Outer Sections Research Articles

Строфика и сонатность в итальянской оперной арии 1720–1730-х годов

At present, the theory of musical form is still dominated by the notion that elements of sonata form in composition began to penetrate into vocal genres or, more specifically, into the opera aria only by the end of the 18th century, when they had already been fully established in instrumental music. In the latest studies devoted to sonata forms, both in Russia and in other countries, there is no mention of the emergence or manifestation of the principles of sonata in opera and vocal music. Nevertheless, in Italian aria (both in serious and comic opera) the principles of sonata form have been forming intensively since the end of the 1720s, i.e., long before these processes were noted in instrumental music. The article analyzes the composition in a number of arias from serious and comic operas by Leonardo Vinci, Johann Adolph Hasse, Giovanni Battista Pergolesi and Gaetano Latilla. In these arias, the sonata principles are reflected in the compositional, thematic and tonal-harmonic planes. All arias are variants of the early two-part (binary) sonata form enclosed by the outer sections of the da capo. The conclusions are as follows: 1) sonata form in arias is based on interaction with the strophic arrangement of the poetic texts containing figurative contrast; 2) sonata form was established in stages, from a distinctly structured exposition (without clear signs of sonata in the second section of the form) to a full binary sonata form with thematic repetition and tonal subordination in the reprise, the priority role in this process played by comic opera. The article contains musical examples and tables. Keywords: sonata form, 18th century Italian opera aria, stanza

Stability Analysis and Augmentation Design of a Bionic Multi-Section Variable-Sweep-Wing UAV Based on the Centroid Self-Trim Compensation Morphing

In this study, a design scheme for a high-aspect-ratio bionic multi-section variable-sweep wing unmanned aerial vehicle (UAV) that utilizes the reverse coordinated change in the sweep angle of the inner and outer wing sections is proposed, which improves the aerodynamic performance and realizes the self-trim compensation of the wing’s centroid. According to the layout characteristics of this type of UAV, a reasonable distribution design of the wingspan ratio of the inner and outer sections is explored, to reduce the impact of aerodynamic center movement and moment of inertia change. The calculation and analysis results show that the coordinated variable-sweep scheme can significantly improve the influence of sweep angle change on the longitudinal static stability margin of UAVs with a high aspect ratio. The coordinated sweep angle change in the inner and outer wing sections can not only reduce the drag during high-speed flight, but also play a significant role in improving the performance of the aircraft at different stages in the mission profile. Appropriately increasing the wingspan proportion of the inner section can reduce the trim resistance of the V-tail, reduce the thrust of the engine, and increase the range and duration of the UAV. From the perspective of stability change, the multi-section variable-sweep wing UAV with a wingspan ratio of the inner and outer sections that is between 1.41 and 1.78 has better dynamic stability performance. Among them, the UAV with a wingspan ratio of the inner and outer sections that is equal to 1.41 has better longitudinal stability performance, while the UAV with a wingspan ratio of the inner and outer sections that is equal to 1.78 has better lateral/directional stability performance.

A flexible anatomical set of mechanical models for the organ of Corti.

We build a flexible platform to study the mechanical operation of the organ of Corti (OoC) in the transduction of basilar membrane (BM) vibrations to oscillations of an inner hair cell bundle (IHB). The anatomical components that we consider are the outer hair cells (OHCs), the outer hair cell bundles, Deiters cells, Hensen cells, the IHB and various sections of the reticular lamina. In each of the components we apply Newton’s equations of motion. The components are coupled to each other and are further coupled to the endolymph fluid motion in the subtectorial gap. This allows us to obtain the forces acting on the IHB, and thus study its motion as a function of the parameters of the different components. Some of the components include a nonlinear mechanical response. We find that slight bending of the apical ends of the OHCs can have a significant impact on the passage of motion from the BM to the IHB, including critical oscillator behaviour. In particular, our model implies that the components of the OoC could cooperate to enhance frequency selectivity, amplitude compression and signal to noise ratio in the passage from the BM to the IHB. Since the model is modular, it is easy to modify the assumptions and parameters for each component.

