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text:
Hammer & Tongs by Theatre Alibi
A company of actors of long-standing association are putting on a show about conflict. But two of the four haven't arrived in time for curtain-up, so Swanny (Derek Frood) and the musical director, Fret (Thomas Johnson), launch into an amusing, hammed-up story about a man setting sail in his tin bath. When the errant pair, Duggan (Jordan Whyte) and Spurge (Michael Wagg), finally enter stage left, already in full-on bicker mode, the scene is set for an hour or so of name-calling, fist-flinging, muck-raking absurdity that claims (so says the website) to 'dig deep into the human compulsion to argue the toss' but which comes across as a rather slight, shambolic sketch show that sits somewhere between a Saturday morning kids' TV programme and a student revue. By the end of it, I was longing for the reappearance of the tin-bath sailor…
Although Theatre Alibi are justifiably renowned for their immersive, inventive productions for younger audiences, Hammer & Tongs is not one of these – the language is too saucily child-unfriendly for that – but neither does it seem quite committed to exploring any adult themes to a satisfactory depth. Admittedly, there seems to be an intention to make a mockery of arguing, since the only way to cope with the 'maddening, saddening, exhausting' nature of it is to laugh in its face, but the execution is such that it's unclear who these characters are and why we should care about their grievances at all.
Interwoven with scenes of the company bickering and sniping 'backstage' are episodes playing out examples of conflict – two children fight over what to watch on TV, their parents then argue about the kids, a groom attacks the wedding DJ after being forced onto the dancefloor, a bullied young man battles his inner demons, called Crushing Doubt and Self Loathio – which have a certain rolling nature that mirrors the circularity of most arguments but which don't offer enough insight into how and why we fight. They seem included just to allow the actors to romp around the stage, farting in each other's faces and hitting each other with foam sticks. And rather than revealing subtextual layers of characterisation or interrogating the process, a meta level seam of self-referential comments – about the 'crap' dialogue, the 'puerile' humour, and the need the work out a decent ending – serve only to highlight the show's actual weaknesses.
I came away no wiser as to why humans argue, or even why these particular characters argue (they might be sick of the sight of each other – there are a number of references to how long they've all been working together – but more likely it's because they're all so irritating). What is clear is that this show is really not for me; I'm obviously a miserable stick-in-the-mud for finding a feast of slapstick punch-ups, complete with schoolyard insults and fart jokes, neither hilarious nor thought-provoking. Sorry.
Reviewed for Exeunt
Posted by Exeter Insider at 11:13
Labels: Arts & Culture, Home, On the Town
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redpajama_set_name: RedPajamaCommonCrawl


text:
/*------------------------------------------------------------------------------------*/
//
//  UIImageView+Mask.m
//
//  Created by Jonathan Morin
//  Copyright (c) 2011,2012,2013 Jonathan Morin. All rights reserved.
//
/*------------------------------------------------------------------------------------*/

#import "UIImageView+Mask.h"

/*------------------------------------------------------------------------------------*/

@implementation UIImageView (Mask)

/*------------------------------------------------------------------------------------*/

+ (void)applyMaskWithImageAndSize:(UIImageView*)a_imageView maskImage:(UIImage*)a_maskImage size:(CGSize)a_size
{
	CALayer * mask = [CALayer layer];
	mask.contents = (id)[a_maskImage CGImage];
	mask.frame = CGRectMake(0, 0, a_size.width, a_size.height);
	a_imageView.layer.mask = mask;
	a_imageView.layer.masksToBounds = YES;
}

/*------------------------------------------------------------------------------------*/

- (void)applyMaskWithImageAndSize:(UIImage*)a_maskImage size:(CGSize)a_size
{
	[UIImageView applyMaskWithImageAndSize:self maskImage:a_maskImage size:a_size];
}

/*------------------------------------------------------------------------------------*/

@end

redpajama_set_name: RedPajamaGithub


text:
Q: cant connect my managedObjectContext from my view to my Delegate i'm using core data on my app and i know i need to connect my managedObjectContext throw the Delegate but i don't know how...
i have a delegate-
AppDelegate.h
#import <UIKit/UIKit.h>

@interface AppDelegate : UIResponder <UIApplicationDelegate>

@property (strong, nonatomic) UIWindow *window;

@property (readonly, strong, nonatomic) NSManagedObjectContext *managedObjectContext;
@property (readonly, strong, nonatomic) NSManagedObjectModel *managedObjectModel;
@property (readonly, strong, nonatomic) NSPersistentStoreCoordinator *persistentStoreCoordinator;
@property (strong, nonatomic) UINavigationController *nav;

- (void)saveContext;
- (NSURL *)applicationDocumentsDirectory;

@end

AppDelegate.m:
#import "AppDelegate.h"
#import "mainViewController.h"
#import "addViewController.h"

@implementation AppDelegate

@synthesize managedObjectContext = _managedObjectContext;
@synthesize managedObjectModel = _managedObjectModel;
@synthesize persistentStoreCoordinator = _persistentStoreCoordinator;
@synthesize nav;

- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
{
    self.window = [[UIWindow alloc] initWithFrame:[[UIScreen mainScreen] bounds]];
    // Override point for customization after application launch.
    self.window.backgroundColor = [UIColor whiteColor];
    //----------------------------------nav-------------------------------------------------
    mainViewController*mainView=[[mainViewController alloc]init];
    nav=[[UINavigationController alloc]initWithRootViewController:mainView];
    mainView.manageObjectContext=self.managedObjectContext;
    [self.window addSubview:nav.view];
    //----------------------------------nav-end---------------------------------------------
    [self.window makeKeyAndVisible];
    return YES;

}

the MainVeiw is not the page that i want to save an Entity in (so i cant Match the objects from the delegate itself), that is another page and i think my problem is that i dont know how to import a delegate id object so i can compare the managedObjectContext to the one on my delegate.
addViewController.h:
    #import <UIKit/UIKit.h>

@interface addViewController : UIViewController  <UIPickerViewAccessibilityDelegate,UIPickerViewDataSource,UITextFieldDelegate>
{
    NSDictionary *allSubjects;
    NSArray* arrSubject;
    NSArray* arrSubSubjects;
    NSManagedObjectContext*manageObjectContext;
}
@property(nonatomic,strong)NSManagedObjectContext*manageObjectContext;
//@property (readonly, strong, nonatomic) NSManagedObjectModel *managedObjectModel;
//@property (readonly, strong, nonatomic) NSPersistentStoreCoordinator *persistentStoreCoordinator;

@property (strong, nonatomic) NSDictionary *allSubjects;
@property (strong, nonatomic) NSArray* arrSubject;
@property (strong, nonatomic) NSArray* arrSubSubjects;

@property (weak, nonatomic) IBOutlet UIScrollView *scrolladdview;
@property (weak, nonatomic) IBOutlet UIPickerView *pickerSubjects;
@property (weak, nonatomic) IBOutlet UITextField *txtDesc;
@property (weak, nonatomic) IBOutlet UITextField *txtUserName;
@property (weak, nonatomic) IBOutlet UITextField *txtPassword;

-(IBAction)createPassword:(id)sender;

@end

addViewController.m
#import "addViewController.h"

@interface addViewController ()

@end

@implementation addViewController
@synthesize allSubjects,arrSubject,arrSubSubjects,pickerSubjects;
@synthesize txtDesc,txtPassword,txtUserName,scrolladdview,manageObjectContext;

-(IBAction)createPassword:(id)sender
{
    NSInteger row;
    NSString*subTypeSelectd=[[NSString alloc]init];

    row = [pickerSubjects selectedRowInComponent:0];
    subTypeSelectd = [arrSubSubjects objectAtIndex:row];

    NSInteger row2;
    NSString*TypeSelectd=[[NSString alloc]init];

    row2 = [pickerSubjects selectedRowInComponent:1];
    TypeSelectd = [arrSubSubjects objectAtIndex:row2];

//here is the error: no visible @interface for 'addViewController' declares the selector 'NSManagedObject'
    NSManagedObject*password=[NSEntityDescription insertNewObjectForEntityForName:@"Password" inManagedObjectContext:[self managedObjectContext]];

    [password setValue:self.txtDesc.text forKey:@"desc"];
    [password setValue:self.txtUserName.text forKey:@"userName"];
    [password setValue:self.txtPassword.text forKey:@"password"];
    [password setValue:subTypeSelectd forKey:@"subType"];
    [password setValue:TypeSelectd forKey:@"type"];

    NSError*error;
    if(![[self manageObjectContext]save:&error])
        NSLog(@"input %@",error);
    else NSLog(@"saved");

    [self.navigationController popViewControllerAnimated:YES];

}

i will love some help!!!

A: You could get it form the AppDelegate itself:
#import "AppDelegate.h"

//...

-(IBAction)createPassword:(id)sender
{
//...
NSManagedObjectContext* context = ((AppDelegate*)[[UIApplication sharedApplication] delegate]). managedObjectContext;
//...
}

A: Here in I see, you have created one context in the AppDelegate, and one in the Addviewcontroller.
Where as you have only one store and one thread, so you should remove the property of the managed object context from the AddviewController.
Also should assign the managedobjectcontext from the delegate in the addViewController by the following code:
{
    AppDelegate *delegate = [UIApplication sharedApplication].delegate;
    NSManagedObjectContext *addViewcontrollerLocalContext  = delegate.managedObjectContext;
}
By doing this all the objects would be saved in the MainObjectContext created by you in the AppDelegate file.

