The use of prepaid debit cards has become increasingly popular in recent years, and most experts believe that this trend will only become more common in the future. Analysts estimate that about $82 billion dollars will have been loaded onto prepaid debit cards by the end of 2012, and by the end of 2019 that annual figure will have jumped to an astonishing $167 billion. The numerous benefits of using prepaid cards have become quite apparent to consumers, and their demand has only spurred on the prepaid industry to greater heights. Even now, high-profile banks such as U.S. Bancorp and JPMorgan Chase have already started offering prepaid debit cards of their own.
But what exactly are the advantages of prepaid debit cards?
It's easy enough to get a prepaid debit card: you just have to prove that you're over 18 and you're good to go. You can buy these cards in a store or, far more common these days, from the Internet. In contrast, establishing a checking account is much more complicated, and the standards required for regular credit cards are far more stringent. With credits cards, many people do not have the required credit scores—a situation which only leaves them with the prepaid option.
Prepaid debit cards are also very easy to use. You can add more money to your account whenever you want. You can use them to purchase items at most retail stores, and you can withdraw money from any ATM machine. It functions just like a standard bank debit card without the need for a checking account. Some prepaid debit cards now also offer savings accounts and the ability to pay bills online.
According to a recent study released in September 2012 which was conducted by Pew Charitable Trusts, people who have the tendency to overdraft will find the use of prepaid debit cards a much cheaper alternative than checking accounts. These results were a surprise to the researchers, who have previously believed otherwise. In their findings, the average inexperienced consumer who tends to overdraw their accounts and thus incur penalties spends less than $30 dollars a month for prepaid cards. In contrast, people with the same spending habits who use checking accounts instead spend an average of $94 every month.
Many parents have come to rely on the use of prepaid debit cards for their children as a way of teaching and enabling them to spend responsibly. Parents can give their children their spending money through this method without having to hand over actual cash or giving the children access to their personal bank accounts. Children also learn how to spend responsibly because most debit cards do not allow users to spend money beyond was what already loaded on to the card.
It is this feature, in fact, that has also caused its popularity among adults as well. With regular credit cards, the temptation to spend over the affordable limits is too great, and some people have simply been unable to stop themselves from incurring massive debts. With a prepaid debit card, this is simply not possible, which prevents users from having to pay exorbitant fees.
This entry was posted in Uncategorized on September 13, 2012 by Don Marks.


Frank Frohmann has 23 years of leadership experience in marketing, sales and pricing. In his current role as a business coach at the German chemicals company Evonik he is focusing on his core competency which is pricing management. Frank Frohmann gained extensive pricing competencies covering inhouse consulting (Bosch, Lufthansa Cargo, Evonik), operative pricing and yield management (Lufthansa Passenger Business) and management consulting (like Simon-Kucher, Homburg & Partner, Roll & Pastuch). His book "Digital Pricing" is the very first work that combines "Digitalisation" (as the most important megatrend) and "Pricing" (as the most effective profit lever). Frank Frohmann will tackle digitalisation trends and pricing challenges and share insights about pricing innovation. In his speech he will show in detail how innovative revenue and price models help companies to generate a sustainable competitive advantage. Frank´s examples on innovative pricing approaches are based on his cross-industry experience, including automotive, industrial goods and machinery as well as service sectors like telecommunications, transportation and tourism.


text:
Howl.
Breaking News: Chantry Flats Closed - A suspect in a crime that occurred in Arcadia late last night has barricaded himself in a property in the Chantry Flats area of the Angeles National Forest ... Arcadia police Lt. Mike Castro said Chantry Flats will remain closed to hikers Sunday until Los Angeles County Sheriff's Deputies remove the suspect from the property.
Part II: It is over. Here is what the Pasadena Star News has. Sounds like it was a very bad date (click here).
Police arrested a man on suspicion of attempted murder and other crimes early Sunday after he tried to drive himself and a woman over a cliff, then barricaded himself inside the home of the Santa Anita Dam keeper for seven hours, authorities said.
Patrick Anthony Gonzalez, 21, of Los Angeles was taken to a hospital for treatment of unknown injuries prior to being booked into jail, Arcadia police Lt. Mike Castro said.
The incident began about 6:30 p.m. Saturday when officers responded to reports of a car that had crashed into a guardrail along Chantry Flats Road, just within the northern city limit, the lieutenant said.
"Further investigation revealed the driver of the vehicle intentionally hit the guardrail in an attempt to kill both himself and his passenger - changing the focus of the investigation from a traffic accident to attempted murder," Arcadia police officials said in a written statement.
Maybe she met him in the Internet. Back to our regularly scheduled blog content.
(The Mod: It is raining now, which for me is 3:51 AM. By the time you read this the sun could be out and the topic line for this post will not be accurate. That is the risk you take when you bring the weather into your reporting. But do you know what? We're not afraid to take chances here at The Tattler. We'll go out on a limb and dare whoever wants to try and saw it off. And you know they rarely do. Also last evening was a Full Wolf Moon, a rare event that is often represented by pictures like the one we have posted here on the left with this article. All of which happened somewhere behind the clouds I am afraid. But the picture is cool and who here hasn't wanted to occasionally howl at the moon? Even when it is lost in the clouds? Anyway, this week's rainy Sunday News includes stories that we thought you might be interested in. Here they are.)
Years after bond's passage, no start on new Sierra Madre school (click here): The Middle School, slated to benefit from a $350 million bond approved in 2008, has been operating out of trailers since the old campus' demolition in 2010.
Troubles at Sierra Madre Middle School began in July 2010 with demolition of the old campus before California's Division of the State Architect had issued approvals for new buildings. Renatta Cooper said former Pasadena Unified supervisors had sold school board members on an early demolition under the pretense that they could save money by using workers already engaged in other district construction projects.
A year later, Pasadena officials were accusing the Division of the State Architect, which must sign off on all public school construction plans, of dragging out the approval process. The agency countered that state workers were waiting on Pasadena to submit design changes needed to meet regulations. Local officials denied that any design changes were needed at that time.
Plans for the campus weren't approved until fall 2012, school district Chief Finance Officer John Pappalardo said. Pappalardo took charge of Measure TT projects last month after board members placed the district's chief facilities officer on leave and suspended a pact with a contractor overseeing some work pending an investigation into the use of bond funds. Officials have declined to specify the nature of the investigation, which is ongoing.
Staff upheaval and budget reductions for most bond-funded projects, meanwhile, have some Sierra Madre parents accusing officials of delaying construction until they can cancel the project by claiming lack of funds. That's what happened to Blair Middle School, which the school district demolished in 2005 and failed to rebuild before exhausting a $240-million bond approved in 1997. The new Blair campus was built later using Measure TT proceeds.
Pappalardo said about $111 million has been spent on or committed to school renovations under the current bond program, with some $274 million in Measure TT proceeds and other construction funding still left in the pipeline.
(Mod: If your kids came home and told you a story like the one above, would you believe them? There are a couple of things driving all of this, and it doesn't have much to do with building our school, or any PUSD outlet for that matter. One is increasingly scarce buildable land, which the PUSD controls a lot of, and with continued steep declines in enrollment just doesn't need so much of it anymore. The other is $274 million in remaining Measure TT bond money. Combine these two ingredients and it is a developer-friendly crooked pol's dream. People need to snap out of their dreamworld and wake up to what is really going on here. It is always about the money.)
Do penalties for smokers and the obese make sense? (click here): Faced with the high cost of caring for smokers and overeaters, experts say society must grapple with a blunt question: Instead of trying to penalize them and change their ways, why not just let these health sinners die prematurely from their unhealthy habits?
Annual health care costs are roughly $96 billion for smokers and $147 billion for the obese, the government says. These costs accompany sometimes heroic attempts to prolong lives, including surgery, chemotherapy and other measures.
But despite these rescue attempts, smokers tend to die 10 years earlier on average, and the obese die five to 12 years prematurely, according to various researchers' estimates.
And attempts to curb smoking and unhealthy eating frequently lead to backlash: Witness the current legal tussle over New York City's first-of-its-kind limits on the size of sugary beverages and the vicious fight last year in California over a ballot proposal to add a $1-per-pack cigarette tax, which was ultimately defeated.
"This is my life. I should be able to do what I want," said Sebastian Lopez, a college student from Queens, speaking last September when the New York City Board of Health approved the soda size rules.
(Mod: What a novel, yet chilling, approach. Government should just butt out and let nature run its course? The war on the fat has begun.)
The Battle for CEQA (click here): California's core environmental protection law, a 43-year-old statute frequently denounced by developers and business interests as a tangle of red tape, is on a Capitol hit list once again. But the political dynamic this year is unusual: Those pushing hard for change are Democrats, including Gov. Brown, the Senate and Assembly leaders and a farm-belt lawmaker.
At issue is the California Environmental Quality Act, or CEQA, which requires builders and others to detail their projects' potential impacts over time on the environment and offer ways to fix them – which helps local zoning commissions and city councils weigh the benefits and negatives of the proposals in their decision-making.
The Act, which Ronald Reagan signed into law in 1970, has long been cited as the underpinning of California's aggressive environmental protections and a shield against well-heeled special interests.
It also is seen as a sort of grass-roots environmental protection law because it is driven by the locals through the courts, not by Sacramento-based regulators. The law has been used to protect everything from ocean waters to tribal burial grounds. It has been altered over the years – 334 times since 1990 alone, by one count -- but its over-arching goal largely remains in place.
"They haven't fundamentally changed CEQA, ever," said Ron Stork of the Friends of the River. "There have been court decisions from time to time. But to some degree, it's a living process and now it's been around for a long time."
The law has protected Californians from "from many tons of toxic air pollution and related health effects, such as childhood asthma. CEQA played a principal role in the electrification of the Port of Los Angeles, making it the cleanest port in the country, improving the working conditions for truckers and health of nearby communities," noted David Pettit of the Natural Resources Defense Council.
But CEQA, long under fire from its traditional foes, is now taking hits from lawmakers, the Democratic allies of environmentalists and others who say – with some evidence – that the law can add years to the approvals needed for major projects to get under way. They argue that the law needs to be modernized.
(Mod: The one-party rulers of this state are obviously in the tank for developers, Realty lobbies, the BIA and whoever else from that disreputable world pumps money into their pockets. CEQA is the one recourse residents and small cities have to halt the depredations of large corporate development interests that want to build nasty things in places that those living there do not ever want to see. The days when we can call the Democrats friends of the environment are pretty much over. They have quite obviously sold us out.)
Recent Legal Actions Further Illustrate EPA's Challenge In Regulating Stormwater Runoff (click here): Within the last few weeks, three separate legal developments have demonstrated the difficulty faced by the United States Environmental Protection Agency (EPA) in regulating stormwater runoff under the Clean Water Act (CWA), 33 U.S.C.§ 1251 et seq. In the first matter, EPA settled a lawsuit with builders and utilities that challenged the Agency's regulations on stormwater runoff at construction sites. The settlement requires EPA to propose new effluent limits for runoff that do not contain numerical turbidity limits (i.e., limits on the suspended material in water that affects its clarity), and to discontinue the monitoring requirement for turbidity in the runoff. Wisconsin Builders Association v. EPA, No. 09-4113 (7th Cir 2012).
Next, the United States Supreme Court reversed a ruling of the Ninth Circuit Court of Appeals that Los Angeles County's Flood Control District had violated its system-wide water-discharge permit because monitoring stations downstream from discharge points reported pollutants in excess of permit limits. The monitoring stations were located in sections of the Los Angeles and San Gabriel rivers that had been lined with concrete to channel and direct water flow during storm and flooding events. These concrete-lined sections were controlled by the Flood Control District.
The Supreme Court held that water flowing from a concrete section of the river to another section was not a "discharge" of pollutants under the CWA, thus overturning the Ninth Circuit's decision. Los Angeles County Flood Control District v. Natural Resources Defense Council, et al., No. 11-460 (U.S. 2013).
Finally, in Virginia Department of Transportation, et al, v. EPA, et al., No. 12-775 (E.D. Va. 2013), the United States District Court for the Eastern District of Virginia sent a clear message to EPA – non-polluted water is not within the Agency's jurisdiction under the CWA, ruling that the Agency may not regulate stormwater runoff flow as a "surrogate" for limiting sediment load into a waterbody.
(Mod: The bandits on the Los Angeles County Board of Supervisors, along with their so-called "Rain Tax," have pretty much been legally kicked to the curb by the Courts. However, you can be sure they haven't given up. When it comes to new and novel ways of emptying the taxpayers' pockets, they can be ruthless.)
Canadians: U.S. Homeland Security knew of Sierra Madre man's porn case in October (click here): The Department of Homeland Security's failure to search Robert Matheson's home in Sierra Madre immediately after his arrest for smuggling and possession of child pornography may have cost Canadian authorities the chance to secure a harsher sentence, officials in Nova Scotia said Wednesday.
Matheson, 67, was arrested Oct.17 at the Halifax Stanfield Airport in Canada after border agents discovered 2,820 pornographic images and 285 videos of teenage boys. Most of the pictures and videos showed teenage boys engaged in sex acts, said Craig Botterill, Nova Scotia Crown Attorney and the lead prosecutor on the Matheson case.
Canadian law enforcement officials contacted the Department of Homeland Security's Los Angeles office about Matheson's arrest on Oct. 20, they said. But federal agents didn't search his home until Monday. The delay compromised the Canadian case against Matheson, Botterill said.
"(The delay) prevented me from painting a full picture of the accused at the sentencing hearing," Botterill said. "We wanted to know whether he was a person with a small amount of child porn on his computer or whether he was a big-time player."
Matheson, who hosted the 2010 campaign kickoff for former Sierra Madre Mayor Joe Mosca and is a member of the foothill city's Chamber of Commerce, was sentenced to 120 days in prison on Dec. 13. DHS officials said the agency has worked closely with Canadian officials since Matheson's arrest in October.
(Mod: This article was published by the Pasadena Star News on Dec 21, 2011, or a little more than one year ago. We have yet to hear the results of any investigation, nor have we ever been given any kind of accounting as to why Matheson was not registered as a sex offender here in Sierra Madre. Despite Federal laws that clearly dictate this must be done. Yet one more proof that when it comes to law enforcement in our little portion of the world, we're pretty much on our own.)
Have a pleasant valley Sunday. Is it still raining?
Couldn't agree more. Let those who overeay and smoke continue to do so. It is their freedom of choice to do so. However, they must also be accountable and responsible for their behavior choices. I shouldn't have to bear the costs of their choices. Let them pay for their own medical care. This is what part of being an adult is all about.
A good accounting of the Libertarian viewpoint. With total freedom comes total responsibility. Do anything you want to do, but never expect the government to come and pick you up if you fall.
I am all for most Libertarian policies. Bt health care is a different thing, and calls for more compassion.
That is the thing about health care in this country. The chance are still good that you'll die even if you get it.
Matheson, Mosca, Moran, Doyle, Buchanan, Walsh, Coluntuono, Levin, et alia . . . if you don't have anything nice to say about someone, don't say anything at all . . . . This should be such a quiet town.
Is there an Air Tax in the works?
only for the clean stuff. the dirty stuff is free. unless you want it cleaned. then you gotta pay a tax for that, too.
That will all change once our downtown gets high density green development, the fresh air 710 tunnel gets built, and all those new green trucks from the ports start flooding into our happy valley. I think it is safe to say that government is working hard to save us. We should all just stand aside and let them do it.
"the law can add years to the approvals needed for major projects to get under way" Exactly - that's the idea. It takes that long for good reasons. Why is that such a problem for developers? They have to wait for their outsized profits?
For Jerry Brown and Elmo Steinberg the only thing environmentalism is good for Is to manufacture the greenwash needed to peddle the destructive development projects of Democratic Party campaign funders. If you want an example of the kind of crap these people are producing, take a look at the Green Committee's Accords. These people are all despicable hypocrites.
Don't kid yourself. Flushing CEQA is all about Union construction jobs, more government control of our lives and property, and more tax $$ to spend. Did I miss anything?
Unions are not dem funders? So is the League of CA Cities, CAR and the BIA. To name just a few. In California the scapegoats come in herds.
Alcoholics don't get liver transplants. We need to save our limited resources for those that care about life. Smokers don't care about their life or others. Let them take out a smoker's policy with premiums that match the risk. Don't require hospitals to treat the uninsured smokers.
They could be dealt with like lepers are handled in some societies even today. A small shack settlement a few miles from any city line would be ideal.
Nicotine is one of the most addictive substances on the earth. While I agree that smokers have to pay their share, I don't agree that they don't care about life - at least not all of them.
It says on the package it gonna kill you.
It says on lottery tickets that you can win millions of dollars if you buy some. Both are sold at liquor stores. People believe what they choose to believe.
I think of smokers more like lab animals that have been experimented on. They pick up the first cigarette through some kind of stimulus like peer pressure (big mistake) and then the addiction takes over any good sense.
Does anyone know the ObamaCare health exchanges will charge 50% more for smokers? Wanna bet the smokers say they don't smoke to get the cheaper price and we get to pay for their medical care?
Good to see the PUSD dance laid out step by step. It's hard to follow, and requires close reading.
I were hearing the story from a distance, I think it would be clear as day that it was full of lies and the real cheats have yet to be revealed.
The more officially anointed and legally vetted spokespersons for the PUSD attempt to explain the Middle School fiasco, the more suspicious people become.
The responsibility gets tossed around like a hot potato.
They're all scared to death that they'll be holding the spud when the music stops.
"A year later, Pasadena officials were accusing the Division of the State Architect, which must sign off on all public school construction plans, of dragging out the approval process. The agency countered that state workers were waiting on Pasadena to submit design changes needed to meet regulations. Local officials denied that any design changes were needed at that time."
This is the part that interests me. What Pasadena officials were accusing the DSA of that? And who SPECIFICALLY was responsible for turning in the plans to the DSA?
Sounds to me like PUSD employees blaming the state for things they needed to do but never did. Shouldn't they have been calling Sacramento a couple of times a day when their plans weren't returned in a timely manner? Seems much too slack on their part to me.
Watch what you say. If you go too far one of Chris Holden's friends will call up and ask if you need any home repairs.
Trying times are ahead for residents and voters of any and all california cities, those political machines hiding out in city halls are still moving ahead with mandates and projects that were dreamed up decades ago.
The machine is still grinding up money like it grew on trees, this of course is counter productive to the realities of the tax based incomes cities are now collecting. This of course doesn't take into account of loans and bonds each city has to repay or payoff, then their are the city hall "light Bulbs" who want to incur more loans and bonds to repay the previous ones?
This scheme seems to mimic the first step down the wrong path many cities took a decade ago, borrowing against the future isn't the smartest thing to do as we have all found out the hard way. Some lost a house to two, others lost their jobs, family and marriage.
Be extra careful when those "pie in the sky" schemer's from city hall concoct another fire "fix it all" plan.
These city hall fools will do and say anything to deflect responsibility from themselves. If history is any measure as to their guilt, then who loses their jobs first? it's not the city hall managers, instead it's the hourly stiffs. Why is that? because we need someone in city hall to oversee the orderly recovery and or closing down the whole misguided operating that they started in the first place.
Hear, hear 11:14.
The Moderator January 27, 2013 at 11:32 AM
Great post. Buchanan's "full service city" and his "do-gooder" speech come to mind. City Hall's constant big sell to the community is that they are essential. They aren't. Somebody needs to handle all the BS paperwork, but beyond that their contribution to the well being of the town is minimal.
It only costs a latte a day. You heard Josh.
What is the cost of a beer at the Bucchaneer? Josh should trade in the commodity prices of things he knows best.
What a grat post ll:14!
If only the dumb voters who vote in these idiots like Moran, Buchanan, Mosca, Walsh, we may have a chance to really change this very bad path we go down.
I wish they would all read what you just posted.
Why were the Sheriffs called? And isn't Chantry Flats a part of Sierra Madre?
Chantry Flats is in a National Forest (with some private property on land leased from the Forest Service.) My guess is that LASD needs to send some heaviliy armed (maybe SWAT) deputies up there to bring in Mr. Stoopid.
Also Mt Wilson and Santa Anita Racetrack or not part of Sierra Madre
That is why I never enter the Mt Wilson Trail Race. I hate to leave town.

