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List of mathematical uses of Latin letters Rr List_of_mathematical_uses_of_Latin_letters > Rr R represents: the Ricci tensor the circumradius of a cyclic polygon such as a triangle an arbitrary relation Riemann curvature tensor Electrical resistance Molar gas constant R {\displaystyle \mathbb {R} } represents the set of real numbers and various algebraic structures built upon the set of real numbers, such as R n {\displaystyle \mathbb {R} ^{n}} . r represents: the radius of a circle or sphere radial distance in a polar coordinate system or spherical coordinate system the inradius of a triangle or other tangential polygon the ratio of a geometric series (e.g. arn−1) the separation of two objects, for example in Coulomb's law a position vector the rate of concentration change of B (due to chemical reaction) denoted rB
Climate forcing agents Summary Climate_forcing These external forcings can be natural, such as variations in solar intensity and volcanic eruptions, or caused by humans. Accumulation of heat-trapping greenhouse gases, mainly being emitted by people burning fossil fuels, is causing global warming. Human activity also releases cooling aerosols, but their net effect is far less than that of greenhouse gases. Changes can be amplified by feedback processes in the different climate system components.
Binary file Viewing Binary_files > Viewing This type of view is useful for a quick inspection of a binary file in order to find passwords in games, find hidden text in non-text files and recover corrupted documents. It can even be used to inspect suspicious files (software) for unwanted effects. For example, the user would see any URL/email to which the suspected software may attempt to connect in order to upload unapproved data (to steal). If the file is itself treated as an executable and run, then the operating system will attempt to interpret the file as a series of instructions in its machine language.
Neurological deficit Associated conditions Neurological_deficit > Signs and symptoms > Associated conditions Epidemiological studies and meta-analysis have shown higher rates of depression and anxiety in patients with FND compared to the general population, but rates are similar to patients with other neurological disorders such as epilepsy or Parkinson's disease. This is often the case because of years of misdiagnosis and accusations of malingering.
Chemical indicator Precise pH measurement PH_indicators > Application > Precise pH measurement An indicator may be used to obtain quite precise measurements of pH by measuring absorbance quantitatively at two or more wavelengths. The principle can be illustrated by taking the indicator to be a simple acid, HA, which dissociates into H+ and A−. HA ⇌ H+ + A−The value of the acid dissociation constant, pKa, must be known. The molar absorbances, εHA and εA− of the two species HA and A− at wavelengths λx and λy must also have been determined by previous experiment.
Multigraph Summary Directed_multigraph In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge. There are 2 distinct notions of multiple edges: Edges without own identity: The identity of an edge is defined solely by the two nodes it connects. In this case, the term "multiple edges" means that the same edge can occur several times between these two nodes.
MediaWiki namespace Groups and restriction of access Talk_pages > Key features > Groups and restriction of access As a result, with minimal exceptions (related to specific tools and their related "Special" pages), page access control has never been a high priority in core development and developers have stated that users requiring secure user access and authorization controls should not rely on MediaWiki, since it was never designed for these kinds of situations. For instance, it is extremely difficult to create a wiki where only certain users can read and access some pages. Here, wiki engines like Foswiki, MoinMoin and Confluence provide more flexibility by supporting advanced security mechanisms like access control lists.
Damping torque Production Damping_torque > Production Fluid friction damping is created through the oscillation of a disk in and out of liquid, normally oil, thus causing it to always oppose motion. This method is very similar to air friction damping, except rather than having air in a chamber, it is replaced with fluid. This method is hindered by the fact that it can only be done vertically, as it requires the liquid to be in an upright position.
Analytic Element Method Summary Analytic_Element_Method The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota. It is similar in nature to the boundary element method (BEM), as it does not rely upon the discretization of volumes or areas in the modeled system; only internal and external boundaries are discretized. One of the primary distinctions between AEM and BEMs is that the boundary integrals are calculated analytically.
Skinner Unaflow engine Summary Uniflow_steam_engine The uniflow type of steam engine uses steam that flows in one direction only in each half of the cylinder. Thermal efficiency is increased by having a temperature gradient along the cylinder. Steam always enters at the hot ends of the cylinder and exhausts through ports at the cooler centre. By this means, the relative heating and cooling of the cylinder walls is reduced.
