text:
Q: Django 1.7 how to access values after annotate I am using Django 1.7 and am trying to do an aggregation query.  They query seems to work until I iterate through the ValueSet.
>> messages = Message.objects.filter(is_outgoing=False)
              .values('contact_id').annotate(Max('created')
>> messages.count()
5

This is correct.  There are only 5 unique contacts.
However, once I do this:
for m in messages:
    do stuff here

Now when I do messages.count()  I get 49 which is the total number of messages not grouped by client.
How can I iterate through the ValueSet and only get the 5 most recent messages?
Edit:
I found out what was happening.  I had Meta.ordering set to '-created' in Message class.  These means that the ORM was adding a group by on created so the query being generated was grouping by both 'created' and 'contact_id'.
I added a order_by() before the annotate() to remove the default ordering and it fixed the problem.
messages = Message.objects.filter(is_outgoing=False)
           .values('contact_id').order_by().annotate(Max('created'))

A: It seems like you alter messages in the "do stuff here" code or after the first iteration.


This is a Banksy tag. He has a video of it being made on his website.
Banksy. Hes taped putting this piece up. Its the bottom right thumbnail "advert"
That's a Banksy piece. I saw on his site like a year ago. That dude is so amazing.


text:
Home Domestic Violence Wisconsin Hudson
Hudson Domestic Violence Lawyers
James CW Bock
Hudson, WI Domestic Violence Attorney
(715) 494-0080 808 Carmichael Road PMB 113
Domestic Violence, Criminal Defense, Divorce and Family
Barbara K. Miller
Hudson, WI Domestic Violence Lawyer with 38 years of experience
(715) 386-9655 615 Second Street
Free ConsultationDomestic Violence, Criminal Defense, Divorce and Family
Hamline University School of Law
I have been in practice in the State of Wisconsin for over 30 years and have been in the Hudson community for over 25. I have a varied litigation practice that is now focused on Family Law, Criminal Defense and Personal Injury. I litigate cases from beginning to closure; meet clients; research and prepare for court hearings; draft pleadings, motions, and appellate briefs.
Autumn Lyn Lindquist
(715) 381-8270 502 2nd St Ste 203
Domestic Violence, Divorce, Family and Municipal
Eau Claire, WI Domestic Violence Lawyer
(715) 322-3368 17 S. Barstow St.
Free ConsultationDomestic Violence, Criminal Defense, DUI & DWI and White Collar Crime
We are the best criminal defense team in Northcentral and Northwestern Wisconsin. We have been helping clients resolve their matters for over 30 years. A criminal or OWI case can leave you with many hardships — from loss of a job, to financial hardships, community stigmatization and psychological and emotional distress. Defending a criminal or drunk driving case is difficult and stressful. You don't have to fight this battle alone. When a loved one is charged with a crime, the impact can be felt throughout the home. Many individuals struggle with enormous stress and anxiety due to the situation. This stress...
Molly French
Osseo, WI Domestic Violence Attorney with 18 years of experience
(715) 597-5300 50556 South Charles Street
Osseo, WI 54758
David Patton
Racine, WI Domestic Violence Lawyer with 9 years of experience
(262) 221-4848 2310 S. Green Bay Rd.
Ste. C203
Domestic Violence, Criminal Defense, Divorce and Juvenile
University of Minnesota - Twin Cities
A versatile, innovative, and adaptable attorney with an attitude of service and broad experience who meets challenges with open-eyed optimism and solutions-oriented creativity, David cares about your case almost as much as you do. He's here to fight for you and to serve as your concierge throughout your encounter with the legal system David gets great results for his clients. With David, you can expect: -fierce courtroom advocacy; -a compassionate and listening ear; -an adviser offering you advanced strategic and tactical advice; -hard-line negotiating on your behalf; -a trusted guide through the legal wilderness; -aggressive motion practice to accomplish your goals; -established relationships with the players in...
David Kowalski
Baraboo, WI Domestic Violence Attorney with 17 years of experience
(608) 448-4700 123 2nd Street
Free ConsultationDomestic Violence, Appeals, Divorce and Family
I am the founding shareholder of Kowalski, Wilson & Vang, LLC. Throughout my career, I have represented clients of diverse financial, ethnic, social, and cultural backgrounds. Experience gained through participation in hundreds of court hearings allows me to serve my clients across the entire spectrum of family issues.. I routinely lecture on family and child-related topics at seminars sponsored by the State Bar of Wisconsin and other legal organizations. For example, in 2010, I was Wisconsin's representative to the American Academy of Matrimonial Lawyers Community Property Symposium in Seattle. From 2015 onward, I was named by my peers as a Rising Star and designated Superlawyer by SuperLawyers magazine, a lawyer review publication....
Michael Edwards
Milwaukee, WI Domestic Violence Attorney with 5 years of experience
(414) 744-2757 3821 S. Howell Ave.
Domestic Violence, Divorce and Family
Marquette University Law School and Drake University
Michael A. Edwards was born in Milwaukee, WI. Michael attended the Drake University in Des Moines, Iowa and graduated in 2014 after earning a Bachelor of Arts degree in Law, Politics & Society and Rhetoric & Communication Studies. Michael graduated from Drake with University Honors.
Michael graduated from Marquette University Law School in 2017 with a Certificate in Sports Law as well as Pro Bono Honors for volunteering nearly 400 hours of his time to pro bono legal services.
Currently, Michael assists clients with family law issues in Fond du Lac and surrounding counties.
While in school, Michael held various internship positions including...
Eric Raskopf
Oconomowoc, WI Domestic Violence Attorney with 31 years of experience
(262) 955-1644 100 S. Main Street
Free ConsultationDomestic Violence, Criminal Defense, DUI & DWI and Traffic Tickets
I have successfully defended the rights of the accused in the full range of criminal and traffic offenses since 1992. I am sensitive to the fact that while I have a busy caseload, this may be your only experience with the criminal justice system. Whether your are accused of a minor traffic violation or a serious felony, you can expect that your matter will be handled with a high level of professionalism, integrity and sensitivity. Remember, it's your case.
Proper communication between attorney and client is the hallmark of effective representation. Clients can expect copies of documents filed on their behalf...
Tracey A Wood
Middleton, WI Domestic Violence Lawyer with 30 years of experience
(608) 490-5779 6605 University Avenue Suite #101
Free ConsultationDomestic Violence, Appeals, Criminal Defense and DUI & DWI
University of Wisconsin Law School
A true Wisconsin native, Attorney Wood earned her undergraduate degree from Marquette University and her law degree from the University of Wisconsin. From the beginning of her legal career, Attorney Wood dedicated herself to defending OWI cases—allowing her to gain valuable experience and insights that are used to help her clients. Attorney Wood is the first Wisconsin attorney to serve on the Board of Regents for the National College for DUI Defense (NCDD) held at Harvard Law School, an organization devoted to furthering education for attorneys in this field of law. She is also a frequent speaker at...
Teuta Jonuzi
Middleton, WI Domestic Violence Attorney with 5 years of experience
As an young and energetic attorney at Tracey Wood & Associates, Teuta Jonuzi fights hard for the rights or her clients.
John Birdsall
Milwaukee, WI Domestic Violence Attorney with 34 years of experience
(414) 928-2309 1219 N. Cass Street
Attorney John Birdsall has more than 30 years of experience and has earned a reputation as one of the most trusted criminal defense lawyers in Milwaukee and the State of Wisconsin. With over 250 jury trails, mostly for serious felonies such as homicide, he has an acquittal rate that is three times the Wisconsin average. John's practice is focused exclusively on defending the wrongly accused, and has recently helped a client named Eddie Gill. After being accused of shooting and killing a Milwaukee resident, John helped uncover that the police has interrogated Gill into confessing when he was in...
Chadwick Kaehne
Neenah, WI Domestic Violence Attorney with 17 years of experience
(920) 383-1350 247 East Wisconsin Avenue
Domestic Violence, Criminal Defense, DUI & DWI and Divorce
University of Dayton School of Law
Mr. Chadwick Kaehne graduated from the University of Wisconsin
with a Bachelor of Science degree in Psychology. Shortly after his
undergraduate studies, Mr. Kaehne founded a mental health clinic serving
clients throughout Winnebago, Fond du Lac, Outagamie, and Brown
counties. Mr. Kaehne established his law practice shortly after
receiving his Juris Doctorate from the University of Dayton School of
Law in Ohio. Using the philosophy grounded from his experiences from the
mental health field, Mr. Kaehne believes that not only should a law
firm be both reputable and aggressive in serving the needs of their
clients; but also passionate, with...
Aaron W Schenk
Pulaski, WI Domestic Violence Lawyer with 15 years of experience
(920) 393-5884 141 S St. Augustine St
Pulaski, WI 54162
For a Green Bay Attorney that PUTS YOU FIRST, look no further! The Schenk Law Firm, LLC is a "Client-First" Law Firm serving Green Bay (Brown County), Appleton (Outagamie County), Oshkosh (Winnebago County), and all other areas in Northeastern Wisconsin & Michigan. The Schenk Law Firm provides powerful legal representation to the people of Wisconsin, we are available for 24/7 Emergency Legal Assistance 911@SchenkLegal.com as well. Our Attorneys are some of the most sympathetic and considerate. Whether you're experiencing a Criminal Felony or Misdemeanor Law Case, Traffic, Probation Revocation, Appeals, Family Law Case, Divorce, Child Custody, Tribal Court, or Federal...
Jeffrey Blessinger
Baraboo, WI Domestic Violence Lawyer with 26 years of experience
Free ConsultationDomestic Violence, Divorce and Family
Family Law Attorney Jeff Blessinger has earned a very strong local and regional reputation as tough and intelligent, yet compassionate in fighting for the rights of his clients. For more than 19 years, Attorney Blessinger has skillfully handled all types of family law cases, from high conflict child custody, child support and maintenance battles, to collaborative divorces, alimony, and paternity issues. Jeff has the skills, experience, reputation, and legal ability to successfully represent and defend you in any family law case, no matter how large or small.
Jeffrey Kippa
Appleton, WI Domestic Violence Attorney
(920) 228-8141 135 E. College Avenue
Domestic Violence, Criminal Defense, DUI & DWI and Juvenile
I opened my office in 2013 and limit my practice exclusively to criminal law. Prior to opening my office, I worked for area firms for about ten years. In deciding to limit my practice to criminal defense, I have been able to focus on helping others out of what is typically the lowest point in their life. That is the hard part about my job - always meeting people at a horrible point in their lives. The best part of my job is helping them through the process and out the other side of things. Providing answers and direction to...
Amy Menzel
Appleton, WI Domestic Violence Lawyer with 16 years of experience
(920) 720-0000 4650 West Spencer Street
Free ConsultationDomestic Violence, Administrative, Criminal Defense and Personal Injury
I understand that when someone comes to me for legal advice, that person is likely at the lowest point in their life, due to a wrongful allegation, terrible decision or unfortunate accident. I am truly committed to helping all of my clients receive the best result in their situation. I treat each case as the unique situation that it is and am committed to going above and beyond what other attorneys would do to ensure that best possible result.
I primarily focus on Criminal Defense and Personal Injury Law. I have found those to be the...
Corey Chirafisi
Madison, WI Domestic Violence Attorney with 25 years of experience
(608) 250-3500 1 S. Pinckney Street
Free ConsultationDomestic Violence, Criminal Defense and DUI & DWI
City University of New York - City College
An accomplished criminal defense attorney in Wisconsin, Corey C. Chirafisi devotes his legal career solely to defending individuals charged with criminal and drunk driving offenses. He handles cases involving Wisconsin state law as well as federal law, and has represented people on every type of criminal charge and all levels of drunk driving charges with rather impressive results in numerous difficult cases. A former prosecutor, Mr. Chirafisi began his career as an assistant district attorney handling criminal matters ranging from disorderly conduct to homicide. He provides this experience to current clients whether they are charged with battery, computer...
Terese J. Singer
(414) 271-6400 1110 N Old World 3rd St
Free ConsultationDomestic Violence, Divorce, Family and Personal Injury
Attorney Singer devotes her practice almost exclusively to helping couples through the difficult process of dissolving their marriage and rebuilding their lives. With over 25 years of experience, she is particularly sensitive to protecting her client's children and the parent's right to remain fully involved in their lives. She also works diligently to insure that her client's financial interests are protected, whether that means fighting for a fair division of property or making sure that maintenance is awarded in the appropriate cases. Her clients are divided equally between men and women and both have their rights and interests vigorously defended....
Sydne French
Brookfield, WI Domestic Violence Lawyer with 17 years of experience
(414) 446-3544 200 S. Executive Drive
Free ConsultationDomestic Violence, Cannabis Law, Criminal Defense and White Collar Crime
