text:
Osinbajo and the conspiracy of nine fingers
February 27, 2017 OPINION/NEWS
Prince Charles Dickson
"Our wife, our wife": come midnight and we will know whose wife she really is.
Did you hear…"Osinbajo is very presidential, he has action" (Really)
Some people said, "He should not deviate from Buhari's policies" (But why should he)
Did you see Osinbajo's wife on TV the other day she looks the part (abeg which part)
Some sabi-sabi people even said, "he is governing from Lagos"(Anyway that was once our capital too)
Don't mind them, El-Rufai is in control (With all the wahala at his backyard)
Saraki is angling to be Vice President, but Osinbajo won't have it (Chai this people don sell us, Saraki should finish with Code of Conduct Bureau)
Even the North has given Osinbajo six conditions (I wonder why six and not eight or twenty)
Actually we currently have three presidents, Buhari, Osinbajo, and others…
If the Pastor says "you will be promoted" will Osinbajo say AMEN.
Hear some Imams are spreading the rumor that Baba was poisoned (By who)
And some group claim that they warned Baba about his kitchen arrangement
How about that gist that finally an Awolowo would be in the Presidency
Also these days, Mr. President seems to be speaking to everyone on phone, I am particular about him telling Adesina whom he now refers to as Femi that Nigerians are "Mischief Makers".
Going forward have you heard that Osinbajo is responsible for the appreciating Naira (But he was head of the Economic Team).
Oh did I forget, some said Osinbajo is the function of the President's magnanimity, you recall Idiagbon too, and Mr. Buhari loves to work from behind.
Yes, I equally saw that write up on, those that have visited Osinbajo since his boss traveled on vacation.
And sure we get to read a lot on social platforms, including the recent exhortation to pray seriously for Osinbajo, because of because; We are praying for Buhari too, and some are praying for you and I know.
Nigeria is one hell of a place, and it is not out of place that I suffer monochopsis these days, meanwhile that "big word" means; the subtle but persistent feeling of being out of place.
Really is Professor Pastor Osinbajo to the rescue, how come silly Nigerians suddenly think he's got some magic wand, the same Nigerians who did not believe in the APC or Change mantra, would it not be safe to say that what is manifest if indeed any, is a function of the promises made by the duo.
Why is it that we are so foolish, and in the words of the Apostle Paul who has bewitched us, why are we so myopic in our hate for each other, so much that I see how some Yorubas are rejoicing or how some Christians are upbeat and how some Muslims are threatening thunder, fire and electricity, should anything happen to Mr. Buhari (of course we need the latter).
So I ask has Osinbajo made any policy and the last time I checked, all those that say this dude is Presidential never stated that he was Vice Presidential. Nigerians are so…before I am accused of saying what I do not know.
Let me end this admonition in this manner; Once upon a time there lived a king. The king was very kind and ruled his people very well. One day he was cutting an apple with the knife and accidentally cut his finger. The king cried aloud and his minister who was devotee of Krishna came running and saw that the king has cut his finger.
The minister tying a cloth to the king's finger said, "Dear king, don't worry, whatever happen its is mercy of Krishna. So be happy and thank your luck and thank Krishna"
The king got very angry and said, "What nonsense you are talking. The blood is coming out. I am crying in pain. You say this is mercy of Krishna. You are a big fool. I will throw you in jail". Shouting thus, the king got his minister thrown in jail. The minister smiled and said aloud, "Whatever happened is mercy of Krishna! Thank you Krishna!"
But one fine morning the fat king went alone for hunting in the forest. There were no guards and no ministers with him. He soon lost his way in the forest and landed in an enemy's tribal kingdom.
Suddenly the tribal king and his soldiers rounded up the king and tied him to a tree. The tribal soldiers then drank and danced around the king and shouted, "Let this king be sacrificed to our Kali". Shouting thus, they all prepared the king for the big sacrifice to Kali devi.
The king was sad, as there was no minister with him to advise how to escape. He was weeping with tears running down his eyes.
The tribal king and the priest came to inspect the king and saw that the king had a bandage on his finger.
The priest then said to the tribal king, "Sir, this king has already cut his finger and the blood has already come out of him. But for our Kali we need fresh blood and a whole body without any cuts. Therefore, this king is unfit to be sacrificed and let him go back to his people." The tribal king agreed and set the king free.
The king got back to his kingdom and related the story to his minister who was in jail. The minister then smiled and said, "See I told you that whatever happens is mercy of Krishna and is for our own good!
On that day you cut your finger it saved your life! And when you put me in jail it also saved my life!" The minister said smiling.
The king was surprised and asked, "How's that!"
The minister replied, "See, wherever you go I have to be with you. But on that day I was in jail. So I did not come with you. If I had come with you, the tribal king would have sacrificed me because my body was whole and no cuts on me. This way I too was saved!
You cutting your finger and me going to jail both happened to our own good! That is what I believed. And this is the moral philosophy that everyone should believe… "Whatever happens; happens to our own good and it is mercy of Krishna!"
If we strongly believe in this moral philosophy we will really stop worrying and make our lives happier and happier… forever and ever! Putting our lives in the hands of Krishna is the most secure way to live our life.
Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare/ Hare Rama, Hare Rama, Rama Rama, Hare Hare.
On intent, hence the number of Krishna devotees is almost negligible I have used them, but the lesson thereof is that there is no Osinbajo, or Buhari, it is about the success of this administration which in turn is the success of Nigeria and Nigerians. The devoid created by Mr. Buhari's extended leave, despite the handover to an acting, has again exposed all the cracks that we are still a divided nation, and still largely do not know what we desire, and continue to be tossed, continually running from the issues, trading and chasing shadows, and it seems we will be on this path for a while, how much time do we have, indeed—Only time will tell.
Currently Prince Charles, is based out of Jos, Plateau State, and conducts field research and investigations in the Middle Belt Region of Nigeria with an extensive reach out to the entire North and other parts. Prince Charles worked on projects for UN Women, Search for Common Ground, and International Crisis Group, among others. He is an alumnus of the University of Jos and the prestigious Humanitarian Academy at Harvard and Knight Center For Journalism, University of Texas at Austin. A doctoral candidate of Georgetown University
Born in Lagos State (South West Nigeria), Prince Charles is proud of his Nigerian roots. He is a Henry Luce Fellow, Ford Foundation grantee and is proficient in English, French, Yoruba Ibo and Hausa. Married with two boys, and a few dogs and birds.
Tags APCBuhariBuhari leaveKrishnaNigeriaOpinionPoliticsPrince Charles DicksonSocietyVice PresidentYemi Osinbajo
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Just when you think you live in a pretty cool place, something like this happens and embarrasses Maine in front of the whole world.
Local nutcase lawyer Tom Connolly decided a political protest could be brought off to better effect by wearing an Osama bin Laden mask and waving a fake AK-47 at the side of I-295.
Via Slublog, via Ace of Spades HQ. Also has a full thread devoted to it over at little green footballs.


text:
Gwen Jorgensen Announces Return To Tri, Long Road To Olympics
Jorgensen—who switched to running in fall of 2017—announced today that she'll be shooting for a spot on the USA's mixed triathlon team relay at the 2024 Paris Olympics, but the 2016 gold medalist faces a surprisingly uphill battle. Read why.
December 13, 2022 Chris Foster
Photo: Sebastian Kahnert/Getty Images
"You guys are finally getting what you've all been asking for, I'm coming back to triathlon," Jorgensen, 36, said in a recorded announcement this morning.
The two-time world ITU WTS world champion and 2016 Olympic gold medalist, who left triathlon in 2017 to pursue a running career, says she is returning to draft-legal WTS racing with her eyes on the mixed team relay event in Paris 2024. "I wasn't able to do [the mixed team relay] at the 2016 Olympics, it wasn't an event at the Olympics yet," she said. "I was super inspired at Tokyo watching Team USA get a silver medal in the team relay, so that is what is really motivating me to get back to triathlon."
RELATED: Photos: Triathlon Mixed Relay Makes Its Exciting Olympic Debut
She went on to say that it'll be difficult to even get on the start line at the first qualifying test event in mid August, as Jorgensen is currently unranked with her most recent WTS result recorded back in 2016.
Gwen's (Not-So-Easy) Path to Paris
According to USA Triathlon's Olympic Qualifying Event Criteria, to gain entry to a WTCS event, an athlete "must be a current member of the Elite Triathlon National Team or has achieved a top 30 performance in a World Triathlon Cup event in the preceding 18 months," along with other criteria. Even then, the U.S. can only send a maximum of five women to the test events.
Jorgensen's lack of a world ranking, recent results, or national team standing, as well as the current depth of American female talent could be challenging—the U.S. has five women ranked in the top 25 of the World Triathlon Championship Rankings as of this writing. While getting into one of the automatic selection events would be very difficult, it wouldn't be impossible to for Jorgensen to claim a discretionary selection spot on the women's Olympic team, based on her interest in the mixed team relay.
That pathway would still be tough, as the discretionary selection would only go into effect if all of the automatic slots were not claimed at the three automatic selection events: Paris in August, 2023; WTC Finals in Pontevedra in September, 2023; and a final event to be determined.
Jorgensen admitted the path will be doubly difficult this time around, as she now has two children, she's decided not to live abroad—as she had in the past—and she says she'll be "forced to race earlier than I'd like to, before I'm fit, before I'm totally ready."
Her last WTC event (then ITU WTS) was the 2016 ITU World Triathlon Grand Final in Cozumel, where she took second to the current reigning Olympic champion, Flora Duffy. Since then, Jorgensen focused on running and achieved a 31:55 10K PR and 2:36 marathon PR in 2018 and finished ninth at the U.S. Olympic Track Trials in the 10K.
RELATED: The 16 Greatest Triathletes of All Time
Video: Gwen Jorgensen's Return to Triathlon
RELATED: Gwen Jorgensen on Her Surprising Decision to Leave Triathlon
13 Questions With Gwen Jorgensen on Her Return to Tri: "I'm Motivated by Big Challenges"
Triathlon News & Notes: Katie Zaferes Elected to USAT Board of Directors, Jonny Brownlee named MBE, and More