Pitting at inclusions of the equiatomic CoCrFeMnNi alloy and improving corrosion resistance by potentiodynamic polarization in H2SO4

The pitting initiation site of an arc-melted equimolar CoCrFeMnNi alloy was investigated, and a method to improve the pitting corrosion resistance of the alloy was proposed. Cr–Mn–O inclusions with S-containing segments on the outer sections were observed; these S-containing segments served as the pitting initiation sites. The S-containing inclusions were removed by potentiostatic polarization and immersion in H2SO4, but pitting corrosion resistance after treatment did not improve. By potentiodynamic polarization in H2SO4, the S-containing inclusions were removed and the passive film on the alloy matrix became Cr enriched, resulting in a significant improvement in the pitting corrosion resistance.

Optimization of Herringbone Grooved Thrust Air Bearings for Maximum Load Capacity

Abstract Many studies in herringbone grooved thrust bearings are focused on searching for the optimal groove parameters to improve the load capacity, but none of them adopt different grooves in different sections. In this study, a novel optimization method of herringbone grooved thrust air bearings is proposed for maximum load capacity by seeking the optimal groove parameters in each section of the bearing independently. An example of an optimized thrust air bearing is presented, and its performance is compared with a non-optimized bearing and a conventionally optimized bearing without dividing grooves into sections. The resultant herringbone grooves are found to have different parameters in the inner and outer sections, which is uncommon in existing grooves. Numerical results show that the novel bearing has a higher load capacity than the non-optimized reference bearing and conventionally optimized bearing. The study shows that the new design can increase load capacity by 30.77%, verified by experiments.

Nutraceutical properties of tamarillo fruits: A vibrational study

Tamarillo (tree tomato) is a subtropical tree that produces edible fruits with health-beneficial properties, since it contains several components with potential therapeutic and chemoprotective activity. The present work reports the first complete vibrational study (Raman and infrared) of this edible fruit. This approach allowed us to determine where the most relevant nutraceutical compounds are located in the fruit, as well as their relative amounts. Particular vibrational signatures were obtained for each part of the fruit, reporting different components for the epicarp (outer and inner sections), the pulp and the seeds, especially regarding the content in phenolic compounds, unsaturated fatty acids/esters and polymeric chains from the cuticular wax. Valuable information, at the molecular level was gathered regarding the nutricional value of tamarillo's fruit, for its different fractions. This is expected to pave the way for its introduction as a promising nutraceutical, based on the potential therapeutic properties of its main components.

Potential for direct application of blue light for photo-disinfection of dentine

The direct application of light for photo-disinfection potentially provides a safe and novel modality to inhibit or eliminate cariogenic bacteria residing upon and within dentine. This study aimed to both; characterize the pattern of transmission of 405 nm light through molar dentine at different tooth locations, as well as, determine the irradiation parameters that are antibacterial for Streptococcus mutans under various growth conditions, including lawns, planktonic cultures, and biofilms. To determine the amount of light (405 nm) transmitted at different anatomical tooth locations; irradiance values were recorded after blue light (470–4054 mW/cm2) had traversed through occlusal, oblique, and buccal dentine sections; and three thicknesses - 1, 2 and 3 mm were investigated. To determine tubular density; scanning electron micrographs from 2 mm outer (dentine-enamel junction) and inner (pulp) dentine sections were analysed. For photo-disinfection studies; S. mutans was irradiated using the same 405 nm wavelength light at a range of doses (110–1254 J/cm2) in both biofilm and planktonic cultures. The inhibitory effect of the irradiation on bacterial lawns was compared by measuring zones of inhibition; and for planktonic cultures both spectrophotometric and colony forming unit (CFU) assays were performed. A live/dead staining assay was utilised to determine the effect of irradiation on bacterial viability in mature biofilms. Data indicated that increasing dentine thickness decreased light transmission significantly irrespective of its orientation. Occlusal and oblique samples exhibited higher transmission compared with buccal dentine. Oblique dentine 405 nm light transmission was comparable with that of occlusal dentine independent of section thickness. An increased tubule density directly positively correlated with light transmission. Irradiation at 405 nm inhibited S. mutans growth in both biofilm and planktonic cultures and a dose response relationship was observed. Irradiation at doses of 340 and 831 J/cm2 led to significant reductions in bacterial growth and viability; as determined by CFU counting and live/dead staining. Data suggests that phototherapy approaches utilising a 405 nm wavelength have therapeutic potential to limit cariogenic bacterial infections both at the surface and within dentine.

