Every sufficiently large even number is the sum of two primes

The binary Goldbach conjecture asserts that every even integer greater than $4$ is the sum of two primes. In this paper, we prove that there exists an integer $K_\alpha$ such that every even integer $x > p_k^2$ can be expressed as the sum of two primes, where $p_k$ is the $k$th prime number and $k > K_\alpha$. To prove this statement, we begin by introducing a type of double sieve of Eratosthenes as follows. Given a positive even integer $x > 4$, we sift from $[1, x]$ all those elements that are congruents to $0$ modulo $p$ or congruents to $x$ modulo $p$, where $p$ is a prime less than $\sqrt{x}$. Therefore, any integer in the interval $[\sqrt{x}, x]$ that remains unsifted is a prime $q$ for which either $x-q = 1$ or $x-q$ is also a prime. Then, we introduce a new way of formulating a sieve, which we call the sequence of $k$-tuples of remainders. By means of this tool, we prove that there exists an integer $K_\alpha > 5$ such that $p_k / 2$ is a lower bound for the sifting function of this sieve, for every even number $x$ that satisfies $p_k^2 < x < p_{k+1}^2$, where $k > K_\alpha$, which implies that $x > p_k^2 \; (k > K_\alpha)$ can be expressed as the sum of two primes.Comment: 32 pages. The manuscript was edited for proper English language by one editor at American Journal Experts (Certificate Verification Key: C0C3-5251-4504-E14D-BE84). However, afterwards some changes have been made in sections 1, 6, 7 and

Quantification of metal release from stainless steel electrodes during conventional and pulsed ohmic heating

Electrochemical reactions at the electrode-solution interface of an ohmic heater can be avoided or significantly limited by choosing appropriate processing conditions in relation to the food properties. In the present work the effect of the electrical parameters (electric field strength and frequency of the applied current signal) and product factors (halides concentration, electrical conductivity and pH) on metal release from stainless steel (type AISI 316 L) electrodes of a batch ohmic heater was investigated. In each experiment, the concentrations of the main constituents of stainless steel (iron, chromium and nickel) released in the heating medium were detected by Inductively Coupled Plasma Mass Spectrometry (ICP-MS) and Atomic Absorption Spectrophotometry (AAS). Results showed that the rate of metal release from the electrodes to the heating medium depends on frequency and applied field strength. However, the use of ohmic heating at a higher frequency than conventional (50 Hz) can significantly (p ≤ 0.05) reduce the flux of metal ions from stainless steel electrodes. Moreover, it was also demonstrated that electrochemical phenomena occurring at the electrode-solution interface strongly depend on the composition, pH and electrical conductivity of the heating medium. Industrial relevance: The magnitude of electrode material released into the heating medium during ohmic processing depends on many factors, whose effects should be known in order to define optimal treatment conditions, electrode material and food properties able to avoid or minimize the undesired phenomenon of contamination of the food product, electrode-fouling and electrode corrosion. This paper contributes to clarifying the effects of electric field strength applied as well as electrical conductivity, pH, and presence of halides in the heating medium on electrode corrosion or release of electrode materials during high frequency (25 kHz, bipolar square wave) pulsed power OH in comparison with conventional (50 Hz sine wave) OH. Interestingly, the use of sufficiently large frequencies may avoid or reduce the extent of electrochemical reactions at the electrode interface, minimizing corrosion and leakage of metals to the heating medium, even when electrode material of low cost and electrochemically active like stainless steel is used

Redes Neuronales Artificiales En La Predicción De La Vulnerabilidad De La Placa De Ateroma

The prediction of the vulnerability of atheroma plaque by means of neural networks allows a rapid response to be given for a specific patient in clinical practice. To perform this prediction, an artificial neural network (ANN) has been developed takes as input data the deformations of the atherosclerotic coronary artery and gives as a result the mechanical properties of the atherosclerotic coronary artery. These have been used to determine the stresses in the fibrotic layer and, ultimately, whether or not the plaque is vulnerable.La predicción de la vulnerabilidad de la placa de ateroma mediante redes neuronales permite dar una respuesta rápida para paciente específico en la práctica clínica. Para realizar dicha predicción se ha desarollado una red neuronal artificial (RNA) que toma como datos de entrada las deformaciones de la arteria coronaria aterosclerótica y da como resultado las propiedades mecánicas de la misma. Éstas se han utilizado para determinar las tensiones presentes en la capa fibrótica y, en última instancia, si la placa es o no vulnerable