Over the past 15 years, Sydne has earned a solid reputation for fighting and winning probation violation revocation hearings. She is known by judges and probation agents for her creative and persuasive Alternatives to Revocation (ATRS). Sydne's background in clinical psychology gives her an edge over other criminal defense attorneys. Her clinical experience and training allows her to find the root cause of behaviors and uses this to help her clients avoid revocation. "I've spent the past 15 years helping people beat revocations, get ATRs, and go back home to their life and their loved...
Corey Mehlos
Madison, WI Domestic Violence Attorney with 8 years of experience
(608) 470-5222 Suite 400, 811 E. Washington Ave.
Attorney Mehlos graduated with honors from the University of Notre Dame and the University of Wisconsin Law School. During law school, Attorney Mehlos participated in the Wisconsin Innocence Project, handling 10 post-conviction homicide and assault cases. That experience provided Attorney Mehlos with the foundation to surgically attack highly-complex cases involving tough facts and tailor creative solutions to achieve outstanding results for his clients. Attorney Mehlos has worked relentlessly to achieve outstanding results for his clients in cases ranging from homicide cases, personal injury lawsuits, to helping families with child protective services. In his first case out of law school, Attorney...
Nicole Muller
(414) 928-2309 1219 N Cass St.
Domestic Violence, Appeals, Criminal Defense and DUI & DWI
Attorney Nicole A. Muller has recently joined Birdsall Obear & Associates, SC as an associate attorney. Not only is Attorney Muller a graduate of Catholic University in Washington D.C. where she studied Political Science and Studio Art, but before going to law school also graduated from Columbia University in New York City. After graduating from Columbia, Attorney Muller decided to dedicate her life to fixing our broken criminal justice system in this country. This passion to bring about positive change is what brought Attorney Muller to the great state of Wisconsin and Marquette University Law School.
Attorney Muller graduated from Marquette...
Amaro Lopez
Neenah, WI Domestic Violence Attorney with 9 years of experience
Attorney Amaro Lopez received his B.A. degree in Spanish Literature from the University of Dallas. He then continued on at the University of Dallas and obtained his Master's Degree in Business Administration with an emphasis in Human Resources. After pursuing a career in Human Resources, Mr. Lopez realized that in order to make a difference in people's lives the way he wanted, he would need to advance his education. He was accepted into the law school at the University of Wisconsin Madison and earned his Juris Doctorate degree. He feels a strong connection to his community and believes that a...
Stephen Zuber
Superior, WI Domestic Violence Lawyer with 31 years of experience
(715) 395-3195 515 Belknap Street, Suite #1
Free ConsultationDomestic Violence, Criminal Defense, DUI & DWI and Divorce
Stephen R Zuber, S.C. Attorney At Law has over 30 years local experience practicing in Superior, Wisconsin as well as in Duluth, Minnesota, and their surrounding areas. No matter what your legal needs, Stephen R. Zuber will represent you diligently, effectively, and will present your case to obtain the most optimal results.??
When someone trusts me to defend them and their good name, I take it very seriously. My clients have the option of choosing any attorney to represent them in court. So, when an individual decides to choose me, I want to provide them with quality representation in return.
Most of...
Jason Daniel Baltz
Shorewood, WI Domestic Violence Attorney with 22 years of experience
(414) 375-0797 4431 North Lake Drive
Shorewood, WI 53211
Free ConsultationDomestic Violence, Business, Criminal Defense and Family
Jason D. Baltz is primarily a criminal defense attorney in Mikwaukee, but he also takes on cases for family law, personal injury, and business law. To contact Attorney Baltz about your legal matter, visit his website, or call his office today!
Britteny Koenig
Oshkosh, WI Domestic Violence Lawyer with 7 years of experience
(920) 739-9909 2001 Bowen St.
Patrick Kiernan Cafferty
Racine, WI Domestic Violence Lawyer
(262) 632-5000 840 Lake Ave
Mr. Cafferty's credentials and awards include: + Graduate of Marquette University Law School + Member of the National Association of Criminal Defense Lawyers + Member of the Wisconsin Association Criminal Defense Lawyers + Named in Super Lawyers Magazine 2008 – 2021 + Earned the Distinguished Martindale-Hubbell AV* Peer Review Rating + Named in Best Lawyers in America 2013-2021 Edition for Criminal Defense Mr. Cafferty has developed solid professional relationships and a reputation of being honest with judges and prosecutors throughout Southeast Wisconsin. From offices in Racine, criminal defense lawyer Patrick Cafferty defends the rights of people charged with state and federal criminal offenses throughout Southeastern Wisconsin and Northern...
Christopher Glinski
Racine, WI Domestic Violence Attorney with 15 years of experience
(262) 632-1555 209 8th St
Attorney Christopher M. Glinski is an aggressive and experienced Racine criminal defense, divorce, and child custody lawyer. He has dedicated his career to aggressively defending the rights of his clients and getting his clients great results. He also handles traffic tickets.
Attorney Glinski has consistently been rated one of the top lawyers in Wisconsin. He was recently recognized as one of the "Top 40 Trial Lawyers under 40" in Wisconsin and nationally recognized as one of the "Top 100 Criminal Defense Lawyers." He works in Racine and Kenosha, Wisconsin.
Call (262) 632-1555 for a free consultation....
Mr. Jamy Richard Johansen
(715) 394-3939 1409 Hammond Ave, Ste 300
Attorney Johansen is a Superior native who graduated from the UWS-Superior with a B.A. in History, cum laude. He earned his J.D. in San Diego, California. While in law school, Johansen worked for Federal Defender's of San Diego, Inc. After passing the bar examination, Johansen began handling cases in Douglas County and surrounding Wisconsin counties. Attorney Johansen has served as both President and Vice President of the Douglas County Bar Association and is a member of the State Bar of Wisconsin. For the past two decades, he has been President of Johansen Law Office, S.C. where he focuses...
Sarah Schmeiser
(608) 661-1054 33 E Main Street
Sarah concentrates on two areas of practice: criminal and traffic defense and immigration law. In the area of criminal and traffic defense, Sarah has defended clients at all levels - from local municipal courts through the Seventh Circuit Court of Appeals. Sarah handles many circuit court trials every year, successfully protecting client interests. Sarah handles all levels of appeal in criminal and traffic cases and has argued several cases in front of the Wisconsin Supreme Court.
Sarah frequently handles charges of drunk driving, sexual assault, substantial battery, theft from employer, delivery of a controlled substance, and all types of criminal and...
Jeffrey T. Oswald
Appleton, WI Domestic Violence Attorney with 26 years of experience
4650 W. Spencer Street
Free ConsultationDomestic Violence, Criminal Defense, DUI & DWI and Juvenile
Chicago-Kent College of Law, Illinois Institute of Technology
I have lived in Appleton, Wisconsin my entire life other than attending college in Madison and law school in Chicago. I started my own law practice within the first year of graduating from law school, and continue to work with my same partners at our law firm Hammett, Bellin & Oswald, LLC. I am proud of the quality of individuals representing our law firm and am happy that we have helped so many people over the years. I am an active member of our community and serve in many different ways. I...
Stephen Govin
Milwaukee, WI Domestic Violence Lawyer with 19 years of experience
(414) 704-4889 1110 N. Old World 3rd Street
Domestic Violence, Criminal Defense and DUI & DWI
Stephen Govin is an experienced and aggressive Criminal Defense Attorney, representing clients in state and federal courts throughout Wisconsin. He is dedicated to providing the highest level of legal services and personal care to clients facing charges from misdemeanors to serious felony offenses.
Stephen received a B.A. in Criminology from Marquette University in 1999. He attended on an athletic scholarship for soccer, where he helped Marquette reach its first NCAA Division I soccer tournament. His J.D. was earned at Marquette University Law School in 2003, focusing on criminal law from his first day. Stephen clerked for the Honorable Victor Manion in...
Brian Nelson
(414) 270-0202 316 N. Milwaukee St
Indiana University Robert H. McKinney School of Law
Criminal defense attorney Brian C. Nelson earned his Bachelor degree from Indiana University in 2012. He continued his legal education at Indiana University, and earned his Juris Doctorate in 2016. During law school, Mr. Nelson focused on trial advocacy and criminal defense, taking every available course and clinic in those fields. In his second year, he interned at the Marion County Prosecutors Office for a semester before leaving to clerk for a private criminal defense attorney. Mr. Nelson was on the board of his legal fraternity, and competed as a member of his school's trial advocacy team his last two...
David K Anderson
Madison, WI Domestic Violence Lawyer with 7 years of experience
(608) 204-5807 411 West Main St. #202
Attorney David K Anderson has been practicing criminal defense for over 6 years. Attorney Anderson focuses solely on Criminal Defense. He defends individuals charged with violating Wisconsin's criminal statutes. His firm, DK Anderson, S.C. specializes in defending against OWIs, drug crimes, property crimes, domestic violence, and violent crimes. We are client focused and work hard to keep the communication channels open so our clients are not left in the dark. We will aggressively defend you and your rights all at an affordable fee.
Robert W Keller
(262) 632-0632 913 Main Street
Attorney Robert W. Keller practices exclusively in the areas of criminal defense law, and has been doing so since 1992. Clients are represented throughout the State of Wisconsin in both State and Federal Courts. Primary counties of practice include Racine, Kenosha and Milwaukee.
Felony Practice:
A majority of the practice is devoted to felony criminal defense. This includes, but is not limited to homicide cases, controlled substance violations, firearms offenses, sexual assault crimes, reckless endangerment and serious theft cases.
Misdemeanor Crimes:
All misdemeanor offenses, including drug offenses and all domestic violence related cases.
Traffic Crimes:
Operating While Intoxicated, Operating After Revocation, Fleeing...
Michael F. Hart
(888) 565-7597 735 N Water St
Michael F. Hart has been one of Wisconsin's leading criminal defense attorneys for the past twenty-nine years. His imposing courtroom presence has distinguished him as a prominent trial lawyer, and his dedication to justice has earned him the recognition of being a Wisconsin Super Lawyer by many of the state's judges and lawyers.
His successes include a variety of practice areas, and his clients range from high-profile members of the National Football League to white collar workers. Most notably, his triumphs include one of the largest defamation awards in Wisconsin history against a private individual, where Michael successfully helped his client...
John Smerlinski
Monona, WI Domestic Violence Attorney with 31 years of experience
(608) 277-0909 5708 Monona Drive, Suite C
Attorney John K. Smerlinski has over 20 years of experience practicing criminal, divorce, and personal injury law in the state of Wisconsin. Attorney Smerlinski specializes in criminal law and can help you with DUI charges, drug charges, misdemeanor charges, and felony charges just to name a few. Smerlinski Law Office S. C. has extensive experience in divorce/family law and personal injury law. The firm has secured over 50 acquittals for clients over the years, and will work hard to get you the best results possible with your case. Contact Smerlinski Law Office today, for a free consultation, to discuss...
Jillian Scheidegger
Jillian J. Scheidegger is a partner at Cafferty & Scheidegger, S.C. Jillian has been with the firm since 2013. She focuses exclusively criminal defense and traffic matters. Her practice includes the representation of adults and juveniles charged with crimes. Her cases typically involve drugs, sexual offenses, property crimes, alcohol and domestic violence. Jillian has represented hundreds of clients, zealously advocating for the best possible result in each and every case. It is important to Jillian that her clients feel informed throughout the process and understand each step of the way. Jillian is passionate about obtaining excellent results for her clients...
William Robert Kerner
(414) 258-5989 6525 W Bluemound Rd
A Traffic Ticket may seem like a small thing, but it can have larger consequences. Often, the fine is the least serious consequence of getting a Traffic Citation.
The experienced and knowledgeable attorneys at Kerner Law Offices can help you fight your tickets and prevent much of the damage and cost they will inflict on you, but only if you take action.
Daniel L. Lambert
(414) 453-0800 933 North Mayfair Road
Experienced Family Law litigator dedicated to thorough and efficient representation of complex divorce, separation, post-judgment modifications and all other areas of family law.
Domestic Violence Attorneys in Nearby Cities
Domestic Violence Attorneys in Nearby Counties
Saint Croix County
The Oyez Lawyer Directory contains lawyers who have claimed their profiles and are actively seeking clients. Find more Hudson Domestic Violence Lawyers in the Justia Legal Services and Lawyers Directory which includes profiles of more than one million lawyers licensed to practice in the United States, in addition to profiles of legal aid, pro bono and legal service organizations.

