Function Of Coordinates Research Articles

Adiabatic collapse of non-homogeneous self-gravitating gas cloud

In this letter, we find the critical mass of a self-gravitating, spherically symmetric gas cloud, above which the fluid, within the bubble, collapses. Our analysis departs from a non-homogeneous equilibrium density, satisfying the Boltzmann relation. A time scale is defined in terms of the adiabatic index of the gas. Subsequently, a sinusoidal perturbation around equilibrium is regarded, thereby leading to a dispersion relation of frequency with wavelength, which does not depend on geometrical curvature effects. Such a formulation clearly justifies that the collapse occurs much faster than predicted by the well-known Jeans approach. The equilibrium profiles of the density, gravitational field, and potential are obtained as functions of the spherical radius coordinate at marginal instability. Since our theory captures the essential physics of gravitational collapse, it can be used as the starting point for several advancements in galactic dynamics.

Influencia de la variación de nutrientes en la alimentación sobre la acumulación de AbrB, esporulación y expresión de cry1Ac durante cultivos por lote alimentado de Bacillus thuringiensis

The biological control agent Bacillus thuringiensis (Bt) coordinates metabolic and gene regulation functions to enter to the differentiation process for the synthesis of spores and Cry toxin proteins. The master regulator for sporulation initiation is Spo0A, while AbrB regulator coordinate cellular functions during vegetative and transition growth. To understand how differentiation is modified during fed-batch cultures (FBC) of Bt under variable nutrient conditions, we conducted fermentations with two different nutrient concentration and feeding times using an industrial medium. Since sporulation efficiency has been lower in FBCs than in batch cultures, AbrB was monitored by Western blot during these cultures. Kinetic parameters were used to stablish timing of cell differentiation process, and fermentations were monitored on-line using impedance spectroscopy. AbrB was accumulated during the entire fed-batch culture, when a medium with the highest concentration of carbon and nitrogen sources (FBC1) were fed. Under these conditions, sporulation efficiency and cry1Ac expression were negatively affected, compared to the wild-type strain. Conversely, when the feeding concentration was only half of FBC1, AbrB accumulates in minor proportion, and sporulation efficiency and cry1Ac expression increased (FBC2). These results suggest that variable nutrient conditions can cause an imbalance in the accumulation of transition state regulators such as AbrB during FBCs, which can be detrimental to produce spores and Cry proteins, that are the main Bt products for biological control of agricultural pests.

Rational Skyrmions

A new method is introduced to construct approximations to Skyrmions that are explicit rational functions of the spatial Cartesian coordinates. The scheme uses ADHM data of a Yang–Mills instanton to produce a Skyrmion with a baryon number that is equal to the instanton number. The formula for the Skyrmion involves only the evaluation of the ADHM data, in contrast to the Atiyah–Manton construction that requires the solution of a differential equation that can only be solved explicitly in the case of a spherically symmetric Skyrmion. Examples with baryon numbers one and two are studied in detail. The energy of the rational Skyrmion with baryon number one is lower than that of the Atiyah–Manton Skyrmion, which is already within one percent of the energy of the true numerically computed Skyrmion. A family of baryon number two Skyrmions is presented, which includes an axially symmetric Skyrmion that smoothly transforms to a pair of well-separated single Skyrmions as the parameter is varied.

Orientational Transitions in Magnetically Compensated Liquid-Crystal Suspensions of Ferromagnetic Carbon Nanotubes

Purpose of research is to study the influence of ferromagnetic carbon nanotubes on orientational transitions in magnetically compensated liquid-crystal suspensions.Methods. The problem was solved in the framework of the continuum theory. By minimizing the Helmholtz free energy functional, a system of Lagrange-Euler equations is obtained that determines the equilibrium dependences of the orientation angles of liquid crystal and impurity ferromagnetic carbon nanotubes directors, as well as the concentration distributions of the dispersed phase of the suspension as a function of the transverse coordinate, material parameters, and magnetic field strength.Results. It is shown that in the presence of an external magnetic field, a liquid-crystal suspension of ferromagnetic carbon nanotubes can be in a non-uniform phase (angular phase) and two uniform phases (planar and homeotropic phases). Expressions for the threshold fields of transitions between coexisting orientational phases are obtained analytically as functions of the material parameters of the composite. Diagrams of the orientational phases of the suspension are plotted.Conclusion. As a result of the research, it was shown that the addition of low concentrations of ferromagnetic carbon nanotubes can significantly reduce the threshold of the magnetic Fréedericksz transition compared to a pure liquid crystal, which is important for various technical applications. The obtained analytical formulas for the threshold fields of transitions between different orientational phases can be used to determine the anchoring energy and material parameters of suspensions of ferromagnetic carbon nanotubes in a liquid crystal.