redpajama_set_name: RedPajamaCommonCrawl


text:
Film Review: 'Pitch Perfect 2'
Published on 13 May 2015 11 December 2017 by CineVue
Producer Elizabeth Banks steps behind the camera in this sequel to Pitch Perfect (2012), which comes with decidedly more anticipation than its predecessor. Taking full advantage of studios' and audiences' post-Bridesmaids (2011) appetite for female-led comedies, the original film became a surprise hit (the second highest grossing musical comedy of all time) and made stars of both Anna Kendrick and Rebel Wilson. The new film follows Beca (Kendrick), leader of the Barden Bellas, as they attempt to win an international a cappella tournament to regain favour following a suspension from the domestic circuit. Banks smartly sticks with what works: sarcastic humour, more than a dash of slapstick and big songs.
The biggest weakness may be that, like many comedy sequels, it's apparent that Pitch Perfect 2's mission is to bring back a group of crowd-pleasing characters rather than have them go anywhere new. The dry wit and hilarious asides mean this isn't a deadly blow, as the cast take full advantage of the stage put in front of them, but it becomes clear from very early on in this film that this is about the journey rather than the destination. There's a loose plot about growing up and moving on, however the sequel has slightly less to say and ends up feeling somewhat lighter than the first. The energy and intelligent dialogue is still there but without the journey towards acceptance that made the backbone of the original, certain narrative diversions (such as The Bellas' retreat or an underground a cappella battle) feel designed for shenanigans rather than moving things forward.
While this will result in an enjoyable experience for people who loved the original, it also results in certain missed notes – Fat Amy's romantic storyline with Adam Devine (as former rival Bumper from the first film) falls flat, while the antagonists of the story, a German a cappella group, are broad stereotypes that don't really affect the plot as they should. The biggest strength is in the Bellas themselves. More confident in their respective roles, Anna Kendrick in particular develops her lead from a prickly outsider to someone slightly more goofy, and by extension a little more likeable. Moments such as her unintentional attraction to the German group's leader or her interactions with the excellent Keegan-Michael Key (playing Beca's irate new boss) underlines her comic timing. Similarly, Wilson is in her element as the brash Fat Amy, bringing another game performance that could well have studio execs masterminding her own spin- off. Elsewhere, the characters that are used sparingly are often the most fun. In particular, Banks and John Michael Higgins steal every scene they're in as the tournament commentators, with improv that would suit a Christopher Guest comedy. The surprisingly abrupt ending underlines the straight forward nature of Pitch Perfect 2, a film which wants nothing more than to bring the gang back. Luckily, that gang has enough talent in it to make for an entertaining couple of hours, however even if the expected big box office is achieved, if Kendrick and co. may be best advised to take their bow while they are still on top.
James Luxford | @JLFilm
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text:
Charles Correll (2 de febrero de 1890 – 26 de septiembre de 1972) fue un humorista y actor radiofónico de nacionalidad estadounidense, conocido principalmente por su trabajo en la serie Amos 'n' Andy, que realizó en equipo con Freeman Gosden. En el show, Correll daba voz a uno de los protagonistas, Andy Brown, además de a otros personajes de reparto.

Biografía

Nacido en Peoria, Illinois, su nombre completo era Charles James Correll. Antes de asociarse con Gosden, Correll trabajó como taquígrafo y albañil. Los dos se conocieron en Durham (Carolina del Norte) mientras trabajaban para la Joe Bren Producing Company. Tanto Correll como Freeman pasaban las vacaciones en Lake Geneva (Wisconsin) en los años 1930, y emitieron Amos 'n' Andy desde allí. Desde 1928 a 1934, nunca tomaron vacaciones alejadas de su programa radiofónico. Para celebrar el trigésimo aniversario de Amos 'n' Andy, la emisión del 19 de marzo de 1958 fue hecha utilizando ambos sus voces reales y llamándose el uno al otro por su propio nombre, algo que nunca antes se había llevado a cabo en el show.

El primer matrimonio de Correll, con Marie Janes, acabó en divorcio el 26 de mayo de 1937. La pareja se había casado diez años antes y no había tenido hijos. El 11 de septiembre de 1937, en Glendale (California), se casó con Alyce McLaughlin, una antigua bailarina; tuvieron seis hijos: Dorothy, Charles, Barbara, John, y Richard. El 5 de julio de 1954, John Correll, su hijo de siete años de edad, falleció de lo que parecía ser un envenenamiento accidental. La autopsia determinó que el niño murió de una infección renal aguda.

Charles Correll falleció en Chicago, Illinois, en 1972, a causa de un infarto agudo de miocardio. En el momento de su muerte se encontraba retirado y vivía en Beverly Hills, California, a pocas manzanas de su compañero radiofónico, Freeman Gosden. Fue enterrado en el Cementerio de Holy Cross, en Culver City, California.

Su hijo, Charles Correll, Jr., también fue actor y director. Así mismo, otro de sus hijos, Richard Correll, se dedicó a la actuación, siendo conocido por su papel de Richard Rickover en Leave It To Beaver, además de producir y dirigir la sitcom televisiva Cosas de casa.

La pareja cómica fue elegida para formar parte del Salón de la Fama de la Radio en 1962; además, Correll fue premiado con una estrella en el Paseo de la Fama de Hollywood, en el 1777 de Vine Street, por su trabajo en la radio en 1969. En 1977, Correll fue admitido, junto con Gosden, en el Salón de la Fama de la National Association of Broadcasters 1977.

Referencias

Enlaces externos

Fotografías en Google

Humoristas de Estados Unidos
Fallecidos por infarto agudo de miocardio
Paseo de la Fama de Hollywood
Nacidos en Peoria (Illinois)

redpajama_set_name: RedPajamaWikipedia


This weekend sees an action packed return to the NW korfball season.
Manchester City will host a free taster session on Saturday 21st January at Sale Leisure Centre from 1 – 2:30pm.
This will be followed by a friendly match between Manchester City and University 2:30 – 4pm.
And don't forget on Sunday there will be a North West Squad training session from 4-7pm, again at Sale Leisure Centre. It will cost £5 to cover costs.
Man Uni have decided that the Lions will not continue in the North West League for the second half of the season. With a heavy fixtures schedule this year all clubs have struggled to put out consistent squads each week. This decision allows Man Uni to play more consistent teams for the remainder of the season!
We're pleased to announce the North West Squad training from 4 – 7 pm on Sunday 22nd January at Sale Leisure Centre. This will be an open session for anyone interested in taking part in the Inter Areas in Nottingham on February 12th.
Mike Brayne will lead the session with assistance from his Warrior's team mate Kev Jones!
For further information contact Rach (Rachel.Swallow@student.Manchester.ac.uk).


text:
\section{Introduction}

In today's  electricity markets, energy and ancillary services serve two different purposes. A particularly important stage is the day-ahead market in which generating units only define an hourly cost for their average energy generation schedule during that unit of time, i.e. a function $C_k(\bar x,h)$, where the hourly energy signal in an horizon ${\cal T}=[t_1,t_2]$, with $t_2=,t_1+HT$ is:
$${\bar x}_k[h]=\int_{t_1+hT}^{(h+1)T} x_k(t)dt, ~~~h=0,\ldots,H-1$$
First, the best portfolio of units is decided by solving the mixed integer linear program that corresponds to the Unit Commitment (UC).  The price is then chosen based on the portfolio of units selected, setting the optimum schedule and is  interpreted as an energy price for that particular period and market settlement.

Demand of electricity does not come in chucks of energy and what is demanded from the market is a continuous time power trajectory. Today's operations catch up in real time in shorter term market settlements and engaging ancillary services reserves.
While it is reasonable for the generation schedules to be merely in the right ballpark and adjust to the actual demand in real time it is important to consider that, using this approximation, one may be throwing away information that is at hand about the inter-hour behavior and, particularly, load ramps that may be difficult to meet with the units committed with the standard UC formulation.
Recently this issue has come to the forefront due to increased variability of the net-demand, particularly at early and late day hours, that are a direct consequence of the increased penetration of solar power.
This phenomenon is often illustrated by the popular {\it duck chart} in Fig. \ref{fig.duckchart}.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=7cm]{duck-chart.jpg}
\caption{The forecast of average California daily load.}
\label{fig.duckchart}
\end{center}
\end{figure}

Metrics for measuring the largest variation range of uncertainty that the system can accommodate were proposed in \cite{ma2009}, while the authors in \cite{lefton2006cost,kumar2012power} proposed methods to quantify the additional cost of generating units incur due to ramping.
At the same time, there have been several proposal to address the issue of ramping shortage which promote better coordination between energy markets, security constrained Unit Commitment and ancillary service markets and higher incentives for ramping services. Oftentimes the framework proposed is tied to the uncertainty of renewables and the Security Constrained UC (see e.g. \cite{wang2008security,wu2015thermal,bouffard2008stochastic,thatte2014robust}). Cases in which the authors more explicitly tied the ramping cost to modeling the ramping needs in the UC are, for instance, \cite{troy2012unit,wu2013hourly,wang2013flexiramp}. On the market side Midcontinent ISO (MISO) \cite{navid2011,navid2012} and the California ISO (CAISO)  \cite{xu2012flexible,abdul2012enhanced} introduced flexible ramping products in their portfolio of resources.

Accounting for the predictable trends and incentivizing the market properly could lead to decisions that reduce the volume of power that is scheduled in real time.  This is, in a nutshell the motivation behind our previous work in \cite{parvania2015UC}, \cite{parvaniaHICSS2016} \cite{KariPSCC2016} that essentially examined how to convert the intractable variational problem of committing generators trajectories, i.e. solving the Unit Commitment (UC) problem, in continuous time, into a tractable problem, resorting to an expansion of the demand and generation trajectories in a signal space spanned by polynomial splines.
We brought the notion of continuous time UC a step further in \cite{parvaniaHICSS2016} where,
assuming we are going to deal with continuous and differentiable trajectories, we defined a unit cost that is a function of both ${x}_k(t)$ and $\dot{x}_k(t)$ $k=1,\ldots,K$, to allow generators to bid also on their ramping capacity, and stimulate market competition in offering ramping services. More recently we proposed to fully generalize export bids
to possibly account for storage capacity available \cite{KariPSCC2016}.

The subject of this paper is describing simple instances of the variational problem that defines the price of electricity without involving the integer variables of the UC, as is customary in computing the price of energy. We focus on the economic dispatch problem with the goal of calculating the  trajectory of the marginal price per unit of power and time, considering a market that maximizes social surplus in the presence of inflexible demand.

The paper is organized as follows.
We start in the following section with the classic economic dispatch problem, but look the the optimization over the entire time horizon and include in the calculation ramping constraints.

\section{The Continuous Time Economic Dispatch Problem and Pricing of Power}
We consider energy market setting in which a set of $K$ generating units compete to sell continuous-time generation trajectory $x_k(t)$ for $k=1,\ldots,K$. The input to the problem is the forecasted load profile $y(t)$ over the day-ahead operating horizon ${\mathcal T}=[t_1,t_2]$ at minimum cost, subject to the constraints of the generating units that include their capacity and ramping limits.
Our interest in this paper is the derivation of the marginal price of electricity by first focusing on the economic dispatch formulation that relaxes the power flow equations and the line flow constraints. We assume that the UC problem has been solved, for instance, following the setup we proposed in \cite{parvania2015UC}. Hence, the $K$ units considered here were the one that were committed by solving the UC problem.

