Transcendental number

In mathematics, a transcendental number is a complex number that is not algebraic, that is, not a solution of a non-zero polynomial equation with rational coefficients. In other words, transcendental numbers are numbers that do not arise from Euclidean geometry or ordinary algebraic expressions.

The most prominent examples of transcendental numbers are π and e. Only a few classes of transcendental numbers are known, indicating that it can be extremely difficult to show that a given number is transcendental.

However, transcendental numbers are not rare: indeed, almost all real and complex numbers are transcendental, since the algebraic numbers are countable, but the sets of real and complex numbers are uncountable. All transcendental numbers are irrational, since all rational numbers are algebraic. (The converse is not true: not all irrational numbers are transcendental.)

Demography

Demography is the statistical study of all populations. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space (see population dynamics). It encompasses the study of the size, structure and distribution of populations, and spatial and/or temporal changes in them in response to birth, death, migration and aging.

Human demography is the most well known discipline of demography, and typically what people refer to when using the term demography. Demographic analysis can be applied to whole societies or to groups defined by criteria such as education, nationality, religion and ethnicity. In academia, demography is often regarded as a branch of either anthropology, economics, or sociology. Formal demography limits its object of study to the measurement of populations processes, while the more broad field of social demography population studies also analyze the relationships between economic, social, cultural and biological processes influencing a population.

The term demographics is often used erroneously for demography, but refers rather to selected population characteristics as used in government, marketing or opinion research, or the demographic profiles used in such research.

Ecozone

An ecozone or biogeographic realm is the largest scale biogeographic division of the earth's surface based on the historic and evolutionary distribution patterns of plants and animals. Ecozones represent large areas of the earth's surface where plants and animals developed in relative isolation over long periods of time, and are separated from one another by geologic features, such as oceans, broad deserts, or high mountain ranges, that formed barriers to plant and animal migration. Ecozones correspond to the floristic kingdoms of botany or zoogeographic regions of mammal zoology. Simply they are a definition of the plants and animals in a region further divided by the land form region. (Example the taiga ecozone in Canada is divided into the taiga plains, and taiga shield.)

Ecozones are characterized by the evolutionary history of the plants and animals they contain. As such, they are distinct from biomes, also known as major habitat types, which are divisions of the earth's surface based on life form, or the adaptation of plants and animals to climatic, soil, and other conditions. Biomes are characterized by similar climax vegetation, regardless of the evolutionary lineage of the specific plants and animals. Each ecozone may include a number of different biomes. A tropical moist broadleaf forest in Central America, for example, may be similar to one in New Guinea in its vegetation type and structure, climate, soils, etc., but these forests are inhabited by plants and animals with very different evolutionary histories.

The patterns of plant and animal distribution in the world's ecozones was shaped by the process of plate tectonics, which has redistributed the world's land masses over geological history.

The term ecozone, as used here, is a fairly recent development, and other terms, including kingdom, realm, and region, are used by other authorities to denote the same meaning. J. Schultz uses the term "ecozone" to refer his classification system of biomes.

Skin testing

For assessing the presence of allergen-specific IgE antibodies, allergy skin testing is preferred over blood allergy tests because it is more sensitive and specific, simpler to use, and less expensive.Skin testing is also known as "puncture testing" and "prick testing" due to the series of tiny puncture or pricks made into the patient's skin. Small amounts of suspected allergens and/or their extracts (pollen, grass, mite proteins, peanut extract, etc.) are introduced to sites on the skin marked with pen or dye (the ink/dye should be carefully selected, lest it cause an allergic response itself). A small plastic or metal device is used to puncture or prick the skin. Sometimes, the allergens are injected "intradermally" into the patient's skin, with a needle and syringe. Common areas for testing include the inside forearm and the back. If the patient is allergic to the substance, then a visible inflammatory reaction will usually occur within 30 minutes. This response will range from slight reddening of the skin to a full-blown hive (called "wheal and flare") in more sensitive patients. Interpretation of the results of the skin prick test is normally done by allergists on a scale of severity, with +/- meaning borderline reactivity, and 4+ being a large reaction. Increasingly, allergists are measuring and recording the diameter of the wheal and flare reaction. Interpretation by well-trained allergists is often guided by relevant literature.[35] Some patients may believe they have determined their own allergic sensitivity from observation, but a skin test has been shown to be much better than patient observation to detect allergy.

If a serious life threatening anaphylactic reaction has brought a patient in for evaluation, some allergists will prefer an initial blood test prior to performing the skin prick test. Skin tests may not be an option if the patient has widespread skin disease or has taken antihistamines sometime the last several days.

DNA replication

DNA replication is the process of copying a double-stranded DNA molecule to form two double-stranded molecules. The process of DNA replication is a fundamental process used by all living organisms as it is the basis for biological inheritance. As each DNA strand holds the same genetic information, both strands can serve as templates for the reproduction of the opposite strand. The template strand is preserved in its entirety and the new strand is assembled from nucleotides. This process is called "semiconservative replication". The resulting double-stranded DNA molecules are identical; proofreading and error-checking mechanisms exist to ensure near perfect fidelity. In a cell, DNA replication must happen before cell division can occur. DNA synthesis begins at specific locations in the genome, called "origins", where the two strands of DNA are separated. RNA primers attach to single stranded DNA and the enzyme DNA polymerase extends the primers to form new strands of DNA, adding nucleotides matched to the template strand. The unwinding of DNA and synthesis of new strands forms a replication fork. In addition to DNA polymerase, a number of other proteins are associated with the fork and assist in the initiation and continuation of DNA synthesis.

DNA replication can also be performed artificially, using the same enzymes used within the cell. DNA polymerases and artificial DNA primers are used to initiate DNA synthesis at known sequences in a template molecule. The polymerase chain reaction (PCR), a common laboratory technique, employs artificial synthesis in a cyclic manner to rapidly and specifically amplify a target DNA fragment from a pool of DNA.