Bryozoans are almost entirely colony-forming animals. Many millions of individuals can form one colony. The colonies range from millimeters to meters in size, but the individuals that make up the colonies are tiny, usually less than a millimeter long. In each colony, different individuals have different functions. Some individuals gather up the food for the colony (autozooids), others depend on them (heterozooids). Some individuals are devoted to strengthening the colony (kenozooids), and still others to cleaning the colony (vibracula). There is only a single known solitary species, "Monobryozoon ambulans", which does not form colonies.
Fossil bryozoans first appear in the early Ordovician and had a huge adaptive radiation. They were abundant throughout the Palaeozoic era: they were one of the most dominant groups of Palaeozoic fossils. They were major components of seabed communities and, like modern-day bryozoans, played an important role in sediment stabilization and binding. They were food sources for many other benthic organisms. During the Lower Carboniferous (Mississippian) 354 to 323 million years ago, bryozoans were so common that their broken skeletons form entire limestone beds.
After a crash at the Permian/Triassic boundary, when almost all species went extinct, bryozoans recovered in the later Mesozoic to become as successful as before. The bryozoan fossil record has more than 15,000 species.
Most fossil bryozoans have mineralized skeletons. The skeletons of individual zooids vary from tubular to box-shaped and contain a terminal aperture from which the lophophore is protruded to feed. No pores are present in the great majority of Ordovician bryozoans, but skeletal evidence shows that epithelia were continuous from one zooid to the next.
One of the most important events during bryozoan evolution was the acquisition of a calcareous skeleton and the mechanism of tentacle protrusion. The rigidity of the outer body walls gave protection against predators, a greater degree of zooid connection, and the evolution of massive colony forms.
Placebo
A placebo is a treatment for a disease or condition which is deliberately ineffective. The motive usually is that if a person believes that a medicine, diet, or other treatment is good for himself or herself, then it is good for the person.
Sometimes sick people who receive a placebo feel like they are getting better, and sometimes their bodies actually do get better. When patients have that response, it is called the "placebo effect". The term "placebo effect" (or "placebo response") was introduced in 1920. It is the response of the subject which causes the observed effect, not the substance.
John Haygarth tested a placebo effect in the 18th century. It showed ""to a degree which has never been suspected, what powerful influence upon diseases is produced by mere imagination"".
Émile Coué, a French apothecary, working between 1882 and 1910, discovered what later came to be known as the "Placebo effect". He reassured his clients by praising each remedy's efficiency and leaving a small positive notice with each medication. In 1901 Coué began to study under hypnosis. In 1913, Coué and his wife founded "La Société Lorraine de Psychologie appliquée". His book "Self-mastery through conscious autosuggestion" was published in England (1920) and in the United States (1922).
Placebos are used as part of blind trials. Blind trials work like this: Some people are given the medicine or treatment being tested, and others are given the placebo. No one knows who gets the real treatment and who gets the placebo. They are "blind" to their treatment.
If researchers notice that the "treatment group" is different from the "placebo group" they will know that the difference is because of the treatment. Without a "placebo group" then researchers cannot know if those changes would have happened anyway, no matter which medicine people had taken.
Placebos can have real effects on patients: that is what "placebo effect" means. Since a landmark paper in 1955 the placebo effect has been recognised and accepted by some, and denied by others. However, there is no doubt that for certain conditions, the placebo effect does exist. Examples are:
Identity (mathematics)
In mathematics, the term identity has several important uses:
An equality in mathematical sense is only true under more particular conditions. For this, the symbol ≡ is sometimes used (note, however, that the same symbol can also be used for a congruence relation as well.)
A common example of the first meaning is the trigonometric identity
which is true for all real values of formula_7 (since the real numbers formula_8 are the domain of both sine and cosine), as opposed to
which is only true for certain values of formula_7 in a subset of the domain.
The concepts of "additive identity" and "multiplicative identity" are central to the Peano axioms.
The number 0 is the "additive identity" for integers, real numbers, and complex numbers. For the real numbers, for all formula_11
Similarly, The number 1 is the "multiplicative identity" for integers, real numbers, and complex numbers. For the real numbers, for all formula_11
A common example of an identity function is the identity permutation, which sends each element of the set formula_19 to itself.
These meanings are not mutually exclusive; for instance, the identity permutation is the identity element in the set of permutations of formula_19 under composition.
Equality
Equality can mean several things:
In sciences:
In humanities:
People and places:
Identity
Identity could mean:
Equality (mathematics)
In mathematics, two things are equal if and only if they are exactly the same in every way. That is, they have the same (mathematical) value and the same mathematical properties. Mathematicians use the equals sign (=) to say this. This defines a binary relation, equality. The statement ""x" = "y"" means that "x" and "y" are equal.
Equivalence in a more general sense is provided by the construction of an equivalence relation between two mathematical objects, that is, two mathematical objects are equivalent if they are related by this relation. In which case, the equivalence is often represented using the symbols formula_1 or formula_2.
A statement that two expressions denote equal quantities is an equation (or an equality). Equations are equal. Inequalities are unequal.
An equality is also a transitive relation. This means that if one object is equal to a second object, and the second object is equal to a third object, then the first object is equal to the third object as well.
Since a predicate is a way of describing something that is true, another way to say this is that if one thing that is true about a variable is not true about the other variable, then they are not "equal" as far as mathematical logic is concerned: two things are only equal if anything that is true about one has to be true about the other.
In geometry, the word congruence is often preferred. Numbers are equal, geometrical objects are congruent. Two shapes are congruent if one can be moved or rotated so that it fits exactly where the other one is. If shrinking or enlarging one of the two objects is needed, then they are not congruent. They are called "similar" instead. The congruence relation is often represented by the symbol formula_3, while the similarity relation is represented by the symbol formula_1.
In computer science, usually, the mathematical definition is used. Very often, the comparison is written "==" (and the assignment, the act of giving a value, is written as "=", or ":="). In object-oriented languages, or languages which have pointers, there is an additional problem. Those languages contain references (which are in fact pointers). If two such references do not reference exactly the same object, then they are different and "a == b" will be false in this case.