Fundamental Formula Research Articles

Static Elastic-Plastic Analysis of a Pipe Structure by the Transfer Matrix Method

Abstract Pipe systems have been widely used in industrial plants such as power stations. In these systems, the displacement and stress distributions often need to be predicted. Analytical and numerical methods, such as the finite element method (FEM), boundary element method (BEM), and frame structure method (FSM), are typically adopted to predict these distributions. The analytical methods, which can only be applied to problems with simple geometries and boundary conditions, are based on the Timoshenko beam theory. Both FEM and BEM can be applied to more complex problems, although this usually requires a stiffness matrix with a large number of degrees-of-freedom. In FSM, although the structure is modeled by a beam element, the stiffness matrix still becomes large; furthermore, the matrix size needed in FEM and BEM is also large. In this study, the transfer matrix method, which is simply referred to as TMM, is studied to effectively solve complex problems, such as a pipe structure under a small size stiffness matrix. The fundamental formula is extended to a static elastic-plastic problem. The efficiency and simplicity of this method in solving a space-curved pipe system that involves an elbow are demonstrated. The results are compared with those obtained by FEM to verify the performance of the method.

Unified Fundamental Formulas for Static Analysis of Pin-Jointed Bar Assemblies

The initial axial forces of members—whatever caused by prestress or external loads—may strongly change the mechanical properties of pin-jointed bar assemblies, to enhance, or even establish their structural stiffness. The structural responses under external disturbance cannot be calculated accurately if the influence of initial axial forces has not been considered appropriately. In this paper, an analytic theory considering the effect of initial internal forces is developed on the basis of linear elasticity hypothesis. The fundamental formulas proposed finally include generalized equilibrium equations and generalized compatibility equations, both of which have square coefficient matrices of full rank being transposed with each other. Generally, this method can be regarded as an extended version of a traditional force method considering the stiffening effect of initial internal forces. Compared with the matrix force method, it has a wider application scenario since few redundant simplifications are employed in the derivation of the formulas. In comparison with the displacement-based algorithm, the proposed method has the inherent advantages of the force method—the physical concepts of each item in equations are fairly explicit; and the combination coefficients of self-stress states and mechanisms are determined simultaneously in solving the structural responses. Thus, it is very helpful for us to essentially comprehend the principle that the pin-jointed bar assemblies resist the external loads.

Crashworthiness assessment of thin-walled double bottom tanker: Influences of seabed to structural damage and damage-energy formulae for grounding damage calculations

This work presents results of numerical analyses with focus on structural performance accounting for seabed topology, and investigation of energy formulae for application in calculation of grounding damage. Study in this work is divided into three stages, i.e. finite element method (FEM) verification using laboratory experiment, numerical calculation of ship grounding using FEM, and comparison of the FEM results with empirical formulae of damage-energy calculation. Fundamental formula of Minorsky is considered with other improvement expression, such as Woisin and Zhang. Investigation suggested that the recent-developed expression produces the closest estimation to the verified FEM results. On the other hand, fundamental formulae of Minorsky is the farthest compared to the FEM, which indicates constant value in the expression needs to be more specific as improved in the Woisin formula.

Estimation Error and the Fundamental Law of Active Management: Is Quant Fundamentally Flawed?

According to widely referenced applications of the Grinold (1989) Fundamental Law theory, simply adding securities to an optimization universe, adding factors to a forecast return model, trading more frequently, or reducing constraints can add investment value to an optimized investment strategy. The authors show with intuitive discussion followed by Monte Carlo simulation that many applications of Grinold theory for optimized portfolio design are often unreliable and self-defeating. Critical limitations of the theory are due to ignoring estimation error (Michaud 1989) and constraints required in practical applications. A substantial fraction of professional actively managed funds may be negatively impacted. This article was originally published as “Estimation Error and the Fundamental Law of Active Management” Is Quant Fundamentally Flawed: by Richard Michaud, PhD, David Esch, PhD, and Robert Michaud, and is available at https://www.newfrontieradvisors.com/media/1798/fundamental-law-march-2020.pdf. <b>TOPICS:</b>Portfolio theory, portfolio construction <b>Key Findings</b> • Estimation error cannot be ignored as a dangerous source of underperformance for quantitative managers, especially when mean-variance optimizers are used to construct portfolios. A substantial proportion of actively managed funds may be impacted by neglecting estimation error. • The four implied principles of management often taught as corollary to Grinold’s Fundamental Law of Active Management—(1) more assets in the investment universe, (2) more factors used in forecasting, (3) more frequent trading, and (4) removing constraints from optimizations—are not necessarily additive in the presence of estimation error and can harm out-of-sample performance when applied aggressively, contrary to the guidance of the Fundamental Law formulas. • Grinold’s formulation of the Fundamental Law is often taught as fact by many institutional education programs. The real-world failure of many of the necessary conditions for the mathematical proof are seldom included in finance curricula but should be noted.