We can assume that generating unit $k$ expresses a cost function $C_k(x;t)$ such that the incremental cost for generating the energy $x(t)dt$ is $C_k(x;t)dt$. This is perfectly compatible with the current practice of giving an hourly or sub-hourly energy cost, since
in that case $C_k(x;t)$ is linear (or piece-wise) linear with respect to $x$, over the horizon ${\mathcal T}$, with exactly the same rate.
The formulation to calculate the market clearing price in continuous time is:
\begin{align} \label{Var1}
\min_{x_1(t),..,x_K(t)}& ~~~ \sum_{k=1}^K \int_{t_1}^{t_2} \!\!C_k(x_k,t)dt \\ \label{Var2}
\mbox{s.t.}~~&\sum_{k=1}^K x_k(t)=y(t)  ~~ (\lambda(t)) ~~ \forall t \in {\mathcal T} \\ \nonumber
&~~ \forall t \in {\mathcal T},~~k=1,\ldots,K \\ \label{Var3}
&x_k(t) -\overline{x}\leq 0 ~~ (\overline{\mu}_k(t))\\\label{Var4}
&\underline{x}_k -x_k(t) \leq 0 ~~ (\underline{\mu}_k(t)) \\ \label{Var5}
&{\dot x}_k(t) -\overline{x}_k' \leq 0 ~~ (\overline{\gamma}_k(t))  \\ \label{Var6}
&\underline{x}_k' -\dot{x}_k(t) \leq 0 ~~ (\underline{\gamma}_k(t))
\end{align}
where $\underline{x}_k$, $\overline{x}_k$, $\underline{x}_k' $, $\overline{x}_k' $ are respectively the upper and lower bounds of the $k$th generation and ramping trajectory, and $\lambda(t)$, $\underline{\mu}_k(t)$, $\overline{\mu}_k(t)$, $\underline{\gamma}_k(t)$, $(\overline{\gamma}_k(t)$ are respectively the Lagrange multipliers associated with the constraints \eqref{Var2}-\eqref{Var6}).
The objective in \eqref{Var1} is to minimize the total continuous-time cost of generating units over the scheduling horizon ${\mathcal T}$, subject to the continuous-time load-generation balance constraint \eqref{Var2}, and the continuous-time generation capacity and ramping constraints in \eqref{Var3}-\eqref{Var6}.
Here, we assume there is no flexibility in $y(t)$ and its trajectory is certain.

The optimization problem in \eqref{Var1}-\eqref{Var6} is a constrained variational problem, and its solution would determine the values of the Lagrange multipliers over the scheduling horizon ${\mathcal T}$, that correspond to the optimal generation trajectories $\mathbf{x}^*(t)$ for the units that are committed.
The Lagrangian function of the variational problem \eqref{Var1}-\eqref{Var6} is:
 \begin{align}\label{eq.lagrangian}
{\cal L}=
& \sum_{k=1}^K \int_{t_1}^{t_2}f_k(x_k,{\dot x}_k,t)dt\\
 f_k(x_k,{\dot x}_k,t)&=C_k(x_k(t),t)+\left(\frac{y(t)}{K}-x_k(t)\right)\lambda(t) \nonumber\\
+& \label{def.f}
\overline{\mu}_k(t)(x_k(t) -\overline{x}_k)+
\underline{\mu}_k(t)(\underline{x}_k -x_k(t)) \\
+&
\overline{\gamma}_k(t)({\dot x}_k(t) -\overline{x}_k') +
\underline{\gamma}_k(t)(\underline{x}_k' -\dot{x}_k(t))\label{def.fk}
\end{align}
In the following, what we refer to as the {\it continuous-time Lagrange multiplier} $\lambda(t)$ function. In fact, each instantaneous balance constraint needs to be weighted by an infinitesimal quantity $\lambda(t)dt$,
just like the cost of supplying $x_k(t)$ over the interval $[t,t+dt)$ grows infinitesimally by $C_k(x_k(t))dt$.
Assuming $y(t)$ and $C_k(x,t)$ are continuous and continuously differentiable function of time, the trajectories $x_k(t)$ and Lagrange multipliers are going to be also continuous and continuously differentiable.
The formulation above is a special case of the classical {\it isoperimetric problem} from Physics (see e.g. \cite{variational}). The key result is that the trajectories $x_k(t)$, $k=1,\ldots,K$ that lead to the minimum ${\cal L}^*\leq {\cal L}$ solutions can be found solving the so called Euler-Lagrange differential equations:
\begin{align}\label{eq.KKT1}
& \frac{\partial  f_k(x_k^*,\dot{x}_k^*,t)}{\partial x_k}-\frac{d}{dt}\frac{\partial f(x_k^*,\dot{x}_k^*,t)}{\partial {\dot x}_k}=0,~ k=1,..,K
\end{align}
 Because there are no specific constraints on the values of the trajectories at least at one of the boundaries of ${\mathcal T}$, there is one additional condition to consider:
\begin{align}\label{eq.dgamma}
\frac{\partial f(x^*_k(t_2),{\dot x}^*_k(t_2),t_2)}{\partial {\dot x}_k}&= \frac{d\overline{\gamma}^*_k(t_2)}{dt}-\frac{d\underline{\gamma}^*_k(t_2)}{dt}=0\\
& ~~k=1,\ldots,K\nonumber
\end{align}

In addition to \eqref{eq.KKT1} the complete Karush-Kuhn-Tucker (KKT) conditions on the optimum trajectories include the following equations:
\begin{align}
&y(t)-\sum_{k=1}^K x^*_k(t)=0  \label{eq.KKT2} \\
&x_k^*(t)-\overline{x}_k\leq 0,~~\underline{x}_k-x^*_k(t)\leq 0,\label{eq.KKT3} \\
&{\dot x}^*_k(t)-\overline{x}_k'\leq 0,~~\underline{x}_k'-{\dot x}^*_k(t)\leq 0, \\
&\overline{\mu}_k(t)( x_k^*(t)-\overline{x}_k)=0,~~
\underline{\mu}_k(t)(\underline{x}_k-x_k^*(t))=0, \label{eq.cse1} \\
&\overline{\gamma}_k(t)({\dot x}_k^*(t)-\overline{x}_k')=0, ~
\underline{\gamma}_k(t)(\underline{x}'_k-{\dot x}^*_k(t))=0, \label{eq.cse2} \\
&\overline{\mu}_k(t),\underline{\mu}_k(t),\overline{\gamma}_k(t), \underline{\gamma}_k(t) \geq 0. \label{eq.df}\\
\forall& t\in {\mathcal T},~~~k=1,\ldots,K\nonumber
\end{align}
All of these equations are decoupled with the exception of the balance constraint.
Based on the definition of $f(x_k,{\dot x}_k,t)$ in \eqref{def.f} we have:
\begin{align}
&\frac{\partial  f(x_k,{\dot x}_k,t)}{\partial x_k}=\frac{\partial  C_k(x_k,t)}{\partial x_k}-\lambda(t)+\overline{\mu}_k(t)-\underline{\mu}_k(t)\label{eq.parx}\\
&\frac{d}{dt}\frac{\partial  f(x_k,{\dot x}_k,t)}{\partial {\dot x}_k}=\frac{d\overline{\gamma}_k(t)}{dt}-\frac{d\underline{\gamma}_k(t)}{dt},\label{eq.pardx}\\~~
&\forall t\in {\mathcal T},~k=1,\ldots,K\nonumber
\end{align}
Therefore, from the \eqref{eq.KKT2} we can conclude a number of things.
\begin{enumerate}
\item
First,
we can derive the following relationship between the Lagrange multiplier function, the marginal cost and the other Lagrange multipliers functions:
\begin{align}\nonumber
&\!\!\!\!\!\!\!\!\lambda^*(t)=\frac{\partial  C_k(x^*_k,t)}{\partial x_k}+
\overline{\mu}^*_k(t)-\underline{\mu}^*_k(t)-\frac{d\overline{\gamma}^*_k(t)}{dt}+\frac{d\underline{\gamma}^*_k(t)}{dt}\\
\forall& t\in {\mathcal T},~~~k=1,\ldots,K \label{eq.mag.price}
\end{align}

\item
For each unit $k$ that is operating strictly within its generation and ramping capacity limits, the complementarity slackness condition \eqref{eq.cse1}-\eqref{eq.cse2} imply that  the multipliers
$\overline{\mu}_{k^*}(t)=\underline{\mu}_{k^*}(t)=0$ and/or $\overline{\gamma}_{k^*}(t)=\underline{\gamma}_{k^*}(t)=0$.

