Generalized Deplanation Hypotheses for Linear and Angular Deformations in Reinforced Concrete Structures under Combined Torsion and Bending

A model of plasticity of reinforced concrete structures is considered, based on on the transformations of the intensity of the “stress-strain” connection by projecting the tensors of this connection, using special transitions for the main angle of deformations, total shear deformations, etc.). At the same time, the modulus of plasticity of concrete, the coefficient of transverse deformations are determined, and complex functions are constructed for linear and angular deformations in sections, taking into account deformation, gradients of deformations during the formation of cracks and stiffness changes. The hypotheses adopted for the calculation model determine the distribution of force flows - blocks for compressed and stretched concrete (first object), "main cracks" from the mechanics of destruction of reinforced concrete, complex functions and a two-cantilever element for modeling the deformation effect of reinforced concrete, developed by the author (second object). Tensile concrete resistance is transferred to the working reinforcement and is modeled using the sum of the average values of the longitudinal and transverse forces, as well as the average reduced coefficient of tension concrete. The "pin (nagel)" effect in the reinforcement crossed by a crack was obtained using the model of the second level of structural mechanics for a reinforcing bar with two pinched ends. The opening of the crack and the shift of the crack edges are simulated. The main force vector in the reinforcement is characterized by the values of longitudinal and transverse displacements (the third object).

Introduction. The paper proposes a method of accounting for energy dissipation for the Timoshenko beam by constructing a damping matrix based on a modified Rayleigh function in the numerical solution of the problem. In this modification, the velocity of displacements is replaced by the velocities of linear and angular deformations. This approach allows us to take into account energy dissipation due to internal friction in the material when both its volume and shape change. The presented technique is promising in practical calculations of structures when shear stiffness has a significant impact on their stress-strain state. Materials and methods. Several proven methods of energy dissipation accounting are considered, including those that make it possible to take into account the energy loss of a moving structure during friction with the external environment (external damping) and dissipation due to friction in the material of the structure deformed in motion (internal damping). Methods for determining the damping coefficients for each of them are presented. The finite element method is used to calculate rod systems. Damping matrices are derived from the condition of stationarity of the total energy of deformation of a mechanical system in motion, including linear and angular deformation rates. Results. Damping matrices proportional to strain rates obtained on the basis of the modified dissipative Rayleigh function are given. A method for determining the damping coefficient taking into account the rates of angular deformation is proposed. Conclusions. The damping matrices presented in the paper describe the energy dissipation during vibrations of mechanical systems due to internal friction in the material. The internal damping matrix was obtained taking into account the influence of linear and angular deformation rates to simulate the dynamic behaviour of short bending structural elements, the deformation of which is described using the Timoshenko model. The performed dimensional check additionally confirms the correctness of the damping matrix construction. Moreover, the dimension of the proposed shear damping coefficient is the same as that of the widely used viscosity coefficient.

ProfCom is a web-based tool for the functional interpretation of a gene list that was identified to be related by experiments. A trait which makes ProfCom a unique tool is an ability to profile enrichments of not only available Gene Ontology (GO) terms but also of ‘complex functions’. A ‘Complex function’ is constructed as Boolean combination of available GO terms. The complex functions inferred by ProfCom are more specific in comparison to single terms and describe more accurately the functional role of genes. ProfCom provides a user friendly dialog-driven web page submission available for several model organisms and supports most available gene identifiers. In addition, the web service interface allows the submission of any kind of annotation data. ProfCom is freely available at http://webclu.bio.wzw.tum.de/profcom/.

Limit summability of functions was introduced as a new approach to extensions of the summation of real and complex functions, and also evaluating antidifferences. Also, limit summand functions generalize the (logarithm of) Gamma-type functions satisfying the functional equation F(x + 1) = f(x)F(x). Recently, another approach to the topic entitled analytic summability of functions, has been introduced and studied by the author. Since some functions are neither limit nor analytic summable, several types of summabilities are needed for improving the problem. Here, I introduce and study functional sequential summability of real and complex functions for obtaining multiple approaches to them. We not only show that the analytic summability is a type of functional sequential summability but also obtain trigonometric summability (for functions with a fourier series) as another its type. Hence, we arrive at a class of real and complex function spaces with various properties. Thereafter, we prove several properties of functional sequential, and also many criteria for trigonometric summability. Finally, we state many problems and future directions for the researches.