THE RESEARCH OF IMPLEMENTATION OF NUMERICAL RIGOROUS MATHEMATICAL METHODS WITH THE PARAMETER OF THE MEMBERS NUMBER IN THE TAYLOR SERIES

The current level of development of geoinformation technologies makes it possible to determine the cartometric properties of terrain objects with a user-defined accuracy. The author of this paper proposes a mathematical model that allows to implement the function of converting geodetic coordinates into rectangular flat Gauss-Kruger projections in a software environment based on the setting of the parameter of the number of members in the Taylor series, adjusting the accuracy of the coordinate transformation and their dimension. The purpose of this work is to implement a mathematical model of a numerical approximate computer method of converting geodetic coordinates into flat rectangular Gauss-Kruger projections. The results of this study will also be used to create functions for converting coordinates from rectangular flat Gauss-Kruger projections to geodetic coordinates and from one 6-degree zone of the Gauss-Kruger projection to another, taking into account the parameter of the number of members in the Taylor series. The proposed mathematical models are recommended to be implemented in the MATLAB or PhyCharm using the necessary libraries. The following studies will focus on determining the areas and lengths of objects located in two or more 6-degree zones of the Gauss-Kruger projection.

Virgin cork colour and porosity as predictors for secondary cork industrial quality

Currently, the selection of the trees to be removed in a thinning, carried out in a young cork oak plantation, is determined by a systematic rule to reach a predefined tree density value, in combination with simple criteria regarding individual tree sanitary conditions and stem shape. Since no criteria regarding the cork are available, thinnings can result in the removal of individuals that would later produce high quality secondary cork, leaving tree producers with lower quality cork. This study aims to test the feasibility of using CIELAB colour space coordinates and porosity values, measured in virgin cork samples, as predictors of the industrial cork quality and porosity obtained in secondary cork, thereby providing additional information usable for the classification of trees prior to the first thinning implementation. The L* and b* colour coordinates, measured in the transverse direction, depicted three main cork quality groups. Other L* and b* colour parameters, measured in the radial direction or in the cork back surface, have also shown statistically different average values while measured in different quality cork samples. Cork porosity from virgin and secondary cork showed a positive moderate monotonic relationship. A hyperbolic model for the prediction of secondary cork porosity was developed based on the virgin cork porosity, with one parameter expressed as a function of virgin cork colour coordinates (R2 =0.445). Results were successful in confirming the hypothesis raised. They may be used for the classification of trees prior to thinning.

An examination of force maps targeted at orientation interactions in moving groups.

Force mapping is an established method for inferring the underlying interaction rules thought to govern collective motion from trajectory data. Here we examine the ability of force maps to reconstruct interactions that govern individual's tendency to orient, or align, their heading within a moving group, one of the primary factors thought to drive collective motion, using data from three established general collective motion models. Specifically, our force maps extract how individuals adjust their direction of motion on average as a function of the distance to neighbours and relative alignment in heading with these neighbours, or in more detail as a function of the relative coordinates and relative headings of neighbours. We also examine the association between plots of local alignment and underlying alignment rules. We find that the simpler force maps that examined changes in heading as a function of neighbour distances and differences in heading can qualitatively reconstruct the form of orientation interactions, but also overestimate the spatial range over which these interactions apply. More complex force maps that examine heading changes as a function of the relative coordinates of neighbours (in two spatial dimensions), can also reveal underlying orientation interactions in some cases, but are relatively harder to interpret. Responses to neighbours in both the simpler and more complex force maps are affected by group-level patterns of motion. We also find a correlation between the sizes of regions of high alignment in local alignment plots and the size of the region over which alignment rules apply when only an alignment interaction rule is in action. However, when data derived from more complex models is analysed, the shapes of regions of high alignment are clearly influenced by emergent patterns of motion, and these regions of high alignment can appear even when there is no explicit direct mechanism that governs alignment.

Functions of SRPK, CLK and DYRK kinases in stem cells, development, and human developmental disorders.

