Abelian varietyIn mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field.
Algebraic varietyAlgebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.
EmpathyEmpathy is the capacity to understand or feel what another person is experiencing from within their frame of reference, that is, the capacity to place oneself in another's position. Definitions of empathy encompass a broad range of social, cognitive, and emotional processes primarily concerned with understanding others (and others' emotions in particular). Types of empathy include cognitive empathy, emotional (or affective) empathy, somatic empathy, and spiritual empathy.
Sorrow (emotion)Sorrow is an emotion, feeling, or sentiment. Sorrow "is more 'intense' than sadness... it implies a long-term state". At the same time, "sorrow — but not unhappiness — suggests a degree of resignation... which lends sorrow its peculiar air of dignity". Moreover, "in terms of attitude, sorrow can be said to be half way between sadness (accepting) and distress (not accepting)".
Small businessSmall businesses are types of corporations, partnerships, or sole proprietorships which have a small number of employees and/or less annual revenue than a regular-sized business or corporation. Businesses are defined as "small" in terms of being able to apply for government support and qualify for preferential tax policy. The qualifications vary depending on the country and industry. Small businesses range from fifteen employees under the Australian Fair Work Act 2009, fifty employees according to the definition used by the European Union, and fewer than five hundred employees to qualify for many U.
Dispositional affectDispositional affect, similar to mood, is a personality trait or overall tendency to respond to situations in stable, predictable ways. This trait is expressed by the tendency to see things in a positive or negative way. People with high positive affectivity tend to perceive things through "pink lens" while people with high negative affectivity tend to perceive things through "black lens". The level of dispositional affect affects the sensations and behavior immediately and most of the time in unconscious ways, and its effect can be prolonged (between a few weeks to a few months).
AweAwe is an emotion comparable to wonder but less joyous. On Robert Plutchik's wheel of emotions awe is modeled as a combination of surprise and fear. One dictionary definition is "an overwhelming feeling of reverence, admiration, fear, etc., produced by that which is grand, sublime, extremely powerful, or the like: [e.g.] in awe of God; in awe of great political figures." Another dictionary definition is a "mixed emotion of reverence, respect, dread, and wonder inspired by authority, genius, great beauty, sublimity, or might: [e.
Simulation theory of empathyThe simulation theory of empathy holds that humans anticipate and make sense of the behavior of others by activating mental processes that, if they culminated in action, would produce similar behavior. This includes intentional behavior as well as the expression of emotions. The theory says that children use their own emotions to predict what others will do; we project our own mental states onto others. Simulation theory is not primarily a theory about empathy, but rather a theory of how people understand others—that they do so by way of a kind of empathetic response.
Moral psychologyMoral psychology is a field of study in both philosophy and psychology. Historically, the term "moral psychology" was used relatively narrowly to refer to the study of moral development. Moral psychology eventually came to refer more broadly to various topics at the intersection of ethics, psychology, and philosophy of mind.
