Integration Rules Research Articles

The findings of character values are integrated in the mathematics learning process (case study in Guangxi Normal University)

Good character values need to be possessed by students at the University. Based on the Regulation of Rector, No. 19 Year 2016, UNNES has 12 Ethics, namely: science for truth, academic freedom, harmony, responsibility, honesty, justice, caring, exemplary, discipline, politeness, non-discrimination, and mutual respect. China is known to have a good character education from elementary school to university level. So, we need a collaboration work with a university in China, namely: Guangxi Normal University (GXNU). Partner Lecturer: Prof. Dr. Guo Yuanbing. The problem: What character values are integrated into the learning process of mathematics at GXNU? The method of research: Qualitative approach. The research subjects of Local Students of GXNU were selected. The main activities in GXNU: Observation, interviews, triangulation, and Focus Group Discussion (FGD) in GXNU, guided by Prof. Dr. Guo Yuanbing. The results (1) The character values that found and grown in GXNU were as follows: Prosperity, Democracy, Civility, Harmony, Freedom, Equality, Justice, Rule of Law, Patriotism, Dedication, Integrity, and Friendship. (2) Lecturer of Mathematics Education of GXNU was given the freedom to apply some or all of the values of character into teaching and learning activities; Character values were not explicitly added into the Lesson Plan of a Math lecturer in GXNU; Violations of the application of character values were left entirely to the lecturer concerned with the support of the institution.

Efficient cut-cell quadrature based on moment fitting for materially nonlinear analysis

Cut-cell quadrature based on the moment fitting scheme generates an accurate numerical integration rule for each cut element with the same small number of point evaluations as a standard Gauss quadrature rule. It therefore significantly increases the efficiency of unfitted finite element schemes such as the finite cell method that have often relied on cut-cell integration with prohibitively many quadrature points. Moment fitting, however, does not directly apply to inhomogeneous integrands as they result from nonlinear material behavior. In this article, we describe a novel modification of moment fitting approach that opens the door for its application in materially nonlinear analysis. The basic idea is the decomposition of each cut cell into material subdomains, each of which can be assigned a physically valid location where constitutive integration and the update of local history variables can be performed. We formulate a moment fitting scheme for each material subdomain using the same quadrature points, such that the resulting weights from all material subdomains can be added and the total number of point evaluations remains the same as in standard Gauss quadrature. We discuss numerical details of the modified scheme, including its ramifications for consistent linearization, and demonstrate its optimal performance in the context of the finite cell method and elastoplasticity.

Contribution and Distribution Flexibility and Tax Pass-Through Entities

The way jurisdictions design their tax systems for business operations can be a contentious issue, as they try to balance the competing goals of raising sufficient tax revenue without unduly inhibiting commercial investment and activities. Such tax design can be of particular importance for small and medium enterprises, which due to their size, inherent characteristics, and resources can struggle with tax compliance. Those attributes can also make business tax regressive. A number of countries around the world have adopted business entities that utilise corporate characteristics, such as liability protection for members and separate legal entity status, but have the characteristic of tax pass-through, with members assessed directly on the income and losses of the entity. Examples include limited liability partnerships (LLPs) in the United Kingdom, look-through companies in New Zealand, and limited liability companies (LLCs) in the United States.In some jurisdictions, these tax pass-through entities have been extremely popular, which in part has been attributed to flexibility for the members in terms of governance and the facilitation of contributions and subsequent distributions. This flexibility is arguably a desired commercial feature of business entities. However, such flexibility with contributions and distributions is seen as a potential risk to tax revenue as there is concern with artificial engineering in order to lower the overall tax burden. This has led to tax integrity measures, which by their very nature can potentially restrict flexibility.For example, LLCs and their members are subject to greater (and potentially more complex rules) when it comes to measuring the cost basis of their membership interests; this then influences members’ ability to utilise allocated losses and the tax treatment of distributions. The flexibility of contributions and distributions for LLPs in the United Kingdom has also raised concerns with the introduction of tax integrity measures. By comparison, the United States’ older tax pass-through entity, the S Corporation, with only one class of membership interest, has fewer integrity rules governing allocations.This Article will critically assess how the flexibility of contributions and distributions by these tax pass-throug entities affects the tax rules that apply to their members. We argue that the flexibility of contributions and distributions appears to be a key characteristic demanded by business entities both for commercial and tax reasons. However, investors need to be cognitive of the inherent complexity and costs that this flexibility may entail. Additionally, it is important for governments and revenue authorities not to unduly restrict flexibility with complex tax integrity rules as it is a fine balance between commercialand revenue needs.

Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are required that reflect microstructural as well as macro-structural instabilities, large deformations, and non-local effects. To this end, a micromorphic computational homogenization scheme has recently been developed, which employs the particular microstructural transformation as a non-local mechanism, magnitude of which is governed by an additional coupled partial differential equation. Upon discretizing the resulting problem it turns out that the macroscopic stiffness matrix requires integration of macro-element basis functions as well as their derivatives, thus calling for higher-order integration rules. Because evaluation of a constitutive law in multiscale schemes involves an expensive solution of a non-linear boundary value problem, computational efficiency of the micromorphic scheme can be improved by reducing the number of integration points. Therefore, the goal of this paper is to investigate reduced-order schemes in computational homogenization, with emphasis on the stability of the resulting elements. In particular, arguments for lowering the order of integration from expensive mass-matrix to a cheaper stiffness-matrix equivalent are outlined first. An efficient one-point integration quadrilateral element is then introduced and a proper hourglass stabilization is discussed. Performance of the resulting set of elements is finally tested on a benchmark bending example, showing that we achieve accuracy comparable to the full quadrature rules, whereas computational cost decreases proportionally to the reduction in the number of quadrature points used.

Numerical calculation of Fourier transforms based on hyperfunction theory

In this paper, we propose a numerical method for calculating Fourier transforms based on hyperfunction theory, a theory of generalized functions based on complex function theory. In the proposed method, we first obtain analytic functions giving the desired Fourier transform as a hyperfunction, and, then, we compute the Fourier transform by using continued fractions to determine the analytic continuation of these analytic functions onto the real axis. Using the proposed method, we can evaluate Fourier transforms that are difficult to evaluate using the conventional numerical integration rules. In addition, we can use the proposed method to evaluate Fourier transforms of hyperfunctions. Numerical examples show the efficiency of the presented method compared to previous methods.

3D thermo-hydro-mechanical coupled discrete beam lattice model of saturated poro-plastic medium

In this paper, we present a 3D thermo-hydro-mechanical coupled discrete beam lattice model of structure built of the nonisothermal saturated poro-plastic medium subjected to mechanical loads and nonstationary heat transfer conditions. The proposed model is based on Voronoi cell representation of the domain with cohesive links represented as inelastic Timoshenko beam finite elements enhanced with additional kinematics in terms of embedded strong discontinuities in axial and both transverse directions. The enhanced Timoshenko beam finite element is capable of modeling crack formation in mode I, mode II and mode III. Mode I relates to crack opening, mode II relates to in-plane crack sliding, and mode III relates to the out-of-plane shear sliding. The pore fluid flow and heat flow in the proposed model are governed by Darcy\'s law and Fourier\'s law for heat conduction, respectively. The pore pressure field and temperature field are approximated with linear tetrahedral finite elements. By exploiting nodal point quadrature rule for numerical integration on tetrahedral finite elements and duality property between Voronoi diagram and Delaunay tetrahedralization, the numerical implementation of the coupling results with additional pore pressure and temperature degrees of freedom placed at each node of a Timoshenko beam finite element. The results of several numerical simulations are presented and discussed.

Approximate integration through remarkable points using the Intermediate Value Theorem

Using the Intermediate Value Theorem we demonstrate the rules of Trapeze and Simpson's. Demonstrations with this approach and its generalization to new formulas are less laborious than those resulting from methods such as polynomial interpolation or Gaussian quadrature. In addition, we extend the theory of approximate integration by finding new approximate integration formulas. The methodology we used to obtain this generalization was to use the definition of the integral defined by Riemann sums. Each Riemann sum provides an approximation of the result of an integral. With the help of the Intermediate Value Theorem and a detailed analysis of the Middle Point, Trapezoidal and Simpson Rules we note that these rules of numerical integration are Riemann sums. The results we obtain with this analysis allowed us to generalize each of the rules mentioned above and obtain new rules of approximation of integrals. Since each of the rules we obtained uses a point in the interval we have called them according to the point of the interval we take. In conclusion we can say that the method developed here allows us to give new formulas of numerical integration and generalizes those that already exist.

