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Scot Dorger with Dorger Associates
Welcome to podcast episode number 16 of the Mobile Alabama Business Podcast with Scot Dorger. My name is Marcus Neto. I Blue Fish, a digital marketing and web design based downtown on Dolphin Street in Mobile. I'm the host of Mobile Alabama Business Podcast where we talk to local entrepreneurs and business owners about their businesses and how they got started. I'd like to thank you for spending time with us today.
In today's show, I sit down with Scot Dorger. Scot is the owner and lead architect for Dorger Software Architects. They're a leading Microsoft Development shop here in Mobile and provide services to a wide range of clients. Scott and his family just so happened to also be my next door neighbors and our kids play together. But even after putting up with living next door to me, he still agreed to come on the podcast. So let's dive right in with Scott Dorger.
Marcus: Today I'm sitting down with my neighbor, Scot Dorger. Scot is the President of Dorger Software Architects, located here in Mobile. Welcome to our podcast, Scot.
Scot: Thank you for having me.
Marcus. So normally when we get started, we like to know a little bit about the person. Just give us some background information about who you are. So do you have family? Do you have kids? Did you go to school here in the area? Did you grow up here? That kind of thing.
Scot: Well, I'm married. My wife is an attorney here in town, Sarah Dorger; she works for Briskman Bunion. We have two kids, Colt and Caden; a boy and a girl, seven and five. I've been in Mobile since college. So we moved over here in '92. I was a military brat, so I've sort of lived all over. I have spent six years in Virginia. I had a stint in Hawaii. It happened to be in Biloxi, when we choose where I was going to go to college, which was (the University of) South Alabama.
Marcus: Oh, so you did go to South.
Scot: I did. I went to south. You know, and what happens, you meet a girl or you get locked down.
Marcus: Next thing you know you're living in Mobile.
Scot: And you know, it's not a bad thing.
Marcus: No, not at all.
Scot: We've lived all over. I like Mobile as much as any place. And I know you've lived in Northern Virginia, which you experienced a lot of growth. The pace of life here is just a little bit more relaxing.
Marcus: Absolutely.
Scot: My dad, he spent 10 years as the CEO of the Tournament of Roses and so that was kind of fun. The Rose Bowl. His last year was Alabama/Texas National Championships. So that was fun. Mind you, it would've been better if LSU was in the game.
Marcus: So we know where your alliance is and why.
Scot: Well that's where I went to law school. But still, it's been a lot of fun. I do -- we used to get to travel out there periodically, and again, every time I come back it's always "I'm glad to be back."
Marcus: Yeah, and breathe a sigh of relief when you get off the plane. Well, tell us about Dorger Software Architects. How long have you been in business? What's your unique position? Give us a little bit of background.
Scot: Well, we started about, actually just over four years ago. We do, we sort of started in custom software development. We're specialties in dot net. And we've got a nice client-base. We've got five big customers, and then we've go a number of smaller customers that we'll do a little jobs, some jobs for.
That business model of customer software development, sometimes it would be a project that we would take on soup to nuts, full thing. Sometimes we would do some staff augmentation where we worked alongside one of our customer's development teams just because they needed some additional help to make deadlines. We've served as the development company or the development group for another software company during this period of time. We're kind of transitioning a little bit more to selling product. I'd like to move that way. There are products that we've developed during the period of time that we've been doing the consulting stuff that's in our wheelhouse, if you will; database, case management for law firms and state governments. I'd like to separate the money that we have coming in from the hours that we work. Anytime you're doing project work, you always, if you want to take a vacation...
Marcus: Well, there's a cap. Literally, if you are basing your earnings on an hourly rate in the services industry, there's a cap on the amount of money that you can earn. And so, we've dealt with this a little bit on ourselves. And in the tech… well, we're both in the tech industry, but in the web development industry, everybody's trying to move to value pricing because the idea is that you're not just paying for the amount of time that it takes for something but you're also paying for all the education that we've paid for or you're paying for the thinking that we do off hours, you're paying for your creativity of being able to come up with ideas outside of that.
I'll admit, as an agency, we have not being able to kind of fully move down that path because there's still resistance I think in the customer base, like "What's the hourly rate on this?" Well, it's like it doesn't really matter. You asked us to do a job. As long as we get you the results that you're looking for and as long as you're earning more on the investment than what we're costing, because that's really the idea right.
Scot: Well, you know, we're even looking more at doing custom software as a service, if you will. We've got some frameworks and toolsets that would allow me to go into a business and say, "Hey, I'm going to put up a database system that's customized to what your business is. But now you're going to subscribe to it on a services basis. We're going to host it. We'll develop it for a very low entry cost. Something much cheaper than you would typically be able to get into if you were buying the software. We're going to host it on our servers in the cloud. We're going to hand the backup and maintenance at the database. The disaster recovery, it'd be web-based technologies. But it builds you a subscription. And if you get a number of those, then you start to have residual revenue. Now, you're not worrying about that next big project coming in. And we've been very fortunate and our income has been pretty predictable since we've started. And the approach that I've taken to grow the business, which was always "hey, I'm going to have work for somebody pretty much before I hire them, and that work is going to -- I know I'm going to have work for a year." Because what I don't want to do is ramp up and then have to ramp down.
Marcus: And with that cycle that long, it gives you a chance to either know whether that work is going to continue after the initial contract is over or to plan ahead and trying to find additional work that -- yeah. I get it. It's one of the things that I think a lot of people that deal with widgets don't understand is the up and down of the services industry. It just makes -- it makes it very interesting. I've been having a lot of talks lately with other agency owners about what metrics they use to gauge the health of their business. And it's very interesting to me that nobody has solved -- and here's my million dollar idea, right -- Nobody has solved that problem for agency owners. And especially agencies that don't have a team of people that do nothing but crunch numbers. Right? And so, we can talk about that over lunch, because I don't want to give too much information away about that.
So, how did you get started in technology? Do you have like an early experience that kind of pushed you in that realm?
Scot: Well, you know, I may date myself a little bit but I mean, we were doing basic programming on the Commodore 64, and 300 modems connecting to bulletin boards and stuff like that. So I mean I always like computers but I'm coin-driven, too. And when I was looking at choosing a career field that was something that I was interested in and wanted to do, I always like the concept of designing fighter planes. But at that time, the defense industry was going down. So Aeronautical Engineer didn't seem the way to go. And Computer Science was sort of up and coming...
Marcus: Because we're about the same age. When we graduated, there were teams of people from companies that most universities trying to get people to come and work for them in technology. I don't know if you had the same experience here at USA...
Scot: You know, I was pretty fortunate. I sort of stumbled into -- I had an internship at CPSI, which was great. And then right after -- right before I graduated, I ended up getting on with Televox Software. And I was there for four years, and that was a good experience. And really, as I look back on some of my business philosophies...
Marcus: You see how that was shaped?
Scot: Yeah, I can see how a lot of that was shaped by the folks that were running the company at that time. My perspective has changed to sum it now. I'm a business owner, too. But I mean, I've always been tech -- it was always computers. That was always where I was going to go. It was interesting really enough. My wife calls me a robot. So I guess I like the logic, the way I...
Marcus: That's just part of being a man, I think.
Scot: ...Could move through it.
Marcus: Our wives aren't listening to this podcast, so we can speak freely, I think.
Scot: But it's [only] me for text messages, she'll send me something and then I'll just be like, "Okay.". Send me something else. "Okay." I acknowledge it.
Marcus: It's confirmation receipt, right? So, is there an area of your business that you're putting a lot of effort into or are there any areas that you're spending a lot of time focusing on?
Scot: Right now we are investing more in this file, the government filing systems. We just stood up a system for the State of Mississippi that does all of their corporation filings. So if you want to form a business, form a LLC, file your annual report, merge your company, all of that stuff is now online with Mississippi. That was a system that we built on top of a system that they already had there. So they had a database management system already in place when we came in. Then we built this later that let them do all of this stuff on top of it.
And for a lack of a more creative term, we call that Dorger forms, okay? Because you're filling out a bunch of forms online. We did -- there's some pretty unique things that we did in this implementation. But again, we've got this layer, but right now, it's sitting on top of another system. And so I know, because I just came back from a conference, that there's a number of states that are going to RFP for systems like what we did in Mississippi. So we're putting some effort in building that underlying system right now. So that's my investment.
Marcus: As an investment in the company that going again back to that product idea that you'll be able to reuse that code. Yeah, I know that's really cool.
Scot: And we're doing something right now, too, that's very similar to the corporation system. We're doing a filing system for the State of Mississippi to allow them to do charities. We've built a system that we think is applicable across many states because it's all based on the URS, which is the Universal Registration Something-something.
Marcus: That's the technical term.
Scot: Yeah. It's just the form, you know, and a bunch of states have adopted, and we're building this based upon that form.
Marcus: So how difficult -- I mean, you said you know a number of states are going to go and have RFPs for that, and for those of you that are listening and they don't speak geek, RFP is Request For Proposal. So basically, when a state agency wants work done, they'll issue an RFP. Or a large business, they'll issue an RFP and then it's your job as the person wanting that business to jump through a bunch of hoops and provide them with the bunch of information in the hopes that they will award you the contract. But you mentioned that you have or you know that a lot of states are going to move in that direction, are there any -- is there anything that you have to do like it registered in those dates or something, or how does that work?