Palliative Care Symptoms assessment and management of children Palliative_Medicine > Pediatric palliative care > Symptoms assessment and management of children By allowing the caregiving to ensue by other qualified individuals, it allows the family time to rest and renew themselves Assess how the child perceives their symptoms (based on personal views) to create individualized care plans. After the implementation of therapeutic interventions, involve both the child and family in the reassessment of symptoms.The most common symptoms in children with severe chronic disease appropriate for palliative care consultation are weakness, fatigue, pain, poor appetite, weight loss, agitation, lack of mobility, shortness of breath, nausea and vomiting, constipation, sadness or depression, drowsiness, difficulty with speech, headache, excess secretions, anemia, pressure area problems, anxiety, fever, and mouth sores. The most common end of life symptoms in children include shortness of breath, cough, fatigue, pain, nausea and vomiting, agitation and anxiety, poor concentration, skin lesions, swelling of the extremities, seizures, poor appetite, difficulty with feeding, and diarrhea.
Geo URI Uncertainty Geo_URI_scheme > Semantics and usual interpretations > Uncertainty It is imposed, is independent of selection process of uncertainty description, there are no other choices. total uncertainty: it is only one parameter representing "all uncertainty", the uncertainty in the spatial measure and uncertainty about object definition or object's center. It is a sum of random variables.
Neural engineering Neuroscience Neural_engineering > Fundamentals > Neuroscience Messages that the body uses to influence thoughts, senses, movements, and survival are directed by nerve impulses transmitted across brain tissue and to the rest of the body. Neurons are the basic functional unit of the nervous system and are highly specialized cells that are capable of sending these signals that operate high and low level functions needed for survival and quality of life. Neurons have special electro-chemical properties that allow them to process information and then transmit that information to other cells.
Search problem Search method Search_problem > Search method Generic search algorithm: given a graph, start nodes, and goal nodes, incrementally explore paths from the start nodes. Maintain a frontier of paths from the start node that have been explored. As search proceeds, the frontier expands into the unexplored nodes until a goal node is encountered.
Triple-stranded DNA DNA replication Triple-stranded_DNA > Biological implications > Genetic instability > DNA replication DNA replication has been shown to affect the function of various DNA repair enzymes. H-DNA formation involves the formation of single-stranded DNA (ssDNA), which is more susceptible to attack by nucleases. Various nucleases have been shown to interact with H-DNA in a replication-dependent or replication-independent manner.A study using human cells found that the nucleotide excision repair (NER) nucleases ERCC1-XPF and ERCC1-XPG induced genetic instability.
Mouse models of human disease Use Mouse_models_of_human_disease > Use The cell cycle in a simple yeast is very similar to the cell cycle in humans and is regulated by homologous proteins. The fruit fly Drosophila melanogaster is studied, again, because it is easy to grow for an animal, has various visible congenital traits and has a polytene (giant) chromosome in its salivary glands that can be examined under a light microscope. The roundworm Caenorhabditis elegans is studied because it has very defined development patterns involving fixed numbers of cells, and it can be rapidly assayed for abnormalities.
Bayesian Inference Computer applications Bayesian_methods > Applications > Computer applications Spam classification is treated in more detail in the article on the naïve Bayes classifier. Solomonoff's Inductive inference is the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols. The only assumption is that the environment follows some unknown but computable probability distribution. It is a formal inductive framework that combines two well-studied principles of inductive inference: Bayesian statistics and Occam's Razor. Solomonoff's universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of x in optimal fashion.
Stackless Python Design Stackless_Python > Design So it allows only cooperative multitasking on a shared CPU and not parallelism (preemption was originally not available but is now in some form). To use multiple CPU cores, one would still need to build an interprocess communication system on top of Stackless Python processes.
Jipp curve Summary Jipp_curve The Jipp curve has been called "robably the most familiar diagram in the economics of telecommunications". The curve is named after A. Jipp, who was one of the first researchers to publish about the relationship in 1963.The number of telephones was traditionally measured by the number of landlines, but more recently, mobile phones have been used for the graphs as well. It has even been argued that the Jipp curve (or rather its measures) should be adjusted for countries where mobile phones are more common than landlines, namely for developing countries in Africa.The term has sometimes been used in analogy for other curves as well, for example as a "postal Jipp curve" plotting letters posted per capita and GDP per capita.
