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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.

(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.

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.

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.

This paper analyzes the evolution of the total revenues of the Spanish Royal Treasury and the changes in its structure between 1680 and 1807. After stagnating in the first half of the century, the revenues of the Royal Treasury increased significantly in constant terms, but rather less in real ones. The stagnation of 1730-1742 is explained by the collapse of the Provincial Revenues, while the growth of 1762-1792 was driven by Customs duties, Fiscal monopolies and Remittances from the Indies, following the liberalizing decrees of the American trade. The war cycle started in 1793 was funded with extraordinary revenues (public debt, donations). A comparison with the British Treasury shows that the revenues of Spanish Treasury grew much less during these wars, due to a set of reasons we deal with in the concluding remarks.

Objective: to build a specialized terminology for the clinical nursing practice for people with COVID-19, based on the Seven Axis Model of the International Classification for Nursing Practice. Methods: a descriptive and documentary study, carried out in April 2020. The terms were extracted from official documents of the Ministry of Health. The data were treated through terminological analysis, that is, the terms were organized through a classification system, which, in this research, was represented by the Seven Axis Model, version 2019. Also in the delimitation of the thematic field of the terminological analysis, the method of cross-mapping was chosen so that the terms resulting from the normalization process, derived from the literature, were cross-referenced with the terms of the International Classification for Nursing Practice in its seven axes. Results: after the normalization process, 472 useful terms were found. These were submitted to cross-mapping, totaling 263 constant terms and 211 non-constant terms. Conclusion: the study allowed identifying terms in the literature, which can be used by nurses in the care of people affected by COVID-19 and will support the stages following the construction of a terminological subset for information and communication to the Nursing practice.

We calculate the constant terms of certain Hilbert modular Eisenstein series at all cusps. Our formula relates these constant terms to special values of Hecke $L$-series. This builds on previous work of Ozawa, in which a restricted class of Eisenstein series were studied. Our results have direct arithmetic applications---in separate work we apply these formulas to prove the Brumer-Stark conjecture away from $p=2$ and to give an exact analytic formula for Brumer-Stark units., Comment: 30 pages

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the $q$-Dyson constant term identity or the Zeilberger--Bressoud $q$-Dyson theorem. The non-zero part of Kadell's orthogonality conjecture is a constant term identity indexed by a weak composition $v=(v_1,\dots,v_n)$ in the case when only one $v_i\neq 0$. This conjecture was first proved by K\'{a}rolyi, Lascoux and Warnaar in 2015. They further formulated a closed-form expression for the above mentioned constant term in the case when all the parts of $v$ are distinct. Recently we obtain a recursion for this constant term provided that the largest part of $v$ occurs with multiplicity one in $v$. In this paper, we generalize our previous result to all compositions $v$., Comment: 13 pages

Value-at-Risk (VaR) is a popular measure of market risk. To convey information regarding potential exceedances beyond the VaR, Expected Shortfall (ES) has become the risk measure for trading book bank regulation. However, the estimation of VaR and ES is challenging, as it requires the estimation of the tail behaviour of daily returns. In this paper, we take advantage of recent research that develops joint scoring functions for VaR and ES. Using these functions, we present a novel approach to estimating the two risk measures based on intraday data. We focus on the intraday range, which is the difference between the highest and lowest intraday log prices. In contrast to intraday observations, the intraday low and high are widely available for many financial assets. To alleviate the challenge of modelling extreme risk measures, we propose the use of the intraday low series. We draw on a theoretical result for Brownian motion to show that a quantile of the daily returns can be estimated as the product of a constant term and a less extreme quantile of the intraday low returns, which we define as the difference between the lowest log price of the day and the log closing price of the previous day. In view of this, we use estimates of the VaR and ES of the intraday low returns to estimate the VaR and ES of the daily returns. We provide empirical support for the new proposals using data for five stock indices and five individual stocks.

We consider the exponential generating function whose coefficients encode the dimensions of irreducible highest weight representations which lie on a given ray in the dominant chamber of the weight lattice. This formal power series can be considered as an exponential version of the Hilbert series of a flag variety. In this context, we compute a simple closed form for the exponential generating function in terms of finitely many differential operators and the Stirling polynomials. We prove that this series converges to a product of a rational polynomial and an exponential, and that, by summing the constant term and linear coefficient of this polynomial, we recover the dimension of the representation.

In addition to the trivial solution in the class of essentially bounded functions with a given weight for the Solonnikov-Fasano homogeneous parabolic problem in an infinite angular domain we establish the existence of the nontrivial solution, up to a constant factor.