redpajama_set_name: RedPajamaCommonCrawl


text:
Tech Car
Spotify enters epic game Mall: to build a more general application distribution platform
Byibmwl
Spotify has now landed in Epic Games mall, which shows epic's ambition to turn the game store in the strict sense so far into a more general application distribution platform. Just like app store and Google play, spotify apps can be downloaded directly from epic game store to PC and MAC devices. < / P > < p > the launch of spotify in epic's game store comes at a time when epic is engaged in a long-term legal battle with apple and Google over the business models of their respective app stores. Epic has sued the two companies over the removal of the mobile version of fortnite, saying it violated antitrust laws and that developers can and should be able to handle payments themselves, avoiding giving 30% of all app revenue to store owners. < / P > < p > Epic Games, launched in December 2018, is still a relatively new digital distribution platform, launched as valve's steam competitor. But from the beginning, epic has offered developers more generous rewards, taking only 12% of developers' income as a share, rather than 30% of valve and apple and Google. < / P > < p > as of January, the number of users of epic game store has exceeded 100 million, and the growth of this number is probably partly due to epic's rich sales and gifts. (a may gift of GTA V was so popular that the store was shut down for many hours.). < / P > < p > with epic's growing user base, developer friendly charging structure, and now hosting one of the most popular apps in the world, epic seems to be proving that non game developers should see its distribution platform as a viable option for other app stores. Global Tech
Gog will cooperate with epic game mall to build a…
Game industry YouTube? Epic invests 15 million into…
By bypassing the shopping mall payment system, play…
Hummer EV new news entertainment system will use…
Amazon plans to build 1500 new small distribution…
Take two president "highly suspicious" subscription…
By ibmwl
Sega Dreamcast's Simpsons Game has been on the Internet for 20 years
Jan 3, 2021 ibmwl
Ign game of the year announced: Hades player choice award: the last survivor 2
Classic mahjong masterpiece Shanghai 3 returns to switch on December 31
Apple's iPhone 13 will come out with the same four sizes as the 12 series wide angle cameras, which will also be upgraded
Famous apple analyst: Apple's market value of 3 trillion US dollars is just around the corner
Cruise is expected to resume? U.S. Agency plans to lift cruise ban from November
Seearch: a good helper in open water rescue
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The word 'journal' comes from Old French 'day'. So it is our daily encounter with ourselves through the mirror, lens and window of words and silence. 'Journal' echoes the word journey, as we travel through inner and outer landscapes. In this retreat we write with the ear, eye and heart.
Dorian Haarhoff is a writer story-teller and mentor. Passionate about developing our innate creativity and imagination, he believes in the power of stories to spread Loving-Kindness, to grow the moment and bring healing. Dorian's workshops are based on his text, The Writer's Voice. He draws his inspiration from mythology, whole-brain theory, narrative therapy, Zen, creation spirituality, the new physics and eco - and Jungian psychology. He is a former professor of English (Namibia) and facilitates story/writing workshops. His poems appear in Quiet Food and The Cake the Buddha Ate.


text:
Europe, Tenders, Vehicles
Italian regional operators launch tenders for hydrogen-powered trains
A number of tenders for new rolling stock, including multiple-units powered by hydrogen and batteries, have been announced by Italian regional operators.
A bid was made public by Calabria Railways (FdC) for the delivery of hydrogen multiple-units (HMU). The tender comprises a definitive order for five trains valued at €65 million as well as a €3.5 million maintenance option.
Another €39 million option for three additional HMUs is included in the contract, along with the same €2.1 million maintenance option. By the end of 2026, the trains are expected to be delivered. The deadline for bids is February 13.
The Sardinian Regional Transport Company (ARST) has announced a tender for the purchase of three HMUs for €39 million with an option to buy five more for €65 million in the Official Journal of the European Union. Bids must be filed by January 31 for the trains, which will run on the 950mm-gauge network of ARST.
A separate tender totaling €16.3 million for a single HMU, also to be installed on the 950mm-gauge network, has also been released by ARST. Bids must be received by February 7 for this tender.
Three 28 million LRVs for the Sassari Metro and seven 33 million LRVs for the Cagliari Metro are among the light rail networks for which ARST has released a tender. Bids must be submitted by March 28 and the estimated contract value is €35.4 million.
For the 950mm-gauge Circumetnea Railway in Sicily, the Italian Ministry of Infrastructure and Transport (MIT) has released a tender for 15 HMUs. The expected total cost of the deal, including maintenance, is €276 million. The deadline for bids is March 3.
A tender for a six-month framework contract for up to 10 battery-electric multiple units (BEMU) for regional services has been released by TUA, the public transportation provider in Abruzzo. Three vehicles have a firm order under the €112.4 million contract. The deadline for bids is February 27.
More EMUs have been ordered from Titagarh Firema for the Lazio region. On December 24, the producer and the area entered into a third agreement for the supply of five six-car MetroMare EMUs for the Rome to Lido di Ostia route. The nearly €43 million contract is for the last five trains from a framework deal for 38 EMUs that was awarded at the start of 2022.


Groundbreaking research by Dr. John Sanford of Cornell University and others has shown that our genes contain tens of thousands of mistakes (mutations), and with each passing generation even more errors are added and passed on.
So it should be no surprise that our ancestors were bigger, stronger, faster and smarter.
The truth is that they had better genes.
This kind of information comes as a shock to many people. It is widely assumed by the general public that humanity is "progressing" and that we are better both physically and mentally than our predecessors were.
'Even our most highly trained athletes pale in comparison to these ancestors of ours,' Dr. Colin Shaw told Outside Magazine.
As I mentioned above, the primary reason for our decline as a species is the systematic deterioration of our genes.
According to Dr. John Sanford of Cornell University, the author of Genetic Entropy & the Mystery of the Genome, each one of us already carries tens of thousands of harmful mutations, and each one of us will pass on at least 100 new mutations to future generations.
Many scientists believe that this will ultimately lead to something called "mutational meltdown".
Geneticists have long worried about the impact of mutations on the human population, and that at a rate of one deleterious mutation per person per generation, genetic deterioration would result.
Earlier reports were based on estimates of mutation rates considerable lower than what we now know to be the case.
Findings going back to 2002 show that the human mutation rate is at least 100 mistakes (misspellings) per person per generation.
Some scientists believe the rate is closer to 300.
Even a rate of 100 has profound implications, and the mutation rate is itself increasing.
Furthermore, most, if not all, mutations in the human genome must be deleterious.
It would appear that the process is an irreversible downward spiral that will end in "mutational meltdown".
This is incredible stuff with absolutely staggering implications.
This sounds strange to many people, especially considering the technological boom that we have seen in modern times, but it is actually true.
Are humans becoming smarter or more stupid?
Comparing our modern lives and technology with that of any preceding generation, one might think we are becoming increasingly smarter.
But, in two papers published in Trends in Genetics, Gerald R. Crabtree of Stanford University claims that we are losing mental capacity and have been doing so for 2,000–6,000 years!
The reason, Crabtree concludes, is due to genetic mutations—which are the backbone of neo-Darwinian evolution.
Based on data produced by the 1000 Genomes Project Consortium and two recent papers in Nature, Crabtree estimates in the first article that, in the past 3,000 years (approximately 120 generations), about 5,000 new mutations have occurred in the genes governing our intellectual ability.
Crabtree bases his conclusion that humankind is losing mental capacity on the ratio between the deleterious and the beneficial mutations.
Confirmed by The Italian Health Ministry.
The Secret Behind The Ebola Virus No One is Talking About.
Seniors Dying From Flu Vaccination (Media Blackout).
To Your Health on Pinterest.
Michael T. Snyder has a new book out he is a former Washington D.C. attorney who now publishes The Truth.