redpajama_set_name: RedPajamaStackExchange


text:
Tickets for The Wolf of Wall Street
The Wolf of Wall Street Theatre Tickets
The Wolf Of Wall Street Theatre location
The Wolf Of Wall Street Showtimes
Based on the memoirs of wealthy criminal stock-broker Jordan Belfort, who was played by Leonardo Dicaprio in the award-winning film, The Wolf of Wall Street theatre production aims to fully immerse you in Belfort's debaucherous and extravagant world. With an impressive performance space of four floors which features 1990s' New York trader schemes and supercars, you can experience first-hand Belfort's extravagant and outrageous journey to wealth and power.
Directed and adapted by Alexander Wright, the director of the immersive Great Gatsby, The Wolf of Wall Street immersive adaptation creates a truly unique and exhilarating experience which, located in London's financial district, will transport you back to 1990s New York.
Recommended age: 18 + (you will be asked to show ID)
In 1987, young entrepreneur Jordan Belfort, who is happily married to his wife, is an entry-level stock-broker at a wall-street firm. Founding his own firm, Stratton Oakmont, with a group of loyal brokers, Belfort becomes incredibly successful by defrauding wealthy investors out of millions.
Indulging in a shockingly hedonistic and lavish lifestyle, Belfort pushes his unbelievable amounts of wealth to the limits whilst engaging in criminal acts. Yet as he soon finds out, the FBI have been closely watching him...
Prepare for an exciting evening of debauchary and live every second of this experience with Belfort through the fully immersive production of The Wolf of Wall Street which is designed to deliver a 360 degree experience...
The Wolf of Wall Street Tickets are at a fixed price of £66.70. Given that you move around the expansive space of the theatre, you cannot select a specific seat so tickets do not vary much in price; they are £70 on saturdays.
There will be an affordable ticket lottery.
Group tickets discount: Groups bookings over 10 or more will receive a £10 discount per ticket. You must use the discount code GROUPW10 at check-out. You can also contact the theatre to book a group ticket.
Please bear in mind that these cheaper tickets exclude Saturday evening performances and the weeks commencing 16th, 23rd and 30th December 2019.
The location of the Wolf of Wall Street immersive theatre production has until now, been shrouded in mystery, yet the exact location, a huge performance space of four floors, has been revealed. We recomnned that you use Google maps and public transport to access the theatre.
The address for the show is:
Stratton Oakmont
5-15 Sun Street
EC2M, 2PT
Tube/train
Located in the heart of London's financial district, the nearest stations are:
Liverpool street: a mainline station and Tube for Central, Circle, Metropolitan, Hammersmith & City Lines and Overground. Seven Minute walk away.
Old Street: mainline station and Tube for the Northern Line. Nine minute walk away.
Moorgate: tube for the Northern, Circle, Metropolitan and Hammersmith & City Lines. 6 minute walk away/
If you are travelling by car, use the NCP car park which is a 3 minute walk away in Finsbury Square.
The nearest bus stops are Finsbury Square/Moorgate Stop J servicing the 153 and Finsbury Square/Moorgate Stop K for the 21, 43, 76 and 141.
The nearest Santander Cycle Docking Stations are Finsbury Circus (7 minute walk) and Wormwood Street (9 minute walk).
There are no seats necessarily available so if you require seating for medical or health reasons, please email ticketing@artstickets.co.uk so that the theatre can arrange to accommodate your needs.
Every Friday 7pm.
Every Saturday 2pm and 7pm
Every Sunday 6pm
Wednesday 13th, 20th and 27th 7pm.
Every Thursday 7pm
Every Saturday 2pm and 7pm.
Every Sunday 6pm.
Monday 30th 7pm.
Tuesday 10th, 17th, 31st 7pm.
Wednesday 4th, 11th, 18th 7pm.
Thursday 5th, 12th, 19th 7pm.
Tuesday 7th &14th 7pm
Wednesday 8th & 15th 7pm
Thursday 2nd, 9th, 16th 7pm
Friday 3rd, 10th & 17th 7pm
Saturday 4th, 11th, 18th 2pm & 7pm
Sunday 5th, 12th, 19th 6pm
Warning: the theatre production uses strobes, flashing lights and loud music.
90s American office wear is recommended for the Wolf of Wall Street immersive theatre experience..
There is a cloakroom available.
There is a restaurant, Willow, which will be opened before, during and after the show. Willow is located on the ground floor, next to the entrance. While the restaurant provides vegetarian, vegan and gluten free options, it cannot guarantee a nut free kitchen.
Photos of The Wolf of Wall Street
the wolf of wallstreet immersive experience
the wolf of wallstreet immersive show london
Several locations
We haven't found tickets for sale for this event.
If you click the follow buttonwe'll tell you if there's any news.
(For instance, if there are new dates or a price drop).
Prior events The Wolf of Wall Street
The Wolf of Wall Street, LondonView map
5 Sun St, London EC2A, Reino Unido, London1
Sunday, 19 Jan
Friday, 11 Oct
Thursday, 10 Oct
Wednesday, 09 Oct
Tuesday, 08 Oct
Kay Mellor's Band Of Gold
The Tiger Who Came to Tea
Tickets for Theatre


text:
Q: Broken line that can go in specific directions: can it end up on its starting point?
Say you have a 2D broken line you move along, but only some directions are allowed (I give you the angles relative to the usual cartesian plane):

*

*(Up-Left):  $]\pi, \dfrac{\pi}{2}[$

*(Down-Left): $]-\pi, \dfrac{-\pi}{2}[$

*(Down-Right): $ ]\dfrac{-\pi}{2}, 0[$
An additional rule is that you cannot go Up-left if you just went Down-right, and vice-versa.
The goal is to prove that if you want to make a cycle out of this line, you always end up with a line that cross it-self.

Context
I'm working on unit-square graphs with a clique number of 2. The directions correspond to which corner of some squares lies inside the other. I'm trying to define some order onto the squares.
This is the last point of a proof that would allow the use of some representation of a graph, ending up with very easy to prove and useful small results.

A: There has to be a self-intersection; the path cannot be a simple polygon.
Suppose the path were indeed simple. A vertex with maximal $y$ coordinate must connect edges that go up and then down. According to the rules, the only way this can happen is first up-left, then down-left. For a simple polygon, this implies the path is oriented counterclockwise. On the other hand a vertex with minimal $y$-coordinate must connect edges that go down-left, then up-left, implying the path is oriented clockwise: a contradiction.


Sharon has been one of the most sincere person we've ever met. Believed she trusted our profession before she met us and confirmed our service real quickly. It was such a pleasure documenting her wedding with Hin. Everyone simply adored her so much and without a word, we knew why! Our shutters were so busy as there were loads and loads of incredible moments – Love, Laughter and Ever Happily After sums those up! Catch and feel from the full coverage!


text:
Black History Now
This site is the Web's largest and most comprehensive collection of historical Black American Biographies. It contains hundreds of inspirational stories of Black American Achievement. Our mission is inspiration… and our mission is education…the kind they don't teach in schools. These extraordinary stories of perseverance and triumph remind us that Black American achievement has influenced every aspect of America's past, and inspire us to even greater heights in the future.
Featured Biography
1917-2002 Charity Adams Earley was a pioneer in the success of both women and African Americans in the U.S. Army. She served as one of the Women's Army Corps (WAC) first black officers, and ultimately attained the rank of major. A Studious Start Earley was born on December 5, 1917, in Columbia, South Carolina, to
[continue reading…]
C. 1682 – ? Cesar was a successful practitioner of traditional African medicine in the southern United States during the middle of the 18th century. In recognition of his accomplishments, the South Carolina legislature took the unprecedented step of freeing him from slavery and awarding him a substantial lifetime stipend. African Roots Born around 1682,
Celia Cruz
1925?-2003 Celia Cruz rose from her musical career in Latin America to become the leading female Afro-Cuban and Salsa vocalist in the United States, becoming a symbol of the spirit of the Cuban expatriate community. Café con Leche Cruz was born Ursula Hilaria Celia de la Caridad Cruz Alfonso in the Santos Suarez district of
1844-? Cathay Williams was the only known female African American Buffalo Soldier. She was the first black woman to be documented for her service in the U.S. Army before women were officially allowed to enlist. Buffalo Woman Williams was born in September of 1844 in Independence, Missouri. Aside from this lone fact, details of her
1907-1996 Nicknamed "Chief" by his aviation students, Charles Alfred Anderson, Sr.. served as the Chief Civilian Flight Instructor for the Tuskegee Institute 's groundbreaking program to train black pilots. When President Franklin D. Roosevelt established a military aviation program at Tuskegee in 1941. Anderson was tasked with training the famous World War II Tuskegee Airmen.
Betsey Stockton
C.1798-1865 Betsey Stockton was born into slavery, and emerged as a religious and academic pioneer. She was instrumental in bringing formal education to indigenous Hawaiians and Native Americans, and in establishing numerous schools. A Young Missionary Sets Sail Stockton was born sometime in 1798, into childhood slavery in Princeton, New Jersey. The identity of her
1912-2002 Benjamin O. Davis, Jr., was one of the pioneering African Americans who attended the military academy at West Point before the second World War. The Air Forces first black general, he commanded the legendary Tuskegee group of fighter pilots in World War II. Service in the Blood Davis was born on December 18, 1912,
Benjamin E. Mays
1894-1984 Benjamin E. Mays was a pastor, a passionate advocate of education, and an inspirational leader in the modern Civil Rights Movement. As the president of Morehouse College in Atlanta for 21 years, he guided the institution as it rose to the top ranks of the nations historically black colleges. God and Education Mays was
Beauford Delaney
1901-1979 Beauford Delaney struggled with poverty, mental illness, and obscurity throughout his career as a painter. Since his death, museum retrospectives have reestablished Delaney as one of America's most vital expressionist painters. A Promising Young Artist Delaney was born in Knoxville, Tennessee, on December 30, 1901. His father, Samuel, was a Methodist minister. His mother,
1912-1987 Known as the "Architect of the March on Washington," Bayard Rustin was a tireless crusader for civil rights in the nonviolent tradition of Mohandas Gandhi. Rustin initiated the Freedom Ride movement by leading 1947's Journey of Reconciliation, and played an instrumental role in the organization of 1963's Great March on Washington for Jobs and


The CHP identified the deceased victims as Thomas Fridrich, 61, of Belden, who was driving the pickup truck; John A. Lowe, 46, of Paradise, driver of the motorcycle; and Crystal A. Smith, 40, of Paradise, his passenger.
Also injured in the three-vehicle accident were James D. Timberlake, 58, of Twain, whose injuries were minor; and Schwamb, who sustained major injuries.
During the course of his investigation, Hollister learned that Schwamb had a prior conviction, which contributed to his charging her with second-degree murder instead of vehicular manslaughter.
Schwamb is scheduled to return to court Friday for continued arraignment and appointment of an attorney. She is being held in the Plumas County jail in lieu of a $3 million bond.
If convicted, Schwamb could face 48 years to life in state prison, Hollister said.


text:
Home Series Podcasts Schools Out: Lessons Learned From Lindsay Unified School District
Schools Out: Lessons Learned From Lindsay Unified School District
Getting Smart Staff
In the past two podcast episodes we've envisioned what the future of learning might look like with the authors of Education Reimagined's new paper, 'School's Out'. We've spoken with Amy Anderson, Scott Van Beck, Nate McClennan, and Oscar Brinson on what a new model of learning might mean for families and communities.
We've also explored the notion that learning can take place anywhere at any time, and we've started unpacking how technology will continue to play a role in the future of learning and work. In our final episode on this topic, Tom speaks with Tom Rooney Superintendent of Lindsay Unified School District. Listen in as they talk about lessons learned from Lindsay Unified School District and how the community can play an active role in the future of learning.
Be sure to read Tom's position paper, School's Out: Who Takes Responsibility for the Education of Young People? in where he describes community educators and the role they would play in a reimagined future of learning.
[:14] About today's episode.
[1:00] Tom welcomes Tom Rooney to the podcast.
[1:09] Tom explains the origin story of the student-centered, performance-based work he's doing at Lindsay Unified School District.
[6:06] About Lindsay Unified's vision of meeting learners at their level and how that guarantees success.
[8:36] How Lindsay Unified's teachers seamlessly work together and the incredible benefits of that.
[11:06] Tom speaks about the support they've received from various organizations and how it has helped Lindsay Unified.
[13:52] The work that Tom and Lindsay Unified have accomplished with the help of Empower Learning.
[15:30] Tom and Tom dive into Tom's paper: "School's Out: Who Takes Responsibility for the Education of Young People?" Tom first speaks about the role professional educators might play if the current system was reimagined.
[19:33] Tom's ideas (from his paper) on the two new roles of personal life coaches and opportunity creators.
[22:04] Barriers and opportunities to Tom's vision for the future of learning in Lindsay.
[24:49] Will there be any transportation barriers in Tom's vision?
[26:55] As Tom thinks about the School's Out conversation, he offers some practical pieces of advice for those in education could work on this week.
Previous episode: Episode 174 — "School's Out: Engaging Families and the Community"
Previous episode: Episode 175 — "School's Out: Anywhere, Anytime Learning, and the Role of Technology"
Education Reimagined
"School's Out: What if Schools, As We Know Them, Didn't Exist?"
"School's Out: What if School Didn't Exist?"
"School's Out: Who Takes Responsibility for the Education of Young People?" (Tom's paper)
Lindsay Unified Public Schools
iNACOL
Transcend Education
Empower Learning
For more, see:
School's Out: What if School Did Not Exist?
School's Out: Engaging Family and the Community
School's Out: Anywhere, Anytime Learning and the Role of Technology
Stay in-the-know with all things edtech and innovations in learning by signing up to receive the weekly Smart Update. This post includes mentions of a Getting Smart partner. For a full list of partners, affiliate organizations and all other disclosures, please see our Partner page.
student-centered
Previous articleFour Keys to Success at the Most Innovative Schools in the World
Next article3 Ways to Help Students Become Better Digital Citizens–Today
How the Micro-Credential Revolution is Transforming Professional Learning


