Mathematical Formula Research Articles

Advanced regression model fitting to experimental results in case of the effect of grinding conditions on a cutting force with the planer technical knives

The use of well-fit models enables users to make better decisions and draw accurate insights, so in this article a multi-step procedure for establishing regression functions for experimental data is presented. This was inspired by the need to determine well-fitted models for the results of the study of the relationship between the input factors of the grinding process of planer knives and the measured grinding power, as well as in relation to the knife cutting force. The sharpening process was carried out under various conditions, making it possible to assess their influence on the results and select the most favorable technological parameters to prepare the knives for operation. The equations adjusted by Excel or other basic methods require additional verification if the mathematical formula and values of the model coefficients correspond to the data and the physical meaning. For this purpose, one-, two- and three-factor analyses were performed to eliminate redundant factors and introduce significant interactions between input parameters. Additional analyses of variance and Tukey, Levene and Brown-Forsythe tests were used to determine the general form of the model. Detailed form of nonlinear models was worked out by comparing the distribution of residuals, looking for outliers and evidence of the presence or absence of collinearity, as well as by determining the values of additional model quality indicators, such as Akaike Information Criterion, Cook’s distance and Variance Inflation Factor. The models presented include a categorization variable (grinding type) and are presented graphically in the form of surface plots. With reference to the technological processes studied, a discussion of the physical significance of the developed models and the influence of the input factors on the model output value was conducted. The analyzes additionally include an evaluation of the model factors using prediction slice plots.

GDPR-anonymous population overlap estimation

The feasibility of many collaborative, data-driven research projects in Public Health and Social Sciences depends on the size of the overlap between the populations of contributing data partners, that is, the number of individuals for whom all parties can provide data. Where the identity of respective population members is subject to privacy protections, the overlap is traditionally estimated using de-identified cryptographic tokens to represent individuals. This does however not meet the strict standard of anonymity under GDPR and potentially runs counter to emerging privacy laws of US States, and may thus impose significant regulatory and governance burdens on research institutions, even at the early scoping stage. We present a novel method for overlap estimation, where two data partners construct a single, anonymous Bloom filter for their populations from which the overlap can be estimated. Two new techniques -- (a) the randomization of the contribution of individual population members to the Bloom filter and (b) an interactive bit-flipping protocol between data partners -- are presented which ensure that the Bloom filters are safe against dictionary attack by one party against the other party. We discuss the security aspects of this method, present the required mathematical formulas for calculating the overlap estimate, and report on the practical performance in terms of computational effort and resulting accuracy. The goal of the method is to facilitate new research by reducing the cost and complexity of initial planning and by making the overlap estimate GDPR-anonymous, and thus safer and subject to less onerous compliance requirements.

From formulae, via models to theories: Dynamic Energy Budget theory illustrates requirements

As sciences mature, they transition from observation and description to explanation and prediction. This transition is associated with qualitative changes in the way quantitative mathematical formulations are constructed and interpreted, resulting in a ‘theory’. Such transitions from phenomenology to theory are happening in biology but the heuristic framework involved is rarely articulated. We here describe how the use of models in research sets model requirements, using Dynamic Energy Budget (DEB) theory to illustrate the more elaborate ones. We first make the distinction between mathematical formulae and models based on their relation to the abstract and real worlds. We then explain how the transition from models to theory affects model construction and parameter estimation, and discuss the concept of parameter estimation-in-context using the database Add_my_Pet on animal energetics. The transition comes with the need to develop auxiliary and meta- theory and to work with multiple datasets, implying constraints for the loss function that is used for parameter estimation. Finally, we discuss the extra requirements for general explanatory models: they need to be explicit on relevant general principles and to be embedded in a wider scientific context. We also discuss how we see theory’s relationship to observation and prediction change in the future as we use it to deal with theoretical and applied problems in biology.