Nanoscale Quantum Thermal Conductance at Water Interface: Green's Function Approach Based on One-Dimensional Phonon Model.

We have derived the fundamental formula of phonon transport in water for the evaluation of quantum thermal conductance by using a one-dimensional phonon model based on the nonequilibrium Green’s function method. In our model, phonons are excited as quantum waves from the left or right reservoir and propagate from left to right of HO layer or vice versa. We have assumed these reservoirs as being of periodic structures, whereas we can also model the HO sandwiched between these reservoirs as having aperiodic structures of liquid containing N water molecules. We have extracted the dispersion curves from the experimental absorption spectra of the OH stretching and intermolecular modes of water molecules, and calculated phonon transmission function and quantum thermal conductance. In addition, we have simplified the formulation of the transmission function by employing a case of one water molecule (N=1). From this calculation, we have obtained the characteristic that the transmission probability is almost unity at the frequency bands of acoustic and optical modes, and the transmission probability vanishes by the phonon attenuation reflecting the quantum tunnel effect outside the bands of these two modes. The classical limit of the thermal conductance calculated by our formula agreed with the literature value (order of W/K) in high temperature regime (>300 K). The present approach is powerful enough to be applicable to molecular systems containing proteins as well, and to evaluate their thermal conductive characteristics.

Involutive moving frames

By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving a wide variety of equivalence problems. The key is a pseudo-group analog of the classic result that characterizes congruence of submanifolds in Lie groups in terms of equivalence of the Lie group's Maurer-Cartan forms. This result, when combined with the fundamental recurrence formulas for the moving frame for pseudo-groups, will allow for a hybrid equivalence method that computationally improves on and illuminates both its progenitors.

Method of Calculating the Limiting Depth of Ruts on the Pavement of Automobile Roads

Proposed the criterion for design pavement, limiting the rut depth RD by limiting value RD lim , which depends on the required values of transport and exploitation characteristics. The solution to the problem is based on the classical dependence of the dynamic coefficient on speed at the point of impact of bodies. In this fundamental dependence, the collision speed of the tire with coated is determined by the speed of the wheel and the depth of the irregularities. From this fundamental formula, the functional dependence of the irregularities depth on the speed of movement, the deformation characteristics of the pavement, the power parameters of the moving load (dynamic coefficient), the distance of entry and exit of the wheel from the rut when overtaking another car is obtained. The analysis of the work of specialists of the road industry, which allowed to establish the limit values of all the factors under consideration for coatings, the state of which is characterized by different assessments (excellent, good and satisfactory). For different conditions of coverage, the limiting values of the rut depth RD lim are given.

Fundamental formulas for modified generalized integral transforms

Various fundamental formulas and results for integral transforms on a function space have been studied in many papers. However, there are many limitations with regard to obtaining the fundamental formulas and results with respect to integral transforms on the function space, because generalized Brownian motion has the nonzero mean function. Despite recent attempts address this problem, it has yet to be resolved. In this paper, based on the definitions of the modified generalized integral transform and (generalized) convolution product on function space, we establish the fundamental formulas relating the two. The fundamental formulas obtained via the translation theorem are applied in several examples to demonstrate the usefulness of our fundamental approach.

Runtime Adaptive Matrix Multiplication for the SW26010 Many-Core Processor

The study of matrix multiplication on the emerging SW26010 processor is highly significant for many scientific and engineering applications. The state-of-the-art work from the swBLAS library, called SWMM, focuses mainly on the infrequent case involving special matrix dimensions and determines the execution action of matrix multiplication by one specified algorithm. To further adapt to various matrix shapes, in this article, we present a runtime adaptive matrix multiplication methodology, called RTAMM, which targets the features of the SW26010 architecture. The execution action of RTAMM is determined dynamically at runtime via several fundamental cost formulas and multiple sets of blocking factors, rather than determining the action at library generation time. With comprehensive trade-offs between the computation and data access, overall architecture-oriented optimization methods are introduced at three levels (macro, assistant, and micro) to fully exploit the computing capability of SW26010. The experiments show that RTAMM can achieve competitive peak performance compared with SWMM. Moreover, in tests on 6000 different matrix multiplication cases, RTAMM outperforms SWMM in 85.55% of the cases, and the improvements range from 5% to 308%, whereas RTAMM is slightly inferior to SWMM in only 1.28% of the cases. These results demonstrate that RTAMM has both great adaptability and considerable performance improvement.

The Quantum Bang Hypothesis: An Alternative to Dark Matter and Dark Energy

We hypothesize that the quantum realm and the cosmos are linked by a scaling relation where the gravitational coupling constant αG is the scale factor and decreases with cosmic time. We propose a simple cosmological model where cosmic inflation, dark energy and dark matter could be redundant concepts. We show that cosmological parameters such as the Hubble constant, the age, density and mass of the observable Universe could be derived simply from quantum parameters. Finally, we propose a fundamental MOND formula with no interpolating function and an acceleration parameter simply derived from the Hubble constant.

