Линейные задачи. Математическая модель задачиOne of the oldest Russian towns, Suzdal, was founded in 1024 as a fortress town on the Kamenka River. It was once the capital of several Russian principalities and has many examples of early Russian architecture. It is probably the most interesting of the Golden Ring towns. The town is fabulously rich in the unique architectural monuments of the 13th-18th centuries including ancient cathedrals and monasteries, bell-towers and churches, one and two-story wooden and brick buildings. The gently winding Kamenka River and flower-drenched meadows make this medieval town with its decidedly rural atmosphere the perfect fairytale setting. Judging by the cupolas, Suzdal may have as many churches as people. The Kremlin, Rizopolozhenskymonastery, the Intercession Cathedral and other landmarks are the most popular places of interest.One cannot, but mention the old Saviour-Euthimiev monastery-fortress: its history reflects development of Russian state during the centuries. It was founded by the prices of Suzdal-Nizhni-Novgorod principalities in the middle of the 14th century.The core of the Euthimiev monastery is the Cathedral of the Transfiguration of the Saviour. It is a typical Russian cathedral that unites various styles of Vladimir-Suzdal architecture. Inside, there are wall paintings, made by masters from Kostroma, under GuryNikitin and SilaSavin supervision. Next to the eastern wall of the cathedral there's a tomb of the Russian Prince Dmitry Pozharsky, one of the leaders of the riot against the Polish invaders. Next to the cathedral there's a bell-tower built between the 16th and 17th centuries. In the year 1766 the empress of Russia Ekaterina II founded a prison in the monastery, where she would put those, who were against the church and monarchy. Undoubtedly, numerous sights of Russia are pride of our people, history and culture monuments and a landscape surrounding them is a unique national property. But very important is the attitude of people to preservation of monuments of culture, it is necessary to make thrifty use of the remained monuments. After all, keeping the past, we are extending the future.
2. МОЖНО ВЗЯТЬ ПОЛНОСТЬЮ!!! А МОЖЕТ – ТОЛЬКО ЧАСТЬ!!! Russia is the biggest country in the world. It has a rich nature, unique history and many places of interest. The biggest city is Moscow, the capital of Russia. The oldest part of Moscow is the Kremlin. The word "Kremlin" means "fortress”. It is considered to be the heart of the city. There are 20 towers on the Kremlin wall which give it a unique appearance. Arbat is by right called the main street of Moscow. The Muscovites value its unique charm created by the architectural pieces of past eras, its freedom and romance praised by the street artists and musicians, its unique spirit of old Moscow - noble and intelligent. Tretyakov Art Gallery is one of the world's richest museums, a treasure-house of the finest works of Russian art from the 11th century to the present day. Today there are over 5000 canvases, more than 3000 works of ancient Russian art, 800 sculptures and 30000 drawings and engravings. In downtown Moscow on a beautiful square there is the main temple of Russia's culture - the Bolshoi Theater. It is one of the world’s biggest opera and ballet theaters. Five-tier house is renowned for its size and excellent acoustics. It is decorated with gilded stucco, murals on the ceiling, and huge tiered crystal chandelier. In 1967 Ostankino Tower was built, which was followed by the future Ostankino television center. The height of the tower is 540 meters. In Europe and Asia Ostankino Tower is the highest one. Today Ostankino television tower has 20 radio and 20 television transmitters. St. Petersburg is the second largest city in Russia. Today it is one of the most important cities in Russia, a city with glorious past and incomparable beauty. One of the most famous monuments in St. Petersburg, the Admiralty building, is decorated with a high needle-shaped spire. The construction of the Admiralty began simultaneously with the construction of the city itself, in 1704. The Admiralty complex also includes Alexandrovsky Garden, opened in 1874. The Mariinsky Theater of St. Petersburg is the most important center of culture recognized not only in Russia but also throughout the world. While in Moscow the main temple of opera and ballet is the Bolshoi Theater, in St. Petersburg it is certainly “Mariinka”. Theater keeps the memory of the great conductors, artists and directors, including the legendary V. Meyerhold. The Hermitage is the largest in Russia and one of the biggest museums in the world. It is very often compared with the Louvre in Paris, although the number of exhibits at the Hermitage main and storage rooms is 10 times more than the Louvre has. During the last 150 years the Hermitage acquired one of the largest art collections in the world – over three million works of art and monuments of world culture dating from the Stone Age to the recent times. Smolny Convent and