redpajama_set_name: RedPajamaCommonCrawl


text:
Daniel Vorländer (1867 – 1941) va ser un químic alemany que va sintetitzar la major part dels cristalls líquids coneguts fins a la seva jubilació l'any 1935.

Vorländer va néixer a Eupen a la Prússia renana (avui Bèlgica). Va estudiar química a les Universitats de Kiel, Munic i Humboldt de Berlín, després de la qual cosa es va convertir en professor a la Universitat de Halle-Wittenberg.

Vorländer va aplicar el seu coneixement de l'estructura molecular per seleccionar aquelles molècules que mostren o poden mostrar l'estat líquid cristal·lí. En particular, una geometria molecular lineal era propícia. Al llarg dels anys Vorländer i els seus estudiants sintetitzaren centenars de compostos cristal·lins líquids. Un descobriment interessant és que entre els cristalls líquids viscosos hi havia molts compostos de sabó i similars al sabó.

Vorländer va servir com a voluntari durant la Primera Guerra Mundial, durant la qual va rebre la Creu de Ferro. Va morir a Halle, Saxònia-Anhalt, l'any 1941.

Referències

Enllaços externs
 Biografia al "Catalogus-professorum-halensis"

Químics alemanys
Alumnes de la Universitat Humboldt de Berlín
Alumnes de la Universitat de Munic
Alumnes de la Universitat de Halle
Alumnes de la Universitat Christian Albrecht de Kiel
Morts a Halle (Saxònia-Anhalt)
Persones de la província de Lieja
Científics valons
Químics belgues

redpajama_set_name: RedPajamaWikipedia


Young Living membership brings along numerous benefits. Commissions, reward points, silver six program, diamond program – all these are rewards of being a Young Living member. However, these rewards can only be obtained when you sign up as a member, attract more people and sponsor their sign ups. And this can only be done when you share your essential oil story.
My Oil Site offers easy customization for all Young Living members. Our step by step guide walks you through the process and helps you select the web layout and color schemes according to your choice. Before working on your website, you can view a 'demo website' to get an idea of what's in store and what options you have to choose from.
My Oil Site offers quick, hassle-free social media sharing. We are aware of the fact that you might have been sharing your essential oil story through a blog or a social media account. Thus, moving to a new platform could cost you repeat customers and sign-ups. As a solution to this problem, we offer quick social media integration and sharing. When you're setting up your website, we make sure that all your social media accounts are linked. This way, you do not lose your customers and sign-ups. Instead, your customers will be amazed to see your new website!
This is one of the most essential aspects of building a website My Oil Site. Our website features a share your story page, through which you can share your own essential oil experiences, in order to attract more customers. We realize the importance of this page which is why this page is setup carefully. For you to make money, your story should be inspirational enough to compel people to sign-up as a member.
Customers decide to sign up after reading your story. What do they have to do? Instead of leaving people wondering, there's a sign up link that makes things easier for them. This page will directly lead them to Young Living membership sign up form and your sponsor ID will appear automatically. Congratulations – you're now entitled to a number of commissions, reward points and other programs!
So, what are you waiting for? Get in touch with us and build your website in no time. In addition to this, you can receive creatively designed business cards from us for your essential oil business.


