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Saint Katherine Greek Orthodox Church
Bakaliko
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Greek Orthodox Metropolis of Atlanta
Regional Dance
Introduction to Hellenic (Greek) Dancing
Greek dancing is an incredibly old tradition that bonds Greek communities together. With roughly more than 4,000 different dances throughout the various 12 regions, it is impossible to learn all the variations and styles in a lifetime. Regions were formed by citizenry and islanders who performed, choreographed, and style their dancing with similarities and purpose, which were distinct from the other regions.
The Grecian Odyssey Dancers learn dances from all the various regions. Each year we research the various regions seeking a specific village or dance style within that region.
The regions we danced in 2020 were:
Aegean Islands Region
Chios is the fifth largest Greek island situated in the Aegean Sea. Chios is notable for its exports of mastic gum and has the nickname "The Mastic Island". Chios is believed by some scholars to be the birthplace of Christopher Columbus. He visited the island to obtain mapping material before his famous voyage leading to the discovery of America.
Chios dances are unique and distinct and rich with history.
Srytos – is a folk dance in which the dancers link hands to form a chain or circle, headed by a leader who intermittently breaks away to perform improvised steps. Aegean syrtos usually opens a performance. This syrtos is danced to the song of "ΜΕΣ ΤΟΥ ΑΙΓΑΙΟΥ ΤΑ ΝΗΣΙΑ" which is a ballot song by many of the islands within the Aegean Sea. It prays for the Virgin Mary to bring peace and calm to the Aegean Sea where the angels flutter and the roses scatter.
Ballos – Stin Agia Markella is a flirting dance in a ballos format. The melody of a ballos is generally joyous and lyrical which is typical of the music of the Aegean Islands. This couples' dance incorporates all the elements of courtship: attraction, flirtation, display of masculine prowess and feminine virtue, pursuit, and rejection followed by eventual capture and surrender. Its origin is in the island culture of Greece. Men could not approach women easily, so they created this dance in order to "flirt" with them.
Agia "Saint" Markella was born in Volissis, Chios. Fleeing the wrath of her pagan father she was mortally wounded, but legend has it her body was consumed by the island and that her blood spilled gave rise to the red nature of the dirt that is distinct to the island and its ability to grow the mastic trees.
Pirgousikos – It's from the pyrgi village of Chios. It's mainly danced during the Greek Halloween which is before the beginning of the Easter great lent. Dancing during this celebration lasted until morning hours. At times the unmarried girls joined the married one so the men of the village can notice them. Fathers tipped the band or "tsambounieri" so he can play all night so the girls can get a chance to be noticed
Trexados – after the pyrgousikos dance the night usually ended with an energetic trexatos dance with the young men leading it. Trexatos means "running", and as such, features a high energy fast paced dance.
Cyclades Region
Armogos is the easternmost island of the Cyclades. While a small island with approximately 2,000 in population today, it played a significant role in the history of Greece. Three distinct cities served as ports that were the center of trade from the east and west. Armogos suffered at the hands of Turkish invaders, pirates, and other hardships along its shoreline. Primary settlements were built inland in fortresses to protect the people. The island was instrumental in the liberation of Greece during the War of Independence in 1821. After its independence was gained, many of the islanders moved to Athens to work as stone cutters, which they were famous for. This led to a decline in the population on the island. Now primarily a few small villages, the island leads a monastic lifestyle. In 1956 the island was nearly destroyed by an earthquake that created a 30-meter-high (about 85 feet) tsunami.
Syrtos – This dance style was originated in western Crete. Historians believe that Crete controlled and ruled the island for many years and instilled some of its customs to the people. Although no evidence can prove this claim to date, it is clear that the Crete people had an influence on the customs and practices of Armogos. None more evident than the Syrto.
Armogos Sousta – formerly a war dance, the sousta is a dance of love and passion. In Greek, "sousta" means spring, and this dance took its name from the springing movements in the dancers' steps. The sousta originated and is more prolific in the Aegean Islands and Crete. As each island and region adapted some form of the sousta dance, each with their own variations, the dance became known as Sousta along with the name of the island or region in order to distinguish these variations.
Nikedre – this dance originated in Naxos, a neighboring island (of which our girls costumes are from), and was meant as a comical dance.
Ballos - The melody of ballos is joyous and lyrical, especially in the Aegean islands. This dance incorporates all the elements of courtship: attraction, flirtation, display of masculine prowess and feminine virtue, pursuit, and rejection, capture and surrender. Its origin is in the island culture of Greece. Men could not approach women easily, so they created this dance to "flirt" with them.
Crete Region
The Pontic migrants and earlier settlers had an influence in some eastern Crete communities in their language, music, and dance. The dances we will be performing from the various Eastern Crete regions will have a Pontic influence with their feet more grounded.
Siganos – comes with a number of tunes from the well-known "kantilies". Most of these dances come from Lasithi and the eastern provinces of Heraklion, which is why Siganos is considered a dance of eastern Crete and especially of Lasithi administration and oversight. In Irakleio the dance is a 6-step dance compared to the 8-step dance in Rethymno (western Crete).
Kastrinos Pidictos – named from the Grand Castle as it was formerly called Heraklion. It is considered a remnant of the ancient Minoan war Pyrixiou dance and represents the efforts of the capture and defense of the Grand Castle at various points in its history.
Sousta – is the remnant of Crete's dance. In its original form it was danced from man to man before the battle. Around 300 AD the dance began to be danced by women as well and thus became erotic. It is even said that women's participation in the sousta was a social requirement of the time. It is said that Sousta was the main bridal dance; however, Srytos has become the more preferred bridal dance.
Prinianos – has its roots in eastern Crete and has been toned down today. it was danced mainly in the area of Ierapetra but also danced in the prefectures of Heraklion. Name derives maybe from the Prinia village. It is also know it as Brimianos because of a strong forward movement.
Ethianos – Another variation of the Cretan dance with its roots from ancient Pyrichio, the Kouretes war dance. It took its name from the village of Ethia of Asterousia where it was first introduced.
Pentozali – every step of the dance is the embodiment with the excessive blood and the vision of liberation and freedom. Every stroke of the foot is depicting the rifles and weapons of the Daskalogiannis Sfakianoi warriors throughout the centuries. The Pyrriihios of the Cretans is the pentozali. Just like that of the Pontians, like the ancient Pyrrhios are dances that now are danced to honor the memory of our heroes.
Epiros Region
Epirote dances are the most slow and heavy in all of Greece. Great balance is required in order to perform these dances. Epirus has historically been a remote and isolated region due to its location between the Pindus mountains and the sea.
It was the brave men of Epiros that provided the first tactical victory of the Allies in World War II. This sparked the famous quote by Winston Churchill who stated, "Greeks don't fight like heroes, heroes fight like Greeks."
The dances in Epiros are often begun with a memorial to the fallen.
Tsamiko - is probably names for the Tsames in Epiros. Some say it is named after the clothes of the Klepthes, the mountain fighters in the Greek War of Independence. Men usually dance it, but certain versions can be danced with both men and women.
Pogonisios – The name of the dance comes from the region of Pogoni in Ioannina region, near the Albanian border. It is the most common dance pattern in Epiros and is a rhythm of many Greek dances. It is danced to many different lyrics, tunes, melodies in a pentatonic scale, and contains a standard 4/4 rhythm but is split in a 2-1-1 style, slow, quick, quick.
Zagorisios Konstantis – Zagori is located near the Albanian border and is a cluster of 46 settlements. The most popular song to dance Zagorisios to is Konstantis. This dance has a 5/4 rhythm unique and seldom heard outside Epiros. The Zagorisios is the most popular dance of the Zagori region in Epiros. This dance, due to the mountainous regions of Epiros is virtually left untouched and is consistently danced the same from village to village with very few and only minor variations.
Paramythia – legend has it that the women of Paramythia performed a slow circular folk-dance on the rocky cliffs of the Thesportian mountains where at the end the danced off the cliff one-by-one in defiance, rather to die than to be raped or taken captive.
Neratzia – is considered a "syrtaki" dance, a common name for a group of traditional Greek dances that feature a "dragging style" as opposed to a more hopping and leaping style.
Ionian Islands Region
June 23, 1953 in the Kefalonia village of Tarkasata the villagers gathered in the "Horostasi" to celebrate its tradition of Αϊ Γιάννη Λαμπαδιάρη, discarding of the May Wreaths made from the mountain wildflowers, into the village fire, while dancers and villagers jumped the flames, unknowingly for the last time. This was the village's last celebration. On August 12, 1953 the village was completely destroyed, and to this day lie in ruins, by the 1953 Ionian Earthquake.
Mermigas – a well known song from the island of Kefalonia. The song is often associated with migration and settlement, stemming from its roots of being brought to Kefalonia and adopted by its people.
Manetas – is a basket weave dance. There are two specific ways the line end looks during the choral separation, depending on the number of dancers. We will demonstrate both ways during our performance.
Divaratikos - we will perform the original version of the dance with less bounce and more reserved. The dance was originally more subdued, but as time went by, the dance became more and more bouncy and livier, in the tradition of Kefalonian dances, where the dancers were "performing" for their audience. We will demonstrate this variation of the dance towards its end. There are multiple different ways the steps are taken in Kefalonia for Divaratikos, depending on the region and area. We will perform the steps specific to the Pylaros region.
Blaxopoules – is very popular Kefalonia couple's dance. As girls and boys weren't allowed to interact, the dance was created and features an element where the boy draws the girl in close (where they would whisper to the girl something flirtatious, personal, etc…, and then back away twisting side-to-side to see if anyone saw them whisper to her.
Ballos - The melody of the Kefalonia Ballos is joyous and lyrical. This dance incorporates all the elements of courtship: attraction, flirtation, display of masculine prowess and feminine virtue, pursuit, and rejection, capture and surrender. The Pylaros version uses the simplest form of Ballos where single couple goes through a series of spontaneous figures to the fascination of the crowd and the other dancers. Generally, there is a single boy lead; however, there are times when it is appropriate to share this spotlight, which we will do in our dance version.
Thrace Region
Thrace is a region of northeastern Greece. Dances from Thrace are predominantly circle dances where the men dance in the front of the line. Thracians prefer music and dance of a relatively quick and brisk tempo. The music of Thrace is characterized by the high pitched melody of the gaida (goatskin bagpipe) or clarinet and the constant steady drumming of the toumbeleki.
Stis Treis – introduced in Thrace in the early 1900's when the newly formed Bulgarian government appointed a Bulgarian mayor for Topolovgard, which was made up of 96% Greeks. About 22,000 refugees left the town to settle in Greece bringing with them Stis Treis. Mainly performed in Kavakli N. Thraki . Hand movement forward and backwards while there is a movement to the right. In west Thraki is also called Tripatos it's called "Stis Treis" which means "three step" due to the 3 step repetition in sets of 4.
Zonaradiko – Most popular and widespread dance in Thraki. Men are in the front and women follow. It can starts in a circle and while the enthusiasm builds up the "protoxoreutis" who is the lead dancer raises his right hand and begins the wrap in and out the line in a snail format until the dancer in end has to dance in an opposite direction. Fast dance with phonetic additions from the dancers. Historic references have the older men dancing this dance holding hand to belts (Zonari means belt) a king the snail format.
Xesyrtos - This dance was originally danced by women the second day of Pasha( Easter) as well as weddings. The girls arrived at the wedding bringing sweets and raki to each other. Fast movement with foot entirely on the ground. Tradition mentions in Thraki that at times this fast dance was performed late night at weddings in order to encourage the guests who have been drinking to go home after celebrating at the wedding for 3 days.
Baidoushka – Before the liberation of northern Greece and southern Bulgaria from Turkish control, dances passed back and forth between the Greeks and the Bulgarians quite often. Baidoushka spread not to Greek Macedonia and Thrace but as far north as Romania. In Bulgaria, baidoushka describes a class of dances much like "pidikhto" or "syrto" in Greece. The meaning of the name is uncertain but is probably from the Bulgarian word for "limping". The name maybe derived from the word "baitak" which means limping without a defect. The word has a Slavik derivative.
Syngathistos - The Syngathistos dance is indicative of a dance form found in the northern provinces of Greece—Epirus, Macedonia, and Thrace—and each with its own distinctive styling. It is called Syngathisto due to a particular movement in its styling which resembles a "sitting" step, and Syngathisto in Greek means "with sitting." It originated from a nomadic tribe and is symbolic of them wandering and searching to feed their herds.
HistoryDance PhotosRegional DanceCostume
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A special project designed by Anna & Eugeni Bach. The MMMMMS House is located on the outskirts of Camallera, Girona, Spain. This house project is placed in a development area adjacent to a village. The house was completed in 2014.
In the construction of this house, the architect must comply with a series of local restrictions that include the implementation of sloped roofs, stone cladding and "Arab" tiles. The main objective of this regulation is to construct a new building to look like old rural houses.
Inspired by the efficient design of a warehouse, the MMMMMS House forward the design of large main volume are supported by some small volumes such as bedrooms, kitchen, and bathrooms that are placed within their own separate compartments.
The house has been designed to be a low energy building. In the summer, the house get very comfortable temperatures without air conditioning with the help of cross-ventilation system in the façades and skylights. While in the winter, warm air is maintained because the thickness of the walls and insulation. In addition, the heating is provided by a high performance of wood-chip heater that connected to solar panels also supplying hot water.


