blogger of the moment" due to the rises of followers through her Fashion Blog, that became popular.[52]
Building brand awareness and credibility is a key implication of good public relations. In some cases, great hype is built about new designers' collections before they are released into the market, due to the immense exposure generated by practitioners.[57] Social media, such as blogs, micro blogs, podcasts, photo and video sharing sites have all become increasingly important to fashion public relations.[58] The interactive nature of these platforms allows practitioners to engage and communicate with the public in real time, and tailor their clients' brand or campaign messages to the target audience. With blogging platforms such as Instagram, Tumblr, Wordpress, and other sharing sites, bloggers have emerged as expert fashion commentators, shaping brands and having a great impact on what is 'on trend'.[59] Women in the fashion public relations industry such as Sweaty Betty PR founder Roxy Jacenko and Oscar de la Renta's PR girl Erika Bearman, have acquired copious followers on their social media sites, by providing a brand identity and a behind the scenes look into the companies they work for.
^ Encyclopædia Britannica, Retrieved from http://www.britannica.com/EBchecked/topic/1706624/fashion-industry, http://www.britannica.com/EBchecked/topic/1706624/fashion-industry/296476/Fashion-design-and-manufacturing, http://www.britannica.com/EBchecked/topic/1706624/fashion-industry/296477/Fashion-retailing-marketing-and-merchandising, http://www.britannica.com/EBchecked/topic/1706624/fashion-industry/296479/Media-and-marketing
Why: Since stumbling across this gorgeous blog, our lives have been so much more colourful. Jess goes beyond the standard #OOTD posts and her site's a sartorial treasure trove full of styling advice, galleries and even some tips for budding bloggers if you're thinking of making this list some day. Her masterfully saturated and unique photography is what sets her apart from the rest of the pack and we still can't stop thinking about her guide to wearing colour this spring…
Fashion is a popular aesthetic expression in a certain time and context, especially in clothing, footwear, lifestyle, accessories, makeup, hairstyle and body proportions.[1] Whereas, a trend often connotes a very specific aesthetic expression, and often lasting shorter than a season, fashion is a distinctive and industry-supported expression traditionally tied to the fashion season and collections.[2] Style is an expression that lasts over many seasons, and is often connected to cultural movements and social markers, symbols, class and culture (ex. Baroque, Rococo, etc). According to sociologist Pierre Bourdieu, fashion connotes "the latest fashion, the latest difference."[3]


text:
Last edited by Arakazahn
Tuesday, July 28, 2020 | History
6 edition of The Emory University Comprehensive Board Review in Internal Medicine found in the catalog.
The Emory University Comprehensive Board Review in Internal Medicine
Published September 21, 1999 by McGraw-Hill Publishing Co .
Contributions Juha P. Kokko (Editor), Sidney F. Stein (Editor)
University launches Emory Vantage to inform community on key issues. Nov. 12, Emory pays tribute to veterans. Nov. 12, Emory School of Nursing Assistant Professor, Dr. Kylie Smith, . Short on time? Need bite-sized chunks of review you can fit into your schedule? Our Internal Medicine Video Board Review is the answer. Study at your own pace with Internal Medicine's favorite on .
A Comprehensive Board Review in Hematology and Medical Oncology September , Robert C. Hickey Auditorium Fl R. Lee Clark Clinic, Holcombe Boulevard The University of Texas MD Anderson Cancer Center . Emory University is a private research university in Atlanta, Georgia. Founded as Emory College in in Oxford, Georgia by the Methodist Episcopal Church, it was named in honor of Methodist bishop Campus: Suburban, acres ( km²).
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Review of the operation of the Prevention of Terrorism (Temporary Provisions) Act 1984
Breaking Loose
Professional core competencies for infection control nurses
List of Irish fishes.
Legends and stories of Ireland
American Window on the World 3 Tea Bk American Wow Nolasco
Discrete Voronoi skeletons
guide to the flowering plants and ferns of Iceland
To amend the Bank holding company act [of 1956]
Vedic Culture
The Emory University Comprehensive Board Review in Internal Medicine Download PDF EPUB FB2
Presented by the Department of Medicine at Emory University School of Medicine, the 42nd Annual Comprehensive Board Review in Internal Medicine is a comprehensive review of Internal Medicine.
Internal medicine with a focus on passing the boards. Whether you're a physician in internal medicine seeking recertification, this comprehensive, field-tested study guide and CD-ROM--based on the /5(2). out of 5 stars emory board review Reviewed in the United States on Febru This book is an example of a concise yet thorough book which covers the 13 sections that are included in the /5.
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This text has its roots in the Emory University internal medicine board review course. It features 14 sections of didactic review (organized by body system) with exam-style questions.
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text:
Corbett, David M.
Corbett, David M. - South Jordan, UT
10459 South 1300 West Suite 101South Jordan, UT 84095
Corbett | Gwilliam PLLC
South Jordan Family Lawyer
The American Society of Legal Advocates has selected David as a Top 40 Under 40 litigation attorney in the State of Utah for 2016.
David has found that passion and creativity separate the best attorneys from the rest. As an intern in the Federal District Court in Waco, Texas while in law school, he observed that the most effective attorneys showed genuine belief in their clients and their rights. He incorporated these lessons into his work with Baylor Law School's celebrated mock trial...
David has found that passion and creativity separate the best attorneys from the rest. As an intern in the Federal District Court in Waco, Texas while in law school, he observed that the most effective attorneys showed genuine belief in their clients and their rights. He incorporated these lessons into his work with Baylor Law School's celebrated mock trial team, for which the school awarded him the American Board of Trial Advocates award.
After law school, David chose to serve the people of Northwest Arizona as a public defender. For five years, he represented men and women charged with all manner of crimes. He has tried cases ranging from murder to DUI to backyard brawls. At the end of one of his trials, an alleged victim approached him in the court hallway and said, "If I ever get in trouble, I want to hire you as my attorney." On another occasion, a juror asked for David's business card after acquitting his client.
In addition to his 50+ criminal trials, he learned the importance of a comprehensive criminal defense. When acquittal was not an option, David consulted with mental health professionals, arranged for treatment, and sought sentencing alternatives that resulted in favorable outcomes for his clients.
As an attorney for Corbett & Pankratz, PLLC, David continues to use his passion, experience, and creativity to serve his clients. He believes in his clients, and he explores many alternatives to solve their problems and enforce their rights.
In addition to his law practice, David is an avid soccer player. He enjoys camping with his wife and three children, where he always reads Edgar Allen Poe stories by the fire. He is fluent in Spanish.
Personal Injury 20%
Appeals 10%
Criminal Law 10%
Juvenile Court 10%
Arizona, 2006
Utah, 2012
U.S. District Court District of Utah, 2013
Utah Association of Criminal Defense Lawyers, 2014 - 2015 (Member)
Arizona Attorneys for Criminal Justice, 2008 - 2011 (Board of Governors)
Baylor University School of Law, Waco, Texas, 2006
Brigham Young University, Provo, Utah, 2003
Honors: Deans List
Major: English
Christensen Corbett & Pankratz, PLLC, Partner, 2012 - 2015
Christensen Thornton, PLLC, Associate, 2011 - 2012
Mohave County Public Defender's Office, Attorney, 2006 - 2011
Federal District Court in Waco, Texas, Intern
Aristotle's Golden Rules of Persuasion, Arizona Attorneys for Criminal Justices, 2009
Decoding Arizona's New Sentencing Code, Mohave County Bar Association, 2010
American Board of Trial Advocates Award, 2006 - Present
Top 40 Under 40 Litigation Attorney in the State of Utah, American Society of Legal Advocates, 2016 - Present
https://www.cglawgroup.com/
https://www.cglawgroup.com/blog/
www.cglawgroup.com/


Although situated in an Anglican cathedral, the two works engage with a multi-national, multi-denominational audience, in keeping with a spiritual environment visited annually by millions of people of all faiths and those of none.
The first of the works to be installed in St Paul's Cathedral was Martyrs in 2014.
On 8th September 2016, Martyrs was joined by a second piece, Mary.
Both works are available to visit in an area of the cathedral designated for contemplation and meditation.
The installations are the first moving-image works to be installed permanently in a cathedral in Britain. They have been gifted to Tate, and are on long-term loan to St Paul's Cathedral creating a collaboration between the two institutions that face each other across the Thames River.


Sometimes you feel like you gotta have a cookie and nothing store made will do. This basic recipe from the King Arthur website will show you how easy it is to make scrumptious gluten free cookies; these are flour free; made with almond paste, sugar, egg whites, almond extract and some powdered sugar. So simple even a 7 year old can make them. No fancy molding, shaping or rolling out. No tricky flours to mix, no meringue to whip. Simple blending, measure it with your tablespoon; shape quickly by pressing with three finger tips and bake. The cookie dough spreads out as it bakes so don't worry if it looks like an artless clump on your baking sheet. It will flatten and round into an attractive cookie.
Almond cloud cookies have a delicate crunch to them, deeply almond in flavor. They look very pretty with the powdered sugar on top. I find them somewhat addictive; can't eat just one cookie. Yes….an almond cloud is a very descriptive name for these delightful treats.
I used ¾ cup white sugar and they were quite sweet enough for me. I also sprinkled the baked cookies with sifted powdered sugar after they came out and cooled a minute or two right on the baking sheet. Don't leave them there more than a couple more minutes or they will be hard to lift off the baking sheet. If you are more cautious in your use of sugar leave that stop off. I cut the sugar down in the dough to 3/4 cup but did sift some powdered sugar on top; makes the cookies even more attractive.
Almond cloud cookies makes about 21 cookies.
Lightly grease (or line with parchment) two rimmed baking sheets.
Stir in the flavorings. I left out the almond oil; didn't have any; fine without it.
Scoop the dough by heaping tablespoons onto the prepared pans. I did eight to a pan. Sprinkle the cookies heavily with confectioners' sugar, then use three fingers to press an indentation into the center of each cookie.
Bake the cookies for 20 to 25 minutes, until they're brown around the edges. Remove them from the oven, and let them cool right on the pan for 4-5 minutes. I froze some and stored some in my cookie jar. They stayed a bit soft making them easy to enjoy a couple days later…I was afraid that they would become tooth breakers upon sitting a while. Nope…still perfect. Get your cookie with these charmers…you won't regret it.


Sakinah, Muhamad Hisham (2017) Tribological behavior of waste cooking oil blended lubricant. Masters thesis, Universiti Malaysia Pahang.
In the current decade, the development of renewable products to replace fossil products is an essential and important issue from industrial, environment, and academic point of views. In the current study, an attempt was made to study the tribological behaviour of waste cooking oil blended with SAE 40, investigate their viscosity and moisture content and also optimized the differemt operating parameter of the tribological performance. Waste cooking palm oil (WCO) was chosen from the most common waste oil using in Malaysia. Waste cooking oil was undergone three types of process, the coarse filtering, dewatering and fine filtering. Moisture content and viscosity analysis were investigated to study the physical properties of blended lubricant as well as the effectiveness of filtration method. Wear and friction performance was evaluated using piston-liner contact tester, and the material use is aluminium 6061 which is the standard material for piston. The design of experiment (DOE) was constructed using Response Surface Methodology (RSM) method. Influence of different operating parameter such as rotational speeds (200 RPM,250 RPM, 300 RPM), volume concentration (SAE 40, 5% and 10% of waste oil), and applied loads (2 kg, 5.5kg and 9kg) investigated and obtain the optimization for different lubricant in tribological behavior. Field Emission Scanning Electron Microscope (FESEM) that equipped with EDX system was used to identify the wear mechanism and element on the surface of the specimen. According to the coefficient of friction versus time result and the weight loss result, the friction coefficient between the three concentrations of oil shows a considerable difference between SAE 40 and two blended lubricant. Based on the properties result, for viscosity, as the concentration of waste cooking oil increases, the viscosity of the bio-lubricant decreases. According to result in moisture content, the moisture content percentage in 0% volume concentration of waste cooking oil is the same with moisture content percentage in 10% volume concentration of waste cooking oil while 5% shows the lowest percentage of the moisture content. Based on SEM result, the wear on the surface specimen decrease as the concentration of waste cooking oil added with engine oil reduce, and it was due to the SAE 40 showed the highest viscosity result compared to 10% concentration because higher viscosity tends to drag the movements between two contact surfaces. It can be said that using a small amount of WCO in the engine oil was not give much impact in the engine component regarding on their coefficient of friction and wear mechanism. From the lubricant properties analysis, it shows that the properties of the blended lubricant approached with the lubricant baseline (SAE 40).