Scot: Most of the states have a procurement system now. Yes, we have to register with the states. Some of them require you to actually register as a foreign corporation in those states. Some of them don't. They just require to pay your annual fee with their state procurement system, and then they'll send out the notices.
So, you know, when I was at this conference there was a lady going around who was a retiring CIO for one of the Secretaries of State, and she's like "I'm going to each of the vendors and I want you to know that there's RFP coming out for a new filing system, and you need to be watching for that to come out." So when it will come out, we'll have to put some effort into responding to it. And then, the sales cycle begins, which is generally with state governments is reasonably slow.
Marcus: Yeah. I can imagine.
Scot: Unless they have money allocated and the RFP comes out, then it's okay. But a lot of times, you might demo to a state and their like "Oh, we love this software."
Marcus: And you don't hear anything for six months.
Scot: And they'd be like "We got to get in the budget." So then they go off and then they -- in the budget, you can't request it until the next budget cycle. A fiscal year later or two years later, you see an RFP that comes out. So a lot -- these things take a while.
Marcus: Wow. So as an entrepreneur, what's the one most important thing that you've learned over the years, or you've been doing this for four or five years and you've had quite a bit of experience, what's the take-home for you?
Scot: Don't be scared. I mean that's really my one take-away is I don't want to say it's easy because certainly it's not easy. And you spend a lot of time stressing about making payrolls, especially when you're first starting up because banks don't like to lend money to startup companies. Fortunately, we're beyond that now. My stress level's gone a way down. But, you know, I was very risk averse, and I was very comfortable working for other people. So, and really, I probably still would be had my hand not been a little forced. And stars aligned for me to go -- well, it's probably less risky for me to go out of my own at this point than it would be to stay where I was.
Marcus: Well, at least as an entrepreneur, as somebody who's calling the shots, you're the one who's calling the shots, right? So you can plan ahead and be smart about it, then oftentimes you can avert disaster, whereas you can't control somebody else's actions that may get you into a sticky spot.
Scot: That's true. But you do have to take risks. And I go back to look at the company that I was with prior to that ultimately ended up financially failing and then getting acquired. But I mean, there were risks that needed to be taken. And as an employee, I could say "Hey, you needed to take those risks." And the owners weren't willing to take those risks. And it sort of let them down the path to where it did.
Marcus: So is there a risk you've taken in the last six months?
Scot: Yes. I mean, I've taken risks and I've spent a lot of money on some things that have not actually panned out. But I've spent some money on things that have panned out and you got to do that sometimes.
Marcus: Yeah. It's interesting to me -- I mean, risks come in many different forms. It's hiring somebody. It's working on a pet project or investing in a platform that you've built out for one client in the hopes that you can parlay that in the other clients. There's a lot of different ways that that appears in an entrepreneurs life. And yeah, your words are kind of speaking to me today because that whole "Don't be afraid, move forward," you know, it's "Use the force, Marcus."
Scot: Well, I mean you've taken some risks. I mean, look at MobileAL.com.
Marcus: Yeah, absolutely.
Scot: I mean that was something you said "Here's an opportunity. I'm going to have to spend some money to do it." And now you're building it up. I mean, that's a risk. You've got an investment in it.
Marcus: Yeah. I know it's a very good point because oftentimes, these pet projects just, you know, they're like "Hey, let's do something fun. Let's do something creative for the business community." And then tens of thousands of dollars of man hours later. And it's like, wait a second, what did we do?
Scot: You know, I've got some of those going on right now where I'm putting my time in or somebody else's time to it. That I guess there's a financial cost to associate with it, but in some cases it's a lot more when you're actually putting money, you're actually writing checks for it.
Marcus: Yeah. It's a little bit more tangible. All right. Are there any books that you've read that have influenced you as a business owner?
Scot: I've got to say I don't have a chance to read many business books anymore. I still have some influence from Steven Covey and some of those books, specifically his "Principle Centered Leadership". I like his concepts. I never really quite got out of the book how to implement it, but -- and I know that I have a series of other books that my dad, as an operations guy, has given me. And I start reading them and they're just so dry.
Marcus: I have great aspirations of reading and I'm getting back into the habit. But what I found is for a period of time I would read the first, say, 50 pages or something and go, "Yup. Got it," and then just move on. So I would imagine you were the same.
Scot: We have the challenge too that we are always having to stay abreast of the technology. So I mean I have to understand all of the new things that are coming out that have some concept of it, and they're -- every year it's changing. And if you're trying to keep up with that, you're trying to run the business you've got pet projects, at some point ...
Marcus: Never mind the wife and kids, right? (laugh)
Scot: Yes. You've got to spend some time with them, too.
Marcus: What other resources -- because I know books may not be something that you have time to sit down and digest, are there any other resources that you found that are helpful to you as either a technologist or a business owner?
Scot: The best resource that we had getting started was a program by Microsoft called The BizSpark. And essentially, what they do for The BizSpark is they give you access to all of their software, all of their development tools for a period of three years. It's a free program. You have to have a certain -- less than a certain number of employees, less than a certain amount of revenue to qualify. You could only have been in business, I mean, less than three years. But that was a very good program because it gave us access to a lot of stuff that I would have had it if to come up with money for otherwise.
Now, we're a Microsoft partner. So we have our -- my software developers all maintain Microsoft certifications. I have to go get client -- certain number of client referrals every year, and then I, of course, have to pay a fee to be a partner. But we have similar benefits to The Biz Spark program now. But that partner program has been a good resource for us.
You know we're members of the Chamber and I don't nearly do what I should with the Chamber, as far as taking advantage to some stuff. I know that they have a program with the Chamber where they have a business of the month, that one of these days I'll probably take advantage of.
Marcus: We need to team up then and go -- you can be my wingman at the next Business After Hours or something like that, too, because ...
Scot: Yeah. I went to the last Gulf Coast Technology mixer that they had and made some good contacts there.
Marcus: Very good. So I find that many business owners are really focused on their business but they also have hobbies that allow them to stay balanced. And I know you well enough to know that you have some of those hobbies. So what do you like to do in your free time?
Scot: First, I think, it's very important for business owners to try to maintain a work-life balance. And one of the things that I had sort of made myself a promise when we went off and did this was that I was going to participate in my kids' activities, and I was going to be there for both of my kids. So, you know, I've coached a lot of my son's and my daughter's sports teams. I happened to really enjoy doing cross fit right now, and swimming or those. But if I'm not doing, I used to like to play video games, and I still do, but right now, my video game choices are relatively slim because I end up by just playing with my kids.
Marcus: Yeah. And my boys benefit from your addiction to video games, I think, because ...
Scot: I can only take so much Mind Craft into area though and I just find in the other time is difficult.
Marcus: That's too funny. So give us a look on your -- at an average day, what does that look like for you? Do you get up at a certain time? Do you start by reading? Or do you have coffee? Or do you just get up and go? I know you have young kids, so oftentimes I can imagine, you just probably get up, get them dressed, get them to school, and then, you know, somehow figure out how to get to work. But what is an average day look like for you?
Scot: Well, obviously, it depends whether we're talking about the summertime or whether it's fall. But when school's in play, my wife likes to get up early and have coffee by herself and a reader. So her alarm goes off and I'll toss and turn for 30 minutes before I decide to get up. But once I get up and either wake up the kids or go down and prepare meals, she likes to drive them to school so unless there's some conflict where she's going to be downtown early, she'll take them.
I usually grab my Red Bull and have my drive now from the Eastern Shore over, you know, probably 7:30 to 8:00 o'clock. Sometimes, depending on what I'm thinking about, I'll either use that time to focus on what I'm going to do in that day or I'll make some phone calls. I've got an employee in New Jersey, so she is on a different time zone; sometimes I call and talk to her early and see what she's got planning for the day. I've got another employee in Pensacola. Same sort of thing, I'm not going to see him in the office, so sometimes I'll get started by talking to him. You know, I typically get into the office by between 8:30 and 9:00. I typically don't take a lunch. I work through lunch and then I end up leaving a little bit before 4:00, to end up, primarily, missing traffic. Because if you wait much longer, especially in the summertime, you're caught in it.
Marcus: That tunnel just backs up like crazy.
Scot: But, you know, and then I'll get over and I'll do cross fit at about 4:30, and then deal with my kids' activities.
Marcus: Yeah, which start up at about 5:00?
Scot: That's right. Well you know, you've got to be at the ball field at 5:30, or swim meets right now -- we're in swim meets season, so swim meets were at Tuesdays. We got to be there by 5:00.
Marcus: That's cool. I love watching -- we are literally neighbors. I wasn't using the euphemism when I said that in the intro. And so, I love watching our kids in the backyard playing baseball together and throwing the ball. You know, they make up this weird games that only kids can -- like they were playing the other day where it was like they were playing baseball, but there were allowed to like throw the ball at the person. And they were wiffle balls but they are allowed to throw the ball at the person to get them out because they don't have enough people to actually fill the team.
And tell us where people can find you.
Scot: My website is dorgersoft.com. My email is scot@dorgersoft.com. Phone numbers are on the website, but 251-281-2001 is our main line. And you can also go to info@dorgersoft.com and that it'll go to a shared mailbox. Somebody would get back with it.
Marcus: Awesome. Well, I want to thank you again for coming on the podcast. And to wrap up, any final thoughts or comments you'd like to share?
Scot: No, I'm good. This was fun.
Marcus: Awesome. Well, I appreciate your willingness to sit with me and share your journey as a business owner and entrepreneur, and it was great talking with you.
Scot: Thank you.
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text:
\section{Introduction}

