text:
By: Elin Hilderbrand
Narrated by: Kathleen McInerney
4 out of 5 stars 4.0 (1,569 ratings)
Silver Girl
Narrated by: Janet Metzger, Marianne Fraulo
Meredith Martin Delinn just lost everything: her friends, her homes, her social standing - because her husband Freddy cheated rich investors out of billions of dollars. Desperate and facing homelessness, Meredith receives a call from her old best friend, Constance Flute. Connie's had recent worries of her own, and the two depart for a summer on Nantucket in an attempt to heal. But the island can't offer complete escape, and they're plagued by new and old troubles alike.
Loved It!!
By Adrianne on 07-16-11
Here's to Us
Narrated by: Erin Bennett
Celebrity chef Deacon Thorpe has always been a force of nature with an insatiable appetite for life. But after that appetite contributes to Deacon's shocking death in his favorite place on earth, a ramshackle Nantucket summer cottage, his (messy, complicated) family is reeling. Now Deacon's three wives, his children, and his best friend gather on the island he loved to say farewell.
Loved it❣
By jveazey on 08-05-16
A warm June evening, a local tradition: The students of Nantucket High have gathered for a bonfire on the beach. But what begins as a graduation night celebration ends in tragedy after a horrible car crash leaves the driver of the car, Penny Alistair, dead and her twin brother in a coma. The other passengers - Penny's boyfriend Jake and her friend Demeter - are physically unhurt, but the emotional damage is overwhelming, and questions linger about what happened before Penny took the wheel.
The Blue Bistro
Narrated by: Christina Delaine
Adrienne Dealey has spent the past six years working for hotels in exotic resort towns. This summer she has decided to make Nantucket home. Left flat broke by her ex-boyfriend, she is desperate to earn some fast money. When the desirable Thatcher Smith, owner of Nantucket's hottest restaurant, is the only one to offer her a job, she wonders if she can get by with no restaurant experience. Thatcher gives Adrienne a crash course in the business...and they share an instant attraction.
A true picture of Nantucket Island in season
By kaethe on 11-05-12
Narrated by: Therese Plummer
The Carmichaels and the Grahams have gathered on Nantucket for a wedding. Plans are being made according to the wishes of the bride's late mother, who left behind The Notebook: specific instructions for every detail of her youngest daughter's future nuptials. Everything should be falling into place for the beautiful event - but in reality, things are far from perfect. While the couple-to-be are quite happy, their loved ones find their own lives crumbling.
Meh. Nothing particularly special about this book.
By Jessica on 01-31-16
In this juicy first novel by Elin Hilderbrand, a series of personal dramas are played out during one summer at a Nantucket Beach Club. It's about the love of summer, summer love, and the special feelings we all have for that special summer place - in this case, a hotel and an island. An engrossing, sexy novel that will sweep you away to the beach any time of the year.
Beach or no beach, an Excellent Listen!
By Danielle on 05-01-13
The Love Season
It's a hot August Saturday on Nantucket Island. Over the course of the next 24 hours, two lives will be transformed forever. Marguerite Beale, former chef of culinary hot spot Les Parapluies, has been out of the public eye for over a decade. This all changes with a phone call from Marguerite's goddaughter, Renata Knox. Marguerite has not seen Renata since the death of Renata's mother, Candace Harris Knox, 14 years earlier. And now that Renata is on Nantucket visiting the family of her new fiancé, she takes the opportunity, against her father's wishes, to contact Marguerite in hopes of learning the story of her mother's life - and death.
Good Listen, but Very Sad Story
Narrated by: Katie Hale
Greg and Tess MacAvoy are one of four prominent couples who count each other as best friends. As pillars of their close-knit community, the MacAvoys, Kapenashes, Drakes, and Wheelers are important to their friends and neighbors, and especially to each other. But just before the beginning of another idyllic summer, Greg and Tess are killed when their boat capsizes during an anniversary sail.
By Joy on 06-29-12
Nantucket Nights
For 20 years, Kayla, Antoinette and Val have performed their own special summer ritual. Once a year, the old friends put aside their daily, separate lives to drink champagne, swap stories, and swim naked under the Nantucket stars. But on one of those bonding nights, one of their trio swims out from the shore and doesn't return. After the surviving friends emerge from their grief, they realize that the repercussions of their loss go far beyond their little circle, and they begin to uncover layers of secrets - and their connections to each other - that were never revealed on the beach.
By C. Reed on 08-08-18
Narrated by: Denice Hicks
Birdie Cousins has thrown herself into the details of her daughter Chess's lavish wedding, from the floating dance floor in her Connecticut back yard to the color of the cocktail napkins. Like any mother of a bride-to-be, she is weathering the storms of excitement and chaos, tears and joy. But Birdie, a woman who prides herself on preparing for every possibility, could never have predicted the late-night phone call from Chess, abruptly announcing that she's cancelled her engagement.
OMG this was the worst narrator!
By Christian on 08-04-10
Narrated by: Rachael Warren
It's summer on Nantucket, and as the season begins, three women arrive at the local airport, observed by Josh, a local boy, home from college. Burdened with small children, unwieldy straw hats, and some obvious emotional issues, the women - two sisters and one friend - make their way to the sisters' tiny cottage, inherited from an aunt. They're all trying to escape from something, and soon Josh is part of the chaotic household, acting as babysitter, confidant, and, eventually, something more....
A whole lotta cancer...
By Jen Bushman on 09-01-18
Harper Frost is laid back, easygoing. She doesn't care what anyone thinks of her. She likes a beer and a shot and wouldn't be caught dead wearing anything fashionable. She's inherited her father's run-down house on Martha's Vineyard, but she can't hold down a job, and her latest romantic disaster has the entire island talking. Tabitha Frost is dignified, refined. She prefers a fine wine and has inherited the impeccable taste of her mother, the iconic fashion designer Eleanor Roxie-Frost.
I love this author
By Janice K. Anderson on 07-14-17
A Summer Affair
Narrated by: Isabel Keating
Sheila Crispin Cook, mother of four young children and nationally renowned glassblower, bites off more than she can chew when she agrees to co-chair a huge benefit concert on Nantucket. Sheila is asked to chair the Nantucket's Children Summer Gala, at least in part because she is the former high-school sweetheart of world-famous rock star Max West.
a long winded affair
By Monika L. Sullivan on 08-19-08
Winter in Paradise
Irene Steele's idyllic life - house, husband, family - is shattered when she is woken up by a late-night phone call. Her beloved husband has been found dead, but before Irene can process this tragic news, she must confront the perplexing details of her husband's death. He was found on St. John, a tropical island paradise far removed from their suburban life. Leaving the cold winter behind, Irene flies down to the beautiful Caribbean beaches of St. John only to make another shocking discovery: her husband had a secret second family. Investigating, she is plunged into a web of intrigue and deceit belied by the pristine white sand beaches of St. John.
By Lynn E. Smith on 11-01-18
Summer People
Narrated by: Beth MacDonald
Every summer the Newton family retreats to their beloved home on Nantucket for three months of sunshine, cookouts, and bonfires on the beach. But this summer will not be like any other. When Arch Newton, a prominent New York attorney, dies in a plane crash on his way home from a business trip, his beautiful widow, Beth, can barely keep things together. Above all, though, she decides that she must continue the family tradition of going to Nantucket, and at the same time fulfill a promise that Arch made before he died.
A good listen
By JessR on 07-30-18
Welcome to the most tumultuous summer of the 20th century. It's 1969, and for the Levin family, the times they are a-changing. Every year, the children have looked forward to spending the summer at their grandmother's historic home in downtown Nantucket. But like so much else in America, nothing is the same.
It's wedding season on Nantucket. The beautiful island is overrun with summer people - an annual source of aggravation for year-round residents. When one lavish wedding ends in disaster before it can even begin - with the bride-to-be discovered dead in Nantucket Harbor just hours before the ceremony - everyone in the wedding party is suddenly a suspect. As Chief of Police Ed Kapenash digs into the best man, the maid of honor, the groom's famous mystery novelist mother, and even a member of his own family, the chief discovers that every wedding is a minefield - and no couple is perfect.
By RMS on 07-27-18
48-year-old Nantucketer Dabney Kimball Beech has always had a gift for matchmaking. Some call her ability mystical, while others - like her husband, celebrated economist John Boxmiller Beech, and her daughter, Agnes, who is clearly engaged to the wrong man - call it meddlesome, but there's no arguing with her results: With 42 happy couples to her credit and all of them still together, Dabney has never been wrong about romance.
By ELLEN on 04-14-19
A friendship is tested in this irresistible pause resister from New York Times best-selling author Elin Hilderbrand.
Nantucket writer Madeline King couldn't have picked a worse time to have writer's block. Her deadline is looming, her bills are piling up, and inspiration is in short supply. Madeline's best friend, Grace, is hard at work transforming her garden into the envy of the island with the help of a ruggedly handsome landscape architect. Before she realizes it, Grace is on the verge of a decision that will irrevocably change her life. Could Grace's crisis be Madeline's salvation?
As the gossip escalates and the summer's explosive events come to a head, Grace and Madeline try desperately to set the record straight - but the truth might be even worse than rumor has it.
©2015 Elin Hilderbrand (P)2015 Hachette Audio
Shamed
The High Tide Club
Elizabeth ♥
Ehhhh
Boring characters (many with idiotic names) and a predictable story. The voice actors do a good job but the characters were all so 2 dimensional and dumb (literally) it was still a very long book to listen to.
susan wieben
Could not put it down
I listened to this audio book every chance I had. Work breaks, in the car and working in the garden. A great read/listen. Waiting for the ending but never wanting it to end. Colorful characters and surprises around every corner. Not my typical book, but it was really good. I hope to see a sequel.
Cluttered story with a hurried finish
The heart of the story: "A woman with writer's block secretly uses her best friend's extra marital affair as fodder for a new blockbuster novel", was a good one… why did the rest of the book need to be cluttered up with other storylines? OK, the husband's storyline was not so bad, and it did relate back to the wife who was cheating on him, but I would have left out all the kid's stuff and the "we live in such a gossipy town" parts… although then the book could not have been called "The Rumor", I guess it could have been called "The Affair".
Stuffing the book with what were in my opinion superfluous storylines, took time away from the good ones. Had they been left out, the Affair storyline could have been further developed, the tension would have had more time to build up and I would have liked more meat for how they got caught and how it all ends, I would have liked to know if they ended up together in the end and does it work out and how does that impact the family etc etc … Really, I think I wanted a totally different book!
As it was, the husband gets involved in some shady dealings that eventually blow up in his face and that sucked all the energy out of the Affair storyline. It felt to me like the author was in a hurry to finish the book and just tossed a grenade into the plot.
klabaty
great story about how even people who are good can make poor decisions and life does go on
Amazon user
CHANDLER, OK, US
Cute, entertaining, and easy listen.
What made the experience of listening to The Rumor the most enjoyable?
I enjoyed the charaters in this book. Liked listening to the different lives of each yet the lives and story was interwoven in a very believale way. I live in a small town and it is so true the different rumors that can start because of the different preception people conclude.
What did you like best about this story?
Cute, real to life and very easy flowing and good fun listen.
Which character – as performed by Kathleen McInerney – was your favorite?
I think she did a wonderful job and could ,listen to her on and on.
Who was the most memorable character of The Rumor and why?
I liked Grace and Eddie. The story between them was very believable.
Any additional comments?
Nice summer listen.
SF girl
SAN FRANCISCO, US, Canada
My first book with this author, but I enjoyed this so much I will listen to her other books. Good evocative descriptions of Nantucket.
Mary Dietrich
Fort Collins, CO United States
Bad decisions all around
Superficial characters making bad decisions who elicit very little interest or sympathy.
There are consequences but everyone is happy!
Brooke Loewenstein
More scandalous than typical Hildebrand
Illicit trysts in the garden shed, prostitution, drugs...a bit less wholesome than the typical novel by this author. A little more plot and a little less character development (since there are so any characters). Very good none the less.
BookReader
Chicago, IL, United States
Released by Hachette Audio in mid-2015, The Rumor is written by Elin Hilderbrand, narrated by Kathleen Mcinnerney, and the unabridged audiobook is just about eleven hours of listening.
Rumors of affairs, most of which are true, and annoying female gossip traverse the pages - which, I guess, was the point. This is definitely a young adult book, as most of the characters are teenagers. The rest are stay-at-home moms with nothing to do other than tend gardens, worry about their teenagers, have juvenile conversation with each other, and gossip.
If you've any level of intelligence beyond say … oh … 10th grade, take a pass at high speed. If you're a teenager, especially the air-head type, go for it. A beach read you'll probably leave at the beach. Based on the silly content of this book, I actually laughed out loud when a character suggested some sophisticated book titles to a teenager. Given all that is The Rumor, that's hilarious - but, the book isn't a comedy - it's a Peyton Place or soap opera.
The narrators did okay - but annoyingly valley-girly. If you're considering The Rumor, do yourself a favor and listen to the sample.
The fact that this book has so many good reviews is baffling. For me, The Rumor was a waste of time - glad I'm not the only reader who had a similar take. Not recommended.
gail1210
I really enjoyed the book!!
It is a fun book to read interesting characters. definitely a girl book, it would be a good book to read on the beach!