Unique in its coverage, Urban Economics and Real Estate allows an instructor to teach separate courses in either urban economics or urban real estate, or a blend of the two topics. The portion on urban economics focuses on urban/suburban growth—physical as well as job growth. The interplay of federal government and local authorities is discussed, and the effects of social problems, such as crime, poverty, and education that often accompany these changes are discussed.
While the latest data sets available are utilized, Urban Economics' emphasis is on economic analysis. The real estate chapters emphasize housing markets, appraisal, business investments, and their relationship to finance. New to this edition is extensive coverage of international issues in cities around the planet. Given the rapidly changing empirical side of urban demography, the text is accompanied by a website with new examples added annually and various discussions/tips about the latest data sets that become available.
John F. McDonald is currently at Roosevelt University, Chicago, as the Gerald W. Fogelson Distinguished Chair in R.E. John McDonald was Emeritus Professor of Economics and Finance at the University of Illinois at Chicago. He holds a Ph.D. in Economics from Yale University. At UIC he has served as Professor of Economics and Finance, Founding Director of the Center for Urban Real Estate, Senior Associate Dean for Academic Affairs and Research, and Interim Dean of the College of Business Administration. Other positions held include Research Director at NCI Research, and Adjunct Professor of Economics in the Graduate School of Business, University of Chicago. Well known for his research in urban economics and real estate, he is listed in Who's Who in Economics and is author of seven books. He currently serves as editor of the Journal of Real Estate Literature.
Daniel P. McMillen is a professor of economics at the University of Illinois at Urbana-Champaign. He has held an appointment at IGPA since 2002. His research interests are urban economics, real estate, and applied econometrics. He is editor of the journal Regional and Urban Economics, and has served on the editorial boards of five other journals. In 1998 and 1999 he served as the chair of the Department of Economics at Tulane University. In 1998, he was a research fellow for the Center for Urban Real Estate and Land Economics at the University of British Columbia. He received his Ph.D. from Northwestern University in 1987.
Part I: Economics and Urban Areas.
Chapter 1. Introduction to Urban Economics.
Chapter 2. Schools of Thought in Urban Economics.
Chapter 3. Location Decisions, Agglomeration Economies, and the Origins of Cities.
Chapter 4. The Economic Functions of Cities.
Part II: Location Patterns in Urban Areas.
Chapter 5. Introduction to Urban Location Patterns: Static Analysis.
Chapter 6. Using the Monocentric City Model.
Chapter 7. Empirical Testing of the Moncentric City Model.
Part III: Urban Housing and Real Estate.
Chapter 8. Housing in Urban Areas.
Chapter 9. Housing Policy in the United States.
Chapter 10. Real Estate Law and Institutions.
Chapter 11. Real Estate Markets.
Chapter 12. Real Estate Development and Investment.
Part IV: Government in Urban Areas.
Chapter 13. The Public Sector in Urban Areas.
Part V: Urban Social Problems.
Chapter 15. An Overview of Urban Social Problems.
Chapter 16. Urban Poverty and Its Spatial Concentration.
Chapter 17. Crime in Urban Areas.
Chapter 18. Education, Labor Markets, and Migration.
Chapter 19. Models of Metropolitan Economic Growth.
Chapter 20. Agglomeration Economies, Technical Change, and Urban Growth.
Chapter 21. Economic Development Policies for Urban Areas.
New chapter on Urban Poverty in Developing Nations to go along with the Poverty in the U.S. Cities chapter.
Extensive international examples from Europe and Asia interspersed throughout the text.


Brick ranch on 1+ ac. Down to studs rehab w/ tall ceilings, HW flooring on first floor, clean lines and high level modern touches. Chef inspired kitchen w/ SS appliances, Granite Counters, glass black splash which opens to DR, Large GR with Modern Stone FP and tons of natural light. Owners Retreat Spa is like staying at a resort, Dbl Vanity, Soaking Tub and shower with enclosure, wireless speaker and tile. 2 secondary Bedrooms and bath.


text:
Q: Does the T-800 punch a hole through the T-1000's head? In the steel mill, after John and Sarah have left the Terminator, the T-800 goes into search mode, looking for the T-1000. After some wrestling, the T-800 attempts to punch the T-1000 in its head. The T-1000's body "morphs" so that its old "head" becomes its arms, and so it takes advantage in the fight.
My question is whether the T-1000, knowing that the punch was coming, morphed simultaneous with the blow, or if the T-800 actually punched through the T-1000.

A: The script indicates that the T-800 Terminator punched clean through the T-1000's 'head'. That being said, fluidity is an integral function of the liquid metal, hence why bullets hitting it cause craters.

It comes off the wall straight at Terminator, who smashes his good
  fist into its face.  The pile-driver blow buries Terminator's fist
  almost to the elbow.
But the T-1000's head morphs in a split-second into a hand which grips,
  geometry shifting faster than we can follow.

Here's the same scene from the official novelisation.

To ward it off, Terminator smashed his good fist into it. The
  pile-driver blow buried the cyborg's fist almost to the elbow in the
  mercurylike face.
But the T- 1000's head morphed in a split-second into a hand that
  gripped Terminator's wrist, and the head "emerged" somewhere else, the
  geometry shifting faster than Terminator could follow. The T-1000
  slammed Terminator into a large conveyor motor, jamming his arm into
  the moving works.

redpajama_set_name: RedPajamaStackExchange


We have three modern, bright, comfortable self-catering cottages (open all year) giving you the opportunity to relax in luxury whilst enjoying the natural beauty of a farm setting. We are in a convenient location to explore the surrounding National Park area with great local amenities on your doorstep; Rushcroft Lodge sleeps 2-3 and the other two barn conversions sleep 4. The light, space, airiness and decor of each, and their individual little private gardens are enchanting and welcoming. There is also a beautiful colourful Gypsy Caravan in the most romantic secluded corner of one of the meadows. Or our cosy Shepherds Hut with stunning views over the farm, it is the perfect place to unwind, sip a glass of wine and watch the sun go down.
Rushcroft also provides outstanding accommodation for up to six horses in vast pastures with automatic water provided, and grass, even in the hottest temperatures, negating the need to feed hay. The whole atmosphere is extremely calm, laissez-faire and relaxed. There is also a beautiful outside menage with an assortment of jumps that you can use at any time.
The campsite (open 23rd May to 4th September), which is separate from the cottages, gently sloping, calm and peaceful with the emphasis on natural camping. Visitors are invited to get away from all the clutter of modern life and experience nature and the great out doors in a convenient and beautiful location.
Altogether the Farm covers about twenty acres, hidden away in a little corner of the New Forest, minutes from some of the best riding, walking and cycling that the Forest has to offer. Also only a few minutes walk from Sway village with pubs, cafe, shops and a rail way station, great if you are looking for a car free break.
You can be assured of attention to detail and a personal approach during your stay.
Lymington, with its beautiful marina and wealth of interesting shops, pubs, cafes and restaurants, is only 15 minutes away from Sway. You can also catch the regular ferry to the sunny Isle of Wight from there. Beaulieu, with its fantastic Motor Museum and Palace, is 20 minutes drive away through the peaceful New Forest National Park with free roaming ponies and stunning wild life to spot along the way.
From Sway you can hop on a train and visit the long sandy beaches, pier, shops and night life of Bournemouth and Poole in one direction or Brockenhurst and Southampton in the other. Horses are also welcome at Rushcroft Farm.
Please telephone Lynn on 07850 258790 for further details.
"I parked on the hard standing and had a lovely view of the undulating area around. The campsite is 'lovingly' looked after by the owners and friends. The added bonus for me was the chance to feed the goats and their kids each morning and evening."


text:
Women System
WOULD BE CARJACKER Shot 6 Times By Pizza Deliveryman in Philadelphia
Women System January 29, 2022 0 comment
Heroes don't always wear capes sometimes; they drive around with lighted pizza signs affixed to the top of their vehicles.
Last night, while a 39-year-old male was making an honest living in the crime-ridden, Democrat-run city of Philadelphia, a violent, armed carjacker, who are a dime a dozen in the so-called "City of Brotherly Love" decided it was his right to steal the pizza deliveryman's vehicle.
The armed pizza deliveryman acted quickly, putting an end to a potentially deadly crime against him and possibly against his next victim as well.
Unfortunately, for the armed man criminal who approached the pizza deliveryman and tried to steal his car, the pizza man, who had a concealed carry permit, drew his gun and blasted the 23-year-old attacker six times, cops told WPVI. The failed thief returned fire but didn't hit the victim, WPVI said.
NYP reports – According to the station, the would-be carjacker was driven to Temple University Hospital, where he was listed in critical condition.
There have already been 90 carjackings in Philadelphia this year as officials in the City of Brotherly Love ramp up patrols to fight a surge in vehicle crime, WPVI stated.
Last year, there were 757 carjackings — up from 404 in 2020, the Philadelphia Inquirer reported. Thursday's shooting was the second time this month a potential carjacking victim flipped the script and opened fire on the person trying to steal their car.
On January 4th, we reported about another armed citizen who saved his life and possibly the lives of many others.
100 Percent Fed Up reported – a Lyft driver in Philadelphia (almost) fell victim to a carjacking in the middle of the day, but luckily was carrying a gun and shot both criminals
The 38-year-old Lyft driver was rear-ended by a Honda in a very public area and, when he stopped his car, the carjacker ran up with an automatic rifle and pointed it at the driver. The driver and woman in his passenger seat both got out and the carjacker got it. When the criminal started to drive off, the Lyft driver – who had a concealed carry permit – shot at the carjacker and hit him twice in the torso.
The second suspect, still in the Honda, tried to run over the Lyft driver, prompting the driver to fire again. This criminal suffered a gunshot wound on his right side.
In a statement from Philadelphia PD's Chief Inspector Scott Small, he expresses how fortunate the victim was to have had a weapon on him for protection. "Fortunately our… victim wasn't shot because he had a rifle put to him," said Small, "and our Lyft driver had a weapon that he used and shot both of the perpetrators."
It is becoming increasingly important for delivery/transportation drivers to have personal protection against the all too common carjackings that are taking place. "[T]his case again illustrates why so many delivery drivers, food delivery drivers, … Uber and Lyft drivers are all running to gun stores and getting legal guns because this is what's happening on a daily basis all around the country," said Keeley.
As carjackings continue to make these bold attacks, it is increasingly important for these drivers to have weapons not only for personal protection but also to protect their passengers and nearby civilians.
Shipping Container Home
Amazing Animals Beauty Tips Cancer Celebrity Depression DIET & NUTRITION Food Funny Healthy Eating Tips Humor Inspirational Interesting Mental health Nature News Photos Sad Science Vintage Women World Beautiful Womens
Blog Archive January (189) December (181) November (263) October (301) September (106) July (265) June (35) March (459) February (495) January (668) December (542) November (565) October (463) September (242) August (218) July (218) June (177) May (118) April (146) March (174) February (156) January (148) December (164) November (194) October (177) September (238) August (212) July (75) June (64) May (181) April (179) March (236) February (367) January (153) December (103) November (102) October (78) September (43) August (28) July (24) June (10) May (28) April (76) March (35) February (3) January (20) December (14) November (26) September (22) August (24) July (3) June (18) May (29) April (49) March (49) February (121) January (150) December (112) November (75) October (107) September (74) August (40) July (28) May (1) March (2) January (3)


