31 research outputs found
ΠΠΈΠ½Π°ΠΌΠΈΠΊΠ° ΠΎΡ Π»Π°ΠΆΠ΄Π΅Π½ΠΈΡ ΠΌΠ΅ΡΠ°Π»Π»ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΈΡΠ΅Π½ΠΈ ΠΏΠΎΡΠ»Π΅ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΈΠΌΠΏΡΠ»ΡΡΠ½ΠΎΠ³ΠΎ ΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΏΡΡΠΊΠ°
ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ ΠΎΡΡΡΠ²Π°Π½ΠΈΡ ΠΌΠ΅ΡΠ°Π»Π»ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΈΡΠ΅Π½ΠΈ ΠΏΠΎΡΠ»Π΅ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ Π½Π° Π½Π΅Π΅ ΠΈΠΌΠΏΡΠ»ΡΡΠ½ΠΎΠ³ΠΎ ΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΏΡΡΠΊΠ° Ρ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΡΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ 3-5 ΠΠΆ/ΡΠΌ2. ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΡ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Ρ Π½Π° ΠΈΠΎΠ½Π½ΠΎΠΌ ΡΡΠΊΠΎΡΠΈΡΠ΅Π»Π΅ Π’ΠΠΠ-4Π (Π΄Π»ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΡ ΠΈΠΌΠΏΡΠ»ΡΡΠ° - 150 Π½Ρ, ΡΡΠΊΠΎΡΡΡΡΠ΅Π΅ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΠ΅ - 250-300 ΠΊΠ). ΠΠΈΠ½Π°ΠΌΠΈΠΊΡ ΠΎΡΡΡΠ²Π°Π½ΠΈΡ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠ³ΠΎ ΠΎΡΠΏΠ΅ΡΠ°ΡΠΊΠ°, ΡΠΎΡΠΌΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΌΠΎΡΠ½ΡΠΌ ΠΈΠΎΠ½Π½ΡΠΌ ΠΏΡΡΠΊΠΎΠΌ Π½Π° ΠΌΠΈΡΠ΅Π½ΠΈ, ΡΠ΅Π³ΠΈΡΡΡΠΈΡΠΎΠ²Π°Π»ΠΈ Π² ΡΠ΅ΠΆΠΈΠΌΠ΅ Π²ΠΈΠ΄Π΅ΠΎ ΡΡΠ΅ΠΌΠΊΠΈ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΈΠ·ΠΎΡΠ°. ΠΡΠΏΠΎΠ»Π½Π΅Π½ Π°Π½Π°Π»ΠΈΠ· ΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° ΠΎΡ
Π»Π°ΠΆΠ΄Π΅Π½ΠΈΡ ΠΌΠΈΡΠ΅Π½ΠΈ Π² ΡΠ°Π·Π½ΡΡ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
: Π² Π²Π°ΠΊΡΡΠΌΠ½ΠΎΠΉ Π΄ΠΈΠΎΠ΄Π½ΠΎΠΉ ΠΊΠ°ΠΌΠ΅ΡΠ΅ ΡΡΠΊΠΎΡΠΈΡΠ΅Π»Ρ ΠΈ Π½Π° Π²ΠΎΠ·Π΄ΡΡ
Π΅
THE STATE POLICY OF SERVICE SECTOR DEVELOPMENT IN THE REPUBLIC OF KAZAKHSTAN
Currently, the service sector is one of the fastest growing sectors in Kazakhstan, so the study of the
service sector and the governmental intervention in it is essential, as it allows one to choose the
instruments and limits of the support. The aim of the article is to study and describe the
increasing role of the modern state policy of Kazakhstan in the development of the service
sector, based on a study of the impact of public investment and government programs.
The paper shows the following results:
1. Implementation of state industrial programs in Kazakhstan leads to an increase in the services
sector (expressed in the GDP structure and employment);
2. For Kazakhstan, there is still a high influence of public investments in the service sector, in
contrast to Russia;
3. The highest rates of innovation activity in the service sector are in the fields associated with
active government presence
THE STATE POLICY OF SERVICE SECTOR DEVELOPMENT IN THE REPUBLIC OF KAZAKHSTAN
Currently, the service sector is one of the fastest growing sectors in Kazakhstan, so the study of the
service sector and the governmental intervention in it is essential, as it allows one to choose the
instruments and limits of the support. The aim of the article is to study and describe the
increasing role of the modern state policy of Kazakhstan in the development of the service
sector, based on a study of the impact of public investment and government programs.
