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For any complete C -algebraic variety X and its associated compact C -analytic space X , it follows from the well known GAGA principle that the algebraic Picard group P i c (X) and the analytic Picard group P i c (X) are isomorphic. Our main purpose here is to investigate an analogous situation for non complete situation, namely C -algebraic affine hypersurfaces. [ABSTRACT FROM AUTHOR]

The concept of Rota–Baxter family algebra is a generalization of Rota–Baxter algebra. It appears naturally in the algebraic aspects of renormalizations in quantum field theory. Rota–Baxter family algebras are closely related to dendriform family algebras. In this paper, we first construct an L∞-algebra whose Maurer–Cartan elements correspond to Rota–Baxter family algebra structures. Using this characterization, we define the cohomology of a given Rota–Baxter family algebra. As an application of our cohomology, we study formal and infinitesimal deformations of a given Rota–Baxter family algebra. Next, we define the notion of a homotopy Rota–Baxter family algebra structure on a given A∞-algebra. We end this paper by considering the homotopy version of dendriform family algebras and their relations with homotopy Rota–Baxter family algebras. [ABSTRACT FROM AUTHOR]

We introduce the concept of Hom-associative algebra structures in Loday–Pirashvili category. The cohomology theory of Hom-associative algebras in this category is studied. Some applications on deformation and abelian extension theory are given. We also introduce the notion of Nijenhuis operators to describe trivial deformations. It is proved that equivalent classes of abelian extensions are one-to-one correspondence to the elements of the second cohomology groups. [ABSTRACT FROM AUTHOR]

We prove that the modular component , constructed in the Main Theorem in Fania and Flamini (Adv Math 436:109409, 2024. https://doi.org/10.1016/j.aim.2023.109409), of Ulrich vector bundles of rank r and given Chern classes, on suitable threefold scrolls X e over Hirzebruch surfaces F e ≥ 0 , which arise as tautological embeddings of projectivization of very-ample vector bundles on F e , is generically smooth, irreducible and unirational. A stronger result holds for the suitable associated moduli space of vector bundles of rank r and given Chern classes on F e , Ulrich w.r.t. the very ample polarization which turns out to be generically smooth, irreducible and unirational. [ABSTRACT FROM AUTHOR]

Strengthening during low‐temperature annealing is a common observation in several nanocrystalline and ultrafine‐grained materials. The origin of such strengthening is generally attributed to various recovery processes leading to restricted dislocation motion. Herein, the observations on recovery‐induced strengthening in cold‐rolled (CR) equiatomic CoCrNi alloys are presented. An increase in hardness is observed for samples deformed to thickness reduction of 35–80% after 2 h of annealing at 500 °C. A detailed microstructural investigation of 80% CR and subsequently annealed samples suggests that both dislocation density and local chemical composition play important role in strengthening. Further, uniaxial tensile tests elucidate the importance of mobile dislocations on strength and ductility of annealed samples. [ABSTRACT FROM AUTHOR]

In this study, the deformation behaviors and mechanical properties of 4H‐SiC single crystals are investigated using microcantilever beam specimens with two different sizes, A and B (A < B). Tensile stress is applied along <1¯1¯$\bar{1} \bar{1}$20> direction. Plastic deformation, or nonlinearity, is observed in the stress–strain curves, and yield stress, or proportional limit, coincides between the two specimens at ≈25 ± 2 GPa. Scanning transmission electron microscopy and transmission electron microscopy studies show that the plastic deformation is due to dislocation activities; multiple‐dislocation pileup areas are observed in both the specimens. Assuming {11¯$\bar{1}$00}/<112¯$\bar{2}$0> prismatic slip which most plausibly occurs in the <1¯1¯$\bar{1} \bar{1}$20> stress application, the critical resolved shar stress is estimated to be 10.9 GPa, which agrees well with the previous studies. Measured fracture strength is 41.9 ± 2.8 and 33.5 ± 2.4 GPa for the A and B, respectively. Dislocation–fracture relationship is discussed on the basis of dislocation‐based fracture mechanics, etc. It is suggested that cracks form within the multiple‐dislocation pileup area, by interaction with dislocation pileups, and act as fracture origins. A's strength is close to an ideal tensile strength of 4H‐SiC in the <112¯$\bar{2}$0> direction, 47–55 GPa. [ABSTRACT FROM AUTHOR]