Zero vector space Properties Zero_object_(algebra) > Properties The zero ring, zero module and zero vector space are the zero objects of, respectively, the category of pseudo-rings, the category of modules and the category of vector spaces. However, the zero ring is not a zero object in the category of rings, since there is no ring homomorphism of the zero ring in any other ring. The zero object, by definition, must be a terminal object, which means that a morphism A → {0} must exist and be unique for an arbitrary object A. This morphism maps any element of A to 0.
Template replication Termination Replication_bubble > Replication process > Termination (This is known as the Hayflick limit.) Within the germ cell line, which passes DNA to the next generation, telomerase extends the repetitive sequences of the telomere region to prevent degradation.
State (thermodynamic) State variables and state functions Thermodynamic_variable > State variables and state functions In the most commonly cited simple example, an ideal gas, the thermodynamic variables would be any three variables out of the following four: amount of substance, pressure, temperature, and volume. Thus, the thermodynamic state would range over a three-dimensional state space. The remaining variable, as well as other quantities such as the internal energy and the entropy, would be expressed as state functions of these three variables. The state functions satisfy certain universal constraints, expressed in the laws of thermodynamics, and they depend on the peculiarities of the materials that compose the concrete system. Various thermodynamic diagrams have been developed to model the transitions between thermodynamic states.
Geometric rigidity Definitions Geometric_rigidity > Definitions A stress is an assignment ω: E → R {\displaystyle \omega :E\rightarrow \mathbb {R} } to the edges of a framework ( G , p ) {\displaystyle (G,p)} . A stress is proper if its entries are nonnegative and is a self stress if it satisfies ω R ( G , p ) = 0 {\displaystyle \omega R(G,p)=0} . A stress satisfying this equation is also called a resolvable stress, equilibrium stress, prestress, or sometimes just a stress.
Final value theorem Deducing limt → ∞ f(t) Final_value_theorem > Final value theorems for the Laplace transform > Deducing limt → ∞ f(t) In the following statements, the notation ' s → 0 {\displaystyle s\to 0} ' means that s {\displaystyle s} approaches 0, whereas ' s ↓ 0 {\displaystyle s\downarrow 0} ' means that s {\displaystyle s} approaches 0 through the positive numbers.
Jean Pierre Flourens Biography Jean_Pierre_Flourens > Biography These experiments led Flourens to the conclusion that the cerebral hemispheres are responsible for higher cognitive functions, that the cerebellum regulates and integrates movements, and that the medulla controls vital functions, such as circulation, respiration and general bodily stability. On the other hand, he was unable (probably because his experimental subjects have relatively primitive cortex) to find specific regions for memory and cognition, which led him to believe that they are represented in a diffuse form around the brain. So, different functions could indeed be ascribed to particular regions of the brain, but a finer localization was lacking.
Software engineering economics Software construction Software_engineering_economics > Tasks in large scale projects > Software construction Software construction, the main activity of software development, is the combination of programming, unit testing, integration testing, and debugging so as to implement the design. Testing during this phase is generally performed by the programmer while the software is under construction, to verify what was just written and decide when the code is ready to be sent to the next step.
Helicase Activation barrier in helicase activity Rna_helicases > Function > Activation barrier in helicase activity Enzymatic helicase action, such as unwinding nucleic acids is achieved through the lowering of the activation barrier ( B {\displaystyle B} ) of each specific action. The activation barrier is a result of various factors, and can be defined using the following equation, where N {\displaystyle N} = number of unwound base pairs (bps), Δ G b p {\displaystyle \Delta G_{bp}} = free energy of base pair formation, G i n t {\displaystyle G_{int}} = reduction of free energy due to helicase, and G f {\displaystyle G_{f}} = reduction of free energy due to unzipping forces. B = N ( Δ G b p − G i n t − G f ) {\displaystyle B=N(\Delta G_{bp}-G_{int}-G_{f})} Factors that contribute to the height of the activation barrier include: specific nucleic acid sequence of the molecule involved, the number of base pairs involved, tension present on the replication fork, and destabilization forces.
The Geometry of Musical Rhythm Topics The_Geometry_of_Musical_Rhythm > Topics In order to study rhythms mathematically, Toussaint abstracts away many of their features that are important musically, involving the sounds or strengths of the individual beats, the phasing of the beats, hierarchically-structured rhythms, or the possibility of music that changes from one rhythm to another. The information that remains describes the beats of each bar (an evenly-spaced cyclic sequence of times) as being either on-beats (times at which a beat is emphasized in the musical performance) or off-beats (times at which it is skipped or performed only weakly). This can be represented combinatorially as a necklace, an equivalence class of binary sequences under rotations, with true binary values representing on-beats and false representing off-beats. Alternatively, Toussaint uses a geometric representation as a convex polygon, the convex hull of a subset of the vertices of a regular polygon, where the vertices of the hull represent times when a beat is performed; two rhythms are considered the same if the corresponding polygons are congruent.