Performance enhancement of NOMA multi-user networks with aerial reconfigurable intelligent surfaces and aerial relay

In this article, we propose a combination of multiple aerial reconfigurable intelligent surfaces (ARISs) with an aerial relay (AR) for improving the performance of multiple users adopting the non-orthogonal multiple access (NOMA) scheme. In particular, two groups of ARIS are utilized, one for aiding ground-to-air (G2A) communication and another one for aiding air-to-ground (A2G) communication. Mathematical formulas of outage probability (OP), throughput, and achievable capacity (AC) of every user in the proposed ARISs-AR-NOMA network are derived over the Nakagami-m channel. The propagation environment recommended for the fifth generation and beyond (5G/B5G) is applied to enhance the practical behavior of the proposed network. To confirm the performance enhancement, we compare the OP, throughput, and AC of the proposed system with the conventional AR-NOMA network (i.e., without ARISs). Numerical illustrations demonstrate the great benefits of the proposed ARISs-AR-NOMA network, its transmit power is dramatically lower than that of the conventional network. Moreover, the throughput and AC of the proposed network are considerably higher than the conventional network’s. Based on the effect of key parameters and network behaviors, various effective solutions are recommended to enhance the performance of the proposed ARISs-AR-NOMA network.

Effect of two-phase viscosity difference and natural fractures on the wormhole morphology formed by two-phase acidizing with self-diverting acid in carbonate rocks

Different types of acids are needed in the field to achieve various acidizing goals. Currently, there are no reliable acidizing models for multiphase flows and complex multiphysics coupling. This paper derives mathematical formulas for the oil–water acidizing process of a situ self-diverting acid combined with thermal–chemical–fracture interactions and discusses the influence of two-phase oil–water mixture and fractures on the wormhole morphology produced by self-diverting acid. The results show that the spent acid following the acid–rock reaction forms a high-viscosity sealing zone, causing the injected acid to be redirected. The self-diverting acid forms more numerous and longer branches than a conventional acid during single-phase acidizing. In the case of two-phase acidizing, the high viscosity difference produces distinct effects when using self-diverting acid compared with conventional acid. Specifically, the self-diverting acid extends the breakthrough time and forms a wormhole morphology with longer and more complex branches, whereas the conventional acid accelerates the breakthrough of the rock. As the viscosity difference decreases, the wormhole morphology of the self-diverting acid gradually approaches that of a single-phase acid. Large-aperture fractures completely determine the wormhole morphology, while smaller apertures determine the branch morphology of the wormhole. Fractures have a negative acidizing effect in the case of the self-diverting acid, unlike conventional acid. The proposed model accurately simulates the complex acidizing process of a self-diverting acid.

Analysis of chi angle distributions in free amino acids via multiplet fitting of proton scalar couplings

Abstract. Scalar couplings are a fundamental aspect of nuclear magnetic resonance (NMR) experiments and provide rich information about electron-mediated interactions between nuclei. 3J couplings are particularly useful for determining molecular structure through the Karplus relationship, a mathematical formula used for calculating 3J coupling constants from dihedral angles. In small molecules, scalar couplings are often determined through analysis of one-dimensional proton spectra. Larger proteins have typically required specialized multidimensional pulse programs designed to overcome spectral crowding and multiplet complexity. Here, we present a generalized framework for fitting scalar couplings with arbitrarily complex multiplet patterns using a weak-coupling model. The method is implemented in FitNMR and applicable to one-dimensional, two-dimensional, and three-dimensional NMR spectra. To gain insight into the proton–proton coupling patterns present in protein side chains, we analyze a set of free amino acid one-dimensional spectra. We show that the weak-coupling assumption is largely sufficient for fitting the majority of resonances, although there are notable exceptions. To enable structural interpretation of all couplings, we extend generalized and self-consistent Karplus equation parameterizations to all χ angles. An enhanced model of side-chain motion incorporating rotamer statistics from the Protein Data Bank (PDB) is developed. Even without stereospecific assignments of the beta hydrogens, we find that two couplings are sufficient to exclude a single-rotamer model for all amino acids except proline. While most free amino acids show rotameric populations consistent with crystal structure statistics, beta-branched valine and isoleucine deviate substantially.