An accurate estimation of the noise power from noisy data leads to better estimation of signal-to-noise ratio (SNR) and is useful in detection, estimation, and prediction. The major contributions of this paper are to estimate the polynomial degree and the noise power from data coming from an underlying polynomial with additive Gaussian noise, using an AR model. The two proposed methods have been inspired by the recent results that all finite degree polynomials have equivalent representation in finite order autoregressive (AR) models, with known AR coefficients and different constant terms. Preliminary experiments in a variety of scenarios provide estimations of the constant term and the standard deviation of these estimations, which are then used as a guide to developing theoretically the probability density functions. In the first stage, the degree of a polynomial is selected by minimizing the variance of the estimations of the constant term in the equivalent AR model. In the second stage, the noise variance is estimated using the estimated degree of a polynomial, a combination of the variance of the estimations of the constant term, and another known parameter. Further computer experiments have been carried out for evaluating the proposed methods for degree and noise power estimations. Four well-known and well-regarded maximum likelihood-based approaches have been used for comparisons.

A reliable prediction of CO2 emissions from marine fleets plays an important role in the low carbon development of shipping industry. However, CO2 emissions from marine fleets have its own inherent trends and the influencing factors might have interaction effects, and these problems make it difficult to build an accurate prediction model. To this end, a novel multivariable trend interaction grey model, named TIGM(1, N), is proposed in this paper. TIGM(1, N) extends the grey prediction model by integrating three different terms, i.e., interaction, trends, and constant terms into the grey action terms of the classical multivariable grey model. Compared with the classical multivariable grey model, TIGM(1, N) effectively reflects the impact of input variable interactions and trends on the system’s behavior. To increase the accuracy, the new model’s adjustment coefficient is optimized to obtain optimal time-response function values. The experimental results show that TIGM(1, N) outperforms linear regression models and other variants of the grey prediction models in predicting the CO2 emissions from Chinese marine fleets. Finally, the new model is applied to predict the marine fleets’ CO2 emissions during 2016–2018 and the results demonstrates the feasibility of the proposed model in low carbon development plan of shipping industry and its value in formulating environmental policies.

The Morris constant term identity is known to be equivalent to the famous Selberg integral. In this paper, we regard Morris type constant terms as polynomials of a certain parameter. Thus, we can take the leading coefficients and obtain new identities. These identities happen to be crucial in finding lower bounds for cardinalities of some restricted sumsets, and in calculating the volume of a Tesler polytope.

Nowadays location estimation using WiFi networks in indoor environments has become a hot research topic. Challenging methods without calibration or hardware integration are essentially required for cost-effective and practical solutions. The Received Signal Strength Indicator-based localization methods offer low cost solutions. However, their propagation models are difficult to characterize due to environmental factors in indoor and multiple parameters. There are a number of works over estimation of location and pathloss exponent presented in the literature. This paper introduces a new method shortly named as ERLAK in order to estimate the K constant term using log normal channel model in addition to the location of mobile station in indoor environment. The ERLAK method has been consistently compared to the well-known Least Square and Weighted Least Square methods. It achieves the least errors in distance estimations compared to the classical methods on especially critical measurement points. It remarkably accomplishes less than 5 m mean errors for distance estimation results particularly when signal is received from all of the access points.

In this paper, we compute constant terms of Eisenstein series defined over a totally real field, at various cusps. In his paper published in 2003, M. Ohta computed the constant terms of Eisenstein series of weight two over the field of rational numbers, at all equivalence classes of cusps. As for Eisenstein series defined over a totally real field, S. Dasgupta, H. Darmon and R. Pollack calculated the constant terms at particular (not all) equivalence classes of cusps in 2011. We compute constant terms of Eisenstein series defined over a general totally real field at all equivalence classes of cusps, and describe them explicitly in terms of Hecke $L$-functions. This investigation is motivated by M. Ohta's work on congruence modules related to Eisenstein series defined over the field of rational numbers., 22 pages

By combining the Gessel--Xin method with plethystic substitutions, we obtain a recursion for a symmetric function generalization of the $q$-Dyson constant term identity also known as the Zeilberger--Bressoud $q$-Dyson theorem. This yields a constant term identity which generalizes the non-zero part of Kadell's orthogonality ex-conjecture and a result of K\'{a}rolyi, Lascoux and Warnaar., Comment: 27 pages

Suppose some classifiers are selected from a set of hypothesis classifiers to form an equally-weighted ensemble that selects a member classifier at random for each input example. Then the ensemble has an error bound consisting of the average error bound for the member classifiers, a term for selectivity that varies from zero (if all hypothesis classifiers are selected) to a standard uniform error bound (if only a single classifier is selected), and small constants. There is no penalty for using a richer hypothesis set if the same fraction of the hypothesis classifiers are selected for the ensemble.

