Generalizations of the derivativeIn mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, geometry, etc. The Fréchet derivative defines the derivative for general normed vector spaces . Briefly, a function , an open subset of , is called Fréchet differentiable at if there exists a bounded linear operator such that Functions are defined as being differentiable in some open neighbourhood of , rather than at individual points, as not doing so tends to lead to many pathological counterexamples.
Data compressionIn information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information.
In vitro fertilisationIn vitro fertilisation (IVF) is a process of fertilisation where an egg is combined with sperm in vitro ("in glass"). The process involves monitoring and stimulating a woman's ovulatory process, removing an ovum or ova (egg or eggs) from her ovaries and letting sperm fertilise them in a culture medium in a laboratory. After the fertilised egg (zygote) undergoes embryo culture for 2–6 days, it is transferred by catheter into the uterus, with the intention of establishing a successful pregnancy.
Lossless compressionLossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes).
Drug deliveryDrug delivery refers to approaches, formulations, manufacturing techniques, storage systems, and technologies involved in transporting a pharmaceutical compound to its target site to achieve a desired therapeutic effect. Principles related to drug preparation, route of administration, site-specific targeting, metabolism, and toxicity are used to optimize efficacy and safety, and to improve patient convenience and compliance. Drug delivery is aimed at altering a drug's pharmacokinetics and specificity by formulating it with different excipients, drug carriers, and medical devices.
Logarithmic derivativeIn mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely scaled by the current value of f. When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln(f), or the natural logarithm of f.
Wirtinger derivativesIn complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives with respect to one real variable, when applied to holomorphic functions, antiholomorphic functions or simply differentiabl
Gonadotropin-releasing hormone agonistA gonadotropin-releasing hormone agonist (GnRH agonist) is a type of medication which affects gonadotropins and sex hormones. They are used for a variety of indications including in fertility medicine and to lower sex hormone levels in the treatment of hormone-sensitive cancers such as prostate cancer and breast cancer, certain gynecological disorders like heavy periods and endometriosis, high testosterone levels in women, early puberty in children, as a part of transgender hormone therapy, and to delay puberty in transgender youth among other uses.
Intestinal epitheliumThe intestinal epithelium is the single cell layer that form the luminal surface (lining) of both the small and large intestine (colon) of the gastrointestinal tract. Composed of simple columnar epithelial cells, it serves two main functions: absorbing useful substances into the body and restricting the entry of harmful substances. As part of its protective role, the intestinal epithelium forms an important component of the intestinal mucosal barrier. Certain diseases and conditions are caused by functional defects in the intestinal epithelium.
Intestinal mucosal barrierThe intestinal mucosal barrier, also referred to as intestinal barrier, refers to the property of the intestinal mucosa that ensures adequate containment of undesirable luminal contents within the intestine while preserving the ability to absorb nutrients. The separation it provides between the body and the gut prevents the uncontrolled translocation of luminal contents into the body proper. Its role in protecting the mucosal tissues and circulatory system from exposure to pro-inflammatory molecules, such as microorganisms, toxins, and antigens is vital for the maintenance of health and well-being.