Knox Theological College offers a 3-year program designed to prepare men for pastoral ministry. All class work is directed to the glory of God and designed for the best preparation of students for their service to God. The program includes teaching in Bible knowledge, preaching skills, pastoral skills, church history, and theology. For purposes of instruction, the Westminster Confession of Faith and the Belgic Confession, Heidelberg Catechism and Canons of Dort are believed to be sound expositions of Biblical principles of faith and doctrine.
Courses are generally taught in 2 or 3 week blocks (with a 1 week break between each course). Classes meet from Tuesdays through Fridays, beginning with devotions at 8:30 am, and continuing until about 12:30 pm, with a half-hour break for tea. For each hour spent in class, a student is expected to spend 2 hours outside of class reading, writing, and studying.
May God be glorified at KTC by raising up men to make disciples of all nations to the glory of Christ!


January at KEG we had workshop on Catherine de Medici Embroidery. This is a counted thread technique and is usually worked on an Italian fabric known as Bratton which today is a 100% loosely woven evenweave linen about 6 threads per centimetre (15 threads per inch), either cream coloured or unbleached. A thick cream-coloured or white twisted 100% cotton thread called "Cotone Povero" [poor cotton] is used for the stitching (done inDouble Running Stitch executed in a particular way), edging and tassels.
February , Workshop on Cross Stitch Biscornu . A biscornu is an interesting little eight-sided pincushion and many stitcher's use them as ornaments, door hangers, or other decorations. Biscornu is made from two embroidered squares sewn together on point; the corner of one square meets the middle of the other as the two pieces are whip-stitched together and stuffed, creating the a quirky, skewed pillow and are finished off with a button in the center of the design top and bottom.
March, workshop on Lamu Caps Embroidery. Donna Pido demonstrated the embroidery technique used to embroider Lamu caps (Lamu is the Kenya's oldest living town). Donna's tips were to use a bodkin (or porcupine quill) to make a hole, then do buttonhole stitch into the hole to make an eyelet. Every eyelet should have at least 20 stitches, but we could aim for 24 by following a clock face and doing 2 stitches for every 'hour' to keep it even.
April, KEG along with KEG hosted an exhibition, "The Magical art of Stitches" which displayed the beautiful needlework by our members. During the exhibition workshops on quilting and embroidery techniques like Assisi card, plastic canvas fridge magnet notebook and pen holder and a Dorset feather stitch tissue packet cover were held. Read more on KEG exhibition….
May, KEG had its AGM this month followed by a workshop Herringbone Stitch. The variety of herringbone stitches are done on a Kikoy fabric that made a beautiful jewellery roll.
June, workshop,on Zalakdoki stitch technique. This is an embroidery from the Kashmir province. This is basically a chain stitch and carries an international market. At KEG we made some lovely yellow, blue, pink colored embroidered flowers on small bags to carry our kits.
July, KEG workshop on Dorset feather stitchery, the tissue packet holder we displayed at the exhibition. This uses chain stitch, button hole stitch and fly stitch.
In coming months KEG is going to have lots more creative workshops where we will learn variety of stitches which will be made into lovely projects.


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It is essential to draw a distinction between the security of the data stored by our customers and the security of the infrastructure that stores this information.
Security of the data stored by our customers:
Our customers are solely responsible for ensuring the security of the resources and application systems that they use with OVH's services. OVH offers tools to help customers secure their data.
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OVH is committed to ensuring optimal security for its infrastructure. This includes implementing a security policy for information systems and meeting the requirements for multiple standards and certifications (ISO/IEC 27001 certification, SSAE18 SOC 1 TYPE II and SSAE18 SOC 2 TYPE II attestations, HIPAA attestation etc.).
You can find a list of these attestations and the ISO 27001 certification and their scope in OVH US's compliance and certification section.
Information Security Management System (ISMS)
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Access to OVH sites
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Audit Logging
Commitments made by OVH in its capacity as a hosting provider
OVH has implemented certain ISMS policies to minimize security risk, protect our organization's sensitive data, and ensure business continuity. Our ISMS policies are updated at least annually, or in response to material changes that warrant a policy update. Annual external audits are also conducted to verify the security of our solutions in accordance with the ISMS policy framework.
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Commitments made by OVH in its capacity as a hosting provider/strong>
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the delivery vestibule is configured in the same way as a single-person mantrap, except larger in area and with no verification of volume or weight, and with badge readers on the outside only;
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messages about security awareness are regularly communicated to all personnel.
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authorizations are issued and monitored by managers, following the principle of least privilege;
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updates are managed automatically,
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there is a procedure for re-imaging/wiping workstations when employees leave the company.
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mobile devices must be registered in a centralized mobile device management (MDM) system before they are granted access to internal resources (WiFi, email, calendars, people directory, etc.);
the security policy used on the mobile device is verified (unlock code, lock time, storage encryption); and
procedures are in place for wiping the mobile device remotely if it is lost or stolen.
Customers are solely responsible for encrypting content communicated through the OVH network.
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an inventory is kept within a configuration manager database;
a tightening process is in place, featuring guides that describe which parameters need to be modified in order to ensure a secure configuration;
access to the administrator features for equipment is reserved to staff listed on control lists;
all equipment is administered via a bastion host, applying the principle of least privilege;
all configurations for network equipment are backed up;
the logs are collected, centralized and monitored on a permanent basis by the network operations team; and
configurations are deployed automatically, based on validated templates.
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all systems and data necessary for continuity of services, reconstructing the IT system, or analysis purposes following an incident is backed up (technical and administrative database files, activity logs, source codes for applications developed internally, configurations for servers, applications and equipment, etc.); and
the intervals, conservation periods and manner of storing backups are defined in accordance with the requirements of each asset backed up; the backup process is covered by a monitoring process, and by an alert and error management process.
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OVH has implemented a logging policy for the servers and equipment used by OVH to deliver its services. Per this policy:
logs are backed up and centrally conserved;
logs are consulted and analyzed by a limited number of authorized personnel, in accordance with the authorization and access management policy; and
tasks are divided up between the teams responsible for operating the monitoring infrastructure and the teams responsible for operating the service. The list of activities that are logged includes the following:
logs of storage servers hosting customer data;
logs of the machines managing the customer's infrastructure;
logs of the machines monitoring the infrastructures;
logs of the antivirus software installed on all equipped machines;
integrity checks of logs and systems, where appropriate;
tasks and events carried out by the customer on their infrastructure;
network intrusion detection logs and alerts, if appropriate;
logs of network equipment;
logs of the infrastructure of the surveillance cameras;
logs of administrator machines;
logs of time servers;
logs of badge readers; and
logs of bastion hosts.

redpajama_set_name: RedPajamaCommonCrawl


Then somewhere between nappies, tears, foot stamping and throwing the butter, broom and fork (oops, sorry about that) you have three young adults who appear to be pretty cool decent human beings…impressive really.
So to assist with the kisses goodbye and transition into independent adulthood, at times of inspiration, I might write my own guide to assist in the continuing development of my three.
5. What others think of you is none of your business. Trust your inner voice and listen to your heart. You know you better than anyone else, so back yourself before others, every time. Be Confident.


I have a 2012 Enclave with a power lift gate. We bought it used in 2014. It has 112k miles. It is still in great shape and has never been wrecked. After having it about a year, when closing the lift gate it caught the left (drivers side) tail light and broke both the inner and outer light housings where they come together.
After repairing the light housings the lift gate still wont close properly when using the automatic feature. The lift gate will close manually.
I have no idea where to start. Any ideas?
Turn off the power lift gate from center console, manually close the lift gate slowly to see if you can find any loose hinges or incorrect alignment.
Post a video if you cannot determine where the problem lies so we can see.
It wont let me upload a video. The drivers side lift arm pops when it is all the way open. Any ideas how to share the video?
I see. So when it closes in auto it goes down all the was as if it may latch and then it reverses? There have been a couple of clunking complaints on the other forum, Acadia I believe. The dealer replaced the actuator and motor but also needs to order a bracket, Another member says he is living with the clunking.
You would need to get into the area of the actuator to see if you may just need a bracket, actuator or adjustment. On my 2008 the whole door would release from the actuator if it met a bind, then all I would need to do is reset it back into place. Your 2012 and my 2015 look different.
Last edited by electbc; 03-19-2019 at 06:55 PM.
Here is a diagram of the components.
You need 10 posts b4 you can add pics and vids.
I just looked at mine, you can remove the little panel to see the actuator. I got inside and used the remote to operate it.
It is hard to imagine what can go bad on it, it is a gear cluster and the actuator arm is connected to the bottom of assembly. Something may be loose or bent on yours. Looking at your second video, maybe it skipped a tooth.
Last edited by electbc; 03-19-2019 at 07:45 PM.


text:
Epiplema subsignaria är en fjärilsart som beskrevs av Walker 1861. Epiplema subsignaria ingår i släktet Epiplema och familjen Uraniidae. Inga underarter finns listade i Catalogue of Life.