\item It is important to note that because, due to the same conditions, the eigenvalues $\overline{\gamma}_{k^*}(t),\underline{\gamma}_{k^*}(t)$ are non negative \eqref{eq.df}, then
zero is also the infimum of the function. Because the function is continuous with continuous derivative in time at the infimum
will also have to be a minimum and have zero derivative. This means that when the ramping constraint is not tight, the following is also true:
\begin{equation}\label{eq.gamma}
\frac{d\overline{\gamma}^*_k(t)}{dt}=0,~~\frac{d\underline{\gamma}^*_k(t)}{dt}=0
\end{equation}
and, thus
\begin{equation}\label{eq.dtpf}
\frac{d}{dt}\frac{\partial  f(x_k,{\dot x}_k,t)}{\partial {\dot x}_k}=0
\end{equation}
\item In our problem, since we assume that the demand is inflexible, to  always have a feasible solution we have to assume that there always exist an extra unit that can be deployed to meet excess demand that arises.
The so called {\it marginal unit} is the unit $k^*(t)$ for which none of the inequality constraints is tight at time $t$ and so $\overline{\mu}_{k^*}(t)=\underline{\mu}_{k^*}(t)=0$ and/or $\overline{\gamma}_{k^*}(t)=\underline{\gamma}_{k^*}(t)=0$ and also \eqref{eq.dtpf} is valid.
In this case, assuming that there is always a unit whose constraints are not tight and denoting by $k^*(t)$ the index of the marginal unit at time $t$
the solution of \eqref{eq.KKT1} is:
\begin{align}\label{eq.marginal}
&\lambda^*(t)=\frac{\partial  C_{k}(x^*_{k},t)}{\partial x_k},~~~~k={k^*}(t),~~\forall t\in {\mathcal T}.
\end{align}
Note that, if the increment in demand has an arbitrary temporal shape, it may be true that only the ramping constraint is tight though the problem is still feasible, in which case the price will include either
$\frac{d\underline{\gamma}^*_k(t)}{dt}$ or $\frac{d\overline{\gamma}^*_k(t)}{dt}$, i.e. there would be a shadow price associated to ramping that increases the price compared to the marginal cost.
\end{enumerate}
It is well known that, absent a load export bid, the marginal price of electricity and the marginal cost of the so called marginal unit are the same, since the social surplus is maximized by having the marginal generator increase its production by one unit if the demand grows by one unit. The same remains true in the continuous time formulation.
We can prove this formally,  to state the following theorem:
\begin{theorem}
With a continuous time import bid and inflexible demand the surplus maximizing price for an additional unit of load per unit of time is the Lagrange multiplier $\lambda^*(t)$ at the optimum schedule, i.e. \eqref{eq.marginal}.
\end{theorem}
\begin{proof}
Let $g_k(x_k,{\dot x}_k,t)$ be:
\begin{equation}
g_k(x_k,{\dot x}_k,t)=f_k(x_k,{\dot x}_k,t)-\frac{y(t)}{K},
\end{equation}
so that we can rewrite the Lagrangian as follows:
\begin{equation}
{\cal L}=\int_{t_1}^{t_2} \left(\lambda(t)y(t)+\sum_{k=1}^Kg_k(x_k,{\dot x}_k,t)\right)dt
\end{equation}
Suppose we increase the load demand by a unit of power $\epsilon$ at all times in ${\cal T}$.
That is, the load is:
\begin{align}
Y(t)&=y(t)+\epsilon,~~~t\in (t_1,t_2)\\
Y(t_1)&=y(t_1),~~Y(t_2)=y(t_2).
\end{align}
The last equations are necessary for the Euler-Lagrange equations to continue to hold.
To evaluate the price this costs, we want to establish at what rate the Lagrangian changes compared to the value ${\cal L}^*$, as our demand of power increases. Let us refer to the new value of the Lagrangian as ${\cal L}^*(\epsilon)$.
Note that at the extremum only the marginal unit can adjust its production and ramp up to meet the increased load, all the remaining unit schedules for $k\neq k^*$ remain unchanged.
Furthermore, since the change in load is a constant lift, the time derivative of the optimum schedule for the marginal unit does not change:
\begin{equation}
X_{k^*}(t)=x_{k^*}^*(t)+\epsilon~\rightarrow~ {\dot X}_{k^*}(t)={\dot x}_{k^*}^*(t).
\end{equation}
These considerations lead to the following:
\begin{align}
{\cal L}^*(\epsilon)-{\cal L}^*=
\int_{t_1}^{t_2} \!\!\!\left(\lambda(t)\epsilon+\frac{\partial g_k(x^*_{k^*},{\dot x}^*_{k^*},t)}{\partial x_{k^*}^*}\epsilon +{\cal O}(\epsilon^2)\right)dt
\end{align}
where the partial derivative with respect to ${\dot x}^*_{k^*}$ is absent since we have no variation in the ramp.
Considering that for the marginal unit:
\begin{align}
\frac{\partial g_k(x^*_{k^*},{\dot x}^*_{k^*},t)}{\partial x_{k^*}^*}&=
\frac{\partial f_k(x^*_{k^*},{\dot x}^*_{k^*},t)}{\partial x_{k^*}^*}\\&=\frac{\partial C_k(x^*_{k^*},t)}{\partial x_{k^*}^*}-\lambda^*(t)=0,
\end{align}
we can conclude that:
\begin{align}
\lim_{\epsilon \rightarrow 0}
\frac{{\cal L}^*(\epsilon)-{\cal L}^*}{\epsilon}=
\int_{t_1}^{t_2} \lambda(t)dt
\end{align}
Hence, $\lambda(t)$ represents the market price per unit of power and per unit of time.
\end{proof}
Note that, had we perturbed the load in a time varying fashion, i.e.:
$$Y(t)=y(t)+\epsilon\eta(t),$$
with $\eta(t_1)=\eta(t_2)=0$, but we never exceed the ramping constraint of the marginal unit,
the result would have been:
\begin{align}
\lim_{\epsilon \rightarrow 0}
\frac{{\cal L}^*(\epsilon)-{\cal L}^*}{\epsilon}=
\int_{t_1}^{t_2} \lambda(t)\eta(t)dt
\end{align}
which leads to the same conclusion. There could be a feasible $\eta(t)$ that
make the ramping constraint tight and, therefore, in that case the price would rise above
the marginal cost and include, as we mentioned, either
$\frac{d\underline{\gamma}^*_k(t)}{dt}$ or $\frac{d\overline{\gamma}^*_k(t)}{dt}$.

\section{Pricing with Generalized Bid Structures}
In an effort to better reflect constraints and costs of the generating units in our previous work we proposed to generalize the bid structure. Specifically, to incentivize suppliers to compete in offering ramping services, in \cite{parvaniaHICSS2016} we proposed to redefine export price bids so that the cost of generation at a certain time was function growing monotonically with respect to both power and the absolute value of the ramp. Later, to incentivize generators to rely on storage capacity in their generation portfolio, in \cite{KariPSCC2016} we generalized the notion further to make the export bid a function of energy, power and ramp.

In this case, the bid may no longer be a simple export bid, but also include a price for purchasing power, as discussed in in \cite{KariPSCC2016}, that would allow the generator to buy at low prices and sell in later period when shortages raise the whole-sale price. Our previous work focused on the UC problem, where the presence of  resources that are more flexible, but constrained in
generation or storage capacity, can better compete in the market and decrease the social
cost of meeting highly variable demand.

Naturally,  the generalized bid impacts the schedule and the price computed through the economic dispatch. Let us start from the first case, where the cost is function of both power and ramp. In this case:
\begin{theorem}
When the generator costs depend on both power and ramp, i.e. $C_k(x_k,{\dot x}_k,t)$, the marginal price, i. e. the price for lifting uniformly during the horizon the power demand by one unit, is:
\begin{equation}
\lambda^*(t)=\frac{\partial  C_k(x^*_k,{\dot x}^*_k,t)}{\partial x_k}-\frac{d}{dt}\frac{\partial  C_k(x^*_k,{\dot x}^*_k,t)}{\partial {\dot x}_k},~~k=k^*.
\label{price.C(x,dotx)}
\end{equation}
\end{theorem}
\begin{proof}
The only thing that has changed compared to the previous case is that the objective is a function of both power and ramp, but Euler-Lagrange equations can still be directly applied. The KKT conditions and \eqref{eq.parx} remain the same, since the constraints have not changed, but a new term appears in \eqref{eq.pardx} due to the ramping constraint, which is not part of the traditional economic dispatch problem:
\begin{align}
&\frac{d}{dt}\frac{\partial  f(x_k,{\dot x}_k,t)}{\partial {\dot x}_k}=
\frac{d}{dt}\frac{\partial  C_k(x_k,{\dot x}_k,t)}{\partial {\dot x}_k}-\frac{d\overline{\gamma}_k(t)}{dt}+\frac{d\underline{\gamma}_k(t)}{dt},\label{eq.pardx-gen}\\~~
&\forall t\in {\mathcal T},~k=1,\ldots,K\nonumber.
\end{align}
Therefore, simply applying the Euler-Lagrange equations, and focusing on the marginal unit for which $\overline{\mu}_{k^*}(t)=\underline{\mu}_{k^*}(t)=0$ and/or $\overline{\gamma}_{k^*}(t)=\underline{\gamma}_{k^*}(t)=0$ and also \eqref{eq.dtpf} is valid the claim follows.
\end{proof}