Frank Eppes, Jr. is a well-known third generation Greenville, SC attorney who literally grew up in the Greenville County Courthouse.
Eppes' father was a well-known circuit judge who presided over the Looper Murder trials and ultimately sentenced Charles Wakefield, Jr. to death.
Eppes worked on Wakefield's behalf in an effort to secure parole for the man his father sent to Death Row.


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text:
\section{Description of de Sitter space}

\noindent
Four-dimensional de Sitter space is a one-sheeted hyperboloid (of radius~$\ell$)
in $\mathbb R^{1,4}\ni\{Z_0,Z_1,\ldots,Z_4\}$ given by
\begin{equation}
-Z_0^2 + Z_1^2 + Z_2^2 + Z_3^2 + Z_4^2 \=\ell^2\ .
\end{equation}
Constant $Z_0$ slices are 3-spheres of varying radius,
yielding a parametrization of dS$_4\ni\{\tau,\omega_A\}$ as
\begin{equation}
\begin{aligned}
 Z_0 \= -\ell\,\cot\tau \quad&\qquad\textrm{and}\qquad\quad
Z_A \= \frac{\ell}{\sin\tau}\,\omega_A {\quad\textrm{for}\quad} A = 1,\ldots,4 \\[4pt]
{\quad\textrm{with}\quad}\qquad \tau\in{\cal I}:=(0,\pi)
\quad&\qquad\textrm{and}\qquad\quad \omega_A \omega_A = 1\ .
\end{aligned}
\end{equation}
The details of the embedding $\omega_A: (\chi,\theta,\phi)\ni S^3\hookrightarrow\mathbb R^4$ are irrelevant.
The Minkowski metric
\begin{equation}
\mathrm{d}s^2 \= -\mathrm{d}Z_0^2 + \mathrm{d}Z_1^2 + \mathrm{d}Z_2^2
+ \mathrm{d}Z_3^2 + \mathrm{d}Z_4^2
\end{equation}
induces on dS$_4$ the metric
\begin{equation}
\mathrm{d}s^2 \= \frac{\ell^2}{\sin^2\!\tau}
\bigl(-\mathrm{d}\tau^2 + \mathrm{d}\Omega_3^2\bigr)
\quad{\quad\textrm{with}\quad}\quad {\mathrm d}\Omega_3^2 {\quad\textrm{for}\quad} S^3\ ,
\end{equation}
showing that dS$_4$ is conformally equivalent to a finite cylinder ${\cal I}\times S^3$.

\bigskip

\section{Reduction of Yang--Mills to matrix equations}

\noindent
We wish to find solutions to the Yang--Mills (and Maxwell) equations on de Sitter space.
Due to their conformal invariance in four spacetime dimensions, we may also study the
problem on the finite Minkowskian cylinder~${\cal I}\times S^3$.

The gauge potential taking values in a Lie algebra~$\mathfrak{g}$ can always be chosen as
\begin{equation}
{\cal A} \= X_a(\tau,\omega) \; e^a
\qquad \textrm{on} \quad {\cal I}\times S^3
\end{equation}
where $X_a\in\mathfrak{g}$, and $\{e^a, a=1,2,3\}$ is a basis of left-invariant one-forms
on $S^3\simeq\textrm{SU}(2)$, with
\begin{equation}
\mathrm{d}e^a + \varepsilon^a_{\ bc}\,e^b{\wedge} e^c \=0 \quad\qquad\textrm{and}\qquad\quad
e^a e^a \= {\mathrm d}\Omega_3^2\ .
\end{equation}
There is no ${\mathrm d}\tau$ component because we picked the temporal gauge ${\cal A}_\tau=0$.
In terms of the $S^3$ coordinates \ ($a,i,j,k=1,2,3$ and $B,C=1,2,3,4$) \
these one-forms can be constructed as
\begin{equation}
e^a \= - \eta^a_{BC} \ \omega_B\,\mathrm{d}\omega_C
\qquad\textrm{ where}\quad
\eta^i_{jk} = \varepsilon^i_{\ jk} \and \eta^i_{j4} = -\eta^i_{4j} = \delta^i_j\ .
\end{equation}
Dual to the $e^a$ are the left-invariant vector fields
\begin{equation} \label{Ralgebra}
R_a \= - \eta^a_{BC}\,\omega_B \frac{\partial}{\partial \omega_C}
\qquad\Rightarrow\qquad
[R_a,R_b] \= 2\,\varepsilon_{abc}\,R_c
\end{equation}
generating the right multiplication on SU(2), so that
an arbitrary function $\Phi$ on $S^3$ obeys
\begin{equation}
\mathrm{d}\Phi(\omega) \= e^a\,R_a \Phi(\omega)\ .
\end{equation}
The full SO(4) isometry group of~$S^3$ is generated by
left-invariant~$R_a$ and right-invariant~$L_a$.

In this language, the gauge field two-form becomes
($\dot{X}_a\equiv\sfrac{{\mathrm d}}{{\mathrm d}\tau}X_a$)
\begin{equation}
\begin{aligned}
 {\cal F} & \= {\cal F}_{\tau a}\,e^\tau{\wedge} e^a + \sfrac12 {\cal F}_{bc}\,e^b{\wedge} e^c \\
& \= \dot{X}_a\,e^\tau{\wedge} e^a +
\sfrac12\bigl(R_{[b}X_{c]}-2\varepsilon^a_{bc}X_a + [X_b, X_c]\bigr)\,e^b{\wedge} e^c\ ,
\end{aligned}
\end{equation}
where we define $R_{[b}X_{c]}=R_bX_c{-}R_cX_b$,
and the Yang--Mills Lagrangian reads
\begin{equation}
\begin{aligned}
 {\cal L} &\= \sfrac18\,{\mathrm tr} {\cal F}_{\mu\nu}{\cal F}^{\mu\nu}\=
-\sfrac14\,{\mathrm tr}{\cal F}_{\tau a}{\cal F}_{\tau a}\ +\ \sfrac18\,{\mathrm tr}{\cal F}_{ab}{\cal F}_{ab}\\
&\= -\sfrac12{\mathrm tr}\bigl\{ \sfrac12\dot{X}_a\dot{X}_a-2X_a X_a
+\varepsilon_{abc}X_a D_{[b} X_{c]} -\sfrac14(D_{[a} X_{b]})(D_{[a} X_{b]})\bigr\}
\end{aligned}
\end{equation}
with the short-hand \ $D_a:=R_a+X_a$.
The Yang--Mills equations using (\ref{Ralgebra}) then take the form
\begin{equation}  \label{YMeom}
\begin{aligned}
\ddot X_a \=& -4\,X_a+ 2\,\varepsilon_{abc}R_{[b} X_{c]} + R_b R_{[b} X_{a]} +  3\,\varepsilon_{abc}\, [X_b, X_c] \\
&\ +2[X_b,R_b X_a] - [X_b,R_a X_b] - [X_a,R_b X_b] - \bigl [X_b, [X_a,X_b]\bigr] \\[4pt]
\=& -4\,X_a+ 2\,\varepsilon_{abc}R_b X_c + R_b R_b X_a - R_a R_b X_b +  3\,\varepsilon_{abc}\, [X_b, X_c] \\
&\ +2[X_b,R_b X_a] - [X_b,R_a X_b] - [X_a,R_b X_b] - \bigl [X_b, [X_a,X_b]\bigr]
\end{aligned}
\end{equation}
with the Gauss law
\begin{equation} \label{YMgauss}
R_a\dot{X}_a + [X_a,\dot{X}_a] \= 0\ .
\end{equation}

\bigskip

\section{Yang--Mills configurations on de Sitter space}

\noindent
The simplest Yang--Mills solutions are most symmetric. To obtain them, let us impose SO(4) symmetry
by setting \ $X_a(\tau,\omega)=X_a(\tau)$.
The Yang--Mills equations then become ordinary matrix differential equations
\cite{lechtenfeld-ivanova, lechtenfeld-popov, lechtenfeld-popov2},
\begin{equation}
\ddot{X}_a \= -4\,X_a+ 3\,\varepsilon_{abc}\, [X_b, X_c] - \bigl [X_b, [X_a,X_b]\bigr]
\qquad\and\qquad [X_a,\dot{X}_a] \= 0\ .
\end{equation}
These three coupled ordinary differential equations for the three matrix functions~$X_a(\tau)$
are still too complicated. However, for the gauge group SU(2), these equations admit some analytic solutions.
So let us choose a spin-$j$ representation of $\mathfrak{g}=su(2)$
and introduce the three SU(2) generators~$T_a$,
\begin{equation}
[T_b, T_c] \= 2\,\varepsilon^a_{bc}T_a \qquad\textrm{and}\qquad
{\mathrm tr}(T_aT_b)\=-4C(j)\,\delta_{ab}\ {\quad\textrm{for}\quad}
C(j)=\sfrac13\,j(j{+}1)(2j{+}1)\ .
\end{equation}
A simple ansatz for the matrices $X_a$ is
\begin{equation}
X_1=\Psi_1 T_1\ ,\quad
X_2=\Psi_2 T_2\ ,\quad
X_3=\Psi_3 T_3
\quad{\quad\textrm{with}\quad} \Psi_a=\Psi_a(\tau)\in\mathbb R\ .
\end{equation}
The resulting simplification of Yang--Mills Lagrangian density,
\begin{equation}
 {\cal L}
\= 4\,C(j)\,\bigl\{\sfrac14\dot{\Psi}_a\dot{\Psi}_a - (\Psi_1-\Psi_2\Psi_3)^2-
(\Psi_2-\Psi_3\Psi_1)^2 - (\Psi_3-\Psi_1\Psi_2)^2\bigr\}\ ,
\end{equation}
suggests an interpretation of $\{\Psi_a\}$ as the coordinates of a Newtonian particle in $\mathbb R^3$
moving in a potential
\begin{equation} \label{tetrapot}
\sfrac12 {\cal V}(\Psi)\ \=\
(\Psi_1-\Psi_2\Psi_3)^2\ \ +\ \ (\Psi_2-\Psi_3\Psi_1)^2\ \ +\ \ (\Psi_3-\Psi_1\Psi_2)^2\ .
\qquad\phantom{-}
\end{equation}
\begin{figure}[h!]
\centering
\includegraphics[scale=1.2]{tetrapot.eps}
\caption{Contours of the Newtonian potential in (\ref{tetrapot}).}
\label{fig1}
\end{figure}

The only analytic nonabelian solutions come from
\begin{equation}
\Psi_1=\Psi_2=\Psi_3=:\Psi
\quad{\quad\textrm{with}\quad}\quad \ddot{\Psi}=16\,\Psi\,(\Psi{-}1)(2\Psi{-}1) \ ,
\end{equation}
leading to elliptic functions $\Psi(\tau)$, except for the special cases
$\Psi(\tau)=0 \  \textrm{or} \ 1$ (the vacuum),
$\Psi(\tau)=\sfrac12$ (the sphaleron),
and the bounce solution in the double-well potential.
The corresponding gauge potential takes the simple form
\begin{equation}
{\cal A} \= \Psi(\tau)\,g^{-1}{\mathrm d} g \quad{\quad\textrm{for}\quad}
g:S^3 \buildrel{1:1}\over{\longrightarrow}\textrm{SU}(2)\ ,
\end{equation}
and the SU(2) color electric and magnetic fields are
\begin{equation}
{\cal E}_a \= {\cal F}_{\tau a} \= \dot\Psi\,T_a \qquad\textrm{and}\qquad
{\cal B}_a \= \sfrac12\varepsilon_{abc}{\cal F}_{bc} \= 2\,\Psi\,(\Psi{-}1)\,T_a\ .
\end{equation}
Their total de Sitter energy and action is finite
and proportional to double-well energy.
These analytic Yang--Mills configurations are related to Minkowski-space solutions
found in the seventies~\cite{dealfaro,luscher,schechter}
(for a review from this period, see~\cite{actor}).
Their stability, however, has been analyzed only recently~\cite{KLP}.