Introduction. When designing buildings and structures it is necessary to ensure mechanical safety throughout the life cycle of the object. During the operation of buildings, situations arise in which monolithic load-bearing structures acquire defects in the area of the slab-column connection (SCC) in girderless slabs. These are, first of all, cracks caused by bending of slabs and slab pushing through by columns. The problem of taking into account the operation of structures with regard to such data of local damages in emergency situations is not sufficiently studied. In a number of cases the loss of bearing capacity of nodes is of brittle nature, which is not allowed by normative documents, as it can lead to progressive, including avalanche-like, destruction of neighboring elements.Materials and methods. The bearing capacity of elements and the degree of resistance to progressive failure of a 9-storey monolithic girderless frame under different scenarios of initial local damages are determined. Three levels of such damage are introduced, and the slab and column connection nodes are modeled by volumetric finite elements. Verification of the computational model is performed experimentally by in-situ pushover tests of the SCC under central load application. Simulia Abaqus software package is used for the purpose of calculations. The CDP model is used for modelling of concrete deformations, and bilinear diagrams with hardening are used for modelling of reinforcement deformations.Results. Experimental data on the deformations of the slab-column connection under longitudinal force loading and realization of the push-through mode are obtained. Taking into account the selected damage levels and experimental data, calculations of the monolithic frame with different damage scenarios in the investigated nodes are carried out. The nature of force redistribution for frames with different levels of such damage and the degree of their danger in the realization of progressive failure are established.Conclusions. It is determined that damages in the nodes of column and girderless slabs interfaces can lead to redistribution of forces and changes in the character of slab operation. These changes can initiate progressive failure in emergency situations in case of structural solutions of nodes with two-sided and three-sided design contours in terms of CP 63.13330 for push-through calculations. Additional design justification is required for such nodes.

Introduction. When designing metal structures, many factors are taken into account, including the suppleness of joints, which affects the results of stress-strain calculations of structural elements. In the design of high-rise buildings, outriggers are provided to distribute wind loads between the core and perimeter columns, reducing horizontal displacements. Considering the suppleness in the joints of the outrigger affects the distribution of forces in the building structure elements, as well as on the building deformations. This paper presents an analysis of the influence of considering the suppleness of outrigger joints on the stress-strain state of structural elements of a steel high-rise building.Materials and methods. The research focuses on a structural model of a 60-story building with an outrigger, modelled using the ETABS software. The suppleness of the joints of the outrigger structures was determined using the IDEA StatiCa software.Results. According to the results of static calculations considering the suppleness of the outrigger joints, when placing one outrigger on the 54th floor, the maximum horizontal displacement at the top of the building increased by 2.9 % compared to calculations without considering suppleness. Placing two outriggers increased it by 4.7 %. The maximum axial force value in the outrigger brace decreased by 23 % compared to calculations without considering suppleness, while the maximum bending moment increased by 10 %.Conclusions. When calculating a high-rise building taking into account suppleness, the values of horizontal displacement at the building’s top increase within 5 %. If it is necessary to limit horizontal displacements, calculations should consider the suppleness of the joints in steel outrigger structures. Additionally, considering suppleness in calculations allows reducing the material intensity of the designed outrigger braces, as the determining force is the axial force, which decreases by about 25 % when calculated considering suppleness.

When it comes to hydropower dam safety, continuous and comprehensive monitoring is increasingly important. Especially for aging dams, this can pose a difficult challenge that benefits from a multimethod analysis. Here, we present the use and suitability of a geophysical method, Ground Penetrating Radar (GPR), for the non-invasive assessment of two distinct types of hydropower dams in Romania: Herculane (a concrete arch dam) and Gura Apelor (an embankment dam with a rockfill and clay core). Unlike traditional monitoring methods for dam safety in Romania, which might provide an incomplete overview, GPR offers a broader, non-destructive approach to evaluating some elements of dam integrity. Here, we present the results of surveys carried out with a 200 MHz antenna on the crests of both dams. The aim was to conduct a rapid assessment of the crest condition and identify the potential damage to the crest that may elude standard monitoring techniques. The surveys provide an imaging indicative of the structural integrity, although this is more challenging in the embankment dam, and additionally we provide significant information regarding the deformations in the upper layers. This complements data from routine topo-geodetical surveys, offering a potential explanation for the vertical displacements observed therein. We highlight several areas of potential deformation as well as degradation in subsurface structures such as rebars. The results underscore the value of GPR in supplementing established dam monitoring methods, highlighting its effectiveness in different contexts and dam types, as well as its potential in shaping future standards for dam safety management in Romania. [ABSTRACT FROM AUTHOR]