MOOC - Create easily with Drimify.
Create MOOC easily online with Drimify, the interactive HTML5 content creation software.
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Personalise the MOOC appearance and user experience in simple steps to create a professional app that works via a link on smartphones, tablets and computers. You don't need any technical skills to design, create MOOC and engage with your audience.
An interface for creating MOOC that's so simple, anyone can do it.
The first MOOCs emerged from the Open Educational Resources (OER) movement. Massive Open Online Course (MOOC), is an open type of distance education that can accommodate a large number of participants. For % CIBLE% this allows participants, teachers and students, to be geographically dispersed and communicate only over the Internet.
MOOC easy to create by anyone, for any project.


text:
Dr. Iskander Rehman
Senior Fellow for International Relations
Asian Geopolitics and Defense Issues
Nuclear Strategy and Deterrence Theory
Military History and Grand Strategy
B.A. in Political Science, Sciences Po Paris
M.A. in Political Science, Sciences Po Paris
M.Res in Comparative Politics, Sciences Po Paris
Ph.D. in Political Science and Asia Studies with distinction (mention tres honorable avec les felicitations du jury) from Sciences Po Paris
Dr. Iskander Rehman is the Senior Fellow for International Relations at the Pell Center for International Relations and Public Policy at Salve Regina University. Prior to joining the Pell Center, Dr. Rehman was a Postdoctoral Fellow in the International Order and Strategy Program (IOS) at the Brookings Institution. He has also served as a Fellow at the Center for Strategic and Budgetary Assessments, a Stanton Nuclear Fellow at the Carnegie Endowment for International Peace, and as a Fellow at the German Marshall Fund, all in Washington, D.C. Dr. Rehman has also lived and worked in India, holding visiting fellowships at the Observer Research Foundation and the Institute for Defense Studies and Analyses, both in New Delhi.
He has published a number of think tank monographs, book chapters, and peer-reviewed articles in journals such as the Naval War College Review, and Asian Security. Dr. Rehman's research has explored a broad range of Asian security issues, from the evolving security relationship between China and India, to Australian defense strategy, and naval nuclear dynamics in the Indo-Pacific. His work has also featured or been cited in The Guardian, The American Interest, The Financial Times, The Economist, The Indian Express, Le Monde, The Diplomat, The National Interest, and BBC World, amongst others. He is a regular contributor for the national security website War on the Rocks, and is currently writing a book which examines the ongoing shifts in historically "non-aligned" or neutral Asian countries' defense postures.
Dr. Rehman holds a BA, Masters of Science, Masters of Research (MRes) and Ph.D. in Political Science (with distinction and a specialization in Asia Studies) from the Institute of Political Studies (Sciences Po) in Paris, France.