text:
The System of Justice in Syria: Current Organization and Future Challenges
INTRODUCTION — One of the most important and delicate reforms to be implemented in Syria is the one concerning the system of justice. In fact, Syria's system of justice is quite often defined through four adjectives: corrupt, bureaucratic, slow and arbitrary. In year 2008, Transparency International's Corruption Perceptions Index ranked Syria 147th out of 179 countries — Syria had receded for the second year in a row. According to the World Bank's "Ease of Doing Business 2009" report and the International Chamber of Commerce, Syria ranks 174th out of 181 countries with reference to the enforcement of contracts — it takes 872 days to conclude a legal dispute. Already people close to President Bashar al-Assad are alarmed by this level of corruption in the legislative, judicial and executive branches of the government. From the legal point of view, random and non-transparent changes in investment law, coupled with the lack of a real independent judiciary undermine investments, especially now that Syria is trying to attract foreign direct investments (F.D.I.s) in order to diversify its economy. In the last years, some actions aiming toward — an at-least-partial reform of the judicial system — have been taken, like the well-publicized establishment of an institute for the training of judges, and the implementation of a commercial arbitration law. Modernization of the judicial administration was understood as a fundamental tool in order to achieve long-term economic and social development as was pointed out some years ago through Syria's Five Year Plan 2006-10.
ROOTS OF THE SYRIAN LEGAL SYSTEM — The Syrian legal system was established for the first time during the Ottoman domination, but since then it has undergone several modifications, which followed the important government changes of the twentieth century (Syrian Arab Kingdom of 1919-20, French Mandate, post-independence republican regime, United Arab Republic of 1958-61, post-secession republic and the current Syrian Arab Republic). Every one of the mentioned political systems thorough which Syria has undergone in the last century has profoundly affected the justice system of the country. The Syrian legal system is mainly based on civil law traditions, Islamic and Egyptian legal traditions.
Today's most important Syrian codifications are:
A) Civil Code of 1949
B) Penal Code of 1949
C) Criminal Procedure Code of 1950
D) Civil Procedure Code of 1953
E) Personal Status Code that is integral part of the Legislative Decree No. 59 of 1983, currently under review
F) Commercial Code 2008
ORGANIZATION OF THE SYRIAN JUSTICE SYSTEM — Both the Judicial Authority Law of 1961 and the Civil Code of 1949 are the basic documents governing the organization and functioning of the justice system. The Ministry of Justice has the role to oversee Syria's civil and criminal courts. Defendants are entitled to nominate a lawyer who provides legal representation. In case defendants do not have the means to pay for a legal representative the courts will provide a lawyer. Except cases involving juveniles or sex offenders, trials are public. The Supreme Judicial Council is the highest judicial authority in Syria. It oversees the judiciary and has the power to appoint, dismiss and transfer Syrian judges. The Syrian president, Bashar al-Assad is the chairman of this authority, while the vice-chairman is the minister of justice. The other six members are five senior civil judges and the deputy to the minister of justice. Historically, Syria has had a dual judicial system with separated secular courts and religious courts. In fact, when in 1949 the Civil Code, the first Commercial Code (the new one dates back to 2008) and the Penal Code were promulgated, the basic idea was to modernize the legal system with the limitation of the applicability of customary law among Bedouin and religious minorities. In other words, Islamic religious courts continued to work in some parts of the country, but their jurisdiction was reduced and confined to issues of personal status (like for instance marriages, divorce, paternity, custody of children and inheritance). Still on the same path, one additional step was done some years later, in 1955, when a personal code related to many aspects of personal status was accepted. This law is very relevant because it modernized sharia through the improvement of the condition of women in Syria and a better definition of inheritance law.
The Syrian court system is structured through five different types of courts:
Civil and Criminal Courts (three-level jurisdiction: first-level court, court of appeal and Court of Cassation)
Security Courts
Religious Courts (two-level jurisdiction: first-level court, and canonical and spiritual divisions of the Court of Cassation)
Administrative Courts (two-level jurisdiction: administrative courts and Council of State)
With reference to the civil and criminal courts there are three levels of jurisdiction. These courts are organized under the Ministry of Justice and they can hear both civil and criminal matters. At the lowest level there are five different kinds of courts: the courts of conciliation (Mahakim Al-Sulh), the courts of first instance (Mahakim Al-Bidaya), the juvenile courts (Mahakim Al-Ahdath), the Customs Court (Al-Mahkama Al-Jumrukiyya) and the Court of Assize.
All the cases brought in front of the first four types of courts are heard by a single judge, who is assigned jurisdiction according to the nature of the case. The fifth first-level court is the Court of Assize, which hears cases where the punishment may exceed a three-year imprisonment time. Decision taken by the conciliation courts, courts of first instance and court of assize may be appealed to the second level, which means a court of appeal or sometimes the Court of Cassation. There are thirty courts of appeal in Syria and seven of them (three criminal and four civil) are located in Damascus, while one civil court and one criminal court are located in every Syrian district. It is true that appeals are difficult to win because the courts do not provide verbatim transcripts of the treated cases, but only summaries prepared by the involved judges. The Court of Cassation in Damascus is the unique third-level court of appeals and has the power to revolve judicial issues. In general, judgments made at a court of appeal are very difficult to be overturned. However, sometimes verdicts could be nullified by the Court of Cassation. This court is subdivided in three-judge specialized panels according to four different areas of action: civil, criminal, canonical and military.
In addition to the secular courts there are other specialized courts that possess a specific jurisdiction to deal with particular subjects. Military courts have the authority to treat both civilian and military personnel. The problem with these courts is that the military prosecutor decides the venue for a civilian defendant and consequently there are continuously complains that the government utilizes military field courts in location outside established courtrooms. These military field courts do not observe all the normal procedures envisaged for the regular non-military courts.
There are two security courts: the Supreme State Security Court (S.S.S.C.) and the Economic Security Courts. The former tries political and national security cases and its judgments are not subject to appeal. This court does not use the same procedures as the courts of regular jurisdiction. In relations to the S.S.S.C., it is very important the role played by the Syrian president, who has to approve a verdict or who can also nullify it and ask for a second trial. The economic security courts were abolished in 2004, but before they were the main judicial bodies in order to treat cases involving financial and economic crimes.
A specialized administrative system for disputes involving the state and its agencies exists in Syrian like in many other civil-law systems. During the existence of the United Arab Republic (1958-61, union between Egypt and Syria) the Syrian Council of State (the most important administrative judicial body) was remodeled following the Egyptian template and still today there are a lot of communalities with reference to the administrative council of state in both countries. In Syria there are two levels of administrative courts. The second level, which is the Council of State, has both advisory as well as judicial functions and it is totally independent from the other courts of general jurisdiction.
The High Constitutional Court is the highest judicial body in the Syrian Republic. Established under the 1973 Syrian Constitution, this court has three specific tasks: adjudicating electoral disputes, ruling on the constitutionality of a law or a decree challenged by the president or the People's Council, and rendering opinions on the constitutionality of bills, decrees and regulations when asked by the president. The High Constitutional Court is not allowed to discuss about the validity of laws proposed by the president and then approved with popular referendums. The court is composed of the president of the court plus four ordinary judges, who serve for a renewable four-year term. The judges are appointed by the Syrian president.
Special jurisdictional bodies are the Islamic courts, the doctrinal courts and the spiritual courts. The first ones are related to cases regarding personal status, family and inheritance disputes between Syrian Muslims and non-Syrian Muslims who accept Islamic personal status in their own countries. The second ones are formed by a judge belonging to the Druze sect. This judge has to decide whether the decisions taken by people belonging to the Druze community are clashing with the teaching of the religion. The spiritual courts are the judicial bodies in charge of subjects linked to personal status for Jewish, Christian and other non-Muslim groups. Decisions given by all the religious courts may be appealed to the canonical and spiritual divisions of the Court of Cassation.
WHAT ARE THE REAL PROBLEMS OF THE JUSTICE SYSTEM IN SYRIA? — The three major problems that the Syrian government has to overcome in the next year are:
1) The amount of time necessary to solve a dispute via the courts
2) The corruption of Syria's legal system
3) The independence of judges
1) The amount of time necessary to resolve a dispute via the courts — When talking with Syrian lawyers the first complain they have in relation to the justice system of their country is the amount of time that it takes to have a dispute solved by a court. Sometimes it happens that cases last more than ten years. Probably, one reason for the delays is that in Syria there is a shortage of judges. Today according to the Syrian Bar Association (S.B.A.) there are around 1,300 judges. Recent analyses by the S.B.A. calculate that there should be at least 3,000 judges and more court rooms in order to reduce disputes duration. Other reasons for the high number of cases per single judge is that many Syrians go to court for very silly reasons without any real consideration of collected evidence and the possibilities of getting a favorable sentence.
Probably, the existence of a proper supervision with reference to the judges' activity — this point is emphasized by lawyers — could permit to save a lot of time. It is true that in Syria there are judicial inspectors, but the problem is still the same: They are few and with too many judges to be followed. The lawyers would like to have the number of these full-time inspectors — now no more than five — increased because, according to them, corruption is the main problem of the judicial system in Syria. After the corruption issue, it clearly emerges that too many judges work too slowly. It is a well-known fact that in Syria in some courts it is the notary that administers justice because the appointed judge is absent.
2) The Corruption of Syria's legal system — Corruption is evident and the same government acknowledges it. In October 2005, 81 judges, i.e., more than 6 percent of the total number of judges — were sacked for alleged corruption. The government has improved wages and insurance for the judges, while at the same time has reduced taxes with the aim of increasing their living standards. The idea is to attract capable people to the profession of judge. It is a huge task because the level of corruption is very high both on the judges' side as well as on the lawyers' side. In fact, Mohammed Walid al-Tesh, who is the president of the S.B.A., recalls that every year the S.B.A. investigates at least 400 claims of corruption among lawyers. In Syria there are today around 23,000 lawyers and 10 to 50 of them are expelled every year by the S.B.A. for professional misconduct. Syria should have better training for judges and lawyers. For this reason everyone who is able to pass the judge selection process is mandatorily send to teach for two years at the Judicial Institute before he may enter the real profession of judge.
3) The Independence of the Judges — Article 131 of the Syrian Constitution (Article 131 [Independence of the Judiciary] The judicial authority is independent. The President of the Republic guarantees this independence with the assistance of the Higher Council of the Judiciary), dating back to 1973, does guarantee the independence of the judiciary. Instead, Article 133 (Article 133 [Independence of Judges] (1) Judges are independent. They are subject to no authority except that of the law. (2) The honor, conscience, and impartiality of judges are guarantees of public rights and freedoms.) stipulates that judges shall be autonomous and subject only to the authority of law.
The Higher Council of the Judiciary is responsible for the administration of the judiciary. It has the authority of appointing, promoting and transferring judges. The president of this council is the Syrian president, while the deputy president is the minister of justice. A lot of criticism is related to the preponderant role played by the minister of justice. This role — although the minister has only one vote — could really limit judicial independence. For some analysts, the presence of the minister of justice can either intimidate or strongly influence the role of the other board members. The S.B.A. strongly denounces the lack of the judicial independence. Already five years ago at the Ba'ath Party Conference some ideas about a modification of the composition of the council had been proposed. Also the former prosecutor general, Ghada Murad (appointed as the Syrian prosecutor general in 1998, the first woman in the whole Arab word to held such a position) thinks that probably Article 65 of the Judicial Authority Law should be amended bringing inside the council the president of the Court of Cassation and sending out of the council the minister of justice.
Still in relations to the independence of judges, another interesting point is linked to the fact that when the investigation process is carried out there could be some heavy measures of offence against the judges. In fact, during the process judges are notified and questioned about all the complaints filed against them and a report is always written. In some cases, they have been referred to the High Judicial Council, a procedure that could last for some years. All these mechanisms are activated with the deliberated intention of delaying the arrival to sentence.
ACTIONS TO REFORM THE JUDICIAL SYSTEM — Some steps have already been implemented, while others have been planned. Summing up, it could be important for Syria to:
A) Increase the standard of living of judges. — In this way capable people could be interested in the profession of judge. In this regard, positive steps such as the increase of wages, a better insurance and a reduction of taxes have already been implemented by the Syrian government.
B) Improve the quality of legal training in relations to both judges and lawyers. — Currently, there are 11,500 students at the Faculty of Law of the Damascus University, thousands of other law students enrolled in one of the other six law schools across the country and few others students (given the high fees) who follow some law courses at the new Syrian private universities — for instance the Kalamoon University, which is well focused on international law. After the law degree, students have to start a two-year practical training under the guidance of a lawyer. On completion of these two years they are entitled to undertake a written and oral exam set by the S.B.A. in order to be admitted to the bar. Apart from the issues linked to overcrowding at the law faculties, becoming lawyer is indeed a tough and long process, but it is also true that — especially at the faculty of law — the curriculum is too much oriented towards abstract learning (theoretical and analytical matters with not a lot of attention given to practical cases). It is now time to offer courses in areas such as international private law, commercial law and arbitration law (especially in light of the partial opening of Syria's economy to foreign companies) and to draw more attention toward practical cases since the university years.
C) Fight with all the available means the problem of corruption. — It could be wise to establish in every governorate a committee (comprising the attorney general, the head of appeals and the oldest judicial inspector) in order to monitor court decisions no matter whether there is a complaint or not. The U.N.D.P. is now organizing a pilot project targeted at increasing both efficiency and transparency of judicial processes through the computerization of administrative procedures. Computerization could reduce significantly corruption. Estimates speak of an 80 percent reduction of unethical conduct. The difficulty here could be in finding the economic resources to bring in all this information and communication technology (I.C.T.). This pilot project, which is implemented in Dera'a, is part of a bigger project whose name is Modernization of the Justice Sector in Syria. This project is worth $815,000 and is co-funded by the Syrian Ministry of Justice, the U.N.D.P., the Swiss Development Agency and the Hollandaise embassy in Syria. The idea is to design a software program capable of simplifying and of permitting much faster administrative court procedures. In addition to this, around 200 judges and employees belonging to the courts of Dera'a Governorate have attended computer literacy courses. The goal is to extend this pilot project also to other governorates. Also the European Union is preparing a judicial modernization project.
D) Judges Interrogation According to Specific Circumstances. — Interrogate judges only when an inspector "finds that a judge has deliberately wronged the complainer, or made a substantial professional mistake in implementing or interpreting the law. Only then should the judge be notified, interrogated and referred to the council for punishment" as the former general prosecutor, Ghada Murad pointed out last year in an interview to the magazine Syria Today.
E) Implement modern and state-of–the art laws. — As a good example, it could be considered the Commercial Arbitration Law (Law No. 4 of 2008), which well meets the requirement of the international business community. Probably, the issues behind the adoption of this law have been the necessity of boosting foreign and domestic investor confidence in the dispute resolution methods — given the faltering capacity of the regular Syrian justice system, the adoption of this law is not a surprise. This law was a long-awaited one in Syria. All this said, the process of drafting and then voting specific laws is only a partial solution to the real problems of the Syrian justice system. Undoubtedly, arbitration has positive features, like the reduced amount of time needed to get a decision. But it has also important drawbacks like the fact that it is final (unless cases of nullity) and that sometimes — especially when local companies are involved — the concerned parties do not want to implement what previously has been decided with the arbitration. If such a situation occurs, the concerned parties have no other solution than recurring to the regular justice system. In other words, the introduction of arbitration law is very welcomed, but it could not be considered as a pure and simple substitute of a proper and streamlined justice system.
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text:
Scottish Parliament UK : S3M-5854 Bill Kidd: Anti-terrorism Fatwa
* S3M-5854 Bill Kidd: Anti-terrorism Fatwa—That the Parliament notes the issuing, on 2 March 2010, of a comprehensive fatwa (religious ruling) by the renowned mainstream scholar, Shaikh Dr Tahir ul-Qadri, prohibiting terrorism and suicide bombings; believes that this comprehensive theological refutation of Islamist terrorism sets an important precedent that will allow other scholars to also condemn the ideas behind terrorism and thus end the religious justification for acts of terrorism, and hopes that this ruling will be promoted by the press and other media as evidence of the true belief system of Muslims across Scotland who are opposed to terrorism and indeed reportedly the most likely to be victims of Islamic extremism.
Supported by: Brian Adam*, Ian McKee*, Stuart McMillan*
Source : http://www.scottish.parliament.uk/business/businessBulletin/bb-10/bb-03-03f.htm


