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Keyword: Liliane Bettencourt
Defending the indefensible: the French state's justification of press censorship in the Bettencourt affair
Nov 3, 2017 By Edwy Plenel
In July 2013, Mediapart was ordered by a French court to remove all its published articles that cited secret tape recordings made by the butler of Liliane Bettencourt which provided evidence of how the late heiress to the L'Oréal cosmetics giant, suffering from dementia, was despoiled of part of her wealth by her close entourage. The tapes were at the centre of what became known as the Bettencourt affair and led to the convictions of several of those involved in the scam. Yet the censorship of the contents of the recordings remains, and Mediapart has challenged the ruling before the European Court of Human Rights (ECHR). Mediapart publishing editor Edwy Plenel analyses here the French state's submission to the ECHR in defence of the censorship, and highlights its absurd and contradictory attempt to justify the violation of the right to know.
Patrice de Maistre
Bettencourt affair
François-Marie Banier
French billionaire L'Oréal heiress Liliane Bettencourt dies at 94
Sep 21, 2017 By La rédaction de Mediapart
She sat atop the L'Oreal empire and ran a philanthropic foundation, but faced an old age clouded by dementia and legal drama.
How the Bettencourt scandal began and ended in a trial of freedom of the press
Jul 13, 2017 By Edwy Plenel
Seven years after the revelation of the so-called "Bettencourt affair", the tentacular scandal of corruption, fraud, tax evasion, conflicts of interest and political funding centred on the entourage of Liliane Bettencourt, heiress of the L'Oréale cosmectics giant, those who exposed the crimes committed against the dementia-suffering billionaire were tried by a Bordeaux appeal court last month for invasion of privacy. They are Bettencourt's butler, who secretly recorded compromising conversations of those who were swindling his employer, and Mediapart and weekly magazine Le Point which published the contents of the tapes. Mediapart publishing editor Edwy Plenel explains here the history of an absurd legal procedure led by a public prosecutor's office that has never accepted an initial court ruling that threw out the case on the grounds of the press's duty to inform and the public's right to know.
Bettencourt 'butler tapes' ruling strikes victory for press freedom and right to know
Jan 12, 2016 By Michel Deléan
In a landmark ruling on Tuesday, five journalists from Mediapart and French weekly news magazine Le Point, together with the former butler of L'Oréal heiress Liliane Bettencourt, were cleared of invasion of privacy charges relating to the publication of the contents of secretly-recorded conversations between the billionaire and her close entourage of legal and financial advisors. The publication of the contents of the tapes, which lifted the lid on a web of corruption and manipulation, contributed to "debates of public and societal interest" and "without entering into elements of private life and family conflicts", concluded the magistrates in Bordeaux following the trial of the six defendants last November. The full text of their ruling is presented in this report by Mediapart legal affairs correspondent Michel Deléan.
The mad week that was: from the 'Butler tapes' to Omar Raddad
Nov 8, 2015 By Hubert Huertas
Last week, journalists from Mediapart and weekly news magazine Le Point stood trial on 'invasion of privacy' charges for having published secretly-recorded conversations that revealed corruption and profiteering by the entourage of L'Oréal heiress Liliane Bettencourt. The prosecution has demanded they receive symbolic fines, and a verdict will be delivered in January. Meanwhile, the tax administration demanded the online press make backpayments for VAT rates that no longer apply. The week was capped by developments in a long-running murder case where the possible proof of a shameful miscarriage of justice remains buried by inertia. Hubert Huertas pulls on a common thread linking all three events.
Journalism on trial in absurd closing act of the Bettencourt saga
Nov 3, 2015 By Fabrice Arfi
Liliane Bettencourt, le 29 mars 2012 © Reuters
This week, five journalists, including Mediapart editor-in-chief Edwy Plenel and Mediapart investigative reporter Fabrice Arfi, stand trial in Bordeaux on charges relating to the violation of personal privacy. The case centres on the publication by Mediapart in 2010 of extracts of secretly recorded conversations between L'Oréal heiress Liliane Bettencourt and her entourage of advisors which revealed a catalogue of corruption and manipulation surrounding the ageing billionaire and which led to the convictions of eight people earlier this year. Here, Fabrice Arfi denounces a trial that flouts press freedom laws and threatens the fundamental 'right to know'.
After Bettencourt – why France's justice system urgently needs reform
May 29, 2015 By François Bonnet
One of the greatest political-financial scandals of France's Fifth Republic has been reduced to the level of just another human interest story of money and greed. The verdicts handed down by the courts in the Bettencourt affair on Thursday – in particular the acquittals of former budget minister Éric Woerth – have stripped the scandal of its powerful political dimension. In doing so, argues Mediapart's editor François Bonnet, France's malfunctioning justice system, dependant as it is on its political masters, has shown yet again that it is suffering from a profound malaise.
Bettencourt affair: ex-minister cleared but jail for society photographer and wealth manager
May 28, 2015 By Michel Deléan
Former government minister and the treasurer of Nicolas Sarkozy's 2007 presidential campaign, Éric Woerth, has been cleared in two separate trials resulting from the extraordinary saga of the Bettencourt affair. But photographer François-Marie Banier has been sentenced to prison for his role in abusing the frailty of France's richest woman, billionaire L'Oréal heiress Liliane Bettencourt, from whom he received up to 414 million euros. Also jailed for abusing Bettencourt's frailty was her former wealth manager Patrice de Maistre. The jail sentences are the climax of a long-running saga that has gripped France, involving secret tapes made by Bettencourt's butler, claims that a circle of advisors and hangers-on preyed off the ageing billionaires, and amid allegations of covert political funding of the right-wing UMP party. At one point former president Nicolas Sarkozy had himself been placed under formal investigation over the affair, though the case against him was later dropped. Woerth, meanwhile, was acquitted both of 'receiving' illicit cash for party funding via Maistre from Liliane Bettencourt – even though judges said there was a "strong suspicion" that some money had been handed over - and, in a separate trial, of 'influence peddling'. The judges' decision to acquit the former minister, while eight other defendants were convicted, means that in effect they have 'de-politicised' the affair. Michel Deléan reports.
Former French minister acquitted in Sarkozy-linked corruption case
May 28, 2015 By La rédaction de Mediapart
Ex-budget minister Eric Woerth found not guilty of exploiting L'Oréal heiress Liliane Bettencourt but two of her associates were jailed.
Sarkozy minister and billionaire Bettencourt's wealth advisor stand trial for influence peddling
Mar 24, 2015 By Michel Deléan
Eric et Florence Woerth
The trial this week of former minister and conservative UMP party treasurer Eric Woerth, charged alongside the former wealth investment manager of L'Oréal heiress and billionaire Liliane Bettencourt with influence peddling, provides a graphic account of backscratching and favour-mongering in the salons and private clubs of French high society and, more importantly, an unseemly intimacy between the political world and finance. Woerth is accused of arranging for Maistre to receive the Légion d'honneur – France's highest award of civil merit – in exchange for his hiring of Woerth's wife as a highly-paid advisor in Bettencourt's personal wealth investment company Clymène. If found guilty, the two men each face a maximum sentence of ten years in prison and a fine of 150,000 euros. Mediapart has gained access to the document prepared by magistrates summarising the evidence against the pair. Michel Deléan reports.
The mist starts clearing in Bettencourt abuse trial
Feb 15, 2015 By Michel Deléan
The trial of ten men accused of profiting from the dementia-suffering multi-billionaire Liliane Bettencourt enters its final stages on Monday, after three weeks of hearings. The court in Bordeaux has heard the extraordinary detail of how a disparate group of defendants, including high-society dandies, wealth managers, lawyers, solicitors and a former minister, gravitated around the fortune of the L'Oréal cosmetic company heiress, as first revealed by Mediapart in 2010. This week the court in Bordeaux will proceed with the last cross-examinations, before hearing the final arguments of the defence and prosecution. Mediapart's legal affairs correspondent Michel Deléan, present in court since the start of the case, reports on the outcome so far.
Bettencourt trial: the humiliation, fear and anger of the accused
Feb 1, 2015 By Michel Deléan
Defendant François-Marie Banier at court for the Bettencourt trial. © Reuters
After predictable procedural wrangles – plus some unforeseen delays – the long-awaited Bettencourt trial got under way in Bordeaux last week. Those on trial, who include a former minister in Nicolas Sarkozy's government, stand accused of either directly preying on the frailty of L'Oréal heiress Liliane Bettencourt or of profiting from it. Eight of the accused gave evidence during the week, all struggling to hide their dismay at being in the dock. The first was writer and photographer François-Marie Banier, a close confidant of Bettencourt from whom he received some 414 million euros, and who told the court he understands nothing about the world of money and business. "I'm not a spoilt child or a dandy," he insisted. Mediapart's legal affairs correspondent Michel Deléan was in court to witness the start of this extraordinary trial.
Ten people stand trial in France over Bettencourt affair
Jan 26, 2015 By La rédaction de Mediapart
The defendants, who face charges relating to exploitation of ageing L'Oréal heiress, include a former minister who is close to Nicolas Sarkozy.
Number of French billionaires rises to 67 despite economic crisis
Jul 11, 2014 By La rédaction de Mediapart
Survey by business magazine Challenges also shows that the richest 500 people in France are worth a massive 390 billion euros between them.
Former French spy chief on trial in phone-tapping scandal
Feb 18, 2014 By La rédaction de Mediapart
Bernard Squarcini says he was acting in national interest by tapping into the phone records of journalist Gérard Davet over Bettencourt story.
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Company BENNI TEICHTEL is located in the city of KARMIEL. The legal address of the company is 49 Ramim, KARMIEL 2186160. Other interesting information can be found on working days by phone +972-4-9980630. The scheme of travel to the company BENNI TEICHTEL can be viewed on the interactive map.


Welcome to a true Mopar-lover's paradise. There's nothing quite like it anywhere in the world with over 2,400 vehicles from all eras of the Chrysler brand, including classics, muscle cars, and high-performance new models all converging on the Carlisle Fairgrounds for a one of a kind weekend.
You need to be here for the enormous showfield that is organized by year, make and model, special indoor displays, activities for the kids, industry guests, and special prizes.
Interested in parts buying? Look no further! You'll be amazed at the size of the swap meet, the variety of vendors, the car corral, and the Manufacturers Midway. Whether you prefer the A, B or E body style – this show has it all! Registration is available online or by calling our office at (717) 243-7855.


