235
1-tarelka; 2-teshiklar, 3-tirqishlar.
5-rasm. Suyuqlik oqib tushadigan tarelkalar
Panjarali tarelkalar
- eni 3...8 mm li tirqishlar yoki frezerlash usulida qilingan
bo‘ladi (1.8 b-rasm). Teshikli va panjarali tarelkalar konstruksiyasi sodda, narxi arzon,
gidravlik qarshiligi nisbatan kichik va montaj qilish oson. Teshikli va panjarali
tarelkalar konstruksiyasi soddaligi, metall sarfi kamligi, montaj osonligi va kichik
gidravlik qarshiligi bilan ajralib turadi.
Foydalanilgan adabiyotlar roʻyxati:
1.
Yusupbekov N.R., Nurmuhamedov H.S., Zokirov S.G. Kimyoviy texnologiya
asosiy jarayon va qurulmalari. – Toshkent: Fan va texnologiyalar, 2015. – 848 b.
2.
Rasuljon, T., Azizbek, I., & Abdurakhmon, S. (2021). Research of the
hydraulic resistance of the inertial scrubber. Universum: texnicheskie nauki, (7-3 (88)),
44-51.
3.
Tojiev, R. J., Isomiddinov, A. S., Axrorov, A. A. U., & Sulaymonov, A. M.
(2021). Vыbor optimalnogo absorbenta dlya ochistki vodorodno-ftoristogo gaza v
rotorno-filtrovalnom apparate i issledovanie effektivnosti apparata. Universum:
texnicheskie nauki, (3-4 (84)), 44-51
IKKI OʻLCHAMLI QOʻZGʻALISHLI MODEL OPERATORINING DISKRET
SPEKTRI
(PhD) Almuratov Firdavs, Bobonazarova Aynura
O‘zbekiston Milliy universiteti Jizzax filiali
Annotatsiya:
Ushbu ishida
𝐿
2
(𝑇)
Hilbert fazosida aniqlangan ikki o’lchamli
qo’zg’alanishli, chiziqli, chegaralangan va o’z-o’ziga qo’shma
𝐻
𝜇𝜆
operator qaralgan.
Ishda
𝐻
𝜇𝜆
operatorning muhim spektrdan chapda va o’ngda faqat bitta yoki ikkita xos
qiymatga ega ekanligi operatorning paremetrlariga bog’liq ravishda o’rganilgan.
Kalit soʻzlar:
Operator, tor, spektr, Veyl teoremasi, Hilbert fazosi.
T = (−π; π]
— bir o’lchamli tor bo’lsin.
𝐿
2
(𝑇)
kvadrati bilan integrallanuvchi
funksiyalarning Hilbert fazosi bo’lsin.
𝐿
2
(𝑇)
Hilbert fazosida aniqlangan quydagi
operatorni qaraymiz:
𝐻
𝜇𝜆
= 𝐻
0
− 𝜇𝑉
1
− 𝜆𝑉
2
, 𝜇, 𝜆 ∈ 𝑅
(2.1)
Bu yerda
𝐻
0
− 𝐿
2
(𝑇) fazoda 𝑐𝑜𝑠𝑥
funksiyaga ko’paytirish operatori,
V
1
va
V
2
lar esa
𝐿
2
(𝑇)
fazoda integral operatorlar, ya’ni
236
𝐻
0
𝑓 = 𝑐𝑜𝑠𝑥 𝑓(𝑥)
𝑉
1
𝑓 = ∫ 𝑓(𝑦)𝑑𝑦
𝜋
−𝜋
, 𝑉
2
𝑓 = 𝑐𝑜𝑠𝑥 ∫ 𝑐𝑜𝑠𝑦 𝑓(𝑦)𝑑𝑦
𝜋
−𝜋
Malumki,
𝑉
1
, 𝑉
2
operatorlar kompakt operatorlar bo’lib, muhim spektrning turg’unligi
haqidagi Veyl teoremasiga ko’ra
𝐻
𝜇𝜆
ning muhim spektri uchun quydagi tenglik o’rinli
𝜎
𝑒𝑠𝑠
(𝐻
𝜇𝜆
) = 𝜎
𝑒𝑠𝑠
(𝐻
0
) = 𝜎(𝐻
0
) = [−1; 1].
Quyidagi to’plamlarni kiritamiz.
𝐺
1
= { (𝜇, 𝜆) ∈ 𝑅
+
2
2√2𝜋
2
𝜇𝜆 − √2𝜋𝜇 − √2𝜋𝜆 > 0 }
𝐺
2
= { (𝜇, 𝜆) ∈ 𝑅
+
2
2√2𝜋
2
𝜇𝜆 − √2𝜋𝜇 − √2𝜋𝜆 < 0 }
𝐺
3
= { (𝜇, 𝜆) ∈ 𝑅
+
2
2√2𝜋
2
𝜇𝜆 − √2𝜋𝜇 − √2𝜋𝜆 = 0 }
𝐺
1
∗
= { (𝜇, 𝜆) ∈ 𝑅
−
2
− 2√2𝜋
2
𝜇𝜆 − √2𝜋𝜇 − √2𝜋𝜆 > 0 }
𝐺
2
∗
= { (𝜇, 𝜆) ∈ 𝑅
−
2
− 2√2𝜋
2
𝜇𝜆 − √2𝜋𝜇 − √2𝜋𝜆 > 0 }
𝐺
3
∗
= { (𝜇, 𝜆) ∈ 𝑅
−
2
− 2√2𝜋
2
𝜇𝜆 − √2𝜋𝜇 − √2𝜋𝜆 > 0 }
Endi
𝐻
𝜇𝜆
operatorning xos qiymatlari uchun o’rinli bo’lgan quyidagi teoremani
keltiramiz.