The new Berkley PowerBait Pro Grubs have been created with pro-designed colors, plus adding a little fish catching flare. The grub has a big profile on a bite-size bait, giving it a big target for attacking fish. Great tail action regardless on fast or slow you move this bait through the water!


Law & Order: SVU is one particular of the ideal crime dramas that has ever appeared on television. I identified no information accessible for the rate at which MC law graduates who re-take the exam pass, so I assume that they pass at the identical average price as all test takers. I personally met a law grad from the university of Miami law, more than $180k in student loans, lives with his parents, and tries to hustle folks by pretending to be a LSAT tutor via craigslist. Often the law places the complete apparatus of judges, police, prisons, and gendarmes at the service of the plunderers, and treats the victim — when he defends himself — as a criminal. There is no nation in the world where the law is kept a lot more within its correct domain: the protection of every person's liberty and property. Millsaps administration, this is a no brainer: Listen to your alums on JJ and get the MC Law College these days! Editor's Note: The author of this post is an incoming associate at a national law firm.
Alternatively, Chevron (as modified by later case law) stands for the idea that an administrative agency's determination of an ambiguous law is due judicial deference, supplied the interpretation is affordable and has gone via notice and comment rule-creating. If logic like that gets you the dean's job, it is no surprise that MC law students are having trouble with the bar. It is only under this law of justice that mankind will attain — gradually, no doubt, but certainly — God's style for the orderly and peaceful progress of humanity. Look at the law grad out of California with more than $170,000 of law college debt and is now an Uber driver. At Bond we have some of the best law teachers and scholars in the country delivering revolutionary law applications employing actually world class teaching facilities.
Where your supervision is coming from an in-property corporate lawyer or a government lawyer, where the person holds a practicing certificate make confident the certificate states that the holder is authorized to supervise legal practice of other folks. Since they have decided that this is the accurate state of affairs, they then demand the use of force in order to substitute their personal inclinations for these of the human race. The annals of history bear witness to the truth of it: the incessant wars, mass migrations, religious persecutions, universal slavery, dishonesty in commerce, and monopolies. Today's liberal arts majors basically can't see law college as the path of least resistance or the wonderful dumping ground for their degrees.
As lengthy as 20 years ago, I knew a Yale Law and a Harvard Law grad who had been struggling in middle age. If law schools cared about their graduates' career outcomes, this crisis would have occurred a decade ago. You and I are on the hook for these loans, but don't single out the law schools. If you can't reconcile these contradictions, then you must conclude that the law can not organize labor and market without having organizing injustice. There are quite a couple of folks from law schools outside MS who sit for the bar exam in MS.
Section 49 of the Uniform Law offers that a holder of an Australian practicing certificate can only engage in supervised legal practice till a period or periods of two years of supervised legal practice has been obtained (or 18 months where the holder completed sensible legal coaching principally below the supervision of an Australian lawyer to qualify for admission to practice).


The WRTR-501 is a wireless router with one 10/100Base-T WAN port and four 10/100Base-T LAN ports. It integrates MIMO technology, which can enhance coverage range and throughput and save the cost to purchase additional wireless equipments to deploy WLAN environment. An external switch allows you to change between Router and AP Modes.
The integrated access point complies with IEEE 802.11n (draft 2.0), providing wireless transmission speeds of up to 300Mbps. It supports WEP and WPA/WPA2 wireless encryption. The WRTR-501 uses WMM (QoS) to prioritize the traffic over the network. A WPS button allows for worry-free wireless security configuration.
The router provides VPN pass-through for IPSec, L2TP and PPTP. It can be easily configured via Web-based configuration utility, including a Quick Setup Wizard.


text:
3RCC 2021 awards presented to Bernhard Voelkl and Pauline Zamprogno
The Swiss 3RCC has awarded Bernhard Voelkl from the Vetsuisse Faculty of the University of Bern the 2021 3Rs Award in recognition of his work supporting researchers to better design animal studies to improve research quality and reduce animal use. The 2021 Young 3Rs Investigator Award went to Pauline Zamprogno from the ARTORG Center for Biomedical Engineering Research, also at the University of Bern, for her contribution to a lung-on-chip model, which aims at replacing animals testing. With their research the awardees not only help promote the 3Rs principle, they communicated their projects in an exemplary manner to encourage other researchers to adopt these novel approaches in their work. The jury consisted of independent external experts from the Charité 3Rs (Berlin, DE) and the North American 3Rs Collaborative/University of Washington (USA) as well as from the Swiss Federal Food Safety and Veterinary Office (FSVO). The jurors emphasised the importance of comprehensive communication as demonstrated by the award winners. The 3Rs Award 2021 and Young 3Rs Investigator Award recipients will receive CHF 4,000 and CHF 1,000 respectively to acknowledge their work in advancing the 3Rs. Furthermore, they will get the opportunity to present their awarded research at the Swiss 3Rs Day 2022 and in a featured video. More information.


- Birthdays. I love feeling special for a day and being allowed to make it all about you! Can't believe it's been a year already!
- Rare photos of me with all 3 children (even if one was covered in hours old face paint). We must remember to take more of those – so important!
- Mothers. Mine has just returned from 3 months in Rwanda. You can read about her travels here. So grateful to have her back. We missed her very much.
- Weekends away. Staying at Mum's this weekend in her gorgeous old home in Heathcote that still hasn't sold. If you are interested in a tree change check out this post.
- Festivals, sunshine & family. Heathcote Food & Wine Festival today with sister Lou & her kids was lots of fun!
Being grateful today & joining in with Maxabella.
Happy birthday Emma! Looks and sounds like you had a wonderful day! LOve the painted faces.
A beautiful list of gratefuls there, happy birthday to you!!
Belated birthday wishes to you! Fantastic photo. Particularly love the facepaint.


Dr. Brar graduated from the University of Southern California (USC) in 1996. She enjoys and specializes in cosmetic dentistry, pediatric, family dentistry and is also a certified Invisalign provider. Her passion for dentistry is the thriving force of her life and her patients will always be her main priority. That is the promise and commitment she makes to each of her patients.
Dr. Brar loves Orange County and enjoys all that it has to offer. She has three kids and likes to spend time with her family. She also enjoys good food, traveling, watching movies, and performing community service. Dr. Brar's personable nature helps her patients through their dental work. She has been providing dental care for over 15 years with the highest standards and uncompromising safety, dedicated to excellence.
She strongly believes in providing stress-free environment & pain-free dentistry. Every opportunity to relieve a patient of their physical and/ or emotional pain gives her the strength to work harder for their benefit. She has won the trust of her patients by providing a relaxing and positive experience.
She takes a keen interest in latest technology developments, and her continued education each year allows her the opportunity to gain an ever greater ability to take care of her patients.
Dr. Brar is a member of Orange County Dental Society, California Dental Association, American Dental Association.
Dr. Rikim Marfatia was raised in Irvine, California. He received his Bachelors of Science from UCLA in Microbiology and Molecular Genetics in 1995. He attended dental school at the University of Southern California in Los Angeles and graduated in 2000.
He has been practicing dentistry in Orange County and the surrounding areas for over 15 years. Over the years he has taken numerous continuing education courses in both general and cosmetic dentistry. He takes great pride in not only providing the highest quality of dental care but also in treating each patient as though they were a part of his own family. He is Invisalign certified.
During his free time, Dr. Marfatia enjoys spending time with his wife, son, and daughter. They enjoy traveling, cycling and going to the movies.


text:
\section{Introduction}\label{intro}
The notion of mutually unbiased bases (MUBs) became  an essential feature of  quantum
mechanics in 1960 in the works of  Schwinger \cite{Schwinger}. In his work, Schwinger  realized that no
information can be retrieved when a quantum state which is prepared in a basis
state is measured with respect to the basis mutually unbiased with the prepared one.
This observation has a striking application  in the well-known BB84 quantum key distribution (QKD) protocol \cite{Bennett}.

Estimating an unknown physical transformation of a state, which is described by a unitary operator, was studied in \cite{Acin}. It is a more challenging problem compared to state estimation because it requires optimal measurements of states both post  and prior to transformation. Such estimation has an immediate application in the alignment of reference frames using quantum spins \cite{Chiribella2004}, and in the field of quantum cryptography but with a lower security threshold \cite{Lucamarini,Chiribella2008}. To improve the security, a notion of ``mutually unbiased unitary-operator bases" (MUUBs) was put forward in \cite{Scott} for unitary operators acting on a $d$-dimensional Hilbert space as  a set of pairwise \emph{mutually unbiased} unitary operator bases. The concept MUUBs was shown to be equivalent to MUBs formed by maximally entangled states (MUMEBs) \cite{Shaari}. In the same paper, Shaari et al. \cite{Shaari} generalized the original MUUBs for unitary operators acting on \emph{subspaces} of a Hilbert space, and considered the distinguishability of unitaries selected from a set of MUUBs and  its use in a QKD setup.

In this paper, we consider another generalization of MUUBs. Motivated by the equivalence between MUUBs in $\C^{d}$ and MUBs formed by maximally entangled states (MUMEBs)  in $\C^{d}\otimes \C^{d}$, we study  mutually unbiased bases formed by special entangled states with a fixed Schmidt number $k$ (MUSEB$k$s) in a general bipartite state space $\C^{d}\otimes \C^{d'}$ $(1\leq k\leq d,d')$,
Let $M_{k}(d,d')$ denote the maximum size of MUSEB$k$s  in $\C^{d}\otimes \C^{d'}$, i.e., the maximum number of mutually unbiased bases formed by special entangled states with Schmidt number $k$. The central problem here is to determine  $M_{k}(d,d')$ in a given bipartite state space and provide bounds for this value.

