the silence of the unspoken word in the minefield of freedom

we fight for love and die for a dignified death

shot up house feels homeless

you fuck in the basement to the sounds of sirens and explosions

***

You are snow therefore you are water

You are slipping through my fingers

You are the air I breathe

You are the poison that takes my breath away

You are the numb rain that washes my tears

You are everything to me and you are nobody to me

You live a thousand miles away inside my head

Your name is night and I am drowning in the darkness of your lighthouse

***

bird drinks blood from a wound

і fall asleep in the glass grass

summer takes me into its cradle

***

resolve only the war in the body of nature

birth and death are bloodier than ever before

due to a broken leg (who?) manages to urinate only on leg

because of a broken soul (who?) manages to cry involuntarily

the kitten inside the mother’s belly swims like a fish

the kitten does not know that he will be born a predator

Systems of Linear Equations and Solving Them Using Cramer’s Rule

Kokand State University    

Faculty of Exact Sciences and Digital Technologies   

Student: Mamadaliyeva Durdona  

E-mail:durdonamamadaliyeva60@gmail.com                                                        

Abstract: In this scientific article, the theoretical foundations and practical application of solving systems of linear equations using Cramer’s rule are described. The method is based on determining the unknowns through determinants and is applicable only when the main determinant is nonzero. The algorithm steps are demonstrated on examples with two and three unknowns, and the general form of the formulas is presented.

Keywords: Cramer’s rule, trapezoid, system of linear equations, algebraic method, determinant, constant term.

Аннотация: В данной научной статье раскрываются теоретические основы и практическое применение решения систем линейных уравнений методом Крамера. Метод основан на определении неизвестных с помощью определителей и применяется только в случаях, когда главный определитель не равен нулю. На примерах с двумя и тремя неизвестными показаны этапы алгоритма и приведена общая форма формул.

Ключевые слова: метод Крамера, трапеция, система линейных уравнений, алгебраический метод, определитель, свободный член.

Systems of linear equations arise in many fields of science, engineering, and economics. Solving such systems efficiently and accurately is an important skill in linear algebra. One of the classical methods for solving systems with a unique solution is Cramer’s Rule, which is based on the concept of determinants.

For systems with a non-zero determinant, Cramer’s rule is one of the simplest and most convenient methods to understand and apply.

                                     References:

·  Azlarov, T., & Mansurov, Kh. (1994). Mathematical Analysis, Vol. 1. Tashkent: “O‘qituvchi”. 315 pages.

·  Azlarov, T., & Mansurov, Kh. (1995). Mathematical Analysis, Vol. 2. Tashkent: “O‘qituvchi”. 336 pages.

·  Ayupov, Sh. A., & Berdikulov, M. A. (2004). Theory of Functions. Tashkent: “O‘AJBNT” Center. 148 pages.

·  Turgunbayev, R. (2008). Mathematical Analysis, Part 2. Tashkent: TDPU.

·  Jo‘rayev, T., et al. (1999). Fundamentals of Higher Mathematics, 2nd ed. Tashkent: “O‘zbekiston”.

Atlantis

Grant her the trident 

with which to conjure up the sunken city,

the square and the compass

to calculate the diameters of the cerebral journey,

as her ark is bent on pursuing

the emerald of a charted symmetry.

Grant her the trident

with which to subdue the dragon

that had been long conceived

in the depth of her contaminated heritage,

as her crusade is bent on surmounting

the convolutions of a mental labyrinth.

Into the Abyss

It will take the seven oceans to cleanse the soiling of our souls,

to flush out the debris from our clogged pores,

to peel off the ugliness

that drapes our tarnished walls,

the soot, the mould.

There are no Charles Darneys in the real world,

a noble spirit that would sacrifice its life

to save a scapegoat’s,

that is plunging down into the abyss

once and for all.

A Visitation

In my world, there are no kings and queens,

hence the concept of monarchy is alien to me,

and this lack of interest

is not intended to manifest

any disrespect

for the royal sect.

In a dream, I descend a flight of ancient steps,

only to view a partly dilapidated wing

of a majestic building,

where I am told by a dark-skinned Usherer

I once had my own dwelling.

At the huge doorway, a young woman,

who wears a white, woolen hat

and a very beautiful shawl,

embraces me with tears of joy.  

The blueness of her eyes vies

with the azure of the skies.

In the morning, I start to wonder at the capacity of our dreams

to evoke people who have no presence in our reality,

but a year later a picture of the woman in her youth

appears on my timeline on Facebook.

I still ponder over what makes a monarch bid me goodbye

three days before she dies?

An Encounter II

I carry my dog five flights of stairs

four times a day,

and as I breathlessly mount the arduous steps

I say to Lucia “the sniper has not caught up with us yet,”

then I plant three kisses on her tiny, velvety head.

But don’t snipers prefer to maintain some distance

between themselves and their intended victims?

I resolve to ascertain this fact on the net

since this topic is still alien to my literary mindset!

Fragrance

Let me remind you that it’s the head that teems with scents,

not thy nostrils!

They only titillate its mucous for fleeting seconds,

or some lingering minutes,

but have a lasting impact upon your cerebral cells

for as long as you live.

