European integrationEuropean integration is the process of industrial, economic, political, legal, social, and cultural integration of states wholly or partially in Europe or nearby. European integration has primarily come about through the European Union and its policies. In antiquity, the Roman Empire brought about integration of multiple European and Mediterranean territories. The numerous subsequent claims of succession of the Roman Empire, even the iterations of the Classical Empire and its ancient peoples, have occasionally been reinterpreted in the light of post-1950 European integration as providing inspiration and historical precedents.
Foundations of mathematicsFoundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.
Trigonometric integralIn mathematics, trigonometric integrals are a family of integrals involving trigonometric functions. The different sine integral definitions are Note that the integrand is the sinc function, and also the zeroth spherical Bessel function. Since sinc is an even entire function (holomorphic over the entire complex plane), Si is entire, odd, and the integral in its definition can be taken along any path connecting the endpoints. By definition, Si(x) is the antiderivative of sin x / x whose value is zero at x = 0, and si(x) is the antiderivative whose value is zero at x = ∞.
SinIn a religious context, 'sin' is a transgression against divine law or a law of God. Each culture has its own interpretation of what it means to commit a sin. While sins are generally considered actions, any thought, word, or act considered immoral, selfish, shameful, harmful, or alienating might be termed "sinful".
Fresnel integralThe Fresnel integrals S(x) and C(x) are two transcendental functions named after Augustin-Jean Fresnel that are used in optics and are closely related to the error function (erf). They arise in the description of near-field Fresnel diffraction phenomena and are defined through the following integral representations: The simultaneous parametric plot of S(x) and C(x) is the Euler spiral (also known as the Cornu spiral or clothoid).
Mortal sinA mortal sin (peccatum mortale), in Catholic theology, is a gravely sinful act which can lead to damnation if a person does not repent of the sin before death. It is alternatively called deadly, grave, and serious. A sin is considered to be "mortal" when its quality is such that it leads to a separation of that person from God's saving grace. Three conditions must together be met for a sin to be mortal: "Mortal sin is sin whose object is grave matter and which is also committed with full knowledge and deliberate consent.
Christian views on sinIn Christianity, 'sin' is an immoral act considered to be a transgression of divine law. The doctrine of sin is central to the Christian faith, since its basic message is about redemption in Christ. Hamartiology, a branch of Christian theology which is the study of sin, describes sin as an act of offence against God by despising his persons and Christian biblical law, and by injuring others. Christian hamartiology is closely related to concepts of natural law, moral theology and Christian ethics.
Eternal sinIn Christian hamartiology, eternal sin, the unforgivable sin, unpardonable sin, or ultimate sin is the sin which will not be forgiven by God. One eternal or unforgivable sin (blasphemy against the Holy Spirit), also known as the sin unto death, is specified in several passages of the Synoptic Gospels, including Mark 3:28–29, Matthew 12:31–32, and Luke 12:10, as well as other New Testament passages including Hebrews 6:4–6, Hebrews 10:26–31, and 1 John 5:16.
Fc receptorIn immunology, a Fc receptor is a protein found on the surface of certain cells – including, among others, B lymphocytes, follicular dendritic cells, natural killer cells, macrophages, neutrophils, eosinophils, basophils, human platelets, and mast cells – that contribute to the protective functions of the immune system. Its name is derived from its binding specificity for a part of an antibody known as the Fc (fragment crystallizable) region. Fc receptors bind to antibodies that are attached to infected cells or invading pathogens.
Fragment crystallizable regionThe fragment crystallizable region (Fc region) is the tail region of an antibody that interacts with cell surface receptors called Fc receptors and some proteins of the complement system. This region allows antibodies to activate the immune system, for example, through binding to Fc receptors. In IgG, IgA and IgD antibody isotypes, the Fc region is composed of two identical protein fragments, derived from the second and third constant domains of the antibody's two heavy chains; IgM and IgE Fc regions contain three heavy chain constant domains (CH domains 2–4) in each polypeptide chain.
Moritz PaschMoritz Pasch (8 November 1843, Breslau, Prussia (now Wrocław, Poland) – 20 September 1930, Bad Homburg, Germany) was a German mathematician of Jewish ancestry specializing in the foundations of geometry. He completed his Ph.D. at the University of Breslau at only 22 years of age. He taught at the University of Giessen, where he is known to have supervised 30 doctorates. In 1882, Pasch published a book, Vorlesungen über neuere Geometrie, calling for the grounding of Euclidean geometry in more precise primitive notions and axioms, and for greater care in the deductive methods employed to develop the subject.
Alexander OstrowskiAlexander Markowich Ostrowski (Олександр Маркович Островський; Алекса́ндр Ма́ркович Остро́вский; 25 September 1893, in Kiev, Russian Empire – 20 November 1986, in Montagnola, Lugano, Switzerland) was a mathematician. His father Mark having been a merchant, Alexander Ostrowski attended the Kiev College of Commerce, not a high school, and thus had an insufficient qualification to be admitted to university. However, his talent did not remain undetected: Ostrowski's mentor, Dmitry Grave, wrote to Landau and Hensel for help.
