Square and triangular numbers

Akmalova Nargiza student of Tashkent State Pedagogical University named after Nizami

Annotation: This article is about square and triangular numbers and their properties. You can get useful information about square and triangular numbers through the article.

Keywords: square, triangle, square numbers, triangular numbers, number, math.

          Numbers may vary. In school lessons, operations are mainly performed on natural numbers, fractional numbers, whole numbers, rational numbers, irrational numbers and real numbers. At the same time, students may have a question: “What other numbers are there in mathematics?”. Of course, there are many types of numbers in the world of mathematics. One such interesting number is the square number.

           Square numbers. Almost everyone knows the shape of a square. A square is a rectangle with equal opposite sides or a rhombus with right angles. (Figure 1). Square numbers, like their name, are numbers that can be placed in the form of a square (Figure 2).

Everyone knows how to calculate the square of a given number, especially if it is not too large. 2 ² = 4, 3 ² = 9, 4 ² = 16 and so on. The answer to the question why the act of multiplying a number by itself is called a square is related to square numbers.

Triangle numbers. Triangular numbers owe their name to a similar construction, now of triangles. Actually we already used triangular numbers in the proof of Lemma 3 above. Triangular numbers are in the form 1, 3, 6, 10, 15, … The general formula is that for every n the number N = n(n+1)/2 is triangular and describes the number of points arranged in a triangular shape with n points on a side as shown below. Where n is the number of crosses on the side of the triangle.here n is the number of crosses on the side of the triangle. (Figure 3)

Properties of triangular numbers:

1.Half of the third triangular number n of the sequence of triangular numbers n is multiplied by n + 1:

2.The sum of the previous triangular number and the nth triangular number, i.e. equal to (n-1)-th n squared:         

3. The difference of n-triangle minus one minus n-triangle is equal to n:

4.The sum of the first n triangular numbers is called the tetrahedral number Sn and is equal to one sixth of the product of n multiplied by (n + 1) and multiplied by     (n + 2):

S _n 

5.Every natural number is the result of the sum of three triangular numbers:

References:

1.    What is a number?, Site link:  http://www.cut-the-knot.org/do_you_know/numbers.shtml#square

• https://www.cut-the-knot.org/do_you_know/diffDist.shtml
• https://www.isallaboutmath.com/triangnum1.aspx (an online and iPod video by Julio de la Yncera)

A piece of my life, from the days spent with my father.

Although I am a girl who does not like simple wealth, but my heart is very delicate, because until this time, my father did not speak harshly to me, even if he beat me, he told us later why he did that. It's true that my father didn't have to explain much to us, but he told us not to get the wrong idea.

From a young age, he was against us wearing shorts. And when my mother said let her dress modernly, and my father always repeated: "If your daughters wear short clothes, whatever mistakes they make, they will not be in paradise, and these walks are not suitable for us. "I liked what my father used to say. Because I felt uncomfortable when I was dressed openly. Even though they were such hard-handed people, they played with us innocently like young children, forgetting the sorrows of the world. 

Even now, that sincere person plays with us not as much as before, but sometimes. That day I went home, my father reprimanded my sister, she was a little upset, after two or three minutes, my father held her hand, raised his little finger as if to say peace. You see, he loves his children very much, even if he hits them a thousand times. But even if we are children, sometimes we do not know how to forget our parents little faults.


Daughter of Kholmurodova Surayyo Sherzod, 2nd year student of the Shahrisabz branch of the Tashkent Institute of Chemical Technology.

METHODS OF DRYING FRUIT PRODUCTS, TECHNOLOGY AND THEIR PACKAGING. 

Institute of Irrigation and Agricultural Technologies of the National Research University of " TIQXMMI" student Abdurahmonov Lazokat Abduvohid daughter 

   Abstract: To prevent wastage of fruits, three fruits are processed and dried. It should be dried in a condition that meets the requirements for drying. The selection of packaging containers for dried products is explained in our article.

    Key words: Biochemical processes, tissues, water, physical processes, capillaries, diffusion, vitamins, moisture.