A Review On Ultrasonic Welding of Various Materials and Their Mechanical Properties

In recent years, in contrast with conventional welding methods, ultrasonic welding has been one of great importance among its relevant applications and materials. The bonding of different materials is always difficult, as the unregulated scale of the grain and the fragile mechanical properties are different than conventional welding techniques. In addition, this research paper offers numerous explanations and uses of the ultrasonic welding technique on different materials and its alloys such as aluminium, steel, titanium, nickel, magnesium and also on fiber reinforced composites and thermoplastics along with their mechanical properties. The key benefits of this method are also discussed such as clean and undamaged welding on outer sections, reliable and solid bonding, and saves time effectively.

Behavior of hydrogen hollow-cone spray depending on the ambient pressure

Hydrogen as a fuel is feasible for future sustainable mobility. Because hydrogen has a low volumetric energy density, high-pressure hydrogen is required for high-speed fuel injection. The objective of this research is analysis of the hydrogen spray behavior depending on the ambient pressure. A high-pressure (10 MPa) hydrogen spray is visualized in a constant volume combustion chamber in which the ambient pressure and injection duration are varied. The schlieren method is utilized to capture the hydrogen spray with a high-speed camera. The characteristics of the hydrogen hollow-cone spray are investigated using high-speed spray images. High ambient pressure decreases the vertical extent of the spray penetration and its area. The centroid of the spray is contracted toward the axis of the injector until the ambient pressure reaches 2.0 MPa, and the pressure difference between the inner and outer sections of the spray is larger for high ambient pressures. At high ambient pressure, the heterogeneity of the hydrogen mixture increases. Owing to the aerodynamic effect, the contracted spray reconstructs the main hydrogen plume at the center of the injector. Moreover, hydrogen travels toward the top of the injector because of the generation of a vortex at the inner side of the spray. Based on the findings, hydrogen direct injection can contribute to sustainable mobility in the future.

Analysis and improvement of the three-column spinal theory

BackgroundDenis and Ferguson et al.’s three-column spinal theory has been widely accepted and applied. However, this three-column theory was proposed based solely on observation and experience without thorough documented data and analysis. The aim of this study was to analyze and improve Denis and Ferguson et al.’s three-column spinal theory to propose a novel three-column concept in epidemiology, morphology and biomechanics.MethodsA retrospective analysis of the computed tomography imaging data of patients with a diagnosis of T11-L5 vertebral fractures was conducted between February 2010 and December 2018. Three-dimensional (3D) distribution maps of fracture lines of all subjects were obtained based on 3D mapping techniques. In addition, a 25-year-old health male volunteer was recruited for the vertebral finite element force analysis.ResultsThe present study enrolled 459 patients (age: 48 ± 11.42 years), containing a total of 521 fractured vertebrae. The fracture lines peaked in the upper and the outer third sections of the vertebra, starting from the anterior part of the vertebral pedicles in 3-D maps. Regarding flexion and extension of the spine, the last third of the vertebral body in front of the spinal canal was one main stress center in the finite element analysis. The stress on the vertebral body was greater in front of the pedicles in the lateral bending.ConclusionThe study reveals that the posterior one-third of the vertebral body in front of the spinal canal and the posterior one-third of the vertebral body in front of the pedicle are very different in terms of fracture characteristics and risks to spinal canal (3D maps and stress distributing graphs), therefore, they should be classified as different columns. We provide strong evidence that Su’s three-column theory complies with the characteristics of vertebral physiological structure, vertebral fracture, and vertebral biomechanics.Graphical abstract