Each scent has its own personal context

an emotional aura,

conjuring up the past

and whatever pertains to thy daily presence,  

a fragrant image

that brings to life all that is aesthetic

and hauntingly pleasant.

a planetary wrong turn

with no off-ramp to the Goldilocks zone

       *

the one-eyed dogcatcher told the boy about a little green farm

       *

he prefers the original artificial taste of Rocket Pops

       *

when translating ‘summer thunder’ was a cinch

       *

locust swarms on the I-80 corridor

the HOV lane transcends

       *

the urge to answer the unknown caller

       *

before Les Mots

I played Wipe Out

on the surface of the sun

       *

a seance of pewter rain falling

an inch at a time

       *

I rushed in to tell about the silver maple leaf

independently astir in the heat 

       *

pennies on the track

how I got to know the long faces of Lincoln

       *

he couldn’t hear the bell crickets

with the air conditioner on full blast

       *

breathing the same air as the bulked-up horsefly

The Footprints of Borges

In labyrinths of ink and knowledge,

a blind guide, illuminating being.

With words, he wove parallel worlds,

mirrors where we see our longings.

In every library, a universe,

on every page, a perverse dream.

Time is an eternally branching river,

and destiny, a garden without winter.

His footprints, shadows in the Aleph,

an echo in the garden of intersecting paths.

In every verse, an echo of his faith,

Borges lives, where reality blurs.

GRACIELA NOEMI VILLAVERDE is a writer and poet from Concepción del Uruguay (Entre Rios) Argentina, based in Buenos Aires She graduated in letters and is the author of seven books of poetry, awarded several times worldwide. She works as the World Manager of Educational and Social Projects of the Hispanic World Union of Writers and is the UHE World Honorary President of the same institution Activa de la Sade, Argentine Society of Writers. She is the Commissioner of Honor in the executive cabinet IN THE EDUCATIONAL AND SOCIAL RELATIONS DIVISION, of the UNACCC SOUTH AMERICA ARGENTINA CHAPTER.

Annotation

This article discusses the attention and opportunities directed by our state towards women, young people with disabilities, and socially vulnerable groups of the population so that the youth of our society can grow up as healthy, educated, hardworking, and independent-minded individuals.

Key words: Society, youth, neighborhood, state, gender equality, power, women, leader.

Today, young people have become a significant part of society who form state authority, influence the internal and external policies of the country, and actively participate in its activities. The role of youth in the relations between the state and society is noticeably increasing. In Uzbekistan as well, this indicator is steadily growing.

The President of the Republic of Uzbekistan, Shavkat Mirziyoyev, emphasized:
“We will continue the state policy regarding youth firmly and consistently. Moreover, we will not only continue but also raise this policy to the highest level as one of our most important priorities, in line with modern requirements. For our youth to become independent thinkers, with high intellectual and spiritual potential, who are not inferior to their peers in any field worldwide, and to live happily — our state and society will mobilize all their strength and opportunities.”
[Mirziyoyev Sh.M. Together We Will Build a Free, Prosperous and Democratic Uzbekistan. Tashkent: “Uzbekistan,” 2016, p.14].

This is one of the greatest examples of the attention given to youth.

Since the future, development, and progress of countries are in the hands of young people, it is important to note the international concepts and terms regarding youth. Each country sets its own age limits for youth. For example, in the USA and Japan, people aged 13–14 up to 29–30 are considered youth; in Bulgaria, 15 to 29; in Russia, 15 to 30; in Germany, “younger youth” are 14–18 and “older youth” are 18–27. According to Article 3 of the Law of the Republic of Uzbekistan “On State Youth Policy,” citizens from the age of 14 up to 30 are classified as youth [http://blog.xabar.uz/post/yoshlar-orasida-huquqiy-savodxonlikni-oshirishda-huquqiy-ta-lim].

This shows that a large portion of the population of Uzbekistan consists of youth. It is therefore necessary to focus on the opportunities provided to them.

In Uzbekistan, various opportunities are being created to enhance the role of youth and raise them as important figures for the future of the state. For instance, democratic reforms were introduced into the management system of neighborhood institutions. New management mechanisms were created, a vertical system for working with youth was established, and problems of young people are now addressed directly within neighborhoods. In order to increase the efficiency of educational and upbringing activities, the Decree of the President of the Republic of Uzbekistan “On Measures for the Fundamental Improvement of the System of Working with Youth in Neighborhoods” (PQ-92, January 19, 2022) was adopted [https://lex.uz/uz/docs/-5831865].

According to this decree, the position of “Youth Leader” was introduced in every neighborhood. Databases such as the “Youth Balance,” “Youth Register,” and the “Youth Portal” were established, with responsibilities assigned to youth leaders. Material assistance, housing subsidies, partial coverage of tuition fees, and support for vocational training and driver’s courses are also being provided.

A significant part of these opportunities is allocated to women. By the Presidential Decree “On Measures to Further Accelerate Systematic Support for Families and Women” (PF-87, March 7, 2022) [https://lex.uz/docs/-5899498], systematic reforms are being carried out to protect women’s rights and interests, increase their social, political, and economic activity, ensure gender equality, and engage women in entrepreneurship.

