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The definition of the complex molecular multipole moment given above is the complex conjugate of the definition given in this article, which follows the definition of the standard textbook on classical electrodynamics by Jackson, except for the normalization.
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definition and complex
A more abstract definition, which is equivalent but more easily generalized to infinite-dimensional spaces, is to say that bras are linear functionals on kets, i. e. operators that input a ket and output a complex number.
Unlike the Muslim world, which has a geo-political and cultural definition that provides a primary identifier for a large swath of the world, Christendom is more complex.
# A biochemists ’ operational definition: Chromatin is the DNA / protein / RNA complex extracted from eukaryotic lysed interphase nuclei.
" Yet the definition according to the esthesic level does not allow that the sounds of classical music are complex, are noises, rather they are regular, periodic, even, musical sounds.
However, whether this is possible depends on how the field of complex numbers is derived in the first place: it may not be possible to distinguish a complex number from its conjugate ( say, 3 + i from 3-i ), since it is impossible to find a property of one that is not also a property of the other, without falling back on the underlying set-theoretic definition.
Although most often used for matrices whose entries are real or complex numbers, the definition of the determinant only involves addition, subtraction and multiplication, and so it can be defined for square matrices with entries taken from any commutative ring.
It is difficult to provide a single concise definition for dharma, as the word has a long and varied history and straddles a complex set of meanings and interpretations.
and in fact this can be used as the definition for the complex logarithm.
These formulas can even serve as the definition of the trigonometric functions for complex arguments x.
This is the same as the definition of the derivative for real functions, except that all of the quantities are complex.
An irreducibly complex system cannot be produced directly ( that is, by continuously improving the initial function, which continues to work by the same mechanism ) by slight, successive modifications of a precursor system, because any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional.
Since the actual physical surface of the Earth is too complex for mathematical analysis two levels of abstraction are employed in the definition of these coordinates.
" The definition can be extended to non-zero complex numbers, as explained below.
However, for many NLP problems, the definition of a gold standard is a complex task, and can prove impossible when inter-annotator agreement is insufficient.
In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
The meaning of terms that stand for complex properties can be given by using terms for their constituent properties in a definition ; simple properties cannot be defined, because they are made up only of themselves and there are no simpler constituents to refer to.
Eukaryotic cells are structurally complex, and by definition are organized, in part, by interior compartments that are themselves enclosed by lipid membranes that resemble the outermost cell membrane.
Because of its complex history and tendency to borrow from other musical and cultural forms, it has been argued that " it is impossible to bind rock music to a rigidly delineated musical definition.
Bernhard Riemann in his memoir " On the Number of Primes Less Than a Given Magnitude " published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.
Mircea Eliade writes, " A first definition of this complex phenomenon, and perhaps the least hazardous, will be: shamanism = ' technique of religious ecstasy '.
Due to the complex history of evolving meanings and contexts, there is no clear or agreed upon definition of the Third World and the term is now less popular than it was during the 1970s and 1980s.
Generalizations of this definition are possible, for instance to complex manifolds and algebraic varieties.
Taking that as the definition of the transfer function < ref > The transfer function is defined by in, e. g., requires careful disambiguation between complex vs. real values, which is traditionally influenced by the interpretation of abs ( H ( s )) as the gain and-atan ( H ( s )) as the phase lag.
definition and molecular
The use of average atomic masses derived from the standard atomic weights found on a standard periodic table will result in an average molecular mass, whereas the use of isotopic masses will result in a molecular mass consistent with the strict interpretation of the definition, i. e. that of a single molecule.
The molecular definition of a stem cell includes many more proteins and continues to be a topic of research.
A molecular dynamics simulation requires the definition of a potential function, or a description of the terms by which the particles in the simulation will interact.
This classification is based on a thorough definition of monophyla based on the most recent morphological and molecular evidence, and it solves the longstanding problems of paraphyly of the Caeciliidae in previous classifications without an exclusive reliance upon synonymy.
The typical definition of " prohormone " includes a steroidal molecule that has the opposite molecular structure to testosterone on either the 3a / b position or the 17b position.
