Involutive Form Research Articles

A study of self-similar vector fields in bianchi type III spacetime via Rif tree approach

Abstract In this study, we use the Rif tree approach to explore self-similar vector fields in Bianchi type III spacetime. This work adopt a computer-based method to transform symmetry equations into an involutive form that is simplified and divides the integration problem into multiple cases, each represented as a tree structure. In some cases, the metric functions are subject to particular constraints. These conditions allow one to solve the system of equations governing self-similar symmetries and provide explicit formulations for the metrics and their corresponding self-similar vector fields. This approach is novel in that it covers not only the analysis of the direct integration strategy but also some metrics that are practically relevant. For a detailed investigation of the created models, stability and physical importance are also considered.

Energy model in Bianchi type-V spacetime via RIF integration techniques

This paper investigates the Noether versus Killing symmetries and their associated conservation laws of Bianchi type-V spacetimes. The study is carried out using the Maple RIFSIMP package, which converts a set of nonlinear differential equations into the reduced involutive form (RIF). This technique generates an RIF tree, where each branch is solved to obtain the explicit forms of Noether symmetries. Separate RIF trees are used to represent each group. We derive a general expression for the Noether symmetry connected to homothety, and then we investigate this Noether symmetry in each separate group. To explore whether dark energy is associated with Bianchi type-V spacetime, we examine the energy density of each spacetime obtained in association with the Ricci scalar. The symmetries of the larger groups, 11- and 17-dimensional, are presented separately in the tables.

Crossed helical gears—simulative studies and experimental results on non-involute geometries

Crossed helical gear units generally consist of a steel worm and a plastic helical gear with an axis crossing angle. Due to the high transmission ratio in a small installation space, they are used in auxiliary and actuating gears such as in window regulators, assembly lines, household appliances and positioning tasks. This paper deals with a calculation approach for crossed helical gears to include non-involute flank geometries for new and optimized gearboxes. The geometry derivation for general flank contours based on a polynomial and extends the geometric possibilities beyond the special case of the involute form. The use of principal curvatures and principal curvature directions to describe freely curved surface geometries enables the calculation of flank pressures, efficiency and sliding paths in the entire contact area. Previous studies confirmed the advantages in the mentioned load characteristics for geometries deviating from the involute. Furthermore, parameter studies show the influences of the individual design parameters and demonstrate the effects on operating behavior, with those a design recommendation for crossed helical gear units with general flank geometries can be created. ZC and ZC‑S geometries are used as calculation examples. With regard to the use of these new geometries in applications, manufacturing is a crucial aspect. Grinding disc parameters as well as a three-roll size to control the worm manufacturing for general flank geometries are necessary and described below. In addition to the theoretical calculation, a ZC crossed helical gear geometry was designed, manufactured and compared to a ZI reference gear in test rigs. This confirmed the advantages in load-carrying capacity and efficiency increase resulting from the calculation and proved the benefits.

Killing Vector Fields of Static Cylindrically Symmetric Spacetime—A Rif Tree Approach

In this paper, we use an algebraic approach to classify cylindrically symmetric static spacetimes according to their killing vector fields. This approach is based on using a maple algorithm to re-cast the Killing’s equations into a reduced involutive form and integrating the Killing’s equations subject to the constraints given by the algorithm. It is shown that this approach provides some additional spacetime metrics, which were not provided previously by solving the Killing’s equations using a direct integration technique. To discuss some physical implications of the obtained spacetime metrics, we use them in the Einstein equations and discuss their significance.

Human Pineal Gland Involutionary Process: New Findings.

In this work, we report preliminary results about the involution of the human pineal gland involution. The detailed analysis of pineal structure was done on autopsy material of 77 persons in age 27-96 using x-ray phase-contrast tomography, histology, and immunohistochemistry. Our study suggests that the pineal gland alteration in older adults may be more profound than has been reported to date. We identified and described a new form of pineal gland involution that eventually led to the total degradation of the pineal gland. To our knowledge, this study is the first to report on the complete replacement of pineal gland parenchyma with connective tissue in older adults.

An analytical study of employee loyalty and corporate culture satisfaction assessment based on sentiment analysis.