Abstract—It is generally recognized that the formation of the fold-and-thrust tectonic structures of mobile belts on continents is associated with crushing and narrowing of the Earth's crust due to collision of lithospheric plates. The deformation of the Caucasian lithosphere in the recent time is generally consistent with these ideas. However, the block differentiation of the Caucasian lithosphere brings specificity into the directionality of recent vertical and horizontal movements. In this paper, we analyze vertical movements of the Caucasus estimated by means of high-precision leveling over a period of more than a century and consider their spatial correlation with the tectonics, seismicity, stress-strain state, and geophysical fields. A clear correlation indicating the deep tectonic nature of the long-term uplifts of the Caucasus crust is revealed. The differentiation of the Arabian plate movement causes partitioning of the Caucasus territory into provinces that differ by the pattern of recent movements, orientation of faults, and stress-strain state of the geomaterial. These provinces also have distinctions in seismicity in terms of the number of seismic events and focal mechanisms of the earthquakes. We propose a model of a deformation mechanism of the Greater Caucasus, which accommodates the long-term trend of the Caucasus uplift in the conditions of general shortening of the Earth's crust. The results of the analysis provide a basis for discussion of a probable mechanism of neotectonic evolution of the Greater Caucasus, which can be used in the seismic hazard assessment of the North Caucasus. [ABSTRACT FROM AUTHOR]

The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this characterization, we define the cohomology of a pre-Leibniz algebra with coefficients in a representation. This cohomology is shown to split the Loday-Pirashvili cohomology of Leibniz algebras. As applications of our cohomology, we study formal and finite order deformations of a pre-Leibniz algebra. Finally, we define homotopy pre-Leibniz algebras and classify some special types of homotopy pre-Leibniz algebras. [ABSTRACT FROM AUTHOR]

Tunnel accidents caused by water leakage are closely related to the segmental joints, and it is therefore significant to control joint deformation. The traditional segmental joints cannot provide sufficient stiffness and strength in complex geological conditions. To solve these problems, in this study, a type of plug-in joint (composed of a sleeve and a pin) was added to the traditional segmental joints and worked in conjunction with the bolts to form a new type of combined splicing joint. The combined splicing joint was tested under four-point bending conditions. Results show that the combined splicing joint can improve the bending stiffness and load capacity of the structure. The number and position of the plug-in joints clearly affect the load capacity of the segmental joint. This study then develops an analytical method to predict the load capacity and bending stiffness of the combined splicing joints. The new combined splicing joint can effectively reduce the deformation of the segmental joints. [ABSTRACT FROM AUTHOR]

The aim of the article is to present the method of modeling the frequency response of the transformer windings with axial displacements. Frequency response analysis (often referred to as FRA or SFRA) is a powerful and sensitive method for testing the mechanical integrity of transformer cores, windings, and press frames in power transformers. The proper interpretation of FRA results is crucial in assessing winding faults. Computer modeling of transformer active part deformations is one way to expand knowledge about the impact of mechanical faults on the shape of the frequency response (FR) curve. The data collected from these models can be used as training data sets for artificial intelligence tools. An automatic tool developed from this approach would significantly improve the accuracy of the FRA method and simplify the interpretation and evaluation of results. The described study utilizes new types of lumped parameter models with input data obtained from the FEM analysis. The research conducted shows the influence of the winding axial deformation on the frequency response curve and provides information on the sensitivity of the FR curve's shape to this type of deformation. A series of tests, which involved measuring and simulating typical axial damages, were conducted to evaluate the effectiveness of the presented algorithms. [ABSTRACT FROM AUTHOR]

We consider quantum (skew) polynomial rings and observe that their graded automorphisms coincide with those of quantum exterior algebras. This allows us to define a quantum determinant that gives a homomorphism of groups acting on quantum polynomial rings. We use quantum subdeterminants to classify the resulting Drinfeld Hecke algebras for the symmetric group, other infinite families of Coxeter and complex reflection groups, and mystic reflection groups (which satisfy a version of the Shephard–Todd–Chevalley theorem). This direct combinatorial approach replaces the technology of Hochschild cohomology used by Naidu and Witherspoon over fields of characteristic zero and allows us to extend some of their results to fields of arbitrary characteristic and also locate new deformations of skew group algebras. [ABSTRACT FROM AUTHOR]

Significance: The accurate correlation between optical measurements and pathology relies on precise image registration, often hindered by deformations in histology images. We investigate an automated multi-modal image registration method using deep learning to align breast specimen images with corresponding histology images. Aim: We aim to explore the effectiveness of an automated image registration technique based on deep learning principles for aligning breast specimen images with histology images acquired through different modalities, addressing challenges posed by intensity variations and structural differences. Approach: Unsupervised and supervised learning approaches, employing the VoxelMorph model, were examined using a dataset featuring manually registered images as ground truth. Results: Evaluation metrics, including Dice scores and mutual information, demonstrate that the unsupervised model exceeds the supervised (and manual) approaches significantly, achieving superior image alignment. The findings highlight the efficacy of automated registration in enhancing the validation of optical technologies by reducing human errors associated with manual registration processes. Conclusions: This automated registration technique offers promising potential to enhance the validation of optical technologies by minimizing human-induced errors and inconsistencies associated with manual image registration processes, thereby improving the accuracy of correlating optical measurements with pathology labels. [ABSTRACT FROM AUTHOR]