Premium Calculation for Insurance Businesses Based on Cyber Risks in IP-Based Power Substations

Insurance is a promising risk transfer tool against switching cyberattacks on power grids that can disrupt operation and potentially lead to widespread outages. This paper emphasizes on a framework of premium calculation for cyber insurance businesses by modeling potential electronic intrusion with steady-state simulation results and its direct hypothesized impacts. The proposed actuarial framework models the operational monetary losses with the hypothesized power outages based on the cyber-reliability assessment and its expected mean time to restore power (MTTRP). The ruin probability is employed as the fundamental formula to determine the feasible insurance premium pool. Hypothesized spatial correlation studies on multiple substation contingencies associated with switching attacks have shown estimated operational losses and expected duration of power restoration, which is translated into the calculation of insurance premium. The proposed actuarial framework is validated using generalized IEEE test cases with modified parameters on substations. The potential implications of grid's hypothetical scenarios are discussed.

ПСЕВДОТЕНЗОРНАЯ ФОРМУЛИРОВКА МЕХАНИКИ ГЕМИТРОПНЫХ МИКРОПОЛЯРНЫХ СРЕД

The possibility of applications of relative tensors concepts to the mechanics of micropolar continuum and, in particular, for the hemitropic micropolar continua is considered. The fundamental tensors and orienting relative scalars in three-dimensional space are introduced. Permutation symbols and absolute Levi-Civita tensors are investigated in further details. Algebraic and differential properties of the relative tensors are discussed. The weights of the fundamental kinematic tensors are determined. The wryness tensor and the asymmetric strain tensor are constructed in terms of the vectors of micro-rotation and displacements. Notions of force and couple traction vectors, associated force and associated couple stress vector, force and couple stresses tensors are discussed in the frameworks of relative tensors algebra. The weights of the basic micropolar elasticity tensors are determined and discussed. The constitutive form of the micropolar elastic potential is introduced as an absolute scalar in order to obtain micropolar constitutive equations. In the linear case, the elastic potential is a quadratic form whose coefficients are pseudoscalars. The weights of the constitutive pseudoscalars are calculated. The dimensionless constitutive micropolar constants and constitutive constants with physical dimensions are discriminated. Statics and dynamics of micropolar elastic continua are developed in terms of relative tensors. Dynamic equations involving displacements and microrotations in the case of semi-isotropic (hemitropic) symmetry are derived and represented by the pseudotensor technique. The paper can be considered as a script of fundamental formulas and concepts related to the algebra and differentiation of relative tensors of arbitrary rank.

Geometry of Figurate Numbers and Sums of Powers of Consecutive Natural Numbers

First, we give a geometric proof of Fermat’s fundamental formula for figurate numbers. Then we use geometrical reasoning to derive weighted identities with figurate numbers and observe some of their applications. Next, we utilize figurate numbers to provide a matrix formulation for the closed forms of the sums thus generating Bernoulli numbers. Finally, we present a formula—motivated by the inclusion-exclusion principle—for as a linear combination of figurate numbers.

VIKOR method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment

In this article, the VIKOR method is proposed to solve the multiple criteria group decision making (MCGDM) with 2-tuple linguistic neutrosophic numbers (2TLNNs). Firstly, the fundamental concepts, operation formulas and distance calculating method of 2TLNNs are introduced. Then some aggregation operators of 2TLNNs are reviewed. Thereafter, the original VIKOR method is extended to 2TLNNs and the calculating steps of VIKOR method with 2TLNNs are proposed. In the proposed method, it’s more reasonable and scientific for considering the conflicting criteria. Furthermore, the VIKOR are extended to interval-valued 2-tuple linguistic neutrosophic numbers (IV2TLNNs). Moreover, a numerical example for green supplier selection has been given to illustrate the new method and some comparisons are also conducted to further illustrate advantages of the new method.

Stability of Meanings versus Rate of Replacement of Words: An Experimental Test

ABSTRACT The words of a language are randomly replaced over time by new ones, but it has long been known that words corresponding to some items (meanings) are less frequently replaced than others. Usually, the rate of replacement for a given item is not directly observable, but it is inferred by the estimated stability which, on the contrary, is observable. This strategy goes back a long way in the lexicostatistical literature, nevertheless nothing ensures that it gives the correct answer. The family of Romance languages allows for a direct test of the estimated stabilities against the replacement rates since the proto-language (Late Classical Latin or Vulgar Latin) is more or less known, and the replacement rates can be explicitly computed. The output of the test is threefold: i) we prove that the standard approach which infers the replacement rates through the estimated stabilities is sound; ii) we are able to rewrite the fundamental formula of Glottochronology for a non universal replacement rate (depending on the item); iii) we provide unquestionable evidence that the stability ranking is far from being the same for different families of languages. This last result is also supported by comparison with the Malagasy family of dialects.