\label{s1}

 Two-phase or multi-phase flows are concerned with  flows with two or more components and have a wide range of applications in nature, engineering, and biomedicine.
 Examples include sediment transport, geysers, volcanic eruptions, clouds, rain in natural and climate system;
 mixture of oil and natural gas in extraction tubes of oil exploitation, oil transportation, steam generators, cooling systems, mixture of hot water and vapor of water in cooling tubes of nuclear power stations in energy production; bubble columns,  aeration systems, tumor biology, anticancer therapies, developmental biology,  plant physiology in  chemical engineering, medical and genetic engineering, bioengineering, and so on. Multi-phase flow  is much more complicated than  single-phase flow due to the existence of a moving and deformable interface and its interactions with multi-phases \cite{Brennen05,Ishii06,Kolev05,Kolev05-2}.

 In this paper, we consider two models of a compressible inviscid isentropic two-fluid flow.  The first one describes the liquid-gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and particles. We now present corresponding systems of equations and review main existing results related to them.

\subsection{Inviscid liquid-gas two-phase flow}
We first consider the equations of the compressible inviscid liquid-gas two-phase isentropic flow:
\begin{equation}\label{1}
\left\{
\begin{array}{l}
 \partial_tm  +{\rm div}\, (m u )=0,\\[6pt]
  \partial_tn  +{\rm div}\, (n u )=0,\\[6pt]
 \partial_t(n u ) +{\rm div}\,(nu\otimes u ) + {\nabla}P=0,
\end{array}
\right.
\end{equation}
where $m=\alpha_g\rho_g$ and $n=\alpha_l\rho_l$ are the gas mass and the liquid mass respectively, the non-negative functions $\alpha_g$  and $\alpha_l$ satisfying the condition  $\alpha_g+\alpha_l=1$ denote the gas and liquid volume fractions respectively,    $\rho_g$ and $\rho_l$ are the gas and liquid densities,  $u$ denotes the mixed velocity of the liquid and the gas, and $P$ is the common pressure for both
phases.

