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Let $p$ be a prime number and $E_{p}$ denote the elliptic curve $y^2=x^3+px$. It is known that for $p$ which is congruent to $1, 9$ modulo $16$, the rank of $E_{p}$ over $\mathbb{Q}$ is equal to $0, 2$. Under the condition that the Birch and Swinnerton-Dyer conjecture is true, we give a necessary and sufficient condition that the rank is $2$ in terms of the constant term of some polynomial that is defined by a recurrence formula., Comment: 16 pages

We are concerned with the tensor equations whose coefficient tensors are M-tensors. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend the method to solve the equation with a nonnegative constant term and establish its convergence. At last, we do numerical experiments to test the proposed methods. The results show that the proposed methods are quite efficient.

Purpose This paper aims to investigate the pass-through (PT) effect in Turkey by using quarterly data for the period 1998: Q1-2019: Q2 to understand the dynamic potential effects of exchange rates on domestic prices. Design/methodology/approach The paper launches several nonlinear models in which the basic determinants of domestic prices in Turkey are determined through Markov regime-switching models (MSMs). Hence, this research follows the variables of the consumer price index (CPI), USD exchange rate, gross domestic product (GDP; demand side of the economy), industrial production index (production side of the economy), economic uncertainty and geopolitical risk index for Turkey. Findings This work explores that the exchange rate and demand side of the economy (GDP) follow a positive nonlinear relationship with CPI at both regimes. The production side of the economy (IP) affects negatively the CPI during regime 0. Economic uncertainty influences the CPI positively at Regime 1, while geopolitical risk has a negative association with CPI at Regime 0. Eventually, the paper provides some policy proposals associated with the impacts of GDP, IP, economic uncertainty and geopolitical risk on CPI in Turkey. Originality/value One may claim that any PT model, which does not observe the possible structural or regime shifts in estimated parameters, might fail to estimate the coefficients unbiasedly and efficiently. Hence, this work differs from available relevant works in the literature since this paper considers linearity or nonlinearity important and reveals that the relevant PT model follows a nonlinear path rather than a linear path, this nonlinear path is converged strongly by MSMs and estimates the significant regime shifts in the constant term and, in parameters of independent variables of PT by MSMs.

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is 1.7 5 ″ . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value 0.87 5 ″ of the Newtonian gravity theory with a magnitude order of 10 − 5 . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition d s = 0 in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

Objectives Globally, nutraceuticals have been increasingly used. Nevertheless, the consumer preferences for nutraceuticals have not been quantitatively investigated. This study used discrete choice experiment (DCE) to examine consumer preferences and willingness to pay for nutraceuticals. Methods Four attributes (ie, the scientific proof of effectiveness, the scientific proof of safety, the source of recommendation, and cost) were identified from a systematic review and focus group interviews. They were used to develop a DCE questionnaire. Consumers at community pharmacies in Malaysia were asked to respond to 8 DCE choice sets. A conditional logit model was employed to obtain the relative importance of each attribute and to estimate respondents’ WTP for nutraceuticals. Results A total of 111 valid responses were analyzed. A negative constant term in the developed model indicated that generally the respondents preferred not to use nutraceuticals before they considered the study attributes. The respondents preferred nutraceuticals with no side effect, clear evidence of effectiveness, and recommendation of a healthcare professional. The respondents were willing to pay $252/month more for nutraceuticals proven with no side effect than for those without proof of safety, and $102/month more for nutraceuticals proven with clear effectiveness than for those without proof of effectiveness. Conclusions Consumers weighed relatively high on the availability of safety and effectiveness proofs when they chose nutraceuticals. The study highlights on the crucial need to inform consumers using clinical evidences of nutraceuticals as the information is highly preferred by consumers.