Reverse degree-based topological indices study of molecular structure in triangular ϒ-graphyne and triangular ϒ-graphyne chain

Topological indices are mathematical descriptors of the structure of a molecule that can be used to predict its properties. They are derived from the graph theory, which describes the topology of a molecule and its connectivity. The main objective is mathematical modeling and topological properties of ϒ-graphyne. Current research focuses on two structures made from hexagonal honeycomb graphite lattices named triangular ϒ-graphyne and triangular ϒ-graphyne chains. The authors have simultaneously computed the first and second Reverse Zagreb indices, reverse hyper-Zagreb indices, and their polynomials. This research also derives mathematical closed-form formulas for some of its fundamental degree-based molecular descriptors. Researchers have been trying to synthesize a novel carbon form called Graphyne. For over a decade but with no success. Recently, some researchers have made a breakthrough in generating Carbons elusive allotrope and solved a long-standing problem in carbon materials. This wonder material is created to rival the conductivity of graphene but with control. These results opened new ways of research in the fields of semiconductors, electronics and optics. Furthermore, graphical and tabular results will help to investigate the structure-property relationships in γ-graphyne.

An efficient and cost-effective methods framework for performing biomechanical analysis on cadaveric skeletal muscle

IntroductionThe structure and arrangement of skeletal muscle fibers is the primary determinant of muscle function. While analysis of morphologic parameters to elucidate muscle structure-function relationships dates to the 17th century, considerable variability in methodology and technique to quantify these relationships exists within the literature. Additionally, applications to assess the impact of non-typical musculoskeletal morphologies on structure-function relationships are limited. This study aims to assemble and present a practical, step-by-step framework of combined methods and techniques for efficiently analyzing biomechanical impacts of cadaveric skeletal muscles. MethodsExisting skeletal muscle biomechanical formulas and experimentally determined parameters for typical fast-acting skeletal muscle were identified in the literature. The methods framework was assembled as a stepwise protocol that includes mathematical formulas, referenced accepted values, optional steps, section breaks, suggested techniques, important notes and footnotes, and materials needed for collecting necessary measurements. Proof of concept was achieved with primary histological data and imaging, along with references to examples where the methods have been successfully applied. ResultsThe assembled framework presents an ordered process for measuring skeletal muscle parameters, calculating the maximal isometric force of a skeletal muscle, and applying that data to understand musculoskeletal mechanics. Histology data, imaging, and a summary of studies that have successfully applied the framework methods provide visual aids and validation for the methods. ConclusionsThis study presents an efficient and convenient framework of combined methods and techniques for investigators to evaluate the biomechanical impact of skeletal muscles. The practical use of this framework should optimize project efficiency and spending, increase study rigor, and minimize procedural variation across different studies. This report may serve as a foundational resource for researchers studying cadaveric muscle biomechanics, and its use especially adds translational clinical value to case analyses of non-typical musculoskeletal morphologies.

Individualized generation of women's prototype based on the classification of body shape

The traditional prototype method only relies on the basic dimensions of the human body such as bust girth and back length to make the prototype pattern, ignoring the differences of human body details dimensions. In order to improve the fit of garments, the research on intelligent generation technology of individualized garment patterns has become one of the hot spots in the field of clothing. Based on the 3D body scanning technology, we proposed a method for generating prototype pattern based on body shape classification. The proposed method takes as inputs the body parameters (width, thickness and angle), while the output of the method is one of the four pattern generation rules-"Y" shape, "V" shape, "I" shape, or "X" shape. 207 subjects were divided into four categories based on the body angle parameters, namely "Y" shape, "V" shape, "I" shape and "X" shape, and a shape recognition model was built. The pattern database is required to obtain pattern generation rules by 3D point cloud reconstruction and flattening. Combined with the human body shape parameters, the mathematical formulas of the feature points on the pattern landmarks are built. The accuracy of body shape recognition model is 97.4%. The error analysis of the predicted pattern parameters shows that 90% of the pattern feature points have a goodness of fit above 0.7. In the 5 main landmarks, the proportion of pattern within the absolute error range is more than 80%, indicating that the prediction effect of the pattern is good. This method can be applied to the process of automatic pattern generation system based 2D measurement to improve work efficiency.

