In any case, there is no special milling or rabbeting required for the panels.

The diagonalizable operator is the special case of this in which Af for each i.

The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of Theorem 10, a special case of this theorem.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

Richard Stewart is no special case.

And while every writer must be dealt with as a special case, the interested student will want to ask himself a number of questions about each.

In either case, it could call a special session of the Legislature later in 1961 to make another stab at raising additional revenues through a tax raiser.

Patrolman George Kimmell, of McClellan Station, said he would recommend a special safety citation for Ralph Sisk, 9230 Vernor east, a third grader at the Scripps School, for his assistance in the case.

It said the tax-freedom of the gain in this case stemmed not from the exempt status of the income but from a special rule on corporate liquidations.

To keep options available for lower case letters and other graphics, the special and numeric codes were arranged before the letters, and the letter " A " was placed in position 41 < sub > hex </ sub > to match the draft of the corresponding British standard.

ANOVA is considered to be a special case of linear regression

which in turn is a special case of the general linear model.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

They also meet in England where Poirot often helps Japp solve a case and lets him take credit in return for special favours.

note that the above online algorithm III is a special case of an algorithm that works for any partition of the sample into sets,:

In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.

In the special case where the field quantities are independent of the z-coordinate we can eliminate to get

By 1912, Ostwald noted that the allotropy of elements is just a special case of the phenomenon of polymorphism known for compounds, and proposed that the terms allotrope and allotropy be abandoned and replaced by polymorph and polymorphism.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

Amdahl's law is often conflated with the law of diminishing returns, whereas only a special case of applying Amdahl's law demonstrates ' law of diminishing returns '.

Some authors, however, consider alkaloids a special case of amines.

The only effect of lack of a center would then be to release the hydrogen atoms to occupy general, rather than special, positions along the ( 111 ) axis.

As a special case, the three naturally occurring isotopes of the element hydrogen are often specified as H for < sup > 1 </ sup > H ( protium ), D for < sup > 2 </ sup > H ( deuterium ), and T for < sup > 3 </ sup > H ( tritium ).

The hydrogen atom has special significance in quantum mechanics and quantum field theory as a simple two-body problem physical system which has yielded many simple analytical solutions in closed-form.

Again the Dirac equation may be solved analytically in the special case of a two-body system, such as the hydrogen atom.

For this reason, in early experiments a special reaction channel was chosen to facilitate the identification: the interaction of an antineutrino with one of the hydrogen nuclei in the water molecules.

Vessels lined with a highly gas-permeable material such as palladium ( which is a high-capacity hydrogen sponge ) create special outgassing problems.

He performed experiments to determine gas pressures during hydrogen explosions using a special chamber fitted with a piston, and was able to distinguish burning of mixtures of hydrogen and oxygen from true explosions.

Some sources state that sixteen chemical elements are required to support human biochemical processes by serving structural and functional roles as well as electrolytes: However, as many as 26 elements in total ( including the common hydrogen, carbon, nitron and oxygen ) are suggested to be used by mammals, as a result of studies of biochemical, special uptake, and metabolic handling studies.

This suggested that the Balmer formula for hydrogen might be a special case with and, where, the reciprocal of Balmer's constant ( this constant h is written B in the Balmer equation article, again to avoid confusion with Planck's constant ).

** Solutions to a special case of the quantum three-body problem known as the hydrogen molecule-ion were found standard quantum chemistry basis sets before realizing they all lead to the same unique analytical solution in terms of a generalization of the Lambert W function.

Gases used include mercury vapor, xenon, neon, and ( in special high-voltage applications or applications requiring very short switching times ) hydrogen.

When Slater entered the University of Rochester in 1917 he took physics courses and as a senior assisted in the physics laboratory and did his first independent research for a special honors thesis, a measurement of the dependence on pressure of the intensities of the Balmer lines of hydrogen.

Each photographic plate is a special black and white emulsion designed for low light conditions and is further enhanced for low light sensitivity by baking in a nitrogen and hydrogen atmosphere.

In 1891, the invention of the gas mantle by the Austrian chemist Carl Auer von Welsbach eliminated the need for special illuminating gas, a synthetic mixture of hydrogen and hydrocarbon gases produced by destructive distillation of bituminous coal or peat, to get bright shining flames.

A special case is arc welding, in which the hydrogen is released from moisture ( for example in the coating of the welding electrodes ; to minimize this, special low-hydrogen electrodes are used for welding high-strength steels ).

For example, vessels lined with a highly gas-permeable material such as palladium ( which is a high-capacity hydrogen sponge ) create special outgassing problems.

He also discovered an alternative to Feynman's time-sliced path integral construction which can be used to solve the path integral formulations of the hydrogen atom and the centrifugal barrier, i. e. to calculate their energy levels and eigenstates, as special cases of a general strategy for treating systems with singular potentials using path integrals.

The characteristic of those liquids to which Trouton ’ s rule cannot be applied is their special interaction between molecules such as hydrogen bonding.

In special cases other materials can be utilized ; for example, palladium membranes permit transport solely of hydrogen.

Sulfide stress cracking has special importance in gas and oil industry, as the materials being processed there ( natural gas and crude oil ) often contain considerable amount of hydrogen sulfide.

Afterward, the thioglycolate must be oxidized with a special solution of hydrogen peroxide or sodium bromate.