In fact, the model \eqref{1} is a simplified version of the following general two-phase flow model:
\begin{equation*}
\left\{
\begin{array}{l}
\partial_tm+{\rm div}\,  (m u_g)=0,\\[3mm]
\partial_tn+{\rm div}\,  (n u_l)=0,\\[3mm]
\partial_t(m u_g+n u_l)+{\rm div}\,  (m u_g\otimes u_g+n u_l\otimes u_l)+\nabla P(m,n)=0,
\end{array}\right.
\end{equation*}
where $m$ and $n$ denote the same as above, and  $u_g$ and $u_l$ denote the gas and liquid velocities respectively. Just as in many papers concerned with viscous liquid-gas two-phase flow, in order to help further understanding the behavior of a solution to the
general model,  we use two densities and only one fluid velocity to study the simplified two-phase flow model, i.e., we restrict ourselves to a flow regime where the liquid and gas velocities can be assumed to be equal: $u_g=u_l=u$. Since the liquid phase is much heavier than the gas phase, we also neglect the gas phase in the mixture momentum equations.

In general, the pressure law $P=P(m,n)$ is a nonlinear complicated function of the densities. We will follow the simplification made in \cite{Evje08,Evje11SIAMJMA} which guarantees that the model is thermo-mechanically consistent in the sense that one can get a basic energy estimate easily. We assume that the pressure $P$ is  a smooth function of $(m, n)$ defined on $(0,+\infty)\times(0,+\infty)$.
As mentioned in \cite{Evje08,Evje11SIAMJMA}, depending on the realistic physical background, three typically different kinds of pressure law are respectively expressed as follows.

The first one has the simple form
\begin{equation}
P(m,n)= (\gamma -1) (m+n)^{\gamma},
\label{2}
\end{equation}
with $\gamma >1$ being a constant. Another one is
\begin{equation}
P(m,n)=C\left(\frac{m}{\rho_l-n}\right)^\gamma ,
\label{es2}
\end{equation}
with constants $C>0$ and $\gamma>1$, and the liquid density $\rho_l= {\rm const}$. The third one is taken in a little bit more complex form
\begin{equation}
P(m,n)=C\left(-b(m,n)+\sqrt{b(m,n)^2+c(m,n)}\right),
\label{es3}
\end{equation}
where $C=a_l^2/2$ and $k_0=\rho_0-({p_0}/{a_l^2})$ are positive constants,
$$
\begin{array}{l}
\displaystyle b(m,n)=k_0-n-\left(\frac{a_g}{a_l}\right)^2m=k_0-n-a_0m,\\[3mm]
\displaystyle c(m,n)=4k_0\left(\frac{a_g}{a_l}\right)^2m=4k_0a_0m,
\end{array}
$$
the constants $a_g$ and $a_l$ are reference sonic speeds in gas and liquid respectively, and the constants $p_0$ and $\rho_0$ are reference pressure and density.

Viscous two-phase flows have been investigated extensively, in particular, the existence, uniqueness, regularity,
asymptotic behavior, decay rate estimates,  and blow-up phenomena of solutions for various one-dimensional and
multi-dimensional viscous two-phase flows have been studied recently. We remark that the exhaustive literature list is beyond the
scope of the paper, and here we just mention some related results in \cite{Du15,Hao12,Wang16,Wen12,YaoL10,YaoL11JDE} (see also references therein) for the multi-dimensional viscous two-phase flow model (the viscous counterpart of system \eqref{1}). The theory of the inviscid two-phase flow \eqref{1} is comparatively mathematically underdeveloped although there have been some numerical studies;  see
\cite{Baudin05,Baudin05-2,Brennen05,Evje07} and references therein.

\subsection{Inviscid bi-fluid and fluid-particle flows}
We now consider another model of the compressible inviscid isentropic two-fluid flow:
\begin{equation}\label{3}
\left\{
\begin{array}{l}
 \partial_tm  +{\rm div}\, (m u )=0,\\[6pt]
  \partial_tn  +{\rm div}\, (nu )=0,\\[6pt]
 \partial_t((m +n) u ) +{\rm div}\,((m +n)u\otimes u ) +{\nabla}P=0,
\end{array}
\right.
\end{equation}
where $m$ and $n$ are the densities of two fluids and $u$ stands for the velocity of bi-fluid. The pressure $P=P(m,n)$ depending on two densities (possibly in a complicated way) is considered in the following form:
\begin{equation}
P=P(m,n)= m^{\alpha} +An^{\gamma}
\label{4}
\end{equation}
with three constants $\alpha \geq 1$, $\gamma \geq 1$ and $A>0$. System \eqref{3} is the inviscid version of a ``simple'' but still realistic bi-fluid model derived from physical considerations in \cite{Ishii06} (see also \cite{Bresch18}).

The viscous version of system \eqref{3} has been investigated extensively. In fact, if $\alpha =1$, $\gamma >1$ and $A=1$, by the asymptotic analysis of a system of coupled kinetic and fluid equations, namely, the Vlasov-Fokker-Planck equation and the compressible Navier-Stokes equations, the authors of \cite{Mellet07,Mellet08} proved the singular limit convergence towards the viscous version of  \eqref{3}.
This kind of model is widely used in the modeling of fluid-particle interactions (see, e.g., \cite{Laurent04}). In this case, its inviscid version \eqref{3} is a two-phase macroscopic model describing the motion of the mixture of fluid and particles, where $n$ is the density of the fluid and $m$ is the density of particles in the mixture. The derivation of the corresponding viscous two-phase macroscopic model from the Vlasov-Fokker-Planck equation and the compressible Navier-Stokes equations was first addressed by Carrillo and Goudon in \cite{Carrillo06}. Recently the existence of a weak solution to the viscous two-phase macroscopic model was proved in \cite{Novotny18,Vasseur17}. At the same time, according to our knowledge, there were almost no mathematical studies of the inviscid equations \eqref{3}.

For the above two models \eqref{1} and \eqref{3} of a compressible inviscid isentropic two-fluid flow, by introducing an entropy-like function, we reduce the equations of both models to a symmetric form which looks like the compressible Euler equations written in the nonconservative form in terms of the pressure, the velocity and the entropy. Basing on existing results for the Euler equations, this gives a number of instant results for both models. In particular, we conclude that all compressive shock waves in these models exist locally in time. For the 2D case, we make the conclusion about the local-in-time existence of vortex sheets under a ``supersonic'' stability condition. In the sense of a much lower regularity requirement for the initial data, our result for 2D vortex sheets essentially improves the recent result in \cite{HWY} for vortex sheets in the liquid-gas two-phase flow.

\section{Elementary symmetrization of two-fluid flow equations}

\label{s2}

Let us first consider system \eqref{1}. As in \cite{RWWZ}, we assume that
\begin{equation}
m >0\quad\mbox{and}\quad n > 0.
\label{4''}
\end{equation}
Our crucial idea is really very simple: we introduce the entropy-like function
\[
S=\frac{m}{n}> 0.
\]
It indeed plays the role of entropy and we will call it the ``entropy'' because, as for the usual entropy, we get the equation
\[
\frac{{\rm d} S}{{\rm d}t}=0
\]
with ${\rm d} /{\rm d} t =\partial_t+({u} \cdot{\nabla} )$, following from the first two equations of system \eqref{1}. Moreover, we can equivalently rewrite the first two equations of  \eqref{1} as
\begin{equation}
\frac{1}{\rho}\,\frac{{\rm d} \rho}{{\rm d}t} +{\rm div}\,u =0,\quad \frac{{\rm d} S}{{\rm d}t}=0,
\label{5}
\end{equation}
where for further convenience we use the notation $\rho :=n$.

We now recalculate the pressure $P$ in terms of $R$ and $S$. For the pressure law \eqref{2} we have
\begin{equation}
P=P(\rho ,S)= (\gamma -1) \rho^{\gamma} (S+1)^{\gamma}.
\label{8'}
\end{equation}
For the equation of state \eqref{es2} we obtain
\begin{equation}
P(\rho ,S)=C\left(\frac{\rho S}{\rho_l-\rho}\right)^\gamma ,
\label{8/2}
\end{equation}
whereas we rewrite \eqref{es3} as
\begin{equation}
P(\rho ,S)=C\left(-b(\rho ,S)+\sqrt{b(\rho ,S)^2+4k_0a_0\rho S}\right),
\label{8/3}
\end{equation}
where $b(\rho ,S):= k_0-\rho-a_0\rho S$.

In view of \eqref{5}, we obtain
\begin{equation}
\frac{{\rm d} \rho}{{\rm d}t}= \frac{1}{P_{\rho}}\,\frac{{\rm d} P}{{\rm d}t}.
\label{6}
\end{equation}
Then, taking into account \eqref{5} and \eqref{6}, we easily symmetrize the system of conservation laws \eqref{1} by rewriting it in the nonconservative form
\begin{equation}
\frac{1}{\rho P_{\rho}}\,\frac{{\rm d} P}{{\rm d}t} +{\rm div}\,{u} =0,\quad
\rho\, \frac{{\rm d}u}{{\rm d}t}+{\nabla}P  =0 ,\quad \frac{{\rm d} S}{{\rm d} t} =0.
\label{8}
\end{equation}
Equations \eqref{8} have absolutely the same form as the compressible Euler equations written in the nonconservative form. Writing down \eqref{8} in a matrix form, we get the symmetric system
\begin{equation}
A_0(U )\partial_tU+\sum_{j=1}^3A_j(U )\partial_jU=0,
\label{9}
\end{equation}
which is {\it hyperbolic} if $A_0>0$, where
\[
U= (P,u,S),\quad A_0= {\rm diag} (1/(\rho P_{\rho}) ,\rho ,\rho, \rho,1),
\]
\[
A_1=\left( \begin{array}{ccccc} \frac{u_1}{\rho P_{\rho}}&1&0&0&0\\[3pt]
1&\rho u_1&0&0&0\\
0&0&\rho u_1&0&0\\ 0&0&0&\rho u_1&0\\
0&0&0&0&u_1\\
\end{array} \right) ,\quad
A_2=\left( \begin{array}{ccccc} \frac{u_2}{\rho P_{\rho}}&0&1&0&0\\[3pt]
0&\rho u_2&0&0&0\\
1&0&\rho u_2&0&0\\ 0&0&0&\rho u_2&0\\
0&0&0&0&u_2\\
\end{array} \right),
\]
\[
A_3=\left( \begin{array}{ccccc} \frac{u_3}{\rho P_{\rho}}&0&0&1&0\\[3pt]
0&\rho u_3&0&0&0\\
0&0&\rho u_3&0&0\\ 1&0&0&\rho u_3&0\\
0&0&0&0&u_3\\
\end{array} \right).
\]

For the pressure law \eqref{2}, $P_{\rho}=\gamma P/\rho$ and, hence, the hyperbolicity condition $A_0>0$ holds under assumptions \eqref{4''}. For the pressure law \eqref{es2}, we have
\begin{equation}
P_{\rho}=\frac{\gamma\rho_l C(\rho S)^{\gamma -1}}{(\rho_l -\rho )^{\gamma +1}},
\label{7/2}
\end{equation}
whereas for the equation of state \eqref{es3} we calculate:
\begin{equation}
P_{\rho}= C\left( 1+ a_0S+\frac{\rho (a_0S+1)^2+k_0(a_0S-1)}{\sqrt{b(\rho ,S)^2+4k_0a_0\rho S}}\right).
\label{7/3}
\end{equation}
One can see that under assumptions \eqref{4''} we have $P_{\rho} >0$ in \eqref{7/2} and \eqref{7/3} (we omit simple calculations for \eqref{7/3}). That is, system \eqref{9} is again hyperbolic.