             When drying fruits, a large amount of moisture in them is lost. The juice strength and osmotic pressure in the cells increase several times, as a result, the development of microorganisms becomes impossible. As a result of the inactivation of enzymes, biochemical processes stop, and the product becomes preserved. The advantage of dried vegetables and fruits over wet fruits and canned products is that it is also a mistake to transport it. Fruit drying cannot be attributed only to the physical process of moisture evaporation. During drying, complex physical and chemical changes occur that depend on the quality of the finished product. Water in fruits is connected differently with tissues. The free water between the cells evaporates as quickly as the moisture on the outer surface. Moisture in small capillaries evaporates with difficulty because it is held by the adsorptive power of the product.

The drying speed increases when the product heats up. At this time, the moisture between its surface and the large cells in the upper part evaporates. Then the temperature and drying speed in the product are moderated. Drying is observed as the moisture on the surface of the product evaporates, and as a result of the upward movement of water in the internal parts of the product, the concentration in the raw material becomes uniform (internal diffusion of moisture). In addition, reverse diffusion occurs, moving from strongly heated upper layers to slightly heated inner parts (thermal diffusion). 

When drying at a constant speed, the rate of external and internal diffusion of moisture should be the same. This can be successfully achieved by maintaining the exact temperature for each vegetable and fruit. An excessive increase in air temperature causes uneven external and internal diffusion of moisture, excessive drying of the external parts of the product, and the appearance of crusts and cracks. Inappropriate changes in the chemical composition - dark compounds appear, taste and aroma change, vitamins C, P, carotene are broken down. The temperature is of great importance, especially in the last period, because hygroscopic and swelling moisture is being lost. Alternative drying procedures have been developed for each type to obtain a high-quality dried product. During drying, a large amount of moisture is lost in a certain time, and the quality of the raw material does not change much. After cooking, the quality of the product approaches the original state.

The speed of drying, the quality of the product depends on the temperature and air speed, the characteristics of the structure and chemical composition of vegetables and fruits, the level of their grinding, placement on the drying surface, and especially the drying method. When using the correct drying technology, the main nutrients in vegetables and fruits are well preserved, and their calorie content increases 10-30 times due to the loss of excess moisture.
The product is dried in two main ways: artificially and naturally. Several types of artificial drying methods are known, including low pressure, spray dryers, and fluid bed drying methods. Sublimation drying is considered a promising method and is based on the loss of moisture in the product under low pressure. In this case, the original substances in vegetables and fruits are kept almost unchanged, and after soaking and thickening, they have properties close to their original state.

Drying fruits in the sun. In Uzbekistan, grapes, apricots, peaches, apples and other fruits, as well as melons, are mainly dried in the sun. Drying can be carried out for a few days in cloudless hot, sunny weather without using excessive fuel and electricity for the technological process. After calibrating the fruits, they are thoroughly washed, then the large ones are divided into four parts, and the small ones are cut into two parts. After removing the middle core and band, cook it in boiling water for 2-3 minutes. After that, it is washed in clean water and smoked. Smoked raw materials are placed on the racks in the drying area and dried in the sun for 4-5 days. After 2-3 days, the fruits are overturned, after which the trays are taken to a shady place and stacked in a certain order. varieties can be stored for a long time because they are resistant to storage. Mostly spilled and non-standard apples are dried. Such products make up 25-50% of the total harvest. Apples of all varieties are harvested. It is possible to prepare high-quality from white and pale yellow apples with more sugar content and more aromatic, fleshy flesh. Drying is mainly carried out by the following me Drying in a simple way, in which the peel of the fruit is not peeled.

French drying, in which the skin of the fruit is removed and the seeds are removed. When dried in this way, the fruits are separated into varieties after picking, washed, cut, peeled, smoked, after drying, they are moistened and stored in boxes. Apples for drying are harvested during technical ripening or 2-3 days before full technical ripening. During this period, depending on the variety, the sugar content of apples should be 8-16%, and the acidity should be 0.2-1%. Before drying, the sorted apples are washed in washing machines or in baths filled with clean water, and are cleaned of dust and dirt from various microorganisms. After removing the apple skin, it is placed in 2-3% brine. This helps to preserve its natural color. 