Cathedral is the magnificent white-and-blue convent and one of the most beautiful architectural complexes in Russia. It is a masterpiece of the brilliant Italian architect Rastrelli, who also designed the Winter Palace. The convent and an institute for young women of noble origin were established here in 1764. This institute was the first educational centre for women in Russia. Nevsky Prospect is St. Petersburg’s main avenue and one of the best-known streets in Russia. In the very first days of St. Petersburg it was simply the beginning of the road to the ancient city of Novgorod, but it quickly became adorned with beautiful buildings, squares and bridges and became the very center of the bustling, rapidly growing city. There are many other big cities and places in Russia that are very interesting and worth of visiting. The Trinity Monastery of Sergiy is the biggest Russian cloister and is situated in the town of Sergiev Possad, not far from Moscow. The cloister was founded by Saint Sergiy of Radonezh in the middle of the 14th century. The architectural ensemble consists of beautiful monuments which date back to the 15-19th centuries. Baikal is of the biggest lakes of our planet. It is the also the oldest (about 25 million years old), and the deepest (1,637 meters) lake in the world. Baikal has the most various flora and fauna. Karelia stretches from the White Sea coast to the Gulf of Finland. Carved out by a glacier thousands of years ago, it contains the two largest lakes in Europe, Lake Ladoga and Lake Onega. Karelia is a beautiful region of hills, lakes, rivers, forest and steppes. Virgin woods, superbly clean lakes and pristine rivers makes Karelia, perhaps one of Russia's best kept hideaways. The Motherland Calls is a statue in Mamayev Kurgan in Volgograd, commemorating the Battle of Stalingrad. It has a sword raised high in the right hand and the left hand extended in a calling gesture. It was designed by sculptor Yevgeny Vuchetich and structural engineer Nikolai Nikitin. Declared the largest statue in the world in 1967, it is the last non-religious statue to be declared the largest. The Golden Ring is a ring of cities northeast of Moscow: Sergiyev Posad, Pereslavl-Zalesskiy, Rostov Velikiy, Yaroslavl, Kostroma, Gus-Khrustalny, Suzdal, Vladimir and others. These ancient towns, which also played a significant role in the formation of the Russian Orthodox Church, preserve the memory of the most important and significant events in Russian history. The towns have been called "open air museums" and feature unique monuments of Russian architecture of the 12th–18th centuries, including kremlins, monasteries, cathedrals, and churches.
3. ТО ЖЕ САМОЕ – ВСЕ ИЛИ ЧАСТЬ!!! Places of interest in Russia Russia is one of the most beautiful countries. The history of the country dates back to Kievan Rus. That is why there are a lot of old cities and places to visit. The most popular city for tourists is Moscow. Moscow is the leading cultural center of Russia. It is world-famous by its architecture, its historical monuments and various places of interest. It looks like out-of-door museum. The oldest and historical part of Moscow is the Kremlin. This is the main tourist attraction in Moscow. It was erected in the ancient times to protect the citizen from the enemy. Within the Kremlin walls there are four cathedrals, a church and six palaces. Besides, there are many museums and exhibitions in the Kremlin. The Kremlin’s unique museum complex includes the world famous treasure-house Armory Chamber, exhibitions in the Assumption Belfry and One-Pillar Chamber and many others. If you are keen on arts you can go the Tretyakov Gallery or to the Pushkin Museum and see a lot of interesting portraits, landscapes and sculptures. Also Moscow is popular by its theatres. There are more than 150 theatrical actors’ associations in Moscow today. In addition to theatrical collectives, the word «theater» also means the buildings for theatrical productions, some of them are the monuments of culture. The most well-known all over the world is the Bolshoi and the Maly Theatres. One more interesting place to see it is Novodevichy Convent, also known as Bogoroditse-Smolensky Monastery. There you can visit Sofia’s tower. In tower of the Novodevichy convent the Princess Sophia was confined by her younger brother Peter I, who wished to take the throne and afraid of the powerful and clever sister. With this history the legend is connected that touching the walls of the tower make dreams comes true. Moscow is a modern city. There are a lot of new engaging places. One of them is Kilometer Zero on the Manezhnaya square. Monument looks like multifaceted star and is called the «Zero kilometer of roads of the Russian Federation». It was established in 1995 as a symbol of the beginning of all of Russian roads. One more popular Russian city is St. Petersburg. It is the second largest city in our country. Nowadays St. Petersburg is a city with big and glorious past, a city of breathtaking beauty. No wonder, that it also has