The paper shows the following results:
1. Implementation of state industrial programs in Kazakhstan leads to an increase in the services
sector (expressed in the GDP structure and employment);
2. For Kazakhstan, there is still a high influence of public investments in the service sector, in
contrast to Russia;
3. The highest rates of innovation activity in the service sector are in the fields associated with
active government presence
Recommended from our members
The formation of intercultural competence based on information and analytical technologies
The choice of a profession is a crucial part of our life. It can be claimed that nowadays many new professions
have appeared connected with information and data analysis. Besides, one should take into account the
importance of intercultural and communicative competence (ICC) and emphasize the need to consider ICC
based on the information and analytical technologies as a positive influence for the future career. The aim of
this research is to investigate the cognitive and communicative process of foreign language education at the
profile or specialized level of a secondary general school. In this regard we set specific tasks to determine the
nomenclature of sub-competencies that are part of the ICC of specialized schools students; draw up a system
of communicative tasks aiming at the formation of ICC of specialized schools students; substantiate the
relevance of integrating information and analytical technologies in the formation of specialized schools
students' ICC. In this paper, we demonstrate a model for the formation of intercultural and communicative
competence of specialized school students based on the information and analytical technologies. All
approaches, stages, and experimental techniques conducted at a specialized school in the city of Karaganda
are detailed
EXPLORING THE MITIGATION OF GREENHOUSE GAS EMISSIONS FROM THE CURRENT MUNICIPAL SOLID WASTE SYSTEM OF KAZAKHSTAN: CASE STUDY OF NUR-SULTAN CITY
As we move forward, municipal solid waste (MSW) landfills, particularly in
developing countries, contribute notably to global greenhouse gas (GHG) emissions.
Therefore, the MSW sector plays a key role in planning strategies for developing countries
such as Kazakhstan to decrease GHG emissions. With respect to the Paris Agreement,
Kazakhstan has set the target of reducing GHG emissions to 15-25% by 2030 compared to the
level of 1991, which will undoubtedly require certain measures in the field of MSW
management. Several recent articles have been published on the waste management sector of
Kazakhstan; however, none have explicitly focused on the impact of greenhouse gas emissions
and possible pathways towards sustainable management. Thus, this paper describes the existing
MSW system in Nur Sultan city as representative for the rest of the country. The quantitative
evaluation of GHG emissions from the existing MSW system in the capital is carried out based
on the IPCC methodology using the SWM-GHG calculator developed by the Institute for
Energy and Environmental Research (IFEU). An assessment and cost analysis of a set of
several suitable MSW management scenarios, such as scenario 1: existing case (15% recycling
rate and 85% disposal), scenario 2: 30% recyclable materials, and 70% sanitary landfill with
gas collection; scenario 3: 30% recyclable materials and 70% biological stabilization and
landfill without gas collection; scenario 4: 30% recyclable materials, 20% composting and 50%
waste to be sent to the WtE plant (incineration). The level of GHG emissions decreases with
the introduction of more integrated waste management methods, but requires more financial
investments. Therefore, Scenario 3 is the most efficient to implement in terms of the
combination of cost of β¬19.4 million/year and magnitude of GHG emissions of 48 kt of CO2
eq/year. The outcomes of this work will help to extrapolate the model to other large cities in
Kazakhsta
MACROPOROUS CELL-LADEN GELATIN/HYALURONIC ACID/CHONDROITIN SULFATE CRYOGELS FOR ENGINEERED TISSUE CONSTRUCTS
Cryogels are a unique macroporous material for tissue engineering. In this work, we
study the effect of hyaluronic acid on the physicochemical properties of cryogel as well as on the
proliferation of a 3D model of mesenchymal stem cells. The functional groups of the synthesized
cryogels were identified using Fourier transform infrared spectroscopy. With an increase in the
content of hyaluronic acid in the composition of the cryogel, an increase in porosity, gel content and
swelling behavior was observed. As the hyaluronic acid content increased, the average pore size
increased and more open pores were formed. Degradation studies have shown that all cryogels were
resistant to PBS solution for 8 weeks. Cytotoxicity assays demonstrated no toxic effect on viability of
rat adipose-derived mesenchymal stem cells (ADMSCs) cultured on cryogels. ADMSC spheroids
were proliferated on scaffolds and showed the ability of the cryogels to orient cell differentiation
into chondrogenic lineage even in the absence of inductive agents. Thus, our results demonstrate an
effective resemblance to extracellular matrix structures specific to cartilage-like microenvironments
by cryogels and their further perspective application as potential biomaterials
Characteristics of cholera strains isolated in Kazakhstan
In the Republic of Kazakhstan there are three types of areas with different cholera infection risk levels for people. Within cholera epidemiological surveillance the cholera strains are annually isolated from people and the environment. In this research, we studied the cholera strains isolated in Kazakhstan for 2013-2015 and they were selected for this study. All cholera strains were locally isolatedfrom people and the environment except one toxigenic imported strain of V. cholerae 01 lnaba which had genes of ctxAB, tcpA. The study showed that there were V cholerae strains which were atypical by their agglutination abilities and sensitivity to cholera phages. It can complicate the cholera laboratory diagnostics especially the diagnostics of V. cholerae Π1 and for timely recognition of cholera it is necessary to carry out the diagnostics combined with molecular and genetic methods. For the study of antibiotic sensitivity or resistance we use eight antibacterial preparations. Cholera strains isolated in Kazakhstan did not have antibiotic resistance to the studied preparations. But the cholera strain brought from Pakistan was resistant to ciprofloxacin. The lack of strong resistance of local strains to the antibacterial drugs studied is encouraging in terms of conducting aetiotropic therapy. However, the possibility of entering of antibiotic-resistant strains into Kazakhstan obliges regularly to monitor strains for their sensitivity to antibacterial drugs
ΠΡΠΎΠ±Π»Π΅ΠΌΡ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ ΡΡΡΠ΄Π΅Π½ΡΠΎΠ² Π½Π° Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΌ ΡΠ·ΡΠΊΠ΅ (EMI) Π² ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠ°Ρ ΠΠ°Π·Π°Ρ ΡΡΠ°Π½Π°
Introduction. Fascination with English medium instruction (EMI) is fast growing in higher education institutions in non-native English-speaking countries, including Kazakhstan. The Kazakhstani government adopted a trilingual education policy in 2007 and the Bologna Process in 2010. Both these initiatives motivated universities to offer academic programmes in the English language. As a result, EMI programmes are offered in over 70 higher education institutions across Kazakhstan. In addition, there are four major Kazakhstani universities which offer academic programmes in English only. Despite the increase in the number of EMI programmes, there is a lack of empirical evidence about the difficulties and challenges faced by students in the EMI programmes. Aim. The present study aimed to investigate the nature, forms, and levels of challenges graduate students face in academic reading and writing in English and the way they cope with these challenges. The study was conducted with graduate students and faculty in 10 selected Kazakhstani universities, which offer academic programmes in EMI. Research methodology and methods. The study is based on a mixed-method design, involving an online survey and semi-structured interviews. The closed-ended questions have been analysed using SPSS software (Statistical Package for the Social Sciences). The grounded theory analysis was utilised to scrutinise open-ended questions and interview transcripts. Results and scientific novelty. The studyβs results indicated two major challenges faced by graduate students in academic reading and writing: the personal-psychological challenge and sociological challenge. The first challenge includes studentsβ previous academic backgrounds, exposure, and learning experiences. The second challenge is related to English academic culture and studentsβ worldviews, concepts, and values about English as a language and medium of instruction. As a result, graduate students experienced a lack of vocabulary, inadequate academic literacy skills, unfamiliarity with academic writing styles in English, and lack of skills to synthesise reading materials. Practical significance. Hence, this study recommends systematising English language programmes across secondary and higher education institutions to help students acquire advanced English language proficiency. Also, the study results suggest that local faculty members should be trained according to international standards in terms of their English language skills and innovative teaching methods.ΠΠ²Π΅Π΄Π΅Π½ΠΈΠ΅. ΠΠ½ΡΠ΅ΡΠ΅Ρ ΠΊ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ Π½Π° Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΌ ΡΠ·ΡΠΊΠ΅ (English Medium Instruction β EMI) Π±ΡΡΡΡΠΎ ΡΠ°ΡΡΠ΅Ρ Π² Π²ΡΡΡΠΈΡ
ΡΡΠ΅Π±Π½ΡΡ
Π·Π°Π²Π΅Π΄Π΅Π½ΠΈΡΡ
ΡΡΡΠ°Π½, Π΄Π»Ρ ΠΊΠΎΡΠΎΡΡΡ
Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΈΠΉ ΡΠ·ΡΠΊ Π½Π΅ ΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠΎΠ΄Π½ΡΠΌ, Π²ΠΊΠ»ΡΡΠ°Ρ ΠΠ°Π·Π°Ρ