Let $Z$ be a unimodular real spherical space. We develop a theory of constant terms for tempered functions on $Z$ which parallels the work of Harish-Chandra. The constant terms $f_I$ of an eigenfunction $f$ are parametrized by subsets $I$ of the set $S$ of spherical roots which determine the fine geometry of $Z$ at infinity. Constant terms are transitive i.e. $(f_J)_I=f_I$ for $I\subset J$, and our main result is a quantitative bound of the difference $f-f_I$, which is uniform in the parameter of the eigenfunction., Final version. 72 pages. Accepted to IMRN

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson theorem or the $q$-Dyson constant term identity. This conjecture was proved by Karolyi, Lascoux and Warnaar in 2015. In this paper, by slightly changing the variables of Kadell's conjecture, we obtain another symmetric function generalization of the $q$-Dyson constant term identity. This new generalized constant term admits a simple product-form expression.

The present times are full of various challenges, as it always used to be. Having in mind the rapid development of science and technology, we inevitably find ourselves under their influence. Thus, technology not only makes our life easier, but is also capable of shaping human perception in new obstacles. It can influence our choices and responsibility beyond them. Such a dynamic rate of producing new ideas and technology does not allow a proper and forehanded evaluation of their response in our near future. Since philosophers work with relatively constant terms, they have to be in the avant-gardé of a conceptual analysis and problem-shaping of the challenges facing modern people. In such circumstances, lecturing philosophy should hold a prominent position. The sphere of morals and ethical evaluations forms value basis for human self-cognition and performs as a stimulus to a more responsibly deliberated life. In this situation, a philosopher finds himself in a crucial role as a person, who provides this knowledge. The use of philosophical means has to start with the analysis of those, who are in charge of their usage. In order to remain frank with the audience and himself, a philosopher should start lecturing from himself, his self-cognition, as well as from a clear deliberation of his personal moral guidelines and personal responsibility. The situation, in which a philosopher shapes his personal ideas, formulates concepts, analyses, and provides arguments without proper elaboration of their premises and basic principles, raises concerns. Within the scope of this article we attempt to designate the term “philosopher” and philosopher’s position in the modern world. In order to articulate this term properly, we suggest a distinction in terminology between “philosophers of aim” and “philosophers of purpose”, which serves as a marker to estimate philosophic activities in their full scope. In my opinion, any philosophic activities, in their basis, perform as a practice of essential responsibility. The abovementioned definitions provide us with an ability to notice a distinction between philosophers and pseudo-philosophers, as well to evaluate the importance of the ones and the perniciousness of the others.

PurposeThis study aims to assess the effects of microfinance institution (MFI) services on the productivity of family farms in Cameroon, in the region of Mbam and Kim. It will be a question, therefore, of determining the level and determiners of the outputs of family farms, in particular those concerned by the cultures of cocoa, beneficiaries of the agricultural services of MFIs.Design/methodology/approachThe authors use the Blinder (1973) and Oaxaca (1973) model of decomposition of the productivity differential between beneficiaries and non-beneficiaries of agricultural credits on a sample of 130 cocoa farming households and four MFIs of the same area between 2008 and 2011.FindingsThe yield gap between beneficiaries and non-beneficiaries of agricultural credits is estimated at 0.19 tons per hectare. This gap is explained positively by the financial aid variable, the farm size variable, which is significant in the explanation of the beneficiaries' level of returns and the constant term. On the other hand, all the socio-economic variables of the farmers contribute to reduce this gap of productivity.Research limitations/implicationsThis financial assistance from CVECA is essential to increase agricultural yields because it helps to cancel out some structural barriers. However, as this improvement in yields is only possible for large farms, the services of the MFIs would rather favor extensification policies. Nevertheless, the study results are limited by the negative effects of the socio-economic characteristics of the farmers on these yields, the study having been revealed without any selectivity bias.Originality/valueThis study seeks to reverse the trend that in rural areas, MFIs are financing agriculture to increase extensification rather than enhancing intensification in sub-Saharan Africa by challenging the role of MFI services in intensification.

