Binomial Form Research Articles

A model for capturing the rate-dependent mechanical behaviour of liquid crystal elastomers

A modelling framework is adopted and adapted here to model the rate-dependent deformation behaviour of liquid crystal elastomers (LCEs). On using an isotropic hyperelastic strain energy function WI1,I2 of binomial form, previously employed for capturing the (quasi-static) deformation of polydomain LCEs, an extension is presented for application to the rate-dependent behaviour of LCEs by incorporating the deformation rate into the model parameters. That is, the model parameters of the core hyperelastic strain energy function W are considered to evolve with, i.e., be a function of, the deformation rate. A specific measure of deformation rate ɛ̇ is utilised, and a particular functional dependency of the hyperelastic model parameters on ɛ̇, of a skewed exponential form, is devised and presented. The ensuing rate-dependent model Wr is then applied to a range of extant experimental datasets, encompassing various LCE specimens and across different deformation rates, under uniaxial loading and including both tension and compression deformations. The model is shown to capture and predict the data favourably. Given the simplic of devising and implementing the presented modelling framework, the flexibility it provides for incorporating different choices of strain energy W function as well as the functional form(s) of the dependency of the model parameters on the deformation rate, and the accuracy of the modelling results, the application of this modelling approach to capturing the rate-dependent deformation behaviour of LCEs is hereby presented.

Innovative house structures for malaria vector control in Nampula district, Mozambique: assessing mosquito entry prevention, indoor comfort, and community acceptance.

Insecticide-treated mosquito bed nets and indoor residual spraying are widely used for malaria vector control. However, their effectiveness can be affected by household members' habits, requiring alternative approaches toward malaria vector control. To assess the effectiveness of modified houses in preventing mosquito entry; to assess the impact of house modifications on indoor air conditions and evaluate the acceptability of modified houses in the community where the study was conducted. Five traditional and five modified houses were constructed in Nampula district, Mozambique and underwent a 90-day overnight indoor mosquito collection using Centers for Disease Control and nitride ultraviolet light traps during the rainy season. Mosquitoes were identified morphologically. Indoor temperature, relative humidity, carbon dioxide levels and wind speed were also collected. The Student's t-test was used to compare the means of the number of mosquitos and environmental factors between both house types. A binomial form of the Generalized Linear Model identified the factors associated with the community volunteer's preference for house type. Modified houses reduced the number of Anopheles by an average of 14.97 mosquitos (95% CI, 11.38-18.56, p < 0.000) and non-Anopheles by 16.66 mosquitoes (95% CI, 8.23-25.09, p < 0.000). Although fewer mosquitoes were trapped in modified houses compared to traditional ones, the modifications were more effective against Anopheles (94% reduction) than for non-Anopheles (71% reduction). The average temperature increased at 0.25°C in modified houses but was not statistically significant (95% CI, -0.62 to 0.12, p = 0.181). Community volunteers preferred modified houses due to reduced mosquito buzzing. The efficacy of modified houses including its acceptability by community, highlight its potential to lower malaria risk. Effective integration of modified houses into the vector control strategy will require raising awareness among communities about malaria risks associated with house structure and training them to modify their houses.

Unraveling the Complexity of Inverting the Sturm–Liouville Boundary Value Problem to Its Canonical Form

The Sturm–Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm–Liouville problem (SLP), this paper explores the intricacies of this classical problem, particularly the relationship between its canonical and Liouville normal (Schrödinger) forms. While the conversion from the canonical to Schrödinger form using Liouville’s transformation is well known in the literature, the inverse transformation seems to be neglected. Our study attempts to fill this gap by investigating the inverse of Liouville’s transformation, that is, given any SLP in the Schrödinger form with some invariant function, we seek the SLP in its canonical form. By closely examining the second Paine–de Hoog–Anderson (PdHA) problem, we argue that retrieving the SLP in its canonical form can be notoriously difficult and can even be impossible to achieve in its exact form. Finding the inverse relationship between the two independent variables seems to be the main obstacle. We confirm this claim by considering four different scenarios, depending on the potential and density functions that appear in the corresponding invariant function. In the second PdHA problem, this invariant function takes a reciprocal quadratic binomial form. In some cases, the inverse Liouville transformation produces an exact expression for the SLP in its canonical form. In other situations, however, while an exact canonical form is not possible to obtain, we successfully derived the SLP in its canonical form asymptotically.