To express the most general bid form, let:
\begin{equation}
z_k(t)=\int_{t_1}^t x_k(t)dt,~{\dot z}_k(t)=x_k(t),~{\ddot z}_k(t)={\dot x}_k(t).
\end{equation}
 The generators cost in this case is a function of the energy power and ramp, i.e.
 $C_k(z_k,{\dot z}_k,{\ddot z}_k,t)$. In this case the {\it isoperimetric problem}  needs to be generalized, due to the presence of the second derivative.
The generalized formulation is now:
\begin{align} \label{Var1-gen}
\min_{\mathbf{z}(t)}& ~~~ \sum_{k=1}^K \int_{t_1}^{t_2} \!\!C_k(z_k,{\dot z}_k,{\ddot z}_k,t)dt \\ \label{Var2-gen}
\mbox{s.t.}~~&\sum_{k=1}^K z_k(t)=y(t)  ~~ (\lambda(t)) ~~ \forall t \in {\mathcal T} \\
&~~ \forall t \in {\mathcal T},~~k=1,\ldots,K\nonumber \\ \label{Var3-gen}
&{\dot z}_k(t) -\overline{x}_k\leq 0 ~~ (\overline{\mu}_k(t))\\\label{Var4-gen}
&\underline{x}_k -{\dot z}_k(t) \leq 0 ~~ (\underline{\mu}_k(t)) \\ \label{Var5-gen}
&{\ddot z}_k(t) -\overline{x}_k' \leq 0 ~~ (\overline{\gamma}_k(t))  \\ \label{Var6-gen}
&\underline{x}_k' -{\ddot z}_k(t) \leq 0 ~~ (\underline{\gamma}_k(t))\\\label{Var7-gen}
&z_k(t) -\overline{z}_k \leq 0 ~~ (\overline{\beta}_k(t))
\end{align}
where \eqref{Var7-gen}
represent the additional energy constraint\footnote{Note that the energy is always positive as long as the lower bound on power $\underline{x}_k\geq 0$.}.
Also in this case we can express the Lagrangian as follows:
 \begin{align}\label{eq.lagrangian-gen}
{\cal L}=
& \sum_{k=1}^K \int_{t_1}^{t_2}\!\!\!f_k(z_k,{\dot z}_k,{\ddot z}_k,t)dt\\
f_k(z_k,{\dot z}_k,{\ddot z}_k,t)&=C_k(z_k,{\dot z}_k,{\ddot z}_k,t)+\left(\frac{y(t)}{K}-{\dot z}_k(t)\right)\lambda(t) \nonumber\\
+&
\overline{\mu}_k(t)({\dot z}_k(t) -\overline{x})+
\underline{\mu}_k(t)(\underline{x}_k -{\dot z}_k(t)) \nonumber\\
+&
\overline{\gamma}_k(t)({\ddot z}_k(t) -\overline{x}_k') +
\underline{\gamma}_k(t)(\underline{x}_k' -{\ddot z}_k(t))\nonumber\\
+&
\overline{\beta}_k(t)(z_k(t) -\overline{z}_k)
\label{def.f-gen}
\end{align}
Following the same principles that lead to the derivation of the Euler-Lagrange equation, we can prove the following:
\begin{lemma}\label{lem.gen-EuLag}
The trajectories that lead to the minimum ${\cal L}^*$ satisfy the following differential equations:
\begin{align}
& \frac{\partial  f_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\dot z}_k}-\frac{d}{dt}\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\ddot z}_k}\nonumber\\
&-\int_{t_2}^t\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,\tau)}{\partial z_k}d\tau=0,~~~ k=1,...,K, t\in {\cal T}\label{eq.EuLag-gen}
\end{align}
in addition to the following KKT conditions:
 \begin{align}
&y(t)-\sum_{k=1}^K {\dot z}^*_k(t)=0  \label{eq.KKT2-gen} \\
&{\dot z}_k^*(t)-\overline{x}_k\leq 0,~~\underline{x}_k-{\dot z}^*_k(t)\leq 0,\label{eq.KKT3-gen} \\
&{\ddot z}^*_k(t)-\overline{x}_k'\leq 0,~~\underline{x}_k'-{\ddot z}^*_k(t)\leq 0, \\
&z^*_k(t)-\overline{z}_k\leq 0,~~\underline{z}_k-z^*_k(t)\leq 0, \\
&\overline{\mu}_k(t)( {\dot z}_k^*(t)-\overline{x}_k)=0,~~
\underline{\mu}_k(t)(\underline{x}_k-{\dot z}_k^*(t))=0, \label{eq.cse1-gen} \\
&\overline{\gamma}_k(t)({\ddot z}_k^*(t)-\overline{x}_k')=0, ~
\underline{\gamma}_k(t)(\underline{x}'_k-{\ddot z}^*_k(t))=0, \label{eq.cse2-gen} \\
&\overline{\beta}_k(t)(z_k^*(t)-\overline{z}_k)=0, ~
\underline{\beta}_k(t)z^*_k(t)=0, \label{eq.cse3-gen} \\
&\overline{\mu}_k(t),\underline{\mu}_k(t),\overline{\gamma}_k(t), \underline{\gamma}_k(t),
\overline{\beta}_k(t
\geq 0. \label{eq.df-gen}\\
\forall& t\in {\mathcal T},~~~k=1,\ldots,K\nonumber
\end{align}
\end{lemma}
\begin{proof}
To prove \eqref{eq.EuLag-gen}, we shall follow the same steps as the proof of Euler-Lagrange equations. Their derivation is based on the fact that if we perturb the optimum point with an energy neutral trajectory as follows:
\begin{equation}
{\dot Z}_k(t)={\dot z}^*_k(t)+\epsilon_k {\dot \eta}_k(t), ~~k=1,\ldots,K
\end{equation}
the functional gradient of the Lagrangian needs to be zero when $\epsilon_k=0$, since
${\cal L}$ is minimized by $z^*_k(t)$, i.e. ${\cal L}^*\leq {\cal L}$. If we assume that $\eta_k(t_2)={\dot \eta}_k(t_1)={\dot \eta}_k(t_2)=0$ ($\eta_k(t_2)$ implies that the perturbation is energy neutral),  this means that the following integrals, no matter the choice of ${\dot \eta}_k(t)$, have to be zero:
\begin{align}
\left.
\frac{\partial {\cal L}}{\partial \epsilon_k}
\right|_{\epsilon_k=0}\!\!\!\!\!\!
&=
\int_{t_1}^{t_2}\left(
\frac{\partial  f_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial z_k}\eta_k(t)
\right.\nonumber\\
\!\!\!\!\!\!&
+\left.
\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\dot z}_k}{\dot \eta}_k(t)
+\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\ddot z}_k}{\ddot \eta}_k(t)
\right)dt\nonumber\\
&=\left.
\left(
\int_{t_1}^t\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,\tau)}{\partial {\dot z}_k}d\tau\right)\eta_k(t)
\right]_{t_1}^{t_2}\label{eq.EuLag-gen-L}\\
&+
\left.
\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\ddot z}_k}{\dot \eta}_k(t)
\right]_{t_1}^{t_2}
\nonumber\\
&+\int_{t_1}^{t_2}\left(
-\int_{t_1}^t\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,\tau)}{\partial {\dot z}_k}d\tau
+\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\dot z}_k}
 \right.\nonumber\\
&-\left.\frac{d}{dt}\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\ddot z}_k}
\right){\dot \eta}_k(t)dt=0~~~k=1,..,K.\nonumber
\end{align}
In \eqref{eq.EuLag-gen-L} only the last integral remains, given that $\eta_k(t_2)={\dot \eta}_k(t_1)={\dot \eta}_k(t_2)=0$ and the integral $\int_{t_1}^t\frac{\partial f(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,\tau)}{\partial {\dot z}_k}d\tau$ is zero at $t=t_1$ because the interval of integration has measure zero. Because  ${\dot \eta}_k(t)$ is entirely arbitrary, the optimum trajectory must satisfy \eqref{eq.EuLag-gen}.
\end{proof}
Considering the definition of $f(z_k,\dot{z}_k,\ddot{z}_k,t)$ \eqref{def.f-gen}, the generalized Euler-Lagrange equation \eqref{eq.EuLag-gen} obtained in Lemma \ref{lem.gen-EuLag} implies that:
\begin{align}
&-\int_{t_1}^t\frac{\partial C_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,\tau)}{\partial {\dot z}_k}d\tau
-\int_{t_1}^t(\overline{\beta}_k(\tau
d\tau\\
&+\frac{\partial C_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\dot z}_k}
-\lambda(t)+\overline{\mu}_k(t)- \underline{\mu}_k(t)
\\
&
-\frac{d}{dt}\frac{\partial C_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\ddot z}_k}
-\frac{d\overline{\gamma}_k(t)}{dt}+\frac{d\underline{\gamma}_k(t)}{dt}=0.
\end{align}
To derive the price we need, once again, to focus on the marginal unit, for which the balance constraint is not tight. We also want to restrict ourselves to the assumption that the generators offering the bids which change their cost based on the energy
$C_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)$ are only suppliers, which make sense since the power is constrained to be positive and if there was an import, it should be negative. This is a subtle point that leads to some simplifications that are not obvious in the general case in which suppliers can switch role and buy power to replenish their capacity.

Once again, because of the KKT conditions and the fact that the multipliers are continuous for the marginal unit $
\overline{\mu}_k(t)=\underline{\mu}_k(t)=0$ and $d\overline{\gamma}_k(t)/dt=d\underline{\gamma}_k(t)/dt=0$.
But what also is important to notice is that for the marginal unit also
\begin{equation}
\int_{t_1}^t\overline{\beta}_k(\tau)d\tau=0
\end{equation}
 as soon as a unit saturates the capacity it can offer,
i.e. $z_k=\overline{z}_k$, and $\overline{\beta}_k(\tau)>0$ the unit can no longer be the marginal unit as it has no more power to offer.
Therefore, denoting by $k^*(t)$ the index of the marginal unit at time $t$ in this case we conclude:
\begin{theorem}
When the generator costs depend on energy, power and ramp, i.e. $C_k(z_k,\dot{z}_k,\ddot{z}_k,t)$, the marginal price of power is:
\begin{align}\label{price.C(x,dotx,ddotx)}
\lambda^*(t)=&
\frac{\partial C_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\dot z}_k}-\frac{d}{dt}\frac{\partial C_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,t)}{\partial {\ddot z}_k}
\nonumber\\
&
-\int_{t_1}^t\frac{\partial C_k(z_k^*,\dot{z}_k^*,\ddot{z}_k^*,\tau)}{\partial { z}_k}d\tau~~k=k^*(t)
\end{align}
\end{theorem}

A few remarks can be drawn out of this analysis which are summarized in the next section.

\section{Discussion}

One of the first questions is how generating units would construct their bids.
This question is hard to answer from a purely technical point of view, as the costs of ramps are mostly associated to the wear and tear of the generating units and, therefore, are not very easy to quantify, while the marginal cost of a certain schedule to offer energy for storage units can be close to zero. Hence, both costs are likely to be {\it opportunity driven costs} rather than clearly quantifiable {\it fuel costs}, as it is for the case of generation of power through fossil fuels.
 However, the aim of our proposed bid is to
allow the market participant to evaluate how to best position themselves to profit from the market environment
directly in the commitment phase. While day-ahead costs may rise, especially in the case of ramping services \cite{parvaniaHICSS2016}, the decisions result in lower real-time costs.
The results we have derived in this paper, namely \eqref{eq.marginal} and \eqref{eq.mag.price} for a regular bid and \eqref{price.C(x,dotx)} and \eqref{price.C(x,dotx,ddotx)} for a generalized bid lead to the following observations
\begin{enumerate}
\item The cost of ramping is naturally apparent in the ED problem when the ramping constraints become tight through the derivative of the instantaneous Lagrange multiplier associated with the ramping constraints, even if one considers the current practice of bidding exclusively as a function of power.
\item Because the marginal price is tied to the marginal instantaneous cost, the price is continuous as long as the cost is continuous. Because net-demand is continuous it is natural to think that if demand lies in a finite function space (this was the hypothesis in \cite{parvania2015UC}) this function space might be adequate to also express the variations in costs. However, the connection between the features of the generators trajectories and the temporal variations in cost is still elusive and requires more investigation.
\item The negative sign of the contributions that come from the dependence on ramping in \eqref{price.C(x,dotx)} has a nice interpretation: by increasing demand of power now, we can offset increasing costs of ramp that follow. If, on the other hand, the cost in ramp is declining (has negative slope in time) the rise in power is penalized.
\item For the energy cost the situation is different: inevitably as time goes on the energy demand grows which rises the marginal cost of power. Thus, the negative term \eqref{price.C(x,dotx,ddotx)}  can potentially be interpreted as a correction term, which rebalances such growth.
\end{enumerate}

\section{Conclusions}
In this paper we derived the continuous time price of electricity in continuous time by solving an Economic dispatch problem with two differences compared to the standard formulation: 1) we included ramping constraints and solved the problem over a certain horizon accounting for possible ramping shortages; 2) we included more complex bids that allow for a change in price due to ramping or relative to the amount of energy that the unit has offered up to a certain point in time.
We have shown that the notion of marginal price can be generalized to the continuous time regime and taken inspiration in solving the variational problem of computing the price from the solution of the so called isoperimentric problem \cite{variational}.