The Cauchy integral formula is a fundamental and critical formula in the complex function, and it has a variety of applications in many aspects such as physics, engineering, and mathematics. This article focuses on the applications in the functions and two main theorems in the Cauchy integral formula. It explores the formula and provides corresponding proofs of the formula. To this end, the aim of the article is to use the Cauchy integral formula to cope with some difficult and complex integrals and functions. As a result, this article denotes to use the formula to simplify the complex and difficult problems and provides a practical and fast method. Hence, the article lists some examples to demonstrate the functions’ use of the Cauchy integral formula. At last, the article may serve as a reference for relevant research and survey in the field of the complex functions and provide insights into the Cauchy integral formula’s uses.

The paper explores the signs of static elastic deformation when operating milling machines. The research is concerned with the issue of simulation of a machine-device-tool-workpiece system for preliminary evaluation of elastic deformation on treatment in order to eliminate rejects. Linear and angular deformations were defined. Total rigidity of a milling machine depends not only on its inherent stiffness and contact rigidity of its components, but also on geometrical characteristics of manufacturing system layout. These characteristics could be evaluated through axes of rigidity. Errors in surface machining depend on both tool deflection and workpiece distortion. That is why it is necessary to analyze workpiece and tool load-deformation curve separately. Especially that their rigidity is determined by different layouts of bearing system. Main deformation values are defined and vectors of axes of rigidity are created. Using the results of the analysis it is possible to select a cutting pattern or change manufacturing system layout so that the resultant of cutting forces comes closer to highest rigidity axis, which reduces elastic deformations and improves working accuracy.

Based on a comprehensive analysis of the experimental studies from the standpoint of their convergence with the theoretical solutions, the computational models of resistance (CMR) of reinforced concrete are proposed. These models include CMR1 - modeling of normal cracks, CMR2 - modeling of inclined cracks, CMR3 - modeling of diagonal cracks, CMR4 - modeling of intersecting cracks in the wall, CMR4* - modeling of cracks in a flat slab, and CMR5 - modeling of spatial cracks in torsion with bending, CMR5* - modeling of spatial cracks in bending with transverse force. Also, a hierarchy of computational models of the second and third levels is proposed. The distribution of intensity of working reinforcement along the cross-section of the calculated element was obtained in an analytical form by creating closed equations of blocks, corresponding to the blocks of the reinforced concrete element under the condition of equality to zero of partial derivatives of the Lagrange function to determine the maximum crack opening width. It is considered the effect proposed by the author on the additional deformation impact of the reaction “concrete - reinforcement” from the discontinuity of concrete during the formation of the crack by means of a special model of the two-cantilever element of fracture mechanics. Hypotheses about the distribution of linear and angular deformations during cross-section with account of gradients of deformations caused by formation of cracks were formulated for a complex-stressed element subjected to torsion with bending. Crack opening is defined as mutual displacements of reinforcement and concrete, taking into account deformation. The consolidation of substructures in the building system is performed by the method of initial parameters.

Relevance of the topic. To identify areas of increased deformation of the earth’s surface of rock blocks containing a mineral Deposit, GPS monitoring measurements of horizontal movements of markes installed at different points are carried out. An actual problem that arises here is the creation of a methodology that reliably describes and predicts the formation and location of deformation zones based on the movements of labels. The aim of the research is to create a methodology for forming, calculating and applying a binary mathematical model that describes and predicts the location and contours of the resulting areal deformations of the earth’s surface of two neighboring rock blocks based on placemark movements. Research methods include mathematical modeling of areal deformation, functional and numerical optimization of the parameters of the created model, experimental calculations and analysis of the distribution of the resulting and predicted deformation in a practical example of placemark movements. Research result. The model is based on the idea of blocks based on the spatial constraints of their horizontal dimensions and elastic properties in the hierarchical mosaic structure of composing rocks. Assuming that the size of a block of the earth’s surface does not exceed 5 km within the limits of a mineral Deposit, the movements of its points are considered in the plane. The resulting areal deformation is represented by the sum of linear and angular deformations. The model parameters were identified using the methods of least squares and parabolic vertex approximations implemented in the specified sequence of iterative calculations using the given optimization formulas. Calculations are regulated by the standard deviation of model and labels displacements. It boils down to the permissible small limit determined by the GPS positioning error. A practical example of interpreting placemark offsets shows the properties of model invariance in a multidirectional spatial coordinate system, as well as the detection of areal deformation zones and the forecast of its contour development. Conclusions. The applicability of the presented methodology for the deformation interpretation of multidirectional movements of the earth’s surface markes registered by the monitoring system is noted. The model’s conclusions about the areal location of deformation zones and its level can be used in predictive estimates and criteria that determine the possibility of safe mining operations in the detected zone and the content of man-made objects in it.