\bigskip

\section{All Maxwell solutions on de Sitter space}

\noindent
The other analytic solutions to (\ref{YMeom}) and~(\ref{YMgauss}) are abelian,
i.e.~excite only a single direction in isospin space.
In this case we can drop the matrix valuedness and treat the $X_a$ as real functions.
Dropping all commutator terms, the Yang--Mills equations~(\ref{YMeom}) turn into
the linear Mawell equations,
\begin{equation}  \label{Maxwelleom}
\ddot X_a \= (R^2-4)\,X_a+ 2\,\varepsilon_{abc}R_b X_c
\end{equation}
where $R^2\equiv R_b R_b$ is the laplacian on~$S^3$,
and we refined the temporal gauge to the Coulomb gauge
\begin{equation}
{\cal A}_\tau = 0 \qquad\textrm{and}\qquad R_a X_a = 0\ ,
\end{equation}
which takes care of the Gauss law.

The coupled wave equations (\ref{Maxwelleom})
may be completely solved by separation of variables.
Seeking factorized complex basis solutions~\footnote{
$Z_a(\omega)$ is not to be confused with the ambient-space coordinates~$Z_A$.}
\begin{equation}
X_a (\tau,\omega) \= Z_a(\omega)\ \mathrm{e}^{\mathrm{i}\Omega\tau}\ ,
\end{equation}
one learns that the frequency $\Omega$ only depends on the SO(4) spin~$2j\in{\mathbb{N}}_0$,
\begin{equation}
-R^2\,Z_a^j(\omega) = 2j(2j{+}2)\,Z_a^j(\omega) \qquad\Rightarrow\qquad
\bigl((\Omega^j)^2-4(j{+}1)^2\bigr)\bigl((\Omega^j)^2-4j^2\bigr) = 0\ ,
\end{equation}
where the second factor appears only for $j{\ge}1$.
The basis solutions~$Z_a^j$ to the linear system come in two types
and carry two further labels $m$ and~$n$~\cite{lechtenfeld-zhilin}:
\begin{itemize}
\addtolength{\itemsep}{0pt}
\item type I : \quad
$j{\geq}0\ ,\quad m = -j,\ldots,+j\ ,\quad n = -j{-}1,\ldots,j{+}1\ ,\quad \Omega^j=\pm2(j{+}1)$\\
\begin{equation} \label{type1}
\begin{aligned}
Z_+^{j;m,n}  &\= \sqrt{(j{-}n)(j{-}n{+}1)/2} \ Y_{j;m,n+1} \\
Z_3^{j;m,n} \,&\= \sqrt{(j{-}n{+}1)(j{+}n{+}1)} \ Y_{j;m,n} \\
Z_-^{j;m,n}    &\= -\sqrt{(j{+}n)(j{+}n{+}1)/2} \ Y_{j;m,n-1}
\end{aligned}
\end{equation}
\item type II :\quad
$j{\geq}1\ ,\quad m = -j,\ldots,+j\ ,\quad n = -j{+}1,\ldots,j{-}1\ ,\quad \Omega^j=\pm2j$\\
\begin{equation} \label{type2}
\begin{aligned}
Z_+^{j;m,n}   &\= -\sqrt{(j{+}n)(j{+}n{+}1)/2} \ Y_{j;m,n+1} \\
Z_3^{j;m,n} \,&\= \sqrt{(j{+}n)(j{-}n)} \ Y_{j;m,n} \\
Z_-^{j;m,n}    &\= \sqrt{(j{-}n)(j{-}n{+}1)/2} \ Y_{j;m,n-1}
\end{aligned}
\end{equation}
\end{itemize}
where $Z_\pm=(Z_1\pm{\mathrm i} Z_2)/\sqrt{2}$,
and the hyperspherical harmonics
\begin{equation}
Y_{j; m,n}(\omega) \qquad{\quad\textrm{with}\quad}\quad m,n = -j,-j{+}1,\ldots,+j \qquad\textrm{and}\qquad 2j=0,1,2,\ldots
\end{equation}
are characterized by~\footnote{
The label $m$ is the eigenvalue of $\sfrac{{\mathrm i}}{2}\,L_3$.}
\begin{equation}
-\sfrac14 R^2\,Y_{j; m,n}=j(j{+}1)\,Y_{j; m,n} \qquad\textrm{and}\qquad
\sfrac{{\mathrm i}}{2}\,R_3\,Y_{j; m,n}=n\,Y_{j; m,n}\ .
\end{equation}

Hence, the general real Maxwell solution ${\cal A}=X_a(\tau,\omega) \; e^a$ is a linear combination with
\begin{equation}
X_a (\tau,\omega) \= \sum_{jmn} \Bigl\{
c^{\textrm{I}}_{j;m,n}\,Z_{a\ \textrm{I}}^{j;m,n}(\omega)\ \mathrm{e}^{2(j+1)\,\mathrm{i}\tau}\ +\
c^{\textrm{II}}_{j;m,n}\,Z_{a\ \textrm{II}}^{j;m,n}(\omega)\ \mathrm{e}^{2j\,\mathrm{i}\tau}\ +\ \textrm{c.c.}\Bigr\}\ .
\end{equation}
Each complex solution yields two real ones (real part and imaginary part). We count
$2(2j{+}1)(2j{+}3)$ real type-I solutions and  $2(2j{+}1)(2j{-}1)$ real type-II solutions ($j{\ge}1$),
which add up to $4(2j{+}1)^2$ solutions for $j{>}0$ and 6 solutions for $j{=}0$, as it should.
Constant solutions ($\Omega=0$) are not allowed;
the simplest ones are $j{=}0$ type~I or $j{=}1$ type~II.
The most general $j{=}0$ configuration is
\begin{equation}
X_a^{(j=0)} \= \Bigl\{
c_{0;0,-1}\sfrac{1}{\sqrt{2}} \Bigl(\begin{smallmatrix} 1\\{-}{\mathrm i}\\0 \end{smallmatrix}\Bigr) +
c_{0;0,0} \Bigl(\begin{smallmatrix} 0\\0\\1 \end{smallmatrix}\Bigr) -
c_{0;0,+1}\sfrac{1}{\sqrt{2}} \Bigl(\begin{smallmatrix} 1\\{\mathrm i}\\0 \end{smallmatrix}\Bigr)
\Bigr\} \ {\mathrm e}^{2{\mathrm i}\tau} \ +\ \textrm{c.c.}\ .
\end{equation}
The parity inversion, which interchanges left and right invariance, relates
spin $j$ \ type I \ solutions with spin $j{+}1$ \ type II \ solutions, swopping labels $m$ and~$n$.
Finally, electromagnetic duality is realized by shifting \ $|\Omega^j|\tau$ \ by \ $\pm\sfrac{\pi}{2}$,
which produces from a solution~${\cal A}$ a dual solution ${\cal A}_D$.
We shall now see that this basis of Maxwell solutions relates to so-called electromagnetic knots in Minkowski space.

\bigskip

\section{Conformal mapping to Minkowski space}

\noindent
The $Z_0{+}Z_4{<}0$ half of dS$_4$ is also conformally related to
future Minkowski space $\mathbb R^{1,3}_+\ni\{t,x,y,z\}$,
\begin{equation}
\begin{aligned} &
Z_0 = \frac{t^2{-}r^2{-}\ell^2}{2\,t}\ ,\quad
Z_1 = \ell\,\frac{x}{t}\ ,\quad
Z_2 = \ell\,\frac{y}{t}\ ,\quad
Z_3 = \ell\,\frac{z}{t}\ ,\quad
Z_4 = \frac{r^2{-}t^2{-}\ell^2}{2\,t} \\[4pt]
&\textrm{with}\qquad
x,y,z\in\mathbb R \quad\qquad\textrm{and}\qquad\quad r^2 = x^2 + y^2 + z^2 \qquad\textrm{ but}\qquad t\in\mathbb R_+\ ,
\end{aligned}
\end{equation}
since \ $t\in[0,\infty]$ \ corresponds to \ $Z_0\in[-\infty,\infty]$ \ but \ $Z_0{+}Z_4<0$.
In these Minkowski coordinates,
\begin{equation}
\mathrm{d}s^2 \=
\frac{\ell^2}{t^2}\,\bigl(-\mathrm{d}t^2 +\mathrm{d}x^2 +\mathrm{d}y^2 +\mathrm{d}z^2\bigr)\ .
\end{equation}
One may cover the entire $\mathbb R^{1,3}$ by gluing a second dS$_4$ copy and using the patch $Z_0{+}Z_4>0$.

We shall employ the direct relation between the cylinder and Minkowski coordinates,
\begin{equation} \label{cyltomink}
\cot\tau = \frac{r^2 {-} t^2 {+} \ell^2}{2\,\ell\,t}\ ,\quad
\omega_1 = \gamma\,\frac{x}{\ell}\ ,\quad
\omega_2 = \gamma\,\frac{y}{\ell}\ ,\quad
\omega_3 = \gamma\,\frac{z}{\ell}\ ,\quad
\omega_4 = \gamma \frac{r^2 {-} t^2 {-} \ell^2}{2\,\ell^2}\ ,
\end{equation}
with the convenient abbreviation
\begin{equation}
\gamma \= \frac{2\,\ell^2}{\sqrt{4\,\ell^2 t^2 + (r^2-t^2+\ell^2)^2}}\ .
\end{equation}
Since $t=-\infty, 0, \infty$ \  corresponds to \ $\tau=-\pi,0,\pi$,
the cylinder gets doubled to \  $2{\cal I}\times S^3$,
and full Minkowski space is covered by the cylinder patch \ $\omega_4 \le\cos\tau$.
\begin{figure}[h!]
\centering
\includegraphics[scale=1.2]{fig0.eps}
\caption{An illustration of the map between a cylinder $2\mathcal{I}{\times}S^3$ and Minkowski space $\mathbb R^{1,3}$.
The Minkowski coordinates cover the shaded area. Its boundary is given by the curve $\omega_4 = \cos\tau$.
Each point is a two-sphere spanned by $\omega_{1,2,3}$, which is mapped to a sphere of constant $r$ and $t$.}
\label{fig2}
\end{figure}
The cylinder time $\tau$ is a regular smooth function of $(t,x,y,z)$, but more useful will be
\begin{equation}
\exp (2\mathrm{i}\,\tau) \= \frac{\bigl[(\ell+\mathrm{i}t)^2+r^2\bigr]^2}{4\,\ell^2 t^2 + (r^2-t^2+\ell^2)^2}\ .
\end{equation}
A slightly lengthy computation yields the Minkowski-coordinate expressions for the one-forms
\cite{lechtenfeld-zhilin},
\begin{equation}
\begin{aligned}
e^0 &\= e^0_\mu\,{\mathrm d} x^\mu \= \frac{\gamma^2}{\ell^3}\Bigl(
\sfrac12(t^2 + r^2 + \ell^2)\,\mathrm{d}t - t\,x^k \mathrm{d}x^k \Bigr)\ ,\\[4pt]
e^a &\= e^a_\mu\,{\mathrm d} x^\mu \= \frac{\gamma^2}{\ell^3}\Bigl(
t\,x^a \mathrm{d}t - \bigl(\sfrac12(t^2 - r^2 + \ell^2)\,\delta^a_k +
x^a x^k + \ell\,\varepsilon^a_{\ jk}x^j \bigr)\,\mathrm{d}x^k \Bigr)\ ,
\end{aligned}
\end{equation}
with the notation
\begin{equation}
(x^i)=(x,y,z) \qquad\and\qquad
(x^\mu)=(x^0,x^i)=(t,x,y,z)\ .
\end{equation}