There have been results in \cite{Tao,Zhang,Liu,Xu,Xu1,Cheng,Han,Scott,Shaari} in which MUMEBs were known only when $d\mid d'$, namely $d'$ is divisible by $d$. We give the first example of MUMEBs when $d\nmid d'$, and  propose a simple construction of MUSEB$k$s for general systems  via matrix spaces. Consequently, we improve all previous results on MUSEB$k$s (MUMEBs).  See Table~\ref{all}  for a summary and comparison with known results.

 The rest of this paper is organized as follows. In Sec.~\ref{Def},  we introduce some related notations and terminologies, and give a one-to-one correspondence between MUSEB$k$s in $\C^{d}\otimes \C^{d'}$ and MUSEB$k$s in $\mathcal{M}_{d\times d'}$. Sec.~\ref{sec:first} provides a construction of two MUMEBs in $\C^{2}\otimes \C^{3}$, which is the first MUMEBs when $d\nmid d'$. In Sec.~\ref{sec:appli}, we show that the two MUMEBs in $\C^{2}\otimes \C^{3}$ constructed in Sec.~\ref{sec:first}  cannot be extended to 4 MUBs in $\C^6$.  In Sec.~\ref{Mks}, we establish a construction of
 $\min \{t_{1},t_{2}\}$ MUSEB$k_{1}k_{2}$s in $\C^{pd}\otimes \C^{qd'}$ from  $t_{1}$ MUSEB$k_{1}$s in $\C^{d}\otimes \C^{d'}$ and $t_{2}$ MUSEB$k_{2}$s in $\C^{p}\otimes \C^{q}$, which yields several new lower bounds in Sec.~\ref{Mbs}. We give the main conclusion and some open problems in Sec.~\ref{conpen}.

\begin{widetext}
	\begin{table}[htbp]
		\caption{Results about MUSEB$k$s in $\C^{d}\otimes \C^{d'}$}($d,q$ have a factorization of prime power, $p_1^{a_1}\leq\cdots\leq p_s^{a_s}$,$(p_1')^{a_1'}\leq\cdots\leq (p_s')^{a_s'}$)\label{all}
		\centering
		\renewcommand\tabcolsep{20.0pt}
		\begin{tabular}{ccc}
			\hline\noalign{\smallskip}
			Conditions                                         &Bounds                             & References\\
			\noalign{\smallskip}\hline\noalign{\smallskip}
			$d\geq2$                              &$M_d(d,d)\leq d^2-1$                                 &\cite{Scott}\\
			$d=2,3,5,7,11$                                   &$M_d(d,d)=d^2-1$                           &\cite{Scott} \\
			$d=p_{1}^{a_{1}}\cdots p_{s}^{a_{s}}$, $p_1^{a_1}\geq 3$     &$M_d(d,d)\geq p_1^{a_1}-1$       &\cite{Liu}\\
			$d\geq 3$, prime power &$M_d(d,d)\geq 2(d-1)$           &\cite{Xu}\\
			$d=p_{1}^{a_{1}}\cdots p_{s}^{a_{s}}$,  odd   &$ M_d(d,d)\geq 2(p_1^{a_1}-1)$             &\cite{Cheng}\\
			$d$, odd prime power                      &$M_d(d,d)\geq (d^2-1)/2$                          &\cite{Xu1}\\
			$d=2^{t}p_{1}^{a_{1}}\cdots p_{s}^{a_{s}}$, $t=0$        &$M_d(d,d)\geq(p_1^{2a_1}-1)/2$          &This paper\\
			$d=2^{t}p_{1}^{a_{1}}\cdots p_{s}^{a_{s}}$, $t=1$       &$M_d(d,d)\geq3$                                  &This paper\\
			$d=2^{t}p_{1}^{a_{1}}\cdots p_{s}^{a_{s}}$, $t\geq 2$ &$M_d(d,d)\geq \min\{2(2^t-1),(p_{1}^{2a_{1}}-1)/2\}$ &This paper\\\hline
			$M_d(d,d')\geq 2, \ell\geq 1$                  &$M_d(d,2^ld')\geq 2$                 &\cite{Zhang}\\
			$q$ and $ d$, both prime powers    &$M_{d}(d,qd)\geq \min\{q,M_{d}(d,d)\}$                    &\cite{Xu}\\
			$q=(p_{1}')^{a_{1}'}\cdots (p_{s}')^{a_{t}'}$, $d$ odd  &$M_{d}(d,qd)\geq         \min\{(p_{1}')^{a_{1}'}+1,M_{d}(d,d)\}$                                                         &\cite{Cheng} \\
			$d, q\geq 2$                  &$M_{d}(d,qd)\geq \min\{N(q),M_{d}(d,d)\}\geq 3$                 &This paper\\
			$d,q\geq 1$	                       &$M_{2d}(2d,3qd)\geq2$.                                        &This paper\\\hline
			$k=2^l$                              &$M_2(3,4k)\geq 2$                                              &\cite{Han}\\
			$k\geq 1$                             &$M_2(3,2k)\geq 2$                                             &This paper \\
			$d, p\geq 2$, $q\geq 1$                &$M_{d}(pd,qd)\geq \min\{N(p),M_{d}(d,qd)\}\geq 3$      &This paper   \\
			\noalign{\smallskip}\hline
		\end{tabular}\label{Res}
	\end{table}
\end{widetext}

\section{Definition and preliminary}\label{Def}

Assume that $1\leq k \leq \min\{d,d'\}$. A (pure) state $\ket{\psi}\in \C^{d}\otimes \C^{d'}$  is  called
a \emph{special entangled state with Schmidt number $k$} if it has  Schmidt decomposition:
\begin{equation*}
\psi=\frac{1}{\sqrt{k}}\sum_{i=0}^{k-1}\ket{i}\ket{i'},
\end{equation*}
where $\{\ket{i}\}$ and $\{\ket{i'}\}$ are orthonormal sets of $\C^{d}$ and $\C^{d'}$, respectively \cite{Shi}.
In particular, a special entangled state with Schmidt number $k$ is a product state when $k=1$, and a maximally entangled state when $k=\min\{d,d'\}$. A basis $\mathcal{B}$ is called a special entangled basis with  Schmidt number $k$ (SEB$k$) in $\C^{d}\otimes \C^{d'}$ if it contains $dd'$ pairwise orthogonal special entangled states with Schmidt number $k$ \cite{Shi,Guo15}. In particular, $\mathcal{B}$ is a maximally entangled state basis (MEB) when $k=\min\{d,d'\}$.

Two orthonormal bases $\mathcal{B}_{1}=\{\ket{\phi_{i}}\}_{i=1}^{dd'}$ and $\mathcal{B}_{2}=\{\ket{\psi_{i}}\}_{i=1}^{dd'}$  of $\C^{d}\otimes \C^{d'}$ are said to be \emph{mutually unbiased} if
\begin{equation*}
|\braket{\phi_{i}}{\psi_{j}}|=\frac{1}{\sqrt{dd'}}, \ (1\leq i, j\leq dd').
\end{equation*}
A set of SEB$k$s $\mathcal{A}=\{\mathcal{B}_{1}, \mathcal{B}_{2}, \ldots, \mathcal{B}_{m}\}$ in $\C^{d}\otimes \C^{d'}$ is called mutually unbaised (MUSEB$k$s) if every pair  $\mathcal{B}_{i}$ and $\mathcal{B}_{j}$ are mutually unbiased.  MUSEB$k$s are  MUUBs when $k=d=d'$, and MUMEBs when $k=\min\{d,d'\}$.
 When $k=d'=1$, MUSEB$k$s are just MUBs \cite{Andreas}, for which the maximum size is denoted by $N(d)$ conventionally.  It is shown that $N(d)\leq d+1$ and $N(d)=d+1$ when $d$ is a prime power \cite{Andreas}.  An open problem is to determine $N(d)$ when $d$ is not a prime power, which has an elementary lower bound ($d=p_1^{a_1}\dots p_s^{a_s}$, $p_1^{a_1}\leq\cdots\leq p_s^{a_s}$):
\begin{equation}\label{nd}
N(d)\geq \min\{N(p_{1}^{a_{1}}),\ldots ,N(p_{s}^{a_{s}})\}=p_{1}^{a_{1}}+1.
\end{equation}
Actually, this bound can be improved in some special cases \cite{Pawe}. It is shown that a complete set of MUBs of a bipartite system contains a fixed amount of entanglement \cite{wpz11}.

Now we define similar concepts in matrix spaces. Let $\mathcal{M}_{d\times d'}$ be the Hilbert  space of all $d\times d'$ complex matrices equipped with inner product
\begin{equation*}\label{inn}
(A,B)=\text{Tr}(A^{\dag}B).
\end{equation*}
There is a one-to-one relation between $\C^{d}\otimes \C^{d'}$ and $ \mathcal{M}_{d\times d'}$ \cite{Guo15}:
\begin{equation*}
\begin{aligned}
|\psi_{i}\rangle=&\sum_{k,l}a_{k,l}^{(i)}|k\rangle|l'\rangle\in \C^{d}\otimes \C^{d'} \Longleftrightarrow A_{i}=[a_{k,l}^{(i)}]\in \mathcal{M}_{d\times d'},\\
&Sr(|\psi_{i}\rangle)=\text{rank}(A_{i}), \ \langle\psi_{i}|\psi_{j}\rangle=\text{Tr}(A_{i}^{\dag}A_{j}),
\end{aligned}
\end{equation*}
where $\{k\}$ and $\{l'\}$ are the computational bases of $\C^{d}$ and $\C^{d'}$, respectively, and $Sr(|\psi_{i}\rangle)$ denotes the Schmidt number of $|\psi_{i}\rangle$.

 Let $\{\frac{1}{\sqrt{k}},\frac{1}{\sqrt{k}},\ldots,\frac{1}{\sqrt{k}}\}_{k}$ denote $k$ values of $\frac{1}{\sqrt{k}}$.
A $d\times d'$ matrix is called a \emph{$k$-singular-value-$\frac{1}{\sqrt{k}}$ matrix} if its nonzero singular values are $\{\frac{1}{\sqrt{k}},\frac{1}{\sqrt{k}},\ldots,\frac{1}{\sqrt{k}}\}_{k}$. Then $|\psi_{i}\rangle$ is a special entangled state with Schmidt number $k$ if and only if $A_{i}$ is a $k$-singular-value-$\frac{1}{\sqrt{k}}$ matrix. Especially, when $k=d=d'$, $|\psi_{i}\rangle$ is a maximally entangled state if and only if $\sqrt{d}A_{i}$ is a unitary matrix. We give the definitions of SEB$k$s and MUSEB$k$s in $\mathcal{M}_{d\times d'}$.

	\begin{definition}
	A set of $k$-singular-value-$\frac{1}{\sqrt{k}}$ matrices $\{A_{i}\}_{i=1}^{dd'}$ of $\mathcal{M}_{d\times d'}$ is called an SEB$k$ if $\text{Tr}(A_{i}^{\dag}A_{j})=\delta_{ij}$.
    \end{definition}

	\begin{definition}\label{defmu}
	Two SEB$k$s $\mathcal{B}_{1}=\{A_{i}\}_{i=1}^{dd'}$ and $\mathcal{B}_{2}=\{B_{i}\}_{i=1}^{dd'}$  in $\mathcal{M}_{d\times d'}$ are said to be \emph{mutually unbiased} if
	\begin{equation*}
	|\text{Tr}(A_{i}^{\dag}B_{j})|=\frac{1}{\sqrt{dd'}}, \ (1\leq i, j\leq dd').
	\end{equation*}
	A set of SEB$k$s $\mathcal{A}=\{\mathcal{B}_{1}, \mathcal{B}_{2}, \ldots, \mathcal{B}_{m}\}$ in $\mathcal{M}_{d\times d'}$ is called  MUSEB$k$s if every pair $\mathcal{B}_{i}$ and $\mathcal{B}_{j}$ are mutually unbiased.
    \end{definition}

Due to the one-to-one relation, an SEB$k$ of $\mathcal{M}_{d\times d'}$ is an SEB$k$ of  $\C^{d}\otimes \C^{d'}$;
MUSEB$k$s in $\mathcal{M}_{d\times d'}$ are MUSEB$k$s in $\C^{d}\otimes \C^{d'}$. When $k=d=d'$, Definition~\ref{defmu} gives  MUMEBs in $\mathcal{M}_{d\times d}$, which corresponds to  MUMEBs in $\C^{d}\otimes \C^{d}$. In this case, multiplying each matrix by a scaler $\sqrt{d}$ gives a set of mutually unbiased unitary bases (MUUBs) in $\C^{d}$ defined in \cite{Scott}. So Definition~\ref{defmu} can be viewed as a generation of MUUBs in  \cite{Scott}, from which we know $M_{d}(d,d)\leq d^{2}-1$ and $M_{d}(d,d)=d^{2}-1$ when $d=2,3,5,7,11$.

\begin{remark}
  In \cite{Shaari}, the authors gave another definition of MUUBs:   Consider two distinct orthogonal bases, $\mA_0$ and $\mA_1$,
 composed of unitary transformations for some subspace
of the vector space $\C^{d}$. $\mA_0$ and $\mA_1$ are MUUBs
provided that \[|\text{Tr}(A_0^{(i)\dag}A_1^{(j)})|^2=c, ~\forall~A_0^{(i)}\in \mA_0, ~A_1^{(j)}\in \mA_1,\]
for $i,j = 1, . . . ,n$ and some constant $c\neq 0$.