Hanging out with foodies is a good thing. You get to bask in a camaraderie of cuisine and take pictures of your plate with impunity. And sometimes you get free cake.
On our recent foodie field trip to Eastern Seaboard we met Caryna of Caryna's Cakes. In the chitchat over our calamari and pig's cheek, we learned that Caryna is a full-time baker who sells baked goods at various markets and supplies some small cafes and coffee shops as well as special orders. As a matter of fact she had been working at a market that very day and had driven straight to meet up with us all in Drogheda. She still had all her market gear in her car. She also mentioned that she had made a pumpkin apricot cake for the market that day, and that she had a few remaining slices in her car. She said she thought it was the kind of cake that would be even better the next day.
Pumpkin. We love pumpkin. Canned pumpkin is one of the items we accept in exchange for room and board in our apartment. When my aunt and uncle came to visit us they moved the cans of pumpkin into a carry-on to reduce weight on a checked bag, forgetting that canned pumpkin is, by Transportation Safety Authority definition, a gel. When questioned about this can of gel my uncle explained very passionately, Oh, I have to take that to my niece. She has to make pumpkin pie! Oh pumpkin pie, the agent said, well, of course. And the pumpkin boarded the plane. Pumpkin pie trumps terrorism risk. As well it should!
So, throughout our wonderful meal a little part of my mind kept thinking about the pumpkin cake in Caryna's car. While eating the black pudding ballotine and sweet potato fries I kept thinking about pumpkin cake. As we left that evening I inquired as to whether I could purchase a slice. Dear reader, she gave us all her leftover pumpkin cake! She even sent it home on the pretty china plate, saying we could return it the next time we meet.
So I rode home from Drogheda with that cake on my lap (see photo at right), and that evening we read about that exact cake on Caryna's blog. I marveled at the power of foodie fate that led that cake from a stranger's kitchen into my home on that magical day.
Bill and I each took a slice to work on Monday. The cake was terrific. Full of those warm spices with perfect cream cheese frosting. We had no shortage of baked goods, having returned from Brown Hound Bakery with a gift box and a lemon cake. The pumpkin apricot cake was not overwhelmed by those treats at all.
Caryna has a great story about the provenance of the pumpkin apricot cake (plus the recipe) on her blog. She also has a recipe inspired by our visit to the Brown Hound Bakery and more information about her baking business.
Did I mention she delivers cakes on a vespa?
Aw shucks! You and the pumpkin cake were obviously fated to meet each other.
I think every expat has a story about the lengths they've gone to to get their hands on some canned pumpkin! I ask anyone visiting us to bring some over too – though now I know to tell them to put it in their checked luggage in case they meet a less understanding person in security than your aunt and uncle did!
I was reading the recipe and I didn't know there were green pumpkins. I guess that would be like rhubarb having both red and green varieties.:) The apricots would add a nice tang. I love apricots.
Duncan is my mum's veg guy! She visits him at Leopardstown and always has a story about him or his Dad.
Hey, that's cool. A good veg guy is pretty exciting and can lead to a bit of disorientation!


Capture the memory of a loved one in a special round pendant. Created by layering small strips of colored glass to create a vibrant, warm look and available in a bold palette that includes eight spectacular colors, our pendants are both energetic and rich. Additionally, our multi-color pendant blends a rainbow of the eight colors into a vivid display of beauty – a treat for all to see, indeed!
Available in two sizes, these pendants feature bold colors that radiate through a soft, circular shape.
Each pendant includes a 36" black hand-dyed silk ribbon that may be threaded through the small hole in the pendant. For those who desire a "dressy" look, a sterling silver pinch bail may be purchased separately.
As with all of our cremation jewelry, our round pendants may be designed with visible (viewed from the back) or hidden (fired into the glass) ashes. All pendants, unless otherwise specified, will be made with hidden ashes.


The Culture Project at 45 Bleecker Street has proved that lightning can strike the same spot twice.
Last year, the theater group showcased "Bridge and Tunnel," featuring Sarah Jones playing multiple New York City roles and tackling prickly issues with humor. The quirky hit was so popular it's slated for a Broadway transfer this spring.
Now, another dazzling one-woman bio-play, "Belfast Blues," written and performed by Geraldine Hughes, is electrifying audiences. Billed as "one wee girl's story about family, war, Jesus and Hollywood," the show recounts Hughes' childhood in strife-torn Belfast in the 1970s and '80s.
And like Jones, who found a mentor in Hollywood mega-star Meryl Streep, Hughes has a high wattage benefactor of her own—Angelica Huston—who, it so happens, just won a Golden Globe for her supporting role in ``Iron Jawed Angels." Wearing simple black jeans and an untucked shirt, the blue-eyed Hughes portrays her young self, and slips effortlessly among 23 other characters, including her parents and neighbors. Against the backdrop of a bleak landscape––the set is by Jonathan Christman––accented with boulders, barbed wire and projected images, she brings her heartaches and hopes to life.
True to Irish tradition, the 34-year-old actress—who has played countless roles on stage and screen—has a gift for storytelling. She recently turned an a press interview into a mini-show, filled with delightfully arch impersonations that drew on her experience growing up during "The Troubles" in her homeland.
DAVID KENNERLEY: How did "Belfast Blues" come about?
GERALDINE HUGHES: I never had any intention of writing anything, but a theater friend heard my stories and said, "I have a notion this will make a really great play." I replied, "I'm not really into one-person shows—they're like a therapy session." But when she got me in front of a mike in a sound studio, something magical happened. Everyone in the room said, "Jeepers, you have to do this and it just has to be you." The show was born that day.
DK: Did you keep a diary?
DK: What was it like performing your first show?
But I'm of the nature that kids know an awful lot more than we give them credit for. And they're more honest. This is a story from a child's point of view and I hope it will make people think beyond just Ireland. I never imagined that in January 2005 my play would still be so relevant. It makes me quite sick.
DK: Did you really try to tell Catholics and Protestants apart as a girl?
GH: Sure. I remember being in the city center with my Mummy, thinking, "There must be Protestants 'round here somewhere." You came from the war zones, mixed at the shopping area and acted like normal people, then went back home to your separate territories. It's sort of mad, when you think about it.
DK: The play conveys the senselessness of war, bigotry and its impact on children. What else?
GH: People of various cultures, backgrounds and personal histories come away with different messages. Vietnam vets say it reminds them of walking the streets and seeing the horrified kids. People who've had run-ins with their folks tell me it's about family dysfunction. Others with drinking fathers say it's about alcoholism.
DK: What do you want audiences to come away with?
GH: A sense of hope. You can't go to the dark moments without it. No matter what you want, no matter what you are born into, keep friggin' dreaming. Because if you work hard and keep focused, there's a way to get there. I mean, just the fact that I'm onstage telling my story proves everything can turn out all right.
DK: Given the show's harrowing personal content, how do you make it through each night? Do you down several Bailey's when you get home?
GH: [Laughs] It's about me, yet it's not about me. It's not literal. I figured out a way of distancing myself, elevating the subject. If it didn't, it would be exhausting. If I thought for one second that I was self-indulgent, God forbid, I'd quit.
DK: Why didn't you escape to America to seek your fortune earlier?
GH: You're the first to ask—it's a wonderful question I've often contemplated. There was definitely an opportunity, but I was only 13 and wasn't able to help myself. Being in an all-girls Catholic school, I felt that education was more important. If my parents had been pushy, I could've had much more of an acting career. With my daddy getting sick, it was a freakin' hard life and the last thing people were thinking was how to get Geraldine on a TV show. I was needed at home. I had to wait till I was old enough to do it myself.
DK: Many solo shows rely on accessories to shift characters. Were you tempted to use them?
GH: No. I absolutely wanted to keep this show in its purest form, no matter how hard I had to work. For me, impersonation comes naturally. If you're honest enough as a performer, the audience will get it. I couldn't fathom cluttering up the stage with glasses or hats or whatever. The trick is to find a gesture to associate with each character. When I hitch up my pants you know it's Daddy. As soon as I clasp my hand to my heart, it's Mummy. During rehearsals, the movements became a sort of dance.
DK: You come from a big Irish family with six kids, but rarely mention your siblings. Why?
GH: We all grew up in the same house but nobody talked, just went about our own business. There was me in my cocoon. I don't even know what my relationship was with my brothers and sisters, so to force it in the play would be makey-uppey. Let them write their own play.
DK: How did Angelica Huston get involved?
DK: What is Huston's role exactly?
GH: Much more than simply lending her name, Angelica is super supportive. She sends important people to see the show. She rang me before the first performance and offered advice to calm my nerves. "You are a powerhouse," she said. "You are a brilliant wee girl and you must continue to tell this story. People are going to listen and be affected." She sent me friggin' flowers!
DK: Now that you're a successful actress, do you ever return to Belfast?
GH: Sure, I took the play back home recently. To present it to the people who also lived that story—to see them stand on their feet and smile—gave me permission to stage the play wherever I want, with pride.


text:
The story of UNMIL [Book]: Engagements with political parties in advance of 2017 elections
The political atmosphere in Liberia was charged with fear and mistrust during 2016 and 2017 as preparations for the presidential and legislative elections scheduled for October 2017 began in earnest. SRSG Farid Zarif led intensified good offices engagements as mandated by Security Council resolution 2333 (2016), with the aim of sustaining an environment conducive to peaceful, transparent and credible elections. He held nine meetings between May 2016 and August 2017 with the leadership of twenty-plus political parties contesting the elections, to encourage dialogue and peaceful campaigning.
With the Liberian Governance Commission, he sponsored a two-day conference in May with all political parties, facilitated by the Inter- Religious Council of Liberia. This led to the parties' adoption of the Farmington River Declaration in the margins of the ECOWAS Summit on4 June in Monrovia, by which they committed themselves to peaceful elections and a seamless transition to a new administration in January 2018. At a second meeting he convened, on 28 July, just prior to the formal campaign period, party leaders reaffirmed their commitment to the Declaration.
Then, two days before the 10 October elections, UNMIL held a function for presidential and vice presidential candidates, inviting representatives from ECOWAS, the AU, EU and international election observer missions to encourage the candidates to help ensure that peace prevailed during and after the elections.
Following the first round of voting, the ruling Unity Party (UP), whose candidate had come in second, joined the third-place Liberty Party's (LP) challenge of the results, charging that fraud had been committed, as well as interference by the sitting President. The Supreme Court put a hold on the second round to hear the complaints.
During the intervening weeks of uncertainty, both SRSG Zarif and his Deputy Waldemar Vrey (DSRSG for Political and Rule of Law) met with the Coalition for Democratic Change (CDC), the UP and the LP, as legal disputes were underway at the National Elections Commission (NEC) and the Supreme Court. SRSG Zarif engaged with candidates to dissuade them from mobilizing their membership to protest the provisional results, and instead seek legal options to address their grievances. All leaders called on their followers to remain peaceful and patient, and a planned march to the NEC headquarters was called off.
The interventions by the UNMIL leadership encouraged the parties to follow the rule of law, to call on their supporters to remain calm as the legal process played out, and to respect the pending Supreme Court decision. Following the Court's ruling on 8 December that opened the door for the run-off election on 26 December, the SRSG and DSRSG engaged again with the CDC and UP leadership and facilitated a dialogue between the parties and the NEC to ensure transparency and calm. Throughout the process, UNMIL worked on coordinating efforts and messaging with local, international and regional actors, notably ECOWAS and AU. The UN Security Council congratulated the Liberian people, Government, political leaders, civil society, media and expressed appreciation for the good offices of the SRSG and the UNMIL leadership for the peaceful conduct of the run-off election.
 Leading the orchestra | Bibi-Masumeh Eng, Chief of Staff
 The story of UNMIL [Book]: Obasanjo visit promotes acceptance of election results


The Printable Play Money available at FreeStuff4Kids is easily the most popular printable on the site. I thought it might be nice to have some Printable Play Checks to go along with them! The address area is blank, so the kids can practice writing their name and address too. Kids can have fun playing bank, writing checks at the "grocery store" and other fun games as they learn about money!