A technological process for hot forging of two-layer forgings with deep cavities and an inverted cone has been developed. A hot forging process flow chart has been analyzed. Digital simulation using QForm software was employed to study the effect of the process parameters on the force characteristics of the metal-forming process, stress-strain condition, and temperature fields of the forging and tooling after each pass. A new design of the die tooling has been proposed. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the formation of the structure and stress–strain state in the joints of AISI 304 stainless steel with a thickness of 2 mm and produced by welding with laser and plasma energy sources. It is established that the microhardness and parameters of the grain and subgrain structures of the welded joint material differ with respect to the dimensions of crystallites, grains, and subgrains according to the welding process. It is shown that, in terms of structure formation, including substructural features, the most favorable structures of 2 mm AISI 304 welded joints are formed by laser–plasma welding. It is predicted that the residual stressed state is less localized with the application of laser–plasma welding than laser welding, and it is characterized by a lower level of residual stresses compared to plasma welding. In all the cases, the maximal stress values are concentrated in the HAZ, and the value obtained using laser–plasma welding is in an intermediate position (431.7 MPa) between those of the laser (443 MPa) and plasma (413.7 MPa) processes. With laser–plasma and laser welding, displacements (deformations) are minimal and close to 0.2 mm. The method of electron speckle interferometry was used, and the results reveal that the error between the calculated and experimental values of equivalent stresses is no more than 6%, which is acceptable. The results of mechanical testing show that, under uniaxial tension, the strength of the welded joints made of AISI 304 steel using laser–plasma and laser welding is the highest and equal to 97% of that of the base metal. [ABSTRACT FROM AUTHOR]

Abstract Magnetic skyrmions are quasi-particles with a swirling spin texture that form two-dimensional lattices. Skyrmion lattices can exhibit defects in response to geometric constraints, variations of temperature or applied magnetic fields. Measuring deformations in skyrmion lattices is important to understand the interplay between the lattice structure and external influences. Geometric phase analysis (GPA) is a Fourier-based image processing method that is used to measure deformation fields in high resolution transmission electron microscopy (TEM) images of crystalline materials. Here, we show that GPA can be applied quantitatively to Lorentz TEM images of two-dimensional skyrmion lattices obtained from a chiral magnet of FeGe. First, GPA is used to map deformation fields around a 5–7 dislocation and the results are compared with the linear theory of elasticity. Second, rotation angles between skyrmion crystal grains are measured and compared with angles calculated from the density of dislocations. Third, an orientational order parameter and the corresponding correlation function are calculated to describe the evolution of the disorder as a function of applied magnetic field. The influence of sources of artifacts such as geometric distortions and large defoci are also discussed.

Introduction. In connection with the constantly existing threats of deliberate damage to the infrastructure of critical facilities using vehicles, the task of development and research of protective structures aimed at preventing this kind of damage becomes relevant and of practical interest. The application of steel ropes as the main load-bearing elements of such structures is substantiated.Materials and methods. The proposed numerical algorithm was used to determine the minimum permissible cross-sectional area of steel ropes based on the requirements for a protective structure in terms of resistance to impact caused by the collision of a car with a given mass and speed. The developed method is based on mathematical modelling of the conditional optimization problem. The objective function was the function of the longitudinal force arising in the steel ropes. At the same time, requirements were made to comply with the conditions of energy conservation and continuity of deformations, as well as strength limitations. A verification calculation of the designed protective structure was carried out in a commercial software package implemented on the generally recognized finite element method. The methodology of the full-scale experiment is presented. A full-scale experiment was carried out in order to determine the true distribution of deformations over the structural elements of the test object under impact.Results. The results of the experimental study are presented. A comparative analysis of the data obtained in the process of numerical and computer simulation, as well as in the course of a full-scale test, was carried out. A slight discrepancy in the values of the controlled parameters obtained by different methods was found.Conclusions. The proposed numerical algorithm for searching the minimum permissible cross-sectional area of steel ropes, based on the requirement of a given strength, confirmed its reliability, and the adopted design solutions of the developed protective structure proved their validity. The results of the research can be used in the design of such engineering structures designed for the physical protection of critical facilities.