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ins and outs Jan. 7, 2011
Emmanuelle Alt Named Editor of French Vogue
Emmanuelle Alt has been named the successor to Carine Roitfeld, who announced her departure as editor-in-chief of French Vogue right before the holidays. Alt, the magazine's fashion director, was the favored choice in the rumors leading up to the announcement and will be the second stylist in a row to helm the title. Condé Nast France president Xavier Romatet made the announcement in a press conference today, noting that in her new role, Alt will have to use … the Internet:
"I give her full confidence to embody and lead this demanding brand and to let is live in all of its different dimensions — including digitally."
Alt begins her new job on February 1, and she says she is thrilled. Roitfeld has said she's been in the office working on the March issue.
EMMANUELLE ALT, RÉDACTRICE EN CHEF DE VOGUE PARIS [Vogue.fr]
Emmanuelle Alt Named French Vogue's New Editor-In-Chief [HuffPo]

redpajama_set_name: RedPajamaCommonCrawl


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Big Brother 18 Cast – Nicole Franzel – The Blonde
By: Anna Catharine Booth on June 23, 2016
Big Brother 18 cast member Nicole Franzel, 23, hails from Ubly, Michigan and is an emergency room nurse. She is a returning houseguest from Big Brother 16, during which she ultimately placed seventh. She had been evicted from the house and was able to re-enter, but she only lasted two more weeks. She has been deemed "the blonde" only because it was strange that none were cast originally, she is really so much more than that.
Nicole Franzel of Big Brother 16 and 18. Photo: Monty Brinton/CBS
Before going through the details of her Big Brother season, we will first go over some of the information from her previous cast biography on the CBS website. Her strategy for BB16 included having a final two deal with a male to excel at physical competitions, but have other alliances on top of that. Unlike some players who think it's best to sleep through the first few weeks, she wanted to win the first Head of Household (HOH) in order to have the best chance to feel out the other players as they come to her for safety.
Nicole has several fears which include heights, surgery, sharks and ghosts. She considers getting a callback from Big Brother casting to be her biggest accomplishment, but I'd think nursing school would be on the top of that list.
Her current CBS profile has some additional information. She is a big fan of Frank Eudy, primarily because of his loyalty. Since he is also in Big Brother 18, maybe they will team up aside from the normal veterans alliance. Nicole describes herself as emotional and knows she needs to keep her guard up. She also realizes that she needs to have a good social game. Hopefully her life motto, "make the most of your situation", will pay off.
Now let's talk about Big Brother 16 and how she ultimately did. First, she could have done better if she hadn't gotten in a showmance with Hayden Voss and let her game get sidetracked. They did end up dating for almost two years out of the house. The picture below is from January 2016; however, she has now said in the Big Brother 18 house that she is single.
Nicole Franzel of Big Brother 16 and 18 and Hayden Voss of Big Brother 16 Photo: Twitter
Nicole was nicknamed Fruit Loop Dingus by fellow houseguest Zach Rance who she never really found herself in an alliance with. They were both in the top 3 for America's Favorite Houseguest, losing to Donny Thompson.
Oddly enough, she was in an alliance during Big Brother 16 called The Weirdos and she is now on Team Freakazoid which is quite the similarity. She is definitely quirky and cute and can fit these team descriptions, in a good way.
One of her main downfalls was that she was loyal to some weak players. Her loyalties were to Donny Thompson, Hayden Voss, Victoria Rafaeli, and Jocasta Odom. Given, Victoria made top three, but she floated to the final HOH. Had she been taken to final two with Cody Calafiore, she would have lost. Unfortunately, they were blindsided by Jocasta's eviction and Hayden went the next week.
Nicole was overthrown as an HOH on a Battle of the Block competition and it was primarily due to rumors that Derrick Levasseur started. He told Christine Brecht that Nicole had been planning to backdoor her even though her real target was Frankie Grande.
As mentioned before, Nicole was originally was evicted week 8, but she participated in a competition to re-enter the house where she lasted an additional two weeks. It's rare that this happened since the houseguests who are brought back are usually main targets.
In her CBS profile, she stated that difficulties on the show for her were being able to find an alliance she can trust and thinking the house has your back when they don't. These definitely ended up to be true. She was in an alliance called The Rationale with Cody Calafiore, Derrick Levasseur, and Hayden Voss. However, based on the above mentioned rumors of the puppet-master Derrick, he obviously couldn't be trusted.
According to Brecht's Twitter account, she does not plan on watching even though she's a "Super Fan" because of Nicole (note: this is just an assumption). Christine had quite the obsession with Cody and did not like when he talked to Nicole. Her official reason per the Tweet below is because it's not an all-stars season.
For those that don't remember, I said I would only watch BB18 if it was All-Stars, and it ain't. I keep my promises. pic.twitter.com/jKgBRvVhIz
— Christine Brecht (@stinestinks) June 22, 2016
Nicole could fare well as long as the newbies don't take out the veterans and she doesn't end up in a showmance that distracts her. Her profile says that she is "flirty", so hopefully she stays out of the showmance scene this year. There are a lot of attractive men in the house, so we will see.
Follow me on Twitter for more Big Brother commentary as well as tweets on a wealth of other TV shows and other general topics. http://www.twitter.com/acbooth8/
Click for Nicole Franzel's in-depth profile, photos & videos!
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AG Fox asks U.S. AG William Barr for Help with Meat Monopolies
Nick Chrestenson Updated: May 5, 2020
Contributing Authors: Peter Christian
Photo Courtesy of Sean Gallup, Getty Images
Montana Attorney General Tim Fox has joined with other state Attorneys General in asking for help from U.S. Attorney General William Barr with giant meat processing plants that are defrauding meat producers and the public.
"80% of the beef processing in American is controlled by just four very large companies and with this kind of concentration, it is always fraught with problems," Fox said. "Market concentration can really give rise to anti-competitive or anti-trust practices. The COVID-19 situation has further exacerbated that whole problem."
Other state attorneys general have asked to join with Fox in going after these price gouging meat processors.
"A little over a week ago, I got a call from Attorney General Wayne Stenehjem because he heard we were doing some work in this area," Fox said. "We got to talking and we decided it is time to get off the dime. We decided to send a request to Attorney General William Barr asking that the U.S. Department of Justice do a thorough investigation into these meat packers and their, what appears to be, anti-competitive practices."
Fox said individual states don't have the clout to force those companies to comply with the law.
"We believe that a civil investigation through the United States' anti-trust laws would really be appropriate," Fox said. "In our letter, we told the attorney general that we stand ready to help. Our office has already identified experts, put together market information, and have provided that information to the U.S. Department of Justice. They have a bigger hammer than we do."
Fox said that in the end, consumers have not been able to realize the benefits that come from a competitive market.
Filed Under: Attorney General Tim Fox, Department of Justice, meat monopolies, U.S. Attorney General William Barr
Categories: Montana News


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Actusnews Wire - Professional broadcaster of corporate and regulated information, authorised by the AMF and the CSSF.
INDIGO GROUP (ex GROUPE INFRA PARK) company press release from 15/10/2018
Infra Park becomes Indigo Group
Infra Park S.A.S adopts its new corporate name Indigo Group S.A.S. in view of enhancing its positioning as a privileged partner of municipalities.
This change of corporate name reflects the Group's new strategic plan called Goal 2025 accompanied by a new organization, which consists of two business lines:
Car parks, on-street parking and related activities (car, district and personal services), with the ambition of offering to cities a comprehensive solution,
Mobility and Digital Solutions (MDS), with the aim of providing individual mobility solutions (bicycles, scooters, motorbikes and cars) using a shared platform and offering digital solutions.
Indigo Group adopts from October 15th, 2018 a new website dedicated to its partners and investors:
www.group-indigo.com
The Group pursues the strategy announced in March 2018 consisting in taking part in market consolidation in countries where it could obtain a leading or co-leading position.
Contact analysts / investors: Press contact:
Erwan Bégos Claire Lise Beaurenault
Tel.: +33 1 49 03 15 80 Tel: +33 1 49 03 12 79
Cell: +33 6 25 71 28 76 Cell: + +33 7 50 68 30 64
ir@group-indigo.com claire-lise.beaurenault@group-indigo.com
About Indigo Group
Indigo Group, holding about 100% of Indigo Infra, OpnGo and INDIGO® weel, is a key global player in car parking and urban mobility, that manages more than 2.3 million parking spaces and related services in 14 different countries. In 2017, Indigo Group revenues and EBITDA amounted to €897.5 million and €310.0 million respectively (Global Proportionate figures).
Indigo Group is indirectly held at 49.2% by investment funds managed by Ardian, 49.2% by Crédit Agricole Assurances, and the remainder by the employees and management of the Group.
Indigo Group
A joint stock corporation with a capital of 160,044,282 euros
Headquarter: 4, place de la Pyramide – Immeuble Ile de France – Bâtiment A
92800 PUTEAUX LA DÉFENSE
800 348.146 RCS Nanterre


Abox42 has added a new HD camera to its white label smart home solution.
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The camera enables users to check out what's happening at home through a dedicated HomeOK app on their smart phone or tablet.
HomeOK is ready to deploy, can be implemented within short time and is easy to launch for any operator. It allows operators to sell new subscription services, which help to increase customer loyalty and generate new income, to secure operators future business.


Private tours in the city of Marrakech. In Tour Travel and More we offer private tours in Marrakech and all of Morocco, offering our clients the possibility to know the main monuments and places of interest of Marrakech, its Medina (walled city) the bustling Jemaa el Fna, the Bahia Palace , its Sadies tombs and many other places. Marrakech is considered one of the most important cities in Morocco and a private tour will allow you to discover all the Moroccan heritage that this city has to offer.


Today Image Trends Inc. announced the final availability of the anti-distortion plugin Fisheye-Hemi as an editing plugin for Aperture 2.1. The plugin will remap your hemispheric images taken with a fisheye lens. So if you take pictures with a fisheye lens this plugin is a must have for you.
Photographers can now easily preserve a normal view of people by not distorting their faces and bodies, as the plug-in straightens vertical lines. Fisheye-Hemi Plug-In uses almost all of the pixel data in that view with no loss of image resolution while displaying the intended composition and framing better than other un-warping programs.
If you're interested in how the plugin works there's a cool in-depth explanation from the guys at Image Trends on their website.
The Fisheye-Hemi plugin is the first plugin from Image Trends coming for Apple's Aperture. Image Trends' president and CEO Dan Sullivan says that the other plugins PearlyWhite and ShineOff are expected to be released within the next 60 days while some mysterious "other products" will follow them too. The plugin costs US$ 29.95 and if you want the plugin for Aperture and Photoshop you get a 50% discount. There's also a free trial version of the plugin available.


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Carlos Fernández Cuenca (Madrid, 1904 - Madrid, 1977) va ser un periodista, historiador del cinema i crític de cinema espanyol. Al llarg de la seva carrera va ocupar diversos càrrecs oficials, fundador i primer director de la Filmoteca Espanyola.

Biografia
Es va llicenciar en dret i en filosofia i lletres per la Universitat Central de Madrid. En la seva joventut va treballar com a redactor dels diaris La Época, La Voz i El Nacional. Des de 1931 també va col·laborar al costat de Onésimo Redondo i Javier Martínez de Bedoya en la redacció del periòdic feixista Libertad de Valladolid. En aquesta època va ser autor de diversos obres, com Historia anecdótica del Cinema (1930) i Panorama del Cine en Rusia (1930). Durant la Guerra Civil es va alinear del costat del Bàndol franquista.