In the field of education, many opportunities are being created. For example, socially active youth receive privileges when applying to universities. A Presidential grant is awarded to the top 200 students with the highest entrance exam scores. Students studying under contracts are provided with education loans, and for active students or those who have completed military service, 35% of their tuition is reimbursed. The introduction of the “Youth Register” has also raised youth policy to a new stage [https://pm.gov.uz/oz/lists/view/2117].

As a result, thousands of unemployed youth in need of social, psychological, and economic support have been registered and provided with targeted assistance.

The First President of Uzbekistan, Islam Karimov, stated:
“The future of our Motherland, the destiny of our people, and the reputation of our country in the world community, first of all, depends on how our children will grow up, what kind of people they will become, and how they will enter life. We must never forget this truth.”
[Karimov I. High Spirituality is an Invincible Power. Tashkent: “Ma’naviyat,” 2008].

This means that it is essential to teach young people how to find their place in life and make effective use of the opportunities available to them.

Attention is also given to youth with disabilities. According to the Presidential Decree (PQ-74, February 27, 2023) [https://www.lex.uz/docs/6391378], individuals with disabilities and their caregivers are granted priority in receiving state services, as well as strengthened legal guarantees and legal support.

President Shavkat Mirziyoyev has noted:
“Building a New Uzbekistan is not just a desire or a subjective phenomenon, but an objective necessity based on historical foundations, current political, legal, socio-economic, and spiritual realities, and the age-old aspirations of our people. The driving force of our reforms is the knowledge, abilities, and potential of our citizens.”
[Mirziyoyev Sh. The Development Strategy of New Uzbekistan. Tashkent: “Uzbekistan,” 2022].

Conclusion

Indeed, the opportunities and attention provided to youth serve as the strongest motivator for us to move forward. If every young person knows how to properly use these opportunities, they will undoubtedly grow into specialists who contribute greatly to the prosperity of our country.

The expansion of educational institutions such as “Presidential Schools,” “Creative Schools,” and “Temurbek Schools” demonstrates the country’s commitment to raising competitive personnel. Youth are also being supported to start businesses through loans, provided with professional training, and ensured employment.

Great importance is also attached to sports, as our compatriots proudly raise the flag of Uzbekistan at international competitions. Special attention is paid to youth with disabilities, who also achieve remarkable success as athletes, artists, teachers, businessmen, and political leaders.

Thus, it is clear that opportunities in Uzbekistan are balanced for all citizens, regardless of whether they are healthy or disabled. This gives us, the youth, great pride and motivation.

The continuous reforms and conditions created for us inspire satisfaction and confidence in our future, ensuring that Uzbekistan develops into a prosperous state with educated, skilled, and active youth.

References

1. Mirziyoyev Sh.M. Together We Will Build a Free, Prosperous and Democratic Uzbekistan. Tashkent: “Uzbekistan,” 2016.
2. Karimov I. High Spirituality is an Invincible Power. Tashkent: “Ma’naviyat,” 2008.
3. Mirziyoyev Sh. The Development Strategy of New Uzbekistan. Tashkent: “Uzbekistan,” 2022.
4. http://blog.xabar.uz/post/yoshlar-orasida-huquqiy-savodxonlikni-oshirishda-huquqiy-ta-lim
5. Decree of the President of the Republic of Uzbekistan PQ-92, January 19, 2022. https://lex.uz/uz/docs/-5831865
6. On Improving the System of Working with Youth in Neighborhoods. http://lex.uz/uz/docs/-5831865
7. Presidential Decree PF-87, March 7, 2022. https://lex.uz/docs/-5899498
8. Youth of New Uzbekistan: Opportunities and Prospects. https://pm.gov.uz/oz/lists/view/2117
9. Decree of the President of the Republic of Uzbekistan PQ-74, February 27, 2023. https://www.lex.uz/docs/6391378

Childhood

Childhood — gone, never to return,

Yet it makes us long in innocence.

That pure, untainted childhood,

I still yearn for it even now.

Growing up is good, yes,

But childhood was the best.

Pain was only in the body,

There were no grudges at all.

Has it truly gone forever?

I’ll spend my life missing it.

Ah, it was so different,

Those wonderful days we miss.

We were children back then,

We knew nothing of sorrow or worry.

We played and were mischievous a little,

Yet still — we were children.

There were no thieves of the heart,

Pain was only in the body.

Everyone was good to us,

We knew nothing of the bad.

And as we grew older,

We learned everything.

If growing up is truly like this,

I’d have been content never to grow up!

Sharifova Saidaxon Kamolliddinjon qizi was born on May 26, 2008, in the village of Kaldushon, Furqat District, Fergana Region, into an educated family.

In 2015, she was admitted to the 1st grade of Secondary School No. 21 in Furqat District, where she is currently an 11th-grade student.

In addition to school textbooks, she attends various extracurricular clubs. Saidaxon is fluent in conversational English. Despite her young age, she is the holder of more than 15 international and official certificates and has actively participated in numerous projects. Her poems have been published by the official publishing house Lulu Press Inc.