Task: Question Answering
Input (English): Context_1 : In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on the type of curve being studied. Context_2 : XLfit is a Microsoft Excel-based plug-in which performs Regression, curve fitting and statistical analysis. XLfit generates 2D and 3D graphs and analyses data sets produced by any type of research. XLfit’s curve fitting engine allows linear and non-linear curve fits, smoothing, statistics, weighting and error bars. Context_3 : A Gompertz curve or Gompertz function, named after Benjamin Gompertz, is a sigmoid function. It is a type of mathematical model for a time series, where growth is slowest at the start and end of a time period. The right-hand or future value asymptote of the function is approached much more gradually by the curve than the left-hand or lower valued asymptote, in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. Context_4 : In the mathematical theory of Kleinian groups, a quasi-Fuchsian group is a Kleinian group whose limit set is contained in an invariant Jordan curve. If the limit set is equal to the Jordan curve the quasi-Fuchsian group is said to be of type one, and otherwise it is said to be of type two. Some authors use "quasi-Fuchsian group" to mean "quasi-Fuchsian group of type 1", in other words the limit set is the whole Jordan curve. This terminology is incompatible with the use of the terms "type 1" and "type 2" for Kleinian groups: all quasi-Fuchsian groups are Kleinian groups of type 2 (even if they are quasi-Fuchsian groups of type 1), as their limit sets are proper subsets of the Riemann sphere. The special case when the Jordan curve is a circle or line is called a Fuchsian group, named for Lazarus Fuchs. Context_5 : Curve is a lesbian magazine published in the United States. It covers news, politics, social issues, and includes celebrity interviews and stories on entertainment, pop culture, style, travel, and a website that hosts an internet forum focusing on lesbian issues, active since 2000. Context_6 : Fresh Pond is a 62 acre pond in the Manomet section of Plymouth, Massachusetts. The average depth is 12 ft and the maximum depth is 30 ft . The southern shore of the pond is located in the Churchill Landing neighborhood, south of Manomet's business district and Manomet Bluffs, west of Fisherman's Landing, north of Cedar Bushes and Shallow Pond, and east of Beaver Dam Pond. Route 3A runs along the southeastern shore of the pond to its most southeastern point where it shoots away at a sharp curve known as the Brown Bear Curve, named after a defunct motel along the shore at that curve. A public beach, boat ramp, and a Native American burial site are located on the western shore of the pond on Bartlett Road, which has two intersections with Route 3A. The closer intersection is south of the Brown Bear Curve, while the other intersection is one mile (1.6 km) north, north of Manomet's business district. The pond is hydrologically associated with a cranberry bog operation located to the west of the pond. An unnamed brook (locally called "Hell's River" by some) heads west through the cranberry bog and ultimately leading to Beaver Dam Brook is the outflow of the pond. Context_7 : In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two main singular integral operators, the Hilbert transform and the Cauchy transform, can be defined for any smooth Jordan curve in the complex plane and are related by a simple algebraic formula. The Hilbert transform is an involution and the Cauchy transform an idempotent. The range of the Cauchy transform is the Hardy space of the bounded region enclosed by the Jordan curve. The theory for the original curve can be deduced from that on the unit circle, where, because of rotational symmetry, both operators are classical singular integral operators of convolution type. The Hilbert transform satisfies the jump relations of Plemelj and Sokhotski, which express the original function as the difference between the boundary values of holomorphic functions on the region and its complement. Singular integral operators have been studied on various classes of functions, including Hőlder spaces, L spaces and Sobolev spaces. In the case of L spaces—the case treated in detail below—other operators associated with the closed curve, such as the Szegő projection onto Hardy space and the Neumann–Poincaré operator, can be expressed in terms of the Cauchy transform and its adjoint. Context_8 : The tripling-oriented Doche–Icart–Kohel curve is a form of an elliptic curve that has been used lately in cryptography; it is a particular type of Weierstrass curve. At certain conditions some operations, as adding, doubling or tripling points, are faster to compute using this form. Context_9 : In thermodynamics, the limit of local stability with respect to small fluctuations is clearly defined by the condition that the second derivative of Gibbs free energy is zero. The locus of these points (the inflection point within a G-x or G-c curve, Gibbs free energy as a function of composition) is known as the spinodal curve. For compositions within this curve, infinitesimally small fluctuations in composition and density will lead to phase separation via spinodal decomposition. Outside of the curve, the solution will be at least metastable with respect to fluctuations. In other words, outside the spinodal curve some careful process may obtain a single phase system. Inside it, only processes far from thermodynamic equilibrium, such as physical vapor deposition, will enable one to prepare single phase compositions. The local points of coexisting compositions, defined by the common tangent construction, are known as binodal (coexistence) curve, which denotes the minimum-energy equilibrium state of the system. Increasing temperature results in a decreasing difference between mixing entropy and mixing enthalpy, thus, the coexisting compositions come closer. The binodal curve forms the bases for the miscibility gap in a phase diagram. Since the free energy of mixture changes with temperature and concentration, the binodal and spinodal meet at the critical or consulate temperature and composition. Context_10 : Closer is a British tabloid magazine published by Bauer Media Group. fact_1 : Closer is a British tabloid magazine published by Bauer Media Group. fact_2 : Curve is a lesbian magazine published in the United States. Question: Closer and Curve, is which type of publication?
Output (English): magazine