According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

If the addition of a functional group takes place at the less substituted carbon atom of the double bond, then the electrophilic substitution with acids is not possible.

Functionalization is the addition of functional groups onto the surface of a material by chemical synthesis methods.

" In general, Harmonist buildings, in addition to being sturdy and functional, were centrally heated, economical to maintain, and resistant to fire, weather, and termites.

In addition, PTs work with individuals to prevent the loss of mobility before it occurs by developing fitness and wellness-oriented programs for healthier and more active lifestyles, providing services to individuals and populations to develop, maintain and restore maximum movement and functional ability throughout the lifespan.

In addition to its function in cost accounting, the WBS also helps map requirements from one level of system specification to another, for example a requirements cross reference matrix mapping functional requirements to high level or low level design documents.

In addition to the aforementioned potential for acute kidney injury, animal studies suggest these acute injuries may progress to scar formation, resulting in loss of functional renal volume.

In addition, the pars reticulata also inhibits dopaminergic activity in the pars compacta via axon collaterals, although the functional organization of these connections remains unclear.

In addition to furniture's functional role, it can serve a symbolic or religious purpose.

In addition, women who have some sort of functional disorder affecting the reproductive system ( e. g., endometriosis, polycystic ovary syndrome, cancer of the reproductive organs ) can go into menopause at a younger age than the normal timeframe.

In addition, they are functional in mediating communication pathways in cell types such as adrenal chromaffin, platelets, and neural cells.

In addition, thymic stromal cells allow for the selection of a functional and self-tolerant T-cell repertoire.

In addition to the greater size of the queen, she has a functional set of ovaries, and a spermatheca which stores and maintains sperm after she has mated.

" This change affected the entire conduct of warfare, since it required the officers to train men in addition to leading them, decreased the size of the basic infantry unit for functional purposes since more specific orders had to be given in battle, and the decrease in herd behavior required more initiative and intelligence from the average soldier.

In addition, children under the age of 18 can be determined to be disabled for SSI purposes " if the individual has a medically determinable impairment or combination of impairments that causes marked or severe functional limitation ( s ), and can be expected to result in death, or has lasted or can be expected to last for a continuous period of not less than 12 months.

In addition to the basic C API, there are also Python, Java, Lisp, Tcl and C ++ among other bindings, like one from Haskell which allows control of Csound from a purely functional environment.

in addition to the actual functional components.

A halogen addition reaction is a simple organic reaction where a halogen molecule is added to the carbon – carbon double bond of an alkene functional group.

A proof written as a functional program: the proof of commutativity of addition on natural numbers in the proof assistant Coq.

In addition to accepting displaced students, university officials also took on the challenge of housing and managing many hurricane victims, converting the Pete Maravich Assembly Center into a fully functional field hospital.

Nice aims to be feature-rich, and as such, in addition to the common features of modern object-oriented programming languages, it implements contracts in the style of Eiffel, class extensibility through multimethods, and many concepts drawn from functional programming such as anonymous functions, tuples, pattern matching (“ value dispatch ”), and parametric polymorphism.

In addition, Frits Zernike proposed still another functional decomposition based on his Zernike polynomials, defined on the unit disc.

The late music is tonal, anticipating the changes in musical language of the early Baroque, during which functional tonality crystallized out of the pre-tonal universe of the late Renaissance ; in addition these late compositions are mainly homophonic, with only occasional polyphonic passages appearing as an animating contrast.

It appears that an Orthodox girl in the community disrupted plans for an outing sponsored by one of the Jewish service groups because she would not travel on Saturday and, in addition, required kosher food.

In addition, the arts benefited from the patronage of such influential groups as the Medici family of Florence, the Sforza family of Milan and Popes Julius II and Leo X.

Such modifications can also determine the localization of the protein, e. g., the addition of long hydrophobic groups can cause a protein to bind to a phospholipid membrane.

Xylenol has two methyl groups in addition to the hydroxyl group, and, for this structure, 6 isomers exist.

In addition to opposing the ADA on grounds of cost, church groups like the National Association of Evangelicals testified against the ADA's Title I ( employment ) provisions on grounds of religious liberty.

Abelian groups generalize the arithmetic of addition of integers.

In one common challenge students are divided into groups and given a quantity of wood sticks, a distance to span, and glue, and then asked to construct a bridge that will be tested to destruction by the progressive addition of load at the center of the span.

In addition to its professional staff, the SIG is supported by its more than 16, 500 member companies who participate in the various working groups that produce the standardization documents and oversee the qualification process for new products and help to evangelize the technology.

Other examples are readily found in different areas of mathematics, for example, vector addition, matrix multiplication and conjugation in groups.

In addition to allowing extra room for the passage of muscles to work the lower jaw, the zygomatic arch also allows for differentiation of separate muscle groups to be involved in biting and chewing.

In addition, the CIA's website reports that the agency aided three different Chilean opposition groups during that time period and " sought to instigate a coup to prevent Allende from taking office ".

In addition, the navy's riverine brigade has been patrolling waterways more aggressively in order to establish safer river transport in the more remote areas in the south and east of the country that are controlled by rebel groups.

In addition, by looking at stylistic changes of ceramics over time is it possible to separate ( seriate ) the ceramics into distinct diagnostic groups ( assemblages ).

In addition to its kehillot and chavurot maintains a kibbutz ( Kibbutz Hanaton ), a moshav ( Moshav Shorashim ), and IDF Garinim, Masorti groups within the Israeli Defense Forces.

In addition, there are numerous commissions and leading groups.

In addition to these, the arrival of new groups of Vikings from northern and western Europe was still commonplace.

In addition to the obscenity lawsuit and being ignored by the mainstream media ( MTV and most radio stations gave such groups scant notice, not to mention airplay ), the band became increasingly disillusioned with the underground scene as well.

These age groups roughly correspond to those standardized by FINA, with the addition of a youngest age group for divers 9 and younger, Group E, which does not compete nationally and does not have a tower event ( although divers of this age may choose to compete in Group D ).

The Estonian dialects are divided into two groups – the northern and southern dialects, usually associated with the cities of Tallinn in the north and Tartu in the south, in addition to a distinct kirderanniku dialect, that of the northeastern coast of Estonia.

In addition to organized sports betting, both legal and illegal, there are many side-betting games played by casual groups of spectators, such as NCAA Basketball Tournament Bracket Pools, Super Bowl Squares, Fantasy Sports Leagues with monetary entry fees and winnings, and in-person spectator games like Moundball.

Palmitoylation is the covalent modification of cysteine ( Cys ) residues via addition of hydrophobic acyl groups, and has the effect of targeting the receptor to cholesterol-and sphingolipid-rich microdomains of the plasma membrane called lipid rafts.

In addition to metalcore some early screamo groups, like Circle Takes the Square and Orchid, have been associated with grindcore by some commentators.

In addition to for-profit theatre troupes, there are several college-based improv groups in the United States that are becoming popularized as a result of programs such as Whose Line is it Anyway ?.