Huge Firedrop for Android Update!
We have finished development on our Android app and have released it in the Play Store - With a whole host of new features, fixes and improvements this update takes Firedrop to the next level!
Backing up your entire device is now as easy as the click of a button. This will automatically run for first time users. If you have used the app before, simply select the Backup Data option from the navigation drawer. You will be greeted with the option to automatically find files of a certain type, such as images, videos and documents, be given a list of files ready to be uploaded to approve or remove and then simply touch the upload button - All files will be backed up to the cloud in the background. Voila!
Our aim is to be the social cloud storage service. Our first step in that direction is direct user to user file sharing. Share a file instantly with another Firedrop member, and they will be sent an android notification showing them you have just sent them a file which they can access directly by touching the notification or viewing their 'Shared with me' folder.
The trash can has been completely revamped. Instead of permenantly erasing your files, We now store them in your trash, where they can be restored at any time or permanently erased if you want to free up some space.
You can now directly preview your PDF documents directly from the cloud. We have also added functionality to use our document viewer for PDF files all over the web.
Direct video streaming has now been implemented to our App. We have created a sleek new media player which communicates directly with our file servers to deliver smooth, native video streaming on the go!
You can now copy files from shared Firedrop links directly to your cloud space, saving you time and bandwidth.
Image thumbnails now load much, much faster and sliding between images in your galleries has improved tenfold utilising the power of the Nginx web server.
We have completely redone the way we serve and accept files for our Android users. The improvements have seen file transfer speeds max out all of our superfast connections! This again, was aided by the lightning fast Nginx server.
We have updated the look of the floating action menu to be clearer, more usable and overall, much prettier to look at.
File transfers are now removed from the complicated list view, and congregated as one whole action in the status bar. You will be shown a simple overall progress bar and notified when actions are complete.
Various fixes which caused crashing and timeouts due to uploading many items at once.
We are very proud of this release and hope our users are as happy with the release as we are. Grab the update from the Play Store today!
We would also love to hear your feedback - Just open a ticket and let us know what you think. If you have any suggestions we cant wait to hear them and get them ready for our next update!


text:
\section{INTRODUCTION}

Study of Galactic parameters, especially of the Galactic rotation
curve, is of great importance in solving a number of problems,
such as estimating the mass of the Galaxy, determining the
distribution of matter, estimating the hidden mass, studying
dynamics and structure of the Galaxy and its subsystems, etc.

For this purpose masers having trigonometric parallaxes,
line-of-sight velocities and proper motions (Reid et al., 2009)
are of great interest. Currently measurements of parallaxes with
mean error of several percents are fulfilled with radio
interferometers for three tens of masers in the various active
high-mass star-forming regions. Because these masers are
associated with very young ($<10^5$~yr) OB stars, their kinematics
reflects the properties of the youngest part of the Galactic disk.

Analysis of motions of 18 masers was made by a number of authors
(Reid et al., 2009; Baba et al., 2009; Bovy et al., 2009;
McMillan~\&~Binney, 2010). For the first time Reid et al. (2009)
suggested that high-mass star-forming regions significantly
($\approx 15$ km s$^{-1}$) lag circular rotation. McMillan \&
Binney (2010) suggest that much of this lag could be accounted for
by increasing the value of the Solar motion in the direction of
galactic rotation from 5 to 11 km s$^{-1}$.

The question of particular interest is the peculiar velocity of
the Sun with respect to the LSR,
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}$. On the basis of
Str\"omberg's relation, Dehnen~\&~Binney~(1998) determined the
vector
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(10.0,5.3,7.2)\pm(0.4,0.6,0.4)\;\mathrm{km\,
s}^{-1}$ using proper motions of $\approx$12000 main sequence
stars from the Hipparcos catalogue. These results were confirmed
by Aumer~\&~Binney~(2009):
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(10.0,5.3,7.1)\pm(0.3,0.5,0.3)\;\mathrm{km\,
s}^{-1}$, who applied the same method to proper motions from the
revised version of the Hipparcos catalogue (van Leeuwen, 2007). In
the work of Sch\"onrich et al.~(2010), where gradient of
metallicity of stars in the Galactic disk was taken into account,
this velocity is different:
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(11.1,12.2,7.3)\pm(0.7,0.5,0.4)\;\mathrm{km\,
s}^{-1}$. Using another approach, Francis~\&~Anderson~(2009)
suggested that this velocity is:
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(7.5,13.5.2,6.8)\pm(1.0,0.3,0.1)\;\mathrm{km\,
s}^{-1}$.

In the present work, we are trying to establish relationship
between motions of all currently known masers having parallaxes,
proper motions and line-of-sight velocities, and parameters of the
Galactic spiral density waves (Lin~\&~Shu, 1964), and to estimate
components of the peculiar velocity of the Sun with respect to the
LSR. This goal is achieved by determining parameters of the
Galactic rotation curve, as well as other kinematic parameters, by
means of Bottlinger's equations. Fourier analysis of periodic
deviations of observational velocities of masers from the Galactic
rotation curve is aimed to obtain some estimates of spiral density
wave parameters.

\section{DATA}

Input data on methanol masers with trigonometric parallaxes and
proper motions from VLBI measurements are taken from the papers of
Reid et al. (2009), Rygl et al. (2010). We added also H$_2$O
masers SVS~13 in NGC~1333 (Hirota et al., 2008a),
IRAS~22196$+$6336 in Lynds 1204G (Hirota et al., 2008b) and
G14.33--0.64 (Sato et al., 2010), with parallaxes and proper
motions measured in the framework of VERA (VLBI Exploration of
Radio Astrometry) program. Note that, for maser NGC~281--W listed
in Reid et al.~(2009), we used observational data obtained by Rygl
et al. (2010) with the quoted uncertainty for 6.7 GHz masers
smaller than the Sato et al. (2008) 22 GHz masers. For the nearest
star-forming region in Orion, along with the data on maser
Orion--KL (Hirota et al., 2007), we use independent VLBA
observations of radio star GMR~A (Sandstrom et al., 2007) with
line-of-sight velocity with respect to the LSR
$(V_r)_\mathrm{LSR}=-4\pm5$~km s$^{-1}$ (Bower et al., 2003). It
is the Bower's et al. (2003) opinion that the GMR~A source is a
young star of T~Tau type (WTTS). We use also a very young object a
supergiant S~Per (Asaki et al.,~2007) with line-of-sight velocity
$V_r=-39.7\pm0.7\;\mathrm{km\,s}^{-1}$ from Famaey et al.~(2005).

All 28 objects being studied are listed in Table~1. In Fig.~1, one
can see only 25 points because $X,Y$ coordinates of some objects
are very close to each other. For example, three masers Cep~A,
IRAS~22198 and L~1206 form practically a single point in the $XY$
plane.

\begin{figure}
\begin{center}
\includegraphics[width = 75mm]   {f-01.eps}
\caption{Coordinates of masers in the $XY$ Galactic plane.
Locations of the Sun and Galactic Centre (GC) are indicated. The
circle of 8~kpc radius is drawn.}
\end{center}
\end{figure}

\begin{table*}
\caption{Data on masers. Velocities $U^1,V^1,W^1$ are residual
velocities with Galactic rotation excluded using parameters (16).}
 \label{t1}
 \begin{tabular}{@{}lrrrrrrc}
 \hline
 Source          & R, kpc & ~~~~~$U^1,$ km s$^{-1}$ & $V^1,$ km s$^{-1}$ & $W^1,$ km s$^{-1}$ &
                $\Delta V_{\theta},$ km s$^{-1}$ & $V_R,$ km s$^{-1}$ & Ref
\\\hline
L 1287            &  8.52 & $ -2.9\pm1.7$ & $-20.7\pm2.6$ & $-10.2\pm2.5$ & $ -5.7\pm2.6$ & $ -5.6\pm1.7$ & (2) \\
IRAS 00420$+$5530 &  9.33 & $  3.0\pm2.7$ & $-19.6\pm4.2$ & $ -1.5\pm0.8$ & $ -2.9\pm4.2$ & $-11.8\pm2.8$ & (1) \\
NGC 281--W        &  9.50 & $ -4.2\pm2.6$ & $ -2.3\pm2.8$ & $-16.0\pm1.7$ & $ 12.8\pm2.8$ & $ -1.2\pm2.6$ & (2) \\
W3 (OH)           &  9.46 & $  4.8\pm2.1$ & $-17.6\pm2.2$ & $ -6.2\pm0.2$ & $ -1.2\pm2.2$ & $-13.1\pm2.1$ & (1) \\
WB 89--437        & 13.05 & $  0.2\pm2.1$ & $-17.1\pm2.1$ & $  2.5\pm3.8$ & $  0.2\pm2.1$ & $ -8.6\pm2.1$ & (1) \\
NGC 1333 (f1)     &  8.21 & $-23.6\pm4.4$ & $-13.5\pm2.3$ & $  0.0\pm2.5$ & $  0.9\pm2.3$ & $ 15.6\pm4.4$ & (3) \\
NGC 1333 (f2)     &  8.21 & $-21.1\pm4.5$ & $  5.5\pm1.8$ & $ 10.0\pm3.5$ & $ 20.0\pm1.8$ & $ 13.3\pm4.5$ & (3) \\
Ori GMR A         &  8.32 & $ -4.7\pm4.1$ & $ -8.8\pm2.3$ & $ -3.1\pm1.7$ & $  5.6\pm2.3$ & $ -3.4\pm4.1$ & (4) \\
Ori KL            &  8.34 & $-17.9\pm4.2$ & $-14.4\pm2.4$ & $ -3.8\pm3.0$ & $  0.3\pm2.4$ & $  9.9\pm4.2$ & (1) \\
S252 A            & 10.08 & $-12.6\pm3.0$ & $-11.1\pm0.6$ & $ -9.2\pm0.3$ & $  3.5\pm0.6$ & $  4.5\pm3.0$ & (1) \\
S255          &  9.56 & $ -7.7\pm3.6$ & $ -0.8\pm9.5$ & $ -4.0\pm10$  & $ 13.7\pm9.5$ & $ -0.8\pm3.6$ & (2) \\
S269          & 13.16 & $ -3.5\pm2.9$ & $-16.2\pm1.2$ & $-11.7\pm0.9$ & $ -2.2\pm1.2$ & $ -4.3\pm2.9$ & (1) \\
VY CMa        &  8.64 & $ -6.1\pm2.9$ & $-16.9\pm3.0$ & $-13.6\pm2.5$ & $ -2.7\pm3.0$ & $ -1.6\pm2.9$ & (1) \\
G232.62$+$0.9 &  9.12 & $ -7.8\pm3.2$ & $-10.5\pm3.1$ & $ -6.4\pm2.2$ & $  4.0\pm3.1$ & $ -0.9\pm3.2$ & (1) \\
G14.33$-$0.64 &  6.92 & $    0\pm10$  & $  -10\pm14$  & $-10.8\pm4.5$ & $    5\pm14$  & $   -8\pm10$  & (1) \\
G23.66$-$0.13 &  5.23 & $ 21.6\pm3.7$ & $ -6.7\pm5.7$ & $ -3.1\pm0.4$ & $ 14.8\pm5.6$ & $-26.8\pm3.8$ & (1) \\
G23.01$-$0.41 &  4.18 & $  1.0\pm4.7$ & $-20.7\pm9.1$ & $ -8.5\pm2.3$ & $ -1.8\pm8.4$ & $-10.8\pm5.8$ & (1) \\
G23.43$-$0.18 &  3.50 & $  -15\pm10$  & $    9\pm22$  & $ -5.3\pm1.8$ & $   13\pm18$  & $ 20\pm16$    & (1) \\
G35.20$-$0.74 &  6.34 & $-21.7\pm3.3$ & $-20.1\pm3.6$ & $-15.7\pm1.5$ & $ -8.2\pm3.6$ & $ 12.2\pm3.3$ & (1) \\
W48           &  5.65 & $-31.1\pm5.7$ & $-16.5\pm7.5$ & $-16.5\pm2.4$ & $ -9.6\pm7.3$ & $ 21.1\pm5.9$ & (1) \\
W51           &  6.08 & $  -24\pm41$  & $  -10\pm35$  & $-10.4\pm3.7$ & $   -7\pm37$  & $   15\pm38$  & (1) \\
V645          &  7.16 & $-14.4\pm2.6$ & $-13.6\pm2.9$ & $-11.4\pm0.5$ & $ -0.8\pm2.9$ & $  6.3\pm2.6$ & (1) \\
Onsala1       &  7.50 & $   -9\pm13$  & $-18.3\pm5.6$ & $ -2.9\pm6.0$ & $ -4.1\pm6.8$ & $    0\pm12$  & (2) \\
IRAS 22198    &  8.26 & $ -4.2\pm3.7$ & $-23.4\pm4.9$ & $  3.0\pm2.1$ & $ -8.6\pm4.9$ & $ -4.6\pm3.7$ & (3) \\
L 1206        &  8.27 & $-12.8\pm4.4$ & $-19.4\pm3.2$ & $ -7.2\pm5.7$ & $ -5.3\pm3.2$ & $  4.4\pm4.3$ & (2) \\
Cep A         &  8.26 & $ -8.9\pm3.8$ & $-16.6\pm4.9$ & $-12.6\pm1.2$ & $ -2.2\pm4.8$ & $  0.7\pm3.8$ & (1) \\
NGC 7538      &  9.30 & $ -2.1\pm2.1$ & $-32.7\pm2.9$ & $-18.1\pm1.0$ & $-16.0\pm2.8$ & $-10.5\pm2.2$ & (1) \\
S Per         &  9.30 & $-16.1\pm1.2$ & $-16.9\pm1.2$ & $-17.2\pm3.1$ & $ -3.9\pm1.1$ & $  7.5\pm1.1$ & (5) \\