Due to the conformal invariance of the Maxwell equations,
our oscillatory solutions on the cylinder~$2\mathcal{I}{\times}S^3$ may be transferred
to a basis of Maxwell solutions on Minkowski space (with certain fall-off properties).
To accomplish this task, we only have to effect the coordinate change~\footnote{
The $S^2$ angular coordinates $(\theta,\phi)$ on both sides can be identified.
The map $(\tau,\chi)\mapsto(t,r)$ realizes the Penrose diagram of Minkowski space
\cite{lechtenfeld-kumar}.}
\begin{equation}
\textrm{from} \qquad
(\tau,\omega)\sim(\tau,\chi,\theta,\phi) \qquad\textrm{to}\qquad
x\equiv(x^\mu)=(t,x,y,z)\sim(t,r,\theta,\phi)\ ,
\end{equation}
so that
\begin{equation}
{\cal A} \= X_a(\tau(x),\omega(x))\,e^a(x) \= A_\mu(x)\,{\mathrm d} x^\mu
\qquad\textrm{ yielding \quad $A_\mu(x)$} {\quad\textrm{with}\quad} A_t\neq0\ ,
\end{equation}
\begin{equation}
\mathrm{d}{\cal A} \= \dot{X}_a\,e^0{\wedge} e^a
-\varepsilon^a_{\ bc} X_a\,e^b {\wedge} e^c
\= \sfrac{1}{2} F_{\mu \nu}\,{\mathrm d} x^\mu {\wedge} {\mathrm d} x^\nu
\qquad\textrm{ yielding \quad $F_{\mu\nu}(x)$}\ .
\end{equation}
From this, we obtain electric and magnetic fields \
$ E_i=F_{i0} \and B_i=\sfrac{1}{2}\varepsilon_{ijk}F_{jk}$.
For the computation it is helpful to recognize that $\exp(2{\mathrm i}\tau)$
is a rational function of $t$ and~$r$. It follows that all physical quantities
(and the gauge potential) are rational functions of the Minkowski coordinates!

\bigskip

\section{All knot solutions on Minkowski space}

\noindent
As we shall see below, the simplest ($j{=}0$) solutions neatly reproduces the celebrated
Hopf-Ra\~nada electromagnetic knot~\cite{elknots,knotreview}.
From our construction, some general features of all knot solutions can be inferred.

Firstly, at spatial infinity (for $t$ fixed) all field strengths decay like $r^{-4}$,
but they fall off only as $(t{\pm}r)^{-1}$ along the light-cone.
Hence, the asymptotic energy flow is concentrated on past and future null infinity
and peaks on the light-cone of the spacetime origin.
Secondly, the ``knot basis'' forms a complete set of finite-action configurations.
Of course, it does not contain plane waves.
Thirdly, the obvious conserved (in Minkowski time) quantities are helicity and energy,
\begin{equation}
h \= \sfrac12 \int \limits_{\mathbb R^3} \ \bigl( A\wedge F + A_D \wedge F_D \bigr)
\qquad\textrm{and}\qquad
E \= \sfrac12 \int \limits_{\mathbb R^3} \!{\mathrm d}^3\! x \ \bigl(\vec{E}^2 + \vec{B}^2\bigr)\ ,
\end{equation}
where the spatial integration is done at fixed~$t$.
Their common scale is determined by the amplitude of the solution, but their ratio
is fixed for the basis configurations.
Both quantities are best computed in the ``sphere frame'' at $t=\tau=0$,
\begin{equation}
F \= \mathcal{E}_a\,e^a {\wedge} e^0 + \sfrac{1}{2} \mathcal{B}_a\,\varepsilon^a_{\ bc}\,e^b{\wedge} e^c\ .
\end{equation}
Let us focus on type~I solutions of a fixed spin~$j$ and suppress these indices.
For those one finds
\begin{equation}
\mathcal{E}_a \= -\mathrm{i}\Omega \sum_{mn}
c_{m,n}\,Z_a^{m,n}\,\mathrm{e}^{ \mathrm{i}\Omega\tau}+\,\textrm{c.c.} \qquad\textrm{and}\qquad
\mathcal{B}_a \= -\Omega \sum_{mn}
c_{m,n}\,Z_a^{m,n}\,\mathrm{e}^{ \mathrm{i}\Omega\tau}+\,\textrm{c.c.}\ ,
\end{equation}
which yields
\begin{equation}
\sfrac12\bigl({\cal E}_a{\cal E}_a+{\cal B}_a{\cal B}_a\bigr) \= 2 \Omega^2
\bigl|{\textstyle\sum}_{m,n}c_{m,n}\,Z_{a}^{m,n}(\omega)\bigr|^2\ .
\end{equation}
The Minkowski energy at $t{=}0$ is easily pulled back to the cylinder frame
and evaluated by exploiting the orthogonality properties of the hyperspherical harmonics
\cite{lechtenfeld-kumar},
\begin{equation}
E \= \sfrac{1}{2\ell}\int \limits_{S^3} \!\!{\mathrm d}^3\Omega_3 \  (1{-}\omega_4)\,
\bigl(\mathcal{E}_a\mathcal{E}_a + \mathcal{B}_a \mathcal{B}_a\bigr)
\=  \sfrac1\ell\,(2j{+}1)\,\Omega^3 \sum_{m,n} |c_{m,n}|^2\ .
\end{equation}
A similar computation produces an expression for the helicity.
It turns out that single-spin solutions (of both types)  have a universal energy-to-helicity ratio \
$E/h=|\Omega|/\ell$.

Fourthly, so-called null fields are easily characterized,
\begin{equation}
\vec{E}^2{-}\vec{B}^2=0=\vec{E}\cdot\vec{B}
\qquad\Leftrightarrow\qquad (\vec{E}\pm{\mathrm i}\vec{B})^2=0
\qquad\Leftrightarrow\qquad \sum_{a} (\mathcal{E}_a\pm{\mathrm i}\mathcal{B}_a)^2=0\ .
\end{equation}
For fixed spin~$j$ and type~I we infer from above that
\begin{equation}
\mathcal{E}_a + {\mathrm i}\mathcal{B}_a \= -2{\mathrm i}\,\Omega\,
\sum_{mn} c_{m,n}\,Z_a^{m,n}(\omega)\,\mathrm{e}^{ \mathrm{i}\Omega\tau}
\qquad\textrm{(no c.c.!)}\ ,
\end{equation}
hence in such a sector we have~\cite{lechtenfeld-kumar}
\begin{equation}
F_{\mu\nu} \quad\textrm{null} \qquad\Leftrightarrow\qquad
\sum_{a} \Bigl(\sum_{mn} c_{m,n}\,Z_a^{m,n}(\omega) \Bigr)^2 = 0\ .
\end{equation}
Given the known form of the functions $Z_a^{m,n}(\omega)$ we can expand
this expression in hyperspherical harmonics and arrive at
$\sfrac16(4j{+}1)(4j{+}2)(4j{+}3)$ homogeneous quadratic equations
for $(2j{+}1)(2j{+}3)$ complex parameters $c_{m,n}$.
This system is vastly overdetermined, but only $4j^2{+}6j{+}1$ equations
are independent, and thus we are still left with $2j{+}2$ free complex parameters
for the solution manifold, which is explicitly parametrized as follows
\cite{lechtenfeld-kumar},\footnote{
These are the generic solutions. There also exist special solutions
with $c_{m,n}=0$ for $|n|\neq j{+}1$.}
\begin{equation}
c_{m,n}(w,\vec{z}) \= {\scriptstyle\sqrt{\binom{2j+2}{j+1-n}}}\
w^{\frac{j+1-n}{2j+2}}\ {\mathrm e}^{2\pi{\mathrm i} k_m\frac{j+1-n}{2j+2}}\ z_m
\quad{\quad\textrm{with}\quad} w\in\mathbb C^* \and  \vec{z}\equiv\{z_m\}\in\mathbb C^{2j+1}
\end{equation}
and a choice of $2j{+}1$ integers $k_m\in\{0,1,\ldots,2j{+}1\}$
(one of which can be absorbed into $z_m$).
Given that the overall scale of the solutions is irrelevant,
the null fields form a complete-intersection projective variety
of complex dimension $2j{+}1$ inside $\mathbb C P^{(2j+1)(2j+3)-1}$.
The simplest example occurs for spin $j{=}0$, where the single
null-field relation $c_{_{0,0}}^2=2\,c_{_{0,-1}}c_{_{0,1}}$
defines a generic rank-3 quadric in $\mathbb C P^2$ or, alternatively,
a cone over $\mathbb C P^1$ lying in $\mathbb C^3$.

\bigskip

\section{Examples}

\noindent
We close with two concrete examples.
First, the $j{=}0$ case represents SO(4)-symmetric Maxwell solutions in de Sitter space,
meaning $X_a(\tau,\omega)=X_a(\tau)$ thus $R_aX_b=0$ and trivializing (\ref{Maxwelleom}) to
\begin{equation}
\ddot X_a \= -4\,X_a \qquad\Rightarrow\qquad
X_a(\tau) \= \xi_a\,\cos\bigl(2(\tau{-}\tau_a)\bigr)\ ,
\end{equation}
which describes an ellipse in $\mathbb R^3$.\footnote{
Every solution $X_a(\tau)$ spontaneously breaks the SO(4) invariance
by the choice of integration constants $(\xi_a,\tau_a)$.}
We may always choose a frame where $\xi_3=0$ and $\tau_2=0$.
The overall amplitude is irrelevant as all equations are linear,
and solutions can be superposed at will. Specializing to
\begin{equation}
\xi_1=\xi_2=-\sfrac18 \and \tau_1=\sfrac\pi4  \qquad\Leftrightarrow\qquad
c_{0;0,-1}=c_{0;0,0}=0 \and c_{0;0,1}\in{\mathrm i}\mathbb R\ ,
\end{equation}
one has a null configuration with components
\begin{equation}
X_1(\tau) = -\sfrac{1}{8} \sin 2\tau\ ,\quad
X_2(\tau) = -\sfrac{1}{8} \cos 2\tau\ ,\quad
X_3(\tau) = 0 \ .
\end{equation}
The result of a short computation yields
\begin{equation}
\vec{E} + \mathrm{i} \vec{B} \= \frac{\ell^2}{\bigl((t-\mathrm{i}\ell)^2-r^2\bigr)^3}
\begin{pmatrix}
(x-\mathrm{i}y)^2-(t-\mathrm{i}\ell-z)^2 \\
\mathrm{i}(x-\mathrm{i}y)^2 + \mathrm{i}(t-\mathrm{i}\ell-z)^2 \\
-2\,(x-\mathrm{i}y)\,(t-\mathrm{i}\ell-z)
\end{pmatrix}\ .
\end{equation}
This is the announced Hopf--Ra\~nada electromagnetic knot~\cite{elknots,knotreview}.
Our approach also yields its gauge potential.