\section{Acknowledgements}
We wish to acknowledge the discussions with Masood Parvania and K\'{a}ri Hreinsson that lead to the question of correctly pricing power and energy trajectories.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


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I'm very excited this week to show work and thoughts from UK furniture designer and maker Edward Teasdale.
Edward Teasdale appeared on the UK Crafts scene in the 1980's. He worked as a furniture designer in industry, a maker and later a teacher, before once again establishing his own workshop in the Lake District, from which he now works, creating pieces for exhibit in selected galleries and for individual clients and collectors.
Elemental and enigmatic, with the intense energy of a rising wave, something alive hums from the pieces below.
From the beginning, Edward made "small consciously modest crafted objects comprising a basic utility and somewhat rough hewn appearance", using found woods.
"I loved climbing into trees when I was young and with school friends built shelters every summer out of natural materials in the woods around my home in the Lake District.
"I progressed from whittling bows, arrows and fishing rods (out of Hazel and Yew) to making sledges, bogies and rafts out of reclaimed materials using my fathers hand tools.
"Without noticing I must have developed a real interest in wood, as well as some skills in designing and making things. Now I appreciate that it's the cleanness, and the visual and tactile warmth of wood, coupled with its versatility as a practical and aesthetic medium that appeals to me.
"Interacting with the physical world has always been central to my life. The natural landscape and built environment inspire me equally but consideration of such things as Art, Sculpture, Architecture and Environmentalism have all played their part in forming my work.
One of my original motivations was to capture something of the qualities of traditional rural buildings that (very naturally) meet essential needs through building by hand with local materials.
All finished pieces are marked (usually centrally on the underside of the bottom) with a 2 digit date stamp e.g. 93 and a separate stamp in the form of a leaf. Most pieces are in private homes and collections in the UK, USA, Australia and New Zealand but examples are also in the possession of the British Council, Arts Council of Great Britain, Usher Gallery Lincoln, UK.
You can read more about Edward on his site here.
I only had a few hours last Saturday to visit the Contemporary Craft Festival at Bovey Tracey, but what a fantastic few hours it was. The work and people that I met there exceeded my expectations; there was such originality, commitment and true skill on every corner.
Visiting last weekend really confirmed to me my love for work made by hand, and the magic invisibly imbued into something that has taken time and physical effort to create. A spoon that has taken five or more hours to carve from a single piece of wood, a pot formed from clay collected on the hillsides, caressed and moved into achingly beautiful shapes, a lampshade decorated with wrap after wrap of a single piece of thread, tucked so gently into the other side. These skills and actions have value and meaning and feeling, and they must be maintained and supported. This is so important.
Julia was one of the first people that I met on Saturday, in the "one year on" tent, showcasing artists and craftspeople who were one year into their new businesses.
Julia works dense hand embroidery into metal gauzes and figuratively manipulated wire lines, before combining them with drawing and screen printing onto fabric and paper. This combination of sculpture and drawn elements, sometimes also incorporating words and phrases, made for a really engaging series of work that I was really drawn into. Each one feels a little like a keepsake box, a collection of memories or stories.
You can make contact with Julia on her blog, here.
I felt an instant connection to Adam's work, as I wandered into his small space in the corner of the tent. Something wonderfully quiet, natural and peaceful sang out into the surrounding crowds.
Looking on his work, I felt a strong sense of the sea and the landscape, something very close to nature. I later learned that Adam lives and works by the coast in West Wales.
Once home, I was fascinated to read more about his work, and took a look at his website and blog. I spent a good while reading there, and found him to be not only an intriguing artist but also an engaging writer and thinker.
The end result is a moving and dreamlike time lapse film, showing not only the gradual disintegration of the jar, but the changing wild landscape, sea, movement of animals, and the sky and stars. It spoke to me of many things, of resilience, of fragility, and the power of the natural world.
The film was shown at an outdoor event in the centre of Buenos Aires on the 17th of May. You can watch a small portion of the film here.
I really encourage you to read more about this project, it is so fascinating and uplifting, and to look more closely at Adam's beautiful work on his site.
It made complete sense as to why his work has such a quality, why it holds something of that passionate connection to nature, even in that crowded, noisy space.
A warm and Autumnal hued space welcomed me in to Jane's beautifully arranged collection of handmade lampshades, framed pictures, bookmarks and jewellery.
I was really taken by the absolute precision and care it must take to wrap each single piece of thread round and through the wood burned holes that decorate each handcrafted piece that she works on. The shades give a beautifully warm light, and are totally unique.
Jane is based in her studio/shop at The Manchester Craft and Design Centre. You can also see more and buy her work from her website here.
Claire's fantastic energy buzzed all about her space as I stepped in to admire her collection of handmade silk scarves. She was dressed beautifully in her own handmade dress from her own line. Once I looked more closely at the designs on each scarf, I was struck by their intricacy and individuality. Each piece of work is finished with delicately layered edgings and hand-embroidered details, and each one seems to tell some story, of the sea, the landscape and environment. They are truly original and stunningly beautiful – you really have to see them in real life to truly appreciate them.
Claire designs and hand prints her scarves and dresses, plus undertakes work as a costume designer and illustrator from her birthplace in Cornwall. You can visit her site here.
Nic was the last person that I met as I made my way out from the crowds. His calm manner and friendliness drew me in to his space, filled with carefully arranged displays of hand carved, traditionally made spoons, ladles and bowls. I really enjoyed the feeling of slow moving time and focus that seemed to fall from the displays and his way of working, there was a quiet honour to each piece of work.
I love that each spoon, each bowl that he creates is slightly different, and is worked with the wood not against it, enhancing each grain and knot and forming it into something original and full of spirit and life.
You can visit Nic's site here.
I hope that I have shared with you a little of the warmth and originality that I found at Bovey Tracey. If you are near at the next event I really encourage you to visit. You can read more about the festival at their website here.
Thanks to everyone for taking the time to let me into their space and take photographs.


OCZ releases its homegrown Intrepid 3600 enterprise SSD for read-intensive workloads. Today Paul compares it other leading SSDs in its class.
OCZ Storage Solutions, a Toshiba Group Company, is a battle-hardened veteran of the SSD market. OCZ was one of the early pioneers of the client SSD market, and some even credit them as the catalyst that touched off SSD usage in mainstream client applications. Toshiba purchased OCZ in January, addressing OCZ's key weakness by giving them direct access to NAND fabrication. OCZ brings an established retail channel and their controller technology to the relationship.
The Intrepid series consists of the 3600 and 3800 models that are available to OEMs or retail markets. Server-side flash is a booming business and the entrance of the fabs into this segment has upset the old model of deploying client-side SSDs into read-centric applications. Fab-enabled companies can provide enterprise features and firmware at very competitive prices.
The Intrepid SSDs are geared for use in appliances and server-side flash deployments. The 800GB Intrepid 3800 features up to 7.48 PB of endurance for write-intensive applications. The 800GB Intrepid 3600 has up to 1.5 PB of endurance and is geared for read-intensive applications, such as web search, media streaming, indexing, and other general-purpose server-side flash deployments. The primary differentiator between the two SSDs lies in the NAND. Both use Toshiba 19nm Toggle, but the higher-endurance 3800 utilizes eMLC to provide more endurance, while the 3600 utilizes standard MLC.
OCZ has provided enterprise storage solutions in the past with their SandForce-powered Intrepid and Deneva offerings. However, the amount of control OCZ exerted over the firmware was limited. For the new Intrepid series, OCZ utilizes the Marvell SS9187 with OCZ's own proprietary enterprise firmware. This gives OCZ the flexibility required to add more enterprise-centric features and functionality. OCZ also offers the drive with locked firmware, ensuring wide compatibility and intense verification, an important consideration for OEM use.
OCZ has custom controller silicon in use in client applications, and validation and qualification cycles are likely already underway for the enterprise segment. OCZ's Everest 2 platform leverages the hardened Marvell 9187 with organic firmware in their inaugural SSD. The Intrepid offers end-to-end full data path protection via CRC (Cyclic Redundancy Check) as the data traverses the internal buffers and caches. OCZ ensures data integrity with advanced ECC algorithms. The Intrepid also features another layer of protection with an integrated RAID-like parity scheme. These techniques provide a 1 per 10E17 UBER rating.
The Intrepid 3600 has a 6GB/s SATA connection and comes in capacities of 100, 200, 400, and 800 GB in the 2.5" form factor. Performance varies by capacity point, but the 400 GB model we have on the test bench provides a solid 90,000 / 38,000 IOPS of 4k random read/write performance. Sequential speed checks in at 515 / 465 MB/s read/write. A quick glance at the competing SSDs indicates the Intrepid is on the upper end of endurance for the read-intensive class.
Power loss protection (PLP) is an expected characteristic of any enterprise-class offering, and the Intrepid series offers PLP with a unique design. The large AVX supercapacitor offers enough capacitance to flush any data in-flight to the NAND in the event of host power loss. MTBF weighs in at 2,000,000 hours and the drive is 256-bit AES-compliant to fulfill encryption requirements.
OCZ focused on providing exceptional performance and consistent latency for the Intrepid 3000 Series. OCZ's performance consistency focus is important; it delivers big dividends in application performance and RAID environments. The Intrepid is five time faster than the previous-generation Deneva in random write and twice as fast in random read workloads.
Enhanced SMART attributes offer temperature logging and monitoring along with other enterprise-specific attributes. The Intrepid is backed by a five-year warranty with dedicated FAE support. OCZ also offers the StoragePeak 1000 software for management. Let's see how the Intrepid 3600 stacks up against the competition.


Detailed below is a list of Properties to Rent in Primrose Hill. Our Search enables you to filter your requirements for property to Rent in Primrose Hill. If there is not a property listed that meets your requirements in Primrose Hill, then please register with us and we will contact you with any new property to Rent in Primrose Hill.


Interesting, as I have been told that there is sufficient detail with the characteristic 'claw' to identify this one to species. Although I don't have the larger Roberts online references appear to confirm this. What are other candidates?
That's excellent Alistair, thanks for the details.
Many thanks Alistair. Your Araneus quadratus will be juvenile at this time of year, but is recognisable as a large juvenile. Records for this species can be submitted directly through the Four Spot Orbweaver page, but I will enter your record into the database.
It is impossible to sure of much from the photograph, but it is most likely to be Amaurobius ferox, a local 'lace weaver spider' usually found under debris and stones etc in gardens or near buildings. It is harmless to humans.
Enlarging and lightening the image makes it clear it is not a tube web spider Segestria species.
I have seen similar looking "stocky", jet black spiders before but none quite as big as this beauty!
This was at the bottom of a hallway with stairs leading up to 2 flats. Location is DE21 4LU, Derby.
Unfortunately I'm quite heavily arachnophobic and this was as close as I dared to get. I believe it's possibly a tube web spider?