We consider a Cauchy problem for a system of two quasilinear equations of the first order with constant terms. The study of the solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms in the original coordinates is based on the method of an additional argument. Theorems on the local and nonlocal existence and uniqueness of solutions to the Cauchy problem are formulated and proved. We prove the existence and uniqueness of the local solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms, which has the same smoothness with respect to $x$ as the initial functions of the Cauchy problem. Sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms are found; this solution is continued by a finite number of steps from the local solution. The proof of the nonlocal solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms relies on global estimates.

This article is concerned with the Bayesian optimal design problem for multi-factor nonlinear models. In particular, the Bayesian $$\varPsi _q$$ -optimality criterion proposed by Dette et al. (Stat Sinica 17:463–480, 2007) is considered. It is shown that the product-type designs are optimal for the additive multi-factor nonlinear models with or without constant term when the proposed sufficient conditions are satisfied. Some examples of application using the exponential growth models with several variables are presented to illustrate optimal designs based on the Bayesian $$\varPsi _q$$ -optimality criterion considered.

The issue of having an intercept term in linear regression model is an unsettled issue in the literature. It can be said that, generally, including the constant term depends on the research. But it must be known that the estimation of parameters differs according to involvement of the constant. If an intercept term exists in the model, the least squares estimate of the slope parameter will be unbiased. In this paper, we compare the results of models that include intercept and do not include intercept term on hypothetic data sets. The approaches are demonstrated via both simulation studies. Simulation-based investigation is carried out under various different scenarios using SAS 9.0 software. Results from the simulation study will be presented. We will discuss scenarios in which case they are advantageous. Keywords: Intercept, linear regression, zero-constant, slope parameter, collinearity Cite this Article Ijomah Maxwell Azubuike, Nwakuya Murren Tobechukwu. On the Omission of Intercept Term in Model Estimation: A Monte Carlo Simulation Study. Research & Reviews: Journal of Statistics . 2020; 9(1): 1-8p.

(c) 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Given a set of noisy data values from a polynomial, determining the degree and coefficients of the polynomial is a problem of polynomial regressions. Polynomial regressions are very common in engineering, science, and other disciplines, and it is at the heart of data science. Linear regressions and the least squares method have been around for two hundred years. Existing techniques select a model, which includes both the degree and coefficients of a polynomial, from a set of candidate models which have already been fitted to the data. The philosophy behind the proposed method is fundamentally different to what have been practised in the last two hundred years. In the first stage only the degree of a polynomial to represent the noisy data is selected without any knowledge or reference to its coefficient values. Having selected the degree, polynomial coefficients are estimated in the second stage. The development of the first stage has been inspired by the very recent results that all polynomials of degree q give rise to the same set of known time-series coefficients of autoregressive models and a constant term μ. Computer experiments have been carried out with simulated noisy data from polynomials using four well known model selection criteria as well as the proposed method (PTS1). The results obtained from the proposed method for degree selection and predictions are significantly better than those from the existing methods. Also, it is experimentally observed that the root-mean square (RMS) prediction errors and the variation of the RMS prediction errors from the proposed method scale linearly with the standard deviations of the noise for each degree of a polynomial.

We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the previously successful methods based on low-rank representations are not directly applicable. We modify the doubling algorithm, making use of the low-rank in the input matrix B . We also solve the challenging problems in the estimation of residuals and relative errors, convergence control and the output of the modified algorithm. Illustrative numerical examples are presented.

Fundamental limits on the error probability of the social learning rule proposed by Lalitha et al. [1] and its variants for decentralized detection over a directed graph is investigated. We show that while social learning algorithms enjoy the benefits that each node in the graph weights the messages received from its neighbors locally to form its private belief and only requires knowledge of the data generating distributions of its own observation, it suffers a gap in the achievable error exponent compared to the centralized case. We propose a generalization of the social learning rule achieving the error exponent in centralized detection with the aid of slight global knowledge. A further analysis reveals that the price of decentralization is at most a constant term in the higher-order asymptotics. To obtain the slight global knowledge needed at each node for achieving the centralized error exponent, we develop a decentralized estimation method for each node to come up with a local estimate of that piece of global knowledge.