We consider an atomic congestion game in which each player participates in the game with an exogenous and known probability $p_{i}\in[0,1]$, independently of everybody else, or stays out and incurs no cost. We first prove that the resulting game is potential. Then, we compute the parameterized price of anarchy to characterize the impact of demand uncertainty on the efficiency of selfish behavior. It turns out that the price of anarchy as a function of the maximum participation probability $p=\max_{i} p_{i}$ is a nondecreasing function. The worst case is attained when players have the same participation probabilities $p_{i}\equiv p$. For the case of affine costs, we provide an analytic expression for the parameterized price of anarchy as a function of $p$. This function is continuous on $(0,1]$, is equal to $4/3$ for $0

Let $P_1,\dots,P_m\in\mathbb{Z}[y]$ be any linearly independent polynomials with zero constant term. We show that there exists a $\gamma>0$ such that any subset of $\mathbb{F}_q$ of size at least $q^{1-\gamma}$ contains a nontrivial polynomial progression $x,x+P_1(y),\dots,x+P_m(y)$, provided the characteristic of $\mathbb{F}_q$ is large enough., Comment: 23 pages; v2: minor changes based on referee comments

Buçalışmada 1980-2016 yılları itibariyle Türkiye’de turizm sektörünün ekonomiüzerindeki etkisini ortaya koymak amaçlanmıştır. Bu bağlamda kurulan ARDLmodelinde turizm gelirlerinin kişi başı GDP büyümesine etkisi ölçülmüştür.Analiz sonucunda bulunan hata düzeltme katsayısına göre sabit terimsiz modeldekısa dönemde meydana gelebilecek bir şokun etkisi 1/1.10 dönemde; sabit terimlimodelde ise 1/1.95 dönemde giderilmektedir. Ayrıca kısa ve uzun dönemdedeğişkenler arasında anlamlı ve pozitif bir ilişkinin varlığı tespitedilmiştir. Türk turizminin ekonomi üzerindeki bu olumlu etkileriniarttırabilmek için sektöre daha fazla önem verilmesi gerektiği düşünülmektedir., In this study, it was aimed to reveal the effect oftourism sector in Turkey on the economy between the years of 1980-2016. Withinthis context, the effect of tourism incomes on the growth rate of GDP percapita in the ARDL model established. According to error correction factorfound as a result of the analysis, the effect of shock that is possible tooccur in the short term within the model without constant term can beeliminated in 1/1.10 term whereas the effect of shock in the model withconstant term can be eliminated in 1/1.95 term. Moreover, a significant andpositive relation between the factors was identified in the short and longterm. It is believed that the sector should be featured more in order toincrease these positive effects of Turkish tourism on economy.

A theoretical approach of asymptote analyzes the algorithms for approximate time complexity. The worst-case asymptotic complexity classifies an algorithm to a certain class. The asymptotic complexity for algorithms returns the degree variable of the algorithmic function while ignores the lower terms. In perspective of programming, asymptote only considers the number of iterations in a loop ignoring inside and outside statements. However, every statement must have some execution time. This paper provides an effective approach to analyze the algorithms belonging to the same class of asymptotes. The theoretical analysis of algorithmic functions shows that the difference between theoretical outputs of two algorithmic functions depends upon the difference between their coefficient of ‘n’ and the constant term. The said difference marks the point for the behavioral change of algorithms. This theoretic analysis approach is applied to algorithms with linear asymptotic complexity. Two algorithms are considered having a different number of statements outside and inside the loop. The results positively indicated the effectiveness of the proposed approach as the tables and graphs validates the results of the derived formula.

Purpose The purpose of this article is to provide some insights on the true nature of bitcoin and to study empirically its performance by using robust models, widely used in the academic literature. Previous studies assess performance with simple measures such as the Sharpe ratio. Such measures are insufficient because they do not take into account the bitcoin’s specificities, such as the possibilities to diversify risk. Design/methodology/approach The authors use quantitative methodologies to assess the performance of financial assets. Performance is defined as a risk-adjusted return. The authors use regression analysis and measure bitcoin’s performance as the constant term (α) of the projection of its returns on the returns of relevant factors of risk. Findings Bitcoin has low correlation with the market index and with factor-mimicking portfolios, which indicates opportunities to diversify risk. The performance of bitcoin (α) is positive and significant; this result is robust across period and world region specifications. Research limitations/implications The true nature of bitcoin is subject of debate and needs further research. Furthermore, other factors should be considered in analysing the bitcoin’s performance, such as those related to investors’ behaviour or political risk. Practical implications The empirical results obtained in this paper may be used by professional portfolio managers to diversify risk and to enhance their portfolio’s performance. Originality/value This paper adds to the literature by arguing that bitcoin has the nature of common stock, and therefore, its performance has to be assessed with models that are relevant for this type of securities. This paper is the first using performance models that adjust returns for relevant sources of risk.