As an important factor related to the interests of enterprises, the attitude and behavior of employees are related to the company's survival and the realization of business objectives. However, in recent years, with the rapid development of emerging industries and industry changes, the turnover rate of employees in the whole enterprise has been greatly improved. Frequent turnover of personnel will have a great impact on the stability of the company, the competitiveness of the enterprise, and the operating cost. Employee loyalty and corporate culture satisfaction assessment is the core of sustainable corporate development, but most of the traditional analysis studies are based on the performance approach, using employee overtime, employee achievement, and company effectiveness as data sources, the former performance data is only a side view of the company's situation, the latter as the data source of this study is a one-sided and involute form, and the data is not stable. Therefore, this paper proposes an analysis of employee loyalty and corporate culture satisfaction assessment based on sentiment analysis, using association rules and sentiment lexicons from anonymous employee evaluations to analyze the actual data.

A comparison of four machine learning techniques and continuous wavelet transform approach for detection and classification of tool breakage during milling process

In machining, the tool condition has to be monitored by condition monitoring techniques to prevent damage by the use of tools and the workpiece. Cutting forces acting on the tool between zero and maximum values cause the cutting edge to crack and break. Predetection of this situation in the cutting tool is very important to prevent any negative situation that may occur. This study introduces a vibration-based intelligent tool condition monitoring technique to detect involute form cutter faults such as tool breakage at different levels during gear production on a milling machine. Machine learning algorithms such as artificial neural network, random forest, support vector machine, and K-nearest neighbor were used to detect the broken teeth and its level of breakage. According to the results obtained, it was observed that all the algorithms are successful in detecting faults in different teeth; also they have identification advantages according to different fault levels. In addition, the time and frequency domain analysis and continuous wavelet transform were used to determine the local faults. The developed machine learning-based detection performances compared the classical time and frequency domain analyses and continuous wavelet transform to prove the effectiveness and precision of the proposed methods. The results showed that all of the machine learning techniques have satisfactory performance to be used as fast and precise detection tools without complex calculations for detecting tool breakage.

Noether Symmetries of Lemaitre-Tolman-Bondi Metric via Rif Tree Approach

In this paper, we have explored Noether symmetries for the Lagrangian corresponding to the Lemaitre-Tolman-Bondi (LTB) spacetime metric via a Rif tree approach. Instead of the frequently used method of directly integrating the Noether symmetry equations, a MAPLE algorithm is used to convert these equations to the reduced involutive form (Rif). The interesting feature of this algorithm is that it provides all possible metrics admitting different dimensional Noether symmetries. These metrics are given in the form of branches of a tree, known as a Rif tree. These metrics are used to solve the determining equations and the explicit form of symmetry vector fields are found, giving 4, 5, 6, 7, 8, 9, 11, and 17-dimensional Noether algebras. To add some physical implications, Einstein’s field equations are used to find the stress-energy tensor for all the explicitly known metrics, and the parameters appearing in the metrics are used to find bounds for different energy conditions.

An 8-periodic exact sequence of Witt groups of Azumaya algebras with involution

Given an Azumaya algebra with involution $$(A,\sigma )$$ over a commutative ring R and some auxiliary data, we construct an 8-periodic chain complex involving the Witt groups of $$(A,\sigma )$$ and other algebras with involution, and prove it is exact when R is semilocal. When R is a field, this recovers an 8-periodic exact sequence of Witt groups of Grenier-Boley and Mahmoudi, which in turn generalizes exact sequences of Parimala–Sridharan–Suresh and Lewis. We apply this result in several ways: We establish the Grothendieck–Serre conjecture on principal homogeneous bundles and the local purity conjecture for certain outer forms of $${\mathbf {GL}}_n$$ and $${\mathbf {Sp}}_{2n}$$ , provided some assumptions on R. We show that a 1-hermitian form over a quadratic étale or quaternion Azumaya algebra over a semilocal ring R is isotropic if and only if its trace (a quadratic form over R) is isotropic, generalizing a result of Jacobson. We also apply it to characterize the kernel of the restriction map $$W(R)\rightarrow W(S)$$ when R is a (non-semilocal) 2-dimensional regular domain and S is a quadratic étale R-algebra, generalizing a theorem of Pfister. In the process, we establish many fundamental results concerning Azumaya algebras with involution and hermitian forms over them.

Gradings on associative algebras with involution and real forms of classical simple Lie algebras

We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a finite-dimensional algebra can be obtained from them via a group homomorphism (although not in a unique way). We classify up to equivalence the fine gradings on simple associative algebras with involution over the field of real numbers (or any real closed field) and, as a consequence, on the real forms of classical simple Lie algebras.

Killing vector fields of Bianchi type I spacetimes via Rif tree approach

In this paper, we have adopted a new approach to study the Killing vector fields of locally rotationally symmetric and general Bianchi type I spacetimes. Instead of directly integrating the set of Killing’s equations, an algorithm is developed in Maple which converts these equations to the reduced involutive form (Rif) and consequently it imposes some restrictions on the metric functions in the form of a tree, known as Rif tree. The set of Killing’s equations is then solved for each branch of the Rif tree, giving the explicit form of the Killing vector fields. The structure of Lie algebra is presented for each set of the obtained Killing vector fields and some physical implications of the obtained metrics are discussed.

A Multistage Cutting Tool Fault Diagnosis Algorithm for the Involute form Cutter Using Cutting Force and Vibration Signals Spectrum Imaging and Convolutional Neural Networks

In a machining system, tool condition monitoring systems are required to get a high-quality product and to prevent the downtime of machine tools due to tool failures. For this purpose, tool condition monitoring systems have become very important during the years since the mechanical faults can cause high cost. This study introduces a multistage cutting tool fault diagnosis method to detect the presence and level of the involute form cutter faults on the by the cutting force and vibration signal analysis. Therefore, different fault levels (low, medium and high) were generated on the involute form cutter as a tool breakage. During the experiments, the cutting force, vibration and acoustic signals were gathered with three different feed rates for each fault level. The gathered signals were processed by a multistage signal processing algorithm developed in the MATLAB environment. As an initial step, the continuous wavelet transform of the obtained signals was taken and saved as an image by the developed algorithm. After that, a convolutional neural network model is trained and tested by using the obtained images. The developed algorithm firstly checks the presence of the cutting tool fault. Once the algorithm labels the cutting tool is damaged, it then checks the damage level of the cutting tool fault. It is observed from the results, cutting force analysis is sufficient for the detection of cutting tool fault. On the other hand, the cutting force signal analysis is insufficient to detect the damage level of the cutting tool. Therefore, the vibration signal analysis is required to detect the damage level of the cutting tool. Results prove that, by the vibration analysis, the developed algorithm could detect not only the presence of the damage on the cutting tool but also the damage level. The results of the algorithm for each stage and signal are given in the results section.

Proper homothetic vector fields of Bianchi type I spacetimes via Rif tree approach

This paper deals with the study of homothetic vector fields of Bianchi type I spacetimes using Rif tree approach. Instead of directly integrating the homothetic symmetry equations, a computer algorithm is used to transform these equations to the reduced involutive form, which splits the problem of integrating these equations into many cases and gives these cases in the form of a tree imposing certain restrictions on the metric functions. Using these restrictions, the set of homothetic symmetry equations is solved to get the explicit form of the metrics and their homothetic vector fields. It is observed that this approach gives some new physically realistic metrics, not given by an earlier study through direct integration technique.

Realization formulas for involutions of matrix-valued positive real odd functions

In a seminal paper Foster (1924) showed that the impedances of lumped electrical circuits generated by inductances and capacitors are positive real odd functions ( PRO for short). For multi-port electrical systems built from inductances and capacitors one obtains matrix-valued PRO functions, denoted PRO m in the case of to × to matrix functions. Like PRO , the class of matrix functions PRO m is also a convex invertible cone, i.e., a convex cone closed under inversion (in the form of involution). Given a minimal, Weierstrass descriptor realization for a function in PRO m , we explicitly compute a minimal, Weierstrass descriptor realization for its involution, and through these formulas we analyse the zero-pole structure of the function.

Human Thymic Involution and Aging in Humanized Mice.

Thymic involution is an important factor leading to the aging of the immune system. Most of what we know regarding thymic aging comes from mouse models, and the nature of the thymic aging process in humans remains largely unexplored due to the lack of a model system that permits longitudinal studies of human thymic involution. In this study, we sought to explore the potential to examine human thymic involution in humanized mice, constructed by transplantation of fetal human thymus and CD34+ hematopoietic stem/progenitor cells into immunodeficient mice. In these humanized mice, the human thymic graft first underwent acute recoverable involution caused presumably by transplantation stress, followed by an age-related chronic form of involution. Although both the early recoverable and later age-related thymic involution were associated with a decrease in thymic epithelial cells and recent thymic emigrants, only the latter was associated with an increase in adipose tissue mass in the thymus. Furthermore, human thymic grafts showed a dramatic reduction in FOXN1 and AIRE expression by 10 weeks post-transplantation. This study indicates that human thymus retains its intrinsic mechanisms of aging and susceptibility to stress-induced involution when transplanted into immunodeficient mice, offering a potentially useful in vivo model to study human thymic involution and to test therapeutic interventions.

A study of energy conditions in Kantowski–Sachs spacetimes via homothetic vector fields

In this paper, we have studied different energy conditions for some metrics arising from the classification of Kantowski–Sachs spacetimes via homothetic vector fields (HVFs). The homothetic equations for Kantowski–Sachs spacetimes are analyzed using a Maple algorithm which transforms these equations to the reduced involutive form (Rif), giving all possible cases in the form of a tree, known as Rif tree, where the branches of the resulting tree give the potential spacetime metrics which may possess proper HVFs. The set of homothetic equations is integrated for all branches of the Rif tree and the explicit form of HVFs is obtained in ease case. For all the obtained metrics, we have found the bounds for different energy conditions. The stability of these metrics is also discussed.

An Efficient Rif Algorithm for the Classification of Kantowski-Sachs Spacetimes via Conformal Vector Fields

In this paper, we classify the Kantowski-Sachs spacetimes via conformal vector fields (CVFs). A Maple algorithm using the ‘Exterior’ package is used to reduce the set of conformal Killing equations to the reduced involutive form (Rif). The algorithm yields a tree, known as the Rif tree, where the branches of the Rif tree give the potential metrics for which the spacetimes under consideration may possess proper CVFs. The set of conformal Killing equations is solved for all the branches of the Rif tree to obtain the explicit forms of CVFs. Some physical implications of the obtained metrics are also discussed.

The temperature field study on the three-dimensional surface moving heat source model in involute gear form grinding

Form grinding is one of the most important finishing processes for obtaining high surface quality gears. Nevertheless, to avoid thermally induced burning and structural change poses a major challenge for this manufacturing technology. Based on the moving heat source model and the superposition principle of heat sources, a comprehensive analytical thermal model for analyzing the heat transfer mechanism of involute gear form grinding was derived. A three-dimensional distribution model of equivalent grinding heat source considering the non-linear distribution of tangential grinding force, grinding parameters, and heat partition ratio was proposed. The FEM (finite element method) simulation of the grinding temperature field was carried out to predict the grinding temperature field using a nested net heat flux equation. Research results have shown that the grinding temperature increases nonlinearly with the rolling angle increasing and the evident peak grinding zone temperature appearing near the tip of the tooth. Through the comparison with the previous experimental measurement results, it is found that the temperature distribution of analytical calculation and numerical simulation agrees well with the measured results.

The Chemical Effect in Medicine Interaction Determining the Form and Speed of Psychical Involution in the Prosthetic Restauration in the Edentulous

The progress made in dentistry during the latest decades is due, conceptually, to the new, systemic vision of man, which has also taken place in this field of medicine. In this context, the link between organic and psychic is indestructible. Thus illness is understood as a drama in which the somatic process has a psychic value, and the mental one has a body value. It is known that the morphological and functional integrity of the dental system, health and vigorousness, gives the individual a state of well-being that affects his somatic and psychic health, as any disturbance at this level entails repercussions in psychological and social behavior. Such a disruption is the total edification that seriously alters not only the dental system but the whole organism, putting various biological and psychosocial problems to the practitioner. The total expression represents not only a physical disability but also a psychological one. A special importance in studying psychological changes at total edentulous presents the psychological aspects of senile involution. This is not only a theoretical but also a practical importance due to the increase in the number of elderly people. Through the researches of the present paper we intend to present the reality of the psychological manifestations in the total edentation, which is objectified on different methods of psychodiagnosis in the first part, in order for the second part to be addressed to problems of prosthetic psychotherapy.The study comprises a group of 43 patients, of whom 24 were men and 19 women with total uni or bimaxilar edentation. Total edentation can be and is responsible for somatopsychic alterations, along with other pathogens, general, local, social, which sometimes can take a dramatic form, converting, where the area is also favorable, a pure somatic disease, for those who are not in psychopathy or even psychosis, although these latter cases are extremely rare and especially in youngsters, which would disrupt not only the person�s behavior as an individual, but also their status, function and social integrity. The treatment of dental and psychological complex is mandatory for any patient, but especially for the elderly, where recovery is more difficult, with disease-specific disorders adding to those of senescence.

Modeling and experimental verification of cutting forces in gear tooth cutting

ABSTRACTDue to complex cutting edge profile of an involute cutter, calculations of chip width and consequently cutting force are quite problematical. This article presents a mechanistic approach in the prediction of cutting force components arising in the course of gear tooth cutting by an involute form cutter. To permit calculation of chip width (and so cutting forces), a discrete model is utilized and cutting force components are then derived using Kienzle approach. Moreover, several experiments are performed under different cutting conditions to prove the effectiveness and accuracy of the used method. The results have revealed that cutting force components can be predicted in form gear tooth cutting with a significant accuracy.