\hline
 \end{tabular}
 \medskip

 {
 Notes. Initial data are taken from:
 (1) -- Reid et al. (2009);  (2) -- Rygl et al. (2010); (3) -- Hirota et al. (2008a);
  (4) -- Sandstrom et al. (2007);
 (5) -- Asaki et al. (2007).}
\end{table*}

Fig.~1 is drawn in galactocentric Cartesian coordinates $X$ and
$Y$. As one can see from this picture, only one maser has inaccurately measured parallax.
That is the maser W51 (in the first Galactic
quadrant), with relative error of parallax $e_\pi/\pi=0.36$.
In fact, only this maser requires calculation of
upper and lower bounds on its distance. But, because this maser
lies in the horizontal part of the Galactic rotation curve, hereafter we use
an average estimate of the heliocentric distance $r\pm
\sigma_r$ or galactocentric distance $R\pm \sigma_R$. The same
distance estimates are used also for other masers.

We reduce line-of-sight velocities of masers with respect to the
LSR to the heliocentric coordinate system using the
standard Solar motion velocity: $(\alpha,
\delta)_{1900}=(270^\circ, +30^\circ)$, $V=20\;\mathrm{km\,s}^{-1}$, hence
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(10.3,15.3,7.7)\;\mathrm{km\,
s}^{-1}$ (Reid et al., 2009).

It is very important for the purposes of our study to know the
accurate value of $R_0$. A review of $R_0$ estimates made by a
number of authors can be found in the paper by Avedisova~(2005),
where the average value is derived as $R_0=7.80\pm0.33$~kpc. Note
that the most reliable values of this parameter were obtained only
recently. Analysis of motion of the star S2 around the black hole
in the Galactic Centre gave $R_0=8.4\pm0.4$~kpc (Ghez et al.,
2008). This value is in a good agreement with observations of
orbits of 28 stars near the Galactic Centre during 16 yr:
$R_0=8.31\pm0.33$~kpc (Gillessen et al., 2009).

In general, modern estimations show that the most probable value
of $R_0$ is close to $8.0$~kpc, and error of its determination is
close to $0.3$~kpc. For the sake of reliability, we'll consider that the value
of $R_0$ lies in the $7.5-8.5$~kpc range.

\section{METHODS}
\subsection{Determining Rotation Curve Parameters}

Method used here is based on the well-known Bottlinger's formulas
(Ogorodnikov, 1958),
where angular velocity of Galactic rotation is
expanded in a series to $n$-th order terms in
$r/R_0$:
$$
\displaylines{
 V_r=-u_\odot\cos b\cos l
     -v_\odot\cos b\sin l
     -w_\odot\sin b -
 \hfill\llap(1)\cr
 -R_0\sin l \cos b[ (R-R_0) \Omega^1_0/1!
 +\ldots+(R-R_0)^n  \Omega^n_0/n!],
  \hfill\cr
 V_l= u_\odot\sin l - v_\odot\cos l + r \Omega_0 \cos b -
 \hfill\llap(2)\cr
-(R_0\cos l - r\cos b) [(R-R_0)\Omega^1_0/1! +
  \hfill\cr
 +\ldots+(R-R_0)^n\Omega^n_0/n!],
  \hfill\cr
 V_b=u_\odot\cos l \sin b
         +v_\odot\sin l \sin b
         -w_\odot\cos b +
 \hfill\llap(3)\cr
 +R_0\sin l \sin b[(R-R_0)\Omega^1_0/1!
 +\ldots+(R-R_0)^n\Omega^n_0/n!],\hfill
 }
$$
where $V_r$ is heliocentric line-of-sight velocity; $V_l =
4.74r\mu_l \cos b$ and $V_b = 4.74r\mu_b$ are proper motion
velocity components in the $l$ and $b$ directions, respectively
(the coefficient $4.74$ is the quotient of the number of
kilometers in astronomical unit by the number of seconds in a
tropical year); $r=1/\pi$ is the heliocentric distance of an
object; proper motion components $\mu_l \cos b$ and $\mu_b$ are in
$\mathrm{mas\, yr}^{-1}$, line-of-sight velocity $V_r$ is in
$\mathrm{km\,s}^{-1}$; $u_\odot,v_\odot,w_\odot$ are Solar
velocity components with respect to the mean group velocity under
consideration; $R_0$ is the galactocentric distance of the Sun;
$R$ is the galactocentric distance of an object; $R$, $R_0$ and
$r$ are in kpc. Velocity $U$ directed towards the Galactic Centre,
 $V$ along the Galactic rotation, and
 $W$ towards the Northern Galactic pole.
The quantity $\Omega_0$ is the Galactic angular rotational
velocity at distance $R_0$, parameters $\Omega^1_0, \ldots,
\Omega^n_0$ are derivatives of the angular velocity from the first
to the $n$-th order, respectively. The distance $R$ can be
calculated using the expression
$$
\displaylines{\hfill
 R^2=r^2\cos^2 b-2R_0 r\cos b\cos l+R^2_0.\hfill\llap(4)
 }
$$
The system of conditional equations (1)--(3) contains $n+4$
unknowns: $u_\odot$,$v_\odot$,$w_\odot$,
 $\Omega_0,\Omega^1_0,\ldots,\Omega^n_0$,
which can be determined by the least-squares method. The system of
equations (1)--(3) is solved with weights of the form
$$
\displaylines{\hfill
 P_{(r, l, b)}=S_0/\sqrt{S_0^2+\sigma^2_{V_{r, l, b} }},\hfill\llap(5)
 }
$$
where $P_r, P_l$ and $P_b$ are the weights of equation for
$V_r$, $V_l$ and $V_b$ correspondingly, and $S_0=8\;\mathrm{km\,s}^{-1}$ is the ``cosmic'' dispersion
averaged over all observations. Errors
$\sigma_{V_l}$ and $\sigma_{V_b}$ of velocities $V_l$ and
$V_b$ can be calculated using the formulas
$$
\displaylines{\hfill
 \sigma_{(V_l, V_b)} = 4.74 r
 \sqrt{\mu^2_{l, b}\Biggl({\sigma_\pi\over \pi}\Biggr)^2+\sigma^2_{\mu_{l, b}}}.\hfill\llap(6)
 }
$$

\subsection{Determining Projections $V_{\theta}$ and $V_R$}

Components of spatial velocities $U,V,W$ of masers are
determined from observed radial (line-of-sight) and tangential
velocities $V_r,V_l,V_b$ in the following way:
$$
\displaylines{\hfill
 U=V_r\cos l\cos b-V_l\sin l-V_b\cos l\sin b,\hfill\cr\hfill
 V=V_r\sin l\cos b+V_l\cos l-V_b\sin l\sin b,\hfill\llap(7)\cr\hfill
 W=V_r\sin b                +V_b\cos b.\hfill
 }
$$
Then we find two projections of these velocities: $V_R$, directed
radially from the Galactic Centre towards an object, and
$V_{\theta}$, orthogonal to $V_R$ and directed towards Galactic
rotation:
$$
\displaylines{\hfill
  V_{\theta}= U\sin \theta+(V_0+V)\cos \theta, \hfill\llap(8)\cr\hfill
  V_R=-U\cos \theta+(V_0+V)\sin \theta, \hfill\llap(9)
}
$$
where $V_0=|R_0\Omega_0|$, and position angle $\theta$ is
determined as $\tan\theta=y/(R_0-x)$, where $x,y$ are Galactic
Cartesian coordinates of an object. In addition, it is assumed
that velocities $U$ and  $V$ are free from the Solar velocity with
respect to mean group velocity $(u_\odot,v_\odot,w_\odot)$
obtained from equations (1)--(3). Errors of projections $V_R$ and
$V_{\theta}$ are estimated from the expressions
$$
\displaylines{\hfill
  \sigma^2(V_{\theta})= \sigma^2_U\sin^2 \theta+\sigma^2_V\cos^2 \theta, \hfill\llap(10)\cr\hfill
  \sigma^2(V_R)= \sigma^2_U\cos^2 \theta+\sigma^2_V\sin^2 \theta, \hfill\llap(11)
}
$$
where errors of spatial velocities $U$ and $V$ are denoted by
$\sigma_U$ and $\sigma_V$, respectively.

We are interested also in heliocentric spatial velocities which
are free from Galactic rotation with parameters (16) but not from
Solar velocity. We denote such velocities by $U^1,V^1,W^1$ (see
Table~1 and Fig.~7). These velocities must satisfy the following
equations:
$$
\displaylines{\hfill
 {\overline U}^1= -u_\odot,\quad
 {\overline V}^1= -v_\odot,\quad
 {\overline W}^1= -w_\odot.\hfill\llap(12)
 }
$$

\begin{figure}
\begin{center}
\includegraphics[width = 75mm]   {f-02.eps}
\caption{Galactic rotation curves
 $V_{\theta}(R)$ for adopted $R_0=7.5,8.0,8.5$~kpc, lines 1,2 and 3.}
\end{center}
\end{figure}

\subsection{Fourier Analysis of Velocities}

At the next step, we consider deviations from circular velocities
$\Delta V_{\theta}$ and galactocentric radial velocities $V_R$.

Spectral analysis consists in applying direct Fourier transform to
the sequence of residual velocities following way:
$$
\displaylines{\hfill
 \overline{V}(\lambda_k)=
 \frac{1}{M}\sum_i^M
 V^i\exp\left(-j\frac{2\pi}{\lambda_k} R_i \right),\hfill\llap(13)
}
$$
where $\overline{V}(\lambda_k)$ is the $k$-th harmonic of Fourier
transform, $M$ is the number of measurements of velocities $V^i$
with coordinates $R_i$,
 $i=1,2,\ldots,M$, and $\lambda_k$ is wavelength in kpc; the latter is equal
to $D/k$, where $D$ is the period of the original sequence in kpc.
In density wave theory, $\lambda$ denotes the distance between
adjacent spiral arms along the Galactic radius vector.

Understanding the results of spectral analysis is easy in the
framework of linear theory of density waves. According to
this approach (Burton~\&~Bania, 1974; Byl~\&~Ovenden, 1978),
$$
\displaylines{\hfill
       V_R =-f_R \cos \chi,\hfill\llap(14)\cr\hfill
 \Delta V_{\theta}= f_\theta \sin\chi,~\hfill\llap(15)
 }
 $$
where $\chi=m[\cot(i)\ln(R/R_0)-\theta]+\chi_\odot$  is phase of
the spiral wave ($m$ is number of spiral arms, $i$ is pitch angle,
$\chi_\odot$ is the phase of the Sun in the spiral wave (Rohlfs,
1977)); $f_R$ and $f_\theta$ are amplitudes of radial and
tangential components of the perturbed velocities which, for
convenience, are always considered positive.

