More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory.

More sophisticated techniques will show proportional differences in optical density.

More sophisticated models can be made using a combination of etched sheets of brass and low temperature castings.

More modern and sophisticated approaches seek to maintain the idea of the morpheme while accommodating non-concatenative, analogical, and other processes that have proven problematic for Item-and-Arrangement theories and similar approaches.

More problematic, and never properly addressed by Cumont or his successors, is how real-life Roman Mithraists subsequently maintained a quite complex and sophisticated Iranian theology behind an occidental facade.

More sophisticated versions may make specific desired changes to the deck's order, while still appearing to be an innocuous normal cut.

More recently, structural equation modeling and path analysis represent more sophisticated approaches to working with large covariance matrices.

More sophisticated methods of signal processing are also used in order to recover useful radar signals.

More sophisticated routers, such as enterprise routers, connect large business or ISP networks up to the powerful core routers that forward data at high speed along the optical fiber lines of the Internet backbone.

Other biographers, such as Peter Ackroyd, have offered a more sympathetic picture of More as both a sophisticated philosopher and man of letters, as well as a zealous Catholic who believed in the authority of the Holy See over Christendom.

More sophisticated transformations include set operations on closed shapes ( union, difference, intersection, etc.

More sophisticated tests use a torsion balance of a type invented by Eötvös.

More sophisticated attackers use DDoS tools for the purposes of extortioneven against their business rivals.

More sophisticated cryptographic systems, such as Anonymous Digital credentials, enable users to communicate pseudonymously ( i. e., by identifying themselves by means of pseudonyms ).

More sophisticated methods may be used to optimize resources across campaigns so that one may predict to which channel and to which offer an individual is most likely to respond ( across all potential offers ).

More sophisticated methods are used in practice for natural language generation.

More recent studies using more sophisticated methodologies have generally refuted these findings: density, land use and public transport accessibility can influence travel behaviour, although social and economic factors, particularly household income, usually exert a stronger influence.

More sophisticated devices which use a graphical screen with touch sensing or screen-edge buttons provide flexibility while minimizing space used: the meaning of the buttons can change with the screen, and selection involves the natural behavior of pointing at what's desired.

More experienced players understand the power of the bishop, but a more sophisticated understanding is required.

More sophisticated tools, worked on both sides of the stone and dating to 600, 000 BC, were found in the Cave of Escale at Saint Estėve-Janson, and tools from 400, 000 BC and some of the first fireplaces in Europe were found at Terra Amata in Nice.

More sophisticated forecasting can include other aspects of traveler decisions, including auto ownership, trip chaining ( the decision to link individual trips together in a tour ) and the choice of residential or business location ( known as land use forecasting ).

More sophisticated systems allow for more information such as lateral and longitudinal acceleration ( or G-force ), throttle position, steering wheel position and brake pressure.

More sophisticated methods were developed and later adopted elsewhere.

More sophisticated turbines ( such as those found in modern jet engines ) may have multiple shafts ( spools ), hundreds of turbine blades, movable stator blades, and a vast system of complex piping, combustors and heat exchangers.

More specifically, " habitats can be defined as regions in environmental space that are composed of multiple dimensions, each representing a biotic or abiotic environmental variable ; that is, any component or characteristic of the environment related directly ( e. g. forage biomass and quality ) or indirectly ( e. g. elevation ) to the use of a location by the animal.

More recently, fullerenes have been detected in outer space.

: More generally, any Euclidean space < sup > n </ sup > with the dot product is an inner product space

More ubiquitous in the late 19th and early 20th centuries, kerosene space heaters were often built into kitchen ranges, and kept many farm and fishing families warm and dry through the winter.

More formally, the Klein bottle is the quotient space described as the square × with sides identified by the relations for and for:

More generally, a meteorite on the surface of any celestial body is a natural object that has come from elsewhere in space.

More operating system code was moved out of the kernel and into user space, resulting in a much smaller kernel and the rise of the term microkernel.

More specifically, there are no elementary events outside the sample space.

More significantly, its curving eastern facade marked the beginnings of the Runden Platz ( Round Platz ), a huge circular public space at the point where the North-South Axis and Potsdamer Straße intersected.

More precisely, space can be viewed as an extremely fine fabric or network " woven " of finite loops.

More generally, if one has a large number of copies of the same system, then the state of this ensemble is described by a density matrix, which is a positive matrix, or a trace class when the state space is infinite dimensional, and has trace 1.

More generally, if a linear operator on a vector space ( possibly infinite-dimensional ) has finite-dimensional range ( e. g., a finite-rank operator ), then the rank of the operator is defined as the dimension of the range.

More generally, in a metric space ( E, d ), the sphere of center x and radius is the set of points y such that.

More generally, a ( topological ) surface with boundary is a Hausdorff topological space in which every point has an open neighbourhood homeomorphic to some open subset of the upper half-plane H < sup > 2 </ sup >.

More precisely, for every Tychonoff space X, there exists a compact Hausdorff space K such that X is homeomorphic to a subspace of K.

More generally, if a given manifold is thought of as an embedded submanifold of Euclidean space one can picture the tangent space in this literal fashion.

More generally, if F is a subset of the algebraic dual space, then the initial topology of X with respect to F, denoted by σ ( X, F ), is the weak topology with respect to F.

More specifically, CORBA is a mechanism in software for normalizing the method-call semantics between application objects residing either in the same address space ( application ) or remote address space ( same host, or remote host on a network ).

More commonly, where the lensing mass is complex ( such as galaxy groups and clusters ) and does not cause a spherical distortion of space – time, the source will resemble partial arcs scattered around the lens.