text:
What is Land Clearing and Mulching in Australia?
Australia's Construction Hire Marketplace
What is Land Clearing in Australia?
Land clearing in Australia is better known as the targeted removal of certain vegetation, brush, trees, stones, and other obstacles. This practice has become increasingly popularised across both commercial and residential projects given its tendency to be the best way to clear brush and small trees.
Land clearing is often undertaken in preparation for construction work but is also a highly sought-after piece of equipment amongst the agricultural industry. The ability to use land clearing in agriculture to clear acreage for cultivation, grazing pastures, and vineyards, is one of many reasons for land clearing to be considered across projects of all natures.
In most cases, land clearing is conducted prior to excavation and levelling activities given the nature of its process. Please note, it is important to look into your local laws and regulations surrounding Land clearing in Australia given the broad range of restrictions and complexities that may arise on occasion.
What is Mulching?
Mulching is the process of breaking down garden and land clearing waste, such as leaves, plant matter, hay, and wood – using mulching machines such as chippers. Mulching is renowned as being an efficient and effective way to return organic materials and nutrients back into the soil through the creation of 'mulch' as an output product.
Mulch can be utilised across a diverse range of commercial and residential applications but is more commonly applied as a top layer on surface soil in efforts to conserve soil moisture, mitigate erosion, inhibit weed growth, and improve fertility and soil health.
What are the different types of Land Clearing Equipment?
Chippers and mulchers are machines designed to breakdown land clearing waste such as wood and plant matter for either reuse as mulch, or as part of disposal efforts. They go by a range of names including shredders, mulchers, chippers, chipper shredders, wood chippers, shredder mulchers, and wood shredders.
What is hydromulching?
Hydromulching, often called hydroseeding, is an effective and fast service for high shear areas, dust control, and revegetation of land. Hydromulching is a planting process that utilises specialised mulch typically made up of a mixture of seed, fiber mulch, fertiliser, water, and a binding agent (although this recipe may differ between suppliers). This product is typically sprayed and is used for slope retention, erosion control, hydroseeding, landfill cover, stockpile cover, odour control, dust control, and even stormwater management.
What are Slashers?
A slasher is typically a post-track loader with a slasher add-on attached. These machines utilise a shredder of sorts, where the front of the machine collected trees and debris, while the back processes and cuts up the debris, leaving it along the ground behind the vehicle.
What are Stump Grinders?
Stump grinders are a special piece of equipment, as either a dedicated power tool or as a machine add-on, used for ripping rooted tree stumps from the ground. They are typically manned by a walking operator and vary in size from as small as a lawnmower to as large as a truck. Stump grinders work by utilising a high-speed disc with teeth that grind a stump down into smaller chips for easy removal.
What are Tree Loppers?
A tree lopper is a piece of tree maintenance equipment that is used to cut and prune branches and twigs. They come in a variety of sizes, typically quite long with cutting blades on the end, where suggested length is dependent on the height and width of targeted trees.
What is the typical cost to clear land?
The cost to clear land may vary greatly depending on current land clearing and mulching hire rates. Mulching and Land Clearing prices may also be significantly impacted by hiring type, project scope, and hire period. Suppliers offering mulching and land clearing services typically have minimum hire periods which can range from three to eight hours.
We've seen rates for Land clearing and mulching machines/ services vary anywhere from $55+/hour for a 4" chipper and mulcher up to $120+/hour for an 18" chipper and mulcher.
Reasons for Land Clearing
In general, there is a broad spectrum of reasons for land clearing services to be utilised across both commercial and residential projects. Land clearing is primarily undertaken in preparation for construction work and is also popular in efforts to clear acreage for the creation of agricultural spaces like grazing pastures and vineyards. In many cases, it is conducted prior to excavation and leveling activities. Efficient and effective land clearing services could land you one step closer to ensuring your properties potential is maximised, whilst warding off potential hazards. Land Clearing in Australia as a whole is potentially one of the most purposeful services available given the diverse landscapes available and the variety of benefits offered
Advantages of Land Clearing
One of the most vital steps in preparing land for a project is to have it cleared. Neglected and untreated landscapes are typically characterised by their overgrown and unsafe terrains which can hold negative connotations for project managers and landlords. Given the volume of 'rough' terrains around – advantages of land clearing in Australia can be highlighted quite effectively. Here are just a few advantages of land clearing:
Land Clearing as a value-added service
Before land clearing services are implemented, affected areas are typically uninhabitable, unsafe, or 'useless'. Though rates vary, often times the cost to clear land is a worthy investment when considering the potential upside of construction and agriculture projects.
Land clearing as a fire prevention measure
Fire prevention is one of the primary reasons land clearing services should be utilised, given the nature of the Australian landscape. Land clearing that is undertaken carefully and effectively can reduce or eliminate fire hazards through the removal of dead and dry vegetation.
Land clearing as damage prevention
Damage prevention is one of the other notable reasons for land clearing in Australia. Professional land clearing services can help eliminate future hazards which may require more destructive forms of land management, preventing unnecessary damage and excessive land clearing prices.
If you're unsure which mulching machine and land clearing equipment or service is right for your project, don't stress. Our talented team here at iSeekPlant are here to listen to your land clearing requirements to help find reliable equipment and services that offer excellent value and peace of mind.
Our directory offers a variety of highly accredited and industry-leading mulching and land clearing services from suppliers throughout major cities like Brisbane, Sydney, Melbourne, Adelaide, Perth, Canberra, Hobart, and Darwin, along with hundreds of regional centres throughout Australia. Get quotes for land clearing equipment or a mulcher here or call us today on 1300 691 912.
iSeekplant Review: Sustainable Land Clearing Solutions
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Article Galaxy™ Customers Benefit From Access To Altmetric Data
Reprints Desk Parent Company Reports Financial Results for Fiscal Fourth Quarter and Full Year 2016
Reprints Desk Parent Company Reports Preliminary Financial Results for Fiscal Fourth Quarter and Full Year 2016
Article Galaxy™ Summer 2016 Version Release Accelerates Research With New Third-Party Integrations And Enhanced Open Access Journal Filtering
Researchers Find Answers With New On-Demand Information Concierge Service
Reprints Desk's Parent Company Announces $5.2 Million Private Placement
Reprints Desk To Focus on Software-as-a-Service (SaaS) Offerings in 2017
Reprints Desk Partners With WWIS, Offers On-Demand Content Delivery To Academic Libraries In South Africa
Reprints Desk's Parent Company Engages Harvey & Company To Identify Corporate Acquisition Targets
Reprints Desk's Parent Company Reports Fiscal Third Quarter 2016 Financial Results
Reprints Desk's Parent Company Reports Fiscal Second Quarter 2016 Financial Results
Jim Rochford
Article Galaxy Revenue up 14% to $5.8 Million, with Article Galaxy Transactions up 31% to 181,000, Driven by 18% Growth in Active Customer Accounts
ENCINO, Calif., Feb. 16, 2016 /PRNewswire/ -- Research Solutions, Inc. (OTCQB:RSSS), a pioneer in providing on-demand access to scientific, technical and medical (STM) information for life science companies, academic institutions, and other research intensive organizations, reported financial results for its fiscal second quarter ended December 31, 2015.
Fiscal Second Quarter 2016 Financial Highlights vs. the Year-Ago Quarter
Article Galaxy revenue increased 14% to $5.8 million.
Article Galaxy gross profit up 3% to $1.3 million.
Article Galaxy transactions increased 31% to 181,135, marking the company's fifth consecutive quarter of more than 20% year-over-year growth in Article Galaxy transactions.
Active Article Galaxy customer accounts increased 18% to 862, with academic customer accounts increasing 55% to 143 and corporate accounts increasing 12% to 719.
Fiscal Second Quarter 2016 Operational Highlights
New OpenAthens™ partnership expands authentication solutions for scientific, technical and medical content access.
Article Galaxy® Autumn 2015 release featured short-term article rentals, instant access to subscription content from online databases and Article Galaxy's order form for requesting documents, as well as a new Article Galaxy Library Portal add-on.
Hosted Content Workflow 2015 conferences in London and Frankfurt with industry thought leaders presenting the future of corporate information.
For the sixth consecutive year named to the EContent 100 list as one of the most influential companies in the digital content industry, along with Google, Amazon, Facebook and other major tech companies.
Fiscal Second Quarter 2016 Financial Results
Total revenue in the fiscal second quarter of 2016 increased 17% to $9.3 million, compared to $7.9 million in the same year-ago quarter. The increase is primarily attributable to increased orders resulting from the acquisition of new customers for Article Galaxy, the company's digital, cloud-based, SaaS solution. Article Galaxy revenue increased 14% in the fiscal second quarter of 2016 to $5.8 million (62% of revenue). Revenue generated by the company's Reprints and ePrint business was up 23% to $3.5 million (38% of revenue).
The increase in Article Galaxy revenue was driven by an increase in transactions, which was up 31% to 181,135 in the fiscal second quarter versus 138,736 in the same year-ago quarter. The number of active customer accounts conducting transactions increased by 18% to 862 in the fiscal second quarter, versus 732 in the same year-ago quarter (see the definition of transactions and active customer accounts in the section, "Transactions and Active Customer Accounts," below). Academic accounts increased 55% from 92 to 143, and corporate accounts increased 12% from 640 to 719 versus same year-ago quarter.
Total gross profit in the fiscal second quarter increased 6% to $1.6 million compared to $1.5 million in the same year-ago quarter. Article Galaxy gross profit increased 3% to $1.31 million, with Reprints and ePrints gross profit up 19% to $290,000.
Total gross profit as a percentage of revenue decreased by 190 basis points to 17.1%. Article Galaxy gross margin decreased 240 basis points to 22.5%, and Reprints and ePrints gross profit decreased 30 basis points to 8.2%.
Net loss from continuing operations in the fiscal second quarter totaled $0.3 million or $(0.02) per diluted share compared to a net loss of $0.1 million or $(0.01) per diluted share in the same year-ago quarter.
Adjusted EBITDA totaled $5,300 in the fiscal second quarter compared to $112,000 in the same year-ago quarter (see definition and further discussion about the presentation of adjusted EBITDA, a non-GAAP term, below).
Cash and cash equivalents at December 31, 2015 totaled $1.8 million compared to $1.4 million at June 30, 2015. The increase in cash was primarily due to cash provided by operating activities.
As of December 31, 2015, there were no outstanding borrowings under the company's revolving line of credit with Silicon Valley Bank, which provides the lesser of $4 million or 80% of eligible accounts receivable. This amount equaled approximately $2.9 million of available credit at December 31, 2015. The company has renewed the revolving line of credit to extend through October 2017, with the material terms remaining mostly unchanged.
At December 31, 2015, the company had net operating loss carry forwards of approximately $6.8 million applicable to federal tax liability expiring in 2030 and approximately $5.0 million applicable to state tax liability expiring in 2020.
Further details about the company's results in fiscal second quarter 2016 are available in its quarterly report on Form 10-Q, available in the investor relations section of the company's website at www.researchsolutions.com.
"During the second quarter, our growth trajectory with Article Galaxy, our SaaS solution for low-cost access to full-text scholarly research, continued its steady climb," said Research Solutions President and CEO Peter Derycz. "Revenue, transactions and new customer acquisitions were up across the board.
"Also, during the quarter we made tremendous progress enhancing Article Galaxy in terms of better security, adding time-saving and cost-saving features, and creating even easier access for researchers. While these enhancements help keep us ahead of the pack, they also stimulate greater customer usage and create new ways for us to monetize the Article Galaxy platform.
"We demonstrated Article Galaxy at the two International Content Workflow conferences we hosted in London and Frankfurt in October. Attendees included representatives from some of the largest corporations in the world, including some major new prospects. The strong level of interest that we receive at these events has helped to greatly expand our sales pipeline, and this has kept our new European sales engineer very busy over the last few months.
"Our strengthening international presence is perhaps one of the most important aspects to consider when evaluating our Article Galaxy business model. At its core is a virtual store that is open 24 hours a day, seven days a week, and accessible from anywhere in the world. While having a sales engineer based in Europe will help drive new customer wins in the region, servicing new international customers does not require the deployment of new offices or other capital resources to the region. This further highlights the tremendous leverage and scalability in our model, and the few barriers we face in terms of greater market expansion.
"Subsequent to the quarter, our unrivaled competitive advantages were highlighted once again when we were selected by Access Copyright as the preferred vendor of document delivery services for their Canadian customers. This win reflects how our customer acquisition efforts have continued to maintain a 90-plus percent closing rate when our solution is evaluated against our competitors.
"As we look ahead to the remainder of the year, we expect to maintain our double digit growth in Article Galaxy transactions, fueled by the uniqueness of our Article Galaxy platform that supports both increasing customer usage and new customer wins. In fact, we have already tracked double-digit revenue and transaction growth in January as compared to the same year-ago period, with this supporting our continued outlook for strong, steady growth with Article Galaxy over the coming quarters."
Research Solutions president and CEO, Peter Derycz, and CFO Alan Urban will host an investor conference call to discuss these quarterly results and the company's outlook, followed by a question and answer period.
Time: 5:00 p.m. Eastern time (2:00 p.m. Pacific time)
Toll-free dial-in number: 1-866-516-3002
International dial-in number: 1-253-237-1159
Conference ID: 44056703
Please call the conference telephone number 5-10 minutes prior to the start time. An operator will register your name and organization. If you have any difficulty connecting with the conference call, please contact Liolios Group at 1-949-574-3860.
The conference call will be broadcast live and available for replay at http://edge.media-server.com/m/p/pa6iftza and via the investor relations section of the company's website at www.researchsolutions.com.
A replay of the conference call will be available after 8:00 p.m. Eastern time on the same day through February 23, 2016.
Toll-free replay number: 1-855-859-2056
International replay number: 1-404-537-3406
Replay ID: 44056703
Fiscal Second Quarter 2016 Financial Summary Tables
The following financial information should be read in conjunction with the unaudited financial statements and accompanying notes filed by the company with the Securities and Exchange Commission on February 16, 2016 in its Quarterly Report on Form 10-Q for the period ended December 31, 2015, and which can be viewed at www.sec.gov.
Three Months Ended December 31,
$ Change
Article Galaxy
Reprints and ePrints
Total gross profit
Change *
As a percentage of revenue:
* The difference between current and prior period gross profit as a percentage of revenue
Net Income (Loss):
Income (loss) from discontinued operations
Total net loss
Transactions and Active Customer Accounts
We define a transaction as an order for a unit of copyrighted content fulfilled or managed in Article Galaxy.
We define active customer accounts as the sum of the average whole and partial customers for the respective quarter or year. A whole customer is one with at least one Article Galaxy transaction in every month of the respective quarter or year. A partial customer is one with at least one Article Galaxy transaction in one or more months, but not every month of the respective quarter or year.
For example, if a customer has at least one transaction in every month of the quarter, they are counted as a whole customer. However, if they have at least one transaction in only one of the three months of the quarter, they are counted as a partial customer (one-third of a customer).
On an annual basis, if a customer has at least one transaction in every month of the year, they are counted as a whole customer. However, if they have at least one transaction in only six of the twelve months of the year, they are counted as a partial customer (one-half of a customer).
Use of Non-GAAP Measure – Adjusted EBITDA
Research Solutions' management evaluates and makes operating decisions using various financial metrics. In addition to the Company's GAAP results, management also considers the non-GAAP measure of Adjusted EBITDA. Management believes that this non-GAAP measure provides useful information about the Company's operating results. The attached tables provide a reconciliation of this non-GAAP financial measure with the most directly comparable GAAP financial measure.
Adjusted EBITDA is defined as net income (loss), plus interest expense, other income (expense), foreign currency transaction loss, provision for income taxes, depreciation and amortization, stock-based compensation, income (loss) from discontinued operations, and other potential adjustments that may arise.
Set forth below is a reconciliation of Adjusted EBITDA to net income (loss):
December 31,
Add (deduct):
Other (income) expense
Foreign currency transaction loss
Provision for income taxes
Depreciation and amortization
Stock-based compensation
(Income) loss from discontinued operations
Adjusted EBITDA
About Research Solutions
Research Solutions, Inc. (OTCQB:RSSS) and its wholly-owned subsidiary Reprints Desk, Inc. (www.reprintsdesk.com) are pioneers in providing on-demand access to scientific, technical, and medical (STM) information for life science companies, academic institutions, and other research intensive organizations. Our customers include 70% of the top 25 pharma companies in the world. Our cloud based software-as-a-service (SaaS) solution, Article Galaxy, provides customers with access to the over one million newly published articles each year in addition to the tens of millions of existing articles that have been published in the past, helping them to identify the content that is critical to their research. We help our customers create and speed discoveries, save time and money, and remain copyright compliant. We have arrangements with numerous STM content publishers that allow electronic access and distribution of their content. In addition to serving end users of content, we also serve STM publishers by facilitating compliance with applicable copyright laws.
About Reprints Desk®
Reprints Desk improves how journal articles and clinical reprints are accessed, procured, and legally used in evidence-based promotions, medical affairs, and scientific, technical, and medical (STM) research. Organizations fueled by intellectual property choose Reprints Desk because of its collaborative business approach, efficient article supply system and services, and commitment to quality post-sales support. Reprints Desk has ranked #1 in the every Document Delivery Vendor Scorecard from industry analyst and advisory firm Outsell Inc. since 2008.
Important Cautions Regarding Forward-Looking Statements
This release contains "forward-looking statements" that include information relating to future events and future financial and operating performance. Forward-looking statements should not be read as a guarantee of future performance or results, and will not necessarily be accurate indications of the times at, or by, which that performance or those results will be achieved. Forward-looking statements are based on information available at the time they are made and/or management's good faith belief as of that time with respect to future events and are subject to risks and uncertainties that could cause actual performance or results to differ materially from those expressed in or suggested by the forward-looking statements. Important factors that could cause these differences include, but are not limited to: changes in economic conditions; general competitive factors; acceptance of the Company's products in the market; the Company's success in obtaining new customers; the Company's success in technology and product development; the Company's ability to execute its business model and strategic plans; the Company's success in integrating acquired entities and assets, and all the risks and related information described from time to time in the Company's filings with the Securities and Exchange Commission ("SEC"), including the financial statements and related information contained in the Company's Annual Report on Form 10-K and interim Quarterly Reports on Form 10-Q. Examples of such forward-looking statements in this release include statements regarding the expected continued improvement and market acceptance of the Article Galaxy platform, and the expected growth of Article Galaxy revenue, transactions, and customers. The Company undertakes no obligation to publicly update or revise any forward-looking statements, whether as a result of new information, future events or otherwise.
Research Solutions, Inc. and Subsidiaries
June 30,
Accounts receivable, net of allowance of $55,732 and $69,731, respectively
Prepaid royalties
Other assets:
Property and equipment, net of accumulated depreciation of $615,617 and $585,410, respectively
Deposits and other assets
Liabilities and Stockholders' Equity
Accounts payable and accrued expenses
Stockholders' equity:
Preferred stock; $0.001 par value; 20,000,000 shares authorized; no shares issued and outstanding
Common stock; $0.001 par value; 100,000,000 shares authorized; 18,364,827 and 18,242,125 shares issued and outstanding, respectively
Accumulated deficit
(15,561,682)
Accumulated other comprehensive loss
Total stockholders' equity
Total liabilities and stockholders' equity
View News Release Full Screen
Consolidated Statements of Operations and Other Comprehensive Income (Loss)
Cost of revenue
Stock-based compensation expense
Loss from operations
Other income (expenses):
Total other income (expenses)
Loss from continuing operations before provision for income taxes
Discontinued operations:
Loss from discontinued operations
Gain from deconsolidation of former French subsidiary
Income from discontinued operations
SOURCE Research Solutions, Inc.
For further information: Media, Research Solutions, Inc., Ian Palmer, Chief Sales and Marketing Officer, Tel +1 (415) 533-8308, ipalmer@reprintsdesk.com; or Investor Relations, Liolios Group, Inc., Ron Both or Geoffrey Plank, Tel +1 (949) 574-3860, RSSS@liolios.com
We accept and process orders all day, every day. Customer support is available 24 hours a day, 7 days a week.
customersupport@reprintsdesk.com
Worldwide Phone:
© Reprints Desk, Inc., A Research Solutions, Inc. Company. All Rights Reserved.