For the case when perturbations $V_R$ and $\Delta V_\theta$ are
considered as periodic functions of logarithm of $R$, the
following expression for the phase is appropriate: $\chi=(2\pi
R_0/\lambda)\ln(R/R_0)+\chi_\odot\approx(2\pi
/\lambda)(R-R_0)+\chi_\odot$ (Mel'nik et al, 2001), what allows us
to use Fourier analysis (13).

In our coordinate system radial velocity $V_R$ is directed from
galactic centre and circular velocity deviation $\Delta
V_{\theta}$ directed along Galactic rotation. Centre of the spiral
arm corresponds to phase $\chi=0$. For definiteness (Rohlfs,
1977), we consider that the centre of the Carina--Sagittarius arm
($R\approx7$~kpc) corresponds to phase $\chi=0$, while the Perseus
arm ($R\approx9$~kpc) corresponds to phase
$\chi\approx-\frac{3}{2}\pi$.

\begin{figure}
\begin{center}
\includegraphics[width = 75mm]   {f-03.eps}
\caption{(a)~Rotational angular velocity and (b)~rotational
circular linear velocity of the Galaxy according to (16) versus
galactocentric distance. Dashed lines denote the bounds of the
confidence interval corresponding to the $1\sigma$ level. Vertical
line indicates the location of $R_0=8$~kpc.}
\end{center}
\end{figure}

\section{RESULTS}
\subsection{Galactic Rotation Curve}

Firstly we investigated solutions of equations (1)--(3) using the
different number of Taylor expansion terms of $\Omega$ for
different values of $R_0$. Direct construction of the rotation
curve using the rotation parameters obtained above showed that
every additional expansion term leads to significant widening of
the confidence interval. We revealed that it is enough to take
three terms of Taylor expansion to construct a smooth,
sufficiently accurate Galactic rotation curve in the
galactocentric distance range of $3<R<14$~kpc. Indeed, adding
subsequent terms to the expansion practically does not change the
shape of the curve, and additional terms do not differ
statistically from zero. So, in this sense we found the optimal
solution. Results of this study are shown in Fig.~2, whence we can
see that the shape of the rotation curve significantly depends on
the adopted value of $R_0$. Thus, variation
$\mathrm{d}R_0=0.5$~kpc leads to variation of the rotational
angular velocity
$\mathrm{d}V_{\theta}\approx20\;\mathrm{km\,s}^{-1}$. As one can
see from Fig.~2, influence of inaccuracy in $R_0$ is particularly
strong in the Solar neighborhood.

Then we obtained solution of (1)--(3) for the fixed value of
$R_0=8.0$~kpc for 84 equations. As a result we found the following
parameters of the Solar velocity with respect to the group
velocity:
$(u_\odot,v_\odot,w_\odot)=(8.0,14.9,7.6)\pm(2.1,1.9,1.6)\;\mathrm{km\,
s}^{-1}$, and parameters of the angular velocity of Galactic
rotation:
$$
\displaylines{\hfill
 \Omega_0  =-31.0\pm1.2\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1},\hfill\llap(16)\cr\hfill
 \Omega^\prime_0= +4.46\pm0.21\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-2},\hfill\cr\hfill
 \Omega^{\prime\prime}_0= -0.876\pm0.067\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-3}.\hfill
}
$$
The unit weight error is $\sigma_0=9\;\mathrm{km\,s}^{-1}$. Oort
constants
 $A=0.5R_0\Omega^\prime_0$,
 $B=\Omega_0+0.5R_0\Omega^\prime_0$
are:
 $A= 17.8\pm0.8\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$ and
 $B=-13.2\pm1.5\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$.
Using these values and taking into account the error
$\sigma_{R_0}=0.3$~kpc, we estimated the circular velocity of the
Solar neighborhood
$V_0=|R_0\Omega_0|=248\pm14\;\mathrm{km\,s}^{-1}$ and its orbital
period around the Galactic Centre
$T=2\pi/\Omega_0=198\pm11$~Myr.

Galactic rotational angular velocity $\Omega(R)$ and
the corresponding linear circular velocity
$V_{\theta}(R)=|R\Omega(R)|$ curves are shown in Figs.~3a and 3b,
respectively.

As one can see from Fig.~3a, errors in parameters (16) lead to
strongly increasing errors in the rotational angular velocity
$\Omega(R)$ when $R>10$~kpc. Due to this the confidence interval
for the linear rotation curve $V_{\theta}(R)$ (Fig.~3b) starts to
exceed the criterion adopted above, $\mathrm{d}V_{\theta}=20$~km
s$^{-1}$, at $R>10$~kpc. In general, we can conclude that the
Galactic rotation curve found above approximates our initial data
with fully adequate accuracy over the range of distances of
$3<R<10$~kpc.

\subsection{Periodic Perturbations}

In Fig.~4, we present distribution of deviations from circular
velocities $\Delta V_{\theta}$ versus $R$ obtained by subtraction
of the rotation curve found above, with parameters (16), from the
initial data. Fourier power spectra estimates (periodograms) of
the sequence $\Delta V_{\theta}$ ($|\overline{\Delta
V_\theta}|^2$) and galactocentric radial velocities $V_R$
($|\overline{V_R}|^2$) versus wavelength $\lambda$ are shown in
Figs.~5a and 5b, respectively. In case of $\Delta V_{\theta}$,
using two main low-frequency Fourier spectrum peaks extending up
to $\lambda=1.3$~kpc, we constructed an approximation curve of the
residuals, as shown in Fig.~4. The amplitude of the approximation
curve was fitted using a chi-square optimization technique. As it
is seen from the picture, the approximation curve is not
representative enough to make any conclusions.

\begin{figure}
\begin{center}
 \includegraphics[width = 80mm]   {f-04.eps}
\caption{Deviations from circular velocities $\Delta V_{\theta}$
after subtraction of the model rotation curve with parameters (16)
versus galactocentric distance; vertical line indicates
$R_0=8$~kpc.}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
 \includegraphics[width = 60mm]   {f-05.eps}
\caption{Periodograms of (a)~deviations from circular velocities
$\Delta V_{\theta}$ and of (b)~radial velocities $V_R$.}
\end{center}
\end{figure}

But we have completely different situation in the case of radial
velocities versus $R$ shown in Fig.~6. In accordance with the main
periodogram peak shown in Fig.~5b, which is the largest one in the
frequency region of interest, perturbations in radial velocities
have an average wavelength of $\lambda=2.0\sim 0.25 R_0$~kpc,
which is in good agreement with results of other authors (see
section 5.2). The approximation curve built using this main
low-frequency Fourier spectrum peak extending from $\lambda=3$ kpc
to $\lambda=1.5$~kpc and fitted using the chi-square optimization,
is shown in bold in Fig.~6. One may clearly see that this curve
gives the most exact description of radial velocities in the
region of the Perseus arm ($R\approx9$~kpc). In this region,
extended as far as the location of the Sun, errors of amplitudes
of radial velocities are less than $\pm1\;\mathrm{km\,s}^{-1}$.
Peak value of the approximation curve reaches
$f_R=6.5\;\mathrm{km\,s}^{-1}$ and at the area close to the Sun it
is about 4.2 km s$^{-1}.$ Confidence intervals for the
approximation curve were determined using Monte-Carlo simulation
for 1000 random samples. In agreement with the approximation
curve, phase of the Sun lies in the interval
$-140^o<\chi_\odot<-120^o$ with the mean value of
$\chi_\odot\approx-130^o$. Radial perturbations in the Solar
vicinity we estimate as periodic function with wavelength
$\lambda=2\pm 0.2$ kpc and amplitude
$f_R=6.5\pm2\;\mathrm{km\,s}^{-1}$.

As it is seen from Fig.~5a and Fig.~5b both periodograms reveal
peaks at wavelength $\lambda=2$ kpc. We estimated probabilities
$p$ of belonging of these peaks to the periodic signal (not to
noise) using simple formula derived by Vityazev (2001):
$|\overline {V}(\lambda)|^2/\sigma_0^2/M\ge-\ln(1-p)$, where
$|\overline {V}(\lambda)|^2$ is periodogram peak value at
wavelength of interest, $\sigma_0^2$ is dispersion of input data
sequence, $M$ is number of data. In the first case we obtained
$p=0.6$ and in the second case $p=0.992$ what justified more
reliable estimation of spiral wave parameters from $V_R$ rather
than from $\Delta V_{\theta}$.

\subsection{Peculiar Solar Velocity with Respect to the LSR}

In Fig.~7, spatial velocities $U^1$ and $V^1$ (see Table~1), free
from Galactic rotation according to parameters (16), are given.
Residual velocity components averaged over 28 masers are
${\overline U}^1,{\overline V}^1,{\overline
W}^1=(-8.6,-13.6,-7.5)\pm(2.1,1.6,1.3)\;\mathrm{km\,s}^{-1}$, with
dispersion vector
$(\sigma_{U^1},\sigma_{V^1},\sigma_{W^1})=(10.8,8.7,6.8)\;\mathrm{km\,
s}^{-1}$.

As one may see from this figure, residual velocities of most of
masers form a sufficiently compact ellipse of smaller dispersion.
Most of deviations from this compact distribution are due to the
following three masers: G23.66$-$0.13, G23.43$-$0.18 and NGC
1333~(f2). The detail NGC 1333~(f2) reflects inner velocity
dispersion within maser NGC 1333 which itself forms an expanding
shell (Hirota et~al., 2008a). Maser G23.66$-$0.13 has
significantly negative radial velocity which reflects a certain
peculiarity in its motion.

\begin{figure}
\begin{center}
 \includegraphics[width = 80mm]   {f-06.eps}
\caption{Radial velocities of masers $V_R$ versus galactocentric
distance $R$. Thin curves mark the confidence interval
corresponding to $1\sigma$ level. Vertical line indicates the
galactocentric distance of the Sun $R_0=8$~kpc.}
\end{center}
\end{figure}

Excluding these three sources, for 25 masers forming a compact
ellipse, we deduced the following mean velocity
 ${\overline U}^1,{\overline V}^1,{\overline W}^1=(-9.1,-15.5,-8.5)\pm(1.9,1.3,1.2)\;\mathrm{km\,
s}^{-1}$, with dispersion
$(\sigma_{U^1},\sigma_{V^1},\sigma_{W^1})=(9.3,6.6,6.1)\;\mathrm{km\,
s}^{-1}$.

The question of great interest is how density wave perturbations
affect the values of the LSR velocity components. Let us denote
components of ``non-perturbed'' peculiar Solar velocity with
respect to the LSR as $(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}$.
For the local case, i.e. for the immediate Solar neighborhood,
under the condition $\chi\approx\chi_\odot$ we have
$$
\displaylines{\hfill
 {\overline U}^1= -(U_\odot)_\mathrm{LSR}-V_R\cos\theta+ \Delta V_{\theta}\sin\theta,\hfill\llap(17)\cr\hfill
 {\overline V}^1= -(V_\odot)_\mathrm{LSR}+V_R\sin\theta+ \Delta V_{\theta}\cos\theta.\hfill\llap(18)
 }
$$
When $\theta\rightarrow 0~(R\approx R_0)$, we have
$\sin\theta\rightarrow 0$ and $\cos\theta\rightarrow1$. Then
$$
\displaylines{\hfill
 {\overline U}^1= -(U_\odot)_\mathrm{LSR}+      f_R\cos\chi_\odot,\hfill\llap(19)\cr\hfill
 {\overline V}^1= -(V_\odot)_\mathrm{LSR}+ f_\theta\sin\chi_\odot,\hfill\llap(20)
 }
$$
where $f_R,f_\theta>0$. As one can see from (19)--(20), signs of
corrections caused by spiral density waves are determined only by
signs of $\cos\chi_\odot$ and  $\sin\chi_\odot$. Adopting that:
mean amplitudes of spiral density wave perturbations in both
tangential and radial velocities are $6.5\pm2\;\mathrm{km\,
s}^{-1}$ and $\chi_\odot=-130^o\pm 10^o$, we obtain, according to
(19)--(20), the following ``non-perturbed'' velocity of
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(5.5,11,8.5)\pm(2.2,1.7,1.2)\;\mathrm{km\,s}^{-1}$.
This result agrees with the estimate of Solar motion by
Sch\"onrich et al.~(2010) and Francis~\&~Anderson~(2009).