Transforming a Quartic Equation to the Binomial Form

Transforming a Quartic Equation to the Binomial Form

On Computing General Root Algorithms Based on Binomial Expansion, Bernoulli’s Method of Continuous Compound Interest, Series Expansion and Other Modification Methods

Most of the Pth root algorithms exhibit high latency or small convergence rates when iteratively computing the roots. Here we present a slew of algorithms based on series expansions of binomial form, and exponential terms that show low latency or small computational cost for finding the Pth root. The latency decreases if the family of series taken are truncated at higher terms. We show that Babylonian method converges quadratically while the binomial series show an increase in convergence rate from quadratic, cubic and higher order O(t^N) convergence rate as the series is sequentially truncated at higher order terms.

Number of integers represented by families of binary forms (II): binomial forms

Number of integers represented by families of binary forms (II): binomial forms

A Tractable Failure Probability Prediction Model for Predictive Maintenance Scheduling of Large-Scale Modular-Multilevel-Converters

Modular-multilevel-converters (MMCs) are vital components in direct current transmission networks. Predictive maintenance scheduling of MMCs requires estimations of the failure probabilities of MMCs during a period of time in the future. Particularly, the predicted future failure probabilities are influenced by two main factors, the mission profiles of the MMCs and the maintenance decisions on the MMCs during the prediction period. This paper proposes a failure probability prediction model (FPM) for MMCs by considering these two factors. First, the expectations of the failure probabilities of the components for all the scenarios of mission profiles are obtained. Second, in predictive maintenance scheduling problems, the decisions to perform the maintenance actions are represented by binary variables. When the number of submodules is very large, using the binomial probability form currently used in reliability engineering to express the “r-out-of-n” failure probability of arms of the MMCs is intractable. Thus, this paper proposes a tractable form (T-form) in FPM by observing that the submodules on one arm are homogeneous. Furthermore, an approximation method, i.e., clustering and assignment (C&A), is proposed to reduce the computation times for calculating the parameters needed by the proposed T-form. Then, we perform a case study that assesses the accuracy and computation time of the C&A approach. The results show that the accuracy of the C&A approach is high and that the computation time is reduced significantly compared with the accurate method. We also show that the computation time for solving the predictive maintenance scheduling problem can be reduced hugely by using the T-form instead of the binomial probability form.

COLLATZ CONJECTURE 3n±1 AS A NEWTON BINOMIAL PROBLEM

The power transformation of Newton's binomial forms two equal 3n±1 algorithms for transformations of numbers n belongs to N, each of which have one infinite cycle with a unit lower limit of oscillations. It is shown that in the reverse direction, the Kollatz sequence is formed by the lower limits of the corresponding cycles, and the last element goes to a multiple of three odd numbers. It was found that for infinite transformation cycles 3n-1 isolated from the main graph with minimum amplitudes of 5, 7, 17 lower limits of oscillations, additional conditions are fulfilled.

有關上古漢語重疊式聯綿詞的考察

As we know, monosyllabic forms occupied a dominant position in the Old Chinese period. However, there are amount of bisyllabic forms in the texts of the pre-Qin period, such as Shijing(《詩經》) and Chuci(《楚辭》). Among them, including a lot of binomial word forms. Since ancient times, scholars have been studying the definition, classification, features and origin of the binomial word forms. In particular, there are various opinions on the origin of the binomial word forms, and many research achievements have been made. Among them, there is a theory that the binomial forms originated from reduplication. Most scholars classified the reduplicative binomes based on the phonological relationship between the two syllables of the binomes. But Sun, Jingtao(2008) divided them into retrogressive reduplication, progressive reduplication, fission reduplication and total reduplication based on the Chinese dialects and cognate language. This study aims to verify whether the four reduplicative types of the Old Chinese classified by Sun, Jingtao(2008) are reasonable. Therefore, this paper collected 1,211 binomes in the Guangyashuzheng, and selected the binomes that fit the theory of Sun, Jingtao(2008). At the same time, in this study, we will only observe his three types of the reduplicative binomes according to the text data and existing research results. They are retrogressive reduplication, progressive reduplication, and fission reduplication. The results of this study confirmed that his classification needed to be reconsidered, and in particular, the need for supplementation was discussed in detail for the hypothesis that the binomes originated from reduplication.

Medicinal Plants Used in the Treatment of Gastrointestinal Disorders in Rupandehi District, Western Nepal

Medicinal plants used for the cure of various diseases since time immemorial. The majority of population of developing countries also used traditional medicine because of poverty and no side effect. Ethnobotany survey was undertaken to collect information from traditional healers on the use of medicinal plants in the treatment of gastrointestinal disorders such as indigestion, lack of hunger, stomach pain, dysentery, diarrhea, constipation, and piles in western Nepal during different season of March 2020 to November 2020. The indigenous knowledge of local traditional healers having practical knowledge of plants in medicine was interviewed in 10 villages of Rupandehi district of western Nepal and native plants used for medicinal purposes were collected through questionnaire and personal interviews during fieldtrips. A total of 34 plant species belonging to 33 genera, and 27 families are documented in this study. The medicinal plants used in the treatment of gastrointestinal disorders by people are listed with botanical name (in binomial form), family, local names, habits, and parts used. This study showed that many people in the studied areas of Rupandehi district still continue to depend on the medicinal plants at least for the treatment of primary healthcare.