Källor

Fjärilar
subsignaria

redpajama_set_name: RedPajamaWikipedia


text:
Mission Cataract USA offers free cataract surgery to people of all ages who have no means to pay.
About Cataracts
About Surgery
Participating Clinics
3 Ways To Market Your Practice Through Volunteer Work
What Doctors say about Mission Cataract USA
Dr. Garcia and OMNI Eye Specialists:
"The Mission Cataract program has always been part of my service for the last 30 years in practice as a community response, as a human response and as a response to my Christian faith as a call to help others in need. I was taught by both my parents and in Catholic school to take care of others in need, and I believe firmly that God has given all of us the opportunity to be good to others.
It has been a blessing for me to be able to serve those most in need in our community by providing the cataract surgeries at no charge, as well as seeing these patients at my office at no charge. By providing this service for free, it keeps all of us humble and grateful for the blessings of intellect and financial strength God has given us as physicians."
Dr. Herbert Ingraham, Dept. of Ophthalmology Geisinger
"Dear Friends of Mission Cataract USA, When we sponsor Mission Cataract at Geisinger in 2019, it will be our 14th edition of what my staff and doctors all refer to as "the best days of the year". Over that time, we have performed 175 surgeries, all free of charge to our less fortunate neighbors in our community. It has been tremendously rewarding to be a part of this program, and it reminds me each year of the reasons I went into medicine all those many years ago. I knew the patients would be grateful, and I knew it was something important to me, a chance to give back. But I hadn't anticipated the response from the other physicians and residents and nurses and support staff, all of whom look forward to the screening day and the surgical day each May. The community has been so very supportive, and anyone I've asked for help has been so compassionate and willing to give of themselves. When I set out to start this Mission Cataract program here, I thought I was giving out the blessings. But I have been profoundly humbled by the blessings I have received and the generosity of spirit I have observed.
Mission Cataract USA is different from taking a Mission trip to Ecuador or Ghana or Nepal. I have been blessed to visit these places as well, but Mission Cataract is different in a profound way. Mission Cataract requires a local community of doctors, nurses, newspaper editors, lay people, church leaders and so many others. I am so blessed when I go abroad. But I truly believe the whole community of Danville, and the surrounding towns and counties who send patients, are truly lifted up as we work together for the less fortunate among us. Good working-class people losing vision can return to their workplace and families. We are ALL better for their willingness to come for help, allowing God's blessing to fall on our entire community. I urge anyone who has not performed this work to give it a try. I promise you, you will receive far more than you give."
Herb Ingraham
Dr. David Shoemaker, Center for Sight
"We are proud to participate in Mission Cataract every year to provide the necessary care and treatment for those who would otherwise go through each day struggling to see," said Dr. David Shoemaker, Founder, CEO and Director of Cataract and Lens Replacement Surgery at Center For Sight. "Restoring the gift of sight to these patients and giving them the opportunity to live meaningful and productive lives is inspiring and gratifying."
Elgibility
Fresno, CA.
© Copyright 2014 Mission Cataract USA All Rights Reserved.
Design and Developed by Netricks


Current Positions: I am Head of International Research at the Agroscope ART Research Institution of the Swiss Federal Department of Economic Affairs (DEA), and Auditor at the District court of Zurich BGZ.
Member of the "Expert group Accessibility" of the Swiss eGovernment standards organisation eCH, member of the Working group on Accessibility Guidelines of the Swiss Government. Lecturer at the Allgemeine Berufsschule Zurich for the Higher Education for Lab Technicians.
Former Positions: Until summer 2011 I was working as Lawyer/Juristischer Mitarbeiter at the Advokatur Prudentia Law.
In research I focus on the applications of information technology in Life Sciences and in Accessibility of web technologies. I received my Masters degree in Sciences at the Swiss Federal Institute of Technology (ETH Zurich) in 1996. More under "Research".
Some projects result in "Publications". Earlier, as assistant at the Institute for Scientific Computing of ETH, I also covered some projects under "Teaching". In real estate, I'm part of the Management Board of Zwingli 40. If You want to contact me by e-mail, snailmail or phone, please choose "Contact".


the band were just getting ready to start on a new project when syd died. it sort of took over what we were doing, as we began to think of all the things... the styles of music, the bands, & the expressive freedom they enjoyed.... as really being syd's lasting legacy. so the album we ended up with is not directly a tribute, but rather a recognition of what he allowed us to see was possible, musically.
we asked daevid allen to do the artwork for us- there was a strong connection there already, & it seemed apt.
for the tenth anniversary of those sessions, we're making more of the recordings available than we could release at the time.


text:
Q: How to get correct value from text file into JTextField I am trying to make some kind of settings in my project. I have a problem with getting value from text file into JFrame. To be more specific - I have a JFrame. From this JFrame I open another JFrame named Settings where is JTextField with value "123" from text file. When I change the value to "123456" and hit the SAVE button it rewrites the text file to "123456" and dispose the Settings JFrame. Everything is fine until now.
When I want to open the JFrame Settings again It opens it with the old value "123". But when I close both JFrames and run it again - the value in Settings JFrame is correct - "123456" ... I think that the text file data are loaded when I run the first JFrame and then the program remembers them and ignores the current values in text file. Any ideas?
JFrame
package javaapplication15;

public class NewJFrame extends javax.swing.JFrame {
    Settings set = new Settings();

    public NewJFrame() {
        initComponents();
    }

    @SuppressWarnings("unchecked")
    // <editor-fold defaultstate="collapsed" desc="Generated Code">
    private void initComponents() {
        jButton1 = new javax.swing.JButton();
        setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE);
        jButton1.setText("jButton1");
        jButton1.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton1ActionPerformed(evt);
            }
        });
        javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
        getContentPane().setLayout(layout);
        layout.setHorizontalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
            .addGap(100, 100, 100)
            .addComponent(jButton1, javax.swing.GroupLayout.PREFERRED_SIZE, 133, javax.swing.GroupLayout.PREFERRED_SIZE)
            .addContainerGap(167, Short.MAX_VALUE))
        );
        layout.setVerticalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
            .addGap(93, 93, 93)
            .addComponent(jButton1, javax.swing.GroupLayout.PREFERRED_SIZE, 39, javax.swing.GroupLayout.PREFERRED_SIZE)
            .addContainerGap(168, Short.MAX_VALUE))
        );
        pack();
    }// </editor-fold>

    private void jButton1ActionPerformed(java.awt.event.ActionEvent evt) {
        new Settings().setVisible(true);  // TODO add your handling code here:
    }

    public static void main(String args[]) {
        //<editor-fold defaultstate="collapsed" desc=" Look and feel setting code (optional) ">
        /* If Nimbus (introduced in Java SE 6) is not available, stay with the default look and feel.
         * For details see http://download.oracle.com/javase/tutorial/uiswing/lookandfeel/plaf.html
         */
        try {
            for (javax.swing.UIManager.LookAndFeelInfo info : javax.swing.UIManager.getInstalledLookAndFeels()) {
                if ("Nimbus".equals(info.getName())) {
                    javax.swing.UIManager.setLookAndFeel(info.getClassName());
                    break;
                }
            }
        } catch (ClassNotFoundException ex) {
            java.util.logging.Logger.getLogger(
              NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (InstantiationException ex) {
            java.util.logging.Logger.getLogger(
              NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (IllegalAccessException ex) {
            java.util.logging.Logger.getLogger(
              NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (javax.swing.UnsupportedLookAndFeelException ex) {
            java.util.logging.Logger.getLogger(
              NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        }
        //</editor-fold>

        /* Create and display the form */
        java.awt.EventQueue.invokeLater(new Runnable() {
            public void run() {
                new NewJFrame().setVisible(true);
            }
        });
    }

    // Variables declaration - do not modify
    private javax.swing.JButton jButton1;
    // End of variables declaration
}

Settings
package javaapplication15;

import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileWriter;
import java.io.IOException;
import java.util.Scanner;

public class Settings extends javax.swing.JFrame {
    static String text;

    public Settings() {
        initComponents();
        try {
            Scanner sc = new Scanner(new FileInputStream("settings.txt"));
            while (sc.hasNextLine()) {
                String line = sc.nextLine();
                if (line.contains("sample=")) {
                    text = line.replaceFirst("sample=", "");
                }
            }
            sc.close();
        } catch (FileNotFoundException fnf) {
            fnf.printStackTrace();
            return;
        }
    }

    @SuppressWarnings("unchecked")
    // <editor-fold defaultstate="collapsed" desc="Generated Code">
    private void initComponents() {
        jTextField1 = new javax.swing.JTextField();
        jButton1 = new javax.swing.JButton();
        setDefaultCloseOperation(javax.swing.WindowConstants.DISPOSE_ON_CLOSE);
        jTextField1.setText(text);
        jButton1.setText("save");
        jButton1.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton1ActionPerformed(evt);
            }
        });
        javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
        getContentPane().setLayout(layout);
        layout.setHorizontalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
            .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
            .addGap(147, 147, 147)
            .addComponent(jTextField1, javax.swing.GroupLayout.PREFERRED_SIZE, 167, javax.swing.GroupLayout.PREFERRED_SIZE))
            .addGroup(layout.createSequentialGroup()
            .addGap(155, 155, 155)
            .addComponent(jButton1)))
            .addContainerGap(86, Short.MAX_VALUE))
        );
        layout.setVerticalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
            .addGap(95, 95, 95)
            .addComponent(jTextField1, javax.swing.GroupLayout.PREFERRED_SIZE, 28, javax.swing.GroupLayout.PREFERRED_SIZE)
            .addGap(41, 41, 41)
            .addComponent(jButton1)
            .addContainerGap(113, Short.MAX_VALUE))
        );
        pack();
    }// </editor-fold>

    private void jButton1ActionPerformed(java.awt.event.ActionEvent evt) {
        // TODO add your handling code here:
        try {
            File file = new File("settings.txt");
            if (!file.exists()) {
                file.createNewFile();
            }
            FileWriter fw = new FileWriter(file, false);
            fw.write("sample=" + jTextField1.getText());
            fw.close();
        } catch (IOException ioe) {
            System.out.println("Nelze zapisovat.");
        }
        dispose();
    }

    /**
     * @param args the command line arguments
     */
    public static void main(String args[]) {
        /* Set the Nimbus look and feel */
        //<editor-fold defaultstate="collapsed" desc=" Look and feel setting code (optional) ">
        /* If Nimbus (introduced in Java SE 6) is not available, stay with the default look and feel.
         * For details see http://download.oracle.com/javase/tutorial/uiswing/lookandfeel/plaf.html
         */
        try {
            for (javax.swing.UIManager.LookAndFeelInfo info : javax.swing.UIManager.getInstalledLookAndFeels()) {
                if ("Nimbus".equals(info.getName())) {
                    javax.swing.UIManager.setLookAndFeel(info.getClassName());
                    break;
                }
            }
        } catch (ClassNotFoundException ex) {
            java.util.logging.Logger.getLogger(
              Settings.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (InstantiationException ex) {
            java.util.logging.Logger.getLogger(
              Settings.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (IllegalAccessException ex) {
            java.util.logging.Logger.getLogger(
              Settings.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (javax.swing.UnsupportedLookAndFeelException ex) {
            java.util.logging.Logger.getLogger(
              Settings.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        }
        //</editor-fold>

        /* Create and display the form */
        java.awt.EventQueue.invokeLater(new Runnable() {
            public void run() {
                new Settings().setVisible(true);
            }
        });
    }

    // Variables declaration - do not modify
    private javax.swing.JButton jButton1;
    private javax.swing.JTextField jTextField1;
    // End of variables declaration
}

A: In constructor of the Settings class , you have never initialized the text for the jTextField1 .
Initialize the jTextField1 using setText method as below :
public Settings() {
        initComponents();
        try {
            Scanner sc = new Scanner(new FileInputStream("settings.txt"));
            while (sc.hasNextLine()) {
                String line = sc.nextLine();
                if (line.contains("sample=")) {
                    text = line.replaceFirst("sample=", "");
                }
            }
            jTextField1.setText(text);
            sc.close();
        } catch (FileNotFoundException fnf) {
            fnf.printStackTrace();
            return;
        }
    }

I understand this is what you want , let me know if you are looking for something else.

redpajama_set_name: RedPajamaStackExchange


text: Q: MVC Chart Helper From Excel Data I want to create a chart using MVC Chart Helper where I read the data stored in an Excel spreadsheet.  I know how to create the chart reading the data from a database but I cannot figure out how to do this from an excel file.  Is this possible?  Thanks.


text:
Квінт Помпей Руф (*Quintus Pompeius Rufus, прибл. 110 до н. е. —88 до н. е.) — політичний діяч Римської республіки.