Second, let us take the real part of the $(j;m,n)=(1;0,0)$ type~I basis solution.
Combining ${\mathrm e}^{4{\mathrm i}\tau}{+}{\mathrm e}^{-4{\mathrm i}\tau}=2\cos4\tau$
and expressing $Y_{1;0,\star}$ from (\ref{type1}) in terms of~$\omega_A$, we get
\begin{equation}
X_\pm = -\sfrac{\sqrt{3}}{\pi}\,(\omega_1{\pm}{\mathrm i}\omega_2)(\omega_3{\pm}{\mathrm i}\omega_4)\,\cos 4\tau \qquad\textrm{and}\qquad
X_3 = -\sfrac{\sqrt{6}}{\pi}\,(\omega_1^2{+}\omega_2^2{-}\omega_3^2{-}\omega_4^2)\,\cos 4\tau \ .
\end{equation}
This solution takes the explicit form (putting $\ell{=}1$)
{\small
\begin{equation*}
\begin{aligned}
(E+&{\mathrm i} B)_x \=
\frac{-2{\mathrm i}}{ \left((t-{\mathrm i})^2-x^2-y^2-z^2\right)^5} \ \times \\%[4pt]
\times\ &\Bigl\{ 2y +3 {\mathrm i} t y -x z +2 t^2 y + 2{\mathrm i} t x z-8x^2 y-8y^3+4yz^2 \\%[4pt]
&+\ 4{\mathrm i} t^3 y -6t^2 xz -8{\mathrm i} t x^2 y-8{\mathrm i} t y^3+4{\mathrm i} t yz^2 +10x^3 z+10xy^2 z -2xz^3 \\%[4pt]
&+\ 2({\mathrm i} t x z+x^2 y+y^3+y z^2)(-t^2+x^2+y^2+z^2) +({\mathrm i} t y- x z) (-t^2+x^2+y^2+z^2)^2\Bigr\}\ ,
\qquad\ \ {}
\end{aligned}
\end{equation*}
\begin{equation} \label{j1sol}
\begin{aligned}
(E+&{\mathrm i} B)_y \=
\frac{2{\mathrm i}}{\left((t-{\mathrm i})^2-x^2-y^2-z^2\right)^5} \ \times \\%[4pt]
\times\ &\Bigl\{ 2x +3 {\mathrm i} t x + y z+2 t^2 x-2{\mathrm i} t y z-8x^3-8xy^2 +4 xz^2 \\%[4pt]
&+\ 4 {\mathrm i} t^3 x +6 t^2y z -8{\mathrm i} t x^3-8{\mathrm i} txy^2 +4 {\mathrm i} t x z^2-10 x^2 yz-10y^3 z +2y z^3 \\%[4pt]
&+\ 2 (-{\mathrm i} t y z+x^3+x y^2+x z^2)(-t^2+x^2+y^2+z^2) +({\mathrm i} t x+ y z)(-t^2+x^2+y^2+z^2)^2\Bigr\}\ ,
\qquad{}
\end{aligned}
\end{equation}
\begin{equation*}
\begin{aligned}
(E+&{\mathrm i} B)_z \=
\frac{{\mathrm i}}{\left((t-{\mathrm i})^2-x^2-y^2-z^2\right)^5} \ \times \\[4pt]
\times\  &\Bigl\{1+2{\mathrm i} t+t^2-11 x^2- 11 y^2 +3 z^2 +4 {\mathrm i} t^3-16{\mathrm i} t x^2-16{\mathrm i} t y^2+4{\mathrm i} t z^2 \\%[4pt]
&-\ t^4-2 t^2 x^2-2t^2 y^2-2t^2 z^2+11 x^4+22x^2y^2+10 x^2 z^2+11y^4-10 y^2 z^2+3z^4 \\%[4pt]
&+\ 2 {\mathrm i} t (t^2-3 x^2-3 y^2-z^2) (t^2-x^2-y^2-z^2) -(t^2+x^2+y^2-z^2)(-t^2+x^2+y^2+z^2)^2\Bigr\}\ .
\end{aligned}
\end{equation*}
}
Figures \ref{fig3} and \ref{fig4} below show $t{=}0$ energy density level surfaces and
a particular magnetic field line.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.43]{figa.eps}
\caption{Energy density level surfaces at $t{=}0$ for the $(1;0,0)$ solution above.}
\label{fig3}
\end{figure}
\begin{figure}[h!]
\centering
\includegraphics[scale=0.43]{figb.eps}
\caption{A particular magnetic field line for the $(1;0,0)$ solution above.}
\label{fig4}
\end{figure}

\bigskip

\section{Summary and discussion}

\noindent
\begin{itemize}
\item
Rational electromagnetic fields with nontrivial topology have been investigated since 1989
\item
We introduced a new construction method based on two insights:
\\[-16pt]
\begin{itemize}
\item
the simplicity of solving Maxwell's equations on a temporal cylinder over a three-sphere
\item
the conformal equivalence of a cylinder patch $\{\tau,\omega\}$ to Minkowski space $\{x\}\equiv\{t,\vec{x}\}$
\end{itemize}
\item
The gauge potential is transferred via \
${\cal A}=X_\nu(\tau,\omega)\,e^\nu=X_\nu(\tau(x),\omega(x))\,e^\nu_{\ \mu}(x)\,{\mathrm d} x^\mu$
\item
Only finite-time $\tau\in(-\pi,+\pi)$ dynamics is required on the cylinder
\item
Our solutions have finite energy and action, by construction
\item
Energy and helicity are easily computed, null fields can be fully characterized
\item
A complete basis was constructed for sufficiently fast spatially and temporally decaying fields
\item
The non-Abelian extension couples different $j$ components of $X_a$ and will be harder to treat
\item
The method may be useful for numerics of Yang--Mills dynamics in Minkowski space
\end{itemize}

\vspace{1cm}

\noindent
{\bf\large Acknowledgments}\\[4pt]
The author is grateful to Gleb Zhilin and Kaushlendra Kumar
for their contributions to \cite{lechtenfeld-zhilin,lechtenfeld-kumar}.

redpajama_set_name: RedPajamaArXiv


A warm climate along the coastline that includes superb natural beaches, mysterious deserts, fertile river valleys and exotic dry woodlands.
A region of varied terrain and temperate climate, dominated by the snow-capped peaks of the Andes rising above 6,000 masl, the highest of which is Mount Huascaran, at 6,768 masl (22,206 ft). It includes deep canyons such as the Colca and Cotahuasi, the two deepest on the planet; and high plains like the plateau of Collao, on the shores of the world's highest navigable lake, Titicaca, at 3,810 masl (12,500 ft).
A region of tropical climate, lush vegetation, and abundant fauna that is part of one of the planet's largest natural reserves. It is here that the confluence of the Maranon and Ucayali rivers forms the Amazon River, the largest in the world.
Peru is organized into 24 regions (Amazonas, Anchas, Apurimac, Arequipa, Ayachuco, Cajamarca, Cusco, Huancavelica, Huanuco, Ica, Junin, La Libertad, Lambayeque, Lima-Provinces, Loret, Madre de Dios, Moqueguea, Pasco, Piura, Puno, San Martin, Tacna, Tumbers, and Ucayali), besides Callao Constitutional Province.
Temperatures and atmospheric cycles vary from one region to another. Coast: There are two clearly-defined seasons on the coast: summer (December-march), when temperatures can reach 27 degrees C (80 degrees F); and winter (April-November), which is very damp and chilly, with temperatures falling to 12 degrees C (53 F). Although it rarely rains on the coast, mist and drizzle are common during the winter. The far north coast enjoys sunshine all year round, with temperatures reaching 35 C (95 F) in the summer.
The climate is dry and temperate, with two clearly defined seasons: the dry season (April-October), with sunny days, very cold nights, and scant rainfall (the ideal time to visit the Andes), and the rainy season (December-March). There is a sharp contrast in temperature between sun and shade, and temperatures can often vary widely during the same day, from 20C (68F) to 2C (35 F).
The climate is tropical and humid. There are two well-defined seasons: the summer or dry season (April to October) with sunny days and temperatures above 30C (86 F), and the rainy season (November-March) with frequent showers and high river levels.
Peru has approximately 32 million inhabitants. The coast shelters 55.9% of the total population, the highlands 29.6% and the jungle 14.5%. The population is mostly mixed, urban, and speaks Spanish, but there are two important minorities: Andean populations, divided in the Quechua and Aymara language families and Amazon populations divided in 14 language families and 42 ethnic groups.


We're leaving for Europe in just few weeks! I've been looking for the perfect winter coat to take with me - one that's warm, stylish and easy to travel with (like I can stuff it in my suitcase if needed). Do I go with a wool pea coat, a down parka, a military-chic jacket, or a light-weight jacket I can layer with? Choosing the right coat has been challenging but thankfully, sites like Pinterest and Polyvore provide endless ideas and options. I love the wool coat by J.Crew I'm wearing but I think it might too heavy to travel with. What do you think? Share your recommendations in the comments below or tag me on Instagram or Twitter!
Blog Party Blog + a Giveaway!


The Federation Wars were fought between the Free-Born and the Federation.
The Federation Wars had been fought since the passing of Allanon. It pitted unification against independence, territorial rights against free will. The Federation wanted Callahorn to be part of the Southland, the Free-born wanted it to be its own country.
The Elves and Dwarves also became involved as the Federation sought to expand and expand.
Sen Dunsidan had been unable to end the war or bring it closer to a meaningful conclusion.


