Broad Background Research Articles

New complexity and approximability results for minimizing the total weighted completion time on a single machine subject to non-renewable resource constraints

We consider single machine scheduling problems with additional non-renewable resource constraints. Examples for non-renewable resources include raw materials, energy, or money. Usually they have an initial stock and replenishments arrive over time at a-priori known time points and quantities. The jobs have some requirements from the resources and a job can only be started if the available quantity from each of the required resources exceeds the requirements of the job. Upon starting a job, it consumes its requirements which decreases the available quantities of the respective non-renewable resources. There is a broad background for this class of problems. Most of the literature concentrate on the makespan, and the maximum lateness objectives. This paper focuses on the total weighted completion time objective for which the list of the approximation algorithms is very short. We extend that list by considering new special cases and obtain new complexity results and approximation algorithms.

On the question of the origins of Berdyaev's creativity. Historical excursion into Russian-Italian cultural relations

The article is devoted to one of the most important sources of Berdyaev's creativity, which is usually overlooked when studying his legacy. We are talking about the philosopher's Italian travels, which had a "huge" influence on his work. But since his trips go far beyond the boundaries of his personal experience alone and fit seamlessly into the general context of Russian-Italian cultural ties, it seemed appropriate to turn to their expanded disclosure within the broader theme of "Italy and Russia" in order, on the one hand, to show the inextricable connection of Berdyaev's Italian travels with this centuries-old tradition, thanks to which formed the soil that will become a breeding ground for many of the defining provisions of Berdyaev's aesthetics. And on the other hand, against this broader historical background of cultural ties between our countries, the declared topic appears more multifaceted, highlighting the full significance and influence of Italian travels on Berdyaev's work, and at the same time demonstrating their far from accidental nature, which caused both his research interest in Italian culture and the conceptual foundations of his philosophical- aesthetic thought. The scientific novelty of the article lies in the fact that it is the first attempt in Russian literature to study Berdyaev's Italian travels as one of the most important sources of his work, which have not yet been the subject of special study. In addition, they are viewed against a broad background of Russian-Italian cultural ties that have been formed over several centuries, which the Silver Age inherited as an established tradition. This makes it possible to identify both their organic connection and continuity with this tradition, and hence their quite natural character, and Berdyaev's active role in the development and strengthening of these ties.

In search of reciprocity: Feminist challenges in Posthumanist thinking – An intellectual meditation

abstract There are many spokes to the critical wheel of Posthuman Feminism. It is a richly diverse field of thinking, and may be considered from multiple vantage points. Indeed, the metaphor of the rhizome, following Giles Deleuze, is more appropriate here and is, in fact, used more frequently in this context. In this article, I shall sketch simple and broad contours of the move towards Posthumanism in general, and Posthuman Feminism in particular, drawing from key Posthuman feminist theorists, such as Rosi Braidotti. Prompted by my own academic journey and learnings as a literary critic and emerging feminist from the 1970s – the “politics of location” from which I speak − I will highlight some of the signposts I am encountering en route to understanding Posthumanism and Posthuman Feminism, as I revise my ways of reading and inhabiting our common world. Developed, against the broad background of my own journey as a critical scholar, the essay is presented as a simple, exploratory introduction to a wide, engaging and convoluted field, and will conclude with a few important challenges for Posthuman feminist intellectual and activist work in the current global and planetary context.

Deutschsprachige Schriftsteller, die Schwedische Akademie und Carl David af Wirsén (Janina Gesches Buch über deutschsprachige Nobelpreisträger für Literatur in der ersten Hälfte des 20. Jahrhunderts)

The presented text consists of two parts. The first is a review of Janina Gesche’s book devoted to the German-speaking winners of the Nobel Prize in Literature in the first half of the twentieth century. Gesche not only meticulously reconstructed the activities of the Swedish Academy, but also showed the cultural German-Swedish relations in this period against a broad background. The second part shows the activities of Carl David af Wirsén (1842–1912), who as secretary of the Academy had a huge impact on who will be honored with the award. Wirsén’s attempt to create his own rules for granting the Nobel Prize ended in failure, as shown by the theory of Pierre Bourdieu.