Життєпис
Походив з плебейського роду Помпеїв. Син Квінта Помпея Руфа, консула 88 року до н. е. У 90 році до н. е. одружився з Корнелією, донькою Луція Корнелія Сулли Фелікса, консула 88 року до н. е., згодом диктатора. У 88 році до н. е. активно підтримував політику батька і тестя проти плебейського трибуна Публія Сульпіція Руфа. Того ж року був убитий під час масових заворушень.

Родина
Дружина — Корнелія Сулла

Діти:
 Квінт Помпей Руф, народний трибун 52 року до н. е.
 Помпея, дружина Гая Юлія Цезаря

Джерела
 Plut. Sull. 8; Mar. 35
 Suet. Caes. 6
 App. BC I 56

Померли 88 до н. е.
Давньоримські політики
Помпеї Руфи


text:
\section{Introduction and statement of results}

 Let $M$ be a closed connected manifold, $TM$ its tangent bundle. Let
 $L:TM\times \mathbb R\to \mathbb R$ be a $C^{\infty}$ Lagrangian. We will assume for
 the Lagrangian the hypothesis of Mather's seminal paper~\cite{M}. The
 Lagrangian $L$ should be:

 \begin{enumerate}
 \item {\it Convex}. The Lagrangian $L$ restricted to $T_xM$, in linear
 coordinates should have positive definite Hessian.
 \item {\it Superlinear}. For some Riemannian metric we have
 $$
 \lim_{|v|\to \infty}\frac{L(x,v,t)}{|v|}=\infty,
 $$
 uniformly on $x$ and $t$.
 \item {\it Periodic}. The Lagrangian should be periodic in time, i.e.
 $$L(x,v,t+1)=L(x,v,t),$$
 for all $x,v,t$.
 \item {\it Complete}. The Euler Lagrange flow associated to the
   Lagrangian should be complete.
 \end{enumerate}

 Let ${\mathcal M}(L)$ be the set of probabilities on the Borel
 $\sigma$-algebra of $TM\times\mathbb S^1$
 that have compact support and are invariant under the Euler-Lagrange
 flow $\phi_{t}$.

 The {\it action} of $\mu\in {\mathcal M}(L)$ is defined by
 \[A_{L}(\mu)=\int L\,d\mu.\]

 Mather defined the function $\alpha:H^1(M,\mathbb R)\to \mathbb R$ as
 \begin{equation}
 \alpha([\omega])=-\min\left\{\int (L-\omega)\,d\mu :\;
 \mu\in{\mathcal M}(L)\right\}.    \label{coho}
 \end{equation}

 For any $k$ in $\mathbb R$ define the $(L+k)$-action of an absolutely
 continuous curve
 $\gamma:[a,b]\rightarrow M$ as
 $$A_{L+k}(\gamma)=\int_{a}^{b}(L+k)(\gamma(\tau),\dot\gamma(\tau),\tau) d\tau $$

 For $t$ in ${\mathbb R}$ we denote by $[t]$ the corresponding point in ${\mathbb S}^1$.
 For any pair of points $(x,[s]), (y,[t])$ on $M\times{\mathbb S}^1$ and $n$ a
 non negative integer, define
 $\mathcal{C}((x,[s]),(y,[t]);n)$ as
 the set of absolutely continuous curves
 $\gamma:[a,b]\to M$ with $\gamma(a)=x$ and $\gamma(b)=y$ such that $[a]= [s]$ and
 $[b]= [t]$, and the integer part of $b-a$ is $n$.

 Let $\Phi^n_k$ be the real function defined on
 $M\times{\mathbb S}^1\times M\times{\mathbb S}^1$ as

 $$\Phi^n_k((x,[s]),(y,[t]))=
 \min_{\gamma \in\mathcal{C}((x,[s]),(y,[t]);n)}
 \{A_{L+k}(\gamma)\}.$$
 so that  $\Phi^n_k=\Phi^n_0+kn$.

 Then the {\it action functional} is defined by
 $$\Phi_k=\inf_n\Phi^n_k,$$
 and the {\it Extended Peierls barrier} by
 $$h_k=\liminf_{n\to \infty}\Phi^n_k.$$
 Thus $\Phi_k\le h_k$.

 \bigskip
 A curve $\gamma:[a,b]\to M$ will be called {\it closed } if
 $\gamma(a)=\gamma(b)$ and $b-a$ is an integer.
 In analogy to the autonomous case~\cite{Ma}, \cite{CDI},
 there is a critical value $c(L)$ given by the following proposition:

 \begin{proposition}\quad

 \begin{enumerate}
 \item If $k<c(L)$, then $\Phi_{k}((x,[s]),(y,[t]))=-\infty$,
 for all $(x,[s]), (y,[t])$ on $M\times{\mathbb S}^1$
 \item
 $$c(L)= \min \{k: \int_{\gamma}L+k \ge 0 {\mbox{ for all closed curves
     $\gamma $}}\}$$
 \item If $k\geq c(L)$, then $\Phi_{k}((x,[s]),(y,[t]))>-\infty$
   for all $(x,[s]), (y,[t])$ on $M\times{\mathbb S}^1$.

\item In terms of Mather's $\alpha$ function we have

 \begin{eqnarray}\label{erg.charac}
     c(L)& = &
-\min \Bigl\{\int Ld\mu :\mu{\mbox { is an invariant probability}}\Bigr\}\\
     & =  &\alpha (0)
   \end{eqnarray}

   Invariant probabilities realizing the infimum above are called
   {\it minimizing measures}.
 \end{enumerate}               \label{basic}
 \end{proposition}
   \bigskip

  From now on, set  $c=c(L)$.

  In contrast with the autonomous case, the action potential~$\Phi_c$
  may fail to be continuous and to satisfy the triangle inequality.
  However, for the extended Peierls barrier we shall prove the following:

 \begin{proposition}\label{barrera}\quad
     \begin{enumerate}
   \item If $k<c$, $h_k\equiv -\infty$.
   \item If $k>c$, $h_k\equiv \infty$.
   \item $h_c$ is finite.
   \item $h_c((x,[s]),(z,[\tau ]))\le
     h_c((x,[s]),(y,[t]))+\Phi_c((y,[t]),(z,[\tau ]))$.

   \item $h_c$ is Lipschitz.
   \end{enumerate}
 \end{proposition}

 Let $H(x,p,t)$ be the Hamiltonian associated to the Lagrangian;
 $$H:T^*M\times{\mathbb R}\to \mathbb R$$
 \begin{equation}
   \label{eq:hamiltonian}
   H(x,p,t)=\max_{v\in T_xM}pv-L(x,v,t)
 \end{equation}

 In~\cite{gafa} the critical  value
 or $\alpha (0)$ for the autonomous case is characterized as

 \begin{align*}
 c(L) &=\inf_{f\in C^{\infty}(M,\mathbb R)}\sup_{x\in M}H(x,d_{x}f)\\
      &=\inf\{k\in\mathbb R:\;\mbox{\rm there exists $f\in C^{\infty}(M,\mathbb R)$
 such that $H(df)<k$}\},
 \end{align*}

 This can be restated in physical terms, by saying that $c(L)$
 is either the infimum of the values of $k\in\mathbb R$ for which
 there is an exact Lagrangian graph with energy less than $k$,
 or the infimum of the values
 of $k\in\mathbb R$ for which there exist smooth solutions of the
 Hamilton-Jacobi inequality $H(df)<k$.

 The second interpretation has a natural  generalization. We will prove
 in section~\ref{Hamilton Jacobi} the following

 \begin{theorem}
 \label{gafaperiodico}
 The critical value, $c(L)$ or $\alpha (0)$  is characterized as the
 infimum of $k$ such that there exists a subsolution
 $f:M\times{\mathbb S}^1\to \mathbb R$ of the Hamilton Jacobi equation,
 $$
 d_tf+H(x,d_xf,t)\le k.
 $$
 \end{theorem}

  We can recover the previous interpretation by using
  the autonomous Hamiltonian ${\mathbb H}(x,p,t,e)=H(x,p,t)+e$
  on $T^*(M\times{\mathbb S}^1)$. Then $df=(d_xf,d_tf)$ is an exact
  Lagrangian graph and $c(L)=\inf_u\sup_{(x,t)}{\mathbb H(d_{(x,t)}u)}$.
  The results in~\cite{gafa} can not be directly applied to this case
  because the Hamiltonian ${\mathbb H}$ does not come from a
  Lagrangian.

  The other values of Mather's alpha  function can be
  similarly characterized by recalling that $\alpha([\omega])=c(L-\omega)$
  and that the Hamiltonian of $L-\omega$ is
  $(x,p,t)\mapsto H(x,p+\omega,t)$.

  In corollary~\ref{Solk=c} we observe that differentiable solutions
  may only exist when $k=c(L)$.

   \bigskip
   \begin{definition}
 Following Fathi~\cite{Fa1} we say that $u:M\times{\mathbb S}^1\to \mathbb R$ is
 a forward weak KAM solution if
 \begin{enumerate}
 \item $u$ is $L+c$ dominated, i.e.
 $$
 u(y,[t])-u(x,[s])\le \Phi_c((x,[s]),(y,[t])).
 $$
 We use the notation $u\prec L+c$.
 \item For every $(x,[s])\in M\times{\mathbb R}$ there exists a curve
   $\gamma:(s,\infty)\to M$ such that
 $u(\gamma(t),[t])-u(x,[s])= A_{L+c}(\gamma|_{[s,t]})$,
 in that case we say that $\gamma$ {\it realizes} $u$.

 \end{enumerate}

 Similarly  $u:M\times{\mathbb S}^1\to \mathbb R$ is
 a backward weak KAM solution if it is dominated and
 for every $(x,[s])\in M\times{\mathbb S}^1$ there exists a curve
 $\gamma:(-\infty,s)\to M$ such that
 $u(x,[s])-u(\gamma(t),[t])=A_{L+c}(\gamma|_{[t,s]}))$

 Let ${\mathcal S}^-$ (resp. ${\mathcal S}^+$) be the set of {\it backward} (resp. {\it
 forward}) weak KAM solutions.

 A point
 $(x,v,[s])\in TM\times{\mathbb S}^1$ is a positive (resp. negative)
 {\it semistatic}  point if the solution
 $\gamma=\gamma_{(x,v,s)}$ of the Euler-Lagrange equation with
 initial conditions
 $(x,v,[s])$, satisfies for all $t$
 \[A_{L+c}(\gamma|_{[s,t]})=\Phi_c((x,[s]),(\gamma(t),[t]));\]
 (resp. $A_{L+c}(\gamma|_{[t,s]})=\Phi_c((\gamma(t),[t]),(x,[s]))$
 for all $t$).

 A point
 $(x,v,[s])\in TM\times{\mathbb S}^1$ is a {\it static} point if it is
 positive semistatic and
 \[A_{L+c}(\gamma|_{[s,t]})=-\Phi_c((\gamma(t),[t]),(x,[s])).\]
 It turns out that if a point is static then its whole
 orbit under the Euler-Lagrange flow is static.