text:
Samsung will pay your installment plan until 2016 if you buy a Galaxy phone (US only)
Competition is fierce in the mobile industry and Samsung is really urging to sell some devices! So much that they are willing to pay part of the phone if you switch to any of their latest handsets! Interested? Of course you are.
Here's how it works. Eligible users are those who buy a Samsung Galaxy S6, S6 Edge, S6 Ede+ or Galaxy Note 5 on an installment plan or lease. Samsung will then give customers a rebate amounting for the full price of your installment payments up until 2016 comes around. You just have to go through an online claim.
The only issue is that there's a $120 limit, but iPhone users can take this deal to the next level. Apple smartphone users can simply pre-register and trade-in their iPhone to get an extra $100 on Google Play Store credit. The process is simple, just head over to the Samsung Promotions page from the eligible iPhone (iPhone 4s and newer) and enter your email. You can then simply turn in your device and get a Galaxy phone from your carrier.
As you can expect, this is only a US offer. Another huge caveat is that for some reason AT&T customers are not qualified. Here the terms and conditions, just in case you need to catch all the small print. Most of it is pretty straight forward, though.
Are any of you signing up? If you are not sure which phone to get, remember we have our reviews on the Samsung Galaxy S6, Galaxy S6 Edge, Galaxy S6 Edge+ and Galaxy Note 5. Go check them out and hit the comments to tell us which one you are getting.
Here are the videos you don't want to miss this week – September 26, 2015
We're just now wrapping up yet another busy week in the Android world. As we get ready for Google to unveil the new Nexus devices in the next couple days, we thought it would be a good idea to catch you up on some of the best Android-related videos of the week.
Both the new Moto 360 and Huawei Watch showed up on our doorstep, and we've wasted no time unboxing and giving you our first impressions on both devices. We've also published our full reviews of the Huawei Mate S and BLU Vivo Air LTE, and brought you some handy tips and tricks for your brand new Samsung Galaxy Note 5.
Without any further ado, here are the videos you don't want to miss this week.
Motorola Moto 360 (2nd Gen.) unboxing and first look
Motorola created one of the best looking Android Wear smartwatches with last year's Moto 360. How does this new one compare? Josh unboxes and gives us his first impressions on the Moto 360 (2nd Gen).
Motorola Moto 360 (2nd Gen.) unboxing and setup
Huawei Watch unboxing and first look
The second-gen Moto 360 is quite the attractive device, but it looks like it has some big competition. Don't miss Josh's unboxing of the Huawei Watch.
Huawei Mate S review
Just recently unveiled at IFA 2015, Huawei's Mate S boasts some impressive specs and features. Does Huawei have another hit on its hands? Check out Gary's review to learn more.
BLU Vivo Air LTE review
BLU has proven itself time and time again in the mid-range smartphone market, but the company's Vivo Air LTE has some quirks you should know about. Don't miss Bailey's full review.
Samsung Galaxy Note 5 – 5 tips and tricks
Want some advice on how to use your new Galaxy Note 5? Josh is here to give you five tips and tricks for the Samsung Galaxy Note 5.
Samsung Galaxy Note 5 – 5 tips and tricks!
Make your own Google Cardboard headset
http://player.ooyala.com/v3/7f2b2d0412e84a188ede8d648751dc42?namespace=OoyalaPlayer1&platform=html5-fallback
var ooyalaplayers = ooyalaplayers || [];
OoyalaPlayer1.ready(function() ooyalaplayers.push(OoyalaPlayer1.Player.create.apply(this, ["ooyalaplayer-1″,"Q4MGpxdzq63IQjC1Fmly3XNDf61QyQIv","auto":true,"showadmarquee":false]) ); );
With the launch of Google Cardboard, VR is making its way to the masses. Here's how to assemble your very own Cardboard headset.
How to make your own Google Cardboard headset
The latest in VR
New Samsung Gear VR reaction at Oculus Connect
Samsung just recently unveiled a new Gear VR headset. Josh got the chance to try it out, and he's here to give you his reaction.
Oculus Touch demo reaction at Oculus Connect
Want some more information on the new Oculus Touch controller for the Rift? Josh will walk you through the basics.
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Free music, cheap apps, FIFA 16 and Eternity Warriors 4 – you don't want to miss Joe's newest episode of Android Apps Weekly!
5 Android apps you shouldn't miss this week – Android Apps Weekly
Google's Nexus 5X hits the FCC with support for all big US carriers
Google's Nexus phones haven't had the best cross-carrier support in the US (ahem, Verizon), but that might change when the Nexus 5X and 6P roll into town. The Nexus 5X has just swung by the FCC for approval, and one filing is for a model that appears to support all four major US carriers in at least some capacity — there are concerns that it might not handle T-Mobile's existing 3G, but this does include Verizon support. There's also a second variant of the LG-made device that removes some frequency bands and appears destined for other countries. There's not much to see beyond this, although the FCC's measurements back rumors that the 5X will have a 5.2-inch screen. Will this Nexus actually work with every major US network when it launches? It's hard to say for sure, but you'll likely get the full scoop at Google's event in a few days.
[Image credit: Android Police]
Via: Android Police, S4GRU
Source: FCC (1), (2)
Nexus 6P presentation leaks in entirety, confirms nearly all the rumored specifications
A slides presentation just surfaced in its entirety containing the majority, if not all of the specifications for the upcoming Nexus 6P. The leak also includes high quality renders, new features and more.
Apparently, the Nexus 6P hasn't leaked enough in the past few weeks. Today, just about all the specifications for the upcoming handset was released free into the wild. The Nexus 6P made by Chinese manufacturer Huawei will feature slightly higher-end specifications when compared to the LG made Nexus 5X. It will also be the larger of the two with its 5.7-inch WQHD IPS-LCD display. The design has been described as a metal unibody, slim and sophisticated. Users will get the toughest build out there when it comes to the screen which will boost Gorilla Glass 4. It will be powered by Qualcomm's Snapdargon 810 processor v2.1. The amount of RAM is still up in the air, but one could expect to see a minimum of 3GB for this handset. Other specs include high-resolution front and rear-facing cameras that can be activated via a tap of the newly included rear mounted fingerprint scanner. Just in case you didn't know, Android 6.0 will be making its debut with this one. The handset will boost a large 3,450mAh battery that is non-removable. Type C is also included with ultra-fast charging capabilities and faster data transfer speeds.
The Nexus 6P's design matches recent leaks and will support dual front-facing speakers. The camera is said to bring fast auto-focusing and improved low light photo taking. The handset will weigh a total of only 178g. Nearing the end of the presentation, Google reminds us about some of the newest features included with Marshmallow such as Now On Tap, new app permissions, a new fingerprint API and better power consumption with dose and app standby.
The handset will come in a variety of color options such as aluminium, graphite, frost, and gold. However, the choices may vary depending on your location. Storage options include 32GB, 64GB and the whopping 128GB many were hoping for. Unfortunately, there has been no word on pricing, but it's rumored that pre-orders will go up on October 13. Google will hold the conference on September 29 in San Francisco, where is will announce the Nexus 6P alongside a LG manufacturer Nexus 5X. Updated Chromecast models are also expected. Screenshots of the entire presentation have been included in the gallery below. Whose excited?
Source: Imgur
Via: Android Police
Come comment on this article: Nexus 6P presentation leaks in entirety, confirms nearly all the rumored specifications
Visit TalkAndroid for Android news, Android guides, and much more!
Google has filed a patent aimed at preventing one from dropping their smartphone
Google just submitted a patent of a rather odd design aimed at preventing users from dropping their smartphone.
The patent pictured above was filed last week by Google. It features a brand new smartphone with a design that will hopefully prevent users from dropping their device. The patent indicates better grip, but comes with a cost of a bad design. It shows rather sharp edges and a thick body. On the rear side it has ridges for one to put their fingers along when holding the device. Ultimately guided at helping users maintain control of their smartphone and preventing it from slipping out of his/her hand. It will be interesting to see if this ever hits the market. We'll keep an eye out.
Source: Patently Mobile
Come comment on this article: Google has filed a patent aimed at preventing one from dropping their smartphone
iPad Mini 4 review: A long wait makes for a potent upgrade
Fans of Apple's smaller iPad Mini caught a tough break last fall when the company unveiled its new tablets for the year. Although Tim Cook & co. lavished plenty of attention on the faster, slimmed-down iPad Air 2, the upgraded iPad Mini 3 was regarded as a mere afterthought. The list of changes was so short, in fact, that some of us wondered why Apple would introduce a performance gap between the Air and Mini lines. Still more people wondered when they'd get a Mini with enough power to match its larger sibling. Turns out, the answer was "a year later." I've been testing the new iPad Mini 4 for over a week now and can say with confidence this is the Mini we should've gotten last year.Slideshow-323041
Apple's design team did most of the heavy lifting with the iPad Air 2 and now we're finally seeing that sleek aesthetic trickle down to the Mini. The 4's fit and finish is still first-rate and, more importantly, the whole package is about a tenth of a pound lighter than last year's model. That might not sound like a dramatic difference, but when you're building a device with a bigger-than-phone-sized screen, every ounce and gram matter. The iPad Air 2 felt almost unnaturally light for its size, so you can imagine how light the even smaller Mini 4 feels — holding it aloft and watching YouTube videos for hours was none too painful.
The Minis were never exactly tanks, of course, but this year's thinner and lighter model (0.65 pound and 6.1mm, the same thickness as the Air 2) makes prolonged, one-handed use a pleasure. The Air-ification of the Mini line also means that handy rotation-lock switch — part of the iPad's hardware formula for years — has been excised. Keeping your screen from spinning around now requires you to swipe up the Control Center and tap an icon down there. This is one of those little changes that most people won't notice until they start feeling around for that familiar nubbin. Despite not using it that frequently, I still miss having it there.
It's easy to imagine Apple just took a shrink ray to an iPad Air 2 and called it a day, but there's more going on here than meets the eye. You see, rather than carry over the modified A8X from the Air 2, Apple kitted out the new Mini with the same A8 processor that's currently powering the iPhone 6, albeit except it's paired with 2GB of RAM instead of one. I've never had much reason to complain about the iPhone 6's performance, and the combination of that chipset and the extra RAM means the Mini 4 is, unsurprisingly, a snappy performer (more on that later). My review unit was a 128GB model, although Apple also offers 16GB and 64GB options with prices starting at $399 for a WiFi-only configuration. Toss in an updated 8-megapixel rear camera, not to mention faster 802.11ac WiFi and 20 LTE bands, and we've got a much-improved device on our hands.
Display and sound
The iPad Air 2 might give you more screen real estate, but the Mini 4 wins on pixel density, hands down. Like the Mini 3 before it, the newest generation squeezes 326 pixels into each linear inch of the device's 7.9-inch screen, making for crisp text and eye-popping visuals. Even better, Apple finally got rid of that tiny gap between the Mini's display panel and the slate of arsenic-free glass covering it; it's all been combined into a single, laminated panel.
What sounds like an exercise in LCD screen minutiae makes for some dramatic changes: It means less glare, better viewing angles and a touch more crispness. When we tested the Air 2 and the Mini 3, the difference in color clarity and saturation was pretty pronounced, but that's thankfully now a non-issue. Oh, and a brief aside: Older Minis also made a bit of a hollow thunk sound when you tapped them a certain way, an issue that's been addressed on the new model.
If you're hell-bent on using the Mini as a media machine, you've probably got a decent pair of headphones to go with it. Thankfully, you needn't fret if you accidentally leave them at home: The speakers housed on the Mini's bottom edge are impressively loud for their size. You won't be able to fill a room with the mid-heavy sound they churn out, but I discovered I could leave a video playing in the kitchen and still hear it while folding laundry downstairs.
iOS 9 is such an important step forward that we just published a few thousand words all about it. Assuming you don't have the time to sift through our full review, here's a quick rundown on what iOS 9 means for the new Mini. In short, Apple's latest software update is focused more on stability and thoughtfulness, using Siri's new proactive smarts to surface information and apps when you might want them. Throw in plenty of neat design changes — like a revamped app switcher and a fantastic "Back" button that lets you follow the breadcrumb trail of apps you were just using — and we've got a more smartly put-together update than we initially gave Apple credit for.Slideshow-322375
iPads got plenty of attention in this update, and fans of mobile multitasking should be especially pleased. Consider Slide Over, which lets you swipe open a drawer full of first-party apps that can be opened in a smaller, separate window that takes up about a quarter of the screen. By jumping into any of those apps, you're effectively putting the other, primary application you were just using on pause until you're done texting or checking Apple News. You can go a step further and drag the line that divides those apps; that resizes both of them until they each take up 50 percent of the screen. Why hello, Split View. Honestly, as neat as this trick is, it feels sort of silly on a screen this small. Running two apps side by side makes sense on a larger display — say, on a full-sized Air 2 or an enormous iPad Pro. Shoehorning two apps onto an 8-inch screen can feel a little claustrophobic after a while.
Then there's picture-in-picture mode, which, yes, is exactly what it sounds like. Any time you play a video in Apple's stock media player, you can tap an icon to shrink it down and stick it in a corner so you won't miss a moment of JK Simmons being an epic jerk in Whiplash. Give that small window a quick pinch-zoom and it'll roughly double in size; the default view on the Mini 4 is pretty tiny, so you'll probably spend most of your time in this mode.
Moving on, the Notes app also now supports richer text formatting (heck yeah, subheadings) and packs a reasonably thorough sketching tool for adding drawings and diagrams to your text. The smaller screens on iPhones make random doodling tricky, but that's not a problem with the Mini's nearly 8-inch screen. All told, iOS 9 is a must-have download, and the Mini 4 gives it plenty of space — and power — to shine.
I'll be the first to admit I sometimes glare at people shooting tab-photos in public, but the appeal is pretty obvious. For one, it might be the only camera folks have on them, and we all know the adage there. A bigger screen also makes it easier to frame shots, and really, who among us couldn't stand to be better at that? What I'm saying is this seemingly silly habit isn't going anywhere, and the iPad Mini 4's rear-facing 8-megapixel camera does a fine job of capturing the world around you. Slideshow-323032
Tablet photos are hardly ever outstanding, but the Mini 4, like the Air 2 before it, is capable of capturing crisp colors and reasonable detail when the light is right. White balance is generally more accurate now too, which is especially apparent since the Mini didn't get left in the display quality dust this time. Things obviously get muddier in dimmer conditions, but really, if you're using a tablet to take photos in the middle of the night, you might want to rethink your strategy. Meanwhile, the front-facing camera is stuck at 1.2 megapixels, but it now has an f/2.2 aperture lens to help suck in the light bouncing off of your face. Still, I haven't noticed much of a difference between this camera and the one in last year's Mini.
Other changes include the ability to shoot in burst mode thanks to the A8 chipset thrumming away inside, and improved support for HDR photos and video. The iPad Mini 4 isn't going to be anyone's first choice for mobile photography, but it's a solid, if unremarkable, performer.
Performance and battery life
I sort of alluded to this earlier, but let's be clear: The Mini 4 is not just a shrunken-down Air 2. The difference in the chipsets powering these things is apparent in our benchmark tests below, but the Mini 4 is still no slouch compared to its more premium cousin. It's buttery smooth as you leap in and out of apps and swipe through web pages. The only time I noticed the Mini's A8 chipset struggling was while running two apps in Split View, and even then, it was only when I was trying to fiddle with both simultaneously. While I'm comparing the Mini 4 to other iPads, it's noticeably quicker to react than last year's Mini. In fact, Apple says the A8's CPU is 30 percent faster than the Mini 3's A7, and that graphical performance is up 60 percent from last year. That helps explain why Asphalt 8 and Modern Combat 5: Blackout ran like a dream, but I'll let the numbers do the rest of the talking.
Geekbench 3.0 3,236 4,510 2,470 3,423
Basemark X 17,212 29,518 14,839 TBD
3DMark IS Unlimited 16,291 21,659 14,595 30,970
SunSpider 1.0 (ms) 349 303 439 463
SunSpider: Lower scores are better.
So, pretty much exactly what I expected: The Mini 4 strikes an appropriate balance between the Mini 3 and the Air 2 (which has the edge thanks to an extra CPU core). Usually it performs just a hair better than last year's iPhones too. Of course, horsepower means nothing without battery power, and the new Mini has that in spades. The usual Apple refrain is that the Mini is rated for about 10 hours of continued use, but that might have been understating things a bit. In our usual video rundown test (video looping with the screen brightness set to 50 percent), the Mini 4 lasted 13 hours and 4 minutes before needing an emergency trip to the power outlet. That's just short of the 13 hours and 45 minutes on last year's model, which isn't bad at all considering the new Mini 4 actually has a smaller, 5,124mAh battery.
The Mini fared similarly well in the battery test called "living with me." After pulling it off of the charger at around 7 AM, schlepping to the office and using it for emails/reading articles/the occasional game, I'd usually wind up with 10 percent remaining when I returned home at 9 PM.
iPad Mini 4 13:04
iPad Air 2 11:15
iPad Air 13:45 (LTE)
Apple iPad Mini 12:43 (WiFi)
Samsung Galaxy Tab S (10-inch) 12:30
Microsoft Surface 3 9:11
Galaxy Tab S2 7:30
If you're in the market for a sleek tablet, consider Samsung's Galaxy Tab S2 (starting at $400 for the 8-inch model). While it lacks the kooky style of its immediate predecessor, the 10-inch screen is one to behold — it is Samsung after all — and it's only 5.6mm thick. The downgraded battery might sting, though: It only managed 7.5 hours in our tests, down from 12.5 hours for the previous-gen model. Itching for something more portable? ASUS just launched its 8-inch ZenPad S, a $200 Android slate with a waistline similar to the Mini 4's and a 2,048 x 1,536 display, to boot. Then there's the iPad Air 2 itself, which is still the most powerful tablet in Apple's roster. It's incredibly sleek and can be held one-handed for longer than you might expect, but its size means it's just not going to fit into some lifestyles. The thing is, it's almost worth trying to see if the size can work for you; prices for the Air 2 start at $499, and sales or buying refurbished can bring that base price down even lower.
Some might gripe about the Mini 4's year-old internals, but after my week of testing, I feel confident saying that it doesn't matter much. The tablet's entire package, from the still-snappy A8 chipset to the beautiful and almost-pocketable screen, to the incredibly sleek chassis, makes it worthy of your consideration. If you're on the lookout for a super-portable tablet with strong fundamentals and great app support, you probably won't find a contender better than this one. That said, if you can fit a bigger tablet into your life, you could easily upgrade into an iPad Air 2 for not much more money and get even more processing power.
Blackberry CEO John Chen awkwardly showcases the Blackberry Priv
Not too long after we brought you some exclusive images of the BlackBerry Priv (aka Venice), the company officially confirmed that its Android-powered smartphone would be launching by the year's end. To get consumers excited about the device before its official launch, BlackBerry CEO John Chen went on camera with Canadian news outlet BNN to showcase the new smartphone… only it seemed like Chen only had a passing familiarity with the device.
The first thing the interviewer asks is to see the slide-out physical keyboard, which is the Priv's spotlight feature. Chen says he's going to hold off on showing that until the end, because it's the big reveal. The interviewer seems fine with this, so Chen jumps into a spec rundown as smooth and graceful as middle-schooler belly-flopping off the high dive.
See also: In his own words: BlackBerry CEO John Chen explains why his company's Priv is all about Android74362
"It runs Google," says Chen, meaning that the Priv runs the Android operating system (which is at least a little better than saying "the Google"). He points out the curved screen which is… curved. He shows off the device's touchscreen capability. He boasts of its cameras and "all that good stuff." He almost pulls up Chrome successfully.
Eventually, Chen seems to realize he should have stuck with shock and awe and left the spec work to someone from the design department. He snaps out the keyboard and…
Well, maybe it speaks to the elegance of the hardware that, even in the midst of this cringe-fest, the keyboard still comes across as slick as hell and damn impressive. The physical keyboard doubles as a touch mouse (which I have my doubts about, but which looks cool nonetheless) and can be snapped in and out of the bottom of the phone.
https://bmplayer-a.akamaihd.net/shareable/embedssl.html?dc=bnn_web&cid=713580&col=766&w=640&h=360&pl=0&plh=0&adSite=ctv.bnn&adZone=shows/thedisruptors&omniAcct=ctvgmtvebnndesktop,ctvgmglobal&section=video%20-%20hub&site=bnn&shareUrl=&v7=player&v8=&v9=&v10=
Blackberry hopes the Priv will draw back all those users who were addicted to physical keyboards for years but who eventually acquiesced to touch keyboards once phones like the Droid 4 slipped out of existence. Whether or not this will work for the one-time mobile giant is yet to be determined, but so far the Priv looks pretty smooth even in the most un-smooth of hands.
We spent two weeks wearing employee trackers: Here's what we learned
This article originally appeared on Fast Company and is reprinted with permission.
By Greg Lindsay
I almost didn't notice I was wearing it, at first. The plastic box strung around my neck was roughly the size and weight of a deck of cards, lighter than I expected. It was only when I spotted the occasional flash of blue light that I remembered this "sociometric badge" was listening to everything I said, where I said it, and to whom—especially if they were wearing a similar device around their own necks. In those cases, our conversations were captured for analysis—ignoring what we said in favor of how long we spoke, and who did all the talking.
I started to turn painfully self-conscious around my first visit to the bathroom: Did the badge know I was in there? Would it listen? Would it freak someone out that I was wearing a giant sensor in the stall next to him? By the time I left the building for lunch, I had zipped it beneath my jacket, less concerned that it was counting my every step than having civilians think I was some new species of Glasshole.
Like Google Glass, sociometric badges were prototyped in Alex "Sandy" Pentland's Human Dynamics Lab within the MIT Media Lab—a place where his cyborg doctoral students once wore keyboards on their heads and no one thought it strange. Unlike Glass, the badges are still a going concern—five years ago, Pentland and several former students spun out a company now called Humanyze to consult for such companies as Deloitte and Bank of America. Just as Fitbits measure vital signs and REM cycles to reveal hidden truths about their wearers' health, Humanyze intends to do the same for organizations—only instead of listening to heartbeats, its badges are alert for face-to-face conversations.
For two weeks in April, Fast Company was one of those subjects. (Humanyze provided the badges and analysis for free.) Twenty Fast Company editorial employees—and me, as a visiting observer—agreed to wear the badges whenever we were in the building. Our goal was to discover who actually speaks to whom, and what these patterns suggest about the flow of information, and thus power, through the office. Is the editor in chief really at the center of the magazine's real-world social network, or was someone else the invisible bridge between its print and online operations? (Or worse, what if the two camps didn't speak at all?) We would try to find out, though we would be hampered somewhat by the fact that not everyone was wearing a badge, and we didn't give Humanyze the full range of data, like integration into our email and Slack conversations, that would allow the company to truly understand our work relationships.
More importantly were the questions we chose to not ask: How did these patterns impact performance? Should editors and writers talk less or more, and what did it mean when they talked amongst themselves? Did it result in more posts on Fast Company's website, or more highly trafficked ones? Demonstrating and understanding these relationships are what Humanyze's clients pay for; perhaps we were too scared to learn.
For the better part of two weeks, staff members suffered the badges in silence. Some people found wearing them uncomfortable and awkward. "It was oppressive," says associate news editor Rose Pastore. "I think it ruined my posture." "It does not play well with statement necklaces," says senior editor Erin Schulte, who, like many others, resented needing to wear the badge on her sternum for maximum audio fidelity (and so the infrared sensors that establish the wearers' identities have a clear line of sight). Several wished it could be a pendant or lapel pin or wristlet—anything less intrusive.
Others complained about the user interface, or lack thereof. The blue twinkling I'd noticed was only one of several colors, none of which had been explained during orientation. Some found this Orwellian; others reported being lulled into complacency by its low-tech appearance and cheap plastic casing. Still more wanted feedback: Was this thing on? Was I doing this right? Cognitive dissonance soon manifested. Writers and editors who complained in one breath about opaque surveillance suggested in the next that only if the badge could replace their Jawbone UPs and Fitbits—in the process capturing their quantified selves for their employer—would the exercise be worthwhile.
Co.Exist editor Morgan Clendaniel took this idea to its logical conclusion, proposing that flat-screens mounted around the office broadcast our interactions in real time, à la the visualizations produced by the likes of Chartbeat, which depicts the performance of individual online stories on a moment-by-moment basis. (A Los Angeles-based startup named Rexter does exactly that.)
Humanyze CEO Ben Waber understands their concerns, from the interference with statement necklaces to the deliberate lack of clarity from the badges. "Lights blinking all the time is distracting," he says. "It's a difficult line to manage." As far as the wearer's comfort goes, he's confident that Moore's Law will reduce the weight of sociometric badges until they are indistinguishable from standard-issue IDs. (The latest version of the badge, which we did not wear, is half the size of the previous iteration.) But he's adamant that the badges will always be worn on the chest, as it's the only way to guarantee conversations will be heard clearly.
Humanyze prides itself on privacy. Several weeks after our badges had been shipped back to Boston for analysis, we each received a link to our individual results. Not only was this data shielded from our employer, we were assured, but Fast Company was also contractually forbidden to ask us what was in our reports. Which explains why Laura Freeman, the "quantitative social scientist" who prepared our reports, was audibly dismayed when I announced my intentions to reverse-engineer them.
In my own case, the results confirmed what I already knew: that I was a marginal figure in the office, which I rarely visit. While I may have spent more time moving and speaking than most participants in order to gin up conversations about the badges, the extent of my connections would be considered subpar at best. ("You can increase your face-to-face network breadth by making an effort to meet new colleagues," my results helpfully suggested.)
The true org chart of Fast Company, based on whom workers interact with.
This made it easier to locate my likely position on the periphery of the network map created by the badges (pictured above). My best guess is that I'm the node at the very bottom, confined to speaking with my fellow "digital writers." We were a chatty group; one of the few surprises was that the seven writers talked more amongst ourselves than any other group (which included an equal number of digital editors, along with a smattering of magazine editors and developers). "Surely, they must be complaining," said Cliff Kuang, Fast Company's director of product.
The other surprise had to do with Kuang himself, who was revealed to be the center of the network. He was the only participant with strong ties to multiple members of the other groups. Editor-in-chief Bob Safian, it turned out, had stopped wearing his badge after only a few days and was likely on the fringes. Executive editor Noah Robischon's position as one of several highly connected digital editors was impossible to determine. But Kuang's central role makes perfect sense in retrospect: As director of product, he straddles multiple domains, and as a former editor of Co.Design, he has prior relationships that aren't reflected on the org chart.
Humanzye also measures how much people on each team move.
Unearthing those relationships, understanding and visualizing them, is perhaps the most potent thing sociometric badges can do. For more than 30 years, the sociologist Ronald S. Burt has mapped and described what he calls "structural holes"—the naturally occurring gaps within organizations. Those who bridge these holes, he has found, produce more ideas, make better decisions, and prosper accordingly. But they aren't necessarily the ones in charge.
To demonstrate, Burt recently mapped the relationships between top managers at one of the largest pharmaceutical giants in the world. He discovered a relative nobody several rungs below the CEO who appeared to be the only person keeping the company's Asian leadership tethered to the mother ship in Europe. When the results were published, Burt told me, the company immediately began grooming him for leadership.
Our experiment had no such tidy ending, however, which leads to the questions posed by critics of the trackers and the quantified workplace: What can this data be used for besides squeezing more work out of its users? There are few use cases outside of fixing the bottom line. If we had a specific business goal, perhaps the data could have been used to make changes to achieve that, but the information didn't do much to improve individual workers' understanding of their jobs.
[Top Photo: Thomas Barwick/Getty Images]
Step inside NASA's astronaut training simulators
Next weekend, theater-goers will watch astronaut Mark Watney battle to survive on the red planet in The Martian. Meanwhile, the Mars One initiative whittles down a list of Earth dwellers to journey to the very same planet by 2020. In a hostile and alien environment like Mars, it takes knowledge, preparation and practice to survive. You can't just, as Watney put it, "science the shit out of this" if you don't have a clue what to expect. To honor past orbital pioneers and future planetary explorers, we look at some of the simulators and mockups that real astronauts used in preparation for launching themselves off this blue orb and into the well-studied, yet unpredictable vastness of space.
[Image: NASA / Mercury astronaut training on gimbal rig 1960]
Slideshow-322653
Insteon and Amazon Echo now support each other
Insteon and Amazon Echo have joined forces to bring support for Insteon's line of lights, dimmers and relays to the Echo's set of devices that can be controlled using voice commands. The ability to use Echo's Alexa to control Insteon devices does not cover everything quite yet, but Insteon says they are working on adding that support.
Currently, Echo users will find they can use use voice commands to turn lights on and off, dim lights with a voice command, or control groups that include up to five items. For example, users could put five lights that make up their living room lighting in one group and then use a command like, "Alexa, set living room lights at fifty percent" to adjust all of them. The groups are agnostic, so Insteon devices can be grouped with hardware like Belkin's WeMo, Phillips Hue, or Samsung's SmartThings. Echo does not yet support Insteon's Scenes feature which supports an unlimited number of devices being combined, but that should be added in the future.
Amazon's Echo will work with the regular Insteon Hub device, but not the Hub Pro which was built specifically for HomeKit.
source: Insteon
via: Engadget
Come comment on this article: Insteon and Amazon Echo now support each other
#News The Nord N10 5G is the first OnePlus phone to get January's security update dlvr.it/RqsB3T https://t.co/lovSznCEh2 2 hours ago