Summary This note discusses two errors in the approach proposed in Canay (2011) for constructing a computationally simple two-step estimator in a quantile regression model with quantile-independent fixed effects. Firstly, we show that Canay’s assumption about n/Ts → 0 for some s > 1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer to the required set of restrictions. These problems are likely to cause incorrect inference in applied papers with large n/T, but the impact is less in applications with small n/T. In an attempt to improve Canay’s estimator, we propose a simple correction that may reduce the bias. The second error concerns the incorrect asymptotic standard error of the estimator of the constant term. We show that, contrary to Canay’s assumption, the within estimator has an influence function that is not i.i.d. and this affects inference. Moreover, the constant term is unlikely to be estimable at rate $\sqrt{nT}$, so a different estimator may not be available. However, the issue concerning the constant term does not have an effect on slope coefficients. Finally, we give recommendations to practitioners and conduct a meta-review of applied papers that use Canay’s estimator.

One of the major challenges several economies of the world is facing today is striking a balance between mitigating environmental degradation amidst the dire desire for economic growth and environmental sustainability. In order to reduce environmental pollution and sustain the environment, countries around the world are embarking on several policy measures to ameliorate climate change and reduce greenhouse gas emissions. On this premise, this study investigates the role of energy, real income and globalization in the quest to achieve environmental sustainability in the case of Italy using Autoregressive Distributed Lag model for empirical estimators and Toda and Yamamoto predictive methodology over the period 1970–2014. Based on empirical results, we found that a percent increase in kg oil equivalent per capita of energy consumed and globalization index led to 0.928% increase and 0.914% decrease in metric ton per capita of CO2 emissions in the short-run, and 1.796% increase and 1.769% decrease in metric ton per capita of CO2 emissions in the long-run, while the real income has no significant impact on the metric ton per capita of carbon emissions level both in the short- and long-run. The autonomous term also showed an interesting result, we found that, holding other factor constant, a percent increase in the constant term will lead to 1.879% decrease in metric ton per capita of carbon emissions in the short-run, and 3.635% decrease in metric ton per capita of carbon emissions in the long-run thus, we infer that Italy has been successful in balancing environmental conversation policies with macroeconomic objectives. This study provides credible policy suggestions for policymakers in energy intense economies around the world.

A simple and elegant solution to determine the asymptotic results for the renewal density as well as for the first and second moments of the number of renewals for the discrete-time bulk-renewal process is presented. The method of generating function is used to find the constant term in the second moment (higher moments can also be found using the same method). In classic texts such as Feller (1968) and Hunter (1983), the constant term is missing even for the non-bulk renewal process. A recent paper by Van der Weide et al. (2007) states that it is not clear how to get the constant term using generating functions and as such they present this result using a different approach. Recently, Chaudhry and Fisher (2012) have responded to this problem by providing the asymptotic results for the non-bulk renewal density as well as for both the first and second moments using generating functions. The purpose of this note is to extend their results to bulk-renewal process in discrete-time, including some numerical results, give an elegant derivation of the asymptotic results and derive continuous-time results as a limit of the discrete-time results.

The aim of this study is to identify the factors that significantly determine the regional spatial differentiation of housing prices as well as housing market activity in Poland. The present research makes the assumption that average housing prices and market activity (number of transactions) are regionally shaped by economic, social, infrastructural and environmental conditions which can be described as a set of diagnostic features ascribed to a given area, constituting a statistical unit. Furthermore, it is assumed that individual effects may appear, being tied to the idiosyncrasies and significance of the given area. The time horizon of the research is 2008-2018. Based on data sourced from the Central Statistical Office a panel data was prepared for each of 380 Polish districts (poviats). Next, parameters were estimated for a single-factor panel model, as well as a two-factor model in which the constant term is different for different time periods and different units. This resulted in a model encompassing both average price determinants, and individual effects which reflect certain regularities of their spatial distribution. Moreover, the research will result in a set of cartograms made with Geographic Information System tools, depicting the random effects resulting from estimates of panel models using the Nerlove and Swamy-Arora transformations.