Biophysical Characteristics of Weyb Watershed, Bale Mountainous Area of the Southeastern Ethiopia

Characterizing the biophysical features at a watershed level is a significant input for analyzing natural resources, for solving potential water resource management problems, for integrated water utilization assessment, for water allocation policy and management. The objective of this study was to assess the biophysical characteristics of Weyb watershed, which is recognized as a potential agricultural zone in southeastern part of Ethiopia, was considered as a case study. Relevant data were used and; ArcGIS, Microsoft Excel sheet and fundamental formulae were applied for the analysis. Accordingly, six current biophysical characteristics of Weyb watershed i.e., watershed area, land use land cover and soils, geomorphology, climate, agricultural practice and population have been analyzed and discussed briefly. The mean annual precipitation, actual evapotranspiration and mean temperature of the watershed are 1015 mm, 970.1 mm and 14 0C respectively. The study results show that the watershed is highly suitable for widespread agricultural production.

A simplified frequency formula for post-tensioned balanced cantilever bridges

The aim of this study is to develop a simplified natural fundamental frequency formula for the post-tensioned balanced cantilever bridges using the Operational Modal and Finite Element Analyses results. For this purpose, experimental and numerical studies were carried out on the five post-tensioned balanced cantilever bridges constructed in the city of Artvin, Turkey. First, the experimental and theoretical dynamic characteristics of the selected five bridges were determined using the ambient vibration-based Operational Modal Analysis and Finite Element Method, respectively. Then, the bridge model, which is given the highest correlation between the experimental and theoretical frequencies, was selected to determine the most important parameters that affected the modal behavior of the bridges. The most important parameters were determined as bridge length and pier height. Theoretical modal analyses were carried out for a series of bridge models with different lengths and heights. Finally, a simplified fundamental frequency formula was developed for the post-tensioned balanced cantilever bridges using the method of least squares considering the frequency values obtained from the theoretical modal analyses of the bridge models. The developed formula was checked with the experimentally obtained values, and it was observed that both sets of results were close to each other.

Transformations of basic hypergeometric series from the viewpoint of substitution of parameter operators

In this paper, we propose an operator method arising from the usual substitution of parameters to transformation formulas of basic hypergeometric series. As applications, some concrete substitutions of parameter operators implied by some known and fundamental transformation formulas are defined, thereby applications to the $${}_{r+1}\phi _{r}$$ series for $$r=1, 2$$ are exploited. Among these applications, three results are of interest: one is an observation that Heine’s transformations are both finite and closed under composition operation; the second one is the equivalency of Watson’s transformation of $${}_2\phi _1$$ series and Weierstrass’ well-known theta function identity; and the third one is a generalization of Morita’s connection formula for two independent solutions to the q-confluent hypergeometric equation.

Quantitative energy-dispersive X-ray fluorescence analysis for unknown samples using full-spectrum least-squares regression

The full-spectrum least-squares (FSLS) method is introduced to perform quantitative energy-dispersive X-ray fluorescence analysis for unknown solid samples. Based on the conventional least-squares principle, this spectrum evaluation method is able to obtain the background-corrected and interference-free net peaks, which is significant for quantization analyses. A variety of analytical parameters and functions to describe the features of the fluorescence spectra of pure elements are used and established, such as the mass absorption coefficient, the $$G_{i}$$ factor, and fundamental fluorescence formulas. The FSLS iterative program was compiled in the C language. The content of each component should reach the convergence criterion at the end of the calculations. After a basic theory analysis and experimental preparation, 13 national standard soil samples were detected using a spectrometer to test the feasibility of using the algorithm. The results show that the calculated contents of Ti, Fe, Ni, Cu, and Zn have the same changing tendency as the corresponding standard content in the 13 reference samples. Accuracies of 0.35% and 14.03% are obtained, respectively, for Fe and Ti, whose standard concentrations are 8.82% and 0.578%, respectively. However, the calculated results of trace elements (only tens of μg/g) deviate from the standard values. This may be because of measurement accuracy and mutual effects between the elements.

Topics on Solid Angles

The purpose of the present work is to derive some solutions for several solid angle cases via a fundamental formula which gives the solid angle for an isosceles triangle. From this formula the solid angle of pyramids is derived but, unlike other presentations, it is shown in a format similar to that of the well-known cone case. Besides the regular polygon cases (straight pyramids), solid angles of some other plane closed curves are calculated. The fundamental formula also leads to some interesting properties showing the not simple behavior of solid angles with the observer point on the curve itself, as it depends on how the observer arrived there. The question of the equi-Ω surfaces is also discussed and calculated in simple cases.