An interval fuzzy number-based fuzzy collaborative forecasting approach for DRAM yield forecasting

Most existing fuzzy collaborative forecasting (FCF) methods adopt type-1 fuzzy numbers to represent fuzzy forecasts. FCF methods based on interval-valued fuzzy numbers (IFNs) are not widely used. However, the inner and outer sections of an IFN-based fuzzy forecast provide meaning information that serves different managerial purposes, which is a desirable feature for a FCF method. This study proposed an IFN-based FCF approach. Unlike existing IFN-based fuzzy association rules or fuzzy inference systems, the IFN-based FCF approach ensures that all actual values fall within the corresponding fuzzy forecasts. In addition, the IFN-based FCF approach optimizes the forecasting precision and accuracy with the outer and inner sections of the aggregation result, respectively. Based on the experimental results, the proposed FCF-II approach surpassed existing methods in forecasting the yield of a dynamic random access memory product.

Characterising life in settlements and structures: Incorporating faecal lipid biomarkers within a multiproxy case study of a wetland village

Roundhouses are ubiquitous features of Iron Age landscapes across North West Europe, yet the way they were used internally is not well understood. We demonstrate how spatial analyses of steroid lipid biomarkers advances our understanding of household activities, living conditions and animal management associated with a well-preserved 5th century BCE roundhouse from Scotland's first Iron Age wetland village, Black Loch of Myrton, especially when combined with more traditional archaeological approaches. Faecal steroids (5β-stanols and bile acids) are well preserved within the wetland roundhouse floor deposits. Diffuse faecal inputs are identified within these deposits, limiting the resolution of faecal source discrimination compared with studies of concentrated faecal remains. However, analysis of both 5β-stanols and bile acids enables discrimination between ruminant (sheep, goat and cattle), pig and horse/human faecal remains. By integrating faunal data and entomological dung indicators we are able to characterise the on-site presence of animals associated with these archaeological structures. Steroids indicate short-lived and/or temporary pulses of dung deposition within the Iron Age roundhouse case study structure, which can be very difficult to determine using other archaeological proxies. Furthermore, our multiproxy results demonstrate the molecular preservation of steroids within deposits that have been subjected to regular floor cleaning, which is associated with the removal macrofossil proxies. Comparisons of multiproxy faecal signatures of the inner and outer sections of the structure show temporal and spatial heterogeneity in usage and living conditions. The faecal signature points to temporary sheltering of animals within the inner section of the structure. The multi-use and division of different activities within the roundhouse, determined by steroids, marks an important contribution to broader archaeological debates surrounding structures, their functions and re-use.

Modeling an Uncertain Productivity Learning Process Using an Interval Fuzzy Methodology

Existing methods for forecasting the productivity of a factory are subject to a major drawback—the lower and upper bounds of productivity are usually determined by a few extreme cases, which unacceptably widens the productivity range. To address this drawback, an interval fuzzy number (IFN)-based mixed binary quadratic programming (MBQP)–ordered weighted average (OWA) approach is proposed in this study for modeling an uncertain productivity learning process. In the proposed methodology, the productivity range is divided into the inner and outer sections, which correspond to the lower and upper membership functions of an IFN-based fuzzy productivity forecast, respectively. In this manner, all actual values are included in the outer section, whereas most of the values are included within the inner section to fulfill different managerial purposes. According to the percentages of outlier cases, a suitable forecasting strategy can be selected. To derive the values of parameters in the IFN-based fuzzy productivity learning model, an MBQP model is proposed and optimized. Subsequently, according to the selected forecasting strategy, the OWA method is applied to defuzzify a fuzzy productivity forecast. The proposed methodology has been applied to the real case of a dynamic random access memory factory to evaluate its effectiveness. The experimental results indicate that the proposed methodology was superior to several existing methods, especially in terms of mean absolute error, mean absolute percentage error, and root mean square error in evaluating the forecasting accuracy. The forecasting precision achieved using the proposed methodology was also satisfactory.