They rested in the fireplace doing nothing; we rested in our recliners and endured the cold.
In the previous townhouse my wife and I lived in, the gas logs served only as decoration. We fired them up a few times, but no heat emanated from them. They merely looked pretty on a cold winter night and made for a cozy atmosphere.
When we moved to another townhouse—which was built on the same pattern as the one we moved from—we assumed the gas logs performed the same purpose. The winter was unusually cold.
As we sat around opening Christmas presents with our daughter and her family, my wife remarked how we'd never used the logs. Our daughter's boyfriend—a handyman of sorts—remarked that he'd take a look at them. Within a few minutes, he had them lit. Within thirty minutes the house was nice and toasty. We had a quick source of heat, but didn't know we had it.
The same thing is often true in my own life. Paul says we can't imagine what God has in store for those who love Him—and sometimes I don't even try to find out.
Like most people—and most believers—I've fallen into the doing trap, thinking that only as I do for God will He pour out blessings on me. Yet, Jesus didn't say the greatest command was doing good works in His name. He said it was loving Him with our entire hearts, souls, and minds.
Jesus demonstrated the essence of the command in His interaction with Martha while visiting her, Mary, and Lazarus. Martha—the good host—ran around doing. Mary chose to sit at Jesus' feet and listen. When Martha objected to her sister's laziness, Jesus informed her Mary had chosen the better thing.
Fulfillment in life will never come from merely doing. Only when the doing flows from a heart filled with God will satisfaction come. God has much in store for us, but we have to experience it in the right order: spiritual disciplines that bring us closer to God and then the doing of good works.
Don't look for your good works to bring God's abundance unless you've first drawn closer to Him. Get filled with Jesus first. Then He'll fill you so you can fill others.
Tweetable: Are you filled up so you can fill others?
Prayer: Father, draw us closer to You so we'll have the desire to draw closer to others.
True, true, true, God fills hearts in many ways. Thanks for joining the Thankful Thursday Blog Hop!
Yes, we are saved through God's generous grace, not through our own doing. When we are closer to God, we WANT to do His good works.
A very appropriate week to reflect deeply on how we can grow closer to God. Joining you from Thankful Thursday.


text:
La  Division des Marines était une division d'infanterie du Corps des Marines des États-Unis.

Elle fut activée le  à Guadalcanal pendant la Seconde Guerre mondiale à partir de trois régiments ayant déjà pris part aux combats dans le Pacifique. Bien que ce soit à cette époque une nouvelle division, plus de la moitié de son effectif était ainsi composée de vétérans.

La division ne participa qu'à la Bataille d'Okinawa et fut désactivée en Chine le , faisant d'elle la seule division de USMC à n'avoir jamais mis le pied sur le territoire américain.

Voir aussi
 Liste des divisions de l'USMC

Division de l'United States Marine Corps
Unité ou formation militaire créée en 1944

redpajama_set_name: RedPajamaWikipedia


text:
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    /**
     * Delays the call of a function within a given context.
     */
    function timeout(fn, millis, context){

        var args = slice(arguments, 3);

        return setTimeout(function() {
            fn.apply(context, args);
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    module.exports = timeout;


text:
\subsection{$\{a,b\} \not\in \Gamma$, $\{a,c\} \in \Gamma$, $\{b,c\} \in \Gamma$}
By \lemref{lem:fpol}, there is $\omega \in \fpol(\Gamma,\nu)$ \st some $f \in \supp(\omega)$ satisfies $f \in \doa b a$.
This means, unless $a \domps\omega b$, that every $g \in \supp(\omega)$ is conservative and that there is \smash[b]{$f' \in \supp(\omega) \cap \upa b a$}.
\be
\item
If $\smallcrosspic c a c a \not\in \Gamma$ and $\smallcrosspic c b c b \not\in \Gamma$, then by \lemref{lem:fpol} we may assume that there is $g,h \in \supp(\omega)$ \st $g \in \doa c a$ and $h \in \doa c b$.
If there is any $i \in \supp(\omega)$ \st $i \in \doa b a$ and \smash[t]{$i \not\in \upa c a$, then $i' = g[i,\overline{i}] \in \doa b a \doa c a$}.
In this case
$\psi = \{ i' \mapsto \frac 1 4, \overline{i'} \mapsto \frac 1 4, h \mapsto \frac 1 4, \overline{h} \mapsto \frac 1 4 \} \in \fpol(\Gamma,\nu)$,
so unless $a \domps\psi b$ we have $h \in \upa b a$.
Note that $h,i' \in \pol(\Gamma \cup \{ \{a,b\} \})$
and unless $a \domps\psi c$ or $b \domps\psi c$ it must hold that $i',h$ are complementary and $(\Gamma \cup \{ \{a,b\} \},\nu)$ is of type \typegwtp\@.

Otherwise it follows by symmetry that $\supp(\omega) \cap \doa b a \subseteq \upa c a \upa c b$, $\supp(\omega) \cap \doa c a \subseteq \upa b a \upa c b$
and \smash[t]{$\supp(\omega) \cap \doa c b \subseteq \upa b a \upa c a$}, this contradicts that $\omega \in \fpol(\Gamma,\nu)$.

\item
If $\smallcrosspic c a c a \in \Gamma$ and $\smallcrosspic c b c b \not\in \Gamma$, then by \lemref{lem:fpol} we can assume \smash[t]{$g \in \doa c b$} for some $g \in \supp(\omega)$.
Here \smash{$\psi = \{ g \mapsto \frac 1 4, \overline{g} \mapsto \frac 1 4, f \mapsto \frac 1 4, \overline{f} \mapsto \frac 1 4 \} \in \fpol(\Gamma,\nu)$}.
Unless $a \domps\psi b$ we have $g \in \upa b a$.
Note that $f,g \in \pol(\Gamma \cup \{ \{a,b\} \})$ and unless $b \domps\psi c$
it must hold that $g, f$ are complementary, so $(\Gamma \cup \{ \{a,b\},\nu)$ is of type \typegwtp\@.

\item
If $\smallcrosspic c a c a \not\in \Gamma$ and $\smallcrosspic c b c b \in \Gamma$, then by symmetry to the case above, $(\Gamma,\nu)$ is of type \typegwtp\@.

\item
If $\smallcrosspic c a c a \in \Gamma$ and $\smallcrosspic c b c b \in \Gamma$, then by $f,f'$, $(\Gamma,\nu)$ is of type \typegwtp\@.
\ee

\subsection{$\{a,b\} \in \Gamma$, $\{a,c\} \in \Gamma$, $\{b,c\} \not\in \Gamma$}
By \lemref{lem:fpol} there is $\omega \in \fpol(\Gamma,\nu)$ \st $(f,\overline f)(b,c) \not\in \smallmispic c b c b$ for some $f \in \supp(\omega)$.
\be
\item
If $\smallcrosspic b a b a \not\in \Gamma$ and $\smallcrosspic c a c a \not\in \Gamma$,
then, by \lemref{lem:fpol}, we may assume \smash{$g \in \doa b a$, $h \in \doa c a$} for some $g,h \in \supp(\omega)$.

\be
\item
If there is $i \in \pol(\Gamma)$ \st \smash[t]{$i \in \doa b a \doa c a$},
then \smash[t]{$\psi = \{ i \mapsto \frac 1 2, \overline{i} \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$} and $a \domps\psi b$, or \smash[t]{$i \in \upa c b$}.
Note that $f' = i[f,\overline{f}]$ is commutative and satisfies $f'(b,c) \in \{a,b\}$.
So $\psi = \{ f' \mapsto \frac 1 2, i \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$
and $f', i$ must be complementary  unless $a \domps\psi b$, $a \domps\psi c$ or $c \domps\psi b$.
This means that $(\Gamma,\nu)$ is of type \typegwtp\@.

\item
Otherwise $\pol(\Gamma) \cap \doa b a \subseteq \upa c a$ and $\pol(\Gamma) \cap \doa c a \subseteq \upa b a$.
\bi
\item
If there is $r \in \pol(\Gamma)$ \st $(r,\overline r)(b,c) \not\in \smallmispic c b c b$ and $r$ is a projection on both $\{a,b\}$ and $\{a,c\}$, then
\bi
\item
if $(r,\overline r)(b,c) \in \smallcrosspic c a c a$ we have $\psi = \{ r \mapsto \frac 1 2, \overline{r} \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $c \domps\psi b$,
\item
if $(r,\overline r)(b,c) = \smallmispic b a b a$, then
$\psi = \{ g[r,\overline{r}] \mapsto \frac 1 2, h[r,\overline{r}] \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $b \domps\psi c$,
\item
otherwise $(r,\overline r)(b,c) = (a,a)$.
Let $g' = g[r,\overline{r}]$, $h' = h[r,\overline{r}]$ and $f' = g'[\pr_1,h']$.
Is is easy to check that
$\psi = \{ f' \mapsto \frac 1 2, \overline{f'} \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $c \domps\psi b$.
\ei

\item
If there is $r \in \pol(\Gamma)$ \st $(r,\overline r)(b,c) \not\in \smallmispic c b c b$ and \smash[b]{$r \in \doa b a \upa c a$}:
\bi
\item
If $(r,\overline r)(b,c) \in \smallflipmispic c a c a$, consider the following.
\bi
\item
If $(h,\overline h)(b,c) \in \smallmispic c a c a$, let $r' = h[r,\overline{r}]$ and $h' = g[h,\overline{h}]$.
Now $\psi = \{ r' \mapsto \frac 1 2, h' \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $c \domps\psi b$.
\item
If $(h,\overline h)(b,c) \in \smallmispic b a b a$, let $r' = h[r,\overline{r}]$ and $h' = h[h,\overline{h}]$.
Now $\psi = \{ r' \mapsto \frac 1 2, h' \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $b \domps\psi c$.
\item
If $(h,\overline h)(b,c) = (a,a)$, let $h' = h[\pr_1,h]$.
Here \smash{$h' \in \upa b a \doa c a$} and $(h',\overline{h'})(b,c) \in \smallmispic b a b a$, so the previous case applies.
\item
If $(h,\overline h)(b,c) \in \smallcrosspic c b c b$, let $h' = r[h,\overline{h}]$.
Here \smash[b]{$h' \in \upa b a \doa c a$} and also $(h',\overline{h'})(b,c) \in \smallflipmispic c a c a$, so other cases can be used.
\ei
\item
If $(r,\overline r)(b,c) \in \smallmispic b a b a$, let $r' = h[r,\overline{r}]$.
Here either $r', h'=r'[h,\overline{h}]$ are complementary and $(\Gamma,\nu)$ is of type \typegwtp,
or $\psi = \{ r' \mapsto \frac 1 2, h' \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $b \domps\psi c$.
\ei

\item
If there is $r \in \pol(\Gamma)$ \st $(r,\overline r)(b,c) \not\in \smallmispic c b c b$ and \smash[t]{$r \in \upa b a \doa c a$},
then by arguments symmetric to the ones above, $(\Gamma,\nu)$ is of type \typegwtp\@.