Objective: to build a term database relevant to nursing practice in the context of COVID-19 infections. Methods: this is a methodological, documentary study, carried out from March to June 2020 at ICNP®/ Universidade Federal da Paraíba center, considered a reference for research and dissemination of ICNP® in Brazil. The findings were collected in databases and analyzed using the PorOnto tool, the consensus technique and the mapping of terms with ICNP®, version 2019/2020. Results: 1,134 relevant terms were identified in literature. When submitted to the mapping technique with the terms of ICNP® Seven Axis Model, it resulted in 531 constant terms and 603 nonconstant terms in this classification. Final considerations: It is proven that nursing practice terms, even in a specific context, are present in the literature and are representative in ICNP®, which will enable the future development of a terminological subset in the context of coronavirus infections.

Recently, Benedetti et al. introduced an Ehrhart-like polynomial associated to a graph. This polynomial is defined as the volume of a certain flow polytope related to a graph and has the property that the leading coefficient is the volume of the flow polytope of the original graph with net flow vector $(1,1,\dots,1)$. Benedetti et al. conjectured a formula for the Ehrhart-like polynomial of what they call a caracol graph. In this paper their conjecture is proved using constant term identities, labeled Dyck paths, and a cyclic lemma., 20 pages, 5 figures

Resumen Introducción. La producción de carne de cerdo en canal en México, ocupó el tercer lugar dentro de la producción de carnes después de la carne de bovino y de aves; el volumen producido de carne de este tipo no ha sido suficiente para cubrir el consumo nacional y disminuir las importaciones. Objetivo. Analizar la evolución de los costos, de la rentabilidad y competitividad de la producción porcina en las regiones de Tejupilco y Luvianos, ubicados en el Sur del Estado de México. Materiales y métodos. La investigación se realizó con información proveniente de cuarenta productores de traspatio y una tecnificada; la metodología utilizada fue la Matriz de Análisis de Política, con la que se elaboraron las matrices de coeficientes técnicos y de los precios de los insumos y del producto, con la que obtuvieron las matrices de presupuesto privado. Resultados. Las rentabilidades privadas (RP) se ubicaron en 26 % para las de traspatio y en 43 % para la tecnificada, mientras que la relación de costo privado (RCP) fue de 0,35 para las de traspatio y de 0,17 para la tecnificada, con lo que se observó una mayor competitividad en esta última. Conclusión. Los indicadores señalan que en 2018, éstos dos tipos de explotaciones porcícolas fueron rentables y competitivos en relación a los obtenidos en 2006, debido principalmente a movimientos en términos constantes de los costos de los insumos, que descendieron y al aumento en el precio del cerdo en pie, lo que contribuyó a que estos productores realizaran acciones tendientes a ser más productivos y eficientes. Abstract Introduction. Meat pork production is rank third of all meats in Mexico after beef and broilers. Production is not enough to supply the national consumption and reduce imports. Objective. Analyze the evolution of costs, profitability and competitiveness of pig production in the regions of Tejupilco and Luvianos, located in the South of the State of Mexico. Materials and methods. The investigation was carried out using information from forty backyard and one technificated farms; A Policy Analysis Matrix was used. Matrices were elaborated of technical coefficients, prices of inputs and product and private budgets. Results. Private returns (RP) were at 26% for backyard ones and 43% for technifhicated one, while private cost ratio (RCP) was 0.35 for backyard ones and 0.17 for technical one, thus, greater competitiveness was observed in the latter. Conclusion. Indicators point out these two types of pig farms were profitable in 2018, and were competitives in relation to those obtained in 2006, it was mainly due to movements in constant terms of inputs costs, which decreased and the increase in the price of live pigs, which contributed producers taking actions to be more productive and efficient.