ATR-FTIR spectroscopy as adjunct method to the microscopic examination of hematoxylin and eosin-stained tissues in diagnosing lung cancer.

Lung cancer remains the leading cause of cancer-related death worldwide. Since prognosis and treatment outcomes rely on fast and accurate diagnosis, there is a need for more cost-effective, sensitive, and specific method for lung cancer detection. Thus, this study aimed to determine the ability of ATR-FTIR in discriminating malignant from benign lung tissues and evaluate its concordance with H&E staining. Three (3) 5μm-thick sections were cut from formalin fixed paraffin embedded (FFPE) cell or tissue blocks from patients with lung lesions. The outer sections were H&E-stained and sent to two (2) pathologists to confirm the histopathologic diagnosis. The inner section was deparaffinized by standard xylene method and then subjected to ATR-FTIR analysis. Distinct spectral profiles that distinguished (p<0.05) one sample from another, called the “fingerprint region”, were observed in five (5) peak patterns representing the amides, lipids, and nucleic acids. Principal component analysis and hierarchical cluster analysis evidently clustered the benign from malignant tissues. ATR-FTIR showed 97.73% sensitivity, 92.45% specificity, 94.85% accuracy, 91.49% positive predictive value and 98.00% negative predictive value in discriminating benign from malignant lung tissue. Further, strong agreement was observed between histopathologic readings and ATR-FTIR analysis. This study shows the potential of ATR-FTIR spectroscopy as a potential adjunct method to the gold standard, the microscopic examination of hematoxylin and eosin (H&E)-stained tissues, in diagnosing lung cancer.

The co-regulation of nitrate and temperature on denitrification at the sediment-water interface in the algae-dominated ecosystem of Lake Taihu, China

Sediment denitrification is a dominant mechanism for nitrogen removal and can help to minimize lake eutrophication. However, the spatio-temporal variability of denitrification rates and its controlling factors in sediments of large shallow lakes are poorly understood. In this study, we investigated the controlling factors on the temporal and spatial variability of denitrification rates in Meiliang Bay in Taihu Lake, China, to determine the contribution of denitrification on the total lacustrine nitrogen budget. We collected 18 intact monthly sediment cores and an additional 36 seasonal sediment cores from January 2013 to January 2014. Cores were collected from the inner and outer sections of Meiliang Bay for analysis of denitrification rates and sediment properties. We also collected in situ surface water samples for water quality analysis. Denitrification rates at the sediment-water interface (SWI) were measured using acetylene inhibition techniques and intact sediment core incubation. We used a t test to determine the differences in water quality and sediment properties between the two sites and a one-way ANOVA to identify seasonal differences in denitrification rates, water quality, and sediment properties. We also applied Pearson’s correlation, distance-based redundancy analysis (db-RDA) and random forest model to identify the relationships between denitrification rates and environmental factors. Denitrification rates ranged from 0.76 to 40.94 μmol N m−2 h−1 and 0.13 to 52.55 μmol N m−2 h−1, with annual mean values of 19.97 and 17.15 μmol N m−2 h−1 for the Inner and Outer Bay, respectively. Sediment denitrification rates in the Inner and Outer Bay showed similar seasonal variability, with the highest values in spring and summer and the lowest values in autumn. Nitrate addition was shown to significantly increase denitrification rates in summer and autumn (P < 0.05); however, carbon addition showed no significant influence on denitrification rates in the four seasons. Our results imply that denitrification rates were nitrate-limited in summer and autumn. Distance-based redundancy analysis (db-RDA) and random forest model showed that denitrification rates were mainly determined by nitrate, temperature, and chlorophyll a (Chla), and that nitrate in the water column was the most important predictor of denitrification rates. In general, denitrification rates showed significant seasonal variability in Meiliang Bay due to the co-regulation of both water temperature and nitrate concentrations. The dominance of each controlling factor on denitrification rates varied in different seasons. Based on our calculations, nitrogen removal by denitrification accounted for approximately 10.7% of the total nitrogen input to Taihu Lake. Therefore, we suggest the need for effective measures to reduce external nitrogen inputs of to Lake Taihu to prevent on-going eutrophication.

