For the case of Jupiter, the radio emission spectrum is definitely not like the spectrum of a black-body radiator, and it seems very likely that the radiation reaching the earth is a combination of thermal radiation from the atmosphere and non-thermal components.

For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.

For the case of a purely inertial autonavigator consisting of three restrained gyros, a coordinate system is used where the sensitive axis of the X accelerometer is parallel to the east-west direction at the base point, and the Y accelerometer sensitive axis is parallel to the north-south direction at the base point.

For the incremental case ( i. e., ), this simplifies to:

For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.

For private suits only the victims or their families could prosecute, while for public suits anyone ( ho boulomenos, ' whoever wants to ' i. e. any citizen with full citizen rights ) could bring a case since the issues in these major suits were regarded as affecting the community as a whole.

For example a two dimensional array with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression: ( in a row major language ) and ( in a column major language ) in the case of a zero-based indexing system.

For this last case, the cohesive fracture can be said to be “ cohesive near the interface ”.

For some specializations within conservation this is still the case.

For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.

For the simple case where the direction of the light beam along the line SE is perpendicular to the motion of the observer then only light emitted at an angle equal to the arc cosine of the ratio of the observer's speed to the speed of light will reach the telescope.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

For larger quantities one must go to a beverage distributor which sells beer only by the case or keg.

For example, bacteria catalyse the breakdown of the mineral pyrite ( FeS < sub > 2 </ sub >) by oxidising the sulfur and metal ( in this case ferrous iron, ( Fe < sup > 2 +</ sup >)) using oxygen.

For case of single stranded DNA / RNA units of nucleotides are used, abbreviated nt ( or knt, Mnt, Gnt ), as they are not paired.

For example in the case of anthrax, it is likely that by 24 – 36 hours after an attack, some small percentage of individuals ( those with compromised immune system or who had received a large dose of the organism due to proximity to the release point ) will become ill with classical symptoms and signs ( including a virtually unique chest X-ray finding, often recognized by public health officials if they receive timely reports ).

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

For case,

For example, most areas of law in most Anglo-American jurisdictions include " statutory law " enacted by a legislature, " regulatory law " promulgated by executive branch agencies pursuant to delegation of rule-making authority from the legislature, and common law or " case law ", i. e., decisions issued by courts ( or quasi-judicial tribunals within agencies ).

For example, civil law can be clearer than case law when the legislature has had the foresight and diligence to address the precise set of facts applicable to a particular situation.

For example, in the case of acetic acid dissolved in water and forming acetate and hydronium ions,

For example, the 1972 Constitution designates the Prime Minister as constitutional successor of the Head of State in case of incapacity, death, resignation or unaccountable absence of the incumbent.

For example, in one case, a prominent Chicana feminist writer and poet has indicated the following subjective meaning through her creative work.

For example in the Netherlands, the law assumes the stronger participant ( e. g. a car driver ) is liable in the case of an accident with a weaker participant ( e. g. a cyclist ) unless it can be proved that the cyclist's behavior could not have been expected.

) For the casuist, the circumstances of a case are essential for evaluating the proper response.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For example, in the Schrödinger picture, there is a linear operator U with the property that if an electron is in state right now, then in one minute it will be in the state, the same U for every possible.

For example, observable physical quantities are represented by self-adjoint operators, such as energy or momentum, whereas transformative processes are represented by unitary linear operators such as rotation or the progression of time.

For example, the condition number associated with the linear equation

For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.

For any n, the divergence is a linear operator, and it satisfies the " product rule "

For the statistics usage, see hierarchical linear modeling.

For a flow, the vector field Φ ( x ) is a linear function of the position in the phase space, that is,

For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about endomorphisms in any category.

For other ways to solve this kind of equations, see below, System of linear equations.

For example, according to ancient Hebrew belief, life takes a linear ( and not cyclical ) path ; the world began with God and is constantly headed toward God ’ s final goal for creation.

For an overview of a linear implementation of this framework, see linear regression.

For other examples of quotient objects, see quotient ring, quotient space ( linear algebra ), quotient space ( topology ), and quotient set.

For example, a bijective linear map is an isomorphism between vector spaces, and a bijective continuous function whose inverse is also continuous is an isomorphism between topological spaces, called a homeomorphism.

For molecules with N atoms in them, linear molecules have 3N – 5 degrees of vibrational modes, whereas nonlinear molecules have 3N – 6 degrees of vibrational modes ( also called vibrational degrees of freedom ).

For every finite dimensional matrix Lie algebra, there is a linear group ( matrix Lie group ) with this algebra as its Lie algebra.

For a population of size n, with a sequence of values y < sub > i </ sub >, i = 1 to n, that are indexed in non-decreasing order ( y < sub > i </ sub > ≤ y < sub > i + 1 </ sub >), the Lorenz curve is the continuous piecewise linear function connecting the points ( F < sub > i </ sub >, L < sub > i </ sub > ), i

For linear relations, regression analyses here are based on forms of the general linear model.

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

For example, consider the case where the function is a linear function of the form

For example, bacterial chromosomes, plasmids, mitochondrial DNA and chloroplast DNA are usually circular double-stranded DNA molecules, while chromosomes of the eukaryotic nucleus are usually linear double-stranded DNA molecules.

For example, in classical mechanics, the derivative is used ubiquitously, and in quantum mechanics, observables are represented by linear operators.