We could not determine the value of $\chi_\odot$ using deviations
from circular velocities of masers. But in order to confirm our
results obtained above using Galactic radial velocities $V_R$ of
masers, we analyzed also a sample of Open Star Clusters (OSCs)
from the compilation of Bobylev et al. (2007) which was based on
the catalog of Piskunov et al. (2006), along with the
line-of-sight velocities from the CRVOCA catalog (Kharchenko et
al., 2007). We selected 117 young OSCs (age $<50$~Myr) in radius
$r<2$~kpc using the following restriction for modulus of residual
velocities: $\sqrt{\Delta U^2+\Delta V^2 +\Delta
W^2}<50\;\mathrm{km\, s}^{-1}$.

Results of analysis of deviations from circular velocities $\Delta
V_{\theta}$ using Galactic rotation parameters (16) and
galactocentric radial velocities $V_R$ are shown in Figs.~8a and
8b, respectively. We can see a good agreement between the
approximation curves shown in panels (a) and (b): wavelengths are
almost similar, difference in phase is about $\pi/2$, peaks are
also comparable (6-8 km s$^{-1}$). Periodograms of deviations from
circular velocities and radial velocities  are shown in Fig.~9. To
obtain approximation curves in Fig.~8, we used low-frequency
Fourier spectra up to wavelengths $\lambda=1.3$~kpc and fitted the
amplitude of perturbations using the chi-square optimization.
Spectral analysis of $V_R$ (Fig.~9b) reveals periodic motion with
wavelength $\lambda=1.9 (0.23R_0)$~kpc. Spectral analysis of
$\Delta V_{\theta}$ (Fig.~9a) displays three dominant peaks at
wavelengths $\lambda=2.21 (0.28R_0), 1.1 (0.13R_0), 0.47
(0.058R_0)$~kpc (compare with results by Clemens
(1985):$\lambda=0.22R_0, 0.12 R_0, 0.05 R_0$).

Now we can compare these results with those obtained using radial
velocities $V_R$ of masers. We can see a good agreement in the
behavior of the approximation curves shown in Fig.~8b and Fig.~6
in the Solar area. Fourier spectrum of radial velocities of masers
$V_R$ reveals a dominant peak of amplitude $6.5\;\mathrm{km\,
s}^{-1}$  at wavelength $2$~kpc. In addition, there is a good
agreement of phase $\chi_\odot\approx -120^o$ using data shown in
Fig.~8b with the result obtained from masers $\chi_\odot\approx
-130^o\pm 10^o$.

\section{DISCUSSION}
\subsection{Galactic Rotation Curve}

The shape of the Galactic rotation curve obtained above is in a
good agreement with the one obtained by Zabolotskikh et al. (2002)
for $R_0=7.5$~kpc as a result of thorough reconciliation of
distance scales of different star groups. The value
$\Omega_0=-31.0\pm1.2\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$ (see
solution (16)) is in a good agreement with the following result
obtained from 18 masers: $-29.9\;\mathrm{km\,
s}^{-1}\mathrm{kpc}^{-1}<\Omega_0<-31.6\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$
(McMillan~\&~Binney, 2010) and with
$\Omega_0=-30.3\pm0.9\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$ (Reid
et al., 2009). Our value $V_0=248\pm14\;\mathrm{km\,s}^{-1}$
($R_0=8$ kpc) is in a good agreement with
$254\pm16\;\mathrm{km\,s}^{-1}$  ($R_0=8.4$ kpc) by Reid et al.
(2009) and $244\pm13\;\mathrm{km\,s}^{-1}$ ($R_0=8.2$ kpc) by Bovy
et al. (2009).

\subsection{Spiral Structure Parameters}

The estimate $\lambda=0.22R_0$ of the distance between adjacent
spiral arms was obtained by Clemens (1985). For $R_0=8.5$~kpc used
here it gives $\lambda=1.8$~kpc which is in a good agreement with
the value $\lambda=2.0$~kpc obtained in our study using 28
selected masers, as well as with $\lambda=1.9$ obtained from 117
young OSCs. Mel'nik et al.~(2001) obtained  the estimate
$\lambda=2.0\pm0.2$~kpc by analyzing velocities of OB associations
in the 3-kpc Solar neighborhood. An independent estimate
$\lambda=1.7\pm0.5$~kpc was obtained from the analysis of $V_R$
velocities of young OSCs in the distance range of $6<R<9$~kpc
(Bobylev et al., 2008).

From the analysis of OB stars and Cepheids,
Byl~\&~Ovenden (1978) found the following parameters of the
Galactic spiral structure
 $f_R=3.6\pm0.4\;\mathrm{km\,s}^{-1}$ and
 $f_\theta=4.7\pm0.6\;\mathrm{km\,s}^{-1}$, $\chi_\odot\approx165\pm1^\circ$, $i=-4.2\pm0.2^\circ$.
According to Clemens~(1985), the value of perturbation amplitude
is $|f_\theta|=5\;\mathrm{km\,s}^{-1}$ at {\bf the} wavelength of
$\lambda=0.22R_0$.

\begin{figure}
\begin{center}
\includegraphics[width = 55mm]   {f-07.eps}
\caption{Heliocentric spatial velocities  $U^1$ and $V^1$ free
from Galactic rotation with parameters~(16).}
\end{center}
\end{figure}

Using Cepheids, Mishurov et al.~(1997) found the following
parameters:
 $f_R=6.3\pm2.4\;\mathrm{km\,s}^{-1}$ and
 $f_\theta=4.4\pm2.4\;\mathrm{km\,s}^{-1}$, $\chi_\odot\approx290\pm16^\circ$, $i=-6.8\pm0.7^\circ$.
Using Hipparcos OB stars and Cepheids, Fern\'andez et al.~(2001)
showed that amplitudes $f_R$ and $f_\theta$ are about
$6-4\;\mathrm{km\, s}^{-1}$ and  $20^\circ<\chi_\odot<284^\circ$.
Mean amplitude of radial perturbations
$f_R=6.5\pm2\;\mathrm{km\,s}^{-1}$ found by us using masers is in
a good agreement with the estimates listed above.

Location of the Sun in the external part of the
Carina--Sagittarius arm is in agreement both with the distribution
of stars and gas (Russeil, 2003) and with density wave theory.

\subsection{Peculiar Velocity of the Sun}

It is worth mentioning some results of determination of the non-perturbed LSR
velocity parameters obtained simultaneously with
parameters of the Galactic rotation, taking into account
perturbations evoked by the spiral wave density. For example,
these are: $(U_\odot,V_\odot)_\mathrm{LSR}=(2,5)\pm(2,2)\;\mathrm{km\,s}^{-1}$
(Mishurov et al., 1997);
$(U_\odot,V_\odot)_\mathrm{LSR}=(7.8,13.6)\pm(1.3,1.4)\;\mathrm{km\,s}^{-1}$
(Mishurov~\&~Zenina, 1999);
$(U_\odot,V_\odot)_\mathrm{LSR}=(9,12)\pm(1,1)\;\mathrm{km\,s}^{-1}$ (L\'epine et
al.,~2001). Let us mention also the results of Fern\'andes et al.~(2001),
obtained using different samples of OB stars:
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(8.8,12.4,8.4)\pm(0.7,1.0,0.5)\;\mathrm{km\,
s}^{-1}$ and of Cepheids:
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(6.5,10.4,5.7)\pm(1.2,1.9,0.7)\;\mathrm{km\,
s}^{-1}$.

From the results listed here, we can see that values of ($U,V$)
components of the LSR velocity are always smaller than the
corresponding components of the standard Solar motion velocity
$(U_\odot,V_\odot,W_\odot)=(10.3,15.3,7.7)\;\mathrm{km\,s}^{-1}$.

\begin{figure}
\begin{center}
\includegraphics[width = 60mm]   {f-08.eps}
\caption{Deviations from (a)~circular velocities $\Delta
V_{\theta}$ and (b)~radial velocities $V_R$ for 117 young OSCs
versus galactocentric distance $R$. Approximation curves are shown
with solid lines. Vertical line indicates galactocentric distance
of the Sun $R_0=8$~kpc. }
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width = 60mm]   {f-09.eps}
\caption{Periodograms of deviations from (a)~circular velocities
$\Delta V_{\theta}$ and (b)~radial velocities $V_R$ for 117 young
OSCs.}
\end{center}
\end{figure}

\section{CONCLUSIONS}

Spatial velocities of all currently known 28 masers having
estimates of trigonometric parallaxes are reanalyzed. To determine
the Galactic rotation curve, we used the first three terms of
Taylor expansion of the Galactic angular rotational velocity at
the galactocentric distance of the Sun $R_0=8.0$~kpc. Coefficients
obtained from Bottlinger's equations are:
 $\Omega_0  =-31.0\pm1.2\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$,
 ${\Omega_0^{'}}= 4.46\pm0.21\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-2}$,
 $\Omega_0^{''}=-0.876\pm0.067\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-3}$.
Oort constants are
 $A=17.8\pm0.8\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$ and
 $B=-13.2\pm1.5\;\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$, which allowed
us to estimate the circular velocity of the Solar neighborhood
rotation $V_0=248\pm14~\mathrm{km\,s}^{-1}$ ($R_0=8$ kpc).

It was found that deviations from circular velocities $\Delta
V_{\theta}$ of masers are not representative enough for any
reliable analysis, while the study of galactocentric radial
velocities $V_R$ of masers allowed us to estimate a number of
useful parameters concerning spiral structure of the Galaxy.
Based on Fourier analysis of velocities $V_R$, we obtained that:
there are periodic perturbations evoked by the spiral density
wave, with wavelength of $\lambda=2.0\pm0.2$~kpc and peak velocity
of $f_R=6.5\pm2\;\mathrm{km\,s}^{-1}$ and velocity of
$4\pm1\;\mathrm{km\,s}^{-1}$ near the location of the Sun; phase
of the Sun in the density wave is $\chi_\odot=-130^o\pm10^o$,
which proves that the Sun is located in the inter-arm space.

Adopting the parameters of spiral density wave found we determined
the following non-perturbed Solar peculiar velocity with respect
to the LSR:
$(U_\odot,V_\odot,W_\odot)_\mathrm{LSR}=(5.5,11,8.5)\pm(2.2,1.7,1.2)\;\mathrm{km\,s}^{-1}$.
In this connection, in the regions near the Sun, velocity
component $(V_\odot)_\mathrm{LSR}$ is influenced mostly by
negative perturbation $\Delta V_{\theta}$ and has smaller value
than the corresponding velocity component
$V_\odot=15.3\;\mathrm{km\, s}^{-1}$ of the Standard Solar motion.

\section*{ACKNOWLEDGMENTS}

The authors are thankful to the anonymous referee for critical
remarks which promoted improving the paper. This study was
supported by the Russian Foundation for Basic Research (project
No. 08--02--00400), and in part by the ``Origin and Evolution of
Stars and Galaxies'' --- ``Program of the Presidium of the Russian
Academy of Sciences and the Program for State Support of Leading
Scientific Schools of Russia'' (NSh--6110.2008.2). The authors are
thankful to Vladimir Kouprianov for his assistance in preparing
the text of manuscript.

{

redpajama_set_name: RedPajamaArXiv