Discourses on Judicial Formalism in Central and Eastern Europe: Symptom of an Inferiority Complex?

Post-communist Central and Eastern European legal cultures in general, and judicial style in particular, are often characterized as formalistic. This article reconstructs two ideological narratives about the formalist heritage of CEE judiciary, variants of which have dominated academic and policy debates about rule of law, judicial reforms and European integration in the last three decades. As the debate becomes linked to deeply rooted and long-term, sometimes traumatic issues of national and political identity, patterns of ideological thinking resurface easily. While it is symptomatic of CEE political cultures that the debate on judicial method has become a battleground for fierce controversies about collective (political) identity, arguably this exemplifies a broader phenomenon. Other weak or peripheral national cultures also face and struggle with issues of collective identity and inferiority complexes which may resurface in professional discourses and seemingly unpolitical domains.

A coupled extended meshfree–smoothed meshfree method for crack growth simulation

A coupled extended meshfree–smoothed meshfree method (CXSMM) is presented for simulating crack growth in 2D solids. In terms of the relationship between the crack surface and the background integration cells, the analysis domain is easy to be divided into discontinuous and continuous regions, in which the meshfree Galerkin method and the smoothed meshfree method are employed to construct the discretized system equations, respectively. To precisely capture the singular stress field near the crack tip, higher order Gauss integration rules are used in the discontinuous region. At the same time, the general smoothed strain technique is utilized in the continuous region for efficient evaluation of the domain integration. In this work, the initiation and propagation of the crack are treated by the aid of the level set algorithm. The CXSMM has the advantages of both extended meshfree method and smoothed meshfree method and can accurately and efficiently model the linear elastic fracture. Several benchmark problems are used to evaluate the accuracy, efficiency and robustness of the proposed method.

Choquet integration by Simpson’s rule with application in Hellinger distance

In non-additive measure theory, there are a few studies on the numerical Choquet integral in continuous case on real line. Recently, based on the statistics software R, Torra and Narukawa (Inf Fusion 31:137–145, 2016) considered the problem of computing a numerical Choquet integral and some algorithms for Hellinger distance between two monotone measures. In this paper, the composite Simpson rule for numerical Choquet integration is proposed. Then some algorithms in Mathematica software are given. As well as, CPU time of the Examples in terms of seconds is reported which shows, in computational view, the presented method has a high speed.

PRINCIPLES OF PUBLIC ADMINISTRATION OF STAFFING OF THE NATIONAL POLICE OF UKRAINE

It is emphasized that in order to fulfill the tasks assigned to the National Police of Ukraine, a stable and highly professional staff is required, capable of properly responding to the challenges and threats in the sphere of internal affairs. Therefore, the purpose of the article is to identify and summarize the system of principles of public administration of personnel support of the National Police of Ukraine on the basis of the theory of administrative law, the analysis of relevant normative-legal domestic and foreign acts, works of scientists and other sources. Thus, in the scientific work the system of principles of public administration of personnel support of the National Police of Ukraine was identified and described as the basic principles of the realization of public power in order to satisfy the society with professional, conscientious, ethically educated police officers, who can potentially carry out preventive activities and restore the rights and freedoms of the process crimes. It is determined that the principles of public administration of personnel of the National Police of Ukraine are the basic provisions, guiding ideas, norms of behavior, which are formulated in the form of a certain scientific provision and are fixed mainly in the legal form, reflect the content, structure, forms and methods of public administration of human resources for law enforcement agencies for the purpose of satisfying the public with professional, conscientious, ethically educated police officers to carry out the tasks assigned to the bodies and units of the National Ukrainian police. It is concluded that the principles of staffing of the National Police of Ukraine should be divided into general (rule of law, legality, political neutrality, integrity, transparency and openness, interaction with the public, patriotism, science, efficiency, competence) and functional-managerial principles (hierarchical, distribution of powers, collegiality and sole command, accountability, quality staffing of the National Police bodies to ensure legal and social workers, etc.).