Teorema 1.
Quydagi tasdiqlar o’rinli:
a).
Agar
(𝜇, 𝜆)𝜖𝐺
1
bo’lsin. U holda
𝐻
𝜇𝜆
operator -1 dan chapda 2 ta xos
qiymatga ega va bu xos qiymatlar uchun quydagi tengsizliklar o’rinli
𝑧
1
(𝜇, 𝜆) < 𝛿
1
(𝜇, 𝜆) < 𝛿
2
(𝜇, 𝜆) < 𝑧
2
(𝜇, 𝜆) < −1
tengsizlik o’rinli bo’ladi. Bunda
𝛿
1
(𝜇, 𝜆) = min
𝜇𝜆
{𝐸
1
(𝜇) , 𝐸
2
(𝜆)}, 𝛿
2
(𝜇, 𝜆) = max
𝜇𝜆
{𝐸
1
(𝜇) , 𝐸
2
(𝜆)}
b).
Agar
(𝜇, 𝜆)𝜖𝐺
2
∪ 𝐺
3
bo’lsa, u holda
𝐻
𝜇𝜆
operator -1 dan chapda yagona
𝐸(𝜇, 𝜆)
xos qiymatga ega.
c).
Agar
(𝜇, 𝜆)𝜖𝐺
1
∗
bo’lsin. U holda
𝐻
𝜇𝜆
operator 1 dan o’ngda 2 ta xos qiymatga
ega va bu xos qiymatlar uchun quydagi tengsizliklar o’rinli
1 < 𝑧
1
(𝜇, 𝜆) < 𝜃
1
(𝜇, 𝜆) < 𝜃
2
(𝜇, 𝜆) < 𝑧
2
(𝜇, 𝜆)
tengsizliklar o’rinli bo’ladi. Bunda
𝜃
1
(𝜇, 𝜆) = min
𝜇𝜆
{𝐸
1
∗
(𝜇) , 𝐸
2
∗
(𝜆) }, 𝜃
2
(𝜇, 𝜆) = max
𝜇𝜆
{(𝐸
1
∗
(𝜇) , 𝐸
2
∗
(𝜆))}
d).
Agar
(𝜇, 𝜆)𝜖𝐺
2
∗
∪ 𝐺
3
∗
bo’lsa, u holda
𝐻
𝜇𝜆
operator 1 dan o’ngda yagona
𝐸(𝜇, 𝜆)
xos qiymatga ega.
237
Foydalanilgan adabiyotlar roʻyxati:
1.
Sh.Yu.Kholmatov, S.N.Lakaev, F.M.Almuratov. On the spectrum of
Schrödinger-type operators on two dimensional lattices.// Journal of Mathematical
Analysis and Applications–USA,2022.–Vol.514.–№2.– 126363.
2.
S.N.Lakaev, A.T.Boltaev, F.M.Almuratov. On the discrete spectra of
Schrödinger-type operators on one dimensional lattices.// Lobachevskii Journal of
Mathematics–Russia, 2022.–Vol.43.– №3.–P.770–783
3.
F.M.Almuratov. Asymptotics for eigenvalues of Schrödinger operator
associated to one-particle systems on one dimensional lattice.// Scientific journal of
Samarkand University. – Samarkand, 2022. – №3. – P. 39–46.
4.
S.N.Lakaev, F.M.Almuratov. Panjaradagi bir zarrachali Schrödinger
operatori xos qiymatlari va ularning yoyilmalari.// Scientific journal of Samarkand
University. – Samarkand, 2018. – №5. – P. 24–33.
5.
S.N. Lakaev, A.T. Boltaev, F.M. Almuratov. On the discrete spectra of
Schrödingeroperators on one dimensional lattices.// “Mathematical analysis and its
applications in modern mathematical physics” International conference. – Samarkand,
2022. –P. 201–203.
6.
A.T.Boltaev, F.M.Almuratov, The Existence and Asymptotics of
Eigenvalues of Schrödinger Operator on Two Dimensional Lattices, Lobachevskii J.
Math. 2022.–Vol.43.– №12.–P. , 3460–3470
7.
F.M. Almuratov, I.B. Avalboyev. Asymptotics of the eigenvalues of a
discrete Schrödingeroperators on two dimensional lattices. // “Mathematical analysis
and its applications in modern mathematical physics” International conference. –
Samarkand, 2022. –P. 28–29.
8.