The in-service condition of a vehicle eventually subject the shock absorber to unforeseen deformations due to external forces such as damping, friction, resistance forces and other factors such as poor road condition characterized by potholes and speed bumps. In this study, a vehicle shock absorber was analysed, considering the in-service condition. Using SOLIDWORKS soft-ware, 2020 version the shock absorber component was modelled with three different materials which were simulated with ANSYS software. From the simulated results, maximum total deformations of 54.286, 49.26 and 47.603 mm as well as maximum direc-tional deformations of 53.303, 48.762 and 47.569 mm were obtained for hard drawn spring wire (A227), alloy steel (A213) and stainless steel (A313) selected as the shock absorber materials. On the other hand, maximum equivalent von-mises stresses of 1205.8, 1204.7 and 1084.6 MPa as well as maximum equivalent strain values of 0.0065269, 0.0061912, 0.0060882. From the simulated results obtained, stainless steel (A313) out of the three shock absorber material exhibited the least deformations, von-mises stress and equivalent strain. However, the three materials had satisfy the failure distortion-energy theory, and may be fea-sible for shock absorber application in actual scenario because the Von-mises stress obtained had not exceeded any of the mate-rial’s yield strength. This was evidence in the low equivalent strain values and the colour distribution across the shock absorber models which was dominated by royal blue colour, indicating that the shock absorber models can still accommodate multiple translated non-proportional loading or still had significant load bearing capacity. The stress-strain deformation analysis in this study can help predict and prevent premature failure, ensuring the longevity of vehicle shock absorbers.

Camptodactyly-arthropathy-coxa vara-pericarditis syndrome (CACP) is a rare hereditary disease of childhood, characterized by camptodactyly, non-inflammatory arthropathy, progressive coxa vara deformity and non-inflammatory sterile pericarditis. Due to the predominant joint involvement in childhood, CACP is often misdiagnosed as juvenile idiopathic arthritis (JIA), leading to delayed diagnosis and unwarranted treatment with antirheumatic drugs. Delayed diagnosis can lead to serious complications such as joint deformities and cardiovascular dysfunction. This case report illustrates once again the diagnostic difficulties associated with this rare syndrome. [ABSTRACT FROM AUTHOR]

This paper aims to perform modal and harmonic response analyses to show how the piston skirt length reacts. The studied aluminium piston was generated in CATIA CAD Software and consequentially this was simulated in ANSYS software using modal and harmonic response tools. The piston finite element model was built to predict the basic modal parameters such as: natural frequencies, vibration modes and deformations. Different grid sensitivity tests have been done to improve the accuracy of the piston model. The piston with larger skirt has shown 77% higher vibration deformations than piston with smaller skirt. The proposed methodology can be easily used by a design engineer to perform dynamic behaviour studies of moving components and assemblies in Internal Combustion engines and not only. [ABSTRACT FROM AUTHOR]

In this research, by using the finite element method, the effect of five parameters (density of a liquid mineral fertilizer (ρ), its temperature (T), tank wall thickness (L), spacing of stiffeners (K) and stiffeners height (h)) on the strength of standard polyethylene rotomolded tanks used for storage of liquid mineral fertilizers (LMF) was studied. Using the Taguchi method, it was found that these parameters are ranked according to the degree of their influence (in decreasing order) on: maximum stresses (ρ>L>h>T>K), maximum stresses in the tank walls (ρ>L>K>T>h) and deformations of the tank ( for DX/DY: ρ>L>h>T>K and for DZ: ρ>L>h>K>T). Validation of the FEM strength calculations was carried out, which showed satisfactory convergence of the calculated and experimental values. Generalized equations are derived that describe the effect of all five studied parameters on P, PW and tank deformations (along the X, Y and Z axes). On the basis of the derived equations, a nomogram has been constructed, which makes it possible to choose the optimal wall thickness that will correspond to the LMF density and storage temperature. Applying the optimal wall thickness ensures a guaranteed service life of at least 50 years, minimizing the risk of environmental accidents caused by tank failure and the release of LMF and associated toxic substances into groundwater. This research offers valuable insights for designing safer and more durable storage tanks for liquid mineral fertilizers. As an optimal design of the tank for storing the most common fertilizer UAN-32 (Urea Ammonium Nitrate, 32 % nitrogen), with a density of 1.32 g/cm³ and at storage temperatures up to 40 °C, the following values of structural parameters are recommended: L=10 mm, K=38 mm, and h=4 mm. [ABSTRACT FROM AUTHOR]

Rota–Baxter algebras are important in probability, combinatorics, associative Yang–Baxter equation and splitting of algebras. This paper studies the formal deformations of Rota–Baxter algebra morphisms. As a consequence, we develop a cohomology theory of Rota–Baxter algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Finally, we prove the cohomology comparison theorem of Rota–Baxter algebra morphisms, i.e. the cohomology of a morphism of Rota–Baxter algebras is isomorphic to the cohomology of an auxiliary Rota–Baxter algebra. [ABSTRACT FROM AUTHOR]