The elementary symmetrization of conservations laws \eqref{1} giving the quasilinear symmetric hyperbolic system \eqref{8}/\eqref{9}, which looks like the symmetric system of the compressible Euler equations, implies a number of results {\it almost for nothing}. For example, we have the local-in-time existence and uniqueness theorem \cite{Kato,VKh} in Sobolev spaces $H^s$ for the Cauchy problem for system \eqref{8}, with $s\geq 3$.

We now consider system \eqref{3}. Let
\begin{equation}
m \geq 0\quad\mbox{and} \quad n >0.
\label{4'}
\end{equation}
We again introduce the ``entropy'' $S=m/n\geq 0$. Introducing also the total density
\[
\rho =m +n >0,
\]
it is easy to see that the first two equations of \eqref{3} are equivalently rewritten as \eqref{5}. Clearly, we again have \eqref{6} with
\begin{equation}
P=P(\rho ,S) =\left( \frac{\rho S}{S+1}\right)^{\alpha} + A\left( \frac{\rho}{S+1}\right)^{\gamma}
\label{eqst}
\end{equation}
and
\begin{equation}
P_{\rho}=\frac{\partial P(\rho ,S)}{\partial \rho}=\frac{\alpha}{\rho}\left( \frac{\rho S}{S+1}\right)^{\alpha} +
\frac{\gamma A}{\rho}\left( \frac{\rho}{S+1}\right)^{\gamma} .
\label{7}
\end{equation}
That is, system \eqref{3} is also equivalently written as the symmetric hyperbolic system \eqref{8}/\eqref{9} (under the hyperbolicity condition \eqref{4'}).

In the next sections, using the symmetric form \eqref{8} of equations \eqref{1} and \eqref{3} and basing on existing results for the Euler equations, we get local-in-time existence results for shock waves and vortex sheets in two-fluid models \eqref{1} and \eqref{3}. We leave for the reader to find another important results taking place for the compressible Euler equations which could be directly (or almost directly) carried over models  \eqref{1} and \eqref{3} by making use of our simple idea of the introduction of the entropy-like function $S=m/n$.

\section{Shock waves}
\label{s3}

We consider system \eqref{1} for $t\in [0,T]$ in the unbounded space domain $\mathbb{R}^3$ and suppose that $\Gamma (t)=\{ x_1-\varphi (t,x')=0\}$ is a smooth hypersurface in $[0,T]\times\mathbb{R}^3$, where
$x'=(x_2,x_3)$ are tangential coordinates. We assume that $\Gamma (t)$ is a surface of strong discontinuity for the conservation laws \eqref{1}, i.e., we are interested in solutions of \eqref{1} that are smooth on either side of $\Gamma (t)$. To be weak solutions of (\ref{1}) such piecewise smooth solutions should satisfy the Rankine-Hugoniot jump conditions
\begin{equation}
[\mathfrak{j}_0]=0,\quad[\mathfrak{j}]=0,\quad \mathfrak{j}\left[u_{N}\right] +
|N|^2[P]=0,\quad \mathfrak{j}[{u}_{\tau}]=0
\label{16}
\end{equation}
at each point of $\Gamma$, where $[g]=g^+|_{\Gamma}-g^-|_{\Gamma}$ denotes the jump of $g$, with $g^{\pm}:=g$ in the domains
\[
\Omega^{\pm}(t)=\{\pm (x_1- \varphi (t,x'))>0\},
\]
and
\[
\mathfrak{j}_0^{\pm}=m (u_{N}^{\pm}-\partial_t\varphi),\quad \mathfrak{j}^{\pm}=n (u_{N}^{\pm}-\partial_t\varphi),\quad u_{N}^{\pm}=({u}^{\pm} {\cdot}{N}),\quad {u}^{\pm}_{\tau}=(u^{\pm}_{\tau _1},u^{\pm}_{\tau _2}),\quad
u^{\pm}_{\tau _i}=({u}^{\pm} {\cdot}{\tau}_i),
\]
\[
{N}=(1,-\partial_2\varphi,-\partial_3\varphi ),\quad
{\tau}_1=(\partial_2\varphi,1,0),\quad {\tau}_2=(\partial_3\varphi,0,1),\quad  \mathfrak{j}:=\mathfrak{j}^{\pm}|_{\Gamma},\quad
\mathfrak{j}_0:=\mathfrak{j}_0^{\pm}|_{\Gamma}.
\]

We now consider shock waves. For them there is a nonzero mass transfer flux across the discontinuity surface: $u_{N}^{\pm}|_{\Gamma}\neq 0$, i.e., $\mathfrak{j}\neq 0$ (as well as $j_0\neq 0$ and $j_0+j\neq 0$). Then, the first two conditions in \eqref{16} imply
\begin{equation}
[S]=0.
\label{17}
\end{equation}
Recalling our notation $\rho :=n$, by virtue of \eqref{16}, \eqref{17}, we get the following jump conditions for shock waves:
\begin{equation}
[S]=0,\quad[\mathfrak{j}]=0,\quad \mathfrak{j}\left[u_{N}\right] +
|N|^2[P(\rho ,S)]=0,\quad [{u}_{\tau}]=0,
\label{16'}
\end{equation}
where $\mathfrak{j}^{\pm}=\rho (u_{N}^{\pm}-\partial_t\varphi)$. Since the ``entropy'' $S$ is continuous, for a fixed $S$  and without the first condition system \eqref{16'} coincides with the Rankine-Hugoniot conditions for {\it isentropic} Euler equations with the equation of state $P=P(\rho ):=P(\rho ,S)|_{S\equiv{\rm const}}$.

According to the results in \cite{M1,M2,Met} and their extension to hyperbolic symmetrizable systems with characteristics of variable multiplicities \cite{Kwon,MZ}, all uniformly stable shocks are structurally stable. Roughly speaking (we do not discuss regularity, compatibility conditions, etc.), this means that if the uniform Lopatinski condition holds at each point of the initial shock, then this shock exists locally in time. In other words, as soon as planar shock waves are uniformly stable according to the linear analysis with constant coefficients, we can make the conclusion about structural stability of corresponding nonplanar shocks. In this sense, the linear analysis with constant coefficients plays crucial role for shock waves.

The free boundary problem for shock waves is the problem for the systems
\begin{equation}
A_0(U^{\pm})\partial_tU^{\pm}+\sum_{j=1}^3A_j(U^{\pm} )\partial_jU^{\pm}=0\quad \mbox{in}\ \Omega^{\pm}(t)
\label{21}
\end{equation}
(cf. \eqref{9}) with the boundary conditions \eqref{16'} on $\Gamma (t)$ and corresponding initial data for $U^{\pm}$ and $\varphi$ at $t=0$. We can reduce this problem to that in the fixed domains $\mathbb{R}^3_{\pm}=\{\pm x_1>0,\quad x'\in\mathbb{R}^2\}$ by the simple change of variables $\tilde{x}_1=x_1-\varphi (t,x')$, $\tilde{x}'=x'$. Dropping tildes, we get a nonlinear initial boundary problem in the half-spaces $\mathbb{R}^3_{\pm}$ with the boundary conditions \eqref{16'} at $x_1=0$. Without loss of generality we can consider the unperturbed shock wave with the equation $x_1=0$. Then, the linearization of the nonlinear initial boundary value problem about its constant solution, with $\widehat{U}^{\pm}=(\widehat{P}^{\pm},\hat{u}^{\pm},\widehat{S}^{\pm})={\rm const}$ and $\hat{\varphi} =0$, gives a linear constant coefficients problem. For the perturbation of the ``entropy'' (we again denote it by $S$) we obtain the separate problem (cf. \eqref{8}, \eqref{17})
\begin{equation}
\partial_tS^{\pm} +(\hat{u}^{\pm}\cdot S) =f^{\pm}\quad \mbox{for}\ x\in\mathbb{R}_3^{\pm},\qquad [S]=g \quad \mbox{at}\ x_1=0,
\label{S}
\end{equation}
where, as usual, we introduce artificial source terms (for the above equations they are $f^{\pm}(t,x)$ and $g(t,x')$) to make the linear problem inhomogeneous.

For problem \eqref{S} we easily deduce the energy identity
\begin{equation}
I(t)-\int\limits_0^t\int\limits_{\mathbb{R}^2}
\left.\left( [\hat{u_1}](S^-)^2 +2\hat{u}^+_1S^-g+\hat{u}^+_1g^2 \right)\right|_{x_1=0}\,{\rm d}x'{\rm d}s=I(0)+2\sum_{\pm}\int\limits_0^t\int\limits_{\mathbb{R}^3_{\pm}}f^{\pm}S^{\pm}{\rm d}x{\rm d}s,
\label{27}
\end{equation}
where
\[
[\hat{u}_1]=\hat{u}_1^+-\hat{u}_1^-\quad\mbox{and}\quad
I(t)=\sum_{\pm}\|{S}^{\pm}(t)\|^2_{L^2(\mathbb{R}^3_{\pm})}.
\]
For {\it compressive} shocks ($[\rho ]>0$), it follows from $[\mathfrak{j}]=0$ that $[u_N]<0$. That is, for the unperturbed planar compressive shock we have $[\hat{u}_1]<0$. Then, for compressive shocks, by standard simple arguments, from \eqref{27} we get the a priori estimate without loss of derivatives
\[
\begin{split}
\sum_{\pm}\Big(\|{S}^{\pm}\|_{L^2([0,T]\times\mathbb{R}^3_{\pm})}+ & \|S^{\pm}_{|x_1=0}\|_{L^2([0,T]\times\mathbb{R}^2)}\Big) \\  & \leq C\left\{ \sum_{\pm}\left(\|{S}^{\pm}_{|t=0}\|_{L^2(\mathbb{R}^3_{\pm})}
+\|f^{\pm}\|_{L^2([0,T]\times\mathbb{R}^3_{\pm})}\right) +\|g\|_{L^2([0,T]\times\mathbb{R}^2)}\right\},
\end{split}
\]
where $C>0$ is a constant.