Nonlinear Analysis of Factors Effecting on Different Reinforced Concrete Slabs

A nonlinear finite element (FEM) three-dimensional model introduced in this investigation well qualified for the examination of different reinforced concrete (RC) slabs till to failure. Three-dimensional isoperimetric quadratic elements with 20-node used to simulate the concrete, while an embedded within the concrete element of one-dimensional axial members applied to simulate the reinforcing bars. Carbon fiber reinforcement laminates were simulate as element externally attached to the brick element. During the loading process, there is an ideal bond connecting the concrete and reinforcing bars in the analysis. Hardening model of elasto-plastic work using to emulate the performance of concrete in compression then it followed by response with a completely plastic and finally is discontinue at the inception of crushing. Two crack patterns with (fixed orthogonal and a smeared crack model) with a tension-stiffening design has been adopted to simulate the concrete in tension with the incorporation of retained tensile stress of post-cracking models and due to cracking a shear retention design that remodel the rigidity of shear modulus. The Modified-Newton Raphson methods including an incremental-iterative technique used for solving the nonlinear equations of equilibrium. A force convergence criterion used to control the convergence of the solution. Integration rule with 27-Gaussian quadrature used as numerical integration in this analysis. The acquire results from the FE analysis are the slabs load-deflection response and stress distribution with numerous parametric investigations to examine the impact of some significant FE and material parameters. In overall, sufficient compromise between the FE solutions and the laboratory results has been achieved.

Synaptic Plasticity Depends on the Fine-Scale Input Pattern in Thin Dendrites of CA1 Pyramidal Neurons

Coordinated long-term plasticity of nearby excitatory synaptic inputs has been proposed to shape experience-related neuronal information processing. To elucidate the induction rules leading to spatially structured forms of synaptic potentiation in dendrites, we explored plasticity of glutamate uncaging-evoked excitatory input patterns with various spatial distributions in perisomatic dendrites of CA1 pyramidal neurons in slices from adult male rats. We show that (1) the cooperativity rules governing the induction of synaptic LTP depend on dendritic location; (2) LTP of input patterns that are subthreshold or suprathreshold to evoke local dendritic spikes (d-spikes) requires different spatial organization; and (3) input patterns evoking d-spikes can strengthen nearby, nonsynchronous synapses by local heterosynaptic plasticity crosstalk mediated by NMDAR-dependent MEK/ERK signaling. These results suggest that multiple mechanisms can trigger spatially organized synaptic plasticity on various spatial and temporal scales, enriching the ability of neurons to use synaptic clustering for information processing.SIGNIFICANCE STATEMENT A fundamental question in neuroscience is how neuronal feature selectivity is established via the combination of dendritic processing of synaptic input patterns with long-term synaptic plasticity. As these processes have been mostly studied separately, the relationship between the rules of integration and rules of plasticity remained elusive. Here we explore how the fine-grained spatial pattern and the form of voltage integration determine plasticity of different excitatory synaptic input patterns in perisomatic dendrites of CA1 pyramidal cells. We demonstrate that the plasticity rules depend highly on three factors: (1) the location of the input within the dendritic branch (proximal vs distal), (2) the strength of the input pattern (subthreshold or suprathreshold for dendritic spikes), and (3) the stimulation of neighboring synapses.

Forcer, a Form program for the parametric reduction of four-loop massless propagator diagrams

We explain the construction of Forcer, a Form program for the reduction of four-loop massless propagator-type integrals to master integrals. The resulting program performs parametric IBP reductions similar to the three-loop Mincer program. We show how one can solve many systems of IBP identities parametrically in a computer-assisted manner. Next, we discuss the structure of the Forcer program, which involves recognizing reduction actions for each topology, applying symmetries, and transitioning between topologies after edges have been removed. This part is entirely precomputed and automatically generated. We give examples of recent applications of Forcer, and study the performance of the program. Finally we demonstrate how to use the Forcer package and sketch how to prepare physical diagrams for evaluation by Forcer. Program summaryProgram title: Forcer.Program files doi:http://dx.doi.org/10.17632/d4jy7mfjxf.1Licensing provisions: GNU General Public License, version 3.Programming language: FORM. The generating scripts are written in Python.Nature of problem: Some physical quantities in perturbative quantum field theories require the evaluation of dimensionally regularized massless propagator-type Feynman integrals. This can be achieved by reducing the integrals in the problem to a set of master integrals and then substituting their values. At the four-loop level, such a reduction becomes highly non-trivial and very time-consuming. One needs an efficient program for the reduction.Solution method: The program recursively applies pre-derived parametric reduction rules for four-loop massless propagator-type Feynman integrals. Many rules were derived from topology substructures and were automatically generated by Python code. Some special cases were carefully optimized in a computer-assisted manner.Restrictions: Limitations come from the fact that reducing too complicated integrals requires too much CPU time and storage space. If rational coefficients become too large to be handled in FORM, then one needs to consider using truncated expansions.

High‐order cubature rules for tetrahedra

SummaryIn this paper, we construct new high‐order numerical integration schemes for tetrahedra, with positive weights and integration points that are in the interior of the domain. The construction of cubature rules is a challenging problem, which requires the solution of strongly nonlinear algebraic (moment) equations with side conditions given by affine inequality constraints. We present a robust algorithm based on a sequence of three modified Newton procedures to solve the constrained minimization problem. In the literature, numerical integration rules for the tetrahedron are available up to order p=15. We obtain integration rules for the tetrahedron from p=2 to p=20, which are computed using multiprecision arithmetic. For p≤15, our approach provides integration rules that have the same or fewer number of integration points than existing rules; for p=16 to p=20, our rules are new. Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, rational, weakly singular and trigonometric test functions over tetrahedra with flat and curved faces. In all tests, improvements in accuracy is realized as p is increased, though in some cases nonmonotonic convergence is observed.

Impact analysis of PEEK/ceramic/gelatin composite for finding behind the armor trauma

A ceramic-based armor system must arrest bullet penetration and dissipate a large amount of impact energy. Taking the total linear momentum transferred to the wearer of a ceramic armor as a measure of the behind-armor ballistic/blunt trauma (BABT), we study the effect on the BABT of adding a thin polyether-ether-ketone (PEEK) layer on the face of a Silicon Carbide (SiC) ceramic target impacted at normal incidence by a full metal jacket bullet traveling at a low velocity. A human torso is simulated by a block of ballistic gelatin. Three-dimensional non-linear large deformations of the system are numerically analyzed using the commercial finite element software ABAQUS/Explicit with the full integration rule to evaluate elemental matrices. Sensitivity tests are conducted with random samples generated by the Latin Hypercube Sampling technique to delineate the influence of the static yield stress, strain hardening, Young’s modulus and the mass density of the PEEK layer as well as of the shear modulus, the mass density and the maximum hydrostatic tensile stress of the ceramic on the BABT. It is found that reducing the acoustic mismatch between the PEEK and the ceramic increased the plastic energy dissipated in the ceramic. For normal impact at 180 m/s of a bullet having kinetic energy of 130 J, the 2 mm thick surface layer decreased the total peak normal force, the normal impulse transmitted, and the maximum pressure transferred from the SiC target to the gelatin layer by 19%, 18% and 32%, respectively. Simulations using a reduced integration rule significantly under-predict the final kinetic energy and the back face displacement of the bullet as compared to those using the full integration rule. For the 2 mm thick PEEK layer located on the top, the middle and the bottom of the SiC plate, the back face displacement is the least for the layer located in the middle but the BABT increased.