text:
John Bruton
Opinions & Ideas
By John Bruton
· International Financial Services Sector combines to create IFSC Ireland to promote and market the IFSC internationally
· Former Taoiseach John Bruton to become Chairman of IFSC Ireland commencing September 1st 2010
IFSC Ireland
Ireland's international financial services industry,in a private sector initiative, has announced its intention to create the role of Chairman of IFSC Ireland. Former Taoiseach and EU Ambassador to the United States, John Bruton, has agreed to accept the position.
The Chairman of IFSC Ireland will work with the industry to promote Ireland as a location of choice for international financial services, to identify opportunities for the development of the IFSC, and will act as a point of contact and advice for potential investors.
Accepting the role, John Bruton said, "I'm delighted to accept this invitation to work with IFSC Ireland to promote Ireland's international financial services industry, which already supports in excess of 25,000 well paid jobs. Bringing jobs to Ireland will be my overriding priority in this new role, on behalf of the organisations who have come together to establish IFSC Ireland."
"The international financial services industry in this country has remained resilient throughout the global downturn and is continuing to act as a source of well paid employment particularly for young qualified graduates. It is also the source of many further spin off jobs. This key group will be the mainstay of our economic recovery and I am particularly pleased to be asked to play a part in ensuring that we continue to generate new employment opportunities in the IFSC for our young people .The IFSC is a global centre of excellence in key areas of banking, fund administration, and insurance. It is a success story that we should be proud of. I hope to be able to put my experience overseas, previously in the public sector and now in the private sector, to use to promote the industry in a manner that maximises the employment benefits of the IFSC for Ireland." Mr Bruton said.
IFSC Ireland has been developed and is being wholly funded by the Irish Funds Industry Association, Financial Services Ireland, the Federation of International Banks in Ireland, the Institute of Bankers, the Irish Stock Exchange, the Irish Association of Investment Managers, and the Dublin International Insurance and Management Association.
A joint statement issued by the organisations establishing IFSC Ireland stated that "We are delighted that John Bruton has accepted our invitation to Chair IFSC Ireland and believe that his outstanding national and international credentials will be key to our renewed drive to exploit the full potential of the IFSC to create new jobs and generate economic activity. The Irish economy faces many challenges including the need to attract investment and stimulate job creation. The establishment and growth of the IFSC was one of the driving forces of Ireland's economic transformation over the last 25 years. The industry believes that the IFSC can, once again, play an important role in supporting our economic recovery. However, in light of the quickening pace of the global recovery in international finance the industry believes that it has a responsibility to take the lead in ensuring that Ireland is positioned to attract further investment in this important area."
Welcoming the development, Barry O'Leary, CEO of IDA Ireland said that;
"IDA Ireland welcomes the creation, by the industry, of IFSC Ireland and the appointment by IFSC Ireland of a Chairman of such global standing to represent it. The Chairman will be supported in his role by IDA .Ireland and will work in close co ordination with them . The international financial services sector in Ireland has proved to be very resilient despite the current economic situation. We believe there are significant investment opportunities for Ireland to win across a broad range of activities within the industry. These will generate highly skilled employment thereby assisting our economic growth and recovery. We look forward to collaborating with the industry and the new Chairman to ensure this comes to pass"
A week in China
The Economist's Seventh EU-SE Europe Summit
John Bruton at The Week in Politics
UK politicians need to put country before party: Former Irish prime minister from CNBC.
RTE Radio1 Brexit doesn't require UK to leave single market or customs union
https://youtu.be/6HdWRkimL08
John Bruton in India
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WHAT STICKING POINTS IN UK/EU TRADE DEAL?
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This application is to facilitate the parents of students studying in Global Indian International School and uses school buses, by providing them bus attendance information and bus location in real-time.
1- Parents can track fleet/bus of their children live on the map using this application along with route, bus number, attendant number, name and stop details.
2- Parent can call directly to bus attendant using call feature in bus info section.
3- Parents can get pickup and drop off timings of their children in buses along with push notifications.
3- Parents can get entering and embarking time of their children in school campus along with push notifications.
4- Parent can receive bus arrival notification prior to the arrival of the bus at their stops either for picking up in morning or dropping off in afternoon.
5- Parents can set preferences for turning off/on multiple notifications.
6- Parents can use this application on multiple phones using same credentials so they can easily be able to monitor their children from their workplaces using their own smartphones.
7- Parent can see monthly attendance report of their children.
8- Parent can get late/absent children notification.
9- Parent can see events in the event calendar.
10- Parent will immediately receive SMS when children will not be picked up by the bus.
* Full Screen and smooth bus tracking.
* Notification Center to see notifications history.
* Enhanced Usability and User Experience.
* Instant feedback feature to send suggestions or report issues.
* Improved stability and performance.
* Minor Layouts and bugs fixes.


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Here are the winners of the Panoramio monthly Contest for November 2008 edition. Those photos were uploaded in November and voted in December. The sponsor ATP will contact the winners during the next 30 days in order to send the prizes.


text:
\section{introduction}
Astrophysical observations of the stars in S-cluster that is located in the vicinity of the Galactic Center give evidences for the existence of supermassive black hole in this region \cite{Gillessen2010,Gillessen2017,Parsa2017,GC2019}. This gives possibilities to study processes that take place in the vicinity of a supermassive black hole as well as to test theories of gravity \cite{SchDetection,SchPrecession,S2in2018,S62_Star}.

The study of electromagnetic radiation of a S-star is used for the mentioned purposes. The most appropriate characteristic of this electromagnetic radiation is the redshift of the spectrum of emitted radiation. The problem of calculation of the redshift in the framework of General Theory of Relativity was considered in many papers (see, e. g. \cite{GrouldS2,DAN2018,S2in2018,Zhang2015,Angelil,Zhang2017,GKT,GRG2018}). We will refer to this problem as direct problem. Unlike many papers, where solution of direct problem is performed using post-Newtonian approximation (see, e. g. \cite{Zhang2015,S2in2018}), our consideration uses full general relativity. Apart from this, for the solution of the direct problem it is necessary to solve boundary value problem for isotropic geodesic that connect of the source and of the observer. In many works (see, e. g. \cite{Zhang2015,GrouldS2}) this problem is solved using the tables of impact parameters, that make the accuracy of the solution no more then step of the data in the table. We solve the problem from the numerical solution of usual non-linear equation, that can be performed with much more accuracy.

Solution of inverse problem is more interesting from the point of view of astrophysical applications. The inverse problem is the calculation of parameters of motion of the star in the vicinity of the supermassive black hole from the data of time evolution of redshift. Solution of inverse problem gives possibility to perform reconstruction of motion of the star in the vicinity of black hole. The method for the solution of the inverse problem, that is based on the direct numerical minimization of the $\chi^2$ function, is presented in \cite{GrouldS2,Zhang2015} (see also Section \ref{TheorModel}). Certain analytical results for the solution of inverse problem that are used not only redshift data, but intensity of the radiation, also is presented in \cite{Tarasenko}.

In the present work we describe the approach that gives possibilities to solve inverse problem using data of time evolution of redshift only. Our main goal is to use analytical expressions for all quantities, describing position of the star and redshift of spectrum lines. We exclude from the obtained equations quantities, that can not be expressed through unknown parameters analytically (this is impact parameter $D$), using expressions not only for the function of redshift $z(\tau)$, but also for the derivative $\mathrm{d}z(\tau)/\mathrm{d}\tau$. Due to this solution of inverse problem is equivalent to the solution of a system of usual non-linear equations. Consideration the optical scalar $\sigma$ as a small parameter gives us possibilities to write down result equations in analytical form. As the first step of the solution we find integrals of motion of the star graphically. For the second step we find more accurate solution using least squares method.

As an example of the solution of inverse problem we consider a mathematical model of star moving in the close vicinity of a supermassive black hole. For this purpose chosen parameters of motion correspond to the star on slightly more closer orbit around black hole than known S-stars (see, e. g. \cite{GC2019,S62_Star}). This gives possibilities to test the approach for the case of strong gravitational field and gives possibilities to use the approach for the cases when the sources on very short distances to the Galactic Center, that can be found in future.

\section{Theoretical model}
\label{TheorModel}
Consider a non-rotating, non-charging black hole. The gravitational field of such black hole can be described by Schwarzschild metric
(see, e. g. \cite{Mi}):
\begin{equation}
\mathrm{d}s^2=\frac{\mathrm{d}r^2}{1-2M/r}+r^2\mathrm{d}\theta^2+r^2\sin^2\theta\mathrm{d}\varphi^2-(1-2M/r)\mathrm{d}t^2\,.
\end{equation}
Here $x^i=\{t,\,r,\,\theta,\,\varphi\}$ are Schwarzschild coordinates. We use system of units such that the speed of light in vacuum $c=1$. In our model mass of the black hole $M$ (in geometrical units) is much larger than the mass of the source $M_s$. For example mass of the supermassive black hole in the Galactic Center $M\approx 4\cdot 10^{6}M_{o}$ \cite{Gillessen2017,S62_Star} and mass of the S-star is $M_s\sim M_{o}$. Because of this consider star as a test particle, moving in the external gravitational field of supermassive black hole. The components of 4-velocity of the star can be found from the geodesic equation. They are have the following form (see, e. g. \cite{Mi}):
\begin{eqnarray}\label{ueq}
&&u^1=\frac{\mathrm{d}t}{\mathrm{d}\tau}=\frac{E}{(1-2M/r)}\,;\nonumber\\
&&u^2=\frac{\mathrm{d}r}{\mathrm{d}\tau}=e_s\sqrt{E^2-(1-2M/r)(1+L^2/r^2)}\,;\nonumber\\
&&u^3=\frac{\mathrm{d}\theta}{\mathrm{d}\tau}=0\,;\nonumber\\
&&u^4=\frac{\mathrm{d}\varphi}{\mathrm{d}\tau}=\frac{L}{r^2}\,,
\end{eqnarray}
where the orientation of the spatial part of coordinate system chosen in such way that the trajectory of the star lie in the plane $\theta=\pi/2$. $L$ is the angular momentum of the star per unit mass and $E$ is the energy of the star per unit mass. $\tau$ is the proper time of the star. Factor $e_s$ takes into account either receding or approaching part of the trajectory under consideration:
$$e_s=\sign\left(\deriv{r}{\tau}\right).$$
From the system of equations (\ref{ueq}) trajectory of motion of the star can be found in analytical form (see, e. g. \cite{Ch}):
\begin{eqnarray}
&&\frac{1}{r}=\frac{1}{r_s(\varphi,\,\delta,\,p_1,\,p_2)}=\nonumber\\
&&\frac{1}{p_2}+\frac{p_2-p_1}{p_1p_2}\sn^2\left[(\varphi-\delta)\frac{1}{2}\sqrt{1-4M/p_2-2M/p_1},\,k_s\right]\,,\notag\\
\label{rsfun}
\end{eqnarray}
where
\begin{equation*}
k_s=\sqrt{\frac{p_2-p_1}{p_1p_2/2-Mp_2-2Mp_1}}\,,
\end{equation*}
$\sn[\varphi,\,k]$ --- Jacobi sinus of the first kind (see \cite{Korn} for definition). $\delta$ --- longitude of the pericenter. $p_1$ and $p_2$ are pericenter and apocenter distances respectively. They are uniquely related to $E$ and $L$ as follows:
\begin{eqnarray}
&&L=\frac{p_1p_2}{\sqrt{-p_1p_2+\dfrac{1}{2}p_1p_2(p_1+p_2)-p_1^2-p_2^2}}\,;\nonumber\\
&&E=\nonumber\\
&&\sqrt{\frac{M^2-p_1p_2+\dfrac{1}{2}(p_1+p_2)\left(4M+\dfrac{p_1p_2}{M}-p_1-p_2\right)}{M^2+\dfrac{1}{2}(p_1+p_2)\left(\dfrac{p_1p_2}{M}-p_1p_2\right)}}\,.\nonumber\\
\label{EL}
\end{eqnarray}

Proper time of the star $\tau$ can be expressed as function of its angular coordinate $\varphi$ by well-known analytical formula (see, e. g. \cite{Ch}):
\begin{equation}\label{taufun}
\tau=\tau_s(\varphi,\,E,\,L)\,.
\end{equation}
Due to cumbersomeness of this formula, we will not write down this expression exactly.