The algebraic numbers $\cos \left(2\pi/n\right)$ and $2\cos \left(\pi/n\right)$ play an important role in the theory of discrete groups , especially in modular group and Hecke groups , and has many applications because of their relation with Chebycheff polynomials . There are some partial results in literature for the minimal polynomial of the latter number over rationals until 2012 when a complete solution was given in $\left[5\right]$ . In this paper we determine the constant term of the minimal polynomial of $\cos (\frac{2\pi}{n})$ over $\mathbb{Q}$ which is important in determining the congruence subgroups of Hecke groups , by a new method .

We study the existence of hypercyclic algebras for convolution operators Φ ( D ) on the space of entire functions whose symbol Φ has unimodular constant term. In particular, we provide new eigenvalue criteria for the existence of densely strongly algebrable sets of hypercyclic vectors.

We formulate and prove a formula for the constant term for a certain class of Laurent polynomials, which include the Dyson conjecture and its generalizations by Bressoud and Goulden. Our method is explicit Combinatorial Nullstellensatz.

This paper considers a number of inventory models with backorders-lost sales mixture, stockout costs, and controllable lead time. The lead time is a linear function of the lot size and includes a constant term that is made of several components. These lot-size-independent components are assumed to be controllable. Both single- and double-echelon inventory systems, under periodic or continuous review, are considered. To authors knowledge, these models have never been previously studied in literature. The purpose of this paper is to analyse and optimise these novel inventory models. The optimisation is carried out by means of heuristics that work on an ad hoc approximation of the cost functions. This peculiarity permits to exploit closed-form expressions that make the optimisation procedure simpler and more readily applicable in practice than standard approaches. Finally, numerical experiments investigate the efficiency of the proposed heuristics and the sensitivity of the developed models.

We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine and Nickl (Ann. Statist. 38 (2010) 1122–1170). We find that adaptation can only be achieved up to a term that depends on the choice of the constant used to define self-similarity, and that this term becomes arbitrarily large for conservative choices of the self-similarity constant. We construct a confidence band that achieves this bound, up to a constant term that does not depend on the self-similarity constant. Our results suggest that care must be taken in choosing and interpreting the constant that defines self-similarity, since the dependence of adaptive confidence bands on this constant cannot be made to disappear asymptotically.

We present a case study in {\it experimental} yet {\it rigorous} mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that {\it automatically conjectures}, and then {\it automatically proves}, closed-form expressions extending Dyson's celebrated constant term conjecture., Comment: 7 pages

Using purely combinatorial means we obtain results on simultaneous Diophantine approximation modulo 1 for systems of polynomials with real coefficients and no constant term.

Greek industrialization in the post war period failed to establish a sustainable manufacturing sector, although initially it managed to differentiate the country's GDP in favor of manufacturing industry and to increase manufacturing exports. After the first oil shock, however, the Greek economy embarked on a long period of deindustrialization in favor of services. Agriculture, although it gradually declined its GDP share as it was expected due to economic growth, it managed to maintain its important role in employment, increased until 1994 its output in constant terms, and kept it constant until 2000. After that year agriculture's output started to decline, especially after 2006 with the implementation of the new Common Agriculture Policy. The current level of agriculture output is below that in 1970 while it contributes to GDP less than 3%. The current paper investigates the reasons of the recent agriculture's collapse, and it identifies long term determinates of the decline of agriculture's competitiveness. It attributes the decline not to the economic recession Greek economy has been experiencing since 2008 with the exception perhaps of a further increase in production costs due to rising energy costs and taxation, while producer prices remained rather constant, but to the lack of technological and organizational improvements, the failure to differentiate production in favor of high value added crops, all together leading Greek agriculture to fail establishing linkages with the other economic sectors, which finally made the sector incapable of being a positive factor of economic growth.

The purpose of the paper is to introduce a new class of strong uniqueness polynomial satisfying Fujimoto's conditions. We shall also show that for a suitably prescribing value of the constant term in the class of polynomials, an SUPM (SUPE) with smallest degree ever can be obtained. We also find corresponding class of unique range sets generated from those of polynomials under weaker sharing hypothesis. Finally, rectifying the results in the application part of (2) we shall reduce the cardinalities of the range sets under some assumptions on the deficiencies of the functions. At the last section we shall place an open question for future research.

Unit cost of secondary education has continued to rise both direct and indirect jeopardizing access to basic education. The debate has concentrated on whom is carrying the burden of secondary education. The descriptive and causal comparative designs were used in this study. The study sample comprised 85 headteachers’, 765 teachers’, 3349 students and one DEO. The findings of the study indicate that on average households and government contribution to secondary education grew by 3.45 and 4.3 times in absolute terms respectively while under constant terms, the household contribution was 23 times and 25 times for day and boarding schools respectively. The government contribution was 15 times over the same time period. It was concluded that the household carry heavy responsibility compared to the government and hence acquisition of secondary education is still a problem to most household.