Using Rule Quality Measures for Rule Base Refinement in Knowledge-Based Predictive Maintenance Systems

As today’s manufacturing domain is becoming more and more knowledge-intensive, knowledge-based systems (KBS) are widely applied in the predictive maintenance domain to detect and predict anomalies in machines and machine components. Within a KBS, decision rules are a comprehensive and interpretable tool for classification and knowledge discovery from data. However, when the decision rules incorporated in a KBS are extracted from heterogeneous sources, they may suffer from several rule quality issues, which weakens the performance of a KBS. To address this issue, in this paper, we propose a rule base refinement approach with considering rule quality measures. The proposed approach is based on a rule integration method for integrating the expert rules and the rules obtained from data mining. Within the integration process, rule accuracy, coverage, redundancy, conflict, and subsumption are the quality measures that we use to refine the rule base. A case study on a real-world data set shows the approach in detail.

Importance Gaussian Quadrature

Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution and weights them accordingly, accounting for the mismatch between the target and proposal. In this work, we present a general framework of numerical integration techniques inspired by the IS methodology. The framework can also be seen as an incorporation of deterministic rules into IS methods, reducing the error of the estimators by several orders of magnitude in several problems of interest. The proposed approach extends the range of applicability of the Gaussian quadrature rules. For instance, the IS perspective allows us to use Gauss-Hermite rules in problems where the integrand is not involving a Gaussian distribution, and even more, when the integrand can only be evaluated up to a normalizing constant, as it is usually the case in Bayesian inference. The novel perspective makes use of recent advances on the multiple IS (MIS) and adaptive (AIS) literatures, and incorporates it to a wider numerical integration framework that combines several numerical integration rules that can be iteratively adapted. We analyze the convergence of the algorithms and provide some representative examples showing the superiority of the proposed approach in terms of performance.

Vortex flows of moist air with non-equilibrium and homogeneous condensation

A small-disturbance model is presented for the complex dynamics of vortex flows of moist air in a straight, circular pipe with non-equilibrium and homogeneous condensation. The model explores the nonlinear interactions among the vortex near-critical swirl ratio and the small amount of water vapour in the air. The condensation rate is calculated according to classical nucleation and droplet growth models. The asymptotic analysis gives the similarity parameters that govern the flow problem. These are the flow inlet swirl ratio , the inlet Mach number , the initial humidity , the number of water molecules in a characteristic fluid element , the inlet centreline super-saturation ratio and the ratio of characteristic condensation and flow time scales . Also, the flow field may be described by an ordinary first-order nonlinear differential equation for the flow evolution coupled with a set of four first-order ordinary differential equations along the pipe for the calculation of the condensate mass fraction. An iterative numerical scheme which combines the Runge–Kutta integration technique for the flow dynamics with Simpson’s integration rule for the calculation of the condensation variables is developed. Specifically, equilibrium states are determined, including the possibility of the appearance of multiple states under the same boundary conditions, and the stability characteristics of these states are described. The model is used to study the effects of humidity and of energy supply from nanoscale condensation processes on the large-scale dynamics of vortex flows as well as the effect of flow swirl on condensation processes in swirling flows.

Numerical Simulations and FPGA Implementations of Fractional-Order Systems Based on Product Integration Rules

Product integration (PI) rules are well known numerical techniques that are used to solve differential equations of integer and, recently, fractional orders. Due to the high memory dependency of the PI rules used in solving fractional-order systems (FOS), their hardware implementation is very difficult and resources-demanding. In this paper, modified versions of the PI rules are introduced to facilitate their digital implementations. The studied rules are PI rectangular, PI trapezoidal, and predict-evaluate-correct-evaluate (PECE) rules. The three modified versions of the PI rules are validated using a benchmark system of differential equations for different sizes of the memory window to show the effect of the window size on the solution accuracy. Additionally, the three modified versions of the PI rules are used to simulate a novel fractional-order chaotic system (FOCS) where its bifurcation diagrams are discussed with the window length parameter. The chaotic system is then implemented on a Field Programmable Gate Array (FPGA). There are only a few trials in literature to implement the fractional PECE algorithm on FPGA, nevertheless, the proposed FPGA realization is compared with the most recent of these trials. The FPGA implementations of the three PI rules are made using Xilinx ISE 14.7 on Artix 7 kit. The achieved throughput are 1280 Mbits/sec for PI rectangular, 128.8 Mbits/sec for PI trapezoidal, and 129.12 Mbits/sec for fractional-order PECE.