Linnett Double-Quartet Theory Luder’s extension of Linnett double-quartet theory – electron-repulsion theory Linnett_Double-Quartet_Theory > Luder’s extension of Linnett double-quartet theory – electron-repulsion theory The author asserts that the s electrons occupy the axial positions, leaving the d electrons to occupy the positions at the vertices of two pentagonal bases of the two constituent pyramids. The electronic structure of the ytterbium atom can be constructed similarly. The s electrons are again assumed to occupy the axial positions while the f electrons occupy the positions at the vertices of two heptagonal bases of the two constituent pyramids. While these results are interesting, they have been contested in the scientific literature due to Luder's abandonment of the octet rule and the author's controversial views on spin correlation. Indeed, one author notes that Luder's works “ a great disservice to Linnett and his method”.
Operating system kernel Hybrid (or modular) kernels Kernel_image > Kernel-wide design approaches > Hybrid (or modular) kernels These types of kernels are extensions of micro kernels with some properties of monolithic kernels. Unlike monolithic kernels, these types of kernels are unable to load modules at runtime on their own. This implies running some services (such as the network stack or the filesystem) in kernel space to reduce the performance overhead of a traditional microkernel, but still running kernel code (such as device drivers) as servers in user space.
Avogadro number Connection to other constants Avogadro_constant > Connection to other constants The Avogadro constant NA is related to other physical constants and properties. It relates the molar gas constant R and the Boltzmann constant kB, which in the SI is defined to be exactly 1.380649×10−23 J/K:R = kB NA = 8.314462618... J⋅mol−1⋅K−1 It relates the Faraday constant F and the elementary charge e, which in the SI is defined as exactly 1.602176634×10−19 coulombs:F = e NA = 9.648533212...×104 C⋅mol−1 It relates the molar mass constant Mu and the atomic mass constant mu currently 1.66053906660(50)×10−27 kg:Mu = mu NA = 0.99999999965(30)×10−3 kg⋅mol−1
E1cB-elimination reaction Chemical kinetics of E1cB-elimination mechanisms E1cB-elimination_reaction > Chemical kinetics of E1cB-elimination mechanisms When trying to determine whether or not a reaction follows the E1cB mechanism, chemical kinetics are essential. The best way to identify the E1cB mechanism involves the use of rate laws and the kinetic isotope effect. These techniques can also help further differentiate between E1cB, E1, and E2-elimination reactions.
Lac operon Regulation Lac_operon > Regulation The protein that is formed by the lacI gene is known as the lac repressor. The type of regulation that the lac operon undergoes is referred to as negative inducible, meaning that the gene is turned off by the regulatory factor (lac repressor) unless some molecule (lactose) is added. Because of the presence of the lac repressor protein, genetic engineers who replace the lacZ gene with another gene will have to grow the experimental bacteria on agar with lactose available on it.
Objective stress rate The incremental loading procedure Objective_stress_rates > Objective stress rates in finite strain inelasticity > The incremental loading procedure For a small enough load step, the material deformation can be characterized by the small (or linearized) strain increment tensor where u {\displaystyle \mathbf {u} } is the displacement increment of the continuum points. The time derivative is the strain rate tensor (also called the velocity strain) and v = u ˙ {\displaystyle \mathbf {v} ={\dot {\mathbf {u} }}} is the material point velocity or displacement rate. For finite strains, measures from the Seth–Hill family (also called Doyle–Ericksen tensors) can be used: where U {\displaystyle \mathbf {U} } is the right stretch. A second-order approximation of these tensors is
Potential applications of carbon nanotubes Solar cells Potential_applications_of_carbon_nanotubes > Solar cells Add sunlight to excite the polymers, and the buckyballs will grab the electrons. Nanotubes, behaving like copper wires, will then be able to make the electrons or current flow.Additional research has been conducted on creating SWNT hybrid solar panels to increase the efficiency further. These hybrids are created by combining SWNT's with photo-excitable electron donors to increase the number of electrons generated.