Find Small Objects in UAV Images by Feature Mining and Attention

With the increasing popularity of Unmanned Aerial Vehicles (UAVs), the accuracy of detecting small objects in large-view images is also expected to increase. However, accurate small object detection is still a challenging problem. Currently, Image Pyramid Network, Feature Pyramid Network (FPN), rich training strategies and data augmentation are widely used to address this problem. To accurately detect small objects, the most important thing is to mine for more feature information. We propose Widened Residual Block (WRB) to break through the bottleneck of residual information gain to extract more feature information. The second is to emphasize or suppress features to prevent small objects from being overwhelmed by a broad background. We introduce an attention mechanism into PANet and propose Enhanced Attention PANet (EA-PANet), which consists of two parts: Context Attention Module (COAM) and Attention Enhancement Module (AEM). COAM outputs attention heatmaps with context, and AEM fuses features from the channel attention module (CAM) and COAM to avoid distraction from a vast background. In addition, we design a lightweight Decoupled Attention Head (DA-head) to dynamically compute important regions for specific tasks and achieve reliable predictions. Experiments show that our method outperforms state-of-the-art (SOTA) detectors. The source code for this work is available at https://github.com/liuxiaolei111/FindSmallObjects.

Варшавский университет в системе высшего (университетского) образования Российской империи в первой трети XIX в.

The article is devoted to the history of the establishment of the University of Warsaw in 1816 and its development until 1831 when the university was closed after the suppression of the November Uprising of 1830–31. The specificity of the University of Warsaw was determined by the fact that during that time the Congress Kingdom of Poland that had been annexed to Russia in 1815 was an autonomous territorial entity and had a separate educational system that was not subordinate to the Ministry of National Education in St Petersburg. Neither Russian nor Polish historiography has made a comprehensive comparison of the University of Warsaw with Russian higher educational institutions due to the isolated status of the former in 1816–31. The article makes an attempt to identify similarities and differences in the functioning of these higher educational institutions on the basis of the documents that regulated the activities of Warsaw and Russian universities. A comparison is made between the structure and organization of the University of Warsaw and other universities of the empire, their collegiate governing bodies, budgets, salaries of professors, admission and terms of study of students, their number, the procedure for awarding academic degrees, etc. The unpopular measures taken by the authorities of the Congress Kingdom of Poland in the field of education in the 1820s, which were accompanied by the increased control over the students and the professors of the university and the attempts to limit its autonomy and divide it into separate higher schools, are shown against the background of the general reactionary policy towards universities. A comparative analysis allows us to draw the following conclusions: the principles of organization of the University of Warsaw and Russian universities that were founded at the beginning of the 19th century had a number of common features, which was associated with borrowing the models of higher educational institutions from Germany and partly from France. Structure, staff and other differences between the educational institutions under consideration were determined by the national features and traditions of Polish education and by greater similarity between the University of Warsaw and the universities of Western Europe. The results obtained contribute to presenting the development of the University of Warsaw in 1816–31 against a broader background and also provide new illustrative material for comparing Russian universities with the “national” universities that existed within the empire.

On a non-Newtonian fluid type equation with variable diffusion coefficient

<abstract><p>Since the non-Newtonian fluid type equations arise from a broad and in-depth background, many research achievements have been gained from 1980s. Different from the usual non-Newtonian fluid equation, there is a nonnegative variable diffusion in the equations considered in this paper. Such a variable diffusion reflects the characteristic of the medium which may not be homogenous. By giving a generalization of the Gronwall inequality, the stability and the uniqueness of weak solutions to the non-Newtonian fluid equation with variable diffusion are studied. Since the variable diffusion may be degenerate on the boundary $ \partial \Omega $, it is found that a partial boundary value condition imposed on a submanifold of $ \partial\Omega\times (0, T) $ is enough to ensure the well-posedness of weak solutions. The novelty is that the concept of the trace of $ u(x, t) $ is generalized by a special way.</p></abstract>

Из паремиологического наследия русинского языка (орнитоним куриця, курка)

The article offers a LinguocuLturoLogical and axiological analysis of Rusin proverbs and sayings by means of the ornithonyms ‘kuritsya', ‘kurka. The total number of such language units is 25. The material was found in the Rusin dictionaries of Dmitro Pop and Ihor Kercha, as well as in numerous paremioLogicaL collections of Ukrainian, Belarussian, Russian and other Slavonic small folklore. When necessary, the author employed non-Slavic sources to expand the areal zone of Rusian ornithological paremioLogy. Ornithological proverbs make an active group of paremioLogicaL animalisms. According to the previous studies, some of these Rusin lexemes (eg. potya) go back to the ProtoSlavic era, demonstrating the value of the Rusin language material for common Slavic reconstructions. The analyzed material shows structural-semantic and figurative diversity: 1. Sayings (resp. phraseological units): Zbyv by piLa khizhj kuri pytati; zdokhLa tota kurochka, shto dvj yaytsya nesLa; kuryacha pamnyat'; kur'om na smikh; kuryachoy oko. 2. Stable comparisons: goLoden, gi meLnikova kurka; kuritsmat'sya gi kvochka na yayts'okh; rozsiLasya gi kvochka; pisati gi kuritsya Labov; takiy gi mokra kuritsya; trafiLosya gi sLipyv kuritsi zirnya; upaLo mu gi sLipyv kuritsi zirnya. 3. Proverbs: Iz kur'mi Ligay, a z kogutami vstavay; Ligay spati iz kur'mi, a vstavay z kogutom; I sLipyv kuritsi zirnya sya trafit'; Komu svaL'ba, a kuritsi smirt'; Komu shto, a kuritsi zirnya; Kotra kuritsya mnogo kodkodache, tota sya maLo nesche; Kuri na sidaLo, baba na LezhaLo; Kuritsya grebe, oby dashto ugrebLa; Kuritsya dumaLa ta y zdokhLa; Kurya kvochtsi ne rozkazue; Yaytse kuritsyu uchit'. 4. MisceLLaneous: Prisyad'te damaLo, oby sya u nas kuri nesLi; Khodi na paL'ts'okh, kid' khochesh imiti kuritsyu na yayts'okh; aLso the figurative Rusin name of the PLeiades, the Seven Stars -' Kurichky'. Rusin proverbs with ornithonymic components reflect the organic unity of the spiritual, mentaL, and bodily characteristics of peopLe and the various situations in which they find themseLves. These proverbs aLso reflect such aspects as emotionaL and mentaL characteristics, physicaL and speech activity, inteLLectuaL properties, physioLogicaL state, etc. The presented facts convincingLy prove the significance of such a characteristic by Linguistic means. Reflecting the conceptuaL universaLity of ornithonyms, they demonstrate both specific interLinguaL and cuLturaL ties with the paremioLogy of other peopLes, and their nationaL specificity, formed in a particuLar territory in a particuLar historicaL period. As compared with simiLar Ukrainian, BeLarussian, and Russian, as weLL as PoLish, SLovak, and Czech proverbs against a broad pan-European background, the specificity of Rusin proverbs and sayings manifests mainLy in their form, not in their content. The didactic meaning of SLavic (incLuding Rusin) paremioLogy remains mainLy internationaL. Thus, the Rusin Language and its cuLture, incLuding paroemias, demonstrate the ancient and inseparabLe unity of SLavic and non-SLavic Europe, constantLy enriching each other with their interpenetration.

"Latin American Switzerland"

The publication acquaints readers with a new serious research of the famous Russian Latin Americanist N.S. Ivanov. The review provides a detailed description of the monograph. It is noted that the publication is the first fundamental multifaceted investigation of the of the history of Uruguay. The author managed to illuminate practically all the most important episodes of the country's history on a broad historical background - the colonial period, the War of Independence, the formation of an independent state, the formation of the country's political structure, its foreign policy position, socio-economic and cultural development. The publication is of undoubted value for specialists, as well as everyone who is interested in the history of Latin America.

A Review on Resistance to Biotic Stress in Leaf-Colored Plant

As sessile organisms, plants have to be subjected to insect attack. Over the long course of evolution, plants have produced many mechanisms to resist this biotic stress such as pigment accumulation. Pigment levels determined depth and distribution of leaf color, thereby indirectly or directly affecting the behavior of insect attack. Therefore, understanding the mechanism of mutual recognition between leaf color and insect will provide important theoretical insight for the cultivation and improvement of new cultivars. This paper outlines leaf-color formation and the effect of pigment on the behavior of insect attack, and explores the challenge of research in the interaction between leaf color and insect, as soon as the potential direction for future development. This will give a broad background for improvements of colored plants with resistance to insect attack.

The Origins of Conservative Ideology in Russia

The review is devoted to the analysis of the book “Romantics, Reformers, Reactionaries. Russian Conservative Thought and Politics in the Reign of Alexander I” by the famous American historian Alexander Martin dedicated to the history of Russian conservatism in the first quarter of the 19th century. The author explores the process of formation of conservative ideology in politics, Russian social thought, culture, and also reveals its origins, defines features that are distinctive from the liberal doctrine. Against the broad background of the political and cultural life of Russia at that time, the complex relationship of various systems of conservative ideology is shown. It is demonstrated that the religious conservatism of such prominent defenders of Catholicism and Orthodoxy as Mestre and Sturdza, the clash of their opposite positions, disputes about the historical fate and civilizational purpose of Christianity, as well as the romantic nationalism of A. S. Shishkov and S. N. Glinka and the noble conservatism of N. M. Karamzin and F. V. Rostopchin reflected the search for new forms of anti-revolutionary conservative worldview. The position of Alexander Martin is especially noteworthy in relation to the significant contribution of conservative thinkers of Alexander's reign to the formation of state policy in the interests of Russia, the formation of the foundations of civil society, the development of national identity, Russian culture and language. The author comes to a reasonable conceptual conclusion that although the early conservatives did not develop a single ideology, they laid the foundation for various forms of Russian conservatism in the second quarter of the 19th – early 20th centuries.

O potrzebie euro-nowelizacji Konstytucji RP

Today, the necessity of adapting the constitution to certain general standards or models is clear. No constitution, including the Constitution of Poland, is a fully independent and autonomous act separate from a broader background. At the present moment, such background is created by e.g. the international models and general rules, and solutions applied in a democratic constitutional state. Every constitution creator wishes to form a truly modern act that will be adequate to the need of the moments and, at the same time, properly (democratically) legitimized, which must respect certain, at least the minimum requirements in the scope of defining the catalogue of principal rules or rights and freedoms of an individual. The so–called standard in constitutional law is an unquestionable fact. This general standard, being the effect of globalization and European integration, can be called a form of Euro–amendment to the Constitution in the broadest possible sense of this expression. Every country must respect it, if it wishes to participate in the family of democratic countries. However, the proper Euro–amendment has a much more modest reach and it covers the part of constitutional matter which pertains to the participation of a state in the European Union directly. The Euro–amendment understood in this way can be divided into the widely understood Euro–amendment (sensu largo), which will contain procedures, e.g. of a country accession to the Union and enforcement of its rights and the narrow Euroamendment (senstu stricto), which should be understood as adaptation of the constitution to the mechanism of a country’s accession to the Economic and Monetary Union and, in consequence, replacement of the national currency with Euro. In Poland, proper Euro–amendment has not been introduced in the wide or in the narrow sense. It seems, however, that it is more and more necessary not only owing to the deepening participation of Poland in the European Union structures but, most of all, owing to the willingness (and the need resulting from the accession treaty) to accept the Euro currency.

ОРГАНИЗАЦИЈА ЗАНАТСТВА У УРБАНИМ ЦЕНТРИМА СРЕДЊОВЕКОВНЕ СРБИЈЕ ORGANIZATION OF CRAFTSMEN IN URBAN CENTERS OF MEDIEVAL SERBIA

Various forms of organization of craftsmen existed in the territory of medieval Serbian countries, in the form of either public or private law relations. While based on numerous data it has been established that there was business cooperation and even association between domestic traders and craftsmen, the issue of formal legal organization of craftsmen in urban centers is less clarified due to poorly preserved sources. In this paper, based on the available parallels, the existing data from written or material sources have been reconsidered. Against such a broad background, it was possible to indicate the presence of elements of formal legal craft organizations – guilds, as suggested by the use of the title of the protomagister in the middle of internal hierarchy in urban centers in medieval Serbia.

THE FRANCISCAN MISSION OF GIOVANNI DA PIAN DEL CARPINE 1245: THE COMPANIONS OF THE PAPAL LEGATE IN BOHEMIA AND THEIR RELATIONSHIP TO RUS’