The paper presents the results of computational analysis of the stress-strain state of reinforced concrete spans of the railway (single-track railway line) overpass over the highway, under specified loads using spatial finite element models. The static load consists of a cohesion of three TEM-18 diesel locomotives and two loaded gondola cars (up to 25 tons per axle). The purpose of this study was to ensure reliable and safe operation of artificial structures on the railroads, as there is a constant increase in transit freight trains from China through the territory of Kazakhstan to near and far abroad, and often the load on the axle reaches 25 tons, and sometimes larger values – up to 27 tons per axle. The results of the study are recommended to be used for inspections and tests of typical girder bridge spans, as well as in the case of monitoring their technical condition with increasing operational loads. [ABSTRACT FROM AUTHOR]

The most important issue regarding the safety and performance of concrete face rockfill dams (CFRDs) is to determine stresses and deformations. However, predictions of crest settlements of CFRDs are usually performed using empirical relationships. In recent years, CFRDs have been constructed much higher and at more complicated topographical and geological dam sites, so numerical analysis is required to evaluate the stress and deformations in the entire dam body. Also, assessing long-term rockfill behaviour and the concrete face membrane crack potential are important for post-construction dam safety. This study evaluates post-construction deformations and crest settlements of a high CFRD under two different loading cases, considering the non-linear elasto-plastic behaviour of the rockfill structure. As a constitutive model, the Duncan–Chang hyperbolic stress–strain model was applied in finite-element simulations considering the failure criterion is isotropic and hardening. Calibration of the rockfill's hyperbolic parameters was performed by comparing the calculated displacements with actual settlement measurements. Computed crest settlements were also compared with those of some CFRDs given in the literature. Calculated crest settlement and other deformations are in good agreement with the rockfill settlement measurements and in acceptable ranges, and do not threaten the dam's safety. [ABSTRACT FROM AUTHOR]

This paper focuses on investigating the stability of a deep foundation pit with hard surrounding rocks at different excavation stages with different supporting schemes by means of numerical calculations. The supporting schemes in question were combinations of one fixed vertical support and four varied transverse supports. Drilled grouting piles were used as vertical supports, and the commonly used steel bracings and prestressed anchorages served as transverse supports. The parameters used to evaluate the stability of the foundation pit at different excavation stages included the lateral displacements of the surrounding rocks, the settlement of the surrounding ground, the axial forces of steel bracings, and displacements at the tops of the drilled grouting piles. Simulation results showed that when a transverse supporting scheme consisting of one-layer steel bracings and prestressed anchorages set at 9 m and 22.5 m underground, respectively, was adopted, the lateral displacements of the surrounding rocks and settlement of the surrounding ground at different excavation stages were the largest compared to those under the other three transverse supporting schemes, while the corresponding values were lower compared to those allowed in Chinese standard GB50007-2011, demonstrating that this kind of supporting scheme is effective in terms of ensuring the safety of the foundation pit at different excavation stages. Moreover, the setting techniques for this kind of supporting scheme were relatively simple, and the corresponding influences of supporting element arrangements on excavation techniques were the lowest. Therefore, one-layer steel bracings and one-layer prestressed anchorages constituted the most suitable transverse supporting scheme for excavating a deep foundation pit with hard surrounding rocks. [ABSTRACT FROM AUTHOR]

Slope instability problems due to widening of roads are very common in mountainous terrains particularly in Indian Himalayan region. Slope instability may occur due to action of different natural as well as anthropogenic activities or through combined action of both. The present paper deals with the slope stability assessment of natural and cut slopes along the Imphal–Moreh section of NH-39 in Manipur state, India. The factor of safety (FoS) for pre- and post-excavations is evaluated, and the FoS with the mitigation measures is examined using limit equilibrium and finite element method. Construction sequences are modeled, and the stability and deformation patterns are evaluated for each construction stage. It is found that about 78% of the slopes is having an angle more than 45° after cutting. The present study suggests that a FoS greater than 1.25 can be achieved by installing a 5.5 m anchor at 18° with the horizontal at a spacing of 1 m. Confirmatory field tests on the anchor are also conducted to ensure the accuracy of the adopted design parameters. This study provides useful informations to researchers and practitioner about the stability assessment of slopes and potential mitigative measures. Similar schemes of mitigative measures are effective for the same/similar geologic conditions in the Indian Himalayan terrain. [ABSTRACT FROM AUTHOR]