Constructal design for a boiler economizer

Replication of minute virus of mice (MVM) induces a sustained cellular DNA damage response (DDR) which the virus then exploits to prepare the nuclear environment for effective parvovirus takeover. An essential aspect of the MVM-induced DDR is the establishment of a potent premitotic block, which we previously found to be independent of activated p21 and ATR/Chk1 signaling. This arrest, unlike others reported previously, depends upon a significant, specific depletion of cyclin B1 and its encoding RNA, which precludes cyclin B1/CDK1 complex function, thus preventing mitotic entry. We show here that while the stability of cyclin B1 RNA was not affected by MVM infection, the production of nascent cyclin B1 RNA was substantially diminished at late times postinfection. Ectopic expression of NS1 alone did not reduce cyclin B1 expression. MVM infection also reduced the levels of cyclin B1 protein, and RNA levels normally increased in response to DNA-damaging reagents. We demonstrated that at times of reduced cyclin B1 expression during infection, there was a significantly reduced occupancy of RNA polymerase II and the essential mitotic transcription factor FoxM1 on the cyclin B1 gene promoter. Additionally, while total FoxM1 levels remained constant, there was a significant decrease of the phosphorylated, likely active, forms of FoxM1. Targeting of a constitutively active FoxM1 construct or the activation domain of FoxM1 to the cyclin B1 gene promoter via clustered regularly interspaced short palindromic repeats (CRISPR)-enzymatically inactive Cas9 in MVM-infected cells increased both cyclin B1 protein and RNA levels, implicating FoxM1 as a critical target for cyclin B1 inhibition during MVM infection.IMPORTANCE Replication of the parvovirus minute virus of mice (MVM) induces a sustained cellular DNA damage response (DDR) which the virus exploits to prepare the nuclear environment for effective takeover. An essential aspect of the MVM-induced DDR is establishment of a potent premitotic block. This block depends upon a significant, specific depletion of cyclin B1 and its encoding RNA that precludes cyclin B1/CDK1 complex functions necessary for mitotic entry. We show that reduced cyclin B1 expression is controlled primarily at the level of transcription initiation. Additionally, the essential mitotic transcription factor FoxM1 and RNA polymerase II were found to occupy the cyclin B1 gene promoter at reduced levels during infection. Recruiting a constitutively active FoxM1 construct or the activation domain of FoxM1 to the cyclin B1 gene promoter via CRISPR-catalytically inactive Cas9 (dCas9) in MVM-infected cells increased expression of both cyclin B1 protein and RNA, implicating FoxM1 as a critical target mediating MVM-induced cyclin B1 inhibition.

This article discusses the development of a method for processing the integral characteristics of electromagnetic devices, which are complex functions. In cases where a complex function has a dependence on a nonmonotonic function, its hyste-resis character is manifested. Such functions are difficult and sometimes impossible, to be processed by numerical dimensional-ity reduction methods (for example, the method of principal components, Wavelet transform). The developed method makes it possible to represent integral functions in an "expanded" form, i.e. get rid of back loops due to the monotonic representation of the nested function. The performed analysis of the dynamic characteristics of electromagnets shows that such processing does not result in the loss of important information, and the charac-teristics can later be transferred to the space of principal components. In this space, characteristics that have already been pro-cessed form a structured dependence and can be separated into clusters.