In modern observational astronomy, stars in the vicinity of Galactic Center are investigated using the wavelength of electromagnetic radiation that has the range of $1 \mu m - 10 m$ (including pulsars, see, e. g. \cite{Gillessen2010}). This is small compare to the scale of motion of the star. Due to this we use the geometrical optics approximation (see, e. g. \cite{Stephani}). In this approximation electromagnetic radiation propagate along a null geodesic with tangent vector $k_i$, that satisfy the following relations:  $k_jk^j=0$ and $k_{i;j}k^j=0$. Therefore, choosing coordinate frame $\tilde{K}: \{t,\,r,\,\tilde{\theta},\,\tilde{\varphi}\}$ such that the observer resides on the axis $\tilde{\theta}=0,$ $\tilde{\varphi}=0$, obtain that trajectory of light ray lie in the plane $\tilde{\varphi}=const$ and (see, e. g. \cite{Mi}):
\begin{eqnarray}\label{keq}
&&k^1=\frac{\mathrm{d}t}{\mathrm{d}\lambda}=\frac{1}{(1-2M/r)}\,;\nonumber\\
&&k^2=\frac{\mathrm{d}r}{\mathrm{d}\lambda}=e_r\sqrt{1-(1-2M/r)D^2/r^2}\,;\nonumber\\
&&k^3=\frac{\mathrm{d}\tilde{\theta}}{\mathrm{d}\lambda}=-\frac{D}{r^2}\,;\nonumber\\
&&k^4=\frac{\mathrm{d}\tilde{\varphi}}{\mathrm{d}\lambda}=0\,,
\end{eqnarray}
where $\lambda$ is an affine parameter along the ray, $D$ is the impact parameter. Factor $e_s$ takes into account either receding or approaching part of the trajectory of light under consideration:
$$e_r=\sign\left(\deriv{r}{\tau}\right).$$
The sign in the expression of derivation of $\tilde{\theta}$ (see equation (\ref{keq})) chosen in such way, that $D>0$ (we consider only trajectories of zero order (see, e. g. \cite{Tarasenko,BisnovatyiRays})).

From (\ref{keq}) obtain the following analytical expression for the trajectory of the ray:
\begin{eqnarray}
&&\frac{1}{r}=\frac{1}{r_r(\tilde{\theta},\,D)}=\nonumber\\
&&\frac{1}{P}-\frac{Qk^2}{2PM}\cn^2\left[\frac{\tilde{\theta}}{2}\sqrt{\frac{Q}{P}}+
\F\left[\arccos{\left(\sqrt{\frac{2M}{Qk^2}}\right)},k\right],k\right]\,,\notag\\
\label{rSol}\\
\nonumber
\end{eqnarray}
where
\begin{eqnarray}
&&Q=\sqrt{P^2+4PM-12M}\,;\\
&&k=\sqrt{\frac{Q-P+6M}{2Q}}\,,
\end{eqnarray}
$cn\left[\varphi,\,k\right]$ and $F\left[\varphi,\,k\right]$ are the Jacobi cosine and the elliptic integral of first kind respectively (see \cite{Korn} for definition). For the real values $P$ has physical meaning of closest approach distance. For the complex values $P$ has no direct physical meaning (see, e. g. \cite{Ch}), but in all cases $P$ can be expressed through the impact parameter $D$ as follows:
\begin{equation*}
P=-\frac{2}{\sqrt{3}}D\sin{\left[\frac{1}{3}\arcsin{\left(\frac{3\sqrt{3}}{D}\right)}-\frac{\pi}{3}\right]}\,.
\end{equation*}

Angular coordinates in both coordinate systems are connected by the relation:
\begin{equation}\label{angles}
\tilde{\theta}=\arccos[\cos(\varphi)\sin(i)]\,,
\end{equation}
where angle $i$ is the inclination of the orbit of the star.

Redshift of the electromagnetic spectrum can be calculated from the formula (see, e. g. \cite{Zhang2015})
\begin{equation}\label{redshiftForm}
z=\frac{\delta\lambda}{\lambda}=\frac{(u_i)_s (k^i)_s}{(u_j)_o(k^j)_o}\,.
\end{equation}
Here $\lambda$ is the wavelength of emitted light, $\delta\lambda$ is the difference between wavelength of the received light and the emitted light. $(k_i)_s$ and $(k_i)_o$ denote the wave vector in the points of radiation and receiving of radiation by the observer respectively. $(u_i)_o$ and $(u_i)_s$ denote 4-velocity vector of the observer and of the star respectively.

In common observational scenario observer resides far away from the source of gravitational field. Therefore metric in the vicinity of observer with good accuracy can be considered as Minkowskian metric. Motion of this observer (for example, motion of the Earth in the case of ground based observer) can be taken into account using the standard formulas (see, e. g. \cite{Damour-DeruelleII,Teukolsky}). Because of this consider only the case of stationary observer, resided on spatial infinity. This means that $(u^i)_o=\{1,\,0,\,0,\,0,\}$. The 4-velocity of the star can be found solving the equations (\ref{ueq}) numerically. But in order to calculate components of the wave vector of the ray it is necessary to solve boundary value problem for the system of differential equations (\ref{keq}) (see FIG. \ref{generalredshift}), such that the solution describes isotropic geodesics intersecting both: world line of the source and world line of the observer. In general case this problem has infinite number of solutions. In this paper we will consider only light rays of 0 order (see, e. g. \cite{Tarasenko, BisnovatyiRays}). Therefore, solution is unique. Observationally, redshift of light from 0 order trajectories can be detected as redshift of the most bright image of the star (see, e. g. \cite{BisnovatyiRays}). In the chosen abbreviations solution of the mentioned boundary value problem reduce to the solution of the following non-linear ordinary equation for the impact parameter $D$:
\begin{equation}\label{BVPeq}
r_s(\varphi,\,p_1,\,p_2)=r_r(\tilde{\theta},\,D)\,.
\end{equation}
Solution for 0 order trajectories corresponds to the solution of (\ref{BVPeq}) with maximal value of $D$.

\begin{figure}[h]
	\includegraphics[width=7 cm]{generalredshift
	\caption{\label{generalredshift} $(k^i)_o$ and $(k^i)_s$ are tangent vectors to null geodesic that intersect both: the worldline of the source and the worldline of the observer.}
\end{figure}

It is follows from the definition of redshift (\ref{redshiftForm}), which can be rewritten in the form
\begin{equation}\label{zform}
z=\delta t_{o}/\delta{\tau}-1\,,
\end{equation}
 where $\delta t_{o}$ and $\delta{\tau}$ are time intervals of the observer and the source between corresponding events (that connected by isotropic geodesic).  Time of observation $t_{o}$ can be found from the following relation
\begin{equation}\label{ttau}
t_{o}=\int_{0}^{\tau}(z(\tau')+1)\mathrm{d}\tau'\,
\end{equation}
where redshift  $z(\tau')$ is considered as a function of the proper time $\tau'$ of the source.

Take into account stationarity of the observer, relation between angles (\ref{angles}), and substitute expression (\ref{ueq}), (\ref{keq}) into (\ref{redshiftForm}). Obtain redshift in the following form:
\begin{eqnarray}\label{zSchwarzschild}
&&z=-1+\frac{E}{1-2M/r}+\frac{DL}{r^2}\beta-e_s e_r\times\nonumber\\
&&\frac{\sqrt{\left(E^2-\left(1-\dfrac{2M}{r}\right)\left(1+\dfrac{L^2}{r^2}\right)\right)\left(1-\left(1-\dfrac{2M}{r}\right)\dfrac{D^2}{r^2}\right)}}{1-2M/r}\,.\nonumber\\
&&
\end{eqnarray}
Here the abbreviation $\beta=\sin(i)\sin(\varphi)/\sin(\tilde{\theta})$ is introduced. The presented equations give possibilities to solve the direct problem: calculation of redshift of electromagnetic spectrum of a star, moving in external gravitational field of supermassive black hole as function of time of observation. We illustrate the presented method by the numerical model with realistic parameters for the star, moving in the vicinity of the Galactic Center. The results of calculation are presented in FIG. \ref{SchwarzschildRedShift2}.

\begin{figure}[h]
	\includegraphics[width=9 cm]{SchwarzschildRedShift2
	\caption{\label{SchwarzschildRedShift2} Redshift of electromagnetic spectrum of a star in the external Schwarzschild gravitational field as function of time of observation $t$. Pericenter distance of the star orbit $p1=60 M$, apocenter distance of the star orbit $p_2=90 M$, inclination of the orbit $i=1.4\, rad$.}
\end{figure}

However, for the astrophysical purposes it is more interesting to solve the inverse problem: determination of the parameters of motion of a star in the external gravitational field of supermassive black hole from the data of redshift of electromagnetic spectrum of the star. In literature the inverse problem solved by minimization of $\chi^2$ function (see, e. g. \cite{GrouldS2,Zhang2015}):
\begin{equation}
\chi^2=\sum\limits_{j=1}^N\left[\frac{(z_j-z_{\text{obs}, j})^2}{\sigma^2_Z}\right]\,,
\end{equation}
where $z_j$ and $z_{\text{obs}, j}$ are the theoretical and the observation values of redshift respectively for the time of observation $t_j$ ($j\in[1,\,N]$). $\sigma^2_Z$ is the dispersion of the observation redshift data. Due to the function $z_{\text{obs}, j}(t)$ has no analytical expression (because of $D$ is the solution of non-linear equation (\ref{BVPeq})), the minimization of $\chi^2$ can be performed only numerically.

In the present work we present another approach, that is based on the derivation of the system of equation for the parameters of motion in analytical form. In order to obtain equations for inverse problem in algebraic form it is necessary to find expressions not only for $z$ but also for $\mathrm{d}z/\mathrm{d}\tau$. This calculation is described in the following section.

\section{Derivative of redshift function}
\subsection{Newman-Penrose null tetrad and optical scalars}
Introduce the following Newman-Penrose null tetrad (see, e. g. \cite{PenroseRindler,N-PCoefficients}) along the world line of the ray of electromagnetic radiation of the star:
\begin{equation}\label{NPtetrad}
k^i,\, n^i,\, m^i\, \bar{m}^i\,.
\end{equation}
Here $k^i$ is the wave vector of the ray. The symbol $\,\bar{}\,$ denotes the complex conjugation. All vectors of (\ref{NPtetrad}) are null. All scalar products between vectors  (\ref{NPtetrad}) are equal to 0 apart from
\begin{equation}
k_in^i=-1;\,m_i\bar{m}^i=1\,.
\end{equation}
Consider congruence of isotropic geodesics that have tangent vectors $k^i$ and intersect the world line of the observer in the time $t_{o}$. Also consider the Newman-Penrose tetrad (\ref{NPtetrad}) in all points of this congruence. Then the components of the vectors of the tetrad in the coordinate basis of $\tilde{K}$ have the form (we chose the affine parameter $\lambda$ such that $k_0$=-1):
\begin{eqnarray}
&&k_j=\left\{-1,\,e_r\frac{\sqrt{1-(1-2M/r)D^2/r^2}}{1-2M/r},\,-D,\,0\right\}\,;\nonumber\\
&&n_j=\left\{-\frac{1}{2}(1-2M/r),\,-\frac{e_r}{2}\sqrt{1-(1-2M/r)D^2/r^2},\right.\nonumber\\
&&\left.\frac{D}{2}(1-2M/r),\,0\right\}\,;\nonumber\\
&&m_j=\nonumber\\
&&\frac{1}{\sqrt{2}}\left\{i\frac{D}{r},\,i e_r r\sqrt{1-(1-2M/r)D^2/r^2},\,r\sin{\tilde{\theta},\,0}\right\}\,;\nonumber\\
&&\hat{m}_j=\nonumber\\
&&\frac{1}{\sqrt{2}}\left\{0,\,-i\frac{D}{r},\,-i e_r r\sqrt{1-(1-2M/r)D^2/r^2},\,r\sin{\tilde{\theta}}\right\}\,.\nonumber\\
\label{NPcomponents}
\end{eqnarray}
For the considered congruence one can obtain the following equations (see, e. g. \cite{N-PCoefficients,AnalyticalLensing,NovikovFrolov}, $\epsilon=k_{[i;j]}=0$ \cite{GRG2018})
\begin{eqnarray}
&&k_{i;j}m^i\bar{m}^j=-\rho\,,k_{i;j}m^im^j=-\sigma\,,\nonumber\\
&&k_{i:j}k^j=k_{i;j}k^i=0\,.
\end{eqnarray}
Here $\rho$ and $\sigma$ are optical scalars. They are obey the following system of equations (see, e. g. \cite{PenroseRindler,N-PCoefficients,AnalyticalLensing,NovikovFrolov}):
\begin{eqnarray}
&&\frac{\mathrm{d}\rho}{\mathrm{d}\lambda}=\rho^2+\sigma^2\,,\nonumber\\
&&\frac{\mathrm{d}\sigma}{\mathrm{d}\lambda}=2\sigma\rho+\Psi_0\,.
\end{eqnarray}
Here $\Psi_0=R_{ijsl}k^{i}m^{j}k^{s}m^{l}=3D^2/r^5$ \cite{AnalyticalLensing}. Chose the affine parameter of the ray $\lambda$ in such way that $\lambda=0$ in the point of radiation. $\lambda_0$ is the value of the affine parameter in the space point of the observer location. In the limit of Minkowsky space-time ($M\rightarrow 0$) obtain $\rho=-1/(\lambda-\lambda_0)$, $\sigma=0$.  Introduce the following abbreviations $\nu=\lambda_0-\lambda$, $X=-1/\rho$. Then obtain
\begin{eqnarray}
&&\frac{\mathrm{d}X}{\mathrm{d}\nu}=-1-X^2\sigma^2\,,\nonumber\\
&&\frac{\mathrm{d}\sigma}{\mathrm{d}\nu}=\frac{2\sigma}{X}-\frac{3D^2}{r^5}\,.\label{OpticalSystem}
\end{eqnarray}
Due to the observer is far from black hole, the initial conditions for the system of equations (\ref{OpticalSystem}) must be chosen as:
\begin{equation}
X(0)=0,\,\sigma(0)=0\,.\label{OpticalInitial}
\end{equation}
The system of equation (\ref{OpticalSystem}) with initial conditions (\ref{OpticalInitial}) can be solved numerically. Only for the sum $\rho+\sigma$ an analytical expression can be obtained (see, e. g. \cite{AnalyticalLensing}):
\begin{eqnarray}
&&\rho+\sigma=-\frac{\dfrac{\mathrm{d}}{\mathrm{d}\lambda}\left(r\sin{\tilde{\theta}}\right)}{r\sin{\tilde{\theta}}}=\nonumber\\
&&-\frac{e_r}{r}\sqrt{1-\left(1-\frac{2M}{r}\right)\frac{D^2}{r^2}}+\frac{D}{r^2}\ctan{\tilde{\theta}}\label{analyticOptics}\,.
\end{eqnarray}
Write down components of vector of 4-velocity of the star in the basis of null tetrad (\ref{NPcomponents}):
\begin{equation}\label{unull}
u^j=\frac{1}{\sqrt{2}}\left(\bar{A}m^j+A\bar{m}^j\right)+Bk^j+Cn^j\,.
\end{equation}
Obtain $-k_ju^j=(1+z)=C$. Denote the components of the killing vector $\frac{\partial}{\partial t}$ as $\xi^j$. Then
\begin{equation}
\xi^j=\frac{1}{2}\left(1-\frac{2M}{r}\right)k^j+n^j\,.
\end{equation}
Also obtain
\begin{equation}\label{Etetrad}
E=-u^i\xi_i=B+\frac{1}{2}\left(1-\frac{2M}{r}\right)(1+z)\,.
\end{equation}
From the relation for the norm of $u_i$ obtain
\begin{equation}\label{normtetrad}
u_ju^j=|A|^2-2(1+z)B=-c^2\,.
\end{equation}
From (\ref{Etetrad}) and (\ref{normtetrad}) follows
\begin{eqnarray}\label{coefftetrad}
&&B=\frac{c^2+|A|^2}{2(1+z)}\,,\nonumber\\
&&|A|^2=-c^2+2E(1+z)-(1-2M/r)(1+z)^2\,.\nonumber\\
\end{eqnarray}

Now, express the time derivative of redshift, using the relation $k_{[j;l]}=0$ (see, e. g. \cite{GRG2018}):
\begin{eqnarray}
&&\frac{\mathrm{d}z}{\mathrm{d}\tau}=-k_{j;l}u^ju^l=-|A|^2 k_{j;l}m^j\bar{m}^l-A^2 k_{j;l}m^jm^l-\nonumber\\
&&\bar{A}^2 k_{j;l}\bar{m}^j\bar{m}^l-2\bar{A}(1+z)k_{j;l}n^jm^l-2 A (1+z)k_{j;l}n^j\bar{m}^l=\nonumber\\
&&|A|^2(\rho+\sigma\cos{2 P_A})-2\sqrt{2}(1+z)\frac{D}{r^3}|A|\sin{P_A}+\nonumber\\
&&\frac{e_r}{r^2}(1+z)^2\sqrt{1-\left(1-\frac{2M}{r}\right)\frac{D^2}{r^2}}\,.\label{derivz}
\end{eqnarray}
Here we use the abbreviation $A=|A|e^{i P_A}$, where $|A|$ and $P_A$ are real. It is follows from numerical calculations, that in the cases, when spatial point of radiation resided far enough from the black hole ($r\agt 20 M$), holds the following inequalities: $\rho\agt\sigma$, $\sigma<<1$ (see FIG (\ref{rho})-(\ref{sigma2}) for illustration).
\begin{figure}[h]
	\includegraphics[width=\columnwidth]{rho
	\caption{\label{rho} $\rho$ as function of parameter $\nu$. Impact parameter $D=50M$.}
\end{figure}
\begin{figure}[h]
	\includegraphics[width=\columnwidth]{sigma1
	\caption{\label{sigma1} $\sigma$ as function of parameter $\nu$. Impact parameter $D=50M$.}
\end{figure}
\begin{figure}[h]
	\includegraphics[width=\columnwidth]{sigma2
	\caption{\label{sigma2} $\sigma$ as function of parameter $\nu$. Impact parameter $D=50M$.}
\end{figure}
Due to this we will neglect the value of $\sigma$ in calculations.

Then, for the time derivative of redshift obtain
\begin{eqnarray}\label{zderivativeRes}
&&\frac{\mathrm{d}z}{\mathrm{d}\tau}=\left[2E(1+z)-\left(1-\frac{2M}{r}\right)(1+z)^2-c^2\right]\times\nonumber\\
&&\left[-\frac{e_r}{r}\sqrt{1-\left(1-\frac{2M}{r}\right)\frac{D^2}{r^2}}+\frac{D}{r^2}\ctan{\hat{\theta}}\right]-\nonumber\\
&&2\frac{D}{r^3}\sin{P_A}\sqrt{2E(1+z)-\left(1-\frac{2M}{r}\right)(1+z)^2-c^2}+\nonumber\\
&&\frac{e_r}{r^2}(1+z)^2\sqrt{1-\left(1-\frac{2M}{r}\right)\frac{D^2}{r^2}}\,.
\end{eqnarray}

In order to obtain an analytical formula, it is convenient to exclude the impact parameter $D$ from the equations (\ref{zSchwarzschild}) and (\ref{zderivativeRes}). Obtain:
\begin{eqnarray}
&&\frac{D}{r}=\frac{\frac{L}{r}\beta\left((1+z)\left(1-\frac{2M}{r}\right)-E\right)\pm\sqrt{\left(E^2-\left(1-\frac{2M}{r}\right)\left(1+\frac{L^2}{r^2}\right)\right)\left(|A|^2+(\beta^2-1)\frac{L^2}{r^2}\right)}}{E^2-1+\frac{2}{r}+\frac{L^2}{r^2}(\beta^2-1)(1-\frac{2}{r})}=\EuScript{F}_1(r,\,z,\,E,\,L,\,i,\,\tilde{\theta})\,;\label{1deriv}\\
&&\text{ and }\frac{D}{r}=\EuScript{F}_2(r,\,z,\,\frac{\mathrm{d}z}{\mathrm{d}\tau},\,E,\,L,\,i,\,\tilde{\theta})=\nonumber\\
&&\frac{r\frac{\mathrm{d}z}{\mathrm{d}\tau}\left(|A|^2\ctan{\tilde{\theta}}-\frac{2(1+z)}{r}|A| S\right)\pm\left(\frac{(1+z)^2}{r}-|A|^2\right)
	\sqrt{\left(1-\frac{2M}{r}\right)\left[\left(\frac{(1+z)^2}{r}-|A|^2\right)^2-r^2\left(\frac{\mathrm{d}z}{\mathrm{d}\tau}\right)^2\right]+\left(|A|^2\ctan{\tilde{\theta}}-\frac{2(1+z)}{r}|A|S\right)^2}}{\left(1-\frac{2M}{r}\right)\left(\frac{(1+z)^2}{r}-|A|^2\right)^2+\left(|A|^2\ctan{\hat{\theta}}-\frac{2(1+z)}{r}|A| S\right)^2}\,.\nonumber\\
&&\label{2deriv}
\end{eqnarray}
Here $S=\sin{P_A}$. An algorithm for making a chose of the sign $\pm$ in formulas (\ref{1deriv}) and (\ref{2deriv}) is given in Appendix A.
In order to find exact expression for $\sin{P_A}$ it is possible to use the low of angular momentum conservation:
\begin{equation}\label{Ldef}
u_i\Psi^i=L=const\,,
\end{equation}
where $\Psi^i$ is Killing vector field, associated with the symmetry of the Schwarzschild metric relative to spatial rotation around arbitrary axis (chose it to be orthogonal to the orbit plane). Components of $\Psi^i$ in the coordinate basis of $\hat{K}$ have the form (see, e. g. \cite{Stephani})
\begin{equation}\label{psi}
\Psi^j=\left\{0,\,0,\,(\cos{i}+\sin{i}\ctan{\tilde{\theta}}\cos{\tilde{\varphi}}),\,\sin{i}\sin{\tilde{\varphi}}\right\}\,.
\end{equation}
Equation of the orbit plane has the following form
\begin{equation}\label{orbitplane}
-\sin{i}\sin{\tilde{\theta}}\cos{\tilde{\varphi}}+\cos{i}\cos{\tilde{\theta}}=0\,.
\end{equation}
From equations (\ref{Ldef}), (\ref{psi}), (\ref{orbitplane}), (\ref{unull}) and (\ref{NPcomponents}) follows
\begin{eqnarray}\label{sinequation}
&&e_r\frac{l}{r}\frac{1-\beta^2}{|A|\sqrt{1-\left(1-\frac{2M}{r}\right)\frac{D^2}{r^2}}}+e_P\beta\sqrt{1-\frac{l^2}{r^2}\frac{(1-\beta^2)}{|A|^2}}=\nonumber\\
&&\beta\sin{P_A}+e_r\frac{\sqrt{1-\beta^2}}{\sqrt{1-\left(1-\frac{2M}{r}\right)\frac{D^2}{r^2}}}\cos{P_A}\,,
\end{eqnarray}
where $e_P$ defined as
\begin{eqnarray}
&&e_P=\sign\left[e_r\beta l\sqrt{1-\left(1-\frac{2M}{r}\right)\frac{D^2}{r^2}}\right.+\nonumber\\
&&\left.e_s D\sqrt{E^2-\left(1-\frac{2M}{r}\right)\left(1+\frac{L^2}{r^2}\right)}\label{e_P}\right]\,.
\end{eqnarray}
The exact solution of (\ref{sinequation}) has the form
\begin{equation}\label{sinP_A}
\sin{P_A}=e_P\sqrt{1-\frac{L^2}{r^2}\frac{(1-\beta^2)}{|A|^2}}\,.
\end{equation}
\section{Inverse problem}
\subsection{Surface of integrals of motion}
The main purpose of the present subsection is to obtain relation between integrals of motion of the star from one hand and the redshift $z$ and the derivative $\mathrm{d}z/\mathrm{d}\tau$ for all moments of proper time from another.
From (\ref{1deriv}) and (\ref{2deriv}) obtain:
\begin{equation}\label{FirstEq}
\EuScript{F}_1(r,\,z,\,E,\,L,\,i,\,\tilde{\theta})=\EuScript{F}_2(r,\,z,\,\frac{\mathrm{d}z}{\mathrm{d}\tau},\,E,\,L,\,i,\,\tilde{\theta})\,.
\end{equation}
The equation (\ref{FirstEq}) gives possibilities to obtain connection between constant parameters of motion $L$, $E$ and $i$ in the case, where radius of radiation $r$ and the angle $\tilde\theta$ are known. Therefore, for the solution of the problem it is necessary to use more equations. For this purpose equations (\ref{1deriv}) and (\ref{BVPeq}) can be used. For this purpose express $\tilde{\theta}$ from (\ref{BVPeq}). Impact parameter $D$ in equation (\ref{BVPeq}) can be expressed using (\ref{1deriv}). Then obtain:
\begin{equation}\label{thetaz}
\tilde{\theta}=f(r,\,\EuScript{F}_1(r,\,z,\,E,\,L,\,i,\,\tilde{\theta}))\,.
\end{equation}
Here $f$ is the certain known function. This equation can be solved relative to $\tilde{\theta}$ using the iteration method. Then, obtain equation:
\begin{equation}\label{SecondEq}
r=r_s(\varphi(\tilde{\theta}(r,\,z,\,E,\,L,\,i),\,i)+\delta,\,E,\,L)\,.
\end{equation}
System of equations (\ref{FirstEq}), (\ref{SecondEq}) that is obtained, has 2 equations and 5 unknown variables. Because of this the solution of the system represents 3-surface in certain mathematical space (points of this space can be parametrized by variables $E$, $L$, $i$, $\delta$). This surface can be determined numerically. The results of calculations for our numerical model of the radiation of the star are presented  (see Fig. \ref{d1pi2}-\ref{Md14pi2}) for each point of redshift data.
\begin{figure}[h]
	\includegraphics[width=\columnwidth]{d1pi2
	\caption{\label{d1pi2}2-sections of solution of  (\ref{FirstEq}), (\ref{SecondEq}) for $i=\pi/2$ and $\delta=1$ by plane {$p_1$, $p_2$} for different points of data (see also Fig. \ref{SchwarzschildRedShift2}}
	\end{figure}
\begin{figure}[h]
    \includegraphics[width=\columnwidth]{d14pi2
    \caption{\label{d14pi2}2-sections of solution of  (\ref{FirstEq}), (\ref{SecondEq}) for $i=\pi/2$ and $\delta=1,4$ by plane {$p_1$, $p_2$} for different points of data (see also Fig. \ref{SchwarzschildRedShift2}}
\end{figure}
\begin{figure}[h]
	\includegraphics[width=\columnwidth]{Md1pi2
	\caption{\label{Md1pi2}Magnification of part of the graphic (Fig. \ref{d1pi2})}
\end{figure}
\begin{figure}[h]
	\includegraphics[width=\columnwidth]{Md14pi2
	\caption{\label{Md14pi2}Magnification of part of the graphic (Fig. \ref{d14pi2})}
\end{figure}
This is seen from Fig. \ref{d1pi2}-\ref{d14pi2} that for each point of data obtained 3-surfaces are not coincide. Therefore, points of intersection of the surfaces gives exact value of integrals of motion of the star. This point can be determined from obtained graphics with high accuracy.

Figures \ref{d1pi2}-\ref{Md14pi2} also illustrate that in the case where the angular parameters are chosen coincident with exact solution, sections have unique point of intersection (Fig. \ref{Md1pi2}), that is correspond to the solution of inverse problem. While for the not exact angular parameters, unique point of intersection does not exists (Fig. \ref{Md14pi2}). From the consideration of such graphics, it is possible to make a decision, that in the certain region of the surface exist only one point of intersection. Therefore, initial approximation to the exact solution of inverse problem can be found from such graphics with quite good accuracy.

\subsection{Solution of inverse problem}
The farther improvement of the results can be obtain using the least squares method. For this purpose use the functions $\tau_s(\varphi,\,E,\,L)$ and $r_s(\varphi,\,E,\,L)$. From (\ref{FirstEq}) obtain the following equation:
\begin{eqnarray}
&&\EuScript{F}_1(r_s(\varphi+\delta,\,E,\,L),\,z,\,E,\,L,\,i,\,\tilde{\theta}(\varphi,\,i))=\nonumber\\
&&\EuScript{F}_2(r_s(\varphi+\delta,\,E,\,L),\,z,\,\frac{\mathrm{d}z}{\mathrm{d}\tau},\,E,\,L,\,i,\,\tilde{\theta}(\varphi,\,i))\label{LSMeq}\,.
\end{eqnarray}
Left hand side of (\ref{LSMeq}) and right hand side of (\ref{LSMeq}) represents certain functions of $\varphi$. It is follows from (\ref{LSMeq}), that these functions must be equal for certain set of unknown parameters $E$, $L$, $i$, $\delta$. Therefore, mentioned parameters can be found using the least squares method. For this purpose in the presented example 10 points for different values of $\varphi$ in the range $[1 rad,\,1.4 rad]$ are chosen. Initial approximation obtain using the results of previous subsection. Obtained results presented in Table \ref{LSM_results}.
\begin{table}[h!]
	\caption{\normalsize\normalcolor Results \label{LSM_results}}
	\begin{tabular}{l c c c}
		\hline
		Parameter & Initial  &  Reconstructed & Exact \\
		         & value     &  value       & value \\
		         &           &    \\
		\hline
		Pericenter distance, $p_1/M$ & 62,0 & 60,1 & 60,0 \\
		Apocenter distance, $p_2$ & 95,0 & 89,1 & 90,0\\
		Orbital inclination, $i$ & 1,5 rad & 1,48 rad & 1,4 rad\\
		Initial phase, $\delta$ & 0,9 rad & 1,0 rad & 1,0 rad \\
		\hline
	\end{tabular}
\end{table}

\section{Conclusion}
The presented approach gives possibilities to solve the inverse problem: reconstruction of motion of a star moving in external gravitational field of supermassive black hole from redshift of the spectrum of received radiation. The presented approach uses properties of congruences of isotropic geodesics in order to formulate problem in terms of solutions of certain usual non linear equations that have form of analytical functions of integrals of motion of the star. The obtain equations are exact equations in General Theory of Relativity (we neglect only by optical scalar $\sigma$). Due to this the presented approach can be used for all possible sources (if they are can be considered as test particles in external gravitational field of black hole) moving on arbitrary distance to the black hole.

Apart from this the approach can be directly used in the case of the data of timing of pulsar, moving in external gravitational field. It is known, that large amount of pulsars anticipated to be detected in the Galactic Center in near future (see, e. g. \cite{Zhang2017}). Pulsars can move in the more close vicinity to supermassive black hole and due to this they are even more interesting for the purpose of testing theories of gravity. It is follows from general formula for the redshift (\ref{zform}), that times of arrival of pulses of pulsar can be expressed through redshift from the following equality:
\begin{equation*}
t_{TOA}^{(N)}=t_{TOA}^{(N-1)}+T_p(z+1)=t_{TOA}^{(N-1)}+T_p\frac{(k^iu_i)_s}{(k^iu_i)_o}\,.
\end{equation*}
Here $T_p$ --- is the pulsar period in the reference frame of the pulsar,  $z$ is the redshift, $t_{TOA}^{(j)}$ --- is the time of arrival of the $j$ th pulse. In the problem of reconstruction of motion of pulsar in the neighbourhood of supermassive black hole exist one more unknown parameter --- $T_p$.

Another interesting application of the results of this paper is possibility of reconstruction of motion of a binary star in the vicinity of black hole. Knowledge of motion of such objects is very important problem in astrophysics and stellar mechanics (see, e. g. \cite{Kozai-Lidov,KLMechanism,KLMechanism2,BinarySBH,GW_BinarySBH}). The approach for the solution of the problem for the case of determination of relative motion of components only, is presented in the previous paper of the authors \cite{IJMPA2020}.

The approach can be used directly to the redshift data for the stars, moving in close vicinity to the supermassive black hole in the Galactic Center (for example, for S62 star \cite{S62_Star}) for the purpose of testing General Theory of Relativity.  For this it is possible to obtain integral of motion of a star from the presented algorithm and to calculate redshift as function of time of observation for future moments of time. Comparison of obtained curve with observational data will give the result of testing. With certain generalizations the approach can be used for the reconstruction of motion of a star in the vicinity of rotating black hole. We leave this problem for a future work.