\item
Otherwise, every $r \in \pol(\Gamma)$ \st $(r,\overline r)(b,c) \not\in \smallmispic c b c b$ satisfies \smash{$r \in \upa b a \upa c a$}.
This contradicts that $\omega \in \fpol(\Gamma,\nu)$.
\ei
\ee

\item
If $\smallcrosspic b a b a \not\in \Gamma$ and $\smallcrosspic c a c a \in \Gamma$,
then, by \lemref{lem:fpol}, we may assume \smash{$h \in \doa b a$} for some $h \in \supp(\omega)$.

If there is $f' \in \supp(\omega)$ \st $(f',\overline{f'})(a,b) \in \smallcrosspic b a b a$ and $(f',\overline{f'})(b,c) \not\in \smallmispic c b c b$, then $\psi = \{h[f',\overline{f'}] \mapsto \frac 1 2, \overline{h[f',\overline{f'}]} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi b$.
And, if there is $i \in \supp(\omega)$ \st $i \in \doa b a$ and $i \not\in \upa c b$, then $\psi = \{i \mapsto \frac 1 2, \overline{i} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi b$.
Since we can assume that no operation in $\supp(\omega)$ is a projection on both $\{a,b\}$ and $\{b,c\}$,
this means that if $j \in \supp(\omega)$ and $j \not\in \upa b a$, then $j \in \upa c b$.
So, unless $\omega$ is \st $a \domps\omega b$ or $c \domps\omega b$, it must hold that $f,h$ are complementary, and $(\Gamma,\nu)$ is of type \typegwtp\@.

\item
If $\smallcrosspic b a b a \in \Gamma$ and $\smallcrosspic c a c a \not\in \Gamma$,
then, arguments symmetric to those in the case above establishes that $(\Gamma,\nu)$ is of type \typegwtp\@.

\item
If $\smallcrosspic b a b a \in \Gamma$ and $\smallcrosspic c a c a \in \Gamma$, the following holds.
If $(f,\overline f)(b,c) \ne (a,a)$, then $\psi = \{f \mapsto \frac 1 2, \overline f \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and either $b \domps\psi c$ or $c \domps\psi b$.
Otherwise $(f,\overline f)(b,c) = (a,a)$ and, by \lemref{lem:extend:arithm}, $(\Gamma,\nu)$ is of type \typegwtp\@.
\ee

\subsection{$\{a,b\} \in \Gamma$, $\{a,c\} \not\in \Gamma$, $\{b,c\} \in \Gamma$}

By \lemref{lem:fpol} there is $\omega \in \fpol(\Gamma,\nu)$ and $f \in \supp(\omega)$ \st \smash{$(f,\overline f)(a,c) \in \smallallpic b a b a$}
and $\nu(f(a,c)) + \nu(f(c,a)) \le \nu(a)+\nu(c)$.
\be
\item
If \smash{$\smallcrosspic b a b a \not\in \Gamma$ and $\smallcrosspic c b c b \not\in \Gamma$},
then, by \lemref{lem:fpol}, we may assume that there is $g,h \in \supp(\omega)$ \st $g \in \doa b a$ and $h \in \doa c b$.
Since $\{a,c\} \not\in \close{\Gamma}$ there is $f \in \pol(\Gamma)$ \st $f(c,a)=b$.
We can assume $f(a,c) \in \{a,b\}$ since otherwise $f'=h[f,\overline f]$ satisfies the property.

If there is $i \in \pol(\Gamma,\nu) \cap \doa b a \doa c b$, then $h' = i[ i[\pr_1,f], \overline{i[\pr_1,f]} ] \in \doa b a \doa c a \doa c b$.
Here $\psi = \{ h' \mapsto \frac 1 2, \overline{ h' } \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$.

Otherwise $\pol(\Gamma) \cap \doa c b \subseteq \upa b a$ and $\pol(\Gamma) \cap  \doa b a \subseteq \upa c b$.
In the following we assume $f(a,c)=f(c,a)=b$ since if this does not hold, then $g[f,\overline{f}]$ satisfies the property.
\bi
\item
If thers is $f \in \supp(\omega)$ that is a projection on $\{a,b\}$, $\{b,c\}$ and satisfies $(f,\overline f)(a,c) \in \smallallpic b a b a$, then
\bi
\item
if $(f,\overline f)(a,c) \in \smallflipmispic b a b a$,
then $\psi = \{ f \mapsto \frac 1 2, \overline{f} \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$,
\item
otherwise $(f,\overline f)(a,c) = (b,b)$.
Note that we might assume $2 \nu(b) \le \nu(a)+\nu(c)$, since otherwise we can modify $\omega$ by setting $\omega(f)=0$ and rescaling the function so that $\sum_{f \in \binopers} \omega(f)=1$. This gives another fractional polymorphism that satisfies our conditions.
Since $h'= h[f,\overline{f}] \in \doa a b \doa c b$, $g' = g[f,\overline{f}] \in \upa a b \upa c b$ and $h'(a,c)=h'(c,a)=g'(a,c)=g'(c,a)=b$,
this means that $(\Gamma,\nu)$ is of type \typebsm\@.
\ei

\item
Otherwise we can assume that $\supp(\omega) = \Omega_1 \cup \Omega_2$, where $\Omega_1 = \supp(\omega) \cap \doa b a \upa c b$
and $\Omega_2 = \supp(\omega) \cap \upa b a \doa c b$.
\bi
\item
If there is $f \in \supp(\omega)$ \st \smash{$(f,\overline f)(a,c) \in \smallflipmispic b a b a$}, then \smash{$f'=g[f,\overline{f}] \in \doa c a$}
and $f \in \doa b a \upa c b$ or $f \in \upa b a \doa c b$.
Assume \wlg the latter holds, then $f',g'=f'[g,\overline{g}]$ are complementary and $(\Gamma,\nu)$ is of type \typegwtp,
or $\psi = \{f' \mapsto \frac 1 2, g' \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$.

\item
Otherwise every $f \in \supp(\omega)$ \st $(f,\overline f)(a,c) \in \smallallpic b a b a$ is commutative and satisfies $f(a,c)=b$.
If there is any $f \in \supp(\omega)$ \st $(f,\overline f)(a,c) \in \smallcrosspic c b c b$, then $\omega$ can be modified by changing $f$ to $h[f,\overline{f}]$.
We therefore assume that every $f \in \supp(\omega)$ that is not a projection on $\{a,c\}$ is commutative on $\{a,c\}$ and satisfies $f(a,c) \in \{b,c\}$.
\bi
\item
If $\nu(a)+\nu(c) < 2\,\nu(b)$, then since not all operations in $\supp(\omega)$ are projection on $\{a,c\}$ it is impossible that $\omega \in \fpol(\Gamma,\nu)$.
\item
If $\nu(a)+\nu(c) \ge 2\,\nu(b)$, then since $\omega \in \fpol(\Gamma,\nu)$ and $\nu(a) < \nu(b)$ there must be $f_1 \in \Omega_1, f_2 \in \Omega_2$ \st $f_1(a,c)=f_2(a,c)=b$.
So $(\Gamma,\nu)$ is in this case of type \typebsm\@.
\ei
\ei
\ei

\item
If $\smallcrosspic b a b a \not\in \Gamma$ and $\smallcrosspic c b c b \in \Gamma$,
then, by \lemref{lem:fpol}, we may assume \smash{$g \in \doa b a$} for some $g \in \supp(\omega)$.
Assume \wlg that $g|_{\{b,c\}} = \pr_1$.
\bi
\item
If \smash[t]{$(f,\overline f)(a,c) \in \smallflipmispic b a b a$}, set $f'=g[f,\overline f]$.
Note that $\psi = \{f' \mapsto \frac 1 4, \overline{f'} \mapsto \frac 1 4, g \mapsto \frac 1 4, \overline{g} \mapsto \frac 1 4\} \in \fpol(\Gamma,\nu)$.
Unless $a \domps\psi c$ it holds that $g \in \upa c a$.
This means that $f',g \in \pol(\Gamma \cup \{ \{a,c\} \})$, so either $a \domps\psi b$
or $f',g$ are complementary and $(\Gamma \cup \{ \{a,c\} \},\nu)$ is of type \typegwtp\@.
\item
Otherwise $f(a,c)=f(c,a)=b$, and
\smash{$g'=g[ g[f,\pr_1], \overline{g[f,\pr_1]} ] \in \doa c a \doa b a$},
so $\psi = \{ g' \mapsto \frac 1 2, \overline{g'} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$.
\ei

\item
If $\smallcrosspic b a b a \in \Gamma$ and $\smallcrosspic c b c b \not\in \Gamma$,
then, by \lemref{lem:fpol}, we may assume \smash{$h \in \doa c b$} for some $h \in \supp(\omega)$.
Assume \wlg that $h|_{\{a,b\}}=\pr_1$.

Since $\{a,c\} \not\in \close{\Gamma}$ there is a binary operation $f \in \pol(\Gamma)$ \st $f(a,c)=b$.
Let $f' = h[f,\overline{f}]$ and note that $(f',\overline{f'})(a,c) \in \smallmispic b a b a$.
\bi
\item
If $(h,\overline h)(a,c) \in \smallflipmispic c a c a \cup \smallcrosspic b a b a$,
then $\psi = \{h \mapsto \frac 1 2, \overline{h} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $b \domps\psi c$.
\item
If $(h,\overline h)(a,c) = (b,b)$, then let $h' = h[\pr_1,h]$ and note that
$\psi = \{h' \mapsto \frac 1 2, \overline{h'} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $b \domps\psi c$.
\item
If $(h,\overline h)(a,c) \in \smallcrosspic c b c b$, then $h'=h[h,\overline{h}] \in \doa c b$, $h'|_{\{a,b\}} = \pr_1$
and $(h,\overline h)(a,c) = (b,b)$, so the previous case is applicable.
\item
If $(h,\overline h)(a,c) = (c,c)$, then
$h'=h[f',h] \in \doa c b$, $(h',\overline{h'})(a,c) \in \smallflipmispic c b c b$ and $h'$ is a projection.
So one of the previous cases apply.
\ei

\item
If $\smallcrosspic b a b a \in \Gamma$ and $\smallcrosspic c b c b \in \Gamma$, then,
\bi
\item
if $(f,\overline f)(a,c) \in \smallflipmispic b a b a$,
then $\psi = \{f \mapsto \frac 1 2, \overline f \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$,
\item
otherwise $(f,\overline{f})(a,c)=(b,b)$ and, by \lemref{lem:extend:arithm}, $(\Gamma,\nu)$ is of type \typegwtp\@.
\ei
\ee