Having in hand the above a priori estimate, we can say that the linearized problem satisfies the uniform Lopatinski condition as soon as its subproblem for the perturbations of $P^{\pm}$ and $u^{\pm}$ does. This subproblem totally coincides with the linearized constant coefficients problem for shock waves in compressible isentropic gas dynamics. Moreover, for the pressure law \eqref{2}  we have the polytropic gas equation of state (cf. \eqref{8'})
\[
{P}(\rho )=c{\rho}^{\gamma},
\]
for the unperturbed constant solution, where $c=(\gamma -1)({S}+1))^{\gamma}>0$ is a constant for a fixed $S=\widehat{S}^{+}=\widehat{S}^-$ (recall that $[\widehat{S}]=0$). It was shown by Majda \cite{M1} that all isentropic {\it compressive} shock waves in a polytropic gas are uniformly stable. Their local-in-time existence was proved in \cite{M2} (see also \cite{Met} for some improvements of the results in \cite{M2}). Basing on these results, we can thus make the conclusion that all compressive shock waves in the compressible inviscid liquid-gas two-phase isentropic flow are structurally stable (for the pressure law \eqref{2}).

For a fixed constant $S=\widehat{S}^{+}=\widehat{S}^-$, the equation of state \eqref{8/2} reads
\[
P(\rho )=c\left(\frac{\rho }{\rho_l-\rho}\right)^\gamma ,
\]
where the constant $c =CS^{\gamma}>0$. The above equation of state $P(\rho )$ is a convex function. The result in \cite{M1} was obtained not only for the polytropic gas equation of state but also for a general case satisfying a stability condition and the subsonic requirement behind of the shock. In particular, according to this result, all isentropic {\it compressive} shock waves are uniformly stable provided that the equation of state is convex. Hence, we conclude that for the pressure law \eqref{es2} all compressive shock waves for model \eqref{1} are structurally stable. In fact, the same is true for the pressure law \eqref{es3} because the equation of state \eqref{8/3} is a convex function of $\rho$ (we omit simple calculations).

For the two-fluid model \eqref{3}, the Rankine-Hugoniot conditions read:
\begin{equation}
[\mathfrak{j}_1]=0,\quad[\mathfrak{j}_2]=0,\quad \mathfrak{j}\left[u_{N}\right] +|N|^2[P]=0,\quad \mathfrak{j}[{u}_{\tau}]=0,
\label{16.2}
\end{equation}
where
\[
\mathfrak{j}_1^{\pm}=m (u_{N}^{\pm}-\partial_t\varphi),\quad \mathfrak{j}_2^{\pm}=n (u_{N}^{\pm}-\partial_t\varphi),\quad
\mathfrak{j}^{\pm}=\rho^{\pm} (u_{N}^{\pm}-\partial_t\varphi),\quad \mathfrak{j}:=\mathfrak{j}^{\pm}|_{\Gamma},
\]
and we recall that $\rho =m+n$ is the total density. For shock waves ($\mathfrak{j}\neq 0$), we again have the ``entropy'' continuity \eqref{17}. The jump conditions \eqref{16.2} can be then equivalently rewritten as \eqref{16'}. Repeating the above arguments made for model \eqref{1}, we reduce the question about structural stability of shock waves for equations \eqref{3} to that for shock waves for the compressible isentropic Euler equations with the equation of state (cf. \eqref{eqst})
\[
{P}({\rho})=c_1{\rho}^{\alpha}+ c_2{\rho}^{\gamma},
\]
for the unperturbed constant solution, where $c_1=({S}/({S}+1))^{\alpha}\geq 0$ and $c_2=A(1/({S}+1))^{\gamma}>0$ are constants for a fixed $S=\widehat{S}^{+}=\widehat{S}^-$. The above equation of state $P(\rho )$ is a convex function (for $\alpha\geq 1$ and $\gamma >1$). That is, we can conclude that all compressive shock waves for the two-fluid model \eqref{3} are structurally stable.

\section{Vortex sheets}
\label{s4}

For vortex sheets there is no mass transfer flux across the discontinuity surface: $u_N^{\pm}|_{\Gamma}=\partial_t\varphi$. For this case,
both the Rankine-Hugoniot jump conditions \eqref{16} and \eqref{16.2} (for models \eqref{1} and \eqref{3} respectively) imply the boundary conditions
\begin{equation}
\partial_t\varphi = u_N^{\pm},\quad [P]=0,
\label{vs}
\end{equation}
which are the same as that for vortex sheets in gas dynamics (full or isentropic).

For model \eqref{1}, the free boundary value problem for vortex sheets is the problem for \eqref{8} in the domains $\Omega^{\pm}(t)$ with the boundary conditions \eqref{vs} and initial data for $U^{\pm}$ and $\varphi$. This free boundary problem totally coincides with that for vortex sheets for the nonisentropic Euler equations studied in \cite{MoTre,MoTreWang}. Note that in \cite{MoTre,MoTreWang} the Euler equations are written in form \eqref{8} for the polytropic gas equation of state (for which $\rho P_{\rho}=\gamma P$). Recall that for the equation of state \eqref{8'} we also have $\rho P_{\rho}=\gamma P$. Even formally, by introducing the ``entropy'' function $s=\ln (S+1)$, we can reduce \eqref{8'} to the polytropic gas equation of state $p=p(\rho , s)= A\rho^{\gamma}e^{s}$, with $A=\gamma -1$ (clearly, the last equation in \eqref{8} stays valid for $s=\ln (S+1)$). On the other hand, the fact that vortex sheets were formally considered in  \cite{MoTre,MoTreWang} for the polytropic gas equation of state is absolutely unessential because the results in \cite{MoTre,MoTreWang} stay valid for a general equation of state (as for 2D vortex sheets for the isentropic Euler equations whose linear and structural stability was proved in \cite{CS1,CS2} under the ``supersonic'' condition).

That is, the linear and nonlinear (structural) stability results obtained in \cite{MoTre,MoTreWang} for 2D vortex sheets can be {\it directly} carried over 2D vortex sheets for equations \eqref{1}. Referring to \cite{MoTreWang}, we conclude that a vortex sheet $x_1=\varphi (t,x_2)$ for the 2D case of \eqref{1} (with $x=(x_1,x_2)$ and $u=(u_1,u_2)$) is structurally stable under the ``supersonic'' condition
\begin{equation}
[u_2] > \big( c_+^{\frac{2}{3}}+ c_-^{\frac{2}{3}}\big)^{\frac{3}{2}},\quad [u_2]\neq \sqrt{2}\,(c_+ +c_-),
\label{supson}
\end{equation}
where $c_{\pm}= c(\rho^{\pm} ,s^{\pm})$ and $c=c(\rho ,s)=\sqrt{P_{\rho}}=\sqrt{\gamma P/\rho}$ (note that the second condition in \eqref{supson} is not physical and appeared in \cite{MoTre} and \cite{RWWZ} due to a requirement of the applied technique). The existence theorem in \cite{MoTreWang} was proved for a finite (not necessarily short) time but under the condition that the initial discontinuity is close to a rectilinear discontinuity corresponding to a constant background solution $\widehat{U}^{\pm}=(\widehat{P}^{\pm},0,\hat{u}_2^{\pm},s^{\pm})$, $\hat{\varphi}=0$, provided that this solution satisfies the ``supersonic'' condition \eqref{supson} (see \cite{MoTreWang} for the whole details: exact assumptions on the initial data, regularity of solutions, etc.). Clearly, instead of the assumption that the initial data are
close to a piecewise constant solution in the existence theorem we could assume that the time of existence is sufficiently short (see, e.g., such a local-in-time existence theorem for current-vortex sheets \cite{T09}).

We can rewrite the speeds $c_{\pm}$ in \eqref{supson} in terms of the original unknowns $m$ and $n$:
\[
c_{\pm}=c(m^{\pm},n^{\pm}),\quad c(m,n)=\sqrt{\frac{\gamma (\gamma -1)(m+n)^{\gamma}}{n}} =\sqrt{\left(1+\frac{m}{n}\right)P_n},
\]
where $P_n=\partial P (m,n)/\partial n$. Now $c_{\pm}$ are written exactly in the same form as in \cite{RWWZ} where the linear stability of 2D vortex sheets for equations \eqref{1} was studied. Introducing the entropy-like function $S=m/n$ and just referring to \cite{MoTre,MoTreWang}, we easily recover not only the linear stability result in \cite{RWWZ} but also a recent structural stability result in \cite{HWY}.

Moreover, referring to the existence theorem in \cite{MoTreWang}, we even essentially improve the nonlinear result in \cite{HWY}. Indeed, the existence of solutions $(U^{\pm},\varphi )\in H^{\mu -7}([0,T]\times\mathbb{R}_{\pm}^2)\times H^{\mu -6}([0,T]\times\mathbb{R})$ was proved in \cite{MoTreWang} for initial data $(U^{\pm}_0,\varphi_0 )\in H^{\mu +1/2}(\mathbb{R}_{\pm}^2)\times H^{\mu +1}(\mathbb{R})$, with an integer $\mu\geq 13$. At the same time, as for current-vortex sheets in \cite{T09}, the existence theorem in \cite{HWY} is proved for initial data and solutions belonging to the anisotropic weighted Sobolev spaces $H^k_*$ (see, e.g., \cite{OSY,Sec00}; one has Sobolev's embedding $H^k_*\hookrightarrow H^{[k/2]}$), instead of the usual Sobolev spaces $H^k$. More precisely, the existence of solutions $(U^{\pm},\varphi )\in H_*^{\mu -1}([0,T]\times\mathbb{R}_{\pm}^2)\times H^{\mu}([0,T]\times\mathbb{R})$ was proved in \cite{HWY} for initial data $(U^{\pm}_0,\varphi_0 )\in H^{2\mu +15}(\mathbb{R}_{\pm}^2)\times H^{2\mu +16}(\mathbb{R})$, with an integer $\mu\geq 15$.