redpajama_set_name: RedPajamaArXiv


Alleppey is a small beautiful land sandwiched between Vembanad lake and Arabian sea. The spectacular Alleppey beach is also a famous picnic spot with a children's park and boating facilities. The 140 year old pier which extends into the sea is an amazing view. The old lighthouse adds beauty to the beach.
Kovalam is the most renowned beach in Kerala for years. This lovely beach with coconut palm and golden sands are situated in the capital city of Kerala Thiruvananthapuram. This sheltered natural bay with warm sand and gentle waves offers so many leisure options including sunbathing, swimming, catamaran cruising, herbal body toning massages etc. There are so many beach resorts, shopping centres and sea food fairs in and around Kovalam.
Shanmugam beach, a popular city beach near Thiruvananthapuram airport is a refreshing destination for city people. So many recreation facilities are available here. This is a favorite spot for sunset watchers. An indoor recreation club, Matsyakanyaka (gigantic sculpture of a mermaid) and a star fish shaped restaurant are the major attractions in Shanmugam beach.
Varkala beach, a quiet and isolated sandy beach is the perfect place to relax without the crowd and bustle of some other beaches in Kerala. The mineral springs and massages in Varkala beach is famous. The wonderful landscape with high rocky cliffs, sand and sea are a spectacular sight. The sunset in Varkala beach is marvellous.
Poovar is a natural wonder where lake, river and sea meet the land. Its an unspoilt beauty of nature. Poovar beach near the Kovalam beach separates the river Neyyar from the sea. Poovar beach is a favorite spot for those who prefer solitude. This tranquil beach is the best place to relax.
This shallow, calm 10 km beach is called the 'The Princess of Arabian Sea'. The beach is located near to Kochi International Airport. This golden beach is an ideal place for swimming, sunbathing, beach volleyball etc. Cherai beach is one among the rare beaches where one can experience the lagoon and ocean separated very close. Tourism fest in December is one of the main event in here.
Fort Kochi beach is the perfect location to sit and relax peacefully. With swaying palm trees, green bushes, rocky surface, the beautiful Chinese fishing net and soft touch of waves make it a favorite hang out. This most beautiful beach in Kerala is an ideal picnic spot with so many eating joints.
The natural beauty and serenity of Kozhikode beach make it a dream place to visit. Kozhikode beach is a favorite spot of sunset viewers. The charm of old light house and two piers is irresistible.
This rock studded beach is historically important being the place where Vasco Da Gama landed first. The unspoilt and unexplored beauty of Kappad beach is situated in Kozhikode.
To experience the excitement of driving into the beach Muzhappilangad is the perfect place to visit. Muzhappilangad, the one and only drive in beach in Kerala bordered by black rocks and shallow water is an ideal place for swimming also. The cleanliness of the beach along with the serene ambiance makes it a favorite spot for tourists.
Dharmadam island, a small island situated 17 km from Kannur is a beautiful landscape covered with coconut palms and dense green bushes. The beach is a eye catching sight from the Muzhappilangad beach. During low tide one can just walk into the island from the beach which is surrounded by rivers and sea.
The beautiful stretch of sand and gentle waves along with a sculpture of mother and child add charm to the Payyambalam beach. Payyambalam beach situated close to Kannur town is a main hang out of people here.
The virgin beauty of Bekal beach is an ideal place for relaxation. The centuries old fort in the beach , Bekal Fort facing the Arabian sea is the major attraction of this beach which add an extra charm to the beauty of this beach and make it a popular tourist attraction.
Apart from these there are so many stunning beaches in Kerala. They include Samudra beach, Thiruvullavaram beach, Thiruvambady beach, kappil beach, Papanasham beach, Vallithura beach, Padinjarekkara beach, Vallikkunnu beach, Valapattanam beach, Beypore beach, Kizhunna beach, Payyoli beach, Meenkunnu beach.


Route: Delegate, Craigie, Mila, Bombala, Bibbenluke, Holt's Flat, Nimitybelle (Nimmitabel), Summer Hill, Rock's Flat, Cooma, Bunyan, Umeralla, Billylingera, Bredbo, Colinton, Michelago, Williamsdale, Queanbeyan, Bungendore, Deep Creek, Tarago, Inveralochy, Tiranna, Goulburn.
The marcher Ernest Albert Corey would go on to receive the Military Medal with 3 bars, the only soldier to do so. He joined the march at Cooma and returned there after the war.
The recruiting march (actually mostly by car and truck) was repeated early in the Second World War. There were re-enactments of the original march in 1988 and 2006.


The story of Rob Harris's '31 sport coupe starts with his buddy Raymond. Raymond found the body discarded in a trash heap. The body had been cut in half and hauled to the trash by a tractor. It had also been hit pretty hard at one point and the left rear corner was pushed in about a foot. That didn't discourage Raymond, though.


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With all of the hype surrounding the environment and reducing emissions from vehicles, factories and manufacturing facilities corporations and individuals alike have jumped onto the green bandwagon. Corporate office buildings are being redesigned and recreated to work harmoniously with the environment. Energy efficient lighting elements and heating and cooling systems that rely on the internal energy of a building or solar sources to power air conditioners and lighting are being reengineered into existing buildings and new edifices are being architecturally engineered to accommodate nature lighting and energy sources that are beneficial to the environment.
Automakers are also involved in reducing vehicle emissions through the introduction and growing interest in hybrid technologies that support low emission gasoline engines combined with electric power plants to increase fuel economy while emitting few pollutants into the atmosphere. Almost every major car manufacturer has joined the hybrid market with a cross system gasoline and electric engine, but the green movement does no stop there. Company sponsored car pools are giving incentives to employees that share rides to work, producing fewer emissions and alleviating congestion, both on the roads and in the parking structures.
Recycling plants and waste management companies have teamed up to provide homeowners with alternatives to piling almost half of the refuse disposed of by households into landfills. Recycled products made from plastic bottles, glass and paper are gaining in popularity as the trend toward recycling continues to expand. Even beyond recycling waste products made of plastic, consumers are mow turning to renewable and reusable products like stainless steel water bottles that can be refilled with clean, clear water or taking natural fiber woven shopping bags to the grocery store instead of loading up on plastic bags that are not biodegradable.
Organic products that are biodegradable are appearing in more grocery stores. Organic products do not rely on chemical treatments for growth of stimulus. Not only are the healthier for consumers, because they are growth without the use of sprayed chemicals they are also better for the environment.
With more and more people contributing to the environment in a positive manner corporations are stepping forward to offer employees incentives and rewards for helping to protect and renew the environment. Companies realizing the need for environmental change to take place are turning to green incentive companies to help inspire and motivate the natural inclination to reduce waste and use replenishable resources. There is still much more that can be done to cut done on harmful emissions and reduce wasted resources, but thanks to the green movement many Americans are helping to heal the plant.
Green Benefits (http://greenbenefits.net) provides environmentally sound products, such stainless steel water bottles, as incentives and perks for individuals, businesses, and organizations that support going green initiatives for the environmental. Art Gib is a freelance writer.


I don't blame the Democrats for wanting to seduce Republicans into a tax-increase trap. Indeed, I completely understand why some Democrats said their top political goal was getting the GOP to surrender the no-tax-hike position.
I'm mystified, though, why some Republicans are willing to walk into such a trap. If you were playing chess against someone, and that person kept pleading with you to make a certain move, wouldn't you be a tad bit suspicious that they weren't trying to help you win?
When I talk to the Republicans who are open to tax hikes, they sometimes admit that their party will suffer at the polls, but they say it's the right thing to do because of red ink.
I suppose that's a noble sentiment, though I find that most GOPers who are open to tax hikes also tend to be big spenders, so I question their sincerity (with Senator Coburn being an obvious exception).
But even if we assume that all of them are genuinely motivated by a desire to control deficits and debt, shouldn't they be asked to provide some evidence that higher taxes are an effective way of fixing the fiscal policy mess?
I'm not trying to score debating points. This is a serious question.
European nations, for instance, have been raising taxes for decades, almost always saying that higher taxes were necessary to balance budgets and control red ink. Yet that obviously hasn't worked. Europe's now in the middle of a fiscal crisis.
So why do some people think we should mimic the French and the Greeks?
But we don't need to look overseas for examples. Look at what's happened in Illinois, where politicians recently imposed a giant tax hike.
The Wall Street Journal opined this morning on the results. Here are the key passages.
Run up spending and debt, raise taxes in the naming of balancing the budget, but then watch as deficits rise and your credit-rating falls anyway. That's been the sad pattern in Europe, and now it's hitting that mecca of tax-and-spend government known as Illinois. …Moody's downgraded Illinois state debt to A2 from A1, the lowest among the 50 states. That's worse even than California. …This wasn't supposed to happen. Only a year ago, Governor Pat Quinn and his fellow Democrats raised individual income taxes by 67% and the corporate tax rate by 46%. They did it to raise $7 billion in revenue, as the Governor put it, to "get Illinois back on fiscal sound footing" and improve the state's credit rating. So much for that. …And—no surprise—in part because the tax increases have caused companies to leave Illinois, the state budget office confesses that as of this month the state still has $6.8 billion in unpaid bills and unaddressed obligations.
In other words, higher taxes led to fiscal deterioration in Illinois, just as tax increases in Europe have been followed by bad outcomes.
Whenever any politician argues in favor of a higher tax burden, just keep these two points in mind.
1. Higher taxes encourage more government spending.
2. Higher taxes don't raise as much money as politicians claim.
The combination of these two factors explains why higher taxes make things worse rather than better. And they explain why Europe is in trouble and why Illinois is in trouble.
The relevant issue is whether the crowd in Washington should copy those failed examples. As this video explains, higher taxes are not the solution.
Heck, I've already explained that more than 100 percent of America's long-fun fiscal challenge is government spending. So why reward politicians for overspending by letting them confiscate more of our income?
Good plan, but we would need them grouped together. Perhaps TX, NM, AZ, LA, OK, NV. Add or subtract at will to gain enough natural resources and coastline to make the new confederation viable.
The only way the USA will survive the monetary debacle is to do a 180 and except the fact that the government let the people down…. stop the insanity!!!!
Both sides of our criminal government need to stand up and take notice, you elected officials all are crooked and are criminals, you all should be brought up on charges and imprisioned!!!!!!!!!!!!!!!!!!!!
I have a dream. A future with all of the productive people of the country crowded into Texas, Florida, Tennessee, Nevada, South Dakota, New Hampshire, Washington, and Wyoming, the states without income taxes. Moving to one of those states and doing the same job is like getting a 10% raise.
Sadly, it is always about power and control. The old saying about "follow the money" is still correct. To retain power, there must be control of the purse, control of production, and ultimately, control of the people. How better to pick winners and losers, to reward and punish, than to have ability to confiscate and re-distribute wealth. It is the silk glove covering the mailed fist. It is the the basis of soft tyranny.


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Jackson Avery
A surgical resident from Mercy West Hospital, Jackson Avery is also called "pretty boy," especially by Cristina Yang.
He is a grandson of the famous surgeon, Dr. Harper Avery. He develops a crush on Cristina, and while inebriated he kisses her at a party, but Cristina breaks the kiss.
In the 6th season finale, he is told by Dr. Shepherd that there is a lockdown in the hospital and is later left by Dr. Hunt and Dr. Altman in the OR with 2 nurses and 1 anesthesiologist.
He is the one who decides that Yang should operate on Shepherd in order to save him. When Mr. Clark (the shooter) takes the OR hostage, he disconnects Shepherd in order to make everyone believe that he is dead until Mr. Clark leaves the room.
It is also revealed later in season 7 that Avery suffers from traumatic nightmares.
Jackson Avery Quotes
I love you. I always have. I love everything about you - even the things I don't like, I love. And I want you with me. I love you and I think that you love me, too. Do you?
Permalink: I love you. I always have. I love everything about you - even the things I don't like, I...
We are not close. That is not something we do.
Permalink: We are not close. That is not something we do.
Jackson Avery Photos
MEREDITH: "You don't get to call me a whore. When I met you, I thought I had found the person that I was going to spend the rest of my life with. I was done! All the boys and all the bars and all the obvious daddy issues, who cares? I was done. You left me. You chose Addison. I'm all glued back together now. I make no apologies for how I chose to repair what you broke. You don't get to call me a whore."
DEREK: "This thing with us is finished. It's over."
MEREDITH: "Finally."
DEREK: "Yeah, it's done."
MEREDITH: "It is done."
Permalink: You don't get to call me a whore. When I met you, I thought I h...
Meredith: You're better than this. You're stronger.
Amelia: Don't make this all your fault. I know you. That's what you do. But, please. Please don't do that.
Maggie: We can't just give up, not after all this time. We have to stand together. We have to fight.
Meredith: Because it's just us now. There were five of us, and now it's just you and I. And it can't be just me. It can't be. I will go down swinging for you, Alex. You know I will. But that means you can't give up. You don't throw the fight. So, whatever you're doing this for... please don't.
Permalink: Because it's just us now. There were five of us, and now it's just you and I. And it can't be...
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