The Waring rank of binary binomial forms

We give an explicit formula for the Waring rank of every binary binomial form with complex coefficients. We give several examples to illustrate this, and compare the Waring rank and the real Waring rank for binary binomial forms.

Zeros of a binomial combination of Chebyshev polynomials

For [Formula: see text], we study the zeros of the sequence of polynomials [Formula: see text] generated by the reciprocal of [Formula: see text], expanded as a power series in [Formula: see text]. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number of zeros of [Formula: see text] outside the interval (−1, 1) is bounded by a constant independent of m.

Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism

We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink number distribution to assess adiabaticity and its breakdown. We consider linear, nonlinear, and exponential cooling schedules, among which the latter provides the most efficient shortcuts to cooling in a given quench time. The non-thermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state.

GESTACOVID project: psychological and perinatal effects in Spanish pregnant women subjected to confinement due to the COVID-19 pandemic

Introduction COVID-19 was declared a pandemic and confinement with movement restriction measures were applied in Spain. Postnatal mental disorders are common but frequently undiagnosed, being a risk period to develop anxiety and depression symptoms. The aim of this study is to evaluate the impact of confinement as depressive and anxiety symptoms in pregnant women (PrW) and puerperal women (PuW) mental health, as well as obstetric and perinatal outcomes during this period. Materials and methods The self-administered survey consists of a total of 28 questions, the first 16 providing contextual information and the following ones corresponding to the GHQ-12 that has been evaluated in a binomial form. A logistic regression model has been used to assess whether the contextual variables acted as a protective or risk factor and its fitting has been represented by a receiver operating curve. Results Of the 754 PrW interviewed, 58.22% were screened positive. Confinement time for these was 54.93 ± 9.75 days. The risk factors that were identified after the refinement have been to have a worse general state of health, to be sadder and to be more nervous. Among the protectors have been found to have a higher Apgar 10 score and induction of labor. The area under the adjusted regression adjustment curve was 0.8056. Conclusions Our results show a high prevalence of depression and anxiety symptoms with strict confinement measures. PrW and PuW must be considered a risk group to develop mental health disorders during disruption circumstances. Using a mental health screening tool could help to identify a group of patients with more risk and to carry out a careful monitoring to allow adequate management.

Fast school closures correspond with a lower rate of COVID-19 incidence and deaths in most countries

School closures have been used as one of the main nonpharmaceutical interventions to overcome the spread of SARS-CoV-2. Different countries use this intervention with a wide range of time intervals from the date of the first confirmed case or death. This study aimed to investigate whether fast or late school closures affect the cumulative number of COVID-19 cases or deaths. A worldwide population-based observational study has been conducted and a range of attributes were weighted using 10 attribute weighting models against the normalized number of infected cases or death in the form of numeric, binominal and polynomial labels. Statistical analysis was performed for the most weighted and the most common attributes of all types of labels. By the end of March 2021, the school closure data of 198 countries with at least one COVID-19 case were available. The days before the first school closure were one of the most weighted factors in relation to the normalized number of infected cases and deaths in numeric, binomial, and quartile forms. The average of days before the first school closure in the lowest quartile to highest quartile of infected cases (Q1, Q2, Q3 and Q4) was −6.10 [95% CI, −26.5 to 14.2], 9.35 [95% CI, 2.16 to 16.53], 17.55 [95% CI, 5.95 to 29.15], and 16.00 [95% CI, 11.69 to 20.31], respectively. In addition, 188 countries reported at least one death from COVID-19. The average of the days before the first school closure in the lowest quartile of death to highest quartile (Q1, Q2, Q3 and Q4) was −49.4 [95% CI, −76.5 to −22.3], −10.34 [95% CI, −30.12 to 9.44], −18.74 [95% CI, −32.72 to −4.77], and −12.89 [95% CI, −27.84 to 2.06], respectively. Countries that closed schools faster, especially before the detection of any confirmed case or death, had fewer COVID-19 cases or deaths per million of the population on total days of involvement. It can be concluded that rapid prevention policies are the main determinants of the countries' success.