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In the context of the continuous development of armoured vehicles and the increasing requirements for the strength and efficiency of armoured vehicles, the study and improvement of torsion shafts becomes relevant to ensure high service life and optimal functioning. The aim of this study is to analyse the torsion shafts of light armoured vehicles to identify possible areas of optimization to increase the strength and durability of these vehicle elements. The methods used include the analytical method, classification method, functional method, statistical method, synthesis method, and others. As a result of the study, a comprehensive analysis and optimization of torsion shafts for light armoured vehicles was carried out to increase their strength and durability. The choice of high-strength material and weight consideration helped to reduce the weight of the vehicle, increasing its efficiency. Geometric design included the use of advanced techniques to optimize the shaft shape, and stress and strain analysis helped determine the optimum parameters. The use of computer modelling and simulation simplified the analysis of the shaft’s behaviour under load. The use of safety factors and consideration of impact loads during operation helped to improve the reliability and durability of the structure. The use of the latest materials and manufacturing technologies allowed achieving the optimum parameters of the transmission element. Testing of the prototypes in real conditions confirmed their efficiency and durability. The optimization of weight and weight distribution was aimed at improving the stability of the armoured vehicle, taking into account the requirements of a particular application and manufacturer. The results indicate the potential for improving the design of torsion shafts to increase the performance and stability of light armoured vehicles. This study makes an important contribution to science, as the identified optimizations and improvements in the design of torsion shafts of light armoured vehicles contribute not only to increasing their strength and durability, but also to the rational use of resources and increasing the overall performance of the vehicle

Uchino initiated the investigation of twisted Rota-Baxter operators on associative algebras. Relevant studies have been extensive in recent times. In this paper, we introduce the notion of a twisted Rota-Baxter operator on a Hom-Lie algebra. By utilizing higher derived brackets, we establish an explicit $ L_{\infty} $-algebra whose Maurer-Cartan elements are precisely twisted Rota-Baxter operators on Hom-Lie algebra s. Additionally, we employ Getzler's technique of twisting $ L_\infty $-algebras to establish the cohomology of twisted Rota-Baxter operators. We demonstrate that this cohomology can be regarded as the Chevalley-Eilenberg cohomology of a specific Hom-Lie algebra with coefficients in an appropriate representation. Finally, we study the linear and formal deformations of twisted Rota-Baxter operators by using the cohomology defined above. We also show that the rigidity of a twisted Rota-Baxter operator can be derived from Nijenhuis elements associated with a Hom-Lie algebra.

The 40Ar–39Ar isotope dating of newly formed micas and chlorites from thrust zones made it possible to establish that they were formed in the Tithonian (150 Ma). Sedimentary rocks from the Devonian to Triassic were involved in thrusts. An older stage of deformations of 257 Ma was established in the Silurian rocks composing the Dream-Head Mountains of Wrangel Island. This age corresponds to the Late Permian stratigraphic interval and indicates the existence of deformations after the Ellesmerian orogeny in the Early Carboniferous. The formation of thrusts was accompanied by the heating of sedimentary sequences up to temperatures of 250–380°C, while the temperature regime in the thrust zone almost did not change. The temperature difference between the thrust zone and under the thrust is not more than 20°C. [ABSTRACT FROM AUTHOR]

It is well-known that the deformation problem of a compact coisotropic submanifold C in a symplectic manifold is obstructed in general. We show that it becomes unobstructed if one only allows coisotropic deformations whose characteristic foliation is diffeomorphic to that of C. This extends an unobstructedness result in the setting of integral coisotropic submanifolds due to Ruan. [ABSTRACT FROM AUTHOR]

In this paper, we define and study (co)homology theories of a compatible associative algebra. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures on a vector space. Then we define the cohomology of a compatible associative algebra A and as applications, we study extensions, deformations and extensibility of finite order deformations of A. We end this paper by considering compatible presimplicial vector spaces and the homology of compatible associative algebras. [ABSTRACT FROM AUTHOR]

Using Hodge theory and Banach fixed point theorem, Liu and Zhu developed a global method to deal with various problems in deformation theory. In this note, the authors generalize Liu-Zhu's method to treat two deformation problems for non-Kähler manifolds. They apply the -Hodge theory to construct a deformation formula for (p, q)-forms of compact complex manifold under deformations, which can be used to study the Hodge number of complex manifold under deformations. In the second part of this note, by using the -Hodge theory, they provide a simple proof of the unobstructed deformation theorem for the non-Kähler Calabi-Yau -manifolds. [ABSTRACT FROM AUTHOR]

