Separate masks were necessary as there were too many cables and mechanics required for all the expressions to fit in one single mask.

This version included pictorial and musical questions but was otherwise mostly faithful to the mechanics of the original board game.

( In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1 ; otherwise it is identical to I.

The earliest use of what would now be called perturbation theory was to deal with the otherwise unsolvable mathematical problems of celestial mechanics: Newton's solution for the orbit of the Moon, which moves noticeably differently from a simple Keplerian ellipse because of the competing gravitation of the Earth and the Sun.

) The earliest use of perturbation theory was to deal with the otherwise unsolveable mathematical problems of celestial mechanics: Newton's solution for the orbit of the Moon, which moves noticeably differently from a simple Keplerian ellipse because of the competing gravitation of the Earth and the Sun.

By doing so, it is possible to handle certain systems, such as aspects of quantum mechanics, that would otherwise be even more complicated.

She is the head of the Technology Department, and specializes in mechanics and odd inventions, some of them blowing up or otherwise malfunctioning in rather hilarious ways.

Some limitations of mechanics ' liens for contractors are that in order to take advantage of the lien rights, the contractor must wait until any of the conditions occur, otherwise the lien will be considered premature:

In fluid mechanics, a splash is a sudden disturbance to the otherwise quiescent free surface of a liquid ( usually water ).

The referee ( called a " dungeon master ") is presented with mechanics for resolving character actions and combat, as well as a large list of " monsters " ( which generally means any creature, sapient or otherwise, which is of a race other than those available to player characters, although, creatures of these ' civilized ' races often make the most formidable and challenging ' monsters ') and treasures with which to reward the players.

But in the absence of a general demonstration of that principle, his results did not command the. confidence which they would otherwise have deserved, and it became desirable to have a theory more certain, and depending-solely on the fundamental laws of mechanics.

Atomic orbitals are the basic building blocks of the atomic orbital model ( alternatively known as the electron cloud or wave mechanics model ), a modern framework for visualizing the microscopic behavior of electrons in matter.

Ever since the origination of quantum mechanics, some theorists have searched for ways to incorporate additional determinants or " hidden variables " that, were they to become known, would account for the location of each individual impact with the target.

Enrico Fermi (; 29 September 1901 – 28 November 1954 ) was an Italian physicist, naturalized American later in his life, particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics.

Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen ( known collectively as EPR ) designed a thought experiment intended to reveal what they believed to be inadequacies of quantum mechanics.

According to the understanding of quantum mechanics known as the Copenhagen interpretation, measurement causes an instantaneous collapse of the wave function describing the quantum system into an eigenstate of the observable state that was measured.

Furthermore, Bob is only able to perform his measurement once: there is a fundamental property of quantum mechanics, known as the " no cloning theorem ", which makes it impossible for him to make a million copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results.

The discrepancy in the partition functions of distinguishable and indistinguishable particles was known as far back as the 19th century, before the advent of quantum mechanics.

Bernard d ' Espagnat a French theoretical physicist best known for his work on the nature of reality wrote a paper titled The Quantum Theory and Reality according to the paper: " The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment.

During the early modern period, scientists such as Galileo, Kepler, and especially Newton, laid the foundation for what is now known as classical mechanics.

Particles are bodies with little ( known ) internal structure, treated as mathematical points in classical mechanics.

In his PhD thesis project, Paul Dirac discovered that the equation for the operators in the Heisenberg representation, as it is now called, closely translates to classical equations for the dynamics of certain quantities in the Hamiltonian formalism of classical mechanics, when one expresses them through Poisson brackets, a procedure now known as canonical quantization.

In quantum mechanics, the particle in a box model ( also known as the infinite potential well or the infinite square well ) describes a particle free to move in a small space surrounded by impenetrable barriers.

In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as " quantum mechanics ".

Quantum mechanics ( QM – also known as quantum physics, or quantum theory ) is a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.

Einstein himself is well known for rejecting some of the claims of quantum mechanics.

The application of quantum mechanics to chemistry is known as quantum chemistry.

For instance, it is known from quantum mechanics that certain aspects of electromagnetism involve discrete particles — photons — rather than continuous fields.

With no solution for this problem known at the time, it appeared that a fundamental incompatibility existed between special relativity and quantum mechanics.

Quantum gravity ( QG ) is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics ( describing three of the four known fundamental interactions ) with general relativity ( describing the fourth, gravity ).

* Second, it is not clear how to determine the gravitational field of a particle, since under the Heisenberg uncertainty principle of quantum mechanics its location and velocity cannot be known with certainty.

Einstein discerned two fundamental propositions that seemed to be the most assured, regardless of the exact validity of the ( then ) known laws of either mechanics or electrodynamics.

However, entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.

The fundamental postulate in statistical mechanics ( also known as the equal a priori probability postulate ) is the following:

Over time, the term stuck in popularizations of quantum physics to describe a theory that would unify or explain through a single model the theories of all fundamental interactions and of all particles of nature: general relativity for gravitation, and the standard model of elementary particle physics — which includes quantum mechanics — for electromagnetism, the two nuclear interactions, and the known elementary particles.

In the late 1920s, the new quantum mechanics showed that the chemical bonds between atoms were examples of ( quantum ) electrical forces, justifying Dirac's boast that " the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known ".

The term wire is also used more loosely to refer to a bundle of such strands, as in ' multistranded wire ', which is more correctly termed a wire rope in mechanics, or a cable in electricity.

Such nonuniform traveling waves are common in many physical problems, including the mechanics of the cochlea and waves on hanging ropes.

There is one exception to the above statement as has been pointed out, and that is that fluids can relax by flowing into fields of lower rates of shear, so the statement should be modified by stating that the mechanics are similar.

If the mechanics are similar, we can also infer that the thermodynamics will also be similar.

These opportunities are to be found in certain cities in such crafts as auto mechanics, carpentry, drafting, electrical work, tool-and-die work, and sheet-metal work.

Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics.

In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space.

These measured positions are then compared with those calculated by the laws of celestial mechanics: an assembly of calculated positions is often referred to as an ephemeris, in which distances are commonly calculated in astronomical units.

Some bicycle parts, particularly hub-based gearing systems, are complex, and many cyclists prefer to leave maintenance and repairs to professional bicycle mechanics.

Linear operators are ubiquitous in the theory of quantum mechanics.

Each incarnation of the BRP rules has changed or added to the core ideas and mechanics, so that games are not identical.

Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical ( i. e. non-quantum ) mechanics.

Ignoring quantum mechanics, the two pictures are equivalent: any

Albert Einstein, in 1922, said regarding contemporary theories of superconductivity that “ with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas ”

Continuum mechanics deals with physical properties of solids and fluids which are independent of any particular coordinate system in which they are observed.

In continuum mechanics a body is considered stress-free if the only forces present are those inter-atomic forces ( ionic, metallic, and van der Waals forces ) required to hold the body together and to keep its shape in the absence of all external influences, including gravitational attraction.

Therefore, the stresses considered in continuum mechanics are only those produced by deformation of the body, sc.

Even larger molecules are treated by classical mechanics methods that employ what are called molecular mechanics.

The Magliozzis are long-time car mechanics.

C *- algebras are now an important tool in the theory of unitary representations of locally compact groups, and are also used in algebraic formulations of quantum mechanics.