THE BOY, THE BOAT, AND THE BEAST comes out in stores in 18 days! And that means I get to start my own #18DaysToMGDebut countdown.
If you haven't seen it, the #18DaysToMGDebut hashtag was developed by the lovely Laurie Morrison, a fellow 2018 middle-grade debut author whose book, EVERY SHINY THING, co-written with Cordelia Jensen, was released on April 17. Eighteen Days because we're 2018 debuters, and a countdown because… it's so fun!
Today's prompt is "Novel Aesthetic," and after I looked up what that meant because I'm very unhip, I fell in love with the collections of images other authors have created for their books.
When I setup this website, I included a gallery of wonderful photographs that had inspired me while I was writing THE BOY, THE BOAT, AND THE BEAST on my home page. I also have a board on my Pinterest account with even more amazing images related to the book.
But for this challenge, I thought I'd try some new ones.
THE BOY, THE BOAT, AND THE BEAST starts out on a beach, but the boy in the story also journeys through a forest and encounters an owl, fireflies and more. Everything scares him. Everything seems out to get him. And he doesn't know where he can be safe. I tried to incorporate some of these things in this aesthetic, to give you a feel for the book.
Have you pre-ordered THE BOY, THE BOAT, AND THE BEAST yet? All pre-orders are eligible for a Thank You Gift, and can be entered to win a special book-themed gift pack.
Personalized copies of THE BOY, THE BOAT, AND THE BEAST are available for pre-order through my fantastic local independent bookstore, BookPeople. The novel is also available for pre-order on IndieBound, Powell's, Book Depository, Books-A-Million, Barnes & Noble, Amazon, Target, Walmart, as well as numerous other independent bookstores.
Check out all my #18DaystoMGDebut posts here.