\subsection{$\{a,b\} \in \Gamma$, $\{a,c\} \not\in \Gamma$, $\{b,c\} \not\in \Gamma$}
By \lemref{lem:fpol} there is $\omega \in \fpol(\Gamma,\nu)$ and $f \in \supp(\omega)$ \st $(f,\overline f)(a,c) \in \smallallpic b a b a$.
By \lemref{lem:hascross}, $\smallcrosspic b a b a \in \Gamma$, or $(\Gamma,\nu)$ is of type \typegmc\@.
Since $\{b,c\} \not\in \close{\Gamma}$ we have $g \in \pol(\Gamma)$ \st
\smash[b]{$(g,\overline g)(b,c) \in \mypic{ \makeline 0 0 \makeline 0 1 \makeline 1 0 \makeline 0 2 \makeline 2 0 }$}.
Let $g' = f[g,\overline g]$, now $(g',\overline{g'})(b,c) \in \smallallpic b a b a$.
\bi
\item
If $(f,\overline{f})(c,b) \in \smallcrosspic c b c b$, then
\bi
\item
if $(f,\overline{f})(a,c) \in \smallflipmispic b a b a$, then $\psi = \{f \mapsto \frac 1 2, \overline{f} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$,
\item
otherwise $(f,\overline{f})(a,c) = (b,b)$.
Let $f' = f[f,\overline{f}]$ and note that $f'|_{\{a,b\}} = \pr_1$, $f'|_{\{b,c\}} = \pr_1$ and $f'(a,c)=f'(c,a)=b$.
With $g'' = g'[g',\overline{g'}]$ and $f'' = g''[\pr_1,f']$ it holds that $\psi = \{f'' \mapsto \frac 1 2, \overline{f''} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$.
\ei
\item
If $(f,\overline{f})(c,b) \in \smallallpic b a b a$, then
\bi
\item
if $(f,\overline{f})(a,c) \in \smallflipmispic b a b a$, then $\psi = \{f \mapsto \frac 1 2, \overline{f} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$,
\item
otherwise $(f,\overline{f})(a,c) = (b,b)$.
Let $f' = f[f,\overline{f}]$ and note that $f'|_{\{a,b\}} = \pr_1$, $f'(b,c),f'(c,b) \in \{a,b\}$ and $f'(a,c)=f'(c,a)=b$.
With $f'' = f'[\pr_1,f']$ it holds that $\psi = \{f'' \mapsto \frac 1 2, \overline{f''} \mapsto \frac 1 2\} \in \fpol(\Gamma,\nu)$ and $a \domps\psi c$.
\ei
\item
If $(f,\overline{f})(c,b) \in \smallcrosspic c a c a$, then $f' = f[f,\overline{f}]$ satisfies $f'|_{\{a,b\}} = \pr_1$,
$(f,\overline{f})(a,c) \in \smallallpic b a b a$ and $(f,\overline{f})(b,c) \in \smallallpic b a b a$, so the previous case applies.
\item
Otherwise $f \in \upa c b$.
\bi
\item
If $(f,\overline{f})(a,c) \in \smallmispic b a b a$, then assume \wlg $f(c,a) = b$.
Let $f'=g'[\pr_1,f]$.
Now $f'|_{\{a,b\}}$ is a projection, $(f',\overline{f'})(a,c) \in \smallallpic b a b a$ and $f' \not\in \upa c b$, so we may use one of the previous cases.
\item
Otherwise $f \in \doa c a$.
Since $\{a,c\} \not\in \Gamma$, there is $i \in \pol(\Gamma)$ \st $i(c,a)=b$.
Note that $f' = i(\pr_1,f)$ satisfies $(f',\overline{f'})(a,c)=(a,b)$.
This takes us to the previous case.
\ei
\ei

\subsection{$\{a,b\} \not\in \Gamma$, $\{a,c\} \in \Gamma$, $\{b,c\} \not\in \Gamma$}
By \lemref{lem:fpol} there is $\omega \in \fpol(\Gamma,\nu)$ and $g \in \supp(\omega)$ \st $g \in \doa b a$.
By \lemref{lem:hascross}, $\smallcrosspic c a c a \in \Gamma$, or $(\Gamma,\nu)$ is of type \typegmc\@.
Unless $a \domps\omega b$ every $i \in \supp(\omega)$ is conservative on $\{a,b\}$.
Since $\{b,c\} \not\in \Gamma$ we also have $h \in \pol(\Gamma)$ \st $h(b,c)=a$.

Let $R$ be the relation generated by $\pol(\Gamma)$ from $\smallcrosspic c b c b$.
Since $h(b,c)=a$, $R$ can not equal $\smallmispic c b c b$ or $\smallcrosspic c b c b$.
Neither does $R$ equal $\mypic{\makeline 2 1 \makeline 1 2 \makeline 0 2 \makeline 2 0}$
or $\mypic{\makeline 2 2 \makeline 2 1 \makeline 1 2 \makeline 0 2 \makeline 2 0}$.
To see this note that;
in the fist case, since $\{c\} \in \Gamma$, it follows that $\{a,b\} \in \close{\Gamma}$, a contradiction,
and, in the second case there can not be a ternary operation $m \in \pol(\Gamma)$ that is arithmetic on $\{a,c\}$, this contradicts that $\{a,c\}$ is a cross-pair.
Hence, there must be $f \in \pol(\Gamma)$ \st $(f,\overline f)(b,c) \in \smallallpic b a b a$.

If $g \not\in \upa c b$,
then $\psi = \{ g \mapsto \frac 1 2, \overline{g} \mapsto \frac 1 2 \} \in \fpol(\Gamma,\nu)$ and $a \domps\psi b$.
We therefore assume $\pol(\Gamma) \cap \doa b a \subseteq \upa c b$.
This means that $\psi = \{ g \mapsto \frac 1 4, \overline{g} \mapsto \frac 1 4, f \mapsto \frac 1 4, \overline{f} \mapsto \frac 1 4 \} \in \fpol(\Gamma,\nu)$. So either $f,g$ are complementary and $(\Gamma,\nu)$ is of type \typegwtp, or $a \domps\psi b$ or $c \domps\psi b$.

\subsection{$\{a,b\} \not\in \Gamma$, $\{a,c\} \not\in \Gamma$, $\{b,c\} \in \Gamma$}
By \lemref{lem:fpol} there is $\omega \in \fpol(\Gamma,\nu)$ and $f',g \in \supp(\omega)$ \st $(f',\overline{f'})(a,c) \in \smallallpic b a b a$ and $g \in \doa b a$.
By \lemref{lem:hascross}, $\smallcrosspic c b c b \in \Gamma$, or $(\Gamma,\nu)$ is of type \typegmc\@.
Assume \wlg that $g|_{\{b,c\}}=\pr_2$.
Let $f$ be any operation in $\pol(\Gamma) \cap \doa c a$.
Such an operation must exist.
Note that $h = g[f',\overline{f'}]$ satisfies $h(a,c)=h(c,a) \in \{a,b\}$. If $h \not\in \doa c a$, then $g[ g[ \pr_1, h ], \overline{g[ \pr_1, h ]} ] \in \doa c a$.
\bi
\item
If $(f,\overline{f})(a,b) \in \smallallpic b a b a$, then
$\psi = \{ f \mapsto \frac 1 4, \overline{f} \mapsto \frac 1 4, g \mapsto \frac 1 4, \overline{g} \mapsto \frac 1 4\} \in \fpol(\Gamma \cup \{ \{a,b\} \},\nu)$.
Unless $a \domps\psi c$ we have $g \in \upa c a$, this means that $f,g \in \pol(\Gamma \cup \{ \{a,b\}, \{a,c\} \})$, so either
$f,g$ are complementary and $(\Gamma \cup \{ \{a,b\}, \{a,c\} \},\nu)$ is of type \typegwtp, or $a \domps\psi b$.

\item
If $(f,\overline{f})(a,b) \in \smallcrosspic c a c a$, then $f' = f[f,\overline{f}] \in \doa c a \doa b a$, so the previous case applies.

\item
If $(f,\overline{f})(a,b) \in \smallcrosspic c b c b$, then assume \wlg that $f(a,b)=c$.
It is easily checked that $g[ f[\pr_1,f], \overline{f[\pr_1,f]} ] \in \doa b a \doa c a$, so the first case applies.

\item
If $(f,\overline{f})(a,b) = (c,c)$, then assume \wlg $f|_{\{b,c\}} = \pr_1$.
Once more we have $g[ f[ \pr_1 ,f ], \overline{f[ \pr_1 ,f ]} ] \in \doa b a \doa c a$, so again the first case applies.
\ei

\subsection{$\{a,b\} \not\in \Gamma$, $\{a,c\} \not\in \Gamma$, $\{b,c\} \not\in \Gamma$}
By \lemref{lem:hascross}, $R = \mypic{ \makeline 2 0 \makeline 1 1 \makeline 0 2 } \in \Gamma$, or $(\Gamma,\nu)$ is of type \typegmc\@.
In what follows we assume that $(\Gamma,\nu)$ is not of type \typegmc\@.
A consequence of this is that, for every binary function $f \in \pol(\Gamma)$, it holds that $f(a,c)=f(c,a)=b$ or $f|_{\{a,c\}}=\pr_1$ or $f|_{\{a,c\}}=\pr_2$.

By \lemref{lem:fpol} there is $\omega \in \fpol(\Gamma,\nu)$ and $g, h, i \in \supp(\omega)$ \st $(g,\overline{g})(a,c) \in \smallallpic b a b a$, $h \in \doa b a$ and $(i,\overline{i})(b,c) \in \smallallpic b a b a \cup \smallcrosspic c a c a$.
Since $R \in \Gamma$ this means that $g(a,c)=g(c,a)=b$, $2 \nu(b) \le \nu(a)+\nu(c)$ and $h \in \upa c b$.
Hence, $h' = g[h,\overline{h}] \in \upa a b \upa c b$ and $h'(a,c)=h'(c,a)=b$.
\bi
\item
If $(i,\overline{i})(b,c) \in \smallcrosspic c a c a$, then $i' = h'[i,\overline{i}] \in \doa c b$ and $i'(a,c)=i'(c,a)=b$.
\item
If $(i,\overline{i})(b,c) \in \smallflipmispic b a b a$, then $i'' = h'[i,\overline{i}]$ satisfies $i''(b,c)=i''(c,b)=a$ and $i''(a,c)=i''(c,a)=b$.
Since $\{a,c\}\not\in\Gamma$ there is some binary $p \in \pol(\Gamma)$ \st $p(a,c)=b$.
This means that $i'=p[i'',h'] \in \doa c b$ and $i'(a,c)=i'(c,a)=b$.
\item
Otherwise $i \in \doa c b$.
Here $i'=g[i,\overline{i}]$ satisfies $i' \in \doa c b$ and $i'(a,c)=i'(c,a)=b$.
\ei
Since $i'$ must preserve $R$ it also holds that $i' \in \upa b a$.
By $i',h'$ we see that $(\Gamma,\nu)$ is of type \typebsm\@.

\section {Proof of \lemref{lem:fpol}}
\label{s:lem:fpol}
We need the following variant of Motzkin's Transposition Theorem that is easy to derive from \thmref{thm:motzkin}.
\begin{theorem}
\label{thm:motzkin:2}
For any $A \in \bbbq^{m \times n}$ and $B \in \bbbq^{p \times n}$, exactly one of the following holds:
\bi
\item $Ax \le 0$, $Bx < 0$ for some $x \in \qplus^n$
\item $A^Ty + B^Tz \ge 0$ and $z \ne 0$ for some $y \in \qplus^m$ and $z \in \qplus^p$
\ei
\end{theorem}

Let $\sigma : D \to \qplus \cup \{\infty\}$ be a function in $\eclose{\Gamma,\Delta}$ and for $\nu \in \Delta$ let $D_{\nu} = \{x \in D : \nu(x)<\infty\}$.
Let $\Omega_1 = \{f \in \binopers \cap \pol(\Gamma) : \nu(f(x,y))<\infty \text{ for every } \nu \in \Delta \text{ and } x,y \in D_{\nu}\}$ and $\Omega_2 = \{f \in \Omega_1 : \{f(a,b),f(b,a)\} \ne \{a,b\} \text{ and } \sigma(f(a,b))+\sigma(f(b,a)) \le \sigma(a)+\sigma(b) \}$.
Assume there are $p_{\nu,(x,y)} \in \qplus$ for $\nu \in \Delta$ and $(x,y) \in D_{\nu}^2$ \st
\bna
\label{ineq:1}
&\ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)} \nu(g(x,y))
\ge \ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)}  \nu(\pr_i(x,y)), \quad g \in \Omega_1, i\in[2],\\
\label{ineq:2}
&\ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)} \nu(g(x,y))
>   \ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)}  \nu(\pr_i(x,y)), \quad g \in \Omega_2, i\in[2].
\ena
We will show that in this case we have $\smallcrosspic{a}{b}{a}{b} \in \wclose{\Gamma,\Delta}$.
Create an instance $I$ of \minhom$(\Gamma,\Delta)$ with variables $D^2$, and objective
\ba
m(\phi) &= \ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)} \nu(\phi(x,y)) + \epsilon \ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} \nu(\phi(x,y)),
\ea
where $\epsilon > 0$ is choosen small enough so that $\phi \in \argmin_{\phi' \in \Omega_1} m(\phi')$ implies
$\phi \in \argmin_{\phi' \in \Omega_1} \sum_{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)} \nu(\phi(x,y))$.
Such a number $\epsilon$ can always be found.
Note that a solution $\phi$ to $I$ with finite measure is a function $D^2 \to D$ \st $\nu(\phi(x,y))<\infty$ for every $\nu \in \Delta$ and $(x,y) \in D_{\nu}^2$.