Increased formation of reactive oxygen species during tumor growth: Ex vivo low-temperature EPR and in vivo bioluminescence analyses

Previous studies have shown that reactive oxygen species (ROS) such as superoxide or hydrogen peroxide generated at low levels can exert a tumor-promoting role via a redox-signaling mechanism. Reports also suggest that both tumorigenesis and tumor growth are associated with enhanced ROS formation. However, whether ROS levels or ROS-derived oxidative marker levels increase during tumor growth remains unknown. In this study, in vivo bioluminescence imaging with a boronate-based pro-luciferin probe was used to assess ROS formation. Additionally, probe-free cryogenic electron paramagnetic resonance was used to quantify a characteristic aconitase [3Fe4S]+ center that arises in the tumor tissue of mouse xenografts from the reaction of the native [4Fe4S]2+ cluster with superoxide. Results indicated that tumor growth is accompanied by increased ROS formation, and revealed differences in oxidant formation in the inner and outer sections of tumor tissue, respectively, demonstrating redox heterogeneity. Studies using luciferin and pro-luciferin probes enabled the assessment of tumor size, ROS formation, and bioenergetic status (e.g., ATP) in luciferase-transfected mice tumor xenografts. Probe-free ex vivo low-temperature electron paramagnetic resonance can also be translated to clinical studies.

Spatio-temporal Distribution Characteristics of the Water Quality in the Jinze Reservoir and Its Inflow

Jinze Reservoir is the main drinking water source for southwest Shanghai. The water quality in the upstream Taipu River and reservoir have an important impact on the performance of the reservoir and the quality of the water supply. Conventional water parameters were analyzed using principal component analysis (PCA) to evaluate seasonal variations in water quality in the upper reaches of Jinze Reservoir. The parallel factor (PARAFAC) was also used to analyze water-soluble dissolved organic matter (FDOM) in the upstream waters and reservoir area. Furthermore, the relationships between water fluorescence intensity and conventional water quality indicators were analyzed using correlation analysis. The results show that water quality in the upper reaches of Jinze Reservoir is worst in the winter, and water quality gradually deteriorates in the outer sections of the reservoir due to external pollution inputs. Ecological purification within the reservoir area functions to improve water quality. The water body FDOM content is mainly composed of proteinoids and humus. Protein-like substances are the main components of this material, and each component exhibits clear spatial and temporal distribution characteristics. External pollution is the main factor affecting the total fluorescence intensity of the FDOM outside of the reservoir. In the reservoir, the ecological environment affects the total fluorescence intensity of FDOM. The total fluorescence intensity of FDOM showed an increasing downstream spatial trend, which was significantly correlated with NH4+-N, petroleum, TOC, chloride, and sulfate content in the water. By detecting the total fluorescence intensity of FDOM, the rapid analysis of water quality can be achieved to inform early warning.

Refractive index sensor based on concentric triple racetrack resonators side-coupled to metal–insulator–metal waveguide for glucose sensing

A refractive index sensor using two concentric triple racetrack resonators with plasmonic metal–insulator–metal (MIM) waveguides is suggested to provide more freedom for sensing applications. Due to momentum matching, intensive coupling happens between the equivalent modes of each section of the resonators. The sensing properties are numerically discussed in terms of the finite difference time domain method. According to the outcomes, when increasing the refractive index of the material in the outer sections of the racetrack resonators, the dip wavelengths show a notable red shift. The sensing performance can be enhanced by using two multiple concentric resonators that effectively increase the strength of the light–analyte interaction, which is useful for sensing applications. Our proposed nanosensor offers a high sensitivity value, sensing resolution, and figure of merit of 1618 nm/RIU, 6.18×10−4RIU, and 89RIU−1, respectively. Also, the racetrack resonators coupled to MIM waveguides can be simply integrated into chip circuits with other optical devices to perform monitoring and filtering tasks.