 We denote by $\Sigma^+$ the set of positive semistatic points.

 For a forward weak KAM solution $u$ we define its
 {\it forward basin} as
 \begin{multline*}
 \Gamma_0^+(u)=\{(x,v,[s])\in\Sigma^+: \\
  u(\gamma_{(x,v,s)}(t),[t])-u(x,[s])=
 \Phi_c((x,[s]),(\gamma_{(x,v,s)}(t),[t]))\, \forall t> s\};
 \end{multline*}
 and define its {\it cut locus} by
 $\pi(\Gamma_0^+(u)\setminus\Gamma^+(u)\big)$, where
 $\pi:TM\times\mathbb S^1\to M\times\mathbb S^1$ is the proyection,
 \[\Gamma^+(u)=\bigcup_{t>0}\phi_t\bigl(\Gamma_0^+(u)\bigr),\]
 and $\phi_t$ is the Euler-Lagrange flow.
 It is easy to see that the sets $\Sigma^+$ and $\Gamma_0^+(u)$ are
 positively invariant and so $\Gamma^+(u)\subset\Gamma_0^+(u)$.
 Similarly, define the backward basins $\Gamma^-_0(u)$,
 $\Gamma^-(u)$ for $u\in{\mathcal S}^-$.
        \end{definition}

 The relevance of weak KAM solutions is that they have several properties,
 including those given by the following theorem.

 \begin{theorem}\label{propiedades}

 If $u:M\times\mathbb S^1\to\mathbb R$ is a weak KAM solution then

 \begin{enumerate}
 \item $u$ is Lipschitz and satisfies the Hamilton Jacobi equation
     \[H(x,d_xu,t)+d_tu=c\]
 at any point of differentiability. Moreover, $d_xu$ and $\dot\gamma$
 are Legendre conjugate.
 \item Graph property: $\pi:\Gamma^+(u)\to M\times\mathbb S^1$ is injective and
   its inverse is Lipschitz.
 \item $u$ is differentiable on $\pi(\Gamma^+(u))$.

 \end{enumerate}
 \end{theorem}

  Observe that since a weak KAM solution $u$ is Lipschitz,
  by Rademacher's theorem it is differentiable Lebesgue almost
  everywhere.

  Define the {\it Aubry set} ${\mathcal A}$ as
  $$
  {\mathcal A}:=\{\,(x,[t])\in M\times\mathbb S^1\,|\, h_c\big((x,[t]),(x,[t])\big)=0\,\}.
  $$
  We define an equivalence relation on ${\mathcal A}$ by $(x,[s])\sim (y,[t])$
  if and only if
 \[
 \Phi_c((x,[s]),(y,[t]))+\Phi_c((y,[t]),(x,[s]))=0. \]
 The equivalence classes of this relation are called
 {\it static classes}.

 Let ${\textgoth A}$ be the set of static classes.
 For each static class $\Gamma\in{\textgoth A}$ choose a point $(p,[s])\in\Gamma$ and
 let ${\mathbb A}$ be the set of such points.

  \begin{remark}\label{Phi=h}

  Observe that by item~4 of proposition~\ref{barrera},
  if $(p,[\tau])\in{\mathcal A}$ then
  $$
  h_c((p,[\tau]),(x,[t]))=\Phi_c((p,[\tau]),(x,[t])).
  $$
  \end{remark}

 \begin{theorem}\label{gonzalo}\quad
 The map $\{f:{\mathbb A}\to{\mathbb R}\,|\, f\text{ dominated }\}\longrightarrow{\mathcal S}^-$
 \begin{equation*}
 f\longmapsto  u_f(x,[t]) =\min\limits_{(p,[s])\in{\mathbb A}}f(p,[s])+
 h_c((p,[s]),(x,[t])),
 \end{equation*}
 and the map $\{f:{\mathbb A}\to{\mathbb R}\,|\, f\text{ dominated }\}\longrightarrow{\mathcal S}^+$
 \begin{equation*}
 f\longmapsto  v_f(x,[t]) =\max\limits_{(p,[s])\in{\mathbb A}}f(p,[s])
 -h_c((x,[t]),(p,[s])),
 \end{equation*}
 are bijections.
 \end{theorem}

 \section{The Peierls barrier}\label{Critical Value}

 We will be using the following lemma due to Mather~\cite{M}.
 We say that an absolutely continuous curve $\gamma:[a,b]\to M$
 is a {\it minimizer } if
 $A_L(\gamma)\le A_L(\eta)$ for any absolutely continuous
 curve $\eta:[a,b]\to M$ with $\eta(a)=\gamma(a)$ and $\eta(b)=\gamma(b)$.
 It turns out that a minimizer is a solution of the Euler-Lagrange
 equation $\tfrac d{dt} L_v=L_x$.

 \begin{lemma}
 \label{le-mather}
 There is $A>0$ such that if $b-a\ge 1$ and
 $\gamma:[a,b]\to M$ is a minimizer, then $|\dot{\gamma}(t)|\le A$
 for $t\in[a,b]$.
 \end{lemma}

The proof of  most of Propositions~\ref{basic} and ~\ref{barrera} follow
standard arguments. We only give the proof of the Lipschitz continuity
of $h_c$.

  \begin{lemma}\label{hiswk} Given $(z,[\sigma])\in M\times {\Bbb S}^1$ define
  \[
  u(x,[t]) := h_c((z,[\sigma];x,[t]),\quad v(x,[t]):=-h_c((x,[t];z,[\sigma]).
  \]
  Then $u\in{\mathcal S}^-$ and $v\in{\mathcal S}^+$.
  \end{lemma}

  \begin{proof}
   By item 4 of proposition~\ref{barrera},
  $h(z,[\sigma]),(x,[t]))\le h_c((z,[\sigma]),(y,[s]))+\Phi_c((y,[s]),(x,[t]))$
  for all $(y,[s]),(x,[t])\in M\times {\Bbb S}^1$. Thus $u\prec L+c$.

  Given $(x,[t])\in M\times {\Bbb S}^1$ choose sequences $n_k\to+\infty$,
  $n_k\in{\mathbb Z}$ and $(x,v_k)\in T_xM$ such that
  $$
  h_c((z,[\sigma]),(x,[t]))=\lim_k
  A_{L+c}\bigl(\gamma_k\vert_{[\sigma-n_k,t]}\bigr),
  $$
  where $\gamma_k(s)=\pi\,\varphi_{s-t}(x,v_k,t)$ is the solution of the
  Euler-Lagrange equation such that $(\gamma_k(t),\dot\gamma_k(t))=(x,v_k)$.
  By lemma~\ref{le-mather}, the norm $\left\Vert v_k\right\Vert$ is uniformly bounded.
  Choose a convergent subsequence $v_k\to w$.
  Let $\eta(s):=\pi\,\varphi_{s-t}(x,w,t)$, then for any fixed $s<0$,
  \begin{align*}
  h_c((z,[\sigma]),(x,[t]))
  &\le h_c((z,[\sigma]),(\eta(s),[s]))+A_{L+c}\bigl(\eta\vert_{[s,t]}\bigr)
  \\
  &=\lim_k h_c((z,[\sigma]),(\gamma_k(s),[s]))
     +A_{L+c}\bigl(\gamma_k\vert_{[s,t]}\bigr)
  \\
   &\le \lim_k A_{L+c}\bigl(\gamma_k|_{[\sigma-n_k,s]}\bigr)
   +A_{L+c}\bigl(\gamma_k|_{[s,t]}\bigr)
   \\
   &=h_c((z,[\sigma]),(x,[t])).
   \end{align*}
   So that
   $u(x,[t])-u(\eta(s),[s])=A_{L+c}\bigl(\eta|_{[s,t]}\bigr)$
    for all $s<0$.

  \end{proof}

  For autonomous lagrangians, dominated functions are Lipschitz.
  In contrast, for time periodic lagrangians the action potential
  is dominated but it is not continuous at $\big((x,s),(x,s)\big)$
  when $(x,s)$ is not in the Aubry set.
  Nevertheless, we have the following:

  \begin{lemma}\label{wk-lip}
  If $u:M\times\mathbb S^1\to\mathbb R$ is a weak KAM solution
  (i.e. $u\in{\mathcal S}^+\cup{\mathcal S}^-$) then it is Lipschitz.
  Moreover the Lipschitz constant does not depend on $u$.
  \end{lemma}

  \begin{proof}
  Assume that $u\in{\mathcal S}^-$, the case $u\in{\mathcal S}^+$ is similar.
 Let $(x,[t_0]),(y,[s_0])\in M\times{\mathbb S}^1$ be nearby points
 with $|s_0-t_0|<\tfrac 14$.
  Let $\gamma:[0,1]\to M$ be a length minimizing geodesic joining $x$ to
  $y$ and let $\tau(r)=t_0+r\,(s_0-t_0)$, $r\in[0,1]$.
  Fix $\delta>1$ and let $z:[t_0-\delta,t_0]\to M$ be such that
  \begin{equation}\label{equ@r=0}
  u(x,[t_0])=u(z(t),[t])+\int_t^{t_0} L(z,\dot z)+c\;dt
  \quad \text{ for all }t_0-\delta<t\le t_0.
  \end{equation}
  For $r\in[0,1]$, let $\eta(r,t)$, $t\in[t_0-\delta,\tau(r)]$, be a locally
  minimizing solution of~(E-L) such that $\eta(r,t_0-\delta)=z(t_0-\delta)$ and
  $\eta(r,\tau(r))=\gamma(r)$.

  Then
  $$
  u(\gamma(r),[\tau(r)])\le
  u(z(t_0-\delta),[t_0-\delta])
  +\int_{t_0-\delta}^{\tau(r)}L\bigl(\eta,\tfrac{\partial\eta}{\partial
  t},t\bigr)+c\;\;dt.
  $$
  with equality for $r=0$. Substracting the equality~\eqref{equ@r=0}
   at $r=0$, we get that
  \begin{equation}\label{Deltau}
  u(\gamma(r),[\tau(r)])-u(x,[t_0])\le
  \int_{t_0-\delta}^{\tau(r)}\big(L+c\big)\;dt
   -A_{L+c}(z|_{[t_0-\delta,t_0]}).
  \end{equation}
  Observe that this formula holds either for
  $s_0\le t_0$ or $t_0\le s_0$.
  As we shall see below, formula~\eqref{Deltau}
  implies that $u(y,s)-u(x,t)\le K\,\big(\, |s-t|+d(x,y)\,\big)$
  for some fixed $K>0$.
  Then changing the roles of $s$ and $t$ we get
  that $u$ is Lipschitz.