Autoimmune inner ear disease Causes Autoimmune_inner_ear_disease > Causes AIED is generally caused by either antibodies or immune cells that cause damage to the inner ear. There are several theories that propose a cause of AIED: Bystander damage – Physical damage to the inner ear may lead to cytokine release that signals for an immune response. This may be a component of the "attack/remission cycle" of AIED. Cross-reactions – Accidental damage of the inner ear by antibodies or T-cells that recognize an inner ear antigen that is similar to a bacterial or viral antigen Genetic factors – Predisposition to developing an autoimmune disorder based on genes inherited Intolerance – The immune system may not be aware of all the antigens present in the inner ear until physical damage releases some of these antigens. As a result, the immune system treats these unfamiliar antigens as foreign and mounts an immune response.Currently, the cross-reactions theory appears to be the favored mechanism of AIED pathogenesis.
Seismic site response Summary Seismic_site_effects Seismic site effects are related to the amplification of seismic waves in superficial geological layers. The surface ground motion may be strongly amplified if the geological conditions are unfavorable (e.g. sediments). Therefore, the study of local site effects is an important part of the assessment of strong ground motions, seismic hazard and engineering seismology in general. Damage due to an earthquake may thus be aggravated as in the case of the 1985 Mexico City earthquake. For alluvial basins, we may shake a bowl of jelly to model the phenomenon at a small scale. This article defines site effects first, presents the 1985 Mexico City earthquake, describes the theoretical analysis of the phenomenon (through mechanical waves) and details several research results on seismic site effects in Caracas.
Type T thermocouple Metallurgical grades Type_K_thermocouple > Practical concerns > Metallurgical grades Precision grades may only be available in matched pairs, where one wire is modified to compensate for deficiencies in the other wire. A special case of thermocouple wire is known as "extension grade", designed to carry the thermoelectric circuit over a longer distance. Extension wires follow the stated E ( T ) {\displaystyle \scriptstyle E(T)} curve but for various reasons they are not designed to be used in extreme environments and so they cannot be used at the sensing junction in some applications. For example, an extension wire may be in a different form, such as highly flexible with stranded construction and plastic insulation, or be part of a multi-wire cable for carrying many thermocouple circuits. With expensive noble metal thermocouples, the extension wires may even be made of a completely different, cheaper material that mimics the standard type over a reduced temperature range.
Finesse Coefficient Basic description Finesse_Coefficient > Basic description In a typical system, illumination is provided by a diffuse source set at the focal plane of a collimating lens. A focusing lens after the pair of flats would produce an inverted image of the source if the flats were not present; all light emitted from a point on the source is focused to a single point in the system's image plane. In the accompanying illustration, only one ray emitted from point A on the source is traced.
Chronic illness Summary Chronic_illness A chronic condition, on the other hand, usually affects multiple areas of the body, is not fully responsive to treatment, and persists for an extended period of time.Chronic conditions may have periods of remission or relapse where the disease temporarily goes away, or subsequently reappears. Periods of remission and relapse are commonly discussed when referring to substance abuse disorders which some consider to fall under the category of chronic condition.Chronic conditions are often associated with non-communicable diseases which are distinguished by their non-infectious causes. Some chronic conditions though, are caused by transmissible infections such as HIV/AIDS.63% of all deaths worldwide are from chronic conditions.
Overloaded function Summary Overloaded_function In some programming languages, function overloading or method overloading is the ability to create multiple functions of the same name with different implementations. Calls to an overloaded function will run a specific implementation of that function appropriate to the context of the call, allowing one function call to perform different tasks depending on context. For example, doTask() and doTask(object o) are overloaded functions. To call the latter, an object must be passed as a parameter, whereas the former does not require a parameter, and is called with an empty parameter field.
Organizational learning Communities of learning Organizational_learning > Relevance > Communities of learning In their study of software development, Boh, Slaughter and Espinosa (2007) found that individuals were more productive the more specialized experience they had with a certain system. Group learning is the next largest community There are conflicting definitions of group learning among researchers studying it. One belief is that group learning is a process in which a group takes action, gets feedback, and uses this feedback to modify their future action.
Map matching Examples and use cases Map_matching > Examples and use cases Uses for map-matching algorithms range from the immediate and practical, such as applications designed for guiding travellers, to the analytical, such as generating detailed inputs for traffic analysis models and the like. Probably the most common use of map-matching is where a traveller has some mobile computer giving him or her directions across a street network. In order to give accurate directions, the device must know exactly where in the street network the user is.