When $\mA_0$ and $\mA_1$ are composed of unitary transformations for  the whole vector space $\C^{d}$, and $c=1$, then this definition reduces to Definition~\ref{defmu} for the  case $k=d=d'$ by  multiplying each matrix by a scaler $1/\sqrt{d}$.
\end{remark}

 \section{The first MUMEBs with $d\nmid d'$}\label{sec:first}

In previous works of \cite{Tao,Zhang,Liu,Xu,Xu1,Cheng}, all  constructions about MUMEBs are for $\C^{d}\otimes \C^{d'}$ with $d\mid d'$. Are there  MUMEBs  in $\C^{d}\otimes \C^{d'}$ when $d\nmid d'$?  We next give an example in this case.

\begin{theorem}
\label{C23}
	There are two MUMEBs in $\C^{2}\otimes \C^{3}$. Namely, $M_{2}(2,3)\geq 2$.
\end{theorem}
\begin{proof}
	Let
	$$\ket{\phi_{m,n}}=\frac{1}{\sqrt{2}}\sum_{p=0}^{1}(-1)^{np}\ket{p}\ket{(p\oplus m)'},$$ where $ n=0,1$, $m=0,1,2,$ and
	 $p\oplus m:=p+m \pmod 3$. It is easy to check that $\{\ket{\phi_{m,n}}\}$ is an MEB in $\C^{2}\otimes \C^{3}$.
	Let $A$ be a $2\times2$ unitary matrix
	$$
	A=\left(
	\begin{matrix}
	A_{00} & A_{01}\\
	A_{10} & A_{11}
	\end{matrix}\right),
	$$
	and let
	$$
	\left(
	\begin{matrix}
	\ket{a_{0}}\\
	\ket{a_{1}}
	\end{matrix}\right)=\left(
	\begin{matrix}
	A_{00} & A_{01}\\
	A_{10} & A_{11}
	\end{matrix}\right)\left(
	\begin{matrix}
	\ket{0}\\
	\ket{1}
	\end{matrix}\right).
	$$
	Denote
	$$\ket{\psi_{m,n}}=\frac{1}{\sqrt{2}}\sum_{p=0}^{1}(-1)^{np}\ket{a_{p}}\ket{(p\oplus m)'},$$ where $ n=0,1$ and $m=0,1,2.$
	Then $\{\ket{\psi_{m,n}}\}$ is also an MEB in $\C^{2}\otimes \C^{3}$.
	By definition, $\{\ket{\phi_{m,n}}\}$ and $\{\ket{\psi_{m,n}}\}$ are two MUMEBs  if and only if
	$$\left|\sum_{p_{2}=0}^{1}\sum_{p_{1}=0}^{1}(-1)^{\lambda}\braket{(p_{1}\oplus m_{1})'}{(p_{2}\oplus m_{2})'}A_{p_{2},p_{1}}\right|=\frac{2}{\sqrt{6}},$$for all $ \lambda=0,1$  and  $m_{1},m_{2}=0,1,2.$
	When $m_{1}=m_{2}$, we have  $|A_{0,0}\pm A_{1,1}|=\frac{2}{\sqrt{6}}$, which implies  $A_{0,0}\bot A_{1,1}$ and $|A_{0,0}|=|A_{1,1}|=\frac{1}{\sqrt{3}}$; when $m_{2}\equiv m_{1}+1 \pmod 3$,  we have  $|A_{0,1}|=\frac{2}{\sqrt{6}}$; when $m_{1}\equiv m_{2}+1 \pmod 3$,  we have  $|A_{1,0}|=\frac{2}{\sqrt{6}}$.
	So we can assume that
	\begin{equation}\label{aia}
	A=\frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	e^{i\theta_{1}} &\sqrt{2}e^{i\theta_{2}}\\
	\sqrt{2}e^{i\theta_{3}} &e^{i(\theta_{1}+\frac{\pi}{2})}
	\end{matrix}\right),
	\end{equation} for some $\theta_i$, $i=1,2,3$.
	Since $A$ is a unitary matrix, $\theta_{i}$ must satisfy the following condition:
	\begin{equation}\label{iai}
	\theta_{2}+\theta_{3}-2\theta_{1}=2k\pi+\frac{3\pi}{2},   \text{ for some }  k\in Z.
	\end{equation}
	Taking
	$$\theta_{1}=0,\ \theta_{2}=\frac{3\pi}{2},\ \theta_{3}=0,$$
	we have
	$$
	A=\frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	1        &-\sqrt{2}i\\
	\sqrt{2} &i
	\end{matrix}\right) \text{ and}
	$$

	$$
	\ket{a_{0}}=\frac{1}{\sqrt{3}}(\ket{0}-\sqrt{2}i\ket{1}),\ \ket{a_{1}}=\frac{1}{\sqrt{3}}(\sqrt{2}\ket{0}+i\ket{1}).
	$$
	Then $\{\ket{\phi_{m,n}}\}$ and $\{\ket{\psi_{m,n}}\}$ are as follows:
	\begin{equation}\label{16}
	\left\{
	\begin{aligned}
	&\ket{\phi_{0,0}}=\frac{1}{\sqrt{2}}(\ket{00'}+\ket{11'})\\
	&\ket{\phi_{0,1}}=\frac{1}{\sqrt{2}}(\ket{00'}-\ket{11'})\\
	&\ket{\phi_{1,0}}=\frac{1}{\sqrt{2}}(\ket{01'}+\ket{12'})\\
	&\ket{\phi_{1,1}}=\frac{1}{\sqrt{2}}(\ket{01'}-\ket{12'})\\
	&\ket{\phi_{2,0}}=\frac{1}{\sqrt{2}}(\ket{02'}+\ket{10'})\\
	&\ket{\phi_{2,1}}=\frac{1}{\sqrt{2}}(\ket{02'}-\ket{10'})
	\end{aligned}
	\right. ,
	\end{equation}
	\begin{equation}\label{17}
	\left\{
	\begin{aligned}
	&\ket{\psi_{0,0}}=\frac{1}{\sqrt{6}}(\ket{00'}+\sqrt{2}\ket{01'}-\sqrt{2}i\ket{10'}+i\ket{11'})\\
	&\ket{\psi_{0,1}}=\frac{1}{\sqrt{6}}(\ket{00'}-\sqrt{2}\ket{01'}-\sqrt{2}i\ket{10'}-i\ket{11'})\\
	&\ket{\psi_{1,0}}=\frac{1}{\sqrt{6}}(\ket{01'}+\sqrt{2}\ket{02'}-\sqrt{2}i\ket{11'}+i\ket{12'})\\
	&\ket{\psi_{1,1}}=\frac{1}{\sqrt{6}}(\ket{01'}-\sqrt{2}\ket{02'}-\sqrt{2}i\ket{11'}-i\ket{12'})\\
	&\ket{\psi_{2,0}}=\frac{1}{\sqrt{6}}(\ket{02'}+\sqrt{2}\ket{00'}-\sqrt{2}i\ket{12'}+i\ket{10'})\\
	&\ket{\psi_{2,1}}=\frac{1}{\sqrt{6}}(\ket{02'}-\sqrt{2}\ket{00'}-\sqrt{2}i\ket{12'}-i\ket{10'})
	\end{aligned}
	\right. .
	\end{equation}

	Thus the above $\{\ket{\phi_{m,n}}\}$ and $\{\ket{\psi_{m,n}}\}$ are two MUMEBs in $\C^{2}\otimes \C^{3}$.
\end{proof}

Note that 	we can also take
	$\theta_{1}=\frac{\pi}{4},\ \theta_{2}=\frac{3\pi}{4},\ \theta_{3}=\frac{5\pi}{4}$ in Eq. (\ref{aia}), then
	$$
	A=\frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	\frac{\sqrt{2}}{2}(1+i)        &-1+i\\
	-1-i&\frac{\sqrt{2}}{2}(-1+i)
	\end{matrix}\right) \text{ and}
	$$
\begin{equation}\label{othermu}
  \ket{a_{0}}  =\frac{1}{\sqrt{3}}(\frac{\sqrt{2}}{2}(1+i)\ket{0}+(-1+i)\ket{1}),
  \ket{a_{1}} =\frac{1}{\sqrt{3}}((-1-i)\ket{0}+\frac{\sqrt{2}}{2}(-1+i)\ket{1}).
\end{equation}
	The above $\{\ket{\phi_{m,n}}\}$ and $\{\ket{\psi_{m,n}}\}$ are also two MUMEBs in $\C^{2}\otimes \C^{3}$. Unfortunately, if $A_{1}$ and $A_{2}$ are two matrices that satisfy the conditions of Eq.~(\ref{aia}) and Eq.~(\ref{iai}), then $A_{1}A_{2}$ cannot satisfy these conditions. It means we cannot construct three MUMEB$s$ in $\C^{2}\otimes \C^{3}$ by this way.

 We should mention that our method of constructing two MUMEBs in $\C^{2}\otimes \C^{3}$  in Theorem~\ref{C23} is similar to that  of constructing MUMEBs in $\C^{d}\otimes \C^{kd}$ from \cite{Tao}, where  a unitary matrix $A$ of size $kd\times kd$ is applied on the latter subspace $\C^{kd}$. However,  using their method, we find that such a $3\times 3$ unitary  matrix $A$ does not exist. So we cannot construct MUMEBs in $\C^{2}\otimes \C^{3}$  by the method in \cite{Tao}.

Before closing this section, we convert $\{\ket{\phi_{m,n}}\}$ and $\{\ket{\psi_{m,n}}\}$ of Eq.~(\ref{16}) and Eq.~(\ref{17}) to  MUMEBs $\mathcal{R}_{1}$ and $\mathcal{R}_{2}$ in $\mathcal{M}_{2\times 3}$,  respectively.
\begin{align*}
\mathcal{R}_{1}=\{&\frac{1}{\sqrt{2}}\left(
\begin{matrix}
1  & 0  & 0\\
0  & 1  & 0
\end{matrix}\right), \ \frac{1}{\sqrt{2}}\left(
\begin{matrix}
1  & 0 & 0\\
0  & -1 & 0
\end{matrix}\right), \ \frac{1}{\sqrt{2}}\left(
\begin{matrix}
0  & 1     & 0\\
0  & 0     & 1
\end{matrix}\right), \\
&\frac{1}{\sqrt{2}}\left(
\begin{matrix}
0   & 1  & 0\\
0   & 0  & -1
\end{matrix}\right), \ \frac{1}{\sqrt{2}}\left(
\begin{matrix}
0     & 0   & 1\\
1     & 0   & 0
\end{matrix}
\right), \ \frac{1}{\sqrt{2}}\left(
\begin{matrix}
0       & 0      & 1\\
-1       & 0      &0
\end{matrix}
\right)\},\\
\mathcal{R}_{2}=\{&\frac{1}{\sqrt{6}}\left(
\begin{matrix}
1          & \sqrt{2} & 0\\
-\sqrt{2}i & i       & 0
\end{matrix}\right), \ \frac{1}{\sqrt{6}}\left(
\begin{matrix}
1          & -\sqrt{2} & 0\\
-\sqrt{2}i & -i       & 0
\end{matrix}
\right), \\
&\frac{1}{\sqrt{6}}\left(
\begin{matrix}
0  & 1   & \sqrt{2}\\
0  & -\sqrt{2}i   & i
\end{matrix}
\right),
\frac{1}{\sqrt{6}}\left(
\begin{matrix}
0  & 1   & -\sqrt{2}\\
0  & -\sqrt{2}i   & -i
\end{matrix}\right), \\
&\frac{1}{\sqrt{6}}\left(
\begin{matrix}
\sqrt{2}& 0   & 1\\
i     & 0   &-\sqrt{2}i
\end{matrix}
\right), \ \frac{1}{\sqrt{6}}\left(
\begin{matrix}
-\sqrt{2}& 0   & 1\\
-i     & 0   &-\sqrt{2}i
\end{matrix}
\right)\}.
\end{align*}

\section{Application}\label{sec:appli}
In this section, we propose an application of the two MUMEBs in $\C^2\otimes\C^3$ constructed in Eqs. (\ref{16}) and (\ref{17}) in Theorem \ref{thm:mumeb}. This is to tackle the special case of a long-standing open problem, namely whether four six-dimensional MUBs exist. The study of MUBs has extensive physical applications in quantum cryptography, tomography, and the construction of Wigner functions. It has been shown that there exist three six-dimensional MUBs, and widely believed that four six-dimensional MUBs may not exist in spite of great efforts from mathematical and physical community
\cite{Boykin05,bw08,bw09,jmm09,mub09,bw10,deb10,wpz11,mw12ijqi,mw12jpa135307,rle11,Sz12,Goyeneche13,mw12jpa102001,mb15,mpw16,
	cy17,chen2018mutually,liang2019h_2}.