In the context of the continuous development of armoured vehicles and the increasing requirements for the strength and efficiency of armoured vehicles, the study and improvement of torsion shafts becomes relevant to ensure high service life and optimal functioning. The aim of this study is to analyse the torsion shafts of light armoured vehicles to identify possible areas of optimization to increase the strength and durability of these vehicle elements. The methods used include the analytical method, classification method, functional method, statistical method, synthesis method, and others. As a result of the study, a comprehensive analysis and optimization of torsion shafts for light armoured vehicles was carried out to increase their strength and durability. The choice of high-strength material and weight consideration helped to reduce the weight of the vehicle, increasing its efficiency. Geometric design included the use of advanced techniques to optimize the shaft shape, and stress and strain analysis helped determine the optimum parameters. The use of computer modelling and simulation simplified the analysis of the shaft's behaviour under load. The use of safety factors and consideration of impact loads during operation helped to improve the reliability and durability of the structure. The use of the latest materials and manufacturing technologies allowed achieving the optimum parameters of the transmission element. Testing of the prototypes in real conditions confirmed their efficiency and durability. The optimization of weight and weight distribution was aimed at improving the stability of the armoured vehicle, taking into account the requirements of a particular application and manufacturer. The results indicate the potential for improving the design of torsion shafts to increase the performance and stability of light armoured vehicles. This study makes an important contribution to science, as the identified optimizations and improvements in the design of torsion shafts of light armoured vehicles contribute not only to increasing their strength and durability, but also to the rational use of resources and increasing the overall performance of the vehicle. [ABSTRACT FROM AUTHOR]

This study systematically examines the behavior of cantilever and anchorage sheet piles influenced by a range of variables, namely dredge level, water table level, anchor interanchor distance, anchors’ number, and the distance from the ground surface. Utilizing a single sheet pile material, the investigation highlights the deformations resulting from these variables, in addition to assessing the effects of different soil types and degrees of saturation. The primary objective centers on the computation of bending moments arising from these factor variations under a constant load, using the finite element theory-based software, Plaxis 2D Connect Edition V20. Sheet pile behavior could be evaluated using this tool by investigating driven depth, maximum bending moments, and horizontal displacements in both anchorage and cantilever sheet piles. To enhance the reliability and realism of findings, outcomes are compared with results from the Pro Sheet program. This comprehensive evaluation furnishes valuable insights into sheet pile deformations under diverse conditions, contributing to the existing body of knowledge and facilitating more robust engineering practices. [ABSTRACT FROM AUTHOR]

When it comes to hydropower dam safety, continuous and comprehensive monitoring is increasingly important. Especially for aging dams, this can pose a difficult challenge that benefits from a multimethod analysis. Here, we present the use and suitability of a geophysical method, Ground Penetrating Radar (GPR), for the non-invasive assessment of two distinct types of hydropower dams in Romania: Herculane (a concrete arch dam) and Gura Apelor (an embankment dam with a rockfill and clay core). Unlike traditional monitoring methods for dam safety in Romania, which might provide an incomplete overview, GPR offers a broader, non-destructive approach to evaluating some elements of dam integrity. Here, we present the results of surveys carried out with a 200 MHz antenna on the crests of both dams. The aim was to conduct a rapid assessment of the crest condition and identify the potential damage to the crest that may elude standard monitoring techniques. The surveys provide an imaging indicative of the structural integrity, although this is more challenging in the embankment dam, and additionally we provide significant information regarding the deformations in the upper layers. This complements data from routine topo-geodetical surveys, offering a potential explanation for the vertical displacements observed therein. We highlight several areas of potential deformation as well as degradation in subsurface structures such as rebars. The results underscore the value of GPR in supplementing established dam monitoring methods, highlighting its effectiveness in different contexts and dam types, as well as its potential in shaping future standards for dam safety management in Romania.

The aim of the article is to present the method of modeling the frequency response of the transformer windings with axial displacements. Frequency response analysis (often referred to as FRA or SFRA) is a powerful and sensitive method for testing the mechanical integrity of transformer cores, windings, and press frames in power transformers. The proper interpretation of FRA results is crucial in assessing winding faults. Computer modeling of transformer active part deformations is one way to expand knowledge about the impact of mechanical faults on the shape of the frequency response (FR) curve. The data collected from these models can be used as training data sets for artificial intelligence tools. An automatic tool developed from this approach would significantly improve the accuracy of the FRA method and simplify the interpretation and evaluation of results. The described study utilizes new types of lumped parameter models with input data obtained from the FEM analysis. The research conducted shows the influence of the winding axial deformation on the frequency response curve and provides information on the sensitivity of the FR curve’s shape to this type of deformation. A series of tests, which involved measuring and simulating typical axial damages, were conducted to evaluate the effectiveness of the presented algorithms.