  Indeed,
  differentiating the right hand side
  and integrating by parts, we have
  $$
  \frac{d\;}{dr}\int_{t_0-\delta}^{t_0+r\,(s_0-t_0)}
  L\bigl(\eta,\tfrac{\partial\eta}{\partial
  t},t\bigr)+c\;\;dt= $$
 $$=\left[L\bigl(\eta,\tfrac{\partial\eta}{\partial
  t},t\bigr)\big\vert_{(r,\tau(r))}+c\right](s_0-t_0)
  +\int_{t_0-\delta}^{\tau(r)} L_x\;\tfrac{\partial \eta}{\partial r}
  +L_v\;\tfrac{\partial^2\eta}{\partial t\partial r}
  $$
  $$=\left[L\bigl(\eta,\tfrac{\partial\eta}{\partial
  t},t\bigr)\big\vert_{(r,\tau(r))}+c\right](s_0-t_0)
  +\frac{\partial L}{\partial
  v}\bigl(\eta,\tfrac{\partial\eta}{\partial
  t},t)\bigr)\Big\vert_{(r,\tau(r))}
  \cdot\frac{\partial\eta}{\partial r}\Big\vert_{(r,\tau(r))}
  $$

  Observe that since $u$ is dominated the realizing curve $z$
  must be a minimizer.
  By lemma~\ref{le-mather},  $\left\Vert\dot z\right\Vert$ is uniformly bounded.
  By the continuity of the solutions of~(E-L) with respect to initial
  values, $\left\Vert\tfrac{\partial \eta}{\partial t}\right\Vert$ is uniformly
  bounded. Hence there is a uniform constant $K>0$ (independent of
  $z(t),x,y,[s_0],[t_0], u$) such that
  $$
  \left\vert L\bigl(\eta,\tfrac{\partial\eta}{\partial
  t},t\bigr)+c\right\vert\le K
  \qquad\text{ and }\qquad
  \left\Vert\tfrac{\partial L}{\partial
  v}(\eta,\tfrac{\partial\eta}{\partial
  t},t)\right\Vert<K.
  $$
  Since $\left.\dfrac{\partial\eta}{\partial
  r}\right\vert_{(r,\tau(r))}=\dot\gamma(r)$,
  we get that
  \begin{align*}
  \frac{d\;}{dr}\left[\int_{t_0-\delta}^{\tau(r)} [L+c]\;\;
  -A_{L+c}(z)\right]
  \le K \; |s_0-t_0| + K\; \left\Vert\dot\gamma\right\Vert.
  \end{align*}
  The value of the right hand side of~\eqref{Deltau} is 0 at
  $r=0$.  Integrating this inequality,
  $$
  u(y,[s_0])-u(x,[t_0])\le K\;\big[ |s_0-t_0|+d(x,y)\big].
  $$
  Interchanging the roles of $(x,[t_0])$ and $(y,[s_0] )$ we obtain that
  the function  $u$ is Lipschitz.

  \end{proof}

    Combining lemmas~\ref{hiswk} and~\ref{wk-lip}
    we get that the functions
    $f,g:M\times \mathbb S^1\to{\mathbb R}$, $f(y,[t])=h_c((x,[s]),(y,[t]))$
    and $g(x,[s])=h_c((x,[s]),(y,[t]))$
    are Lipschitz. This implies that $h_c$ is Lipschitz.
 \section{Subsolutions of the Hamilton Jacobi equation}
 \label{Hamilton Jacobi}

Following the same ideas as in~\cite{gafa}, one obtains
  \begin{lemma}
 \label{menor}
 If $k$ is a real number such that  there exists a function
 $f$ in $C^1(M \times{\mathbb S}^1)$
 subsolution of the Hamilton Jacobi equation
 $$H(x,d_xf)+d_tf\le k$$
 Then $k \ge c(L)$.
 \end{lemma}

 \begin{lemma}
 \label{dif}
 Let $k\geq c(L)$. If $f:M\times{\mathbb S}^1\to\mathbb R$ is differentiable at
 $(x,[t])\in M\times{\mathbb S}^1$ and satisfies
 $$
 f(y,[t_2])-f(x,[t_1])\le\Phi_k (x,[t_1],y,[t_2])
 $$
 for all $y$ in a neighbourhood of $x$, then $H(x,d_{x}f)+d_tf\le k$.
 \end{lemma}

  \begin{proposition}
 For any $k>c(L)$ there
 exists $f\in C^\infty(M\times{\mathbb S}^1,\mathbb R)$ such that
 $H(x,d_xf,t)+d_tf<k$.                    \label{mayor}
 \end{proposition}

 We give a proof of the following fact
  \begin{corollary}\label{Solk=c}
  If $u$ is a $C^{1+\text{\rm Lip}}$ global solution of the
  Hamilton-Jacobi equation
  $u_t+H(x,u_x,t)=k$, then $k=c(L)$ and $u$ is a weak KAM solution in
  ${{\mathcal S}}^-\cap{{\mathcal S}}^+$.
  \end{corollary}

  \begin{proof}
  By lemma~\ref{menor}, $k\ge c(L)$. Let
  ${\mathcal L}_t(x,v)=L_v(x,v,t)$ be the conjugate
  moment associated to $L$ and
  let $\xi(x,t)$ be the vector field defined by

   $\xi(x,t)={\mathcal L}_t^{-1}(u_x)\in T_xM$.
   Then the vector field $(\xi,1)$ in $M\times{\mathbb S}^1$
   is Lipschitz.  Let $\rho_t$ be the flow of
   $(\xi,1)$ in $M\times{\mathbb S}^1$.
   From the Hamilton-Jacobi equation
   we get that
   \begin{equation}\label{diffdom}
   d_{(x,[t])}u\cdot (v,1) = u_x(x,t)\cdot v + u_t\cdot 1
   \le L(x,v,[t])+k.
   \end{equation}
   and that
   \begin{equation}\label{OnVectF}
   d_{(x,[t])}u\cdot(\xi(x,t),1)=L(x,\xi(x,t),t)+k
   \qquad\text{for all }(x,[t])\in M\times{\mathbb S}^1.
   \end{equation}
   Integrating equation~\eqref{diffdom} along absolutely continuous
   curves $(\gamma(t),[t])$
   in $M\times{\mathbb S}^1$ from $(x,[s])$ to $(y,[t])$, we get that
   $$
   u(y,[t])-u(x,[s])\le\inf_\gamma \oint_\gamma (L+k)
   =\Phi_k\big((x,[s]),(y,[t])\big).
   $$
   So that $u\prec L+k$.

   Also, integrating equation~\eqref{OnVectF},
   we get that the orbits of $\rho_t$ realize $u$ in the sense
   of the definition of a weak KAM solution.
   In particular, the orbits of $\rho$ are global minimizers
   of the $(L+k)$-action, and thus they are solutions of the
   Euler-Lagrange equation.

   It remains to prove that $k=c(L)$.
   Let $\nu$ be an invariant
   Borel probability for $\rho_t$ and let $\mu$ be its lift to
   $TM\times{\mathbb S}^1$ using the vectorfield $\xi$.
   Then $\mu$ is an invariant probability
   of the Lagrangian flow and, by equation~\eqref{OnVectF},
   $$
   \int(L+k)\;d\mu=\int du\;\; d\mu = 0.
   $$
   This implies that $k\le c(L)$.
   Thus $k=c(L)$ and also $\mu$ is a minimizing measure.
  \end{proof}

 \section{Weak KAM solutions}\label{weak KAM}

 \noindent{\bf Proof of theorem~\ref{propiedades}:}

 We first prove  item~1.
  By lemma~\ref{wk-lip}  we have   that
  $u$ is Lipschitz and hence it is differentiable almost everywhere. Let
  $(x,[t])$ be a point of differentiability, then by lemma~\ref{dif} we have
 $$H(x,d_xu,t)+u_t \le c.$$
 Moreover let $\gamma :[t,\infty)\to M$ be such that
 $$
 u(\gamma(s),[s])-u(x,[t])=A_{L+c}(\gamma|_{[t,s]}),
 $$
 $$
 \lim_{s\to t} \frac{u(\gamma(s),[s])-u(x,[t])}{s-t}
 = \lim_{s\to t} \frac{1}{s-t}
 \int_{t}^s(L+c)(\gamma(s),\dot\gamma(s),[s]) ds,
 $$
 so
 $$d_{x}u(x,[t])\dot\gamma +d_tu(x,[t])= L(x,\dot\gamma,t)+c.$$
 Therefore
 $$c=d_{x}u\,\dot\gamma-L+d_tu \le H(x,d_{x}u,t)+d_tu\le c.$$

 So $u$ is a solution of the Hamilton Jacobi Equation and $d_{x}u$ and
 $\dot\gamma$ are related by the Legendre transformation of $L$.

 \qed

 \noindent{\bf Proof of the Graph Property:}

 We need the following lemma due to Mather, a proof of which can be
 found in~\cite{M}.

 \begin{lemma}
  \label{L:MATHER2}
   Given $A>0$  there exists
   $K>0$  $\varepsilon_1>0$ and  $\delta>0$ with the following property: if
  $\left\vert v_i\right\vert <A$,
  $(p_i,v_i,[t_i])\in TM\times{\mathbb S}^1$, $i=1,2$ satisfy
   $d((p_1,[t_1]),(p_2,[t_2]))<\delta$ and
  $d((p_1,v_1,[t_1]),(p_2,v_2,[t_2]))\ge K^{-1}d((p_1,[t_1]),(p_2,[t_2]))$
   then, if  $a\in{\mathbb R}$ and
  $x_i:{\mathbb R}\to M$, $i=1,2$, are the solutions of $L$ with $x_i(t_i)=p_i$,
  $\dot{x}_i(p_i)=v_i$, there exist solutions $\gamma_i:[t_i-\varepsilon,t_i+\varepsilon]\to M$
  of $L$ with $0<\varepsilon<\varepsilon_1$, satisfying
  \begin{align*}
  \gamma_1(t_1-\varepsilon)=&x_1(t_1-\varepsilon) \quad , \quad \gamma_1(t_2+\varepsilon)=x_2(t_2+\varepsilon) \, ,\\
  \gamma_2(t_2-\varepsilon)=&x_2(t_2-\varepsilon) \quad , \quad \gamma_2(t_1+\varepsilon)=x_1(t_1+\varepsilon) \, , \\
  S_L(x_1\vert_{[t_1-\varepsilon,t_2+\varepsilon]}&)
  +S_L(x_2\vert_{[t_2-\varepsilon,t_1+\varepsilon]})>S_L(\gamma_1)+S_L(\gamma_2)
  \end{align*}
  \end{lemma}
 We now prove the graph property. Let $(p_1,v_1,[t_1])$,~$(p_2,v_2,[t_2])
   \in\Gamma^+(u)$
   and suppose that $K\,d((v_1,[t_1]),(v_2,[t_2]))>
   d((p_1,[t_1]),(p_2,[t_2]))$, where $K$ is
   from lemma~\ref{L:MATHER2} and the $A$ that we input
   on lemma~\ref{L:MATHER2} is from
   lemma~\ref{le-mather}. Let $y^+_i=x_i(t_i+\varepsilon)$, $i=1,2$,
   and $y^-_i=x_i(t_i-\varepsilon)$ for $\varepsilon$ small,  then
 \begin{equation}
     \label{eq:diag1}
     u(y^+_1,[t_1+\varepsilon])-u(y^-_1,[t_1-\varepsilon])=
 \Phi_c((y^-_1,[t_1-\varepsilon]),(y^+_1,[t_1+\varepsilon]))
   \end{equation}
 \begin{equation}
     \label{eq:diag2}
    u(y^+_2,[t_2+\varepsilon])-u(y^-_2,[t_2-\varepsilon])=
 \Phi_c((y^-_2,[t_2-\varepsilon]),(y^+_2,[t_2+\varepsilon]))
   \end{equation}
   Then using that $u\prec L+c$ and  lemma~\ref{L:MATHER2} , we get that
   \begin{multline}
     \label{eq:diag3}
     u(y^+_2,[t_2+\varepsilon])-u(y^-_1,[t_1-\varepsilon])+
     u(y^+_1,[t_1+\varepsilon])-u(y^-_2,[t_2-\varepsilon]) \\
 \le S_{L+c}(\gamma_1)+S_{L+c}(\gamma_2)\\
 <S_{L+c}(x_1\vert_{[t_1-\varepsilon,t_2+\varepsilon]}
  +S_{L+c}(x_2\vert_{[t_2-\varepsilon,t_1+\varepsilon]})\\
 =\Phi_c((y^-_1,[t_1-\varepsilon]),(y^+_1,[t_1+\varepsilon])+
 \Phi_c((y^-_2,[t_2-\varepsilon]),(y^+_2,[t_2+\varepsilon]).
   \end{multline}

 Which is a contradiction with the sum of ~\eqref{eq:diag1} and
 ~\eqref{eq:diag2}.
 \qed

  \bigskip

 \noindent{\bf Proof of item~3:}

 Let $(x,[s])$ in $\pi \Gamma^+(u)$, let
 $(\sigma (\tau), [\alpha(\tau)])$
 be a curve on $M\times \mathbb S^1$ with $\sigma (0)=x, \alpha (0)=s $. Let
 $\gamma_s$ be the curve such that

 $$u(\gamma_s(t),[t])-
 u(\gamma_s(s-\delta),[s-\delta])= A_{L+c}(\gamma_s|_{[s-\delta,t]}).$$

 Since $(x,[s])$ is  in $\pi \Gamma^+(u)$ we can make a backwards
 variation $(\gamma_\tau)$ of the solution $\gamma_s$. That is,
 $ \gamma_{\tau}:[s-\delta, \alpha(\tau)]\to M$ is a  solutions of
 the Euler -Lagrange equation joining the points $p=\gamma_s(s-\delta)$ and
 $\sigma (\tau)$.