To explain the application, we refer to the vectors in an orthonormal basis in $\C^n$ as the column vectors of a unitary matrix. In particular we refer to the computational basis as the identity matrix. Hence, the existence of four six-dimensional MUBs is equivalent to the existence of the identity matrix, and three complex Hadamard matrices (CHMs) which are MU. If they exist then we refer to the three CHMs as the so-called MUB trio \cite{cy17}. From Lemma 11 (ii) and matrix $Y_6$ of \cite{cy17}, we have found the following criterion of determining when a CHM belongs to an MUB trio.
\begin{lemma}
	\label{le:mub=trio}
	\begin{enumerate}[(i)]
	\item  A CHM belongs to an MUB trio if and only if so does its transpose.

	\item  If a CHM has a $2\times3$ real submatrix then it does not belong to any MUB trio.
		\end{enumerate}
\end{lemma}
Now we are in a position to present the application of the two MUMEBs in Eqs. (\ref{16}) and (\ref{17}).
\begin{theorem}
	\label{thm:mumeb}
	The two MUMEBs in Eqs. (\ref{16}) and (\ref{17}) cannot be extended to four MUBs.
\end{theorem}
\begin{proof}
	In the following, we express the two MUMEBs as two unitary matrices $U$ and $V$, respectively.
	$$
	U=	\left(
	\begin{matrix}
	\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 & 0 & 0 & 0 \\
	0&0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} &0 &0 \\
	0&0 &0 &0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\
	0&0 &0 &0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}}\\
	\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & 0&0 &0 &0 \\
	0&0 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & 0& 0
	\end{matrix}
	\right),
	$$
	and
	$$
	V=\left(
	\begin{matrix}
	\frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}} & 0 & 0 & \frac{\sqrt{2}}{\sqrt{6}} & -\frac{\sqrt{2}}{\sqrt{6}} \\
	\frac{\sqrt{2}}{\sqrt{6}} & -\frac{\sqrt{2}}{\sqrt{6}} &
		\frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}} & 0 & 0 \\
		0 & 0 & \frac{\sqrt{2}}{\sqrt{6}}  & -\frac{\sqrt{2}}{\sqrt{6}} & \frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}} \\
		-\frac{\sqrt{2}i}{\sqrt{6}}  & -\frac{\sqrt{2}i}{\sqrt{6}}  & 0 & 0 & \frac{i}{\sqrt{6}} & -\frac{i}{\sqrt{6}} \\
		\frac{i}{\sqrt{6}} & -\frac{i}{\sqrt{6}} & -\frac{\sqrt{2}i}{\sqrt{6}} &-\frac{\sqrt{2}i}{\sqrt{6}} & 0 & 0 \\
		0& 0& \frac{i}{\sqrt{6}} & -\frac{i}{\sqrt{6}} &
		-\frac{\sqrt{2}i}{\sqrt{6}}  & -\frac{\sqrt{2}i}{\sqrt{6}}
		\end{matrix}
		\right).
	$$

	One can verify that the lower left $2\times3$ submatrix of $U^{\dagger} VQ$ is
	$\left(
	\begin{matrix}
	-\frac{1}{\sqrt{6}} & -\frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}}	\\
     \frac{1}{\sqrt{6}} &\frac{1}{\sqrt{6}}&\frac{1}{\sqrt{6}}
     \end{matrix}
	\right)$, where the diagonal unitary $Q=\diag(-i,-i,1,1,1,1)$. Hence $U^{\dagger} V Q$ does not belong to any MUB trio in terms of Lemma \ref{le:mub=trio}. We have proven the assertion.
\end{proof}
Our results restrict the form of MUB trio, if it really exists.  Following the proof of Theorem \ref{thm:mumeb}, one can similarly show that the other pair of MUMEBs constructed at Eq.~(\ref{othermu}) cannot be extended to four MUBs too. We may conjecture that, any two MUMEBs cannot be extended to four MUBs.

\section{A Recursive Construction of MUSEBks}\label{Mks}

In this section, we give a construction of MUSEB$k_{1}k_{2}$s in $\C^{pd}\otimes \C^{qd'}$ from  MUSEB$k_{1}$s in $\C^{d}\otimes \C^{d'}$ and MUSEB$k_{2}$s in $\C^{p}\otimes \C^{q}$ for any positive integers $d$, $d'$, $p$ and $q$.

For any two sets $\mathcal{S}=\{A_{1},A_{2},\ldots,A_{n}\}$ and  $\mathcal{T}=\{B_{1},B_{2},\ldots,B_{m}\}$, define $\mathcal{S}^{\mathrm{T}}:=\{A_{1}^{\mathrm{T}},A_{2}^{\mathrm{T}},\cdots,A_{n}^{\mathrm{T}}\},$ and
$$\mathcal{S}\otimes\mathcal{T}:=\{A_{i}\otimes B_{j}\mid i=1,\ldots, n, j=1,\ldots,m\}.$$

\begin{theorem}
\label{mum}
	If there are $t_{1}$ MUSEB$k_{1}$s in $\C^{d}\otimes \C^{d'}$ and $t_{2}$ MUSEB$k_{2}$s in $\C^{p}\otimes \C^{q}$, then there are $ \min \{t_{1},t_{2}\}$ MUSEB$k_{1}k_{2}$s in $\C^{pd}\otimes \C^{qd'}$. Namely,
	\begin{equation}
	M_{k_{1}k_{2}}(pd,qd')\geq \min\{M_{k_{1}}(d,d'),M_{k_{2}}(p,q)\}.
	\end{equation}
\end{theorem}
\begin{proof}We prove it by using the language of MUSEB$k$s in $\mathcal{M}_{d\times d'}$. Let $\mathcal{S}_{1}=\{A_{1},A_{2},\ldots,A_{dd'}\}$ and $\mathcal{S}_{2}=\{B_{1},B_{2},\ldots,B_{dd'}\}$ be two  MUSEB$k_{1}$s in $\mathcal{M}_{d\times d'}$, that is, $A_{i},B_{j}$ are $k_1$-singular-value-$\frac{1}{\sqrt{k_1}}$ matrices,  $Tr(A_{i}^{\dag}A_{j})=\delta_{i,j}$, $Tr(B_{i}^{\dag}B_{j})=\delta_{i,j}$ and $|\text{Tr}(A_{i}^{\dag}B_{j})|=\frac{1}{\sqrt{dd'}}$.

	Similarly, let $\mathcal{T}_{1}=\{C_{1},C_{2},\ldots,C_{pq}\}$ and  $\mathcal{T}_{2}=\{D_{1},D_{2},\ldots,D_{pq}\}$  be two  MUSEB$k_{2}$s in $\mathcal{M}_{p\times q}$, then $C_{i},D_{j}$ each have $k_{2}$  singular values $\frac{1}{\sqrt{k_{2}}}$, $Tr(C_{i}^{\dag}C_{j})=\delta_{i,j}$, $Tr(D_{i}^{\dag}D_{j})=\delta_{i,j}$ and  $|\text{Tr}(C_{i}^{\dag}D_{j})|=\frac{1}{\sqrt{pq}}$.

	Then $\mathcal{S}_{1}\otimes \mathcal{T}_{1}$ and $\mathcal{S}_{2}\otimes \mathcal{T}_{2}$ are two sets of $dd'pq$ matrices in $\mathcal{M}_{pd\times qd'}$. We prove that they are two  MUSEB$k_{1}k_{2}$s in $\mathcal{M}_{pd\times qd'}$.

	First, we show that $\mathcal{S}_{1}\otimes \mathcal{T}_{1}$ and $\mathcal{S}_{2}\otimes \mathcal{T}_{2}$ are two SEB$k_{1}k_{2}$s. We only prove it for $\mathcal{S}_{1}\otimes \mathcal{T}_{1}$, the other one is similar.  Since each $A_{i} \otimes C_{j}\in \mathcal{S}_{1}\otimes \mathcal{T}_{1}$ has nonzero singular values $\{\frac{1}{\sqrt{k_{1}k_{2}}},\frac{1}{\sqrt{k_{1}k_{2}}},\ldots,\frac{1}{\sqrt{k_{1}k_{2}}}\}_{k_{1}k_{2}}$, it is a $k_1k_2$-singular-value-$\frac{1}{\sqrt{k_1k_2}}$ matrix. Next, $\text{Tr}[(A_{i}\otimes C_{j})^{\dag}(A_{i'}\otimes C_{j'})]=\text{Tr}(A_{i}^{\dag}A_{i'})\cdot\text{Tr}(C_{j}^{\dag}C_{j'})=\delta_{i,i'}\delta_{j,j'}$, so they are orthogonal if $(i,j)\neq (i',j')$.

	Finally, the mutually unbiased property follows from the fact that $|\text{Tr}[(A_{i}\otimes C_{j})^{\dag}(B_{i'}\otimes D_{j'})]|=|\text{Tr}(A_{i}^{\dag}B_{i'})|\cdot|\text{Tr}(C_{j}^{\dag}D_{j'})|=\frac{1}{\sqrt{pdqd'}}$.

	Let $t=\min\{t_{1},t_{2}\}$. Assume that $\mathcal{S}_{1},\mathcal{S}_{2},\ldots,\mathcal{S}_{t}$ are $t$ MUSEB$k_{1}$s in $\mathcal{M}_{d\times d'}$, and $\mathcal{T}_{1},\mathcal{T}_{2},\ldots,\mathcal{T}_{t}$ are $t$ MUSEB$k_{2}$s in $\mathcal{M}_{p\times q}$.
	It is easy to see that $\{\mathcal{S}_{1}\otimes \mathcal{T}_{1}, \mathcal{S}_{2}\otimes \mathcal{T}_{2},\ldots \mathcal{S}_{t}\otimes \mathcal{T}_{t}\}$ is a set of $t$ MUSEB$k_{1}k_{2}$s in $\mathcal{M}_{pd\times qd'}$ from the above analysis.
\end{proof}

Theorem~\ref{mum} gives a useful generic  construction of MUSEB$k$s (MUMEBs).  We illustrate its importance in several cases.

	When $k_1=d\leq d'$ and $k_2=p\leq q$, we obtain the case for MUMEBs,
	\begin{equation}\label{meb}
	M_{pd}(pd,qd')\geq \min\{M_{d}(d,d'),M_{p}(p,q)\}.
	\end{equation}

\begin{example}\label{rem1}	There are five MUMEBs in $\C^{2}\otimes \C^{4}$ and three MUMEBs in $\C^{2}\otimes \C^{6}$ \cite{Tao}, then we can construct at least three MUMEBs in $\C^{4}\otimes \C^{24}$, that is, $M_{4}(4,24)\geq \min\{M_{2}(2,4),M_{2}(2,6)\}\geq 3$.
\end{example}

Observing that Theorem~\ref{mum} does not require $d\leq d'$ and $p\leq q$, and the fact that $M_{k}(d,d')=M_{k}(d',d)$, we can get the following different example.

\begin{example}
From five MUMEBs in $\C^{2}\otimes \C^{4}$ and three MUMEBs in $\C^{2}\otimes \C^{6}$, we can also construct three MUSEB$4$s in $\C^{8}\otimes \C^{12}$, that is, $M_{4}(8,12)\geq \min\{M_{2}(4,2),M_{2}(2,6)\}\geq 3$.
\end{example}

Now we consider Theorem~\ref{mum} when some parameters of $d,d',p,q$ equal one. Observing that $\mathcal{M}_{1\times d'}$  is exactly the same  space as $\C^{d'}$,  an SEB$1$ in $\mathcal{M}_{1\times d'}$ is an orthonormal basis in $\C^{d'}$,  and MUSEB$1$s in $\mathcal{M}_{1\times d'}$ are indeed MUBs in $\C^{d'}$. Namely,  $M_{1}(1,d')=N(d')$. Hence,  Eq~(\ref{nd}) is a special case of  Theorem~\ref{mum}  when $k_1=k_2=d=p=1$. When $p=1$ (or $q=1$), we have the following corollary.