The article aims to analyze the participation of Franciscan missionaries from Bohemia in the embassy of Giovanni da Pian del Carpine to the Mongol khan in the context of Rus’-Czech relations in the middle of the XIIIth century. Research methodology. The research methodology is based on a systematic approach to the study of socio-political, military, and socio-economic phenomena in their development and relationships, based on the principles of scientificity, objectivity, systematicity, and historicism. In the study, general scientific and special historical methods were used, namely: comparative-historical, critical, problem-chronological, source-based, and analytical methods. The scientific novelty of the article is that historiography has not yet paid attention to the bohemian origins of the two members of the Carpine mission. In addition, this fact did not fit into the broader background of Rus’-Czech relations at the time. The role of the Pope in resolving the international situation in Central and Eastern Europe is highlighted, as well as how this relates to the policies of the Czech Przemyslids and the Galician-Volynian Romanovychi. Conclusions. It was noted that the factor of the emergence of nomads and their threat to Europe was crucial for the Czech-Rus’ contacts, which became part of the eastern policy of the Apostolic Capital. Since, in the conditions of the Mongol threat, both the Przemyslids and the Romanovychi actively communicated with the Pope, the Czech-Rus’ communication became inevitable. With this in mind, the article draws attention to the following points. First, the amount of knowledge about Rus’ in Bohemia at that time was analyzed. Secondly, the preconditions that contributed to the Czech-Rus’ rapprochement with Rome, despite the unfavorable policy of the German emperor, were highlighted. Third, the Rus’-Czech relations of the middle of the XIIIth century and their manifestation in the form of the Galician-Czech union in the following decades were interpreted in the international context. The events of the war for the inheritance of the Babenbergs in 1246–1278 and the Czech-Rus’ relations in their context should be considered as a continuation of the political line initiated by the Pope and executed by the Franciscans.

Lowland amphibians - recalculation of data on effects of diluted thyroxine

Our previous paper described methodological problems and a generally acceptable pooling method for metamorphosis experiments and application of that method to the results of multicentre experiments performed over the course of two decades (1990 - 2010) on highland amphibians (Rana temporaria) treated with a homeopathically prepared high dilution of thyroxine (“30x”). Differences between treatment groups thus calculated were in line with those obtained with other pooling methods: Thyroxine 30x does slow down metamorphosis in highland amphibians. This follow up paper provides a broader background on metamorphosis physiology and describes application of the pooling method to experiments with Rana temporaria from lowland biotopes both with a moderate dilution of thyroxine (“8x”) and with 30x. Analogously prepared water was used for control (water 8x or 30x). Development was, again as above, monitored by documenting the number of animals that had entered the 4-legged stage. Experiments were carried out between 1990 and 2000 by different researchers independently and in blind. As it is well known, metamorphosis can be speeded up by thyroxine 10-8 mol/l; interestingly, thyroxine 8x may produce a reverse, i.e. inhibiting effect (p < 0.01). In contrast to the inhibiting effect of thyroxine 30x on highland larvae (see above), 2-legged lowland larvae did not react to thyroxine 30x (p > 0.05). However, an inhibiting effect on lowland larvae was found when animals were treated from the spawn stage on (p < 0.01).

Effects of substrate phonon absorption on the resonance behavior of metal–insulator–metal metamaterial terahertz absorbers

We have investigated the effects of substrate phonon absorption on the resonance behavior of metal–insulator–metal (MIM) double-layer metamaterial absorbers (MMAs) in the terahertz (THz) frequency range. A sharp resonant absorption dip is clearly observed for a metamaterial-on-ground-plane (MMOGP) structure fabricated on a semi-insulating (SI) GaAs substrate when THz radiation is incident from the surface metamaterials (MMs) side. However, when the THz is incident from the substrate side to the ground-plane-on-metamaterial (GPOMM) structures fabricated on a SI GaAs substrate, we find that the resonance dip is almost merged into the broad background of acoustic phonon absorption. The resonant absorption is recovered when the GaAs substrate is replaced with a high-resistivity Si substrate. These findings demonstrate that the choice of substrates is very important to suppress the absorption by acoustic phonons absorption in the THz range and achieve high-quality factor resonance.

Effect of Reactive Ion Etching on the Luminescence of GeV Color Centers in CVD Diamond Nanocrystals.