Human developmental disorders encompass a wide range of debilitating physical conditions and intellectual disabilities. Perturbation of protein kinase signalling underlies the development of some of these disorders. For example, disrupted SRPK signalling is associated with intellectual disabilities, and the gene dosage of DYRKs can dictate the pathology of disorders including Down's syndrome. Here, we review the emerging roles of the CMGC kinase families SRPK, CLK, DYRK, and sub-family HIPK during embryonic development and in developmental disorders. In particular, SRPK, CLK, and DYRK kinase families have key roles in developmental signalling and stem cell regulation, and can co-ordinate neuronal development and function. Genetic studies in model organisms reveal critical phenotypes including embryonic lethality, sterility, musculoskeletal errors, and most notably, altered neurological behaviours arising from defects of the neuroectoderm and altered neuronal signalling. Further unpicking the mechanisms of specific kinases using human stem cell models of neuronal differentiation and function will improve our understanding of human developmental disorders and may provide avenues for therapeutic strategies.

Fifth-order nonlinear Schrödinger equation as Routhian reduction of the nonlinear Klein–Gordon model

We consider the nonlinear Klein–Gordon model with polynomial nonlinearity involving odd and even powers. We elaborate a hybrid Hamiltonian and Lagrangian approach, which is generally referred to as Routh’s procedure, to describe the nonlinear modulation of wave packets assuming the wave field envelope to be a slow function of time and coordinate. An extended fifth-order nonlinear Schrödinger equation is obtained from the Routhian equation for a complex canonical variable that couples the wave field and its momentum. This canonical variable is expressed in terms of the amplitude of fundamental harmonic and its derivatives with respect to coordinate. The resulting fifth-order nonlinear Schrödinger equation is demonstrated to be a Hamiltonian system under a certain constraint imposed on its model parameters. When compared with other techniques used to derive high-order nonlinear Schrödinger models, our approach preserves the Hamiltonian structure of the governing equations for the fundamental harmonic, while the input of higher harmonics is taken into account by means of variational principle applied to the averaged Routhian. In this way, it represents the most general tool for the reduction of nonlinear wave equations to high-order envelope models for slowly modulated wave packets.

Complete separation of variables in the geodesic Hamilton-Jacobi equation in four dimensions

We list all metrics of arbitrary signature in four dimensions which admit complete separation of variables in the Hamilton–Jacobi equation for geodesic Hamiltonians. There are only ten classes of separable metrics admitting Killing vector fields, indecomposable quadratic conservation laws, and coisotropic coordinates. Canonical separable metrics parameterized by several (up to twelve) arbitrary functions of single coordinates are written explicitly. The full set of independent conservation laws in involution for each canonical metrics is also found.

Ultra-precision grinding of monocrystalline silicon cylindrical mirror

As one of the important functional components in the optical diagnosis system, the processing accuracy of monocrystalline silicon cylindrical mirror directly affects the overall performance of the entire experimental device. In order to obtain high-precision monocrystalline silicon cylindrical optical elements, the coordinate transfer function models of the diamond wheel in the cylindrical surface parallel grinding process were established, and the forming process scheme was proposed based on the wheel dressing precision and element grinding precision. At the end, the experiment for a monocrystalline silicon cylindrical mirror with size of 440mm × 50mm was carried out. The PV value of form error after grinding was about 2.7μm, which proved the correctness of the transfer function and the forming process scheme of monocrystalline silicon cylindrical optical element.

Numerical investigation of convergence of Fourier series, poly-nomials, and method of finite elements

Purpose. To compare the efficiency of using finite elements with variable and averaged mechanical and geometric parameters and to investigate the convergence of results obtained by the semi-analytical finite element method (SAFEM) using Fourier series and polynomials with the results obtained by the finite element method (FEM). The methods. The construction and development of an algorithm for studying the stress-strain state of spatial bodies with variable and averaged mechanical and geometric parameters were carried out based on SAFEM. Findings. Solvability indicators of SAFEM were obtained for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters. Numerical convergence studies of results obtained using SAFEM with Fourier series, polynomials, and the finite element method were conducted for a benchmark example, which was the Boussinesq problem for a half-space subjected to a concentrated force. The results indicate that the convergence of the investigated coordinate functions in the considered problem is of the first order. The originality. The obtained solvability indicators of SAFEM for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters allow for the study of various classes of problems. Numerical convergence studies using Fourier series, polynomials, and the finite element method were conducted for the benchmark example. Practical implementation. The practical significance lies in the development of a methodology for determining the stress-strain state of relevant spatial elements of structures with variable and averaged mechanical and geometric parameters subjected to arbitrarily distributed spatial loads.

RNA-Binding Proteins Regulate Post-Transcriptional Responses to TGF-β to Coordinate Function and Mesenchymal Activation of Murine Endothelial Cells.

Endothelial cells (ECs) are primed to respond to various signaling cues. For example, TGF (transforming growth factor)-β has major effects on EC function and phenotype by driving ECs towards a more mesenchymal state (ie, triggering endothelial to mesenchymal activation), a dynamic process associated with cardiovascular diseases. Although transcriptional regulation triggered by TGF-β in ECs is well characterized, post-transcriptional regulatory mechanisms induced by TGF-β remain largely unknown. Using RNA interactome capture, we identified global TGF-β driven changes in RNA-binding proteins in ECs. We investigated specific changes in the RNA-binding patterns of hnRNP H1 (heterogeneous nuclear ribonucleoprotein H1) and Csde1 (cold shock domain containing E1) using RNA immunoprecipitation and overlapped this with RNA-sequencing data after knockdown of either protein for functional insight. Using a modified proximity ligation assay, we visualized the specific interactions between hnRNP H1 and Csde1 and target RNAs in situ both in vitro and in mouse heart sections. Characterization of TGF-β-regulated RBPs (RNA-binding proteins) revealed hnRNP H1 and Csde1 as key regulators of the cellular response to TGF-β at the post-transcriptional level, with loss of either protein-promoting mesenchymal activation in ECs. We found that TGF-β drives an increase in binding of hnRNP H1 to its target RNAs, offsetting mesenchymal activation, but a decrease in Csde1 RNA-binding, facilitating this process. Both, hnRNP H1 and Csde1, dynamically bind and regulate specific subsets of mRNAs related to mesenchymal activation and endothelial function. Together, we show that RBPs play a key role in the endothelial response to TGF-β stimulation at the post-transcriptional level and that the RBPs hnRNP H1 and Csde1 serve to maintain EC function and counteract mesenchymal activation. We propose that TGF-β profoundly modifies RNA-protein interaction entailing feedback and feed-forward control at the post-transcriptional level, to fine-tune mesenchymal activation in ECs.

Nonlinear Oscillations and Buckling Prediction for Shallow Convex Shells

Since 2010, the testing of thin-walled shallow shells has revealed that the ultimate internal stresses, under which the shells lose their stability (collapse), appeared to be lower than those predicted by the buckling theory used in American and European standards. The existing norms are based on the static theory of shallow shells proposed in 1930 with stable solutions for thin-walled structures within the nonlinear theory. These stable solutions differ significantly from the forms of equilibrium common to small initial loads. The minimum load, under which an alternative form of equilibrium exists, was used as the ultimate load. In the 1970s, this approach was proved to be unacceptable for complex loadings that were not a part of the real world in the past but are now the case with thinner products operated under complex conditions. Therefore, the initial theories on bearing capacity evaluations must be revisited. The new theory could be built on the basis of recent mathematical results establishing that the estimates made per two schemes (three-dimensional dynamic theory of elasticity and dynamic theory of shallow convex shells) were asymptotically close. Green's special function is introduced to convert the Foppl-von Karman system into a resolving integro-differential equation. The obtained nonlinear equation allows for the separation of variables and has numerous time-periodic solutions that satisfy the Duffing equation with a "soft spring". Numerical analysis enables determining the amplitude and period of oscillations depending on the properties of Green's function. This paper reviews an experimental setup in which oscillations are generated with the probing load directed normally to the surface of the shell. The experimental measurements of the resonance displacements as a function of coordinates and time enable the calculation of the safety factor for the bearing capacity of the structure using the non-destructive method under operating conditions.