Spectral-element formulation of multi-transmitting formula and its accuracy and stability in 1D and 2D seismic wave modeling

Application of local artificial boundary conditions in high-efficient spectral element method (SEM) is a problem that needs further study, where difficulties focus on how to design an appropriate numerical scheme of artificial boundaries that is in good accordance with the unequally-spaced grid nodes and high-order property of the element. Liao's local artificial boundary, i.e. multi-transmitting formula (MTF), provides a convenient way of implementing arbitrary-order displacement-type boundaries because it is defined directly in discrete form and can be transformed into numerical schemes by using merely some interpolation approaches. A new set of numerical schemes of MTF is developed and its accuracy and stability are thoroughly discussed in the application of spectral-element simulation of 1D and 2D seismic wave propagation. The new MTF scheme cannot be written into a binomial form like the traditional one does. This fact has a significant influence on numerical properties of high-order boundary, but merely slightly affects the performance of lower-order boundaries which are daily used in practical simulations. Numerical examples compared with viscous-spring or perfectly matched layer (PML) boundary exhibits that stable and quite good accuracy can be achieved by using the proposed method.

Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts

This study proposes a class of nonlinear hysteretic integer-valued GARCH models in order to describe the occurrence of weekly dengue hemorrhagic fever cases via three meteorological covariates: precipitation, average temperature, and relative humidity. The proposed model adopts the hysteretic three-regime switching mechanism with a buffer zone that are able to explain various characteristics. This allows for having consecutive zeros in the lower regime and large counts to appear up in the upper regime. These nonlinear hysteretic integer-valued GARCH models include Poisson, negative binomial, and log-linked forms. We utilize adaptive Markov chain Monte Carlo simulations for making inferences and prediction and employ two Bayesian criteria for model comparisons and the relative root mean squared prediction error for evaluation. Simulation and analytic results emphasize that the hysteretic negative binomial integer-valued GARCH model is superior to other models and successfully offers an alternative nonlinear integer-valued GARCH model to better describe larger values of counts.

Binomial polynomials mimicking Riemann's zeta function

ABSTRACT The (generalized) Mellin transforms of Gegenbauer polynomials have polynomial factors , whose zeros all lie on the ‘critical line’ (called critical polynomials). The transforms are identified in terms of combinatorial sums related to H. W. Gould's S:4/3, S:4/2, and S:3/1 binomial coefficient forms. Their ‘critical polynomial’ factors are then identified in terms of hypergeometric functions. Furthermore, we extend these results to a one-parameter family of critical polynomials that possess the functional equation . Normalization yields the rational function whose denominator has singularities on the negative real axis. Moreover, as along the positive real axis, from below. For the Chebyshev polynomials, we obtain the simpler S:2/1 binomial form, and with the nth Catalan number, we deduce that and yield odd integers. The results touch on analytic number theory, special function theory, and combinatorics.

Using Generalized Linear Mixed Models to Predict the Number of Roadway Accidents: A Case Study in Hamilton County, Tennessee

Introduction: A method for identifying significant predictors of roadway accident counts has been presented. This process is applied to real-world accident data collected from roadways in Hamilton County, TN. Methods: In preprocessing, an aggregation procedure based on segmenting roadways into fixed lengths has been introduced, and then accident counts within each segment have been observed according to predefined weather conditions. Based on the physical roadway characteristics associated with each individual accident record, a collection of roadway features is assigned to each segment. A mixed-effects Negative Binomial regression form is assumed to approximate the relationship between accident counts and several explanatory variables including roadway characteristics, weather conditions, and several interactions between them. Standard diagnostics and a validation procedure show that our model form is properly specified and suitably fits the data. Results: Interpreting interaction terms leads to the follow findings: 1) rural roads with cloudy conditions are associated with relative increases in accident frequency; 2) lower/moderate AADT and rainy weather are associated with relative decreases in accident frequency, while high AADT and rain are associated with relative increases in accident frequency; 3) higher AADT and wider pavements are associated with relative increases in accident frequency; and 4) higher speed limits in residential areas are associated with relative increases in accident frequency. Conclusion: Results illustrate the complicated relationship between accident frequency and both roadway features and weather. Therefore, it is not sufficient to observe the effects of weather and roadway features independently as these variables interact with one another.

Control synthesis by full state vector in systems with fractional-order derivatives using Caputo-Fabrizio operator

In the paper, the control system synthesis by means of the full state vector is considered when using fractional derivatives in the description of this system. To conduct research in the synthesized system with fractional derivatives in the Caputo--Fabrizio representation, a fundamental matrix of the system is formed, which also allows us to analyze the influence of initial conditions on the processes within the system. In particular, the finding of the fundamental matrix of the system in the case of multiple roots of a characteristic polynomial, which are obtained by transforming the synthesized system to the binomial form, is demonstrated. The influence of the fractional derivative index and the location of the roots of the characteristic polynomial transformed to the binomial form on the system operation is analyzed.