\begin{cor}
\label{seb}
	If there are $t_{1}$ MUSEBks in $\C^{d}\otimes \C^{d'}$, $t_{2}$ MUBs in $\C^{q}$, then there are at least $\min\{t_{1},t_{2}\}$ MUSEBks in $\C^{d}\otimes \C^{qd'}$. Namely,
	\begin{equation}\label{k1k}
	M_{k}(d,qd')\geq \min\{N(q),M_{k}(d,d')\}.
	\end{equation}
	If $k=d\leq d'$, then
	\begin{equation}\label{mdq}
	M_{d}(d,qd')\geq \min\{N(q),M_{d}(d,d')\},
	\end{equation}
and
	\begin{equation}\label{mpd}
	M_{d}(pd,d')\geq \min\{N(p),M_{d}(d,d')\}.
	\end{equation}
\end{cor}

\begin{remark}
	As $N(q)\geq 3$ for general $q\geq 2$ \cite{Andreas}, by  Eq.~(\ref{mdq}), \emph{if $M_{d}(d,d')\geq 2$, then $M_{d}(d,qd')\geq 2$ for any $q\geq 2$.}
	This improves the result in \cite{Zhang}, which only showed that if $M_{d}(d,d')\geq 2$, then $M_{d}(d,2^{l}d')\geq 2$.
\end{remark}

	From Eq.~(\ref{mpd}), we give a method to construct MUSEB$k$s  from MUBs and MUMEBs. In fact, we can construct MUSEB$d$s in $\C^{pd}\otimes \C^{d'}$ from MUBs in $\C^{p}$ and MUMEBs in $\C^{d}\otimes \C^{d'}$ for any $p\geq 2$.

\begin{example}\label{33}
	We can construct three MUSEB$3$s in $\C^{6}\otimes \C^{6}$ from three MUMEBs in $\C^{3}\otimes \C^{3}$ and three MUBs in $\C^{2}$. Namely, $M_{3}(6,6)\geq 3$.   For three MUMEBs in $\C^{3}\otimes \C^{3}$, we construct the following three bases in $\mathcal{M}_{3\times 3}$ with $w=e^{\frac{2\pi i}{3}}$ and $i=\sqrt{-1}$.
\begin{widetext}
	\begin{align*}
	\mathcal{S}_{1}=\{&\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2  &w+2   & w+2\\
	2w^{2}+1 &w+2      &w^{2}+2w\\
	w^{2}+2w  &w+2      &2w^{2}+1
	\end{matrix}\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2  &w^{2}+2w  &2w^{2}+1\\
	2w^{2}+1 &w^{2}+2w &w+2\\
	w^{2}+2w  &w^{2}+2w &w^{2}+2w
	\end{matrix}
	\right),
	\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2       &2w^{2}+1   &w^{2}+2w\\
	2w^{2}+1  &2w^{2}+1   &2w^{2}+1 \\
	w^{2}+2w  &2w^{2}+1   &w+2
	\end{matrix}
	\right),\\
	&\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2     & w+2        &w+2\\
	w+2     & w^{2}+2w   &2w^{2}+1\\
	w+2     & 2w^{2}+1   &w^{2}+2w
	\end{matrix}\right),
	\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2   &w^{2}+2w  &2w^{2}+1\\
	w+2   &2w^{2}+1  &w^{2}+2w\\
	w+2   &w+2        &w+2
	\end{matrix}
	\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2  &2w^{2}+1   &w^{2}+2w\\
	w+2  &w+2        &w+2 \\
	w+2  &w^{2}+2w   &2w^{2}+1
	\end{matrix}
	\right),\\
	&\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2        &w+2        &w+2\\
	w^{2}+2w   &2w^{2}+1   &w+2\\
	2w^{2}+1   &w^{2}+2w   &w+2
	\end{matrix}\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2        &w^{2}+2w    &2w^{2}+1 \\
	w^{2}+2w   &w+2         &2w^{2}+1\\
	2w^{2}+1   &2w^{2}+1   &2w^{2}+1
	\end{matrix}
	\right),
	\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	w+2       &2w^{2}+1  &w^{2}+2w\\
	w^{2}+2w  &w^{2}+2w  &w^{2}+2w\\
	2w^{2}+1  &w+2       &w^{2}+2w
	\end{matrix}
	\right)\},\\
	\mathcal{S}_{2}=\{&\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	0  & 3w^{2} & 0\\
	3w & 0      & 0\\
	0  & 0      & 3
	\end{matrix}\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	0  & 3 & 0\\
	3w & 0 & 0\\
	0  & 0 & 3w^{2}
	\end{matrix}
	\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	0  & 3w  & 0\\
	3w & 0   & 0\\
	0  & 0   & 3w
	\end{matrix}
	\right),
	\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	3w^{2}  & 0 & 0\\
	0       & 0 & 3w\\
	0       & 3 & 0
	\end{matrix}\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	3w^{2}& 0   & 0\\
	0     & 0   & 3\\
	0     &3w   & 0
	\end{matrix}
	\right),\\
	&\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	3w^{2}  & 0   & 0\\
	0       & 0   & 3w^{2}\\
	0       & 3w^{2}  & 0
	\end{matrix}
	\right),
	\frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	0       & 0    & 3w^{2}\\
	0       & 3w   & 0\\
	3       & 0 & 0
	\end{matrix}\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	0     &0    &3w\\
	0     &3w^{2}   & 0\\
	3     &0   & 0
	\end{matrix}
	\right), \ \frac{1}{3\sqrt{3}}\left(
	\begin{matrix}
	0       & 0   &3\\
	0       &3   &0\\
	3       &0  & 0
	\end{matrix}
	\right)\},\\
	\mathcal{S}_{3}=\{&\frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	1  & 0  & 0\\
	0  & 1  & 0\\
	0  & 0  & 1
	\end{matrix}\right), \ \frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	1  & 0 & 0\\
	0  & w & 0\\
	0  & 0 & w^{2}
	\end{matrix}
	\right), \ \frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	1  & 0      & 0\\
	0  & w^{2}  & 0\\
	0  & 0      & w
	\end{matrix}
	\right),
	\frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	0   & 0 & 1\\
	1   & 0 & 0\\
	0   & 1 & 0
	\end{matrix}\right), \ \frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	0     & 0   & w^{2}\\
	1     & 0   & 0\\
	0     & w   & 0
	\end{matrix}
	\right),
	\frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	0       & 0      & w\\
	1       & 0      &0\\
	0       & w^{2}  & 0
	\end{matrix}
	\right),\\
	&\frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	0       & 1   & 0\\
	0       & 0   & 1\\
	1       & 0   & 0
	\end{matrix}\right), \ \frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	0     &w    &0\\
	0     &0   & w^{2}\\
	1     &0   & 0
	\end{matrix}
	\right), \ \frac{1}{\sqrt{3}}\left(
	\begin{matrix}
	0       &w^{2}   &0\\
	0       &0       &w\\
	1       &0      & 0
	\end{matrix}
	\right)\}.
	\end{align*}
For three MUBs in $\C^{2}$, choose
	$$\mathcal{T}_{1}=\{(0,1),(1,0)\}, \ \mathcal{T}_{2}=\{\frac{1}{\sqrt{2}}(1,1),\frac{1}{\sqrt{2}}(1,-1)\}, \
	\mathcal{T}_{3}=\{\frac{1}{\sqrt{2}}(1,i),\frac{1}{\sqrt{2}}(1,-i)\}.$$
\end{widetext}
Then $\{\mathcal{S}_{1}\otimes \mathcal{T}_{1}, \mathcal{S}_{2}\otimes \mathcal{T}_{2},\mathcal{S}_{3}\otimes \mathcal{T}_{3}\}$ is a set of three MUMEBs in $\C^{3}\otimes \C^{6}$ by Eq.~(\ref{mdq}), and  $\{\mathcal{T}_{1}^{\mathrm{T}}\otimes \mathcal{S}_{1}\otimes \mathcal{T}_{1}, \mathcal{T}_{2}^{\mathrm{T}}\otimes\mathcal{S}_{2}\otimes \mathcal{T}_{2},\mathcal{T}_{3}^{\mathrm{T}}\otimes\mathcal{S}_{3}\otimes \mathcal{T}_{3}\}$ is a set of three MUSEB$3$s in
$\C^{6}\otimes \C^{6}$ by Eq.~(\ref{mpd}).
\end{example}

\section{Lower Bounds for MUMEBs}\label{Mbs}

Through out this section, we always assume that $d=2^{t}p_{1}^{a_{1}}p_{2}^{a_{2}}\cdots p_{s}^{a_{s}}$, where $p_{1},p_{2},\ldots p_{s}$ are distinct odd primes such that $3\leq p_{1}^{a_{1}}\leq p_{2}^{a_{2}}\leq \cdots \leq p_{s}^{a_{s}}$. For convenience, we define $M_{1}(1,1):=\infty$.

\begin{theorem}\label{dddlower}
	For any positive integer $d\geq 2$, we have $M_{d}(d,d)\geq 3$. In particular,
	\begin{enumerate}[(i)]
		\item $M_{d}(d,d)\geq \frac{p_{1}^{2a_{1}}-1}{2}$ when $t=0$;
		\item $M_{d}(d,d)\geq 3$ when $t=1$;
		\item $M_{d}(d,d)\geq \min\{2(2^t-1),\frac{p_{1}^{2a_{1}}-1}{2}\}$ when $t\geq 2$.
	\end{enumerate}
\end{theorem}
\begin{proof} By Eq.~(\ref{meb}), we have
\begin{equation*}
  M_{d}(d,d)\geq
  \min\{M_{2^t}(2^t,2^t),M_{p_{1}^{a_{1}}}(p_{1}^{a_{1}},p_{1}^{a_{1}}),\ldots,M_{p_{s}^{a_{s}}}(p_{s}^{a_{s}},p_{s}^{a_{s}})\}.
\end{equation*}
Since $M_{p_{i}^{a_{i}}}(p_{i}^{a_{i}},p_{i}^{a_{i}})\geq\frac{p_{i}^{2a_{i}}-1}{2}$  by \cite{Xu1},  $M_{d}(d,d)\geq\min\{M_{2^t}(2^t,2^t), \frac{p_{1}^{2a_{1}}-1}{2}\}$. Then the three cases follow from the fact that $M_1(1,1)=\infty$, $M_{2}(2,2)=3$ and $M_{2^t}(2^t,2^t)\geq 2(2^t-1)$ by \cite{Xu}.
\end{proof}

Theorem~\ref{dddlower} gives a general lower bound $M_{d}(d,d)\geq 3$ for any $d\geq 2$, which is similar to the case of MUBs $N(q)\geq 3$ for any $q\geq 2$.

By Eq.~(\ref{mdq}) and Eq.~(\ref{mpd}), we have the following corollary.
\begin{cor}
\label{ddqdl}  For all integers $d, p, q\geq 2$, we have
	\begin{equation}\label{dkd1}
	M_{d}(d,qd)\geq \min\{N(q),M_{d}(d,d)\}\geq 3,
	\end{equation}
	\begin{equation}
	M_{d}(pd,qd)\geq \min\{N(p),M_{d}(d,qd)\}\geq 3.
	\end{equation}
\end{cor}

\begin{remark}
	In \cite{Cheng}, it was shown that $M_{d}(d,qd)\geq \min\{(p_{1}')^{a_{1}'}+1,M_{d}(d,d)\}$ when $d$ is an \emph{odd} number.
	Eq. (\ref{dkd1}) extends this result for any number $d\geq 2$.
\end{remark}

We have the following corollary by applying Eq.~(\ref{meb})  with Theorem~\ref{C23} and Eq.~ (\ref{dkd1}).

\begin{cor}\label{21k}
	There are at least two MUMEBs in $\C^{2d}\otimes \C^{3qd}$ for any positive integers $q$ and $d$. Namely,
	\begin{equation}\label{002}
	M_{2d}(2d,3qd)\geq 2.
	\end{equation}
	There are at least two MUSEB$2$s in $\C^{3}\otimes \C^{2k}$ for any $k\geq 1$. Namely,
	\begin{equation}\label{112}
	M_{2}(3,2k)\geq 2.
	\end{equation}
\end{cor}

\begin{remark}
	Corollary~\ref{21k} shows that two MUMEBs exist  in $\C^{d}\otimes \C^{d'}$ for infinitely many parameters $d,d'$ satisfying $d\nmid d'$. The result of Eq.~(\ref{112}) is better than that in \cite{Han}, which only showed that $M_{2}(3,4k)\geq 2$  where $k=2^{l}$.
\end{remark}

\begin{example}
	There are two MUMEBs in $\C^{6}\otimes \C^{9}$, $\mathcal{R}_{1}\otimes \mathcal{S}_{1},\mathcal{R}_{2}\otimes \mathcal{S}_{2}$. Namely, $M_{6}(6,9)\geq 2$. Here, $\mathcal{R}_{1}, \mathcal{R}_{2}$ are from Sec.~\ref{sec:first}, and $\mathcal{S}_{1}, \mathcal{S}_{2}$ are constructed in Example~\ref{33}.
\end{example}

\section{Conclusion}
\label{conpen}

In this paper we  studied constructions of MUSEB$k$s (MUMEBs) and provided several better lower bounds on the maximum size of MUSEB$k$s. See Table~\ref{all} for a conclusion of all known results. By similar arguments as in \cite{Shaari}, one can consider the issue of distinguishability of SEB$k$s selected from a set of MUSEB$k$s and the use of MUSEB$k$s in a QKD setup. We can also consider the mutually unbiased measurements consisting of MUSEB$k$s, which plays a special role in the problem of state determination \cite{Woot}.