Then it is taken in trays and fumigated with sulfur and cured in sulfur anhydride solution. During smoking, 1.5-2 grams of sulfur are added for every 1 kilogram of apples. Smoking should last 25-40 minutes. Instead, it can be treated with 0.1-0.2% sulfuric anhydride solution for 1-2 minutes. Depending on the drying method, air temperature, and the size of the apples, drying can last from 3-5 to 14-15 days. When peeled and dried, up to 12-15%, when peeled, up to 17-20% of apple peel can be obtained, sugar content can be 43-62, acidity can be up to 1-4%. The moisture content of the dried product should not exceed 20%. In this moisture, the bark becomes elastic, and when crushed, it becomes inflexible. The finished product can be put on sale after 10-15 days of storage in the boxes, i.e. after the moisture level has increased. 

Apple peel should be stored in a clean, disinfected building at a temperature of 0-10, with an air humidity of 60-65%. Quality apple peel can be obtained mainly from the following apple varieties: Pervenes Samarkandda, Delishes, Zolotoy grayma, Parmen zimniy zolotoy, Grafensteinsky and Osenniy zolotoy.

         References:
1. Kh.Ch.Boriyev, A.T.Merganov, SH.I.Umidov and others "Technology of storage and processing of agricultural products"-Tashkent 2022, 24 pages.
2. Kh. B. Shomurodov, S. Y. Islamov. Technology of storage and primary processing of agricultural products. - Tashkent: 2020, 200 pages.
3. Tursunov. S. Plant science. "Ijod-press", 2019
4. https://kompy.info

TEACHING PROFESSION IN UZBEKISTAN

A teacher is a pedagogue, an employee of the secondary and higher education system, and is engaged in teaching pupils and students.
A teacher, a teacher is a specialist who carries out educational work with students in secondary general education schools, academic lyceums and vocational colleges of various fields. 

High School Teachers are called teacher, and pedagogue is also used to refer to teachers. The teaching profession has existed since ancient times as a special type of human activity. Because a
person can continue and develop his life only because of education. 

Historical and cultural monuments found in ancient centers of civilization such as Assyria, Babylon, Egypt, Turkestan, India, China show that the teaching profession was formed in these countries in very ancient times. During these times, the most intelligent, experienced people were teaching and they had great privileges over others.

During the period when the society was flourishing, attention to it was high, or the society prospered because the position of the Teacher rose. After the October coup, and in order to fulfill the task of making the masses fully literate, which the Soviets set before them, a systematic training of teachers was launched in Turkestan. 

Because there was a need for specialists working in the schools opened all over the country. For this reason, teachers were not involved in the war in the first years of the Soviet government. During the Shura period, when the education system was subordinated to ideology, teachers were turned into a dominant policy-making force. They were involved more than the norm in various ideological, political and organizational activities not directly related to education. Engaging in uncharacteristic activities has led to a decline in the reputation of teachers.

Like other republics of the former Union, in Uzbekistan, from April 10, 1936, the title (specialty) of private teachers was introduced by the Ministry of Education and Culture of the USSR. Since then, a person who has graduated from an educational institution and passed the state exam will be officially given the title of teacher. 

After Uzbekistan gained independence, special attention was paid to teacher training. This is reflected in the Education Law (adopted on August 29, 1997) and the National Training Program. In Uzbekistan,
teachers are trained at universities and pedagogic schools. In the course of their pedagogical activity, teachers acquire scientific knowledge and develop their pedagogical skills. A teacher training system has been introduced in the country, every teacher is given the opportunity to receive free pedagogical and methodical support at teacher training institutes. Teachers and Mentors Day is celebrated as a national holiday in Uzbekistan every year on October 1. The republic has such honorary titles as People's Teacher of the Republic of Uzbekistan and Honored Public Education Worker of the Republic of Uzbekistan and Honored Youth Coach of the Republic of Uzbekistan. 

Teachers have the shortest working hours and the longest paid vacation. Also, public education for teachers and pedagogical newspapers and magazines, including Marifat in Uzbek, Uchitelskaya Gazeta and Teachers Gazette in Russian, People's Education; Primary Education and Continuing Education and Education Development Journals, and Education and Education Language and Literature Education and pedagogical and methodical literature
are published.

When I came to the higher education institution for the first time, my teacher Iroda Boybekova accepted me. They are very kind and intelligent people. They always help us. I want to be a good teacher like them. Iroda Boybekova is the ideal woman for me. My favorite teachers are Zaynab Egamnazarova and Nafisa Adambayeva. I want to become a teacher like them in the future.