F.M. Almuratov. Expansion of eigenvalues of Schrödingeroperators on one
dimensional lattices.// “4th -International Conference on Research in Humanities,
Applied Sciences and Education”.–Germany, 2022.–P.152–154.
9.
S.N. Lakaev, F.M. Almuratov. On the discrete spectrum of lattice
Schrödinger operators in one and two dimensions.// “Modern methods of mathematical
physics and their applications” Republican scientific conference. – Tashkent, 2020. –
P. 143–146.
10.
S.N. Lakaev, Sh.Yu. Kholmatov, F.M. Almuratov. Coupling constant
threshold for one-particle discrete Schrödinger operators.// “Mathematical analysis and
its application to mathematical physics” Scientific programm of the international
conference . – Samarkand, 2018. – P. 85–86.
11.
Turakulov, Olim Kholbutayevich, and Uktam Haydarovich Halimov.
"TENDENCIES FOR THE DEVELOPMENT OF TECHNICAL EDUCATION FOR
FUTURE ENGINEERS." Mental Enlightenment Scientific-Methodological Journal
2022.2 (2022): 307-316.
12.
Юлдашев, Турсун и Клара Холманова. «НЕЛИНЕЙНОЕ ИНТЕГРО-
ДИФФЕРЕНЦИАЛЬНОЕ
УРАВНЕНИЕ
ФРЕДГОЛЬМА
С
ВЫРОЖДАЮЩИМСЯ ЯДРОМ И НЕЛИНЕЙНЫМ МАКСИМУМ».
Журнал
математики и информатики
1.3 (2021).
238
13.
Содиков, Тохир Аслиддинович, et al. "НЕКОТОРЫЕ МЕТОДЫ
ПРИВЕДЕНИЯ К КАНОНИЧЕСКОМУ ВИДУ И ОПРЕДЕЛЕНИЯ ТИПА
ДИФФЕРЕНЦИАЛЬНЫХ
УРАВНЕНИЙ
С
ЧАСТНЫМИ
ПРОИЗВОДНЫМИ."
МОЛОДОЙ
ИССЛЕДОВАТЕЛЬ:
К
ВЕРШИНАМ
ПОЗНАНИЯ
. 2023.
14.
Xolmanova, K. "Maksimum belgisi ostida funksional parametrni o’z ichiga
olgan
integro-defferensial
tenglamalar
sistemasi
uchun
boshlang’ich
masala."
ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ
международный научный электронный журнал
(2022).
15.
Baxtiyor, Po‘latov, et al. "BA’ZI BIR MUHIM XOSMAS
INTEGRALLARNI
HISOBLASHDA
FRULLANI
FORMULASIDAN
FOYDALANISH."
International Journal of Contemporary Scientific and Technical
Research
(2023): 363-367.
16.
Baxtiyor P. et al. BA’ZI BIR MUHIM XOSMAS INTEGRALLARNI
HISOBLASHDA FRULLANI FORMULASIDAN FOYDALANISH //International
Journal of Contemporary Scientific and Technical Research. – 2023. – С. 363-367.
17.
Xoljigitov D., Isroilov I. GRAFLAR NAZARIYASI YORDAMIDA
MANTIQIY MASALALARNI YECHISH //Журнал математики и информатики. –
2022. – Т. 2. – №. 2.
18.
Xoljigitov D., MANTIQIY I. I. G. N. Y. MASALALARNI YECHISH
//Журнал математики и информатики. – 2022. – Т. 2. – №. 2.
19.
o‘latov, B., & Ibrohimov, J. (2023). BA’ZI RATSIONAL
FUNKSIYALARNI
INTEGRALLASHDA
OSTRAGRADSKIY
USULIDAN
FOYDALANISH. Talqin
Va
Tadqiqotlar, 1(21).
извлечено
от
http://talqinvatadqiqotlar.uz/index.php/tvt/article/view/377
20.
Ibrohimov Javohir Bahrom o‘g‘li. (2022). OCHIQ CHIZIQLI QAVARIQ
TO‘PLAMDA
POLINOMIAL
QAVARIQLIKNING
YETARLI
SHARTI. International Journal of Contemporary Scientific and Technical
Research, 1(2),
363–365.
Retrieved
from
https://journal.jbnuu.uz/index.php/ijcstr/article/view/203
21.
Ibrohimov Javohir Bahrom o‘g‘li, & Po‘latov Baxtiyor Sobirovich. (2022).
OCHIQ
CHIZIQLI
QAVARIQ
TO‘PLAMDA
POLINOMIAL
QAVARIQLIK. PEDAGOGS
Jurnali, 10(3),
96–104.
Retrieved
from
http://pedagoglar.uz/index.php/ped/article/view/1184.
GAZLARNI TOZALASHDA INNOVATSION USUL VA APPARATNING
SAMARADORLIGI
t.f.f.d., (PhD) A.A. Axrorov, A.A. Botirov
Farg‘ona politexnika instituti, O‘zbekiston
Annotatsiya:
Maqolada, gazlarni ho‘l usulda toazlovchi rotor-filtrli apparatda
o‘tkazilgan tajribaviy tadqiqotlarda olingan ma’lumotlar berilgan. Tajriba natijalariga