For a River-Sea ship hull with a relatively low torsional rigidity due to the large deck openings, the analysis of the effect of torsion induced warping stress[1] on the structural strength as well as the ultimate hull strength interaction relationships between the torsion and vertical bending is of significant importance. The present study deals with the ultimate strength of a River-Sea ship under combined action of bending and torsion by the means of numerical and experimental research. Based on the results, a proposed equation defining the ultimate strength interaction relationship for this River-Sea ship is given.

In this paper, modeling of contours by a time-varying autoregressive (TVAR) model is considered. In general, a contour function is not a stationary process, and stationary models are often unsatisfactory in representing local features. Recently, there have been advances in time-series modeling of nonstationary processes. In a typical TVAR modeling approach, autoregressive coefficients are expanded as a linear combination of deterministic functions. In this paper, a low-order discrete Fourier transform (DFT) is used to expand autoregressive coefficients. It is based on the fact that a contour is represented by a complex function, and the model coefficients need to be expanded by a set of complex functions. The parameter estimation and order selection in TVAR models are also considered. A least squares estimator of the TVAR model parameters is presented, and the maximum likelihood approach for determining the model order is also presented. The efficacy of the TVAR modeling approach in modeling a closed contour is demonstrated by estimating the time-varying spectrum of a synthetic contour by different approaches, and is tested by detecting curvature extrema points of synthesized contours. For the classification of contours of planar shapes, the estimated TVAR model parameters are used as features. A neural network is used to classify TVAR features extracted from complex contour functions. In the classification experiment with contours of various planar shapes, about 97% of samples are correctly classified.

The Andean Amazon is an endangered biodiversity hot spot but its forest dynamics are less studied than those of the Amazon lowland and forests from middle or high latitudes. This is because its landscape variability, complex topography and cloudy conditions constitute a challenging environment for any remote-sensing assessment. Breakpoint detection with Landsat time-series data is an established robust approach for monitoring forest dynamics around the globe but has not been properly evaluated for implementation in the Andean Amazon. We analyzed breakpoint detection-generated forest dynamics in order to determine its limitations when applied to three different study areas located along an altitude gradient in the Andean Amazon in Ecuador. Using all available Landsat imagery for the period 1997–2016, we evaluated different pre-processing approaches, noise reduction techniques, and breakpoint detection algorithms. These procedures were integrated into a complex function called the processing chain generator. Calibration was not straightforward since it required us to define values for 24 parameters. To solve this problem, we implemented a novel approach using genetic algorithms. We calibrated the processing chain generator by applying a stratified training sampling and a reference dataset based on high resolution imagery. After the best calibration solution was found and the processing chain generator executed, we assessed accuracy and found that data gaps, inaccurate co-registration, radiometric variability in sensor calibration, unmasked cloud, and shadows can drastically affect the results, compromising the application of breakpoint detection in mountainous areas of the Andean Amazon. Moreover, since breakpoint detection analysis of landscape variability in the Andean Amazon requires a unique calibration of algorithms, the time required to optimize analysis could complicate its proper implementation and undermine its application for large-scale projects. In exceptional cases when data quality and quantity were adequate, we recommend the pre-processing approaches, noise reduction algorithms and breakpoint detection algorithms procedures that can enhance results. Finally, we include recommendations for achieving a faster and more accurate calibration of complex functions applied to remote sensing using genetic algorithms.

In the electromagnetic field formed by coaxial cables, electromagnetic waves of different frequencies are shown to propagate at the same speed (the speed of light c). Therefore, the variational method, which is based on the fact that electromagnetic waves of different frequencies have different propagation speeds, cannot be applied. In this session, the characteristics of light propagating through an electromagnetic field of glass, suitable for applying the variational method and for constructing lenses, are determined. Although the electromagnetic field is derived from the properties of dielectrics, it has been demonstrated to be equivalent to a circuit that represents the Schrödinger equation used in quantum mechanics. In other words, it may be possible to apply electromagnetic fields from classical physics (circuit theory) to quantum mechanics. Quaternions and wave functions that are considered to be related to complex functions will be the topic of future studies because the Schrödinger equation is a complex function.