ΡΡΠ°Π½. ΠΡΠ°Π²ΠΈΡΠ΅Π»ΡΡΡΠ²ΠΎ ΡΡΡΠ°Π½Ρ ΠΏΡΠΈΠ½ΡΠ»ΠΎ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΡ ΡΡΠ΅Ρ
ΡΡΠ·ΡΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ Π² 2007 Π³ΠΎΠ΄Ρ ΠΈ ΠΠΎΠ»ΠΎΠ½ΡΠΊΠΈΠΉ ΠΏΡΠΎΡΠ΅ΡΡ Π² 2010 Π³ΠΎΠ΄Ρ. ΠΠ±Π΅ ΡΡΠΈ ΠΈΠ½ΠΈΡΠΈΠ°ΡΠΈΠ²Ρ ΠΏΠΎΠ±ΡΠ΄ΠΈΠ»ΠΈ ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΡ ΠΏΡΠ΅Π΄Π»Π°Π³Π°ΡΡ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ Π½Π° Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΌ ΡΠ·ΡΠΊΠ΅. Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΎΠ½ΠΈ ΠΏΠΎΡΠ²ΠΈΠ»ΠΈΡΡ Π² 70 Π²ΡΠ·Π°Ρ
ΠΠ°Π·Π°Ρ
ΡΡΠ°Π½Π°. ΠΠΎΠ»Π΅Π΅ ΡΠΎΠ³ΠΎ, Π½Π° Π΄Π°Π½Π½ΡΠΉ ΠΌΠΎΠΌΠ΅Π½Ρ Π΅ΡΡΡ ΡΠ΅ΡΡΡΠ΅ ΠΊΡΡΠΏΠ½ΡΡ
ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠ° Ρ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ°ΠΌΠΈ ΠΈΡΠΊΠ»ΡΡΠΈΡΠ΅Π»ΡΠ½ΠΎ Π½Π° Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΌ ΡΠ·ΡΠΊΠ΅. ΠΠ΅ΡΠΌΠΎΡΡΡ Π½Π° ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ EMI, ΠΎΡΡΡΡΡΡΠ²ΡΡΡ ΡΠΌΠΏΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ Π΄Π°Π½Π½ΡΠ΅ ΠΎ ΡΡΡΠ΄Π½ΠΎΡΡΡΡ
ΠΈ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ°Ρ
, Ρ ΠΊΠΎΡΠΎΡΡΠΌΠΈ Π² Π½ΠΈΡ
ΡΡΠ°Π»ΠΊΠΈΠ²Π°ΡΡΡΡ ΡΡΡΠ΄Π΅Π½ΡΡ. Π¦Π΅Π»Ρ. ΠΠ°Π½Π½ΠΎΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈΠ·ΡΡΠ°Π΅Ρ ΠΏΡΠΈΡΠΎΠ΄Ρ, ΡΠΎΡΠΌΡ ΠΈ ΡΡΠΎΠ²Π½ΠΈ ΠΏΡΠΎΠ±Π»Π΅ΠΌ, Ρ ΠΊΠΎΡΠΎΡΡΠΌΠΈ ΡΡΠ°Π»ΠΊΠΈΠ²Π°ΡΡΡΡ ΠΌΠ°Π³ΠΈΡΡΡΠ°Π½ΡΡ ΠΈ Π΄ΠΎΠΊΡΠΎΡΠ°Π½ΡΡ ΠΏΡΠΈ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΌ ΡΡΠ΅Π½ΠΈΠΈ ΠΈ ΠΏΠΈΡΡΠΌΠ΅ Π½Π° Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΌ ΡΠ·ΡΠΊΠ΅, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠΎ, ΠΊΠ°ΠΊ ΠΎΠ½ΠΈ ΡΠΏΡΠ°Π²Π»ΡΡΡΡΡ Ρ ΡΡΠΈΠΌΠΈ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ°ΠΌΠΈ. ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΠΎΡΡ ΡΡΠ΅Π΄ΠΈ ΡΡΡΠ΄Π΅Π½ΡΠΎΠ² ΠΌΠ°Π³ΠΈΡΡΡΠ°ΡΡΡΡ ΠΈ Π΄ΠΎΠΊΡΠΎΡΠ°Π½ΡΡΡΡ, Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠ΅ΠΏΠΎΠ΄Π°Π²Π°ΡΠ΅Π»Π΅ΠΉ ΠΈΠ· 10 Π²ΡΠ±ΡΠ°Π½Π½ΡΡ
ΠΊΠ°Π·Π°Ρ
ΡΡΠ°Π½ΡΠΊΠΈΡ
Π²ΡΠ·ΠΎΠ², ΠΏΡΠ΅Π΄Π»Π°Π³Π°ΡΡΠΈΡ
Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ Ρ EMI. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ ΠΈ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ. ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅Ρ Π΄ΠΈΠ·Π°ΠΉΠ½ ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ², Π²ΠΊΠ»ΡΡΠ°ΡΡΠΈΠΉ ΠΎΠ½Π»Π°ΠΉΠ½-ΠΎΠΏΡΠΎΡ ΠΈ ΠΏΠΎΠ»ΡΡΡΡΡΠΊΡΡΡΠΈΡΠΎΠ²Π°Π½Π½ΡΠ΅ ΠΈΠ½ΡΠ΅ΡΠ²ΡΡ. ΠΠ°ΠΊΡΡΡΡΠ΅ Π²ΠΎΠΏΡΠΎΡΡ Π±ΡΠ»ΠΈ ΠΏΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Ρ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠ°ΠΊΠ΅ΡΠ° (SPSS). ΠΠ΅ΡΠΎΠ΄ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠ΅ΠΎΡΠΈΠΈ Π±ΡΠ» ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ Π΄Π»Ρ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° ΠΎΡΠΊΡΡΡΡΡ
Π²ΠΎΠΏΡΠΎΡΠΎΠ² ΠΈ ΡΡΠ°Π½ΡΠΊΡΠΈΠΏΡΠΎΠ² ΠΈΠ½ΡΠ΅ΡΠ²ΡΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΈ Π½Π°ΡΡΠ½Π°Ρ Π½ΠΎΠ²ΠΈΠ·Π½Π°. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π²ΡΡΠ²ΠΈΠ»ΠΈ Π΄Π²Π΅ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ, Ρ ΠΊΠΎΡΠΎΡΡΠΌΠΈ ΡΡΠ°Π»ΠΊΠΈΠ²Π°ΡΡΡΡ ΡΡΡΠ΄Π΅Π½ΡΡ ΠΏΡΠΈ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΌ ΡΡΠ΅Π½ΠΈΠΈ ΠΈ ΠΏΠΈΡΡΠΌΠ΅: Π»ΠΈΡΠ½ΠΎΡΡΠ½ΠΎ-ΠΏΡΠΈΡ
ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΈ ΡΠΎΡΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠ°Ρ. ΠΠ΅ΡΠ²Π°Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° Π²ΠΊΠ»ΡΡΠ°Π΅Ρ Π² ΡΠ΅Π±Ρ ΠΏΡΠ΅Π΄ΡΠ΄ΡΡΠΈΠΉ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΎΠΏΡΡ ΡΡΡΠ΄Π΅Π½ΡΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΠΎΠΏΡΡ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ. ΠΡΠΎΡΠ°Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° ΡΠ²ΡΠ·Π°Π½Π° Ρ Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΉ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΊΡΠ»ΡΡΡΡΠΎΠΉ ΠΈ ΠΌΠΈΡΠΎΠ²ΠΎΠ·Π·ΡΠ΅Π½ΠΈΠ΅ΠΌ, ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΡΠΌΠΈ ΠΈ ΡΠ΅Π½Π½ΠΎΡΡΡΠΌΠΈ ΡΡΡΠ΄Π΅Π½ΡΠΎΠ² Π² ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΈ Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠ³ΠΎ ΡΠ·ΡΠΊΠ° ΠΊΠ°ΠΊ ΡΠ·ΡΠΊΠ° ΠΈ ΡΡΠ΅Π΄ΡΡΠ²Π° ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ. Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΡΡΠ΄Π΅Π½ΡΡ ΡΡΠΎΠ»ΠΊΠ½ΡΠ»ΠΈΡΡ ΡΠΎ ΡΠ»Π΅Π΄ΡΡΡΠΈΠΌΠΈ ΡΡΡΠ΄Π½ΠΎΡΡΡΠΌΠΈ: Π½Π΅Ρ
Π²Π°ΡΠΊΠ° ΡΠ»ΠΎΠ²Π°ΡΠ½ΠΎΠ³ΠΎ Π·Π°ΠΏΠ°ΡΠ°, Π½Π΅Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΡΠ΅ Π½Π°Π²ΡΠΊΠΈ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π³ΡΠ°ΠΌΠΎΡΠ½ΠΎΡΡΠΈ, Π½Π΅Π·Π½Π°Π½ΠΈΠ΅ ΡΡΠΈΠ»Π΅ΠΉ Π°ΠΊΠ°Π΄Π΅ΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠΈΡΡΠΌΠ° Π½Π° Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΌ ΡΠ·ΡΠΊΠ΅ ΠΈ ΠΎΡΡΡΡΡΡΠ²ΠΈΠ΅ Π½Π°Π²ΡΠΊΠΎΠ² ΡΠΈΠ½ΡΠ΅Π·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΡΠΈΡΠ°Π½Π½ΠΎΠ³ΠΎ. ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ Π·Π½Π°ΡΠΈΠΌΠΎΡΡΡ. Π’Π°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ, Π΄Π°Π½Π½ΠΎΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄ΡΠ΅Ρ ΡΠΈΡΡΠ΅ΠΌΠ°ΡΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠ³ΠΎ ΡΠ·ΡΠΊΠ° Π² ΡΡΠ΅Π΄Π½ΠΈΡ
ΠΈ Π²ΡΡΡΠΈΡ
ΡΡΠ΅Π±Π½ΡΡ
Π·Π°Π²Π΅Π΄Π΅Π½ΠΈΡΡ
, ΡΡΠΎΠ±Ρ ΠΏΠΎΠΌΠΎΡΡ ΡΡΠ°ΡΠΈΠΌΡΡ ΠΎΠ²Π»Π°Π΄Π΅ΡΡ Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΈΠΌ ΡΠ·ΡΠΊΠΎΠΌ Π½Π° ΠΏΡΠΎΠ΄Π²ΠΈΠ½ΡΡΠΎΠΌ ΡΡΠΎΠ²Π½Π΅. ΠΡΠΎΠΌΠ΅ ΡΠΎΠ³ΠΎ, ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°ΡΡ, ΡΡΠΎ ΠΌΠ΅ΡΡΠ½ΡΠ΅ ΠΏΡΠ΅ΠΏΠΎΠ΄Π°Π²Π°ΡΠ΅Π»ΠΈ Π΄ΠΎΠ»ΠΆΠ½Ρ Π±ΡΡΡ ΠΎΠ±ΡΡΠ΅Π½Ρ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΌΠ΅ΠΆΠ΄ΡΠ½Π°ΡΠΎΠ΄Π½ΡΠΌΠΈ ΡΡΠ°Π½Π΄Π°ΡΡΠ°ΠΌΠΈ, Π²ΠΊΠ»ΡΡΠ°Ρ Π½Π°Π²ΡΠΊΠΈ Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠ³ΠΎ ΡΠ·ΡΠΊΠ° ΠΈ ΠΈΠ½Π½ΠΎΠ²Π°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ.The research study is funded by Nazarbayev University under Collaborative Research Programme Grant β 021220CRP1322.ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠΈΠ½Π°Π½ΡΠΈΡΡΠ΅ΡΡΡ ΠΠ°Π·Π°ΡΠ±Π°Π΅Π² Π£Π½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠΎΠΌ Π² ΡΠ°ΠΌΠΊΠ°Ρ
Π³ΡΠ°Π½ΡΠ° ΠΡΠΎΠ³ΡΠ°ΠΌΠΌΡ ΡΠΎΠ²ΠΌΠ΅ΡΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ β 021220CRP1322
Optimal Packing of Two Disks on Torus
The article is devoted to recently established connection between the packing problem of disks on torus and the effective conductivity of composites with circular inclusions. The packing problem is usually investigated by geometrical arguments, the conductivity problem by means of elliptic functions. An algorithm is developed in order to determine the optimal location of two disks on torus formed by the hexagonal lattice and square lattice. The corresponding minimization function is constructed in terms of expressions consisting of elliptic functions with unknown arguments. The numerically found roots coincide with the previously established optimal points by a pure geometrical study