Currently the authoritative molecular discipline in this field of study is protein-protein interactions ( PPI ), although the working definition does not preclude inclusion of other molecular disciplines such as those defined here.
In the fields of pharmacology and biochemistry, a small molecule is a low molecular weight organic compound which is by definition not a polymer.
There is no single definition of molecular similarity, however the concept may be defined according to the application and is often described as an inverse of a measure of distance in descriptor space.
As the gradient generated from this process is able to perform useful work these types of systems, by definition, are examples of molecular machinery.
Another definition of null allele concerning molecular markers, refers to such a marker in the case it can no longer be detected because of a mutation.
Today, there is some debate about the definition and even existence of the shape resonance in some systems observed with molecular spectroscopy.
In the same year, in collaboration with Lou Siminovitch, a trailblazer for molecular biology in Canada, they obtained evidence that these same marrow cells were capable of self-renewal, a crucial aspect of the functional definition of stem cells that they had formulated.
In the same year, in collaboration with Lou Siminovitch, a trailblazing Canadian molecular biologist, they obtained evidence that these cells were capable of self-renewal, a crucial aspect of the functional definition of stem cells that they had formulated.
definition and moment
( To be precise: for the definition of the dipole moment one should always consider the " dipole limit ", where e. g. the distance of the generating charges should converge to 0, while simultaneously the charge strength should diverge to infinity in such a way that the product remains a positive constant.
The astronomical new moon, sometimes known as the dark moon to avoid confusion, occurs by definition at the moment of conjunction in ecliptical longitude with the Sun, when the Moon is invisible from the Earth.
The exact point of intersection of the Earth's axis and the Earth's surface, at any given moment, is called the " instantaneous pole ", but because of the " wobble " this cannot be used as a definition of a fixed North Pole ( or South Pole ) when metre-scale precision is required.
The definition of torque states that one or both of the angular velocity or the moment of inertia of an object are changing.
By definition this is the largest number of concurrent system users that the system is expected to support at any given moment.
In discussions of the virial theorem, a different definition of moment of inertia is introduced, often qualified as moment of inertia about a point ( as opposed to an axis ).
The definition extends to any object X in n-dimensional space: its centroid is the intersection of all hyperplanes that divide X into two parts of equal moment.
The form of the definition involves a " product moment ", that is, the mean ( the first moment about the origin ) of the product of the mean-adjusted random variables ; hence the modifier product-moment in the name.
The 1949 book The God That Failed contains Louis Fischer's definition of " Kronstadt " as the moment in which communists or fellow-travelers decide not just to leave the Communist Party but to oppose it as anti-communists.
When the ball finally did get into the net it was at Shilton's end, in the first moment which formed part of the whole definition of Shilton's career.
The preferred definition of a magnetic moment has changed over time.
For example, in the current loop definition, the area is measured in square meters and I is measured in amperes, so the magnetic moment is measured in ampere – square meters ( A m < sup > 2 </ sub >).
The magnetic field between poles ( see figure for Magnetic pole definition ) is in the opposite direction to the magnetic moment ( which points from the negative charge to the positive charge ), while inside a current loop it is in the same direction ( see the figure to the right ).
By definition the moment vector is perpendicular to every displacement along the line, so d • m = 0, where "•" denotes the vector dot product.
1 − b + b ln b, hence ab ≤ e < sup > a </ sup > − b + b ln b for all non-negative a and b. This estimate is useful in large deviations theory under exponential moment conditions, because b ln b appears in the definition of relative entropy, which is the rate function in Sanov's theorem.
Although the status of Ceres is unknown at the moment in astrology, due to its new definition as a dwarf planet, it has been suggested as the ruler of Virgo or Taurus.
A more conventional definition of lead time in the supply chain management realm is the time from the moment the customer places an order ( the moment you learn of the requirement ) to the moment it is received by the customer.
The book contains Fischer's definition of " Kronstadt " as the moment in which some communists or fellow-travelers decide not just to leave the Communist Party but to oppose it as anti-communists.
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