Pick, for every $g \in \binopers \setminus \pol(\Gamma)$, a relation $R_g \in \Gamma$ \st $g$ does not preserve $R_g$.
Add for each pair of tuples $t^1,t^2 \in R_g$ the constraint $(( (t^1_1,t^2_1), \dots, (t^1_{\ar R_g},t^2_{\ar R_g}) ), R_g)$.
Now a solution to $I$ is a binary polymorphism of $\Gamma$.
Hence, if $\phi$ is a solution to $I$ with finite measure, then $\phi \in \Omega_1$.
Clearly $\pr_1$ and $\pr_2$ satisfies all constraints and are solutions to $I$ with finite measure.
By \eqref{ineq:1} the projections are also optimal solutions.
By \eqref{ineq:2} any function in $\Omega_2$ has a larger measure than $\pr_1$ or $\pr_2$.
Hence, if $P = \{(\phi(a,b),\phi(b,a)): \phi \in \optsol(I)\}$ we have $\argmin_{(x,y)\in P} (\sigma(x)+\sigma(y)) = \smallcrosspic a b a b$, and therefore $\smallcrosspic a b a b \in \wclose{\Gamma,\Delta}$.

This of course means that the system \eqref{ineq:1}+\eqref{ineq:2} can not be satisfied.
We can write \eqref{ineq:1}+\eqref{ineq:2} as
\begin{flalign*}
&& \ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)} (\nu(\pr_i(x,y))-\nu(g(x,y))) &\le 0, &\mathpalette\mathllapinternal{g \in\Omega_1, i \in [2],}\\
&& \ssum{\nu \in \Delta, (x,y) \in D_{\nu}^2} p_{\nu,(x,y)} (\nu(\pr_i(x,y))-\nu(g(x,y))) &<   0, &\mathpalette\mathllapinternal{g \in\Omega_2, i \in [2]}.
\end{flalign*}
If this system lacks a solution $p_{\nu,(x,y)} \in \qplus$ for $\nu \in \Delta, (x,y) \in D_{\nu}^2$, then by \thmref{thm:motzkin:2}, there are $z_{i,j,g} \in \qplus$ for $i,j \in [2]$, $g \in \Omega_1$ \st
\begin{flalign*}
&& \ssum{i \in [2], j \in [2], g \in \Omega_j} (\nu(\pr_i(x,y))-\nu(g(x,y))) z_{i,j,g} &\ge 0, &\mathpalette\mathllapinternal{\nu \in \Delta, (x,y) \in D_{\nu}^2,}
\end{flalign*}
where $z_{i,2,g} > 0$ for some $i \in [2], g \in \Omega_2$.
So
\begin{flalign*}
&& \ssum{i \in [2], j \in [2], g \in \Omega_j} (\nu(x)+\nu(y)-\nu(g(x,y))-\nu(g(y,x))) z_{i,j,g} &\ge 0,\quad\quad\quad\quad\quad &\mathpalette\mathllapinternal{\nu \in \Delta, (x,y) \in D_{\nu}^2,}
\end{flalign*}
and with $z_{j,g} = z_{1,j,g} + z_{2,j,g}$ we have
\begin{flalign*}
&& \ssum{j \in [2], g \in \Omega_j} (\nu(x)+\nu(y)-\nu(g(x,y))-\nu(g(y,x))) z_{j,g} &\ge 0,\quad\quad\quad\quad\quad &\mathpalette\mathllapinternal{\nu \in \Delta, (x,y) \in D_{\nu}^2,}
\end{flalign*}
Let $z'_{j,g} = z_{j,g} + z_{j,\overline g}$ and note that
\begin{flalign*}
&& \ssum{j \in [2], g \in \Omega_j} (\nu(x)+\nu(y)-\nu(g(x,y))-\nu(g(y,x))) z'_{j,g} &\ge 0,\quad\quad\quad\quad\quad &\mathpalette\mathllapinternal{\nu \in \Delta, (x,y) \in D_{\nu}^2,}
\end{flalign*}
and therefore, since $z'_{j,g} = z'_{j,\overline g}$ for $j \in [2]$,
\begin{flalign*}
&& \ssum{j \in [2], g \in \Omega_j} (\nu(x)+\nu(y)-2\nu(g(x,y))) z'_{j,g} &\ge 0, &\mathpalette\mathllapinternal{\nu \in \Delta, (x,y) \in D_{\nu}^2,}
\end{flalign*}
Note that by construction $z'_{2,g} > 0$ for some $g \in \Omega_2$.
We can rewrite this system into
\begin{flalign*}
&& \ssum{g \in \binopers} \omega(g) \nu(g(x,y)) &\le \frac{1}{2} ( \nu(x) + \nu(y) ), &\mathpalette\mathllapinternal{\nu \in \Delta, (x,y) \in D_{\nu}^2,}
\end{flalign*}
by defining $\omega : \binopers \to \qplus$ as
\ba
\omega(g) =
\frac{ \chi_{\Omega_1}(g) 2z'_{1,g} + \chi_{\Omega_2}(g) 2z'_{2,g} }
     {\sum_{g \in \binopers} (\chi_{\Omega_1}(g) 2z'_{1,g} + \chi_{\Omega_2}(g) 2z'_{2,g} )}.%
\footnotemark
\ea%
\footnotetext{Here $\chi_\Omega : \binopers \to \{0,1\}$ is the indicator function for the set $\Omega$.}
Clearly $\omega \in \fpol(\Gamma,\Delta)$ and $\omega(g) > 0$ for some $g \in \Omega_2$.

\section {Proof of \lemref{lem:hasconst}}
\label{s:hasconst}

Let $D = \{a,b,c\}$ and $\nu : D \to \qplus$ be \st $\nu(a) < \nu(b) < \nu(c)$.
We assume that $(\Gamma,\nu)$ is a min-core.
Let:
\ba
\gamma_1 = \mypic{ \makeline 2 0 \makeline 0 2 },\,
\gamma_2 = \mypic{ \makeline 1 0 \makeline 0 1 },\,
\gamma_3 = \mypic{ \makeline 1 2 \makeline 2 1 },\,
\gamma_4 = \mypic{ \makeline 2 0 \makeline 1 2 },\,
\gamma_5 = \mypic{ \makeline 1 0 \makeline 0 2 },\,
\gamma_6 = \mypic{ \makeline 2 0 \makeline 1 1 },\,
\gamma_7 = \mypic{ \makeline 2 0 \makeline 1 1 \makeline 0 2 }.
\ea

\begin{lemma}
\label{lem:hascross}
If $(\Gamma,\nu)$ is not of type \typegmc, then $\gamma_i \in \wclose{\Gamma,\nu}$, for some $i \in [7]$.
\end{lemma}
\begin{proof}
We will make use of the following fact~\cite[Lemma~5.6]{maxonesgen}:
If $(\Gamma,\nu)$ is of type \typegmc, then for every $R \in \Gamma$ we have $(\min_\nu \pr_1(R), \dots, \min_\nu \pr_{\ar(R)}(R) ) \in R$.
We say that a relation $R$ is generalised min-closed if this property is satisfied.

If $\Gamma$ is not of type \typegmc, then there is $R \in \Gamma$ that is not generalised min-closed.
Consider first the case when $\ar(R)=2$.
Let $w_1$ be the $\nu$-minimal element in $\pr_1(R)$, and $w_2$ be the $\nu$-minimal element in $\pr_2(R)$.
Let $q_1$ be the $\nu$-minimal element in $\{ x : (x,w_2) \in R\}$, and $q_2$ be the $\nu$-minimal element in $\{ y : (w_1,y) \in R\}$.
Set $\alpha = \frac{\nu(q_2)-\nu(w_2)}{\nu(q_1)-\nu(w_1)}$.
Now either $\argmin_{(x,y) \in R} \alpha \nu(x) + \nu(y)$ or its inverse is one of $\gamma_1,\dots,\gamma_7$.
This establishes the claim for $\ar(R)=2$.
Assume it holds also for every relation $R$ with $\ar(R)<m$.
Let $R_i = \{ (x_1,\dots,x_m) \in R : x_i \text{ is $\nu$-minimal in } \pr_i(R) \}$.
If $R_i$ is not generalised min-closed for some $i \in [m]$, then $\pr_{[m]-i}(R)$ is not generalised min-closed, so the result follows from the inductive hypothesis.
Otherwise $(q,w_2,\dots,w_m), (w_1,r,w_3,\dots,w_m) \in R$ where $w_i$ is the $\nu$-minimal element in $\pr_i(R)$ and $q$, $r$ are not $\nu$-minimal elements in $\pr_1(R)$ respective $\pr_2(R)$.
This means that $P = \{ (x,y) : (x,y,z_3,\dots,z_m) \in R \text{ and $z_i$ is $\nu$-minimal in } \pr_i(R)\}$ is not generalised min-closed, so again, the result follows from the inductive hypothesis.
\hfill\qed
\end{proof}

By \lemref{lem:hascross} we know that $\gamma_k \in \wclose{\Gamma,\nu}$, for some $k \in [7]$.
This immediately yields two constants: $\pr_1(\argmin_{(x,y) \in \gamma_k} \nu(x))$ and $\pr_1(\argmin_{(x,y) \in \gamma_k} \nu(y))$.

We may \wlg assume that one of these constants is $a$ since we always have $\argmin_{x \in D} \nu(x) = \{a\} \in \wclose{\Gamma,\nu}$.
Assume that the second constant is $c$ (the arguments for the other case is analogous).
Let $f = \{ a \mapsto a, b \mapsto a, c \mapsto c \}$.
Since $\Gamma$ is a min-core, we have $f \not\in \pol(\Gamma)$.
We must therefore have a wittiness $P \in \Gamma$ \st $t \in P$ but $f(t) \not\in P$.
Let $P' = \{ x : (z_1,\dots,z_{\ar(P)}) \in P \}$ where $z_i = c$ if $t_i=c$, $z_i = a$ if $t_i=a$ and $z_i = x$ otherwise.
Clearly $\{b\} = \argmin_{x \in P'} \nu(x)$.

\end{document}

redpajama_set_name: RedPajamaArXiv


text:
Узбеков — фамилия.

 Узбеков, Рашид Якубович (1953—2001) — советский футболист, советский и азербайджанский тренер.
 Узбеков, Умирзак Узбекович (род. 1947) — советский и казахстанский государственный и политический деятель.
 Узбеков, Шагибек — штабс-ротмистр Башкирской армии (1918—1919), член Башкирского военного совета.

 Узбекова, Динара Галиевна (1933—2020) — советский и российский фармаколог.

См. также
 Юзбеков, Зейдула Кадималиевич


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