Després de la instauració del Règim franquista, durant la postguerra va ocupar nombrosos càrrecs polítics, com a cap del Sindicat Nacional de l'Espectacle i del Sindicat Espanyol Universitari (SEU), o conseller nacional del Movimiento. A més, va estar al capdavant del Departament Nacional de Cinematografia i de la revista Primer Plno. Més enllà dels seus càrrecs oficials, va ser redactor de Marca, crític de Ràdio Nacional d'Espanya (RNE) i del diari Ya. Com a cap del Departament Nacional de Cinematografia va participar en la signatura de l'Acord Cinematogràfic Hispano-Italià de 1942, en plena contesa mundial, pel qual tots dos països estrenyerien la seva cooperació en matèria cinematogràfica. Durant l'etapa franquista es va convertir en el principal historiador espanyol sobre cinema, sent a més el fundador —i primer director— de la Filmoteca Nacional en 1953. També va ser director de l'Escola Oficial de Cinema i del Festival de Cinema de Sant Sebastià.

Família
És besoncle segon del poeta i filòleg Luis Alberto de Cuenca.

Premis
Medalles del Cercle d'Escriptors Cinematogràfics

{| class=wikitable border=1
|- bgcolor="#CCCCCC"
! Any || Categoria || Treball
|-
|1945||Millor labor literària||
|-
|1948||Millor labor literària||A RNE
|-
|1949||Millor llibre||Historia del cine'
|-
|1963||Premi José de la Cueva||Labor periodística
|-
|}

 Obres
 Historia anecdótica del cinema (1930)
 Cervantes y el cine (1947)
 Bibliografía cinematográfica española (1956)
 30 años de documental de arte en España: (Filmografía y estudio) (1967)
 La guerra de España y el Cine'' (1972)

Referènciess

Bibliografia

Periodistes madrilenys
Cinema a Espanya
Crítics de cinema espanyols

redpajama_set_name: RedPajamaWikipedia


Medieval silver penny probably of Henry VI, restored (1470-1471) possibly of Edward IV, first or second reign (1461-1470) or (1471-1483) datng to AD 1465 -1476. Initial mark unclear, minted at York under George Neville or when Sede Vacante. North (1991: 88, 91 or 94) 1594-5, 1599, 1623, 1645,1650 or 1651.


I enjoyed a fabulous test sail aboard Bavaria's old Cruiser 45 five years ago off Grenada, and came away impressed both with the boat's performance and its accommodations. I was intrigued, therefore, when I learned that Bavaria had updated and recreated the 45 as the new Cruiser 46 and looked forward to comparing it with its predecessor after it debuted in late 2014.
To add strength, the hull is stiffened with an inner grid. The cast iron keel is secured with 20mm stainless steel bolts and Plexus adhesive. The deck, also cored with Airex, is bedded in polyurethane sealant on a 3¼in flange and is screwed down at 8in intervals.
Functionally the Cruiser 46's deck is very similar to the 45's, and the biggest difference is aesthetic. Gone are the concave cabinhouse sides that gave the 45 a distinctive, somewhat eccentric appearance. The new configuration is subtler, much sleeker and nicely complements the high-sided, short-ended hull.
As on the old boat, the twin helm stations are right aft, poised in front of an enormous electrically-controlled fold-down transom. There are also a pair of clever flip-up foot cleats to keep you standing upright when steering, and visibility forward from either helm is good. The standard Lewmar Evo winches on our test boat were a tad undersized, but there is plenty of room on the cockpit coamings to upgrade to larger winches and install secondaries if you like. Control lines, including the lines from the split twin-mainsheet bridle, are led aft to an array of Spinlock XTS clutches on the coachroof.
Ergonomics are very good, with high coamings to support your back when seated and a strong fixed cockpit table with folding leaves to brace against when the boat is heeling. Storage is also good, with two large, albeit shallow, under-seat cockpit lockers and a huge lazarette aft. Forward, behind the handy Quick windlass, there's a separate sail locker under the deck, with just enough room to stow two large sails neatly flaked down in bags.
The biggest change here is that the nav station, which was largely vestigial and awkwardly placed on the old 45, has been removed, and instead the saloon table has been equipped with twin nav desk drawers, so that it can be used for studying charts and such. There is also now an optional centerline island with a fold-down settee seat that sits between the saloon table and the in-line galley that stretches along the port side of the boat. The fold-down seat is not terribly comfortable, but the island provides great support for a cook working in a seaway and includes a number of useful and easily accessible storage spaces.
The galley itself has copious amounts of counter space, thanks in part to a front-loading Waeco refrigerator, and all horizontal surfaces have nice deep fiddles to keep things in place. The three-burner Techimplex stove is directly opposite the island, so you can brace against it while cooking. Our test boat was also equipped with a handy top-loading Isotherm fridge/freezer.
As on the old boat, there is an enormous master stateroom forward with an en suite head and a dedicated shower in its own separate mini-cabin. The stateroom, if desired, can be split into two much smaller double staterooms by installing a removable centerline bulkhead, a feature, I suspect, that will appeal only to charter-fleet operators.
The twin aft staterooms, each with its own head, are among the best I've seen anywhere. There's lots of headroom, the berths are large and comfortable, and there's plenty of ambient light. Ventilation, as is often the case in this part of a boat, remains a challenge: a good argument for ordering the optional 29,000 BTU air conditioner.
Our test boat came equipped with a slightly fractional Seldén rig with an in-mast mainsail furling system and a Furlex 304S furler for the 110 percent jib forward. The standard sails are by Elvstrom. The shrouds are anchored outboard near the gunwales, so flying a large overlapping genoa is pretty much out of the question. To keep going in light air, you would be well advised to pony up for the optional gennaker.
Our boat had never been sailed before the day of our test, having just arrived from the factory, and we spent a lot of time getting the sails to set properly. Once dialed in, however, the boat performed well in the 15 to 17 knots of true wind we enjoyed on Chesapeake Bay that day. Our maximum boat speed was 8.5 knots clocked at a 60-degree apparent wind angle, which compared well to the 9.3 knots I made at the same angle on the old 45 off Grenada in 20 knots of breeze. That 45 was very well prepared, with a standard slab-reefed mainsail, and could comfortably point as high as 35 degrees. On this less-well-prepared boat, with a furling mainsail, the best we could manage was 40 degrees.
Helm response, experienced via the twin-wheel Jefa steering system, was excellent. The boat is extremely wide aft, but is equipped with twin rudders, so it's easy to control even when well heeled. The steering groove is not that wide, so you can't get too distracted, but careful attention to the wheel is amply rewarded.
Our boat carried the optional 75hp Volvo diesel with a saildrive leg (the standard plant is 55hp) and made excellent progress under power. Maintaining a tempo of 2,200 rpm we hit 7.8 knots in mildly lumpy conditions. At full throttle (2,800 rpm) we made 8.8 knots. The boat turned smartly at speed in just one boat length and was easy to control backing down.
The engine itself should be easy to work on. The engine compartment is very tall, with excellent access from the front and reasonable access from the sides.
Bavaria has done a good job here refining and improving what was already a very good mass-production cruising boat. In terms of space and comfort, the Cruiser 46's interior accommodations are equal to any of its competitors. In terms of performance, if set up properly, it is a superior vessel.


text:
\section{\textsc{Introduction}}

\ Throughout the paper we denote by $\mathbb{R}_{+}=(0,\infty )$, $\mathbb{R
_{-}=(-\infty ,0)$ and $\mathbb{R=(-\infty ,\infty )}$.

For $a,b\in \mathbb{R}_{+}$ with $a\neq b$ the Stolarsky means $S_{p,q}(a,b)
$ were defined by Stolarsky \cite{Stolarsky.48.1975} as

\begin{equation}
S_{p,q}(a,b)=\left\{
\begin{array}{ll}
\left( {\dfrac{q(a^{p}-b^{p})}{p(a^{q}-b^{q})}}\right) ^{\frac{1}{p-q}} &
\text{if }p\neq q,pq\neq 0, \\
\left( {\dfrac{a^{p}-b^{p}}{p(\ln a-\ln b)}}\right) ^{\frac{1}{p}} & \text
if }p\neq 0,q=0, \\
\left( {\dfrac{a^{q}-b^{q}}{q(\ln a-\ln b)}}\right) ^{\frac{1}{q}} & \text
if }p=0,q\neq 0, \\
\exp \left( \dfrac{a^{p}\ln a-b^{p}\ln b}{a^{p}-b^{p}}-\dfrac{1}{p}\right) &
\text{if }{p=q\neq 0,} \\
\sqrt{ab} & \text{if }{p=q=0.
\end{array
.\right.  \label{1.1}
\end{equation
Also, $S_{p,q}(a,a)=a$. The Stolarsky means contain many famous means, for
example, $S_{1,0}(a,b)=L(a,b)$ --the logarithmic mean, $S_{1,1}(a,b)=I(a,b)$
--the identric (exponential) mean, $S_{2,1}(a,b)=A(a,b)$ --arithmetic mean,
S_{3/2,1/2}(a,b)=He(a,b)$ --Heronian mean,
S_{2p,p}(a,b)=A^{1/p}(a^{p},b^{p})=A_{p}$ --the $p$-order power mean,
S_{p,0}(a,b)=L^{1/p}(a^{p},b^{p})=L_{p}$ --the $p$-order logarithmic mean,
S_{p,p}(a,b)=I^{1/p}(a^{p},b^{p})=I_{p}$ --the $p$-order identric
(exponential) mean, etc.

Stolarsky means are also called "extended means" \cite{Leach.85.1978}, or
"difference means" \cite{Pales.131.1988b}, and belong to the "two-parameter
family of bivariate means".

Another well-known two-parameter family of bivariate means was introduced by
C. Gini in \cite{Gini.13.1938}. That is defined as

\begin{equation}
G_{p,q}(a,b)=\left\{
\begin{array}{ll}
\left( {\dfrac{a^{p}+b^{p}}{a^{q}+b^{q}}}\right) ^{1/(p-q)} & \text{if
p\neq q, \\
\exp \left( \dfrac{a^{p}\ln a+b^{p}\ln b}{a^{p}+b^{p}}\right) & \text{if }
p=q.
\end{array
\right.  \label{1.2}
\end{equation
The Gini means also contain many famous means, for example,
G_{1,0}(a,b)=A(a,b)$ --arithmetic mean, $G_{1,1}(a,b)=Z(a,b)$ --the
power-exponential mean, $G_{p,0}(a,b)=A^{1/p}(a^{p},b^{p})=A_{p}$ --the $p
-order power mean, $G_{p,p}(a,b)=Z^{1/p}(a^{p},b^{p})=Z_{p}$ --the $p$-order
power-exponential mean, etc.

It is clear that Stolarsky and Gini means both have the form of $\left(
\frac{f(a^{p},b^{p})}{f(a^{q},b^{q})}\right) ^{1(p-q)}$, where $f$ is a
positive homogeneous function and $p\neq q$. A function in this form is
called a "two-parameter homogeneous function generated by $f$" by Yang \cit
{Yang.6(4).101.2005} and denote by $\mathcal{H}_{f}(p,q;a,b)$. Furthermore,
if it is a mean of positive numbers $a$ and $b$ for every $p,q$, then all
these means are members of "two-parameter family of bivariate means" and,
for short, "two-parameter $f$-means".