ИНФОРМАЦИЯЛЫК ТЕХНОЛОГИЯЛАРДЫ ОКУТУУДА МАТЕМАТИКАЛЫК МОДЕЛДИН ОРДУ

This paper discusses technologies for using mathematical modeling methods in teaching information technology. A method for selecting the types of problems to be solved using mathematical modeling and decision-making methods is proposed. Mathematical modeling makes it possible to present current information in a more compact, structured form, since mathematical formulas are designed to allow you to write the current problem in a more concise, understandable and memorable form. Another important area that can be used in educational projects is the assessment and calculation of alternative energy sources that are more efficient than the electricity used today. Of great interest is also the study of the dynamics of human reproduction in modern society. When implementing the above projects with the help of a computer, you can find a solution to the problem, create a simulation model and display a graphic image using software such as PowerSim.

Joint load-bearing behaviors and interface failure mechanism of encased coal samples under uniaxial compression

Concrete-encased coal pillars that serve as an effective support structure in coal mines have attracted increasing attention. This paper aims to explore the coupling bearing behaviors and the properties of interface force transfer between the interior coal and the encasing concrete. Laboratory uniaxial compression experiments were conducted on encased coal samples. Additionally, an interface force formula was derived based on deformation coordination and equilibrium conditions, and a mathematical formula was developed to estimate the load-bearing capacities of both the interior coal and the encased concrete. The research indicates that the stress–strain curve of the concrete-encased coal samples exhibits a distinct “double-peaked” phenomenon, and the load is transferred from the interior coal to the external concrete during the failure process. In the early stages of failure, the interface force enhances the strength of the coal pillar, while the lateral strain of the interior coal column exacerbates the damage to the encasing concrete. Moreover, the force at the concrete-coal interface is proportional to the axial loads and the mechanical properties of both materials. The strength of the coal pillar is significantly enhanced by lateral confinement. This study provides an experimental basis and theoretical analysis support for reducing the disaster of coal pillar instability.

Estimation of urinary volume through ultrasonography in dog cadavers and experimental models.

The urinary volume and residual urine volume are pieces of information that can provide relevant clinical data for dogs and cats, especially those hospitalized. Thus, the present study aimed to evaluate mathematical formulas described in human and veterinary literature to estimate urinary volume in dogs and experimental models. For this purpose, nine male dog cadavers and twelve experimental models were used to evaluate residual volume, small, medium, and large, using three different formulas. Data were obtained by three different examiners: two ultrasonographers and one nonultrasonographer. Each examiner recorded three longitudinal and transverse images, obtaining measurements of width, length, and height at each proposed volume. The measurements were then averaged, and the result was added to the formulas, thus estimating urinary volume. All three formulas achieved higher accuracy in estimating smaller volumes, with a gradual decrease as urinary volume increased. The error of all formulas was less than 10%, even when compared with evaluations in experimental models and dogs. There was variation in estimation between ultrasonographers and nonultrasonographer examiners; however, this variation was low, allowing for the assertion that both can apply the technique. Thus, it is concluded that estimating urinary bladder volume using mathematical formulas and 2D ultrasound is accurate and, therefore, an alternative and viable option for evaluating the urinary tract.

A method for evaluating the design scheme of continuous measuring bridge of the instrumented wheelset