 Since $u $ is dominated we have

 \begin{eqnarray*}
   u(\sigma (\tau), [\alpha (\tau)])-u(x,[s]) & = & u(\sigma (\tau), [\alpha
 (\tau)])-u(p,[s-\delta])-(u(x,[s])-
 u(p,[s-\delta])) \\
  & \le &  A_{L+c}(\gamma_{\tau}|_{[s-\delta,\alpha (\tau)]})-
  A_{L+c}(\gamma_s|_{[s-\delta,s]}) \\
  & = & A_{L+c}(\gamma_{\tau}|_{[s-\delta,s]})-
  A_{L+c}(\gamma_s|_{[s-\delta,s]}) +A_{L+c}(\gamma_{\tau}|_{[s,\alpha (\tau)]})
 \end{eqnarray*}

 Dividing by $\tau-s$ and taking limits as $\tau $ tends to $s$ and
 using the fact that $\gamma_\tau$ is a solution of the Euler-Lagrange
 equation, we obtain

 $$\limsup_{\tau \to s} \dfrac{u(\sigma (\tau), [\alpha
   (\tau)])-u(x,[s])}
 {\tau-s}\le L_v(\dot \gamma_s,s)\cdot\sigma'(0)+ L+c(\dot\gamma_s,s)\alpha'(0)$$

 Similarly we can make a forward variation to get

 $$\liminf_{\tau \to s} \dfrac{u(\sigma (\tau), [\alpha (\tau)])-u(x,[s])}
 {\tau-s}\ge L_v(\dot \gamma_s, s)\cdot \sigma'(0)+ L+c(\dot \gamma_s, s)\alpha'(0)$$

 \qed

 \noindent{\bf Proof of theorem~\ref{gonzalo}:}

  Let $u\in{\mathcal S}^-$, since $u$ is dominated, then
  \begin{equation}\label{u<uh}
  u(x,[t])\le\min\limits_{(y,[r])}u(y,[r])+\Phi_c((y,[r]),(x,[t])).
  \end{equation}
  Let $\gamma:]-\infty,t]\to M$ be such that for all $s\le t$,
  $$
  u(x,[t])-u(\gamma(s),[s])=A_{L+c}\bigl(\gamma\vert_{[s,t]}\bigr).
  $$
  Then $\gamma(s)$ is semistatic and the minimum in~\eqref{u<uh}
  is realized at every point $(\gamma(s),[s])$ with $s< t$.
  Choose a convergent sequence $(\gamma(s_n),[s_n])\to (p,[\tau])\in
  M\times {\Bbb S}^1$, with $s_n\to-\infty$. Then by  lemma~\ref{AlSemi}
  below,
  $(p,[\tau])$ is in the Pierls set. Therefore, using the continuity
  of $\Phi_c$ at $(p,[\tau])$ (see lemma~\ref{PhiContP} below)
  and~\eqref{u<uh}, we have that
  \begin{align}
  u(x,[t])&=u(p,[\tau])+\Phi_c((p,[\tau]),(x,[t]))
          \notag\\
          &=\min_{(q,[\sigma])\in{\mathcal A}}u(q,[\sigma])+\Phi_c((q,[\sigma]),(x,[t])).
          \label{u=uP}
  \end{align}

  We show now that it is enough to choose one point on each
  static class to achieve the minimum on~\eqref{u=uP}.
  Suppose that $(p,[\tau])$ and $(q,[\sigma])$ are in the same
  static class. Then
  \begin{align*}
  \Phi_c((q,[\sigma]),(x,[t]))
  &\le\Phi_c((q,[\sigma]),(p,[\tau]))+\Phi_c((p,[\tau]),(x,[t]))\\
 &\le\Phi_c((q,[\sigma]),(p,[\tau]))+\Phi_c((p,[\tau]),(q,[\sigma]))
      +\Phi_c((q,[\sigma]),(x,[t]))\\
  &=\Phi_c((q,[\sigma]),(x,[t])).
  \end{align*}
  So that
  $\Phi_c((q,[\sigma]),(x,[t]))=\Phi_c((q,[\sigma]),(p,[\tau]))+\Phi_c((p,[\tau]),(x,[t]))$.
  Moreover,
  \begin{align*}
  u(p,[\tau]) &\le u(q,[\sigma]))+\Phi_c((q,[\sigma],p,[\tau])) \\
  &\le u(p,[\tau])+\Phi_c((p,[\tau]),(q,[\sigma]))+\Phi_c((q,[\sigma]),(p,[\tau]))\\
  &=u(p,[\tau]).
  \end{align*}
  So that $u(q,[\sigma])+\Phi_c((q,[\sigma]),(p,[\tau]))=u(p,[\tau])$. Thus
  \begin{align*}
  u(q,[\sigma])+\Phi_c((q,[\sigma]),(x,[t]))
   &= u(q,[\sigma])+\Phi_c((q,[\sigma]),(p,[\tau]))+\Phi_c((p,[\tau]),(x,[t])) \\
   &= u(p,[\tau])+\Phi_c((p,[\tau]),(x,[t])).
  \end{align*}
  So that $u=u_f$, with $f=u\vert_{\mathbb A}$.

  Observe that by definition, if $f:{\mathbb A}\to{\mathbb R}$ is dominated,
  then $u_f\vert_{\mathbb A}\equiv f$. This implies that
  the map $\{f\text{ dominated}\}\mapsto u_f$ is injective.

  Finally, it remains to prove that if $f:{\mathbb A}\to{\mathbb R}$ then
  $u_f\in{\mathcal S}^-$. This follows from lemma~\ref{hiswk}
  and lemma~\ref{minwk} below.

  \qed

  \begin{lemma}\label{AlSemi}
  If $\gamma:]-\infty,t_0]\to M$ is semistatic and $s_n\to-\infty$
  is such that
  $\lim_n\big(\gamma(s_n),[s_n] \big)=(p,[\tau])$ exists.
  Then $(p,[\tau])$ is in the Aubry set.
  \end{lemma}

  \begin{proof}
  Let $\varepsilon>0$ be small. Chose $n_0>0$ such that for $n>n_0$, we have
  $$
  |s_n-\tau\mod1|<\tfrac\e2
  \qquad,\qquad
  d(\gamma(s_n),p)<\tfrac\e2.
  $$
  Let $\lambda^-_n:[\tau,s_n+\varepsilon\mod1]\to M$ be a minimizer with
  $\lambda^-_n(\tau)=p$, $\lambda^-_n(s_n+\varepsilon\mod1)=\gamma(s_n+\varepsilon)$.
  By lemma~\ref{le-mather}, $\left\Vert \dot\gamma\right\Vert$ is uniformly
  bounded. By the same argument, using the first variation
  formula, as in proposition~\ref{barrera}.c,
  $$
  A_{L+c}(\lambda^-_n)\le K_1\,\big[\,
  d\big(\gamma(s_n),p\big)+|s_n+\varepsilon-\tau\mod1|\,\big]
  \le 3\,\varepsilon\, K_1.
  $$
  Let $\lambda^+_n:[s_n-\varepsilon \mod 1,\tau]\to M$ be a minimizer with
  $\lambda^+_n(s_n-\varepsilon)=\gamma(s_n-\varepsilon)$, $\lambda^+_n(\tau)=p$.
  Similarly,
  $$
  A_{L+c}(\lambda^+_n)\le 3\,\varepsilon\;K_1.
  $$
  We have that
  \begin{align}
  h_c\big((p,[\tau]),(p,[\tau])\big)
  &\le\liminf_{N\to\infty} A_{L+c}(\lambda^-_N)
    +A_{L+c}\big(\gamma|_{[s_N+\varepsilon,s_n-\varepsilon]}\big)
    +A_{L+c}(\lambda^+_n)
    \notag\\
  &\le 6\,\varepsilon\,K_1
  +\liminf_N A_{L+c}\big(\gamma|_{[s_N+\varepsilon,s_n-\varepsilon]}\big).
  \label{AlSemi.1}
  \end{align}

  Adding the action of $\gamma$ on the intervals with
  endpoints $s_N-\varepsilon<s_N+\varepsilon<s_n-\varepsilon<s_n+\varepsilon$
  and using that $\gamma$ is semistatic on
  $[s_N-\varepsilon,s_n+\varepsilon]$, we have that
  \begin{align}\label{AlSemi.2}
  A_{L+c}\big(\gamma|_{[s_N+\varepsilon,s_n-\varepsilon]}\big)
  =\Phi_c&\big((\gamma(s_N-\varepsilon),s_N-\varepsilon)\,,\,(\gamma(s_n+\varepsilon),s_n+\varepsilon)\big)
  \notag\\
  &-A_{L+c}\big(\gamma|_{[s_N-\varepsilon,s_N+\varepsilon]}\big)
  -A_{L+c}\big(\gamma|_{[s_n-\varepsilon,s_n+\varepsilon]}\big).
  \end{align}
  Comparing $\Phi_c$ with the action of a minimal length
  geodesic, parameterized by the {\it small} interval
  $I=[s_N-\varepsilon \mod1,\,s_n+\varepsilon \mod1]$
  of length $\varepsilon\le\ell(I)\le3\varepsilon$, with
  \begin{align*}
  \text{speed}
  &\le \tfrac1\varepsilon\;d\big(\gamma(s_N-\varepsilon),\gamma(s_n+\varepsilon)\big)
  \le \tfrac 1\varepsilon\;\big[\,\varepsilon\,\left\Vert\dot\gamma\right\Vert
  +d\big(\gamma(s_N),\gamma(s_n)\big)+\varepsilon\,\left\Vert\dot\gamma\right\Vert\,\big]
  \\
  &\le 2\,\left\Vert\dot\gamma\right\Vert+1;
  \end{align*}
  we have that
  $$
  \Phi_c\big((\gamma(s_N-\varepsilon),s_N-\varepsilon)\,,\,
  (\gamma(s_n+\varepsilon),s_n+\varepsilon)\big)
  \le\ell(I)\;\big[\,\max_{|v|\le 2\,\left\Vert\dot\gamma\right\Vert+1}
  L+c\,\big]
  \le 3\,\varepsilon\,K_2.
  $$
  The two actions in~\eqref{AlSemi.2} are bounded by
  $2\,(2\varepsilon\cdot K_2)$. Thus, from~\eqref{AlSemi.2},
  $$
  A_{L+c}\big(\gamma|_{[s_N+\varepsilon,s_n-\varepsilon]}\big)\le 7\,\varepsilon\,K_2.
  $$
  From~\eqref{AlSemi.1},
  $$
  0\le h_c\big((p,[\tau]),(p,[\tau])\big)
  \le 6\,\varepsilon\,K_1+7\,\varepsilon\,K_2.
  $$
  Now let $\varepsilon\to0$.
  \end{proof}