Substituting $f=S_{r,s}(x,y)$ into $\mathcal{H}_{f}(p,q;a,b)$, Yang \cit
{Yang.8(2005).3.Art.8, Yang.149286.2008} defined a class of more general
two-parameter means without trying to prove it, that is, "four-parameter
homogeneous means" denote by $\boldsymbol{F}$$(p,q;r,s;a,b)$. Witkowski
later proved that $\boldsymbol{F}$$(p,q;r,s;a,b)$ are means of positive
numbers $a$ and $b$ in \cite[6.4]{Witokwski.12(1).2009.Art.3}. For sake of
statement, we recall the four-parameter means $\boldsymbol{F}$$(p,q;r,s;a,b)$
as follows.

\begin{definition}[\protect\cite{Yang.149286.2008, Witokwski.12(1).2009}]
Let $(p,q),(r,s)\in \mathbb{R}^{2},(a,b)\in \mathbb{R}_{+}$. Then
\boldsymbol{F}$$(p,q;r,s;a,b)$ are called four-parameter means if for $a\neq
b
\begin{equation}
\text{$\boldsymbol{F}$}(p,q;r,s;a,b)=\left( {\frac{L(a^{pr},b^{pr})}
L(a^{ps},b^{ps})}\frac{L(a^{qs},b^{qs})}{L(a^{qr},b^{qr})}}\right) ^{\frac{
}{(p-q)(r-s)}}\text{ if }pqrs(p-q)(r-s)\neq 0,  \label{1.3}
\end{equation
o
\begin{equation}
\boldsymbol{F}(p,q;r,s;a,b)=\left( \frac{a^{pr}-b^{pr}}{a^{ps}-b^{ps}}{\frac
a^{qs}-b^{qs}}{a^{qr}-b^{qr}}}\right) ^{\frac{1}{(p-q)(r-s)}}\text{ if
pqrs(p-q)(r-s)\neq 0;  \label{1.4}
\end{equation
$\boldsymbol{F}(p,q;r,s;a,b)$ are defined as their corresponding limits if
pqrs(p-q)(r-s)=0$, for example:
\begin{eqnarray*}
\boldsymbol{F}(p,p;r,s;a,b) &=&\underset{q\rightarrow p}{\lim }\boldsymbol{F
(p,q;r,s;a,b)=\left( {\frac{I(a^{pr},b^{pr})}{I(a^{ps},b^{ps})}}\right) ^
\frac{1}{p(r-s)}}\text{ if }prs(r-s)\neq 0,p=q, \\
\text{$\boldsymbol{F}$}(p,0;r,s;a,b) &=&\underset{q\rightarrow 0}{\lim
\boldsymbol{F}(p,q;r,s;a,b)=\left( {\frac{L(a^{pr},b^{pr})}{L(a^{ps},b^{ps})
}\right) ^{\frac{1}{p(r-s)}}\text{ if }prs(r-s)\neq 0,q=0, \\
\text{$\boldsymbol{F}$}(0,0;r,s;a,b) &=&\underset{p\rightarrow 0}{\lim
\text{$\boldsymbol{F}$}(p,0;r,s;a,b)=G(a,b)\text{ if }rs(r-s)\neq 0,p=q=0,
\end{eqnarray*
where $L(x,y),I(x,y)$ denote logarithmic mean and identric (exponential)
mean, respectively, $G(a,b)=\sqrt{ab}$. And, $\boldsymbol{F}(p,q;r,s;a,a)=a$.
\end{definition}

As has been mentioned above, the four-parameter homogeneous means
\boldsymbol{F}$$(p,q;r,s;a,b)$ are generated by Stolarsky means or extended
means, and clearly contain many two-parameter means, for instance (see \cite
Table 1]{Yang.149286.2008}),

\noindent $\boldsymbol{F}(p,q;1,0;a,b)=S_{p,q}(a,b)$ --two-parameter
logarithmic means, that is, Stolarsky means;

\noindent $\boldsymbol{F}(p,q;2,1;a,b)=G_{p,q}(a,b)$ --two-parameter
arithmetic means, that is, Gini means;

\noindent $\boldsymbol{F}(p,q;1,1;a,b)=I_{p,q}(a,b)$ --two-parameter
identric (exponential) means, where $I_{p,q}(a,b)$ is defined a
\begin{equation}
I_{p,q}(a,b)=\left\{
\begin{array}{ll}
\left( {\dfrac{I(a^{p},b^{p})}{I(a^{q},b^{q})}}\right) ^{1/(p-q)} & \text{if
}p\neq q, \\
Y^{1/p}(a^{p},b^{p}) & \text{if }{p=q,
\end{array
\right.  \label{1.5}
\end{equation
here $Y(a,b)=Ie^{{1-G^{2}/L^{2}}},I,L,G$ are identric (exponential),
logarithmic, geometric mean, respectively;

\noindent $\boldsymbol{F}(p,q;3/2,1/2;a,b)=He_{p,q}(a,b)$ --two-parameter
Heronian means, where $He_{p,q}(a,b)$ is defined a
\begin{equation}
He_{p,q}(a,b)=\left\{
\begin{array}{ll}
\left( {\dfrac{a^{p}+(\sqrt{ab})^{p}+b^{p}}{a^{q}+(\sqrt{ab})^{q}+b^{q}}
\right) ^{1/(p-q)} & \text{if }p\neq q, \\
a^{\frac{a^{p}+(\sqrt{ab})^{p/2}}{a^{p}+(\sqrt{ab})^{p}+b^{p}}}b^{\frac{
\sqrt{ab})^{p/2}+b^{p}}{a^{p}+(\sqrt{ab})^{p}+b^{p}}} & \text{if }{p=q,
\end{array
\right.  \label{1.6}
\end{equation}

\noindent etc. Hence, we prefer to call the four-parameter homogeneous means
$\boldsymbol{F}$$(p,q;r,s;a,b)$ as "more extended means" in what follows.

Study of two-parameter means containing Stolarsky and Gini means is
interesting and has attracted the attention of a considerable number of
mathematicians.

The monotonicity of $S_{p,q}(a,b)$ with respect to parameter $p$ and $q$ was
verified by Leach and Sholander \cite{Leach.85.1978}. Qi (\cit
{Guo.29(2).1999} \cite{Qi.126(11).1998} \cite{Qi.211.1997} \cit
{Qi.22(2).1999} \cite{Qi.9(1).1999} \cite{Qi.224(2).1998}) \cit
{Qi.3(3).2000}) has also researched by using different ideas and simpler
methods. Gini \cite{Gini.13.1938} showed $G_{p,q}(a,b)$ increases with
either $p$ or $q$ (see also \cite{Farnsworth.93(8).1986}). Yang \cit
{Yang.6(4).101.2005} gave two unified discriminants for monotonicities of
the two-parameter homogeneous functions $\mathcal{H}_{f}(p,q;a,b)$ and
obtained the same monotonicity results again. Moreover, Yang \cit
{Yang.149286.2008} has proved that the more extended means $\boldsymbol{F
(p,q;r,s;a,b)$ are strictly increasing (decreasing) in either $p$ or $q$ if
r+s>(<)0$.

The comparison problem for Stolarsky means $S_{p,q}(a,b)\leq S_{r,s}(a,b)$ (
a,b\in \mathbb{R}_{+}$) was solved by Leach and Sholander \cit
{Leach.92.1983}. P\'{a}les \cite{Pales.131.1988b} presented a new proof for
this result. In \cite{Pales.32.1989} P\'{a}les solved the same comparison
problem on any subinterval $(\alpha ,\beta )$ of $\mathbb{R}_{+}$. The same
comparison problem of Gini means $G_{p,q}(a,b)$ was dealt with by P\'{a}les
\cite{Pales.131.1988a, Pales.103.1992}. Applying unified comparison theorem
given in \cite{Pales.32.1989}, a more generalized comparison problem for
more extended means $\boldsymbol{F}$$(p,q;r,s;a,b)\leq \boldsymbol{F}$
(u,v;r,s;a,b)$ ($a,b\in \mathbb{R}_{+}$) has been solved by Witkowski
recently (see \cite{Witokwski.12(1).2009}). Other references involving these
comparison problems can be found in \cite{Dodd.12.1971}, \cit
{Carlson.79.1972}, \cite{Brenner.3.1978}, \cite{Burk.92.1985}, \cit
{Pales.32.1989}, \cite{Losonczi.7(1).2002}, \cite{Neuman.15(2).2003}, \cit
{Czinder.9(4).2006}

Losonczi and P\'{a}les \cite{Losonczi.62.1996, Losonczi.126.1998}
established the Minkowski inequalities for the Stolarsky in 1996 and Gini
means in 1998, respectively. Since symmetry of the two classes of means, and
so they perfectly dealt with the bivariate convexities with respect to
(a,b) $ actually. The H\"{o}lder type inequality, that is, geometrical
convexity for Stolarsky means $S_{p,q}(a,b)$ was proved by Yang \cit
{Yang.6(4).17.2005, Yang.4(34).2010}.

For the univariate log-convexity of Stolarsky means with respect to
parameters, Qi first proved that

\textbf{Theorem Q (}\cite[Theorem 1]{Qi.130(6)(2002)}\textbf{). }\textit{If
$p,q\geq 0$\textit{, then }$S_{p,q}(a,b)$\textit{\ are log-concave in both }
p$\textit{\ and }$q$\textit{. If }$p,q\leq 0$\textit{, then }$S_{p,q}(a,b)
\textit{\ are log-convex in both }$p$\textit{\ and }$q$\textit{.}

In 2003, Neuman and S\'{a}ndor \cite{Neuman.14(1).2003} showed this property
is also true for Gini means $G_{p,q}(a,b)$. Four years later Yang \cit
{Yang.10(3).2007} presented an unified treatment for log-convexity of the
two-parameter homogeneous functions $\mathcal{H}_{f}(p,q;a,b)$ in either $p$
or $q$, and obtained the Qi's and Neuman and S\'{a}ndor's results again. In
2008, this unified treatment was applied to the more extended means
\boldsymbol{F}$$(p,q;r,s;a,b)$ and obtained the following

\textbf{Theorem Y (}\cite[Theorem 2.3]{Yang.149286.2008}\textbf{). }\textit
If }$r+s>(<)0$\textit{, then }$F(p,q;r,s;a,b)$\textit{\ are strictly
log-concave (log-convex) in either }$p$\textit{\ or }$q$\textit{\ on }
(0,\infty )$\textit{\ and log-convex (log-concave) on }$(-\infty ,0)$\textit
.}

In 2010 Yang \cite{Yang.1(1).2010} further proved that\ for fixed $q\in
\mathbb{R}$ the two-parameter symmetric homogeneous function $\mathcal{H
_{f}(p,q;a,b)$ is strictly log-convex (log-concave) in $p$ on $(\frac{|q|-q}
2},\infty )$ and log-concave (log-convex) on $(-\infty ,-\frac{|q|+q}{2})$
if ${{\mathcal{J}=(x-y)(x}\mathcal{I}{)_{x}<(>)0}}$, where{\ }${\mathcal{I
=(\ln f)_{xy}}$. This improved the Qi's and Neuman and S\'{a}ndor's results.

It might be because of complexity, up to now the research for log-convexity
of the two-parameter means in parameters has only been limited to the
univariate cases. In other words, that research for bivariate
log-convexities of the two-parameter means in parameter pair remains a blank.