For the existence of  MUSEB$k$s, there are still many open questions. For example, which $d$ can achieve the upper bound $M_{d}(d,d)\leq d^{2}-1$ besides $2,3,5,7,11$? Can we improve the lower bound of $M_{d}(d,qd)\geq 3$?  Are there three MUMEBs in $\C^{2}\otimes \C^{3}$,  while there are three MUBs in $\C^{6}$. Are there MUSEB$k$s in $\C^{d}\otimes \C^{d'}$
when $k\nmid d d'$? Are there MUMEB  in $\C^{d}\otimes \C^{d'}$ for any $d\nmid d'$? The minimum unsolved case is $\C^{2}\otimes \C^{5}$.

\begin{acknowledgements}
FS and XZ were supported by NSFC under Grant No. 11771419,  the Fundamental Research Funds for the Central Universities,	and Anhui Initiative in Quantum Information Technologies under Grant No. AHY150200. LC was supported by the  NNSF of China (Grant No. 11871089), and the Fundamental Research Funds for the Central Universities (Grant Nos. KG12080401 and ZG216S1902).

\end{acknowledgements}

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


Larnaca police are investigating the burglary of a jewellery shop on a side street near the Phinikoudes promenade early on Monday morning.
The Cyprus News Agency said the burglary was reported to the police by the owner at around 4.50 am when the alarm went off.
It said that the burglars had gained access by breaking a glass pane in the front door and made off with jewellery from the shop window and from the interior, the value of which has still not been estimated.
The shop had an alarm but no CCTV. Police are investigating and are looking for CCTV footage from the area that may have recorded the perpetrators' movements.


text:
Somerset Chamber bestows awards at annual gala
By New Richmond Newsroom on Feb 7, 2019 at 1:50 p.m.
Somerset Middle School teacher Joe Hutter took home the Service Outstanding Achievement Recognition Award (S.O.A.R.). Chamber President Brett Link presents the award to Hutter. Tom Lindfors / RiverTown Multimedia 1 / 8
Sheri Soderquist accepted one of the awards on behalf of the First National Community Bank. The bank has been serving the community for 100 years. (from left) Chamber President Brett Link, Soderquist, Chamber Executive Director Beckah Whitlock. Tom Lindfors / RiverTown Multimedia 2 / 8
Somerset Chamber Executive Director Beckah Whitlock and Chamber President Brett Link presented the Director's Award which recognizes competency, leadership and entrepreneurship to Chamber Photographer Doug Peterson. Tom Lindfors / RiverTown Multimedia 3 / 8
Sandy Nemec, also known as Mrs. Somerset, stole the show as she accepted her Legacy Award to a standing ovation from Chamber President Brett Link. Tom Lindfors / RiverTown Multimedia 4 / 8
Somerset Chamber award winners (from left) included Joe Hutter - S.O.A.R. Award, Sandy Nemec - Legacy Award, Meg Tryba - Legacy Award on behalf of Somerset Public Library, Doug Peterson - Director's Award. Tom Lindfors / RiverTown Multimedia5 / 8
Superintendent Dr. Mark Bezek explained the goal of the coalition was to build a common vision for the whole community founded on the premise that, "We are stronger together than we are separately." Tom Lindfors / RiverTown Multimedia6 / 8
Meg Tryba accepted a Legacy Award on behalf of the Somerset Public Library. from Chamber President Brett Link. Tom Lindfors / RiverTown Multimedia 7 / 8
Multimedia Sales Representative Judy Monette accepted the other special award on behalf of the New Richmond News recognized for its 150 years of service to the community. (From left) Chamber Executive Director Beckah Whitlock, Monette, Chamber President Brett Link. Tom Lindfors / RiverTown Multimedia 8 / 8
There probably should have been an award just for attending the Somerset Chamber of Commerce Awards Dinner & Gala Tuesday night at the White Eagle Golf Club in Hudson. The snow which started midday intensified leading up to the start of festivities at 5 p.m. making for hazardous driving conditions. The conditions took their toll on attendance with only the most hearty present to enjoy the pork tenderloin or chicken chardonnay. Nonetheless the show did go on emceed by Executive Director Beckah Whitlock and Board President Brett Link. Following opening remarks by Link, Whitlock recapped highlights from the Chamber's activities in 2018 focusing on the Bridging Somerset project and Heavy Metal Tour. Whitlock explained the Bridging Somerset project assembled representatives from the village and town boards, school board, community foundation, and chamber to create a coordinated strategic plan for Somerset. "I knew that we needed to create a foundation that would create a sustainable, long-lasting chamber if we were going to succeed. Having a strategic plan in place allows us to know where we can support our members in the most efficient manner and in the best way possible," said Whitlock. Whitlock yielded the podium to School District Superintendent Dr. Mark Bezek to elaborate on the strategic planning process. Bezek explained the goal of the coalition was to build a common vision for the whole community founded on the premise that, "We are stronger together than we are separately." Bezek reiterated a refrain familiar to all those who have participated in the planning process: "If we don't act now and do something quick, we're going to end up like a Route 66 town where everyone just bypasses us. It's incumbent on us to really support each other and work in the same direction." Detailed information about the strategic plan can be found at: somersetchamber.org. Bezek concluded by thanking local businesses for supporting the school district and reminding community members of the two referendum questions they will be asked to decide on the April 2, 2019 ballot. He framed the first question as a $28 million bonding request to improve security, upgrade facilities and complete deferred maintenance. He framed the second question as an operational request to keep, maintain and expand programs the district offers to students. Whitlock described the Chamber's 2018 Heavy Metal Tour as a collective effort between the Chamber, school district and local manufacturing companies. The tour started by inviting school administrators and teachers to actually tour local companies to meet business owners and familiarize themselves with what companies expect of employees. Their visit was followed by tours with seventh graders and finally with tours by high school students to introduce them to local companies and make them aware of employment opportunities in their backyard. Prior to announcing award winners, Whitlock announced two new initiatives the Chamber will be undertaking in 2019, the downtown Business Coalition and the Women's Business Initiative. For more information about either initiative contact Whitlock at 715-247-3366 or by email: beckah@somersetchamber.org. The snow storm prevented Amy McCune from attending the ceremony and accepting her award for Business of the Year (Amy McCune & Associates) in person while Ambassador of the Year Award Winner, Jonathan Timm of Edward Jones was out of town. Somerset Middle School teacher Joe Hutter took home the Service Outstanding Achievement Recognition Award (S.O.A.R.) while Meg Tryba accepted a Legacy Award on behalf of the Somerset Public Library.
Sandy Nemec, also known as Mrs. Somerset, stole the show as she accepted her Legacy Award to a standing ovation.
"All the things that I did over the years, I didn't do it for the recognition, I did it because I love Somerset. I love the community, I love the people, I love the kids, and I just gave whatever I could. Thank you very much," said a tearful Nemec. Whitlock presented the Director's Award which recognizes competency, leadership and entrepreneurship to Chamber Photographer Doug Peterson. Peterson is the founder of two businesses including Airsoft Xtreme, a participant in the Hudson Police Explorers program and studying to get certified as an EMT all while still in high school and handling photography duties for the Chamber. The evening concluded with the presentation of two special awards recognizing two businesses for their longevity and sustained service to the community. Sheri Soderquist accepted one of the awards on behalf of the First National Community Bank. The bank has been serving the community for 100 years. RiverTown Multimedia sales representative Judy Monette accepted the other special award on behalf of the New Richmond News recognized for its 150 years of service to the community. Whitlock read from a statement prepared by Regional Editor Sarah Nigbor, "We tell the stories of our community. We are there for every moment good and bad. We document your history. We tell the stories of your lives as you invite us into your homes, businesses, sporting events, happiest occasions, and darkest tragedies. We are thankful for our readers' loyalty over 15 decades and proud to be your hometown newspaper."
Explore related topics:BusinessannouncementsSomerseteventsSmall business


text:
Volume 1 2008
Vol. 1: Issue 1S
Tamsulosin and Tamsulosin Plus Tolterodine for Treatment of Women with Lower Urinary Tract Symptoms
Introduction and Objectives: Women with overactive bladder and other lower urinary tract symptoms (LUTS) may not improve through monotherapy with antimuscarinic agents or alpha-blockers. To evaluate the efficacy and safety of tamsulosin and tamsulosin plus tolterodine in women with lower urinary tract symptoms, we assessed changes of international prostate symptom scores (IPSS), bladder diary variables, and safety and tolerability following 2 different treatments.
Methods: A randomized, multicenter trial at 4 urology centers involving women over 18 years or older who had a total IPSS of 8 or higher and a bladder diary documenting micturition frequency (8 times per 24 hours), urgency (> 1 episode per 24 hours), and nocturia ((2 episodes). Additional inclusion criteria were maximal urinary flow rate (Qmax, 15 ml per second) with postvoid residual urine (PVR, < 50 ml). Patients were randomly assigned to receive tamsulosin (0.2 mg, N = 40) or both tamsulosin (0.2 mg) plus tolterodine (2 mg, N = 40) for 12 weeks.
Results: IPSS decreased significantly in both groups. IPSS at baseline, at week 4, at week 8, and at week 12 was 23.33, 17.00, 16.50, 12.17 in tamsulosin group and 23.20, 18.20, 17.60, 15.00 in tamsulosin plus tolterodine group, respectively. Qmax at baseline and at week 12 was 11.90 ml/sec and 19.38 ml/sec in the tamsulosin group and 10.44 ml/sec and 20.72 ml/sec in the tamsulosin plus tolterodine group. At week 12, PVR was increased from 7.67 ml to 17.67 ml in the tamsulosin group and from 10.60 ml to 13.20 ml in the tamsulosin plus tolterodine group. Likewise, other diary variables such as urgency, frequency, nocturia, quality of life (QoL), PPBC, and OAB-q were also markedly improved in both groups by week 12. However, there were no significant differences in the changes of these variables between 2 groups.
Conclusions: Although there were no significant differences between the 2 groups, both tamsulosin monotherapy and treatment with tamsulosin plus tolterodine improved IPSS, QoL, Qmax, and PVR in women with LUTS.
KEYWORDS: LUTS, Women


In the mPOP™ we've created something that's aesthetically simple and elegant, yet loaded with intuitive design features. At just 10cm high and 30cm wide the mPOP is easily transportable, whilst the Bluetooth cable means only one mains cable is needed for operation.
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Clear LED display for status information such as paper low, Bluetooth pairing status etc.


text:
Monardella sheltonii is a species of flowering plant in the mint family known by the common name Shelton's monardella.

It is native to the mountains of northern California and southern Oregon, including the Klamath Mountains and Sierra Nevada, where it grows in chaparral, forest, and other habitat, often on serpentine soils.

Description
Monardella sheltonii is a rhizomatous perennial herb producing an erect stem lined with pairs of oppositely arranged lance-shaped leaves. The inflorescence is a head of several flowers blooming in a cup of leaflike bracts 1 to 3 centimeters wide. The five-lobed purple flowers are 1 to 2 centimeters long.

The Concow tribe called the plant bul-luk'-tō (Konkow language).

References

External links
 Calflora Database: Monardella sheltoni (Shelton's coyote mint, Shelton's monardella)
 Jepson Manual eFlora (TJM2) treatment ofMonardella sheltonii
 USDA Plants Profile
 UC Photos gallery: Monardella sheltonii

sheltonii
Flora of California
Flora of Oregon
Flora of the Klamath Mountains
Flora of the Sierra Nevada (United States)
Natural history of the California chaparral and woodlands
Natural history of the California Coast Ranges
Taxa named by John Torrey
Flora without expected TNC conservation status

redpajama_set_name: RedPajamaWikipedia


text:
restoring the hall
Wednesday 18/03/20
Loans Village Hall - Closed
The local community company (LCCL) has decided to close Loans Village Hall as of 18 March to...
Loans Community Council
The monthly Community Council Meeting is open to all residents.
7.00pm at Loans Village...
Our Village,
Our community may be small but it has a long and proud history. Look around and you'll see lots of reminders of the past. Loans has a close relationship with Troon and Dundonald, but still holds on to a distinct identity.
With no school or church, the Village Hall is the heart of our community. There's something going on there most days: bridge, dancing, keep-fit, meetings, parties and even a monthly church service.
This website aims to stimulate interest, provoke new ideas and to encourage participation. Welcome to 'Life in Loans'!
get involved plans
A message to EU citizens in Scotland
THIS IS A MESSAGE FROM THE SCOTTISH GOVERNMENT
Following decisions by the UK Government, the UK has now left the EU.
We know that EU citizens have questions about what happens next...
There will be no Remembrance Day Parade this year due to current Covid restrictions. The Community Council and Scouts intend place a wreath at the memorial without ceremony or a gathering.
Loans Village Hall
34 Main Street, Loans, KA10 7EX
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