Development of advanced hybrid mechanistic-artificial intelligence computational model for learning of numerical data of flow in porous membranes

Numerical analysis and machine learning regression were carried out for understanding and description of ozonation process combined with membrane separation. The main focus was on mass transfer modeling to simulate concentration distribution of ozone in liquid phase. Machine learning regression models were utilized to decrease the computational expenses of CFD (Computational Fluid Dynamics) simulations. For machine learning models, we compared the performance of three regression models, namely Gaussian Process Regression (GPR), Deep Neural Network (DNN), and Extreme Gradient Boosting (XGB or XGboost) for predicting the obtained output of CFD simulations which was ozone concentration in the feed, i.e., C (mol/m3) as function of radial and axial coordinates. Hyper-parameter tuning for these models was performed using the Tabu Search algorithm. The results indicate that both GPR and DNN models achieved excellent prediction accuracy, with R-squared values of 0.99999 and 0.99998, respectively. Also, the RMSE for GPR and DNN were 3.8481E-03 and 4.9835E-03, respectively, while their maximum errors were 6.08501E-02 and 4.47909E-02, respectively. On the other hand, the XGB model showed a lower performance, with an R-squared value of 0.99402, an RMSE of 8.9484E-02, and a maximum error of 4.51381E-01

Bending Vibration and Buckling Analysis Of Nonhomogeneous Nanotubes Using Nonlocal Elasticity Theory and Gdq Method

In this paper structural analysis of nonhomogeneous nanotubes has been carried out using nonlocal elasticity theory. Governing differential equations of nonhomogeneous nanotubes are derived. Nonlocal theory of elasticity has been employed to include the scale effect of the nanotubes. Nonlocal parameter, elastic modulus, density and diameter of the cross sections are assumed to be functions of spatial coordinates. General Differential Quadrature (GDQ) method has been employed to solve the governing differential equations of the nanotubes. Various boundary conditions have been applied to the nanotubes. Present results considering nonlocal theory are in good agreement with the results available in the literature. Effect of various geometrical and material parameters on the structural response of the nonhomogeneous nanotubes has been investigated. Present results of the nonhomogeneous nanotubes are useful in the design of the nanotubes.

To Foundations of General Theory Relativity

It i s shown that the foundations of the generally accepted theory contain a number of contradictory and unfounded statements. The geometric properties of the three-dimensional Riemannian space are successively described. It is shown that this space is locally Euclidean. The metric tensor can be algebraically diagonalized. In this case, all diagonal elements are equal to each other and differ from unity by a function of coordinates, which is called the gravitational potential. It is shown that this function is a solution of the differential equation of potential theory. If this solution is such that the potential can be represented by equipotential surfaces, then the trajectory of free motion of a material particle lies on this surface. The trajectory on the surface is a geodesic line determined by the initial conditions. The numerical value of the potential on the surface is included in the definition of the maximum possible speed on this surface, that is, a constant equal to the speed of light in vacuum is multiplied by a value less than one, determined by the value of the potential.

A Posteriori Improvement in Projection Method

This work is devoted to the renement of the approximate solution, obtained by the projection method. The proposed approach uses expanding the design space by adding new coordinate functions. As a result, it is possible to clarify previously obtained solution using small computer resources. Applying this approach to the finite element method allows produce a local renement of the mentioned solution. Suggested Approach illustrated in the finite element method for a boundary value problem second order in one-dimensional and two-dimensional cases.

Extremal metrics for combinations of Laplace eigenvalues and minimal surfaces into ellipsoids

We give a variational method for existence and regularity of metrics which minimize combinations of eigenvalues of the Laplacian among metrics of unit area on a surface. We show that there are minimal immersions into ellipsoids parametrized by eigenvalues, such that the coordinate functions are eigenfunctions with respect to the minimal metrics. This work generalizes the author's maximization for one eigenvalue among metrics of unit area on a surface related to minimal surfaces into spheres. This work also generalizes the previous characterizations of critical metrics for one eigenvalue to any combination of eigenvalues from target spheres to target ellipsoids.

Impact on Protective Device Sequence of Operation in Case Distributed Generation Integrated to Distribution System

This study aims to evaluate the impact of the distributed generator (DG) connection to the grid. The simulated results present the parameters of the system required to install DG on the end of the main distribution feeder. Various parameters, such as voltage, current, and protective relay coordination are modelled after the actual provincial electricity authority (PEA) distribution system. Various case studies compared the coordination without and with DG connections to the grid by finding the difference of protective devices. The results indicate that the malfunction can be fixed in order of priority protective devices, which operate according to the parameter setting. Additionally, the coordinate functions between the recloser and fuse devices in both phase and ground configurations in the operating zone prevented the drop-out fuse melting or burning out. Based on the result, this problem is fixed by providing a directional recloser device and increasing the fuse-link rated with 40k installation for replacing the conventional sizing, which can improve the performance in case of fault occurrence to investigate the reliability and stability of the distribution system.