The aim of this paper is to investigate the bivariate log-convexity of the
more extended means $\boldsymbol{F}$$(p,q;r,s;a,b)$ in a parameter pair
(p,q)$. Our approach is to use the well properties of homogeneous functions
and an integral representation for the two-parameter homogeneous function
\emph{\ }$\mathcal{H}_{f}(p,q;a,b)$ to obtain an unified discriminants for
the bivariate log-convexity in parameter pair $(p,q)$. From this the problem
for bivariate log-convexity of the more extended means $\boldsymbol{F}$
(p,q;r,s;a,b)$ with respect to a parameter pair is successfully solved. As
special cases, the bivariate log-convexity of the Stolarsky means, Gini
means, two-parameter identric (exponential) means and two-parameter Heronian
means with respect to parameters easily follows.

Additionally, we also investigate a special two-parameter homogeneous
function but not a mean passingly, whose bivariate log-convexity can
generate some interesting and useful inverse inequalities for Stolarsky and
Gini means.

\section{\textsc{Bivariate Log-convexity of Two-parameter Homogeneous
Functions }}

In this section, we will deal with bivariate log-convexity of two-parameter
homogeneous function generated by $f$ with respect to parameters. For this
end, we first recall definition of two-parameter homogeneous function
generated by $f$ as follows.

\begin{definition}
\label{d2.1}Let $f$: $\mathbb{R}_{+}^{2}\backslash \{(x,x),x\in \mathbb{R
_{+}\}\rightarrow \mathbb{R}_{+}$ be a homogeneous, continuous function and
has first partial derivatives. Then the function $\mathcal{H}_{f}:\mathbb{R
^{2}\times \mathbb{R}_{+}^{2}\rightarrow \mathbb{R}_{+}$ is called a
homogeneous function generated by $f$ with parameters $p$ and $q$ if
\mathcal{H}_{f}$ is defined by for $a\neq b$
\begin{eqnarray}
\mathcal{H}_{f}(p,q;a,b) &=&\left( {\frac{f(a^{p},b^{p})}{f(a^{q},b^{q})}
\right) ^{1(p-q)}\text{ if }pq(p-q)\neq 0,  \label{2.1} \\
\mathcal{H}_{f}(p,p;a,b) &=&\exp \left( \frac{a^{p}f_{x}(a^{p},b^{p})\ln
a+b^{p}f_{y}(a^{p},b^{p})\ln b}{f(a^{p},b^{p})}\right) \text{ if }p=q\neq 0,
\label{2.2}
\end{eqnarray
where $f_{x}(x,y)\ $and $f_{y}(x,y)\ $denote first-order partial derivatives
with respect to first and second component of $f(x,y)$,$\ $respectively; if
\underset{y\rightarrow x}{\lim }f(x,y)$ exits and is positive for all $x\in
\mathbb{R}_{+}$, then further defin
\begin{eqnarray}
\mathcal{H}_{f}(p,0;a,b) &=&\left( {\frac{f(a^{p},b^{p})}{f(1,1)}}\right)
^{1/p}\text{ if }p\neq 0,q=0,  \label{2.3} \\
\mathcal{H}_{f}(0,q;a,b) &=&\left( {\frac{f(a^{q},b^{q})}{f(1,1)}}\right)
^{1/q}\text{ if }p=0,q\neq 0,  \label{2.4} \\
\mathcal{H}_{f}(0,0;a,b) &=&a^{\frac{f_{x}(1,1)}{f(1,1)}}b^{\frac{f_{y}(1,1
}{f(1,1)}}\text{ if }p=q=0,  \label{2.5}
\end{eqnarray
and, $\mathcal{H}_{f}(p,q;a,a)=a$.
\end{definition}

\begin{remark}
Witkowski \cite{Witokwski.12(1).2009.Art.3} proved that if $f(x,y)$ is a
symmetric and $1$-order homogeneous function, then for all $p,q$ $\mathcal{H
_{f}(p,q;a,b)$ is a mean of positive numbers $x$ and $y$ if and only if
f(x,y)$ is increasing in both variables on $\mathbb{R}_{+}$. In fact, it is
easy to see that the condition "$f(x,y)$ is symmetry" can be removed.
\end{remark}

For simpleness, $\mathcal{H}_{f}(p,q;a,b)$ is also denoted by $\mathcal{H
_{f}(p,q)$ or $\mathcal{H}_{f}(a,b)$.

From the published relative literatures, it is complex and difficult to
investigate the monotonicity and log-convexity of $\mathcal{H}_{f}(p,q;a,b)$
for a concrete function $f$ such as $f=L,A,I$. But it becomes to be simple
and easy by using well properties of homogeneous function, which have played
an important role in \cite{Yang.6(4).101.2005}, \cite{Yang.10(3).2007}. We
will show these properties is still useful and efficient in the study of
bivariate log-convexity of $\mathcal{H}_{f}(p,q;a,b)$ with respect to
parameters.

\begin{lemma}[{\protect\cite[Lemma 3, 4]{Yang.10(3).2007}}]
\label{lem2.1}{Let $f:\mathbb{R}_{+}^{2}\backslash \{(x,x):x\in \mathbb{R
_{+}\}\rightarrow \mathbb{R}_{+}$}$\ $be a homogenous and three-time
differentiable function. Denote by $T(t):=\ln f(a^{t},b^{t})$ ($t\neq 0)$,
the
\begin{eqnarray}
{T}^{\prime }(t) &=&\frac{a^{t}f_{x}(a^{t},b^{t})\ln
a+b^{t}f_{y}(a^{t},b^{t})\ln b}{f(a^{t},b^{t})}  \notag \\
{T}^{\prime \prime }(t) &=&-xy\mathcal{I}\ln ^{2}(b/a),\text{where }\mathcal
I}=(\ln f)_{xy},  \notag \\
{{T}^{\prime \prime \prime }(t)} &{=}&{-Ct^{-3}\mathcal{J},}\text{ where }{
\mathcal{J}=(x-y)(x}\mathcal{I}{)_{x},}C=}\frac{{xy\ln }^{3}{(x/y)}}{{x-y}}
>0,}  \label{2.8}
\end{eqnarray
where $x=a^{t}$, $y=b^{t}$.
\end{lemma}

\begin{remark}
It follows from (\ref{2.8}) that
\begin{equation}
\limfunc{sgn}({{T}^{\prime \prime \prime }(t)})=\mathcal{-}\limfunc{sgn}({t}
\limfunc{sgn}(\mathcal{J)}.  \label{2.9}
\end{equation}
\end{remark}

The following property is also crucial in the proof of Theorem \ref{th2.2}.

\begin{lemma}[{\textbf{\protect\cite[Property 4]{Yang.10(3).2007}}}]
\label{lem2.2}{If }${{T}^{\prime }(t)}$ is continuous on $[q,p]$ or $[p,q]$.
Then ${\ln }\mathcal{H}_{f}(p,q)$ can be expressed in integral form as
\begin{equation}
{\ln }\mathcal{H}_{f}(p,q)=\left\{
\begin{array}{ll}
\dfrac{1}{p-q}{\int_{q}^{p}{T}^{\prime }(t)d}t\text{ } & \bigskip \text{if
p\neq q \\
{{T}^{\prime }(q)}\text{ } & \text{\bigskip if }p=
\end{array
\right. ={\int_{0}^{1}{T}^{\prime }(tp+(1-t)q)dt.}  \label{2.10}
\end{equation}
\end{lemma}

We now recall the definition\ and criterion theorem of bivariate convex
(concave) functions.

\begin{definition}
Let $\Omega \subseteq \mathbb{R}^{2}$ be a convex domain and $E\subseteq
\mathbb{R}$. Then a bivariate function $\Phi :\Omega \rightarrow E$ is said
to be convex (concave) on $\Omega $ if for any pairs
(x_{1},y_{1}),(x_{2},y_{2})\in \Omega $ and $\alpha ,\beta >0$ with $\alpha
+\beta =1$ the following inequality
\begin{equation}
\Phi (\alpha x_{1}+\beta x_{2},\alpha y_{1}+\beta y_{2})\leq (\geq )\alpha
\Phi (x_{1},y_{1})+\beta \Phi (x_{2},y_{2})  \label{2.11}
\end{equation
holds.
\end{definition}

\begin{theorem}
\label{th2.1}Let $\Omega \subseteq \mathbb{R}^{2}$ be an open domain and
E\subseteq \mathbb{R}$ and the bivariate function $\Phi :\Omega \rightarrow
E $ is two-time differentiable. Then $\Phi (x,y)$ is strictly convex
(concave) over $\Omega $ if and only if both the following inequalities
\begin{equation}
\Phi _{xx}>(<)0\text{ \ \ and\ }\Delta =\Phi _{xx}\Phi _{yy}-\Phi _{xy}^{2}>0
\label{2.12}
\end{equation
hold.
\end{theorem}

Next we are ready to give and prove criterion theorem for the bivariate
log-convexity of two-parameter homogeneous functions with respect to
parameter pair.

\begin{theorem}
\label{th2.2}Let $f:\mathbb{R}_{+}^{2}\backslash \{(x,x),x\in \mathbb{R
_{+}\}\rightarrow \mathbb{R}_{+}$ be a homogenous and three-time
differentiable function. If
\begin{equation*}
\mathcal{J}=(x-y)(x\mathcal{I})_{x}<(>)0\text{, where }\mathcal{I}=\left(
\ln f\right) _{xy},
\end{equation*
then the bivariate function $(p,q)\rightarrow \mathcal{H}_{f}(p,q)$ is
strictly log-convex (log-concave) on $\mathbb{R}_{+}^{2}$ and log-concave
(log-convex) on $\mathbb{R}_{-}^{2}$.
\end{theorem}

\begin{proof}
It suffices to verify (\ref{2.12}) holds.

(1) When $(p,q)\in \mathbb{R}_{+}^{2}$. It is obvious to (\ref{2.10}) be
true. Two times partial derivative calculations for (\ref{2.10}) lead to{\
\begin{eqnarray*}
\frac{\partial ^{2}\ln \mathcal{H}_{f}(p,q)}{\partial p^{2}} &=&
\int_{0}^{1}t^{2}{T}^{\prime \prime \prime }(tp+(1-t)q)dt,} \\
\frac{\partial ^{2}\ln \mathcal{H}_{f}(p,q)}{\partial q^{2}} &=&
\int_{0}^{1}(1-t)^{2}{T}^{\prime \prime \prime }(tp+(1-t)q)dt,} \\
\frac{\partial ^{2}\ln \mathcal{H}_{f}(p,q)}{\partial p\partial q} &=&
\int_{0}^{1}t(1-t){T}^{\prime \prime \prime }(tp+(1-t)q)dt.}
\end{eqnarray*
}

By (\ref{2.9}), for $t\in \lbrack 0,1]$ and $(p,q)\in \mathbb{R}_{+}^{2}$ we
see ${{T}^{\prime \prime \prime }(tp+(1-t)q)>(<)0}$ if $\mathcal{J}=(x-y)(
\mathcal{I})_{x}<(>)0$, it follows that $\frac{\partial ^{2}\ln \mathcal{H
_{f}(p,q)}{\partial p^{2}}={\int_{0}^{1}t^{2}{T}^{\prime \prime \prime
}(tp+(1-t)q)dt}>(<)0$.