  \bigskip

   \begin{lemma}\label{PhiContP}
  If $\lim_n(y_n,[s_n])=(p,[\tau])\in{\mathcal A}$ then for all
  $(x,[t])\in M\times{\Bbb S}^1$,
  \begin{align*}
  \lim_n\Phi_c\big((y_n,[s_n]),(x,[t])\big)
  =\Phi_c\big((p,[\tau]),(x,[t])\big)
  =h_c\big((p,[\tau]),(x,[t])\big).
  \end{align*}
  \end{lemma}

  \begin{proof}

  Recall that by remark~\ref{Phi=h},
  $h_c((p,[\tau]),(x,[t]))=\Phi_c((p,[\tau]),(x,[t]))$.
  By item~4 of proposition~\ref{barrera},
  \begin{align}
  \Phi_c((p,[\tau]),(x,[t]))
    &=h_c((p,[\tau]),(x,[t])) \notag\\
    &\le h_c((p,[\tau]),(y_n,[s_n])) + \Phi_c((y_n,[s_n]),(x,[t]))
    \label{Phi=h.1}\\
    &\le h_c((p,[\tau]),(y_n,[s_n])) + h_c((y_n,[s_n]),(x,[t]))
    \notag\\
    &\le h_c((p,[\tau]),(y_n,[s_n])) + h_c((y_n,[s_n]),(p,[\tau]))
     + \Phi_c((p,[\tau]),(x,[t]))
     \label{Phi=h.2}
  \end{align}
  Using that $h_c$ is continuous, taking $\lim_n$ on inequalities
  ~\eqref{Phi=h.1} and~\eqref{Phi=h.2}, we get that
  $\lim_n\Phi_c((y_n,[s_n]),(x,[t]))=\Phi_c((p,[\tau]),(x,[t]))$.

  \end{proof}

  \bigskip

  \begin{lemma}\label{minwk}\quad

  If ${\mathcal U}\subset{\mathcal S}^-$, let  ${\mathfrak u}(x,[t]):=\inf_{u\in{\mathcal U}}u(x,[t])$ then
  either ${\mathfrak u}\equiv-\infty$ or ${\mathfrak u}\in{\mathcal S}^-$.

  If ${\mathcal V}\subset{\mathcal S}^+$, let  ${\mathfrak v}(x,[t]):=\sup_{v\in{\mathcal V}}v(x,[t])$ then
  either ${\mathfrak v}\equiv+\infty$ or ${\mathfrak v}\in{\mathcal S}^+$.
  \end{lemma}

  \begin{proof}
  Since $u\prec L+c$ for all $u\in{\mathcal U}$,
   for all $(x,[s]),(y,[t])\in M\times
  {\Bbb S}^1$,
  \begin{align}
  u(y,[t])&\le u(x,[s])+\Phi_c((x,[s]),(y,[t])), &&\text{ for all } u\in{\mathcal U},
  \notag \\
  \min_{u\in{\mathcal U}}u(y,[t])={\mathfrak u}(y,[t])&\le
  u(x,[s])+\Phi_c((x,[s]),(y,[t])), &&\text{ for all } u\in{\mathcal U},
  \notag \\
  {\mathfrak u}(y,[t])&\le {\mathfrak u}(x,[s])+\Phi_c((x,[s]),(y,[t])).\label{fu-domi}
  \end{align}

  Now fix $(x,[t])\in M\times {\Bbb S}^1$ and fix a sequence $u_k\in {\mathcal U}$
  such that ${\mathfrak u}(x,[t])=\lim_k u_k(x,[t])$. Let $(x,v_k,[t])\in \Gamma^-(u_k)$.
  By lemma~\ref{le-mather}, $\left\Vert v_k\right\Vert$ is uniformly bounded.
  We can assume that $v_k\to w$. Let
  $\gamma_{v_k}(s):=\pi\,\varphi_{s-t}(x,v_k,t)$ and
  $\gamma_{w}(s):=\pi\,\varphi_{s-t}(x,w,t)$. Then
  \begin{align*}
  u_k(x,t)=u_k(\gamma_{v_k}(s),[s])+A_{L+c}\bigl(\gamma_{v_k}|_{[s,t]}\bigr),
  &&\text{ for all }s<t,
  \end{align*}
  Since $\gamma_{v_k}\overset{C^1}\longrightarrow \gamma_w$
  uniformly on bounded intervals,
  using that by lemma~\ref{wk-lip} all the $u_k$'s have the
  same Lipschitz constant,
  taking the lim inf on $k$ we get that
  \begin{align}
  {\mathfrak u}(x,t)\ge {\mathfrak u}(\gamma_{w}(s),[s])+A_{L+c}\bigl(\gamma_{w}|_{[s,t]}\bigr),
  &&\text{ for all }s<t,\label{fu-realized}
  \end{align}
  The domination condition~\eqref{fu-domi} implies
  that~\eqref{fu-realized} is an equality.
  \end{proof}

redpajama_set_name: RedPajamaArXiv


This is my attempt at a Gestalt image. After many fits of frustration as to what I should strive to achieve, this is what I came up with. My artwork is comprised of rectangular boxes of various widths and lengths. Each of my rectangles are arrange in a manner to comprise letters of the alphabet to form words. I thought it would be fitting that as they are a form of one shape they come together to form words to have a meaning.
As in the Gestalt principle they come together to communicate a message to the audience. It is late, this is my activity and it is the end!


text:
"Zimska" je skladba in peti single dua BQL iz leta 2018. Glasbo je napisal Raay, tekst pa Vera Landa.

Snemanje
Skladbo je produciral Raay Music. Tako single izdan pri Nika Records, kot tudi videospot, ki so ga posneli Karo Media & Raay Music v sodelovanju z Metrum Films, je uradno izšel 1. 1. 2018 na portalu YouTube.

Zasedba

Produkcija
 Raay – glasba
 Vera Landa – besedilo
 Raay Music – aranžma, produkcija

Studijska izvedba
 Rok Piletič – vokal
 Anej Piletič – vokal

Sklici in opombe

Zunanje povezave
 "Zimska" besedilo

Pesmi leta 2018
Singli leta 2018
Slovenske skladbe
BQL


The Panorama XXL, the Musée des Beaux-Arts and Rouen Cathedral are just some of the sites recommended by our team that you should visit during your stay. Discover the top 5 spots the Norman capital, not to be missed under any circumstances during your visit. Combining arts, history and modernity, these museums and monuments will leave you moved.
A well-known figure in the history of Rouen and that of France, Joan of Arc's memory is retold in the historical center of Rouen. Come and discover her history situated within the Archdiocese, wher she was judged.
The History Museum presents the epic story of Joan of Arc and reveals her legend by using the latest in multimedia technologies.
A French exclusive situated on the banks of the Seine River in Rouen – a cultural scene exhibiting huge panoramic works by Yadegar Asisi, a German artist who has revived and renewed this ancient art.
The first exposition was, Rome 312, followed by Amazonia – a spectacular rainforest discovery that will be on presentation at the Panorama XXL until May 22, 2016. The next exciting installment will be end of May 2016, with the gigantic fresco of Rouen 1431, depicting life during the time of Joan of Arc.
In the heart of the historic town, the Cathedral of Rouen encapsulates the evolution of Gothic art, since the beginning of its construction in the 12th century on the foundations of a 4th century Basilica and a Roman vestige.
Its cast iron spire rises 151 meters tall and is the highest of France! The Cathedral of Rouen is the only cathedral in France to still have an adjoining Archbishop Palace still in use by the Archbishop.
This architectural marvel consists of a Gothic belfry, a Renaissance arcade and a dial, and a 18th century fountain. The belfry houses the bells of the city and one of the oldest clock mechanisms in Europe, which was in operation from the 14th century up to 1928.
Discover its history whilst ascending the buildings numerous floors and admire the rooftop view once you reach the top. The perfect place to get a breathtaking birds eye view of rue du Gros-Horloge!
The Museum of Fine Arts brings together one of the most prestigious art collections of France. Paintings, sculptures, drawings and objects from various other art forms, spanning from the 15th century to the present day. From Perugino, Veronese, Rubens, Caravaggio, Velázquez, Ribera to Poussin.
Its permanent collections are free to visit throughout the year.
But of course, it is that the top 5, there is many things to discover in Rouen and in the metropolis.


text:
Klopp to focus on "solutions internally" rather than spending big this summer
Will O'Callaghan willocallaghan
Liverpool manager Jurgen Klopp says the new Premier League champions won't be spending "millions and millions" on players in the upcoming transfer window.
Adam Lallana and Xherdan Shaqiri are set to leave Anfield at the end of the campaign but the Liverpool boss is planning to promote fringe players rather than spend big.
"Covid has of course influenced both sides with ins and outs, that is completely normal, and it's just not likely that it will be the most busy summer in the world," Klopp said of his plans.
"But maybe at a later point in the year, if the transfer window is still open, we will know more. But this squad, look at it, It is not a squad you have to change now and say 'OK, we need this position and this position'.
"We don't have a first XI, I say we have a first 16 or 17, they can all play to the same level. But we have to use this, 100 per cent.
"We cannot spend millions and millions and millions because we want to or we think it is nice to do. We never wanted that.
"We want to strengthen this squad and this squad is strong. The problem with a strong squad is how do you improve a strong squad in the transfer market?
"It works with money, obviously, that is possible. But it never works only with money.
"You have to be creative and we try to be creative. We try to find solutions internally and there is still a lot to come: we have three or four players who can make big steps."
Jurgen Klopp Liverpool Premier League Transfers
Klopp 'very positive' about Salah contract situation
Three more positive Covid cases in Liverpool squad
Conte and Klopp call for one-legged Carabao Cup semi-finals
Klopp gambles popularity as he suggests players not being prioritised


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THE COMPANY behind plans for a new crematorium near Oswestry has said more work must be done before they commit to the project.
The Westerleigh Group revealed its proposal to build and manage the single-storey building off the old A5 in Nesscliffe last month when it hosted a public exhibition.
They have now confirmed background work is being carried out in conjunction with Shropshire Council before a formal planning application is submitted.
It comes after the company submitted an application for a screening opinion last week.
A spokesperson for the Westerleigh Group said: "We have received positive feedback from the exhibition that we held at Nesscliffe Village Hall in September.
The proposed building would include 96-seat chapel, a waiting room, public toilets, administrative offices and a crematory, and parking for more than 80 vehicles.
In the grounds there would be a memorial park with landscaped areas, a scattering lawn, and space for 'living memorials' where trees could be dedicated to loved ones.
The Westerleigh Group expects to hold around four funerals a day at the new site.
They say it is needed as the nearest serving the Oswestry area currently are Shrewsbury and Pentrebychan in Wrexham with journeys taking more than 30 minutes in a cortège.