RFP based Fusion-Fission Hybrid reactor model for nuclear applications

The Reversed Field Pinch (RFP) configuration looks to be an attractive option for fusion-fission hybrid reactors: the toroidal magnetic systems would be made of copper coils instead of more expensive superconductive magnets; fusion conditions could be reached by ohmic heating only, therefore additional heating systems would not be required; the fission blanket could be located in the most external part of the torus thus facilitating maintenance operations. The paper aims at assessing the potentialities, such as fuel fertilization and/or nuclear waste transmutation and electricity production of a hybrid reactor with a RFP fusion core (R = 6 m, a = 1) whose conceptual design and plasma performances are based on RFX-mod, the largest RFP experiment currently in operation. Fusion conditions can be reached by heating a D-T plasma up to 9.6 keV by ohmic heating, generated by a 20 MA plasma current induced and sustained by flux swing only. The neutron flux (2.1 × 1013 fast neutron/cm2/s) is used to breed tritium in both the inner and outer blanket sections and induce fission reactions in dedicated areas in the external blanket section where Pu + MA (60%)-Zr (40%) rods are located. Both neutronic and safety analyses corroborate the viability of a FFH reactor with a RFP core.

X-ray densitometric indices of proximal phalanx, medial phalanx and ungular pelvic limb bones as criteria for age diagnosis of cattle in forensic veterinary expertise

Morphological parameters of biological material are extremely informative in diagnostic studies, in particular, to determine the species, sex, time of death, the term of burial. The most informative object for these tasks is the skeleton, because changes in the bones are stored for a long time, while soft tissue is subjected to rotting. Bone tissue is the most durable, but at the same time, it is very labile and reacts to all metabolic processes in the body. The object of the study was proximal phalanx, medial phalanx and ungular bone of the pelvic limb of cattle ranging in age from newborn to 12 years old. Radiography of the proximal phalanx, medial phalanx and ungular bones of the pelvic limb was performed on the Arman apparatus. The bones were subjected to X-ray in the lateromedial projection. The inner and outer sections of the tubular bone were determined. The mathematical modeling of the interaction of X-rays and the cortical layer of bones of fingers (proximal phalanx, medial phalanx and ungular) of cattle was carried out in this work. It is established that this process is described by Bouger's law. The physico-mathematical model of proximal phalanx, medial phalanx and ungular bones has been calculated, on the basis of which it was possible to calculate the X-ray densitometric indices of these bones of cattle. The age features of dynamics of X-ray densitometric indices of the proximal phalanx, medial phalanx and ungular bones were established and a method of determining the age of cattle according to this criterion was proposed. A mathematical model for the proximal phalanx, medial phalanx and ungular bones of the pelvic limbs of cattle that can be applied in X-ray densitometry uses: for the average third proximal phalanx – section of heterogeneous tubular structure modeled by a semicircle; for a medial phalanx bone – a section of a triangular shape; for the ungular bone – a heterogeneous structure, the plantar surface is inscribed in a rectangle. The process of interaction of X-rays with the bone structure of the examined pelvic limb bones can be described by Bouguer's law. The developed mathematical modeling of this interaction and the algorithm for its analysis is the basis for determining the age of cattle for X-ray densitometric indices of the proximal phalanx, medial phalanx and ungular bones of pelvic limbs. By X-ray densitometry of the proximal phalanx and medial phalanx bones of the pelvic limbs extremities one can diagnose the age of bovine animals from birth to 5 years, but according to ungular bones – from birth to 10 years. X-ray densitometry of medial phalanx and ungular bones of pelvic limbs can be used for diagnosing bovine cattle in a complex with other morphological, chemical and physical methods of investigation.