text:
package main

import (
	"flag"
	"fmt"
	"os"

	"github.com/felixge/genfs"
)

func main() {
	if err := run(); err != nil {
		fmt.Fprintf(os.Stderr, "error: %s\n", err)
		os.Exit(1)
	}
}

func run() error {
	var (
		includeF = flag.String("include", "", "Regular expression for files and directory paths to ignore.")
		excludeF = flag.String("exclude", "", "Regular expression for files and directory paths to exclude.")
		pkgF     = flag.String("pkg", "main", "Pkg name for the generated file.")
		varF     = flag.String("var", "fs", "Name of the variable to hold the fs.")
	)
	flag.Parse()
	var filters []genfs.Filter
	if *includeF != "" {
		f, err := genfs.IncludeRegexp(*includeF)
		if err != nil {
			return fmt.Errorf("-include: %s\n", err)
		}
		filters = append(filters, f)
	}
	if *excludeF != "" {
		f, err := genfs.ExcludeRegexp(*excludeF)
		if err != nil {
			return fmt.Errorf("-exclude: %s\n", err)
		}
		filters = append(filters, f)
	}
	files, err := genfs.Files(flag.Arg(0), filters...)
	if err != nil {
		return err
	}
	return genfs.WriteSource(os.Stdout, *pkgF, *varF, files)
}

redpajama_set_name: RedPajamaGithub


text:
Q: Delete first 3 characters and last 3 characters from String PHP I need to delete the first 3 letters of a string and the last 3 letters of a string. I know I can use substr() to start at a certain character but if I need to strip both first and last characters i'm not sure if I can actually use this. Any suggestions?

A: As stated in other answers you can use one of the following functions to reach your goal:

*

*substr($string, 3,
-3) removes 3 chars from  start and end

*trim($string, ",") removes all specific chars from start and end

*ltrim($string, ".") removes all specific chars from start

*rtrim($string, ";") removes all specific chars from end

It depends on the amount of chars you need to remove and if the removal needs to be specific. But finally substr() answers your question perfectly.
Maybe someone thinks about removing the first/last char through string dereferencing. Forget that, it will not work as null is a char as well:
<?php
$string = 'Stackoverflow';
var_dump($string);
$string[0] = null;
var_dump($string);
$string[0] = null;
var_dump($string);
echo ord($string[0]) . PHP_EOL;
$string[1] = '';
var_dump($string);
echo ord($string[1]) . PHP_EOL;
?>

returns:
string(13) "Stackoverflow"
string(13) "tackoverflow"
string(13) "tackoverflow"
0
string(13) "ackoverflow"
0

And it is not possible to use unset($string[0]) for strings:

Fatal error: Cannot unset string offsets in /usr/www/***.php on line **

A: Use
substr($var,1,-1)

this will always get first and last without having to use strlen.
Example:
<?php
    $input = ",a,b,d,e,f,";
    $output = substr($input, 1, -1);
    echo $output;
?>

Output:
a,b,d,e,f

A: substr($string, 3, strlen($string) - 6)

A: Pass a negative value as the length argument (the 3rd argument) to substr(), like:
$result = substr($string, 3, -3);

So this:
<?php
$string = "Sean Bright";
$string = substr($string, 3, -3);
echo $string;
?>

Outputs:
n Bri

A: I don't know php, but can't you take the length of the string, start as position 3 and take length-6 characters using substr?

A: $myString='123456789';
$newString=substr($myString,3,-3);

redpajama_set_name: RedPajamaStackExchange


text:
Q: Tried to make a simple adder in c++.Compiled successfully but the output is wrong created NOT,AND,OR and XOR functions(using NAND) then created the 'adder_prim' and  'adder_carry' functions for the primary output and the carry. Used the standard full adder circuit and put it in a loop(10 cycles so should be able to add til 2031).
entered the input in the code itself(X is 139,Y is 74) just to see if it's working properly or not.
instead of 216(correct ans) it's coming 196 and i have no clue why.

int NAND(int i,int j)
{
    int A;
    A=((i==1)&&(j==1))?0:1;
    return A;
}

int NOT(int i)
{
    int A=NAND(i,i);
    return A;
}

int AND(int i,int j)
{
    int A=NOT(NAND(i,j));
    return A;
}

int OR(int i,int j)
{
    int A=NAND((NAND(i,i)),NAND(j,j));
    return A;
}

int XOR(int i,int j)
{
    int A=OR(AND(i,NOT(j)),AND(NOT(i),j));
    return A;
}

int adder_prim(int,int,int);
int adder_carry(int,int,int);

int _tmain(int argc, _TCHAR* argv[])
{
    int Z[10];
    int C=0;

    int X[]={0,0,1,0,0,0,1,0,1,1};
    int Y[]={0,0,0,1,0,0,1,0,1,0};

    for(int i=0;i<10;i++)
    {
        Z[i]=adder_prim(X[i],Y[i],C);
        C=adder_carry(X[i],Y[i],C);
    }

    for(int j=0;j<10;j++)
    {
        cout <<Z[j];
    }

    getch();
    return 0;
}

int adder_prim(int a,int b,int c)
{
    int O=XOR(XOR(a,b),c);
    return O;
}

int adder_carry(int a,int b,int c)
{
    int C=OR(AND(XOR(a,b),c),AND(a,b));
    return C;
}

A: You need to add the least significant bit first, not the most significant bit:
for(int i=9;i>-1;i--)
{
    Z[i]=adder_prim(X[i],Y[i],C);
    C=adder_carry(X[i],Y[i],C);
}