text:
Exploitation in focus
This article is more than 4 weeks old
'I told my daughter I'd be home': long ordeal ends for crew stranded at sea
Abandoned at sea in desperate conditions for 18 months, the MV Azraqmoiah's crew have finally been reunited with their families
Exploitation in focus is supported by
Karen McVeigh
@karenmcveigh1
Mon 17 Jun 2019 07.19 EDT Last modified on Mon 17 Jun 2019 07.20 EDT
Captain Ayyappan Swaminathan, right, with members of the MV Azraqmoiah cargo ship's crew. Photograph: Courtesy of Human Rights at Sea
After 18 months stranded on a cargo vessel miles off the coast of the United Arab Emirates, with little food or water, no wages and little means of communication, Captain Ayyappan Swaminathan's ordeal is finally over.
In April, the Guardian reported the story of Ayyappan and his 10-strong crew, one of the most extreme cases of seafarer abandonment in recent years.
On Sunday night, Ayyappan said his "cup is overflowing" with happiness after an emotional reunion with the family he hasn't seen since he left India, in January 2017. Speaking from his home in Kumbakonam, with his wife, Menaka and daughter, Aniya, who turned seven last week, Ayyappan said: "I cannot describe what it felt like to hold my daughter again after so many days and nights. I'm really happy. She is also very happy."
He last saw Aniya when she was four years old.
Captain Ayyappan Swaminathan reunited with his wife, Menaka and seven-year-old daughter, Aniya. Photograph: Jaffer Shadiq/Mission To Seafarers
It marks the end of a long, drawn-out case where the captain and crew were abandoned by the vessel owner, Elite Way Marine Services, unable to leave the ship fearing the loss of their claim to thousands of dollars in unpaid wages.
Ayyappan sent the Guardian a video that recorded the emotional moment he finally left his ship, MV Azraqmoiah, shot from a speedboat carrying him safely to shore.
"When I touched land, I felt like flying – oh my God," said the merchant seaman of 20 years. "This is the day we dreamed of. My cup is overflowing again and again."
Ayyappan, who thanked everyone who helped him, said he had now been paid 80% of the $84,000 (£66,000) salary owed to him.
Free at last: Captain Swaminathan films the ship where he endured two years of hardship - video
His two colleagues, Rajib Ali, a cook from India, and Ibrahim Adam Iazim, chief officer from Sudan, were also repatriated. Other members of the crew, who accepted 40-60% of their owed salaries, left the ship in April.
The seafarers endured terrible hardship aboard, as their supplies dwindled and finally ran out, prompting them to seek help to survive. Ali's father passed away in August 2018, yet still they waited for the wages. There were days when a lack of fuel left the vessel in darkness in the busy shipping lane, endangering the crew and other ships. The Indian consulate and the charity Mission to Seafarers were able to help by providing food and water.
In all, 36 sailors in at least seven vessels were abandoned by Elite Way Marine Services, according to the Federal Transport Authority (FTA) in the UAE. The case was first highlighted by the International Transport Workers' Federation (ITF).
UAE-owned Elite Way Marine Services told the Guardian in April that they failed to pay the seafarers from Azraqmoiah and other ships after encountering financial problems, but promised they would be paid soon. Captain Ibrahim Gafar, Elite Way's operations manager, said the company had previously been unwilling to sell any of its vessels to release money for wage payments because unfavourable market conditions meant he would not get a good price, but they later found a buyer for one while another was being sold for scrap. "We have a financial problem," said Gafar at the time. "For one and a half years the market has been down. Any person would not give a good price for the vessel."
The company could not be contacted for this article.
It has since emerged that the international attention brought by the Guardian's coverage in April and May helped to pressurise the owners to act.
In February, Mission to Seafarers and the FTA took legal action against the vessel's owner over the unpaid salaries. The first ship was arrested under maritime law in April, followed by other vessels, including the Azraqmoiah, which was sold to pay the seafarers' salaries. The FTA has banned the company from operating in UAE waters.
Jasamin Fichte, of the law firm Fichte & Co, said the vessel's owner had "made a mockery" of the UAE legal system. She vowed to lobby for better regulations.
Fichte said: "It's obvious to everyone involved the ship owner has to pay their wages. If it hadn't been for our actions, the crew would not have been paid at all. But the vessel owner got away with paying less. He has made a mockery of the legal system here."
The conditions on the ship were "horrible", she added.
"Such actions would be considered criminal in many jurisdictions. Seafarers were suffering from physical and psychological conditions. We were worried for their safety. No food, no water, no air conditioning in 40 degree heat – it's not something I would wish on anybody."
Fichte said she will meet with the UAE government to talk about how they can stop the rising problem of vessel owners abandoning crew in their waters. A law to seize abandoned ships is already under discussion in the country.
Abandoned at sea: the crews cast adrift without food, fuel or pay | Karen McVeigh
Rev Andy Bowerman, the Middle East and south-east Asia director of Mission to Seafarers, praised Ayyappan for helping to highlight the "unacceptable" issue of abandonment at sea.
"He realised that if he held out for longer, he would highlight the issue – and there is a bigger issue here," said Bowerman. "At some point the UAE has got to change its approach to seafarers."
He urged the UAE to sign up to an amendment to the maritime labour convention, which guarantees better protection for seafarers by requiring ships to carry insurance to pay them if they are abandoned.
Worldwide, 4,866 seafarers on a total of 336 vessels have been abandoned on board ship since 2004, according to a database by the International Maritime Organization and the International Labour Organization.
"The flag states should do more," said Mohamed Arracedi, the ITF's coordinator for the Arab world and Iran, who has dealt with over 100 cases of abandonment and recovered $1.26m in owed wages in 2018. "Many of the cases we are dealing with in the Emirates are severe abandonment cases. Why do owners abandon their ships in the UAE? A little bit of speculation, it is probably a lack of regulation. They know if they abandon ships in Spain, the port states can intervene and the maritime labour convention is applied. These things can be solved quicker."


Jonathan Djanogly opens Luminus Group's new 55 bed extra care facility in St Ives.
Jonathan hosting a St Ives U3A visit to the House of Commons.
Jonathan welcoming Longsands Academy students to the House of Commons, where the topics of discussion included Brexit and the US elections.
Jonathan with the Head of Huntingdon Nursery School, Kay Dimelow, discussing funding issues during a visit to the nursery.
Jonathan meeting with Education Minister Nick Gibb MP, along with fellow MPs Heidi Allen, Lucy Frazer and Daniel Zeichner, to highlight the urgency of the issue of introducing a fairer funding formula for Cambridgeshire's schools.
Jonathan commemorating International Polio Eradication Day by planting purple crocuses at St Neots Parish Church.
Jonathan visiting the Sacred Stones Willow Row barrow in Hail Weston, the first of its kind to be built in Cambridgeshire for 3,500 years.
Jonathan meeting with the Prime Minister to discuss corporate governance proposals.
Jonathan meeting lifelong St Neots resident Sid Wildber who has been awarded the Legion d'honneur by the French government in recognition of his role in the Normandy landings and the liberation of France in the Second World War.