This paper proposes a method for evaluating the design scheme of continuous measuring bridge of the instrumented wheelset, based on the theory of continuous measurement of wheel-rail forces, Finite Element Analysis, and Levenberg-Marquardt algorithm. The elastic strain at each placement point of the strain gauge on the web surface of the wheel is expanded into Fourier series, and the general mathematical expressions of the output signals for each symmetric component, each bridge, and the synthesized bridge are provided. Nine typical measuring bridge schemes of strain gauge arrangement on the wheel web surface and seven typical measuring bridge schemes of strain gauge arrangement inside the measuring holes are given. The finite element model of the wheel is established using software ABAQUS, and the moving force is applied to the rolling surface of the wheel for simulation calculations. The output signals of 16 typical measuring bridges are then obtained. By utilizing the mathematical formulas of the bridge outputs and the simulation results, a matrix expression describing the relationship between amplitudes of all harmonics and the bridge output is given, and the amplitudes of all the former 20 orders harmonics of the bridge signal are obtained by applying Levenberg-Marquardt algorithm. Based on the analysis results of the harmonic amplitudes, a method is proposed to quantitatively evaluate the output signals of a single bridge (which can be either harmonic or triangular wave) and the synthesized bridge. The mathematical expressions of the evaluation indicators are provided within the range of 0 to 1. Finally, the analysis results of the evaluation indicators for 16 typical measuring bridges are presented and compared. The proposed method is not only applicable to the bridge design of the instrumented wheelset but also to the evaluation of signals from channels of the data collector when the instrumented wheelset is being calibrated on the test rig.

Study on unified expression of event occurrence flexible logic based on superposition quantum states

To determine the multi logical relationship in the process of cause event leading to result event, a unified expression of flexible logic of event occurrence based on the superposition of multi quantum states is proposed. According to the premise that the logical relationship between any numbers of events can be simplified to the logical relationship between the two events, 20 kinds of flexible logical relationships are studied, and 16 of them are selected to establish the unified expression of flexible logic of event occurrence. By studying those 16 kinds of logical relationships, 8 kinds of logical relationships without obvious correlation are further determined, and finally the unified expression of event occurrence flexible logic of superposition of three quantum states is formed. The result shows that the expression can express 8 kinds of superposition states of logical relationships at the same time, and the different logical forms in the probability of occurrence of result events can be obtained. Finally, the characteristics of the expression and the problems that may be encountered in the process of solving are analyzed. And through the example analysis, the usage process and function of the present method were explained. It can be used to express the logical relationship between the cause event and the result event in the system fault evolution and determine the probability of fault occurrence.

A Solar-Wind based EV Charging Station Model using MATLAB Simulink

Abstract Transportation is becoming more and more necessary every day. One such form of transportation that has been around for a century is the electric vehicle (EV). It has less of an effect on pollution, climate change, and resource depletion because it requires less resources. Many people find it challenging to charge their electric cars in off-grid locations, which lowers the uptake of EVs. In this scenario, a charging station powered by locally available renewable energy sources like solar, wind, biogas, and tidal energy would be a better option. In this paper an attempt has been made to examine a charging station model from renewable energy sources Solar and Wind. The solar-wind energy-based charging system drastically cuts down on the amount of fossil fuels used to generate electricity, which also minimizes emissions of CO2 and carbon-related pollutants. Wind and solar energy are used in conjunction and are complementary to one another. A charging controller which takes into account State of Charge (SOC), the number of linked EVs, and the arrival time of those EVs is used. The power transfer will be managed by this controller. By carefully considering each level, including the solar plant, wind plant, battery storage system, and controlling technology, the charging station is modeled in the best possible way. Simple model is used to describe each stage of the charging station, and designed with appropriate mathematical formulae. By understanding the demand for charging and pairing it with the appropriate energy storage system and auxiliary devices, this charging model can be used in off-grid locations.

PROBLEMATIC ISSUES OF MECHANICS OF DEFORMABLE SOLIDS, AFFECTING THE ACCURACY OF ITS TECHNOLOGICAL APPLICATIONS. 1. INTRODUCTION

The need for an intelligible consideration of some problems in the mechanics of a deformable solid, which strongly affect the accuracy and reliability of mathematical models and calculation formulas obtained on its basis when solving specific engineering and technological problems in the production of various metal products, is substantiated.