Kurbanova Shakhriyo, Sherali's daughter, was born on May 15, 2004 in the village of Kenguzar, Sariosia District, Surkhandarya Region. The first poetry collection of 2017, "You are the only holy Motherland!" published under her name. Later, the books Magic Pen and Country Gardens were published. Shahriyo Kurbanova is an official member of the international organization Iqro Foundation of India. 

Adhamova Laylo Akmaljon qizi 

The conversations I started in a good mood are going well.

If I start in a bad mood, it doesn't go far. The target is not being reached.

Posts written in a good mood are useful.

Even the neighborhood newspaper is boring to write in a bad mood.

I learn when I read a book in a good mood.

If I read in a bad mood, I fall asleep.

A disaster, an unexpected problem, the mistakes of others - many things are beyond our sphere of influence. We cannot control.

We can control our good mood. The decision that affects our lives the most is our mood.

Choose to be in a good mood. The rest will come by itself.

PROSPECTS OF USING GEOTHERMAL ENERGY SOURCES IN UZBEKISTAN 

Student of Tashkent State Agrarian University
Kadyrova Arofat Abdukarimovna

This article talks about the importance of using geothermal energy sources in the conditions of Uzbekistan. Information is given about the basis of the widespread use of alternative energy sources, not traditional energy sources, their current state, and the reforms and news that are being carried out in this regard in our country.Today, we are living in a time where modern new age generations and innovative and digital technologies that require almost no manual labor are progressing and growing. It can be seen from this that the machines that make our heavy work light, our complex work easy and even our long journey closer now require energy. They now run on electricity instead of gasoline. 

First of all, one thing should be emphasized: "We cannot imagine our life without electricity."

Today, no matter what the field is, electricity is needed. Due to the many actions being carried out now, our development is developing day by day, and the lifestyle of our people is improving more and more. It is worth noting that the adoption of the strategy of supplying the country with electricity until 2030 in our Republic is of great importance for further development, efficient use of alternative energy sources and development of technologies. According to the strategy, it is planned to increase the production capacity of electricity from 5900MW to 29200MW by 2030 and to reduce the consumption of natural gas and reduce the losses in electricity transmission as much as possible.

According to the concept, the consumption of natural gas in the production of electricity will be reduced from 16.5 billion cubic meters to 12.1 billion cubic meters. This plan includes reduction of losses in electricity transmission by 2.35% and in distribution by 6.5%.
Now we will talk about where and how we get electricity. 

We know that we receive electricity in a traditional way, that is, through TPPs. TPP stands for Thermal Power Plant. In thermal power plants, thermal energy is converted into electrical energy and transmitted to us through power transformers. And this borad will suffer many losses until it reaches our home. In particular, this happens in a large unit at the station itself. Thermal power plants operate mainly by burning coal, natural gas and fuel oil. These fuels are sources of energy that are running out. One of the harmful aspects of thermal power plants is large energy losses, and another is a very negative impact on the environment. The toxic gases emitted from it go up into the sky and poison our ecology, harming the natural air, and there is also the problem of disposal of the waste from it. 

However, its advantage is that it is much cheaper than other types of energy production, which is why we have electricity at the expense of TPPs. However, by now, traditional methods are being abandoned in the developed countries of the world. Therefore, the use of renewable energy sources remains very effective.
The use of alternative energy sources can be a little expensive, but it is not harmful. That is, it can be obtained without harming the environment. In this regard, many innovations and reforms are being carried out in this regard in our country. In particular, the verdict of our honorable president Shavkat Miromonovich Mirziyoyev "On measures to accelerate the introduction of renewable energy sources and energy-saving technologies in 2023" can be cited. 

The effect of the words said in the verdict can be seen in the example of Bukhara region. 

In accordance with the verdict, the first turbine with a height of 100 meters and a blade length of 84 meters was erected in Bukhara region this year as part of the construction of a wind power plant. There are 157 more installations from this device. The first capacities of the stations are expected to be put into operation in 2024.

Now, let's talk about geothermal energy. This type of energy is an alternative and renewable energy. Geothermal energy is heat energy in the earth's crust, which comes from the earth's crust and radioactive decay. That is, simply put, artesian water or hot spring. We know that from somewhere in the mountainous regions of our republic, when water comes out, it turns into a sanatorium and it is said that there is a hot spring. 