The negatively charged germanium-vacancy GeV− color centers in diamond nanocrystals are solid-state photon emitters suited for quantum information technologies, bio-sensing, and labeling applications. Due to the small Huang–Rhys factor, the GeV−-center zero-phonon line emission is expected to be very intensive and spectrally narrow. However, structural defects and the inhomogeneous distribution of local strains in the nanodiamonds result in the essential broadening of the ZPL. Therefore, clarification and elimination of the reasons for the broadening of the GeV− center ZPL is an important problem. We report on the effect of reactive ion etching in oxygen plasma on the structure and luminescence properties of nanodiamonds grown by hot filament chemical vapor deposition. Emission of GeV− color centers ensembles at about 602 nm in as-grown and etched nanodiamonds is probed using micro-photoluminescence and micro-Raman spectroscopy at room and liquid nitrogen temperature. We show that the etching removes the nanodiamond surface sp2-induced defects resulting in a reduction in the broad luminescence background and a narrowing of the diamond Raman band. The zero-phonon luminescence band of the ensemble of the GeV− centers is a superposition of narrow lines originated most likely from the GeV− center sub-ensembles under different uniaxial local strain conditions.

Acoustic allometry, background stream noise and its relationship with large-bodied and voiceless rheophilic frogs

Anurans that breed in rivers and cascade streams need to deal with the influence of the low-frequency water flow noise that could interfere with their acoustic communication. To overcome that, some species display visual signals or emit high-pitched calls. However, there is a constraint related to body size [snout-vent length (SVL)] that limits the anurans' calling frequency range. Thus, to evaluate if water noise influences this allometric relationship, we analysed hylodid frogs’ SVL, dominant frequencies of advertisement call, and background noise to which individuals are submitted. Although Hylodes and Crossodactylus have differences in morphology and natural history, we found negative acoustic allometry in both genera. This allometry may be part of the explanation of the absence of advertisement calls in Megaelosia and Phantasmarana genera. Based on the large body lengths of Megaelosia and Phantasmarana species, if they could call, it would be low-pitched and acoustically masked by the stream noise. Besides, we found a positive relationship between Hylodes phyllodes advertisement call and background sound pressure level (SPL), thus, the analysed individuals, emitted louder calls when submitted to louder background SPLs. This study exemplifies the complexity of acoustic allometry in rheophilic species: we evidenced a strategy for intraspecific communication effectiveness in rivers and streams with broad water flow background noise; and how acoustic allometry coped with background noise could be implying in unexpected trait evolution, as lack of vocalization in anurans.

Broad background in electron diffraction of 2D materials as a signature of their superior quality

An unusually broad bell-shaped component (BSC) has been previously observed in surface electron diffraction on different types of 2D systems. It was suggested to be an indicator of uniformity of epitaxial graphene (Gr) and hexagonal boron nitride (hBN). In the current study we use low-energy electron microscopy and micro-diffraction to directly relate the BSC to the crystal quality of the diffracting 2D material. Specially designed lateral heterostructures were used to map the spatial evolution of the diffraction profile across different 2D materials, namely pure hBN, BCN alloy and pure Gr, where the alloy region exhibits deteriorated structural coherency. The presented results show that the BSC intensity has a minimum in the alloyed region, consequently showing that BSC is sensitive to the lateral domain size and homogeneity of the material under examination. This is further confirmed by the presence of a larger number of sharp moiré spots when the BSC is most pronounced in the pure hBN and Gr regions. Consequently, it is proposed that the BSC can be used as a diagnostic tool for determining the quality of the 2D materials.

Influence of different ultrasonic transducers on the precision of fastening force measurement

In the assembly process of aero-engines, the accurate measurement of bolt fastening force is particularly important, which is related to the normal operation of the entire system. Ultrasonic non-destructive testing has been applied to bolt fastening force measurement and has a broad application background. The core device of the ultrasonic transducer is a piezoelectric ceramic wafer, and the normal operation of the wafer is affected by the power frequency and external stress. For the same type of bolt with the same nominal diameter, the ultrasonic transducer wafers of different diameters will cause the transducer wafers to be subjected to different external stresses. According to the acoustoelastic effect, the relationship between the variation of time of flight (TOF) and bolt fastening force of different types of ultrasonic transducers is established. Then the measurement errors of various models are calculated and analyzed. The experimental results show that when the nominal diameter of the bolt is close to the diameter of the wafer of the ultrasonic transducer, the fastening force measurement accuracy of the bolt is the highest. When small or large size transducer is used, the measurement accuracy will be reduced due to energy and external stress. When a transducer with a higher center frequency is used to measure the fastening force of the bolt rod, the accuracy of the model established due to the faster attenuation of the sound wave is reduced, and the accuracy of the measurement result is reduced. Therefore, in order to ensure the accuracy of the fastening force measurement in the aerospace field, when selecting an ultrasonic transducer, the impact of the transducer size and center frequency should be fully considered.