Exploiting the waste heat in a proton exchange membrane fuel cell with a capacitive salinity/heat engine

For fully utilizing the low-grade waste heat (LGWH) of the proton exchange membrane fuel cell (PEMFC), a novel coupled system primarily involving a PEMFC and a capacitive salinity/heat engine (CSHE) is proposed. Based on thermodynamic and electrochemical theories, mathematical formulas of the power output, efficiency, and exergy efficiency are deduced accounting for the significant irreversible losses within the coupled system. The superiority is expounded by contrasting the generic performance characteristics of the sub-systems and the coupled system. In addition, numerical results demonstrate that the maximal power output density and its corresponding efficiency and exergy efficiency of the coupled system enhanced by 11.43%, 12.75%, and 9.96%, respectively, over the PEMFC alone under the same operating conditions. Furthermore, the impacts of some parameters, for instance, proton exchange membrane (PEM) thickness, the PEMFC working temperature and working pressure, electric charge density ratio, charging cut-off voltage, and Stern layer distance, on the coupled system performance are meticulously discussed. The results of the study may supply a reference for the design and operation of such a salinity gradient energy recovery system and create a new pathway for recycling LGWH from PEMFC.

To compare horizontal strabismus deviation as assessed from photographs with that in the strabismus clinic using the prism bar.

To compare the deviation in cases of horizontal strabismus as assessed from photographs with the measurements as obtained in the strabismus clinic. After obtaining informed consent, we recruited subjects with manifest horizontal strabismus. We took a frontal flash photograph from a distance of 50 cm using smart-phone-based cameras with the flash light vertically aligned with the lens. After projecting the photograph on a laptop and using a vernier caliper, we measured the horizontal corneal diameter of the non-strabismic eye and the decentration of reflex in the strabismic eye taking limbus as the reference point. We converted these values to degrees by using a conversion factor of 7.5°/mm and further to prism diopters (PD) by the standard mathematical formula 100*tanθ. We included 74 subjects aged between 5 and 40 years with manifest horizontal deviation from 20 to 85 PD. We found a statistically significant correlation of 82.6% (P value < 0.001) between the clinic and photographic measurements. Agreement analysis suggested that the photographic measurements measured on average 7 PD less (95% confidence interval: 4.6 to 9.2) than clinical measurements along all values of misalignment, although the difference between the two methods decreased as the quantum of deviation increased. Linear regression revealed an r2 of 68% and provided a predictive equation to derive clinic equivalent measurements from photographic estimates. We believe our simple method provides robust evidence that a photographic estimation can provide the basic information of the size of the deviation to plan possible surgeries, especially in situations of a tele-consultation. This is an easy approach to both understand and master and should form the armamentarium of most orthopticians and strabismologists.

A mathematical model to predict “low-lying” posterior communicating artery aneurysms in neurosurgical practice

“Low-lying” posterior communicating artery (PCoA) aneurysms require great attention in surgical clipping due to their distinct anatomical characteristics. In this study, we propose an easy method to immediately recognize “low-lying” PCoA aneurysms in neurosurgical practice. A total of 89 cases with “low-lying” PCoA aneurysms were retrospectively analyzed. All patients underwent preoperative digital subtraction angiography (DSA) examinations and microsurgical clipping. Cases were classified into the “low-lying” and regular groups based on intraoperative findings. The distance- and angle-relevant parameters that reflected the relative location of the aneurysms and tortuosity of the internal carotid artery were measured using 3D-DSA images. The data were sequentially integrated into a mathematical analysis to obtain the prediction model. Finally, we proposed a novel mathematical formula to preoperatively predict the existence of “low-lying” PCoA aneurysms with great accuracy. Neurosurgeons might benefit from this model, which enables them to directly identify “low-lying” PCoA aneurysms and make appropriate surgical decisions accordingly.

BDD‐based optimized majority/minority gate using electro‐optic Mach‐Zehnder interferometer

AbstractIn this article, an optical majority/minority circuit has been designed using four electro‐optic Mach‐Zehnder interferometers. The binary decision diagram (BDD) is used to optimize the Boolean logical expression. In this design we get two outputs, one performs majority logic and the other performs minority logic simultaneously. Numerical simulation has been done with the obtained data from the beam propagation method. Pseudo‐eye diagram is also plotted to find amplitude modulation (AM) and extinction ratio (ER). AM and ER are found nearly 0.4 and 13 dB, respectively. A new parameter, the optical circuit complexity factor (OCC) factor has been calculated and from the result, it has been shown that the proposed design is more optimized than other majority/minority gate designs so far.