So, how promising is the use of geothermal energy sources in our country? Of course, it is promising, because Uzbekistan is a country with huge reserves of water, which is a source of geothermal energy. It has been determined that there are geothermal waters in every part of its regions. Scientific research shows that the average gradient of geothermal waters in our country is 40C/km. The heat vapor flow is equal to 0.06 W/m2. Compared to annual indicators, the gross potential of geothermal waters in our country is estimated at 160.8 thousand tons of oil energy. 

Of course, we cannot get electricity directly through this energy, but it is being done in other countries, why can't we do it now? Our exact location may not be rich in active volcanic zones, but that doesn't mean it's just accessible. After all, it is possible to find a solution if you do as much research as possible. If water at a certain depth, i.e. 300 or more depth, is brought to the surface of the earth and heated through specially insulated turbines, it will certainly be possible to obtain electricity from it, and this will certainly become one of the major changes in the field of green energy in our country. 

Of course, environmentally safe and most importantly clean renewable energy.

In conclusion, it can be said that in the current developing period, I think we should not get tired of working on new scientific researches and new discoveries. Because no matter what we do, we find easy ways and implement them in order to satisfy our needs and our own comfortable life and safety, and all this is only for ourselves, for the comfortable and healthy lifestyle of the new generation. Therefore, we should not stop searching. 

Why should I cry?!

If I die my spirit flies to the sky 
If they cry with blue on the Earth they are him for I 
Say him that she's gone for coming back never- because she died 
Why do I have to cry, do they cry 

If friends have tears-causes are expressed 
We said it for the soul, or what or else 
This sadness stuck me into the darkness 
If any questions, say she flied to the sky 
Why do I have to cry, do they cry 

Bunches of the life throw away flowers 
The life of one flower is ending as bu(rgeon)d 
Making me feel that events in my heart 
They left me leaving such torture as peeks 
Nibble my inside-I became downward 
Why do I have to cry, do they cry 

Reason-memory(memento) martyr me by after by after 
Heart burning continuously (my mind) hurts (mine) my mind 
Versus winds standing my patience 
Roars saying "oh" - tough protestation
"Don't cry" they say, flower glamourous 
But cannot say we don't make you cry, tongue wonders 
Left me, won't come back that sweetheart liar 
Why do I cry, do they cry 

Kindness in eyes, words without words 
Exists spark still, intends glowing 
But the possessor of fire burning another 
Every moment tells fiery words 
Getting away, not coming back my valentine-without tolerance, pert (without justice-fired) 
Why do I cry, do they cry 

Causing impatience they left me, of course 
Have you reached at your pointed distance, (at the end ?) destinations 
Did you deliberately hurt me, finally again (at the end) ? 
Or again brought me to the grain, at the end ? 
Oh my chosen valentine chose the other 
Have you left me forever - entirely end ? 
Yourself whisper, who could I make mine-my lovely anymore(then) ? 
Why do I cry, do (they) cry 

I will leave this world one day 
Right towards to my God, his forward (away)  
At that time He will give me Happiness huge endless 
I do live in the garden of Paradise with gladness 
My patience's travelled unending space 
Before it ends, impart(deliver) me to Your Ways 
Oh My God, I will go back to You, without any doubts 
I am Your servant(creature, prayer), I am (only, just) Yours  
Forgive my sins, My Lord who created, (I am thoughtless) 
You are aware and listener as well(also) with patience 
The time hasn't been taken down for us - mysterious 
Why do I have to cry, (but) do they cry 

My heart hurt, causing that satisfaction night 
I find my soul out dead at (next) that dawn 
No hearts to feel anymore then 
I will shut it (forever) till the end 
And that life unmatched and with locked hair 
From my Happiness into the moments 
Why is sadness finding spaces ?  
That annoyed(uneasy) psyche  is abandoned(ruin), insulted 
That fire is not for intolerant jack, anymore again 
Why do I cry, do they(he, all) cried...?!

Mukhlisa Safarova was born on August 13, 2001, in the Surkhandarya region of the Republic of Uzbekistan. She is 21 years old and has a deep interest in poetry. She is the author of numerous poems, songs, stories, and articles. Currently, she is a second-year student at the University of World Economy and Diplomacy. She was awarded the Peace Ambassador nomination in a competition organized by the Iqra Foundation and has served as a representative of the SPCS organization in the United Kingdom, as well as a Global Education representative for Wisdom University, earning certificates and winning various competitions and contests.