For the equations of state \eqref{es2} and \eqref{es3} as well as for model \eqref{3} we still can use the results obtained in \cite{MoTre,MoTreWang} and make the conclusion about the structural stability of 2D vortex sheets under the ``supersonic'' condition \eqref{supson} with $c_{\pm}=\sqrt {P_{\rho}(\rho^{\pm} ,S^{\pm})}$, where the value $P_{\rho}$ is given by \eqref{7/2},  \eqref{7/3} and \eqref{7} respetively.

\bigskip

\section*{Acknowledgements}
The research of L.Z. Ruan was supported in part by the Natural Science Foundation of China $\#$11771169, $\#$11331005, $\#$11871236, Program for Changjiang Scholars and Innovative Research Team in University $\#$IRT17R46, and the Special Fund for Basic Scientific Research of Central Colleges $\#$CCNU18CXTD04.

redpajama_set_name: RedPajamaArXiv


Why do my Unreal projects keep breaking?
I've had 4-5 projects stop working for no reason. I'll be using the engine and simulating normally, then all of a sudden, when I hit stop it makes a strange noise. After that the project doesn't work anymore. No crash report or errors or anything.
After the project makes the strange sound, it never plays properly again. Permanently broken, won't possess the character.
crash sound fail play .


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The level of projected cuts which could result from the implementation of the Browne report is unlike the scale of what any of us have ever faced. What would a 20% cut do to our jobs, courses, libraries, facilities, support services?
Also, what would happen if students were expected to pay £7,000 a year, or possibly more, in fees? This would result in England having the the most expensive public degrees in the world, with families having to shell out between £76,000 and 136,000 to put two children through university.
If there is an open market in fees, this will create a 2-tier university system, with the most well-resourced universities charging the highest fees, and the most under-resourced universities charging the lowest. This would drastically exacerbate inequality in education.
The report also proposes to create a market in student places which it suggests will facilitate a large reduction in public funding which 'may be equivalent to removing all funding from anything other than priority subjects'. Goldsmiths, because it focuses on arts, humanities and social sciences, will be particularly vulnerable. Because of this, it is especially important that we rise to the challenge.
SMT have a responsibility to join our campaign to defend education. We call on them to not accept the Coalition Government's argument that there is no alternative, or the cuts for which they have no mandate. We also call on them to defend Goldsmiths' unique character as an institution that both supports cutting edge research and also has a strong widening participation agenda. We ask them to support our campaign against education cuts and to put pressure on politicians, particularly Liberal Democrats, to stick to their pre-election pledge.


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The city of Dinant inaugurates a giant saxophone in tribute to SELMER
The city of Dinant (Belgium), birthplace of Adolphe Sax, and the International Adolphe Sax Association, paid a magnificent tribute to Henri SELMER Paris on Sunday, September 18, to celebrate their partnership initiated in 1994.
It was in the sunshine on the banks of the Meuse River that the people of Dinant were able to attend a musical show retracing with humor and precision the history and connection between Adolphe SAX and Henri SELMER Paris. Nearly one hundred years ago, Henri Selmer acquired the inventor's workshops, integrating his staff and know-how, thus becoming his universal legatee.
And since in Belgium nothing's left half done, the show ended with the inauguration of a giant saxophone, symbol of the transmission from Adolphe Sax to Henri Selmer. The graphic design of the instrument draws its inspiration from the latest SELMER saxophones. You can now come to Dinant to admire the Supreme in XXXL size!
Henri SELMER Paris is very proud of this tribute. This superb wink shows the recognition of a craftsmanship of more than 100 years in which Henri SELMER Paris strives to keep alive the spirit of Adolphe Sax by participating in the influence of his most brilliant invention.
A huge thank you to the City of Dinant and its burgomaster Thierry Bodlet, for their warm welcome. We would also like to thank the entire team of the International Adolphe Sax Association (especially Wendy and Marc) for this partnership of almost 30 years. A very special and friendly thank you to the unavoidable Alain Crepin who works with so much passion, composes and orchestrates all these festivities since 1994!
We look forward to seeing you all in November 2023 for a new edition of the International Adolphe Sax Competition.
© Jean-Pol Sedran Photographie
► The website of the International Adolphe Sax Association
► The International Adolphe Sax Competition
► Adolphe Sax and the invention of the saxophone
[Know-how] Clarinet finishing
Finishing is the last stage in the manufacture of the clarinet, before the instrument is checked and
Comité Colbert : Henri SELMER Paris joins the most prestigious French houses
The Comité Colbert groups together 84 houses and 16 cultural institutions in the fashion, craftsmans
[Agenda] Henri SELMER Paris events
Committed to the development of instrumental practice for all, the emergence of talent and the influ
Anatomy of the saxophone
The saxophone consists of four major parts : the removable neck (or crook), the body, the bow and th

redpajama_set_name: RedPajamaCommonCrawl


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Overcoming a bottleneck in carbon dioxide conversion
(Nanowerk News) If researchers could find a way to chemically convert carbon dioxide into fuels or other products, they might make a major dent in greenhouse gas emissions. But many such processes that have seemed promising in the lab haven't performed as expected in scaled-up formats that would be suitable for use with a power plant or other emissions sources.
Now, researchers at MIT have identified, quantified, and modeled a major reason for poor performance in such conversion systems. The culprit turns out to be a local depletion of the carbon dioxide gas right next to the electrodes being used to catalyze the conversion. The problem can be alleviated, the team found, by simply pulsing the current off and on at specific intervals, allowing time for the gas to build back up to the needed levels next to the electrode.
The findings, which could spur progress on developing a variety of materials and designs for electrochemical carbon dioxide conversion systems, were published in the journal Langmuir ("Transient Effects Caused by Gas Depletion during Carbon Dioxide Electroreduction"), in a paper by MIT postdoc Álvaro Moreno Soto, graduate student Jack Lake, and professor of mechanical engineering Kripa Varanasi.
MIT researchers have identified a problem that tends to limit chemical processes for turning carbon dioxide into fuel or other useful chemicals — and ways of addressing that problem. (Image: Varanasi Lab)
"Carbon dioxide mitigation is, I think, one of the important challenges of our time," Varanasi says. While much of the research in the area has focused on carbon capture and sequestration, in which the gas is pumped into some kind of deep underground reservoir or converted to an inert solid such as limestone, another promising avenue has been converting the gas into other carbon compounds such as methane or ethanol, to be used as fuel, or ethylene, which serves as a precursor to useful polymers.
There are several ways to do such conversions, including electrochemical, thermocatalytic, photothermal, or photochemical processes. "Each of these has problems or challenges," Varanasi says. The thermal processes require very high temperature, and they don't produce very high-value chemical products, which is a challenge with the light-activated processes as well, he says. "Efficiency is always at play, always an issue."
The team has focused on the electrochemical approaches, with a goal of getting "higher-C products" — compounds that contain more carbon atoms and tend to be higher-value fuels because of their energy per weight or volume. In these reactions, the biggest challenge has been curbing competing reactions that can take place at the same time, especially the splitting of water molecules into oxygen and hydrogen.
The reactions take place as a stream of liquid electrolyte with the carbon dioxide dissolved in it passes over a metal catalytic surface that is electrically charged. But as the carbon dioxide gets converted, it leaves behind a region in the electrolyte stream where it has essentially been used up, and so the reaction within this depleted zone turns toward water splitting instead. This unwanted reaction uses up energy and greatly reduces the overall efficiency of the conversion process, the researchers found.
"There's a number of groups working on this, and a number of catalysts that are out there," Varanasi says. "In all of these, I think the hydrogen co-evolution becomes a bottleneck."
One way of counteracting this depletion, they found, can be achieved by a pulsed system — a cycle of simply turning off the voltage, stopping the reaction and giving the carbon dioxide time to spread back into the depleted zone and reach usable levels again, and then resuming the reaction.
Often, the researchers say, groups have found promising catalyst materials but haven't run their lab tests long enough to observe these depletion effects, and thus have been frustrated in trying to scale up their systems. Furthermore, the concentration of carbon dioxide next to the catalyst dictates the products that are made. Hence, depletion can also change the mix of products that are produced and can make the process unreliable. "If you want to be able to make a system that works at industrial scale, you need to be able to run things over a long period of time," Varanasi says, "and you need to not have these kinds of effects that reduce the efficiency or reliability of the process."
The team studied three different catalyst materials, including copper, and "we really focused on making sure that we understood and can quantify the depletion effects," Lake says. In the process they were able to develop a simple and reliable way of monitoring the efficiency of the conversion process as it happens, by measuring the changing pH levels, a measure of acidity, in the system's electrolyte.
In their tests, they used more sophisticated analytical tools to characterize reaction products, including gas chromatography for analysis of the gaseous products, and nuclear magnetic resonance characterization for the system's liquid products. But their analysis showed that the simple pH measurement of the electrolyte next to the electrode during operation could provide a sufficient measure of the efficiency of the reaction as it progressed.
This ability to easily monitor the reaction in real-time could ultimately lead to a system optimized by machine-learning methods, controlling the production rate of the desired compounds through continuous feedback, Moreno Soto says.
Now that the process is understood and quantified, other approaches to mitigating the carbon dioxide depletion might be developed, the researchers say, and could easily be tested using their methods.
This work shows, Lake says, that "no matter what your catalyst material is" in such an electrocatalytic system, "you'll be affected by this problem." And now, by using the model they developed, it's possible to determine exactly what kind of time window needs to be evaluated to get an accurate sense of the material's overall efficiency and what kind of system operations could maximize its effectiveness.
Source: By David Chandler, MIT
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Zim's gold industry shines
By Tafara Mtutu | Nov. 25, 2022
ZIMBABWE is on the verge of shattering a 30-year annual gold deliveries record of 35,1 tonnes set in 2018 after cumulative deliveries of 29,5 tonnes were recorded in the 10 months to October 2022.
Gold deliveries to the country's sole buyer, Fidelity Printers and Refiners (FPR), slid to a record low in 2008 after high inflation and adverse policies forced the sector's large-scale miners to halt operations.
Deliveries picked up after the country officially adopted the greenback in 2009 and the trend remained firmly upwards until the re-introduction of the Zimbabwean dollar as the sole legal tender in 2019 saw gold deliveries plunge again.
However, favourable policies aimed at redirecting smuggled gold to FPR has underscored the sector's recovery in the last two years.
The mining sector's paramount importance has become even more apparent in the last three years because of its ability to generate foreign currency.
According to the Reserve Bank of Zimbabwe (RBZ), the mining sector accounted for 66%, 71%, and 81% of total cross-border receipts in 2019, 2020, and 2021, respectively.
Gold receipts, in particular, accounted for c.34% of these receipts, on average, between 2019 and 2021 and we attribute this to the firm gold price since 2020 and favourable policies.
We also observe that, at a granular level, artisanal miners drive the bulk of the deliveries. In 2022 to September, these miners accounted for 66% of all gold deliveries, while primary producers delivered the remaining 34%.
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Gold output improves, still below projections
In comparison, large-scale miners delivered 88% of total gold output in 2013 and small-scale miners accounted for only 12%. We identify several policies that were implemented that boosted output mainly from both small-scale as well as primary producers, which we unpack below.
In June 2021, the central bank announced a 5% incentive for deliveries above 20kg by small-scale farmers. In addition, the bank scrapped royalties applicable to small-scale miners, reduced the cost of importing cash, and began to buy gold at the prevailing international price.
The bank also committed to spot payments to artisanal miners after they lamented a backlog of up to two weeks, and removed foreign currency retentions for small-scale farmers. These moves were appetising even to smugglers who have since diverted their gold to FPR.
The central bank and government also implemented some incentives to primary producers, albeit less than what artisanal miners are privy to.
The central bank waivered the 60/40 foreign currency retention policy only on incremental exports for companies that list on Victoria Falls Stock Exchange (VFEX), and this was instrumental in Padenga Holdings' migration from ZSE to VFEX as well as the listing of Caledonia's depository receipts on the foreign-currency denominated exchange.
This also tied in well with the government's import duty exemption on capital equipment worth over US$10 000 for incorporated companies. These incentives saw primary producers recapitalise their operations with funding from internally generated foreign currency as well as foreign currency from incremental exports.
These incentives have also been supplemented efforts by these large-scale miners. In the past two years, Caledonia has ramped up production through capital investment on Blanket mine as well as acquisitive growth.
The entity acquired the mining claims at Maligreen in Zimbabwe's Midlands province in 2020 and The Bilboes project located in Bulawayo in July 2022. These developments are anticipated to result in Caledonia's annual gold tonnage exceeding two tonnes in the coming years.
Padenga recommissioned the Eureka mine in 2021, which became fully operational in the first half of 2022. As a result, Padenga's gold division is expected to produce more than 1,7 tonnes of gold in 2022.
Mines minister Winston Chitando is confident that the country could reach 60 tonnes in gold deliveries in 2022 and 100 tonnes in 2023, a feat we think is possible if large-scale miners are afforded the same privileges as artisanal and small-scale miners, and business confidence is strong enough to lure international capital.
Our expectations of gold output in 2022 currently stand at a relatively conservative 36,5 tonnes because of operational disruptions that typically come with rainfall during the festive months.
Local investors can tap into the gold industry's good run by investing in Caledonia and Padenga. Our valuations place Caledonia's fair value at US$12,97 per share and Padenga's fair price at US$0,29, which are almost at par with current market prices of US$13 and US$0,25.
However, we note that Caledonia depository receipts are incredibly illiquid, making Padenga a better investment for the interested investor.
Investors seeking more direct exposure should consider the Mosi-Oa-Tunya gold coin. However, we opine that the coin is extensively exposed to the gold price, which we think is hovering at unsustainable price levels.
Mtutu is a research analyst at Morgan&Co. — tafara@morganzim.com or +263 774 795 854.
Fidelity Printers Refiners (FPR) Reserve Bank Of Zimbabwe
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The government does not consider concentrates as raw or unprocessed lithium.
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Mars S01 Complete Hindi 480p 720p 1080p HDrip Dual Audio [ हिंदी + English] All Episodes 1-6 Bluray .
Six men and women travel to Mars to colonise the planet in 2033. The scientists and people behind the real-life mission show how they are to achieve this feat.
Mars is a documentary and science fiction television series produced by National Geographic, which premiered on November 14, 2016, on their channel, and FX. Prior to its official air date, it was launched in a streaming format on November 1, 2016. It blends elements of real interviews with a fictional story of a group of astronauts as they land on the planet Mars.
The series is based on the 2015 book How We'll Live on Mars by Stephen Petranek. The narrative alternates between the years 2016, 2033 and 2037, using 2016 interviews to explain events unfolding in the story. The series was filmed in Budapest and Morocco.