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App Development & Design
How to Design an App: A Practical Guide
Android / iPhone & iPad / Mobile App Development & Design
How do I design an app?
A beginner's guide to app design
Step 1: Think of an idea
Step 2: Lay out a spec
Step 3: Choose a mobile app design platform
Step 4: Build a wireframe
Step 5: Create a prototype
Step 6: Perform final visual design and submit prototype to the developer
App design tips and tricks
Prioritize features
Remove clutter
Make navigation simple and understandable
Minimize user input
Avoid jargons
Use gestures the right way
Everything simple and consistent
Keep up with the native feel
Mobile app design means developing the visual elements of an app. It includes making both the user interface (UI) and user experience (UX) excellent. Mobile app design is all about creating a mobile application UI/UX that meets (or even exceeds) the end user's expectations.
Many use the terms "app development" and "app design" interchangeably. They are not the same.
Mobile app development includes the entire process of creating an app, while the app design portion is part of the app development process that makes the app look and feel good. To develop an app, you need an idea, decide on the platform (Android, iOS, or both) to develop your app on, and then design your app. You would typically create a prototype design in the early stages of app development. This prototype will become a reference for the final development work that is performed in the app development tool of your choice.
Image Credit: pexels.com
Both app development and app design begin with an idea. Your app should create an opportunity or help solve a problem users are facing. When it comes to app design as well, you can come up with an innovative user interface, something that will be well-received. For example, in 2010, the Windows Phone 7 introduced its Dark Mode feature, which has since been copied by many operating systems, platforms, and major applications like Android, Facebook, and Google Chrome.
A specification or spec is a brief of what you want the app to do, how it should look and behave. It is the written requirements of a project. It is the instruction pamphlet, which can be given by a client, or prepared by the designer themselves. A spec can be simple, with general guidelines. Or it can be very detailed, and consist of the transition requirements when you open different app pages, for instance.
An example specification page. Image Credit: mattsoave.com
Nowadays, mobile app design platforms are mostly drag-and-drop, allowing you to add fonts and colors and various design elements into your prototype without coding. Some of the best app design tools would be Sketch, Adobe XD, Origami and Proto.io. We also have curated a list of the Best Mobile App Design Software in 2020.
Image Credit: adobe.com
Wireframes are also known as low fidelity mockups. They are the most basic layout of your application, which consist of the structural and navigational flow guidelines. Wireframes can be done using a design tool, or even on a pencil and paper. They answer the question, "How will the application work?"
A wireframe is a pictorial representation of the spec. They are usually made up of lines and boxes, and where pictures, fonts, and other design elements like buttons, maps, and tables are placed in the app.
An example app wireframe. Image Credit: justinmind.com
Prototyping means converting the wireframe into an actual design with the required structure, flow, colors, buttons and pictures, and getting a better idea of how the final product would look like.
A prototype is the putting together the entire UI/UX of the app, minus the actual functions. For example, say you are planning to build a messaging app. A prototype will let you do everything except send and receive messages.
Many mobile design tools provide users with a graphical user interface (GUI) for prototyping. Some tools allow the designers to export the design codes. The app developer can then add the app's functionalities on top of the design codes to complete the development process.
Wireframe vs Prototype. Image Credit: upwork.com
The final stage of the design process consists of polishing the prototype, and making the user experience good. This includes creating a sleek navigation flow, editing terms to make the app jargon free and minimizing user input.
In addition, you will need to ensure that the design reflects the brand message that the app owner wants it to portray.
Finally, you submit the design to the app developers. They will take your design and put in the necessary code to make the app function.
You should know which features are necessary and what you can afford to omit from your application. Users dislike a confusing user experience. Make sure every action your user takes is per the core functionalities of the app.
For example, a video editing app will not need a GPS. An e-commerce website should allow you to snap a picture of your product and upload it.
Minimalism is one of the biggest app and web design trends in 2020. It means your app should look as simple as it can so that its content stands out. Don't overload your users with random images, buttons, and lines of text. Rather, increase the number of pages by prioritizing one action per screen.
Image Credit: netlifyusercontent.com
Navigation should be simple and familiar to your users. You should create a good information flow architecture, letting people know exactly where they are in the app, and where they should click to reach their destination.
Use standard navigation components like side drawers and tab bars that people are used to.
Image Credit: medium.com
For example, in a game app, the option to mute should be inside the game settings. Thus, the game settings icon should be in a place where the player can easily find it. You can also use breadcrumbs – they reveal the user's position in an application with a lot of pages.
You must aim to minimize user input while they navigate around the app or enter data. You should add auto-fills; for example, when you register a Whatsapp new account, your phone code will be automatically entered when you specify your home country.
If you are building a game, you should make the controls as simple as possible. The number of buttons should be minimal and accessible. You can't afford to add a lot of confusing control combinations to make the character take action.
Take the popular mobile game PES 2020. They used to have buttons, but after lots of complaints, they now let users play the game by swiping the screen.
On the right, there are buttons for pass, clear, through, and dash? On the left is the directional stick. You can play the game by swiping on the direction to want to play the ball.
You should use simple, understandable words in your app. Instead of using industry-specific terms, acronyms, or brand phrases, use terms that everyone comprehends.
For example, in a transportation app, you can use the term "big bus" with the seat size information in place of "'coach". Similarly, in a banking app, you can use "Monthly Installments" instead of "EMI".'
Avoid using gestures for common navigation: For example, while moving from one page to another on an app, it is usually better to use a button rather than having to swipe. But it also depends on the type of app and context. For a phone gallery, swiping is a better option to move from one picture to another.
Use common gestures: Rather than making your own custom gestures, your app should use industry-standard ones. People hate to learn a lot of things just to use an application. For instance, to zoom a photo, the gesture should be a pinch or double-tap.
Remember, you are designing an app and not a 1980's room wallpaper. You shouldn't add overly fancy fonts, pictures, or colors in the name of decoration.
Gmail 2010 vs Gmail 2019: The design has become simpler.
Be consistent with the color and theme. Don't change the look or the feel of the app when users move from one page to another.
Image Credit: designwoop.com
Android and iOS have different kinds of aesthetics attached to them. The applications running in those operating systems also have different types of icons, themes, and navigation. You need more navigational buttons for iOS, because its devices don't have a built-in back button like most Androids do.
Androids use side drawers, while Apple uses tab bars.
You can build a cross-platform application, but your design should be compliant with the kind of motif people expect to see on different types of operating systems.
There is also a difference between an app and a website. Your app shouldn't look like a website; for instance, links on text content are good for a website, but they don't go well with mobile apps.
Conclusion: Designing an app means making it look and feel good. To do that, you need to have a proper idea in place, write a spec, design a wireframe, and finally, build a prototype. There are various guidelines to a good app design. The most important ones: feature prioritization, cleanliness (clutter free), easy navigation, minimal user input, skipping the jargons, employing the correct gestures, and following the platform's native feel.
The Best Mobile App Development Tools in 2020
Best Mobile App Design Software in 2020
Python for App Development: A Concise Guide
The 10 Rules of App Icon Design
A Beginner's Guide to Android App Development
How to Use AI in Mobile App Development
Tracking & Monetization
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Project Aspiro:
A career planning and employment resource for people who are blind or partially sighted
Sponsored by World Blind Union
Project Aspiro
Meet individuals who are blind or partially sighted and enjoy meaningful employment in a wide range of fields. See them discuss education, interview techniques, workplace accommodations, overcoming barriers, and more.
For everyone that is interested in submitting success stories to Project Aspiro, please follow the suggested interview format.
Canadian Success Stories
Rhodes Scholar and Diamond Jubilee Medal winner; Aaron talks about the value of mentorship and following your dreams.
Aaron's story
Carla talks about what having a rewarding career has meant to her and how it has increased her confidence and independence.
Carla's story
Radio Production Manager
Lindsay, ON, Canada
Ken has been working since he was 15 years old. Learn how his computer skills landed him a job in radio production.
Ken's Story
Chelsea talks about her professional and educational journey and her current role as a Research Assistant at CNIB.
Chelsea's story
Union Awareness Trainer
Oshawa, ON, Canada
Phil talks about how perseverance and learning new skills enabled him to re-enter the workforce after losing his vision.
Phil's story
Chris launched his company 26 years ago and has never looked back. Find out the keys to Chris's success as a business owner.
Chris' story
Brantford, ON, Canada
Co-op student and future chef extraordinaire, Conner, talks about her passion for cooking and her dreams of becoming a professional chef.
Conner's story
Jason Fayre
Lead Accessibility Expert
Born blind, Jason discusses his successful career history, the obstacles he faced advancing his career and how he overcame them.
Jason's story
International Success Stories
Jamey Cook
Spanish Interpreter
Carrboro, NC, USA
Jamey is self-employed as a freelance interpreter of Spanish, helping others with everything from medical appointments to travel planning.
Jamey's story
Alex Kolberg
Apprentice Chef
Alex and his employer, Kristian, discuss Alex's work as an apprentice chef at The Taxpayer – a restaurant in Adelaide, Australia.
Alex's story
Sokun Prum Vireak
Assistant, Ministry of Foreign Affairs
Sokun describes his job and how he reached this goal, including his education and the support he received.
Sokun's story
Bridget Jolley
In this audio interview, Bridget describes her job and how she performs it competently with low vision.
Bridget's story
Danielle Pollock
Customer Service Assistant
In this audio interview, Danielle talks about her work and the assistance she received to secure employment.
Danielle's story
Hamish MacKenzie
Global Accessibility Manager
In this audio interview, Hamish discusses the obstacles he had to overcome to adapt to his sudden vision loss in a car accident and return to work
Hamish's story
Simon Tunjio
Support & Sales Consultant
In this audio interview, Simon tells of how he immigrated from Papau New Guinea to Australia and found work.
Simon's story
Czarina Mercado
In this video interview, Czarina speaks about her employer and how well she has adapted to life without vision.
Czarina's story
Jennie-Lyn Gabriel
Olongapo, Philippines
Learn about how Jennie-Lyn dealt with her vision loss and the support she received from Resources for the Blind Inc., and the city of Olongapo to succeed.
Jennie-Lyn's story
Marx Melencio
Marx speaks of how he managed to deal with a sudden onset of vision loss in the middle of his life and the success he carved out in the workplace afterwards.
Marx's story
SOK Chamroeun
Senior Financial Advisor
In this video, Chamroeun talks about his work for CaFinCo Limited, a microfinance company and his educational experiences.
Chamroeun's story
Mohamed Saber
Orléans, France
In this audio interview, Mohamed talks of his work for Orange Telecommunications where he works with various associations for digitial accessibility.
Mohamed's story
Gerry Ellis
Gerry has worked 30+ years for a bank in Dublin and also freelances as an accessibility and usability consultant.
Gerry's story
Neang Sarith
Svay Rieng, Cambodia
Neang Sarith discusses how he studied and with assistance was able to succeed in the business world.
Neang's story
Karolis Verbliugevicius
Karolis is an entrepreneur who owns three businesses in Lithuania. Karolis, who lost his vision as a young adult, tells his story of how to succeed in business.
Karolis's story
Martin Kieti
Martin discusses the joy of working with other visually impaired people throughout Africa and helping them to achieve their goals.
Martin's story
Gertrude Fefoame
Global Advocacy Advisor
Gertrude shares with listeners how much she enjoys her role in changing people's lives through mentoring.
Gertrude's story
Michiko Tabata
Michiko is a long-term employee with a Japanese bank, who credits her success in securing employment to her university's disabled student support worker
Michiko's story
Tony Takei
Legal Counsellor
Tony discusses the importance of working and living independently for him following the challenges he faced growing up with decreasing vision.
Tony's story
Lars Bosselmann
Lars shares his belief in the importance of his experiences gained through internships and studying abroad.
Lars' story
NOV Sokneang
Administrative and HR Officer
Kampong Cham, Cambodia
Sokneang, a young man who works at the Provincial Office of Culture and Fine Arts of Kampong Cham in Cambodia speaks of the value of education and networking.
Sokneang's story
Fernando Galarraga
Ministry of Culture, Musician
Argentinian Republic
Blinded as a young man, Fernando discusses the joy of working in an area he loves and the hard work in other areas he had to do first to gain work experience.
Fernando's story
Lusia Lieves
SENIAT, Human Resources
Luisa discusses her work experiences and how she managed accommodations so that she could work competitively. Her competency has enabled her to succeed.
Lusia's story
Harch Chhem
Harch describes his part-time job at Kampuchean Action for Primary Education. In addition to his own studies, Harch teaches English to primary students in Cambodia.
Harch's story
Oksana Chuchunkova
Employment Program Coordinator
Oksana began her career as a self-employed massage therapist and has worked at a variety of jobs before accepting her current position helping others to find employment.
Oksana's story
Ojak Simon
Entrepreneur and Beekeeper Instructor
Ojak has his own company in Uganda where he is training other individuals with visual impairment to establish beekeeping enterprises. In 2017, Ojak Simon won the Holman Prize.
Ojak's story
Ngim Sinart
Dine in the Dark Restaurant Guide
Ngim tells the story of how her study of English helped her land a job at Dining in the Dark (DID) Restaurant where she works as a guide.
Ngim's story
Caren Burns
Vision Australia, Trainee Library Officer
Melborne, Australia
In this interview, Caren describes how she captured a traineeship at the Vision Australia Library where she is currently working.
Caren's story
Oyut Bayaraa
International Relations Manager
Ulaanbaatar, Mongolia
Oyut describes her work as a translator; and then, following her sight loss, as the International Relations Manager for the Mongolian National Federation of the Blind.
Oyut's story
Success Stories From Other Organizations
Royal National Institute of Blind People
This IS Working
Profiles of people who are blind or partially sighted who've learned to overcome barriers and find success in their professional and personal lives.
Action for Blind People
Employment Success
Video by Action for Blind People showcasing a successful story of employment in the UK and the Access to Work scheme.
Iowa Department for the Blind
Vision Australia
Employment Services - Case Studies
Three case studies of individuals who are blind or partially sighted who've carved successful careers paths.
European Blind Union (EBU)
Vision in Enterprise
Information about the EBU's Vision in Enterprise project, which focuses on entrepreneurship for visually impaired people. A video, The Story of Yiota, a self-employed baker in Cypus is included.
LWL – Vocational Training Centre for the Visually Impaired
Successful at Work
Offers several examples of the rehabilitation and job placement of people with disabilities including blind and visually impaired people in Soest, Germany.
American Foundation for the Blind CareerConnect
These first-hand accounts from CareerConnect mentors are stories of how the mentors have successfully worked as individuals with vision impairment. There are also interviews with mentees who describe what they've learned from CareerConnect mentors.
Eyes on Success Podcasts
A series of weekly podcasts hosted by Peter and Nancy Torpey about products, services & daily living tips for the visually impaired; as well as, interviews with successfully employed adults who are blind or partially sighted.
National Industries for the Blind
The individuals profiled in these NIB video clips work in a variety of jobs from manufacturing to managerial throughout the United States.
Connecting Without Limits
The Journey to Light
It is the story of Dang Hoai Phuc, Director of Sao Mai Vocational and Assistive Technology Center for the Blind in Vietnam. Phuc has been working in assistive technology for the blind for 17 years.
San Francisco LightHouse for the Blind and Visually Impaired
Rehabilitation, Employment and Ambition
The San Francisco-based LightHouse offers a unique mix of living skills, literacy and employment readiness programs to prepare blind or newly blind individuals for a competitive work environment. They also award 3 individuals $25,000 each per year for an ambitious project of their choosing with The Holman Prize.
American Council of the Blind
BlindAbilitiy
A video created by the American Council of the Blind to highlight the abilities of blind individuals. Click here for a non-descriptive version of the video.
About Project Aspiro
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CNIB: Program Partner
Ontario Trillium Foundation: The Ontario Trillium Foundation is an agency of the Government of Ontario