On the other hand, using Cauch-Scharz inequality give
\begin{eqnarray*}
\Delta &=&\frac{\partial ^{2}\ln \mathcal{H}_{f}(p,q)}{\partial p^{2}}\frac
\partial ^{2}\ln \mathcal{H}_{f}(p,q)}{\partial q^{2}}-\left( \frac{\partial
^{2}\ln \mathcal{H}_{f}(p,q)}{\partial p\partial q}\right) ^{2} \\
&=&{\int_{0}^{1}t^{2}{T}^{\prime \prime \prime }(tp+(1-t)q)dt}\text{ }
\int_{0}^{1}(1-t)^{2}{T}^{\prime \prime \prime }(tp+(1-t)q)dt} \\
&&-\left( {\int_{0}^{1}t(1-t){T}^{\prime \prime \prime }(tp+(1-t)q)dt}\text{
}\right) ^{2}\geq 0.
\end{eqnarray*
With equality if and only if $t=k(1-t)$ for all $t\in \lbrack 0,1]$, where
k $ is a constant. But this is obviously impossible, which means the above
inequality is strict.

Applying Theorem \ref{th2.1}, it follows that bivariate function
(p,q)\rightarrow \ln \mathcal{H}_{f}(p,q)$ is strictly convex (concave) on
(0,\infty )\times (0,\infty )$ if $\mathcal{J}=(x-y)(x\mathcal{I})_{x}<(>)0
, which is exactly our result required.

(2) When $(p,q)\in \mathbb{R}_{-}^{2}$. By (\ref{2.9}) we see ${{T}^{\prime
\prime \prime }(tp+(1-t)q)<(>)0}$ for $t\in \lbrack 0,1]$ if $\mathcal{J
=(x-y)(x\mathcal{I})_{x}<(>)0$. It follows that\ $\frac{\partial ^{2}\ln
\mathcal{H}_{f}(p,q)}{\partial p^{2}}<(>)0$. Also, $\Delta \geq 0$ is still
valid and strict. From Theorem \ref{th2.1} it follows that bivariate
function $(p,q)\rightarrow \ln \mathcal{H}_{f}(p,q)$ is strictly concave
(convex) on $\mathbb{R}_{-}^{2}$ if $\mathcal{J}=(x-y)(x\mathcal{I
)_{x}<(>)0 $.

This completes the proof.
\end{proof}

\section{\textsc{Main Results}}

Equipped with Theorem \ref{th2.2}, we are in a position to solve the problem
for bivariate log-convexity of the more extended means $\boldsymbol{F
(p,q;r,s;a,b)$ in a parameter pair $(p,q)$.

\begin{theorem}
\label{th3.1}For fixed $(r,s)\in \mathbb{R}^{2},(a,b)\in \mathbb{R}_{+}^{2}
, the more extended means $\boldsymbol{F}(p,q;r,s;a,b)$ are strictly
bivariate log-concave (log-convex) on $[0,\infty )\times \lbrack 0,\infty )$
and strictly bivariate log-convex (log-concave) on $(-\infty ,0]\times
(-\infty ,0]$ with respect to $(p,q)$ if $r+s>(<)0$.
\end{theorem}

\begin{proof}
It follows from \cite[Proof of Theorem 2.3]{Yang.149286.2008} that $\mathcal
J}=(x-y)(x\mathcal{I})_{x}<(>)0$ if $r+s<(>)0$ for $f=S_{r,s}(x,y)$.
Applying Theorem \ref{th2.2} and noting that clearly $\boldsymbol{F
(p,q;r,s;a,b)$ are continuous at $(p,q)=(c_{1},0),(0,c_{2}),(0,0)$,
c_{1}c_{2}\neq 0$, our desired result follows.
\end{proof}

With $(r,s)=(1,0),(2,1),(1,1),(3/2,1/2)$, the following corollary are
immediate.

\begin{corollary}
\label{Cor.3.1}Stolarsky means $S_{p,q}(a,b)$, Gini means $G_{p,q}(a,b)$,
two-parameter identric (exponential) means $I_{p,q}(a,b)$ and two-parameter
Heronian means $He_{p,q}(a,b)$ are all strictly bivariate log-concave on
[0,\infty )\times \lbrack 0,\infty )$ and strictly bivariate log-convex on
(-\infty ,0]\times (-\infty ,0]$ with respect to $(p,q)$.
\end{corollary}

\section{\textsc{Applications}}

Many classical and new inequalities for bivariate means can easily follow
from Theorem \ref{th3.1}. For simpleness and convenience of statements in
the sequel, we denote $\boldsymbol{F}(p,q;r,s;a,b)$ by $\boldsymbol{F}(p,q)
, and note that for $pr-ps\neq 0$
\begin{eqnarray*}
\mathbf{F}(p,2p) &=&\left( \frac{a^{pr}+b^{pr}}{a^{ps}+b^{ps}}\right)
^{1/(pr-ps)}=G_{pr,ps}(a,b), \\
\mathbf{F}(p,0) &=&\left( {\frac{L(a^{pr},b^{pr})}{L(a^{ps},b^{ps})}}\right)
^{\frac{1}{p(r-s)}}=S_{pr,ps}(a,b), \\
\boldsymbol{F}(p,p) &=&\left( {\frac{I(a^{pr},b^{pr})}{I(a^{ps},b^{ps})}
\right) ^{\frac{1}{p(r-s)}}=I_{pr,ps}(a,b), \\
\mathbf{F}(p/2,3p/2) &=&\left( {\dfrac{a^{pr}+(\sqrt{ab})^{pr}+b^{pr}}
a^{ps}+(\sqrt{ab})^{ps}+b^{ps}}}\right) ^{1/(pr-ps)}=He_{pr,ps}(a,b);
\end{eqnarray*
for $pr-ps\neq 0$ they are defined as corresponding limits.

The following are some practical examples of Theorem \ref{th3.1}.

\begin{Application}
\textbf{Some generalizations of classical inequalities for means.}

\begin{itemize}
\item \textbf{Generalized Lin Inequality}. From bivariate log-convexity of
Stolarsky means it follows that $\sqrt{\mathbf{F}(1/3,2/3)\mathbf{F}(1,0)
\leq \mathbf{F}(2/3,1/3)$, simplifying yields $\mathbf{F}(1,0)\leq \mathbf{F
(1/3,2/3)$, that is,
\begin{equation}
S_{r,s}(a,b)\leq G_{r/3,s/3}(a,b).  \label{3.1a}
\end{equation
Putting $(r,s)=(1,0)$, $(1,1)$ yield $L(a,b)\leq A_{1/3}(a,b)$, $I(a,b)\leq
Z_{1/3}(a,b)$. In which the former is Lin inequality \cite[Theorem 1
{Ling.81.1974}, the latter was proved first by Yang \cite[(5.16)
{Yang.10(3).2007}.

\item \textbf{Generalized Jia-Cao Inequality. }Similarly, $\mathbf{F
^{2/3}(1,0)\mathbf{F}^{1/3}(1/4,3/4)\leq $ $\mathbf{F}(3/4,1/4)$ yields
\mathbf{F}(1,0)\leq \mathbf{F}(3/4,1/4)$, that is,
\begin{equation}
S_{r,s}(a,b)\leq He_{r/2,s/2}(a,b).  \label{3.1b}
\end{equation
Putting $(r,s)=(1,0)$ yields $L(a,b)\leq He_{1/2}(a,b)$, which is Jia-Cao
inequality \cite[Theorem 1.1]{Jiagao.4(4).2003}.

\item \textbf{Generalized S\'{a}ndor Inequality }\cite{Sandor.15(1997)}:
From $\sqrt{\mathbf{F}(2,0)\mathbf{F}(0,2)}\leq \mathbf{F}(1,1)\ $it follows
that $\mathbf{F}(1,1)\geq \mathbf{F}(2,0)$, that is,
\begin{equation}
I_{r,s}(a,b)\geq S_{2r,2s}(a,b).  \label{3.1c}
\end{equation
Putting $(r,s)=(1,0)$, $(1,1)$, $(2,1)$ yield $I(a,b)\geq L_{2}(a,b)$,
Y(a,b)\geq I_{2}(a,b)$, $Z(a,b)\geq A_{2}(a,b)$, here we have used the
formula $I(a^{2},b^{2})/I(a,b)=Z(a,b)$ (see \cite{Sandor.38.1993}, \cit
{Yang.6(4).101.2005}). In which the first and the third inequality due to
\'{a}ndor \cite{Sandor.40.1990}, \cite{Sandor.15(1997)}, the second one was
presented by Yang \cite[(5.12)]{Yang.10(3).2007}\textbf{.}
\end{itemize}
\end{Application}

\begin{Application}
\textbf{Some new inequalities for two-parameter means.}

\begin{itemize}
\item \textbf{New inequality 1.} The bivariate log-convexity of Stolarsky
means yields $\mathbf{F}^{3/4}(2/3,1/3)\mathbf{F}^{1/4}(1,0)\leq \mathbf{F
(3/4,1/4)$, it follows that
\begin{equation*}
\mathbf{F}(1,0)\leq \mathbf{F}^{4}(3/4,1/4)\mathbf{F}^{-3}(2/3,1/3),
\end{equation*
that is,
\begin{equation}
S_{r,s}(a,b)\leq He_{r/2,s/2}^{4}(a,b)G_{r/3,s/3}^{-3}(a,b).  \label{3.1d}
\end{equation
Putting $(r,s)=(1,0)$ yields $L(a,b)\leq He_{1/2}^{4}(a,b)A_{1/3}^{-3}(a,b)$
given in \cite[(4.5)]{Yang.1(1).2010}, which is obviously superior to Lin
and Jia-Cao\textbf{\ }inequality because $L\leq He_{1/2}\leq A_{1/3}$, .

\item \textbf{New inequality 2.} From $\mathbf{F}^{1/5}(1,1)\mathbf{F
^{4/5}(3/4,1/4)\leq \mathbf{F}(4/5,2/5)$ it follows that $\mathbf{F
(1,1)\leq \mathbf{F}^{5}(4/5,2/5)\mathbf{F}^{-4}(3/4,1/4)$, which yields,
\begin{equation}
I_{r,s}(a,b)\leq G_{2r/5,2s/5}^{5}(a,b)He_{r/2,s/2}^{-4}(a,b).  \label{3.1e}
\end{equation
Putting $(r,s)=(1,0)$, $(2,1)$ yield $I(a,b)\leq
A_{2/5}^{5}(a,b)He_{1/2}^{-4}(a,b)$, $Z(a,b)\leq
G_{4/5,2/5}^{5}(a,b)He_{1,1/2}^{-4}(a,b)$, here we have used the formula
I(a^{2},b^{2})/I(a,b)=Z(a,b)$ again.
\end{itemize}
\end{Application}

Lastly, We close this paper by giving a result for bivariate log-convexity
of the two-parameter homogeneous function of difference \cit
{Yang.6(4).101.2005}\emph{\ }and illustrating its applications.