Inteligência e rendimento escolar: contingências de um relacionamento menos óbvio no final da adolescência

[Resumo] As relações entre as habilidades cognitivas dos alunos e o seu rendimento escolar estão demonstradas, contudo nem sempre suficientemente compreendidas e explicadas em face da multiplicidade de variáveis intervenientes no rendimento académico. Assim, tomando os resultados da aferição nacional da Bateria de Provas de Raciocínio (BPR – versão 10/12), analisamos as suas correlações com indicadores de rendimento escolar (classificações nas disciplinas de Língua Portuguesa e de Matemática, assim como o número de retenções escolares anteriores) de estudantes do ensino secundário. O estudo toma uma amostra nacional de alunos (n=1050) repartidos pelo 10º (n=449), 11º (n=315) e 12º (n=286) anos de escolaridade, devidamente estratificada e recolhida de forma aleatória. Os resultados obtidos sugerem oscilações nos índices de correlação obtidos consoante a natureza das provas cognitivas aplicadas (tipo de conteúdo dos itens), a especificidade dos indicadores de rendimento escolar, o ano escolar, o agrupamento de estudos e o género dos alunos. Por outro lado, as correlações diminuem à medida que se avança na escolaridade, sendo mais elevadas junto das alunas e daquelas que prosseguem estudos na área das humanidades. Esta diminuição alerta para a importância crescente de outras variáveis, para além da capacidade intelectual, no rendimento académico à medida que se avança na escolaridade

Significant increase of global anomalous moisture uptake feeding landfalling Atmospheric Rivers

One of the most robust signals of climate change is the relentless rise in global mean surface temperature, which is linked closely with the water-holding capacity of the atmosphere. A more humid atmosphere will lead to enhanced moisture transport due to, among other factors, an intensification of atmospheric rivers (ARs) activity, which are an important mechanism of moisture advection from subtropical to extra-tropical regions. Here we show an enhanced evapotranspiration rates in association with landfalling atmospheric river events. These anomalous moisture uptake (AMU) locations are identified on a global scale. The interannual variability of AMU displays a significant increase over the period 1980-2017, close to the Clausius-Clapeyron (CC) scaling, at 7 % per degree of surface temperature rise. These findings are consistent with an intensification of AR predicted by future projections. Our results also reveal generalized significant increases in AMU at the regional scale and an asymmetric supply of oceanic moisture, in which the maximum values are located over the region known as the Western Hemisphere Warm Pool (WHWP) centred on the Gulf of Mexico and the Caribbean SeaMinisterio de Ciencia, Innovación y Universidades | Ref. RTI2018-095772-B-I00Xunta de Galicia | Ref. ED431C 2017/64-GRCMinisterio de Economía y Competitividad | Ref. CGL2015-65141-RXunta de Galicia | Ref. EDB481B 2018/069Fundação para a Ciência e a Tecnologia | Ref. PTDC/CTA-MET/29233/2017Fundação para a Ciência e a Tecnologia | Ref. CEECIND/00027/201

Desarrollo de un modelo híbrido para reproducir el crecimiento de la placa de ateroma

Se está desarrollando un modelo híbrido capaz de predecir el crecimiento de la arteria coronaria con aterosclerosis a largo plazo. Este modelo combina las ecuaciones de convección-difusión-reacción con un modelo basado en agentes para estudiar los fenómenos emergentes del comportamiento celular y sus efectos a nivel de tejido

Estimación de las propiedades mecánicas de la placa de ateroma utilizando Redes Neuronales Artificiales

Predecir las propiedades mecánicas de la placa de ateroma en paciente específico es crucial para identificar el riesgo de infarto o ictus cerebral de forma rápida y eficiente en la práctica clínica a partir de la información obtenida por ecografía intravascular por ultrasonidos (IVUS)

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum

Código de conduta. Prevenção da introdução e dispersão de flora e fauna exótica invasora: agentes ambientais

De forma intencional ou involuntária, o ser humano transporta espécies entre locais desde tempos imemoriais. No entanto, nos últimos 50 anos, o ritmo de introdução de espécies exóticas no meio natural acelerou de forma alarmante, tornando-se numa das principais causas de perda de biodiversidade. A globalização, juntamente com as alterações climáticas, a destruição de habitats, o aumento do trânsito de pessoas e o comércio, são hoje os principais responsáveis pela perda de biodiversidade a nível global, acarretando também graves prejuízos para a economia e a saúde humana

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis