Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

Although it is sometimes used as a ' distance metric ', KL divergence is not a true metric since it is not symmetric and does not satisfy the triangle inequality ( making it a semi-quasimetric ).

Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory.

Although they also have a toroidal magnetic field topology, stellarators are distinct from tokamaks in that they are not azimuthally symmetric.

Although their shell may be so fine as to be transparent, it is nevertheless calcareous ; their shells are bilaterally symmetric and can vary widely in shape: coiled, needle-like, triangular, globulous.

Although US export regulations historically restricted key lengths to 56-bit symmetric keys ( e. g. Data Encryption Standard ), these restrictions are no longer in place, so modern symmetric algorithms typically use computationally stronger 128-to 256-bit keys.

Although their definition involved a choice of basis and consideration of the corresponding real symmetric matrix A, Sylvester's law of inertia means that they are invariants of the quadratic form q.

Although the X-ray target is removed in electron mode, the beam must be fanned out by sets of thin scattering foils in order to achieve flat and symmetric dose profiles in the treated tissue.

Although one can take the star of any tensor, the result is antisymmetric, since the symmetric components of the tensor completely cancel out when contracted with the completely anti-symmetric Levi-Civita symbol.

Although Desargues ' theorem chooses different roles for these ten lines and points, the Desargues configuration itself is more symmetric: any of the ten points may be chosen to be the center of perspectivity, and that choice determines which six points will be the vertices of triangles and which line will be the axis of perspectivity.

Although it is often intuited as a metric or distance, the KL divergence is not a true metric — for example, it is not symmetric: the KL from P to Q is generally not the same as the KL from Q to P. However, its infinitesimal form, specifically its Hessian, is a metric tensor: it is the Fisher information metric.

Although a general tridiagonal matrix is not necessarily symmetric or Hermitian, many of those that arise when solving linear algebra problems have one of these properties.

Although the fatty acid is symmetric, the resulting eicosanoids are chiral ; the oxidation proceeds with high stereospecificity.

Although radial symmetry is usually given as a defining characteristic of radiates, a few members of the class Anthozoa, which are now considered as the most basal and oldest group of cnidarians, are actually bilateral symmetric.

Although he initially assumed a symmetric affine connection, like Einstein he later considered the nonsymmetric field.

Although originally described in terms of symmetric Turing machines, that equivalent formulation is very complex, and the reducibility definition is what is used in practice.

Although this version is considered the " standard " version performed today, research into Janáček's manuscripts suggests that the Intrada was intended to be played at the beginning of the work as well, creating a symmetric nine-movement form with the Vĕruju at its center.

Although it has a symmetric structure, Ionizing one phosphate happens at a very different levels of acidity than ionizing both: pK < sub > 1 </ sub > = 3 and pK < sub > 2 </ sub > > 7. 5.

Although distortion can be irregular or follow many patterns, the most commonly encountered distortions are radially symmetric, or approximately so, arising from the symmetry of a photographic lens.

Although some of these houses and colleges have established links to various Oxford and Cambridge colleges, the ties are not transitive so it is impossible to make a four – column chart.

Although the primary mathematical properties of the middle number at the center of the Lo Shu, and the interrelation of all the other numbers to it, might seem enough to account for the deep fascination which the Lo Shu held for the Old Chinese philosophers, this was actually only a beginning of wonders.

Although earlier precursors to this presentation exist, its invention is generally credited to Russian chemist Dmitri Mendeleev in 1869, who intended the table to illustrate recurring trends in the properties of the elements.

Although all of these behaviors merge into each other seamlessly in various bonding situations so that there is no clear line to be drawn between them, nevertheless behaviors of atoms become so qualitatively different as the character of the bond changes quantitatively, that it remains useful and customary to differentiate between the bonds that cause these different properties of condensed matter.

Although water forms the large majority of the cytosol, its structure and properties within cells is not well understood.

Although formal certification of his freedom from Burghley's control was deferred until May 1572, Oxford was finally granted the income of £ 666 which his father had intended him to have earlier, but properties set aside to pay his father's debts would not come his way for another decade.

Although there are important differences between them, all of them were materialists who believed that the world was made up of a single substance, matter, the motions and properties of which could be used to explain all phenomena.

Although these experiments cannot detect individual gravitons, they might provide information about certain properties of the graviton.

Although the properties of sugar had been known in India in antiquity, it was not traded as a sweetener until industrial-scale production developed in the 6th century.

Although a DNA molecule cannot exist without physical properties, these properties are constrained by higher level ordering principles.

Although spun out of licensed properties, Shang-Chi is a Marvel-owned character and has been firmly established as a part of the Marvel Universe with guest appearances in numerous other titles, such as Marvel Team-Up, Marvel Knights and X-Men.

Although muonium is short-lived, physical chemists use it in a modified form of electron spin resonance spectroscopy for the analysis of chemical transformations and the structure of compounds with novel or potentially valuable electronic properties.

Although spin and the Pauli principle can only be derived from relativistic generalizations of quantum mechanics the properties mentioned in the last two paragraphs belong to the basic postulates already in the non-relativistic limit.

Although early humans gathered uncultivated plant materials for food and employed the medicinal properties of vegetation for healing, most modern human use of plants is through agriculture.

Although the term polymer is sometimes taken to refer to plastics, it actually encompasses a large class of compounds comprising both natural and synthetic materials with a wide variety of properties.

Although precursors exist, the current table is generally credited to Dmitri Mendeleev, who developed it in 1869 to illustrate periodic trends in the properties of the then-known elements ; the layout has been refined and extended as new elements have been discovered and new theoretical models developed to explain chemical behavior.

Although many proteins can fold unassisted, simply through the chemical properties of their amino acids, others require the aid of molecular chaperones to fold into their native states.

Although similar to alcohols, phenols have unique properties and are not classified as alcohols ( since the hydroxyl group is not bonded to a saturated carbon atom ).

Although these polymers have other properties of of contemporary protein as well, identity with the latter is not a necessary inference ". Some theories of abiogenesis propose that proteinoids were a precursor to the first living cells.

Although these first studies focused on the counterintuitive properties of entanglement, with the aim of criticizing quantum mechanics, eventually entanglement was verified experimentally, and recognized as a valid, fundamental feature of quantum mechanics.

Although radium is not as well studied as its stable lighter homologue barium, the two elements have very similar properties.

Although scopolamine is sometimes portrayed in the media as a dangerous drug, its anticholinergic properties give it some legitimate medical applications in minute doses.

Although diamond s ( top left ) and graphite ( top right ) are identical in chemical composition — being both pure carbon — X-ray crystallography revealed the arrangement of their atoms ( bottom ) accounts for their different properties.

Although isotopes of a single element are normally described as having the same chemical properties, this is not strictly true.

Although a supersolid is a solid, it exhibits so many characteristic properties different from other solids that many argue it is another state of matter.