Substituting $f(x,y)=D(x,y)=|x-y|$ ($x,y>0$ with $x\neq y$) into the
two-parameter homogeneous function $\mathcal{H}_{f}(p,q;a,b)$ leads to
\begin{equation}
\mathcal{H}_{D}(p,q;a,b):=\left\{
\begin{array}{ll}
\Big|{\dfrac{a^{p}-b^{p}}{a^{q}-b^{q}}}\Big|^{1/(p-q)} & \text{if }p\neq q{,}
\\
e^{1/p}I^{1/p}(a^{p},b^{p}) & \text{if }p=q
\end{array
\right.  \label{3.4}
\end{equation
which is called two-parameter homogeneous function of difference.

For $\mathcal{H}_{D}(p,q;a,b)$, we have shown $\mathcal{J}=(x-y)(x\mathcal{I
)_{x}<0$, where $\mathcal{I=(}\ln \mathcal{D)}_{xy}$, in \cite[pp. 510
{Yang.10(3).2007} and by Theorem \ref{th2.2} we obtain

\begin{theorem}
\label{th3.2}$\mathcal{H}_{D}(p,q;a,b)$ is strictly bivariate log-convex on
(0,\infty )\times (0,\infty )$ and bivariate log-convex on $(-\infty
,0)\times (-\infty ,0)$ with respect to $(p,q)$.
\end{theorem}

By Corollary \ref{Cor.3.1} and Theorem \ref{th3.2}, we have the following.

\begin{corollary}
\label{Cor.3.2}For any $(a,b),$ $(p_{1},q_{1}),(p_{2},q_{2})\in \mathbb{R
_{+}^{2}$ and $\alpha ,\beta >0$ with $\alpha +\beta =1$, the following
double inequalitie
\begin{equation}
1\leq \frac{S_{\alpha p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2}}(a,b)}
S_{p_{1},q_{1}}^{\alpha }(a,b)S_{p_{2},q_{2}}^{\beta }(a,b)}\leq e^{\tfrac
\alpha }{L(p_{1},q_{1})}+\tfrac{\beta }{L(p_{2},q_{2})}-\tfrac{1}{L(\alpha
p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2})}}  \label{3.5}
\end{equation
hold.
\end{corollary}

\begin{proof}
Corollary \ref{Cor.3.1} and Theorem \ref{th3.2} yield
\begin{eqnarray}
S_{p_{1},q_{1}}^{\alpha }(a,b)S_{p_{2},q_{2}}^{\beta }(a,b) &\leq &S_{\alpha
p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2}}(a,b),  \label{3.6} \\
\mathcal{H}_{D}^{\alpha }(p_{1},q_{1};a,b)\mathcal{H}_{D}^{\beta
}(p_{2},q_{2};a,b) &\geq &\mathcal{H}_{D}(\alpha p_{1}+\beta p_{2},\alpha
q_{1}+\beta q_{2};a,b),  \label{3.7}
\end{eqnarray
respectively. (\ref{3.6}) implies that the first inequality of (\ref{3.5}).
To obtain the second one, note $\mathcal{H
_{D}(p,q;a,b)=(p/q)^{1/(p-q)}S_{p,q}(a,b)=e^{1/L(p,q)}S_{p,q}(a,b)$ ($p,q>0
) and substitute into (\ref{3.7}), thus (\ref{3.7}) can be written as
\begin{equation*}
e^{\frac{\alpha }{L(p_{1},q_{1})}+\frac{\beta }{L(p_{2},q_{2})
}S_{p_{1},q_{1}}^{\alpha }(a,b)S_{p_{2},q_{2}}^{\beta }(a,b)\geq e^{\frac{1}
L(\alpha p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2})}}S_{\alpha p_{1}+\beta
p_{2},\alpha q_{1}+\beta q_{2}}(a,b),
\end{equation*
which is equivalent to the second one of (\ref{3.5}).

The proof is complete.
\end{proof}

For Gini means, we also have similar result.

\begin{corollary}
\label{Cor.3.3}For any $(a,b),$ $(p_{1},q_{1}),(p_{2},q_{2})\in \mathbb{R
_{+}^{2}$ and $\alpha ,\beta >0$ with $\alpha +\beta =1$, the following
double inequalit
\begin{equation}
1\leq \frac{G_{\alpha p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2}}(a,b)}
G_{p_{1},q_{1}}^{\alpha }(a,b)G_{p_{2},q_{2}}^{\beta }(a,b)}\leq e^{\tfrac
\alpha }{L(p_{1},q_{1})}+\tfrac{\beta }{L(p_{2},q_{2})}-\tfrac{1}{L(\alpha
p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2})}}  \label{3.8}
\end{equation
holds.
\end{corollary}

\begin{proof}
The first inequality follows from bivariate log-convexity of Gini means,
that is, Corollary \ref{Cor.3.1}. It remains to prove the second one. Form
Theorem \ref{th3.2} we hav
\begin{equation*}
\mathcal{H}_{D}^{\alpha }(2p_{1},2q_{1};a,b)\mathcal{H}_{D}^{\beta
}(2p_{2},2q_{2};a,b)\geq \mathcal{H}_{D}(2\alpha p_{1}+2\beta p_{2},2\alpha
q_{1}+2\beta q_{2};a,b).
\end{equation*
It is easy to verify that$\mathcal{\ H}_{D}(p,q;a,b)G_{p,q}(a,b)=\mathcal{H
_{D}^{2}(2p,2q;a,b)$, which is applied to the above inequality and a simple
equivalent transformation lead to
\begin{equation*}
\frac{G_{\alpha p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2}}(a,b)}
G_{p_{1},q_{1}}^{\alpha }(a,b)G_{p_{2},q_{2}}^{\beta }(a,b)}\leq \frac
\mathcal{H}_{D}^{\alpha }(p_{1},q_{1};a,b)\mathcal{H}_{D}^{\beta
}(p_{2},q_{2};a,b)}{\mathcal{H}_{D}(\alpha p_{1}+\beta p_{2},\alpha
q_{1}+\beta q_{2};a,b)}.
\end{equation*
Using relation $\mathcal{H}_{D}(p,q;a,b)=e^{1/L(p,q)}S_{p,q}(a,b)$ ($p,q>0$)
mentioned previous again and the first inequality of (\ref{3.5}), the right
side of the above inequality is lees than or equal to
\begin{equation*}
e^{\tfrac{\alpha }{L(p_{1},q_{1})}+\tfrac{\beta }{L(p_{2},q_{2})}-\tfrac{1}
L(\alpha p_{1}+\beta p_{2},\alpha q_{1}+\beta q_{2})}.}
\end{equation*}

The proof ends.
\end{proof}

From Corollary \ref{Cor.3.2}, \ref{Cor.3.3}, we can easily estimate the
upper and lower bounds of the ratio of means. Some of which are contained in
the following.

\begin{Application}
\textbf{Some classical double estimation inequalities.}

\begin{itemize}
\item \textbf{Stolarsky-Yang Inequality }\cite[(1.6)]{Stolarsky.87.1980
\textbf{,} \cite[Remark 9]{Yang.10(3).2007}.

Putting $(p_{1},q_{1})=(4/3,2/3),(p_{2},q_{2})=(2/3,4/3),(\alpha ,\beta
)=(1/2,1/2)$ in (\ref{3.5}) and simplifying yield
\begin{equation}
1\leq I/A_{2/3}\leq \sqrt{8}e^{-1}\approx 1.0405.  \label{3.9}
\end{equation}

\item \textbf{S\'{a}ndor-Yang Inequality }\cite{Sandor.38.1993}, \cite
Remark 9]{Yang.10(3).2007}\textbf{.}

Putting $(p_{1},q_{1})=(1/2,3/2),(p_{2},q_{2})=(3/2,1/2),(\alpha ,\beta
)=(1/6,5/6)$ in (\ref{3.5}) and simplifying yield
\begin{equation}
1\leq A_{2/3}/He\leq 3/\sqrt{8}\approx 1.0607.  \label{3.10}
\end{equation}
\end{itemize}
\end{Application}

\begin{Application}
\textbf{Some new double estimation inequalities}.

\begin{itemize}
\item \textbf{New double estimation inequalities 1.} Putting
(p_{1},q_{1})=(1,1),(p_{2},q_{2})=(3/2,1/2),(\alpha ,\beta )=(1/3,2/3)$ in
\ref{3.5}) and simplifying and some simple equivalent transformations yield
\begin{equation}
0.9249\approx 16\sqrt{2}e^{-1}/9\leq I/A_{2/3}^{3}He^{-2}\leq 1.
\label{3.11}
\end{equation}

\item \textbf{New double estimation inequalities 2.} Putting
(p_{1},q_{1})=(6/5,6/5),(p_{2},q_{2})=(4/5,4/5),(\alpha ,\beta )=(1/2,1/2)$
in (\ref{3.5}), (\ref{3.8}) and simplifying yield
\begin{eqnarray}
1 &\leq &I/\sqrt{I_{6/5}I_{4/5}}\leq e^{1/24}\approx 1.0425,  \label{3.12} \\
1 &\leq &Z/\sqrt{Z_{6/5}Z_{4/5}}\leq e^{1/24}\approx 1.0425.  \label{3.13}
\end{eqnarray}

\item \textbf{New double estimation inequalities 3. }Putting
(p_{1},q_{1})=(1/2,3/2),(p_{2},q_{2})=(3/2,1/2),(\alpha ,\beta )=(1/2,1/2)$
in (\ref{3.8}) and simplifying yield
\begin{equation}
1\leq Z/(2A-G)\leq 3e^{-1}\approx 1.1036.  \label{3.14}
\end{equation}
\end{itemize}
\end{Application}

Additionally, many other unknown and interesting inequalities for means can
be derived from theorems and corollaries in this section and no longer list
here.

redpajama_set_name: RedPajamaArXiv


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text:
Frictionless Access Bridging the Gap Between Physical, Logical and Digital
By Paul Aronhime, VP of Federal & Commercial Sales, IDEMIA I&S North America
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An individual's existence is often characterized through digital attributes that begin as early as birth. Names, birthdates, social security numbers, street addresses, email addresses, and medical histories work together to represent who a person is. Attributes must often be combined to assert the uniqueness of a given identity. Facial images, fingerprints, driver's license, where others are more unique, such as the SSN. They all can work together towards defining a single individual. Biometric images and templates are also digital attributes that encompass biological aspects and physical features unique to a person. Faces, fingerprints, irises, voices, scarring, birthmarks, and tattoos can be seen as unique features, attributable to one unique person. Finally, digital attributes may include authoritative credentials from trusted third parties that attest to one's identity. These credentials rely on the previous digital attributes—PII and enrolled biometrics—to be a valid source of identity verification. Digital activities contain online digital footprints, such as social site likes and shares, photos, purchase history, and mobile phone usage.
Theft of personal identity information (PII) is rampant due to exploits by bad actors taking advantage of static data verification methods such as "something you have" and "something you know." These techniques are proving insufficient as identity proofing techniques. Things that you have, such as ID cards, can be lost or stolen; and things you know such as passwords and security questions are sometimes shared or could be compromised and become purchasable on the dark web. What is needed is a method for upfront identity verification and ongoing user authentication. Interconnecting these processes can be achieved by integrating digital attributes and activities into a holistic multi-modal system to support the collection, aggregation, and proofing of multiple elements to form an identity fabric on a single platform. This fabric allows for previously verified identities to be confirmed through both active and passive methods, reducing the burden placed on users by traditional multi-factor authentication methods. It also enables attestation to only what is required for a specific transaction without exposing additional, non-essential information.
The concept of a multi-modal identity fabric for initial and continual identity verification is illustrated in the following hypothetical scenario: John is a contractor working in the defense industry and will be attending a meeting at a nearby military installation. His meeting sponsor within the Department of Defense (DoD) initiates the visit and requests John to submit the required biographic and credential information to conduct a background check and register with force protection for the installation. Previously, John would have submitted this information via email to his point of contact (POC), who has the information vetted. When John arrived at the installation, he would have gone to the Visitor Control Center (VCC), presented his identification, had his photo taken, and received a pass to enter the facility. However, using a digital identity platform streamlines the enrollment, vetting, and access process using a cutting-edge identity fusion system that combines best-in-class biometric, credential, and biographic information to enable near-instantaneous vetting and rules-based facility access. Using smart technologies, the facility can address potential threats while enabling secure but flexible access, with continuous vetting as John travels throughout the facility.
This concept can be achieved through simple actions of the visitor. First, John (visitor) leverages his smartphone to take photos of his credential, face / selfie photo, and fingerprints. His credential is validated visually, as well as through automated checks against the issuing authority. His facial biometrics are matched to his credential, including full liveness detection. Once John has been verified, his biometrics and biographic data are vetted against established systems of records (SOR) in government and third-party databases. The results are then verified back into his consolidated identity. At this stage, John is ready to access the installation, and can do so without having to visit the VCC since the information was collected remotely. John uses his biometrics, either his face or fingerprints, to authenticate himself at the access control point. The access points leverage biometrically enabled fast lanes to reduce congestion and improve traffic flow by performing vehicular based real-time facial recognition on the move. The key outcomes of the platform include:
Reduced bottlenecks at access points using "fast lanes" with contactless biometric fingerprint and facial recognition technology.
Increased real-time situational awareness of personnel and visitors at entry and while on the installation using biometrically verified credentials.
Improved overall installation safety.
Enhanced security of mission-critical assets and infrastructure using identity resolution, continuous vetting, and insider threat risk reduction solutions.
The value of this holistic and frictionless digital identity solution isn't restricted to single points of interaction like access control; it enables enhanced real-time situational awareness, improved safety and security, and increased efficiencies. Whether leveraging current infrastructure or Intelligent video surveillance systems, it provides this awareness beginning with the identity verification and risk assessment process beyond the physical perimeter—reading license plates and identifying faces as vehicles and pedestrians approach the access point. This same solution can be applied to interior spaces, where the pattern of life of known individuals can be monitored and deviations from expected patterns, such as where an individual enters a restricted zone, can be used to alert security force personnel. These capabilities can be achieved through centralized video processing of preexisting surveillance feeds or pushed to the edge through an embedded alerting platform. This will become especially useful with the expansion of dedicated wireless Internet of Things sensors. Enabling cameras to operate with edge processing and send data to central cloud services for data aggregation across the enterprise. It is with these features that we can apply a Zero Trust architecture or even an ICAM solution to physical security to ensure that physical authentication mirrors the capabilities of virtual interaction. This is just one example of how identity can be leveraged. Similarly, we can apply an identity / biometric solution to better secure and gain access to a network, applications, and data – pushing the identity fabric to the edge, bridging the gap between physical, logical, and digital.


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Bee Cuts Workforce By 11 Percent
The Sacramento Bee announced another round of layoffs Monday. 128 employees are now out of work. That brings the total number of job cuts to 300 since last summer as the newspaper deals with declining revenue and a deepening recession.
By Steve Milne
The Bee is cutting 29 jobs in its newsroom alone. Reporter Ed Fletcher got word that his job is safe.
"On one hand you're happy that you know you're not going to be looking for a job. On the other hand a lot of good friends have lost their job. So it's a difficult time for everybody."
In addition to the newsroom cuts, The Bee is eliminating jobs in circulation, production and advertising. All totaled, it's 11% of the paper's workforce.
Pam Dinsmore is The Bee's community affairs director. She says the paper is faced with plunging ad revenues plaguing the entire publishing sector.
Dinsmore says despite the cuts they'll still be able to report thoroughly on both state government and Northern California.
"The Capital Bureau was not impacted by any of the cuts and that remains a top priority as well as continuing to cover the region as the most trusted media source."
But Nick Burnett who heads Communications Studies at Sacramento State says The Bee's coverage can't help but be affected.
"It has to impact it. I don't see how you can simply take an organization and just begin slicing away the veteran reporter corps without having some kind of impact on the coverage."
Neil Henry is a professor at the Graduate School of Journalism at UC Berkeley. He says The Bee and other newspapers play an important watchdog role. The fact that newspapers are shrinking doesn't bode well for their task of holding officials accountable.
"Whether the public realizes it or not, we are losing a significant vehicle for information and service to Democratic society."
This latest round of cuts at The Bee is part of wider reductions made by the newspaper's parent corporation - McClatchy Company.
Rick Edmonds with the journalism think-tank Poynter Institute says McClatchy's troubles can be traced to its decision to buy the Knight Ridder newspaper chain three years ago.
"They really need those profits to pay off their debt. So it pretty directly relates to the level of debt they took on in that purchase."
The purchase left McClatchy $2 billion in debt, even though the chain's newspapers are reportedly still turning a profit.
Bee reporter Ed Fletcher…who also represents the California Media Workers Guild…says that's something his union regrets.
"If the guild had a time machine we'd go back in time and tell them not to buy Knight Ridder but we don't. So we're all sort of dealing with the difficult economy and the fact that we have to keep making payments on this debt or we'll go bankrupt like a lot of companies."
Fletcher and other employees who didn't get laid off face wage cuts of up to six-percent and could be forced to take a week of unpaid leave.
Monday, March 9, 2009 3:30 PM
Tuesday, March 10, 2009 3:00 AM


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Dow Jones Industrial Average Today Rising as 20,000 Level within Reach
By Garrett Baldwin, Behavioral Trading Specialist, Money Morning • December 16, 2016
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The Dow Jones Industrial Average is rising again on Friday as investors keep a sharp eye on another round of economic data and a rallying U.S. dollar.
The greenback received a huge boost this week after the U.S. Federal Reserve hiked interest rates and signaled that the U.S. economy was gaining strength. There is now talk the Fed could raise interest rates up to three times in 2017.
On Thursday, the Dow bounced back from Wednesday's triple-digit decline as the stronger U.S. dollar and improving economic data fueled optimism.
Let's look at the numbers from Thursday for the Dow, S&P 500, and Nasdaq:
Dow Jones: 19,852.24; +59.71; +0.30%
S&P 500: 2,262.03; +8.75; +0.39%
Nasdaq: 5,456.85; +20.18; +0.37%
Here's a look at today's most important market events and stocks, plus a look at Friday's economic calendar.
What's Ahead for the Dow Jones Industrial Average Today
The Dow is projecting a 43-point gain on Friday, pushing the index within reach of the psychologically important barrier of Dow 20,000.
Don't Miss: How to Make a Killing… When Everyone Else Is Panicking
With interest rates on the rise, investors are wondering if the post-election rally is over. But here at Money Morning, we recommend that investors buy stocks now that are able to outperform the market regardless of what the Fed does with interest rates. That's why we've put together this guide on how to invest after an interest rate hike.
The WTI crude oil price today was pushing higher this morning as markets realized that OPEC has begun its planned production cuts. WTI prices added 0.8% in pre-market hours thanks to the combination of OPEC cuts and word that U.S crude inventory levels fell last week.
Meanwhile, Brent crude gained 0.5% in pre-market hours.
Money Morning Global Energy Strategist Dr. Kent Moors has said that the biggest challenge for OPEC and non-OPEC producers will be the enforcement of its deal. Kuwait, Saudi Arabia, and Abu Dhabi have all formally informed their customers that they are proceeding with strategic cuts to their production. But there's another story that just hit the energy markets. In fact, it's a looming energy crisis concerning one of Europe's richest countries. And this could be the most important story that you read all day.
Shares of Yahoo! Inc. (Nasdaq: YHOO) are recovering from a huge decline on Thursday. The stock plunged more than 6.1% yesterday on news that the company was hacked in 2013. The cyberattack compromised 1 billion email accounts and could end up costing the company $1 billion in its deal with Verizon Communications Inc. (NYSE: VZ). Verizon said that it will explore a lower price for the core assets of Yahoo or pull out of the deal altogether. The buyout is supposed to close in the first quarter of 2017. Here's everything you need to know about the Yahoo hack 2016.
Stocks to Watch Today, Dec. 16, 2016
Shares of Facebook Inc. (Nasdaq: FB) gained more than 0.2% in pre-market hours. Though the company's shareholders approved a 3-for-1 stock split earlier this year, many are wondering will Facebook stock split after new details emerged from a class-action lawsuit filed in April. Here's the latest on the FB stock split and what it means for investors.
Shares of Mondelez International (Nasdaq: MDLZ) were up another 1% in pre-market hours on speculation that the company is about to be acquired. According to Bloomberg, Kraft-Heinz Co. (NYSE: KHC) is considering a bid to purchase the global snack manufacturer.
Keep an eye on Trivago (Nasdaq: TRVG) as the hotel search website operator is preparing to launch public trading. The firm's initial public offering has been priced at $11 per share, raising $287 million in the process. Still, that $11 figure is well below the anticipated range of $13 to $15 a share.
In earnings news, shares of Oracle Corp. (NYSE: ORCL) fell 2.5% after the company fell short of Wall Street expectations. Though the firm topped EPS expectations by a penny, it reported weaker than expected revenue. The company did surpass rival Salesforce.com Inc. (NYSE: CRM) in cloud-based sales, but investors still seemed disappointed by the company's quarterly report.
On a light day of earnings, lookout for a quarterly report from Triangle Petroleum Corp. (Nasdaq: TPLM).
Today's U.S. Economic Calendar (all times EST)
Housing Starts at 8:30 a.m.
Atlanta Fed Business Inflation Expectations at 10 a.m.
Richmond Federal Reserve Bank President Jeffrey Lacker speaks at 12:30 p.m.
Baker Hughes Inc. Rig Count at 1 p.m.
An $80 Billion Cover-Up? Feds use obscure loophole to threaten retirees… Under the watchful eye of Congress, the government will soon be implementing a controversial plan that threatens the retirement of millions of Americans. And they're using an obscure loophole buried in Title 29 of the U.S. Labor Code to do it. If you have a 401(k), IRA, or any type of retirement account, this could cause you to miss out on $68,870 or more. Full Story
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Garrett Baldwin is a globally recognized research economist, financial writer, and consultant with degrees from Northwestern, Johns Hopkins, Purdue, and Indiana University. He is a seasoned financial and political risk analyst, with a focus on stocks, hedge funds, private equity, blockchain, and housing policy. He has conducted risk assessment projects for clients in 27 countries, and consulted on policy and financial operations for some of the nation's largest financial institutions, including a $1.5 trillion credit fund, a $43 billion credit and auto loan giant, as well as two of the largest Wall Street banks by assets under management.
Garrett joined Money Map Press as an economist and researcher in 2011, specializing in alternative strategies with an emphasis on fundamental and technical analysis.
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