You can tag any of your teammates in conversations or customer profiles throughout Kimoby.
This can be helpful when you are assigning a conversation to another user, communicating internally, etc.
From any ongoing conversation or customer profile, click on Internal Note or Notes above your message box.
In the yellow background box, click on @ or enter an @ sign from your keybord and a list of all users in your account will appear.
Select the user you wish to tag in your internal note. You can tag as many users in your internal note as you wish.
From any ongoing conversation or customer profile, click on the internal note icon, at the bottom of your message box.
Click on the paper plane icon to add your note in the conversation.
Instantly, the user that was tagged in your message will receive a notification that he was tagged in the app.


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Mysteries, Short and Sweet
Agatha Christie 100 - Death in the Clouds
Another in a row of Poirot novels that are never less than solid, and frequently much better than that. Read on to see what I thought of this particular story.
The plane from Paris to London is full of passengers - among others a pair of architects, a dentist, a mystery novelist, and a certain Belgian detective. But before touching down on British soil, one of the passengers is found dead - and it looks like a suspicious death, especially once Hercule Poirot finds a blowdart next to the deceased woman.
Like Three Act Tragedy, this is another of those Poirot stories where he allows a couple of people affected by the crime to become a major part of the investigations, letting them initiate contact with other suspects. But unlike that earlier novel, in this one Poirot is a much more active participant in those investigations.
As befits a Christie novel from the mid 30s, the setup is rather lovely, and the misdirection is deftly handled by the author. The limited list of suspects that the plane provides contributes to make this one of my favourite Christies, and the final revelation of the villain is great. Sure, part of the motive for the crime is held back until very shortly before the dénouement, but overall this is very enjoyable.
I'll rate this an 83 out of 100, because there's very little wrong with it - and a lot of things that are just perfect.
The Swedish title is a variation of the British (and American: Death in the Air) title - Den flygande döden means The Flying Death. All the different title variations are good, in my opinion.
Apart from the first Swedish cover, which is another one of those lazy "title on the front page" jobs, I think we have a uniformly excellent round of covers available to us for this title. The Zebra cover from 1961 features the blowpipe and the tiny dart, while the Delfinserien cover from 1979 - which is the one I have - again uses Fontana's cover which focuses on the wasp.
Meanwhile, the mid 80s Bonniers cover (again, the hardcover version has some minor differences) has a lovely version of the airplane among the clouds. Oh, I can't choose which one I like best, they're really nice, all of them.
Posted by Christian_Henriksson at 14:06 3 comments:
Agatha Christie 100 - The Moving Finger
It's been a while since we had a look at a Miss Marple story, but in this incongruous re-read we've now reached the third novel featuring that worthy lady.
Airman Jerry Burton has been wounded and is dispatched with his stylish sister Joanna to small town Lymstock, which seems to be haunted by anonymous letters. One letter is received by Mrs. Symmington, and she promptly commits suicide. But just one week later, her housemaid disappears, only to be found murdered. Does this mean that the previous death was in fact murder too? While Jerry is more occupied with the late Mrs. Symmington's daughter Megan, the vicar's wife invites her old friend Miss Marple to take a closer look at the goings-on in Lymstock.
While this is a Miss Marple novel, she's only in the final quarter of the book - the rest is squarely focused on Jerry Burton and his household and his burgeoning interest in Megan Hunter. The mystery plot itself is thin enough for a short story, but fortunately, Christie is still in her winning streak here in the early 40s, and manages to get Lymstock and its characters to come to life, making the reader interested in reading on and finding out what will happen to them on the way.
Miss Marple doesn't really have to do much once she appears on the scene - she simply listens to Jerry telling the whole story from the beginning and notes some of the salient points, before pointing the finger to the villain of the piece.
It's a rather lovely novel, but don't come to this if you're looking for one of those complex Christie mystery puzzles. I'll rate this 72 out of 100, because I did like it a lot. I do have to wonder what happened with Mrs. Symmington's two young sons at the end.
So, here we have another Christie novel where the Swedish title differs completely from the English one. As I understand it, The Moving Finger is a reference to Rubaiyyat of Omar Khayyam. Since it's not as generic as many of the 20s titles we've seen, I like it a bit more. In Sweden, Rubaiyyat is almost unknown, and so the publishers invented their own title which refers more to the story itself. Mord per korrespondens can roughly be translated as Murder by Correspondence. Not the most exciting title, and I have a hard time deciding which one I like best. Perhaps the English one just pips it this time.
The first Swedish edition of this novel was published the same year as the first Swedish edition of The Body in the Library, making 1944 a thorough introduction of Miss Marple for the Swedish reading public. The cover of this first edition looks like it's trying to portrait Fantasio from the Spirou comics. I suppose that's intended to be Jerry, which is appropriate, I guess. The second cover, from 1951, is more stylised and has lost Jerry from the cover, but is otherwise fairly similar to the earlier one.
Zebraserien gives us a femme fatale reading a letter which is... well, not their best cover. It's the one I have, because it's the only mass-market paperback edition published in Sweden. In 1973, we get one of those covers that I always compare with the Fontana covers in Britain. In this case it's not very surprising, because it is actually taken from that edition. It might be the one I like best here. (The 1984 cover has the same image, as you can see, it's just designed a bit differently.)
Finally, if the 1988 edition had also been published as a paperback, then it would have been my go to version. It's not fantastic, though I suppose it gets its message across with the envelope with a skull stamp. But it's better than the Zebra one, that's for sure!
Posted by Christian_Henriksson at 19:41 No comments:
Agatha Christie 100 - Three Act Tragedy
We return to Poirot with this mystery, which for a change features Mr. Satterthwaite from the Harley Quin stories.
There is a gathering at Sir Charles Cartwright's, and among the guests are Hercule Poirot, Mr. Satterthwaite and Sir Charles's friend Sir Bartholomew Strange. But the person who dies from poisoning is the mild-mannered Reverend Stephen Babbington... However, some time later Sir Bartholomew dies at a similar gathering, in the same manner, and Poirot gets suspicious - surely these two deaths must be connected somehow?
As we've established, this comes in the middle of Christie's upwards trajectory. The previous Poirot was a masterpiece, and there are several novels of that ilk to come. I'm not sure I see this one quite at those high levels, but it's a very good mystery indeed. While the misdirection is somewhat familiar, there's a lot of good clueing and Christie does her best to befuddle the reader.
This might be the first instance where Christie allows a group of her characters to start investigating the crime for their own reasons, with Poirot acting like the grand armchair detective in the background and making the all-important connections towards the end. In previous stories, Poirot has always been at the centre of investigations.
I'll rank this a 66 out of 100. It's a middling 30s Christie mystery, but a middling 30s Christie mystery is better than almost everything else you might read in the genre.
In Swedish, it would sound very awkward to structure the title the way the English title is structured - Treakterstragedin is very cumbersome. So we fiddled about a little with it - Tragedi i tre akter means Tragedy in three acts.
The very first edition is another one of those that look very dull with the title plastered all over the cover. (Cf. Lord Edgware Dies and many more).
I've not actually managed to establish with 100 % certainty that the second cover is from the 1947 edition, but I haven't found any other edition that it could be from, so everything indicates that it is. It's a better cover, though the artist seems to suffer from the misconception that one of the murders takes place onstage.
I like the colours of the Zebra edition from 1970. If you look closely, that is in fact a man's shoe in the background, making the cover more sinister than it immediately appears. It's the one I own, so I'm happy it's the best one here.
For the two mid 80s covers, the artist seems to have focused on the Greek origin of the word "tragedy". None of the covers are bad per se, but there's nothing inherently Christie-y about them.
Agatha Christie 100 - Why Didn't They Ask Evans?
A non-series novel in the middle of a slew of Poirot titles, how does this story hold up with all those classics surrounding it?
Bobby Jones is out golfing when he comes across a man who seems to have fallen down a cliff. His golfing partner goes to find help while Bobby remains with the man, who is obviously dying. But before expiring, the man utters the words that have given this novel its title. When an attempt at Bobby's life is made a little later, he and his friend Lady Frances "Frankie" Derwent decide to investigate...
Well, this was one of the titles I was looking forward to, because I didn't remember too much of it. Unfortunately much of the plot came back to me while reading it, so I wasn't very surprised at the twists and turns. The reader is well advised to remember that this is NOT a mystery novel, it's another one of Christie's romantic adventure thrillers. In fact, while I was reading it I felt as if this was almost the same story as the later N or M. We'll see if I still think so when I re-read that novel...
And yes, this story is a Tommy & Tuppence story in all but name - I am still a little baffled as to why Christie chose to invent a new pair of sleuths for this one. It's a fun story, but there is very little detection. What we get is a couple of annoying deus ex machina scenes and a pair of protagonists that, while being good companions on the road towards the dénouement, just stumble and fumble about before a hunch gives them the solution.
I'd rank this 44 out of 100. While it's a fun ride, everything's a bit too coincidental, and I also question how Christie chooses to deal with her villains.
In translating the British title of this novel, the Swedish publishers had a small problem, because the word "ask" can be translated in two different ways in Swedish, depending on whether it means "ask a question" or "ask someone to do something", though I guess that both interpretations could be valid with this story. In the end, they went with the latter, and otherwise Varför bad de inte Evans? is a literal translation.
The first translation of this story had to wait almost a decade. It features a cover that isn't bad at all. The steep cliffs are quite evocative. The only thing missing is the golf connection, but I guess all the other covers make up for that.
The Zebra edition and Delfinserien use the same cover, nicked from the first British Fontana edition, though the later one is just a tad more colourful. I like it quite a bit. The mid 80s cover is perhaps too focused on the golf thing, making this seem like one of P. G. Wodehouse's golf story collections.
The cover from 1990 also concentrates on the golf setting, and I like the tiny detail that the golf ball is a skull. And talking about skulls, the rather well-made mid 90s cover also has one, this time in place of an eye. It doesn't really scream mystery - apart from that skull - but I like the way that it presents a face both in profile and en face.
To be honest, I think this might be one of the novels with the best Swedish covers overall so far.
Agatha Christie 100 - Murder on the Orient Express
Perhaps you've heard of this one? It's the one where...
Hercule Poirot has been helping the French army with a sticky situation in Syria, and is now due to return to Britain again. He does so by riding the famous Orient Express, which is unusually crowded for the season. In the middle of Yugoslavia - as it was then known - the train gets stuck in the snow, but what is worse - one of the passengers is found murdered with a slew of stab wounds in his chest!
So we reach the second of Christie's stone cold classics. Over the last decade or so, there's been a few mumblings that it's a bit gimmicky and there's too much focus on interviews with the train passengers. Pish posh is what I say to that. This is a great, great detective story. The interviews are interesting, especially as soon as Poirot makes the important discovery that the murder is connected to a previous kidnapping in the USA.
I really don't have much else to say about this novel. If you haven't read it before, then you should, and if you have and you didn't like it, then you should read it again, because you're wrong.
This gets a 97 out of a 100. Why only 97? Well, it might very well be Christie's best novel, but I have to leave room for a novel to overtake it if it turns out that this re-read brings me another favourite.
So, Christie's second classic, and obviously there's been a lot of Swedish editions of this one. Us Swedes made a tiny change to the title when translating it, putting the "murder" in the definite form unlike the English title. By the way, this is an excellent title, as opposed to all those "murder at [manor]" for one simple reason, and that is that the reader can be expected to know what the "Orient Express" is and therefore have all sorts of associations and connotations, while "Styles", "End House" or "Hazelmoor" will not immediately tell the reader anything. Just to explain my personal idiosyncracy...
The first cover above is one of those dull ones where the publishers couldn't even come up with an image, instead just plastering the title all over the cover. The cover from 1953 is better, though unfortunately looks a bit like a parody with the amount of surprise shown by those two men.
The covers continue to improve with the Zebra one from the late 50s. A fine cover with the corpse and train window and snow, but minus points for not capitalising "orientexpressen". Delfinseriens cover is not one of their best - unfortunately it's the one I own - though at least they manage to show both snow and train, tiny as it is. But that mountain, is that really in the story?
There are two editions with film tie-in covers. The one from 1974 is not particularly good. If I remember correctly, it's taken at one of the stations the train stops at, but you'd be hard-pressed to know from that picture. While the 2017 one is uncomfortably modern in its design, it is still quite a bit more exciting. The train and the fog and the dim lights set a great atmosphere.
But let's get back to normal book covers, and let's do it with one of the best here: Bonniers's 1984 edition gets almost everything right. The one thing to improve it would have been to show the snow surrounding the train. The edition from 1990, again to commemorate Christie's 100 year jubilee, is okay, I guess. But it really could have been from any mystery story with a murder committed with a dagger.
Which also goes for the 2001 cover. To be honest, there's not much difference between that one and a couple of the covers for The Murder of Roger Ackroyd. The more recent cover from 2014 is in some ways a repeat of the mid 80s cover. It adds in a bit more background with the mountains and what could possibly be interpreted as snowflakes, but unfortunately only presents the train in silhouette. Making the O in the title look "oriental" is a nice touch.
Agatha Christie 100 - The Sittaford Mystery
Interestingly, this is a detective novel featuring none of Christie's regular characters, unlike most other non-series novels, which are almost uniformly adventure thrillers.
In Sittaford, the villagers are having a gathering at mysterious and stylish Mrs. Willett's, and they decide to hold a séance - as you do - where the spirits spell out that a murder has been committed in the neighbouring town. Their friend Captain Trevelyan is supposed to have been killed. One of the guests, Major Burnaby, decides to investigate further, and lo and behold! it turns out to be true. Suspicions quickly fall on one of Trevelyan's nephews, whose fiancée decides to investigate the case more fully.
It's interesting that Christie didn't put Battle in this novel, I think he could easily have taken the place of Inspector Narracott, or even Mr. Duke. You might argue that Emily Trefusis is the actual detective in the novel, but it's not as if Battle didn't have help from young amateurs in his previous outings...
Overall, this is a fairly good story. I feel that Christie could have made more out of the wintery settings, but Sittaford and neighbouring town Exhampton are described skilfully. Emily Trefusis is a fun acquaintance, though I question some of her life choices. Her investigative ways are very similar to Miss Marple's.
The main problem with the novel is that it feels a bit disjointed. Emily isn't introduced until we've come a long way into the narrative, and in fact most of that early part is focused on Inspector Narracott's investigations.
I do feel like a parrot, but at least this is the final novel in this streak where Christie uses a certain type of misdirection to fool her readers - if they read these in order I wonder how fooled they would be?
This novel is worth a 55 out of a 100. A bit average for a Christie story, but on the whole a worthwhile experience that any mystery fan should enjoy.
While the English title for this book is again somewhat generic - the custom of naming a novel by jumbling up words like mystery/murder/puzzle and <insert name of country house/nobleman/place here> has never been a favourite of mine - the Swedish one is no less generic, just in a different way. Mördande seans simply means Murderous Séance. I still think it's better, though.
This was the second to last Christie novel to be translated into Swedish, which means there are very few editions available. The first one from 1986 looks suitably impressive with a country house surrounded by snow and the transparent skull in the ominous sky. A favourite of mine. (Again, there are some slight typographical differences between the hardcover and paperback editions using this cover - this is the paperback version, which is also the one I own.)
And here's a surprise, a book club edition which doesn't completely muck up the cover. In fact, the artist very much seems to have used the earlier cover as a basis to create his own impression, because all the elements from the 1986 cover are there. It is by far the best book club cover I've seen.
ahsweetmysteryblog
Beneath the Stains of Time
Composed Almost Entirely of Books
crossexaminingcrime
The Green Capsule
In Search of the Classic Mystery Novel
The Invisible Event
Justice for the Corpse
Mysteries Ahoy!
Noah's Archives
Ontos
The Reader Is Warned
Other good mystery resources
Deckarhyllan
Christian_Henriksson


text:
// Copyright © 2017 Chocolatey Software, Inc
// Copyright © 2011 - 2017 RealDimensions Software, LLC
//
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// you may not use this file except in compliance with the License.
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namespace chocolatey.infrastructure.app.configuration
{
    using System;
    using System.Xml.Serialization;

    /// <summary>
    ///   XML config file config element
    /// </summary>
    [Serializable]
    [XmlType("add")]
    public sealed class ConfigFileConfigSetting
    {
        [XmlAttribute(AttributeName = "key")]
        public string Key { get; set; }

        [XmlAttribute(AttributeName = "value")]
        public string Value { get; set; }

        [XmlAttribute(AttributeName = "description")]
        public string Description { get; set; }
    }
}

redpajama_set_name: RedPajamaGithub


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