such names, as “Northern Palmyra”, "The Venice of the North" and others. St. Petersburg with more than 80 museums is rightly considered as a historical city. There are over 1,000 historical monuments. The most attractive place for tourists is the Hermitage. It is one of the world’s biggest museums. The Hermitage Ensemble consists of five buildings. The oldest and the biggest of them is the Winter Palace, the former royal residence. It was founded in 1764, when Catherine purchased a collection of 225 Dutch and Flemish painting. Nowadays its collection includes over 2700 exhibits placed in 350 halls. The city has many monuments of religious life of the country. Saint Isaac's Cathedral or Isaakievskiy Soboris is the largest cathedral in the city. Since 1928 it is a museum, but the church community registered in June 1991, has the opportunity to conduct divine services on special days. Decoration of the Cathedral includes the largest collection of Russian monumental painting of the mid-nineteenth century, which includes more than 150 works. The Kazan Cathedral is an outstanding monument of architecture and fine arts. It was built in nineteenth century to store the miraculous icon of the Mother of God of Kazan. The closest in time and style of the prototype of the Kazan Cathedral is the Cathedral of St. Peter in Rome. As Moscow, St. Petersburg has got a lot of modern interesting places. One of them is Mosaic courtyard on the Fontanka. Everything here is decorated with coloredglass, even the benches, sundials and kids’ playground. The courtyard is located in front of the Small Academy of Arts. The skillful hands of students and teachers created this bright area, which can be called a «Mosaic Universe». Moreover, the city is attractive by its nature, parks and gardens. Mikhailovsky garden is one of the most beautiful gardens of St. Petersburg. The territory of the garden is large enough: it is eight hectares. Mikhailovsky garden gives an admire by its picturesque landscape and a calm quiet atmosphere. The garden is famous for its stunningly beautiful lattice, perhaps, the most beautiful in the city on the Neva. Also, our country is famous for the Ural, which is well-known as an industrial center of Russia. Ekaterinburg, the capital of the Urals, is rightfully considered to be one of the most interesting cities of our country. Ekaterinburg is not only industrial, but cultural center. There are more than 30 museums including several museums of Ural mineral and jewelers, historical and new monuments, theatres and many others fascinating places. All citizen love the center of the city, where the heart of Ekaterinburg is located. There you can find the Embankment of the Iset River (the Plotinka). It is a favorite place of the youth, where you can enjoy the coolness of the river Iset in the summer time and a wonderful view of the whole city. There is Ekaterinburg Museum of Fine Arts there. The Museum is known for its collections, many of which are of world importance. For example, the unique collection of the Ural art casting of the XIX - XX centuries, the centerpiece of which is the famous Kaslinsky cast-iron pavilion - the only in the world of architectural structure made of cast iron, which is in the Museum's collection. Our city has some architectural symbols of spirituality of the country. One of them is the Temple-on- Blood in Honour of All Saints Resplendent in the Russian Land. The church was built on the site of the Ipatiev House, where Nicholas II, the last Emperor of Russia, and several members of his family and household were shot by the Bolsheviks during the Russian Civil War. The church symbolizes the Romanov sainthood. The Temple-on-Blood is not only the current Cathedral, but the Museum complex. In the Museum part there are a number of exhibits dedicated to the last months of the life of the Emperor Nicholas II and his family. There are a huge number of beautiful, magnificent, interesting places, which can tell a lot about our country and its history.. But it is very important to preserve monuments of culture. It is necessary to make thrifty use of the remained monuments. After all, keeping the past, we are extending the future.
Линейные задачи. Математическая модель задачи Общую задачу линейного программирования можно сформулировать следующим образом. Найти такие значения
условиям неотрицательности
и для которых линейная функция (целевая функция)
достигает экстремума (максимума или минимума). Вектор Опр. 1 Множество Оптимальным планом или оптимальным решением задачи линейного программирования называется план, доставляющий наибольшее (наименьшее) значение линейной функции (1.3). В общем случае: -могут участвовать ограничения -ограничение на знак может иметь только часть переменных (может иметь, а может не иметь).
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, которые удовлетворяют системе ограничений
(1.1)
(1.2)
(1.3)
, координаты которого удовлетворяют системе (1.1) и (1.2) называют опорным планом или допустимым решением задачи линейного программирования.