Vector subspace Independence, basis, and dimension Subspace_(linear_algebra) > Descriptions > Independence, basis, and dimension {\displaystyle (2t_{1},t_{1},5t_{2},t_{2})=t_{1}(2,1,0,0)+t_{2}(0,0,5,1).} The subspace S is two-dimensional. Geometrically, it is the plane in R4 passing through the points (0, 0, 0, 0), (2, 1, 0, 0), and (0, 0, 5, 1).
Nucleophilic acyl substitution Carboxylic acids Nucleophilic_acyl_substitution > Reactions of acyl derivatives > Carboxylic acids While esterification reactions with diazomethane often give quantitative yields, diazomethane is only useful for forming methyl esters.Thionyl chloride can be used to convert carboxylic acids to their corresponding acyl chlorides. First, carboxylic acid 1 attacks thionyl chloride, and chloride ion leaves. The resulting oxonium ion 2 is activated towards nucleophilic attack and has a good leaving group, setting it apart from a normal carboxylic acid.
Liquid Cooling and Ventilation Garment Heat exchanger Liquid_Cooling_and_Ventilation_Garment > Technology > Heat exchanger For portable earthbound applications, the heat exchanger for cooling the liquid can be very low-tech, consisting simply of a container for holding ice, and an electric pump to circulate water from the container through the tubing. The return water is cooled by the melting ice and again pumped through the tubes. Regulation of flow is done by varying pump speed or using an adjustable flow valve.
Deterministic concurrency Implementations Coroutine > Implementations One important difference between threads and coroutines is that threads are typically preemptively scheduled while coroutines are not. Because threads can be rescheduled at any instant and can execute concurrently, programs using threads must be careful about locking. In contrast, because coroutines can only be rescheduled at specific points in the program and do not execute concurrently, programs using coroutines can often avoid locking entirely.
Electrical Power Explanation Electric_power_source > Explanation Electric power is transformed to other forms of energy when electric charges move through an electric potential difference (voltage), which occurs in electrical components in electric circuits. From the standpoint of electric power, components in an electric circuit can be divided into two categories:
Organic polymers Mixing behavior Polymer_main_chain > Properties > Phase behavior > Mixing behavior Since polymeric molecules are much larger and hence generally have much higher specific volumes than small molecules, the number of molecules involved in a polymeric mixture is far smaller than the number in a small molecule mixture of equal volume. The energetics of mixing, on the other hand, is comparable on a per volume basis for polymeric and small molecule mixtures. This tends to increase the free energy of mixing for polymer solutions and thereby making solvation less favorable, and thereby making the availability of concentrated solutions of polymers far rarer than those of small molecules.
Correlation coefficient Summary Correlation_coefficient A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement. As tools of analysis, correlation coefficients present certain problems, including the propensity of some types to be distorted by outliers and the possibility of incorrectly being used to infer a causal relationship between the variables (for more, see Correlation does not imply causation).
Effusive rock Chemistry Effusive_rock > Characteristics > Chemistry Additional classifications may be made on the basis of other components, such as aluminum or iron content.Volcanic rocks are also broadly divided into subalkaline, alkaline, and peralkaline volcanic rocks. Subalkaline rocks are defined as rocks in which SiO2 < -3.3539 × 10−4 × A6 + 1.2030 × 10−2 × A5 - 1.5188 × 10−1 × A4 + 8.6096 × 10−1 × A3 - 2.1111 × A2 + 3.9492 × A + 39.0 where both silica and total alkali oxide content (A) are expressed as molar fraction. Because the TAS diagram uses weight fraction and the boundary between alkaline and subalkaline rock is defined in terms of molar fraction, the position of this curve on the TAS diagram is only approximate.
Cauchy–Rassias stability Summary Cauchy–Rassias_stability In 1978, Themistocles M. Rassias succeeded in extending the Hyers' theorem by considering an unbounded Cauchy difference. He was the first to prove the stability of the linear mapping in Banach spaces. In 1950, T. Aoki had provided a proof of a special case of the Rassias' result when the given function is additive.
Zero-point field Non-zero expectation value Quantum_Vacuum > Non-zero expectation value If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a measurement problem. In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates. In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass.
Apoplast Summary Apoplast The apoplast is important for all the plant's interaction with its environment: The main carbon source (carbon dioxide) needs to be solubilized, which happens in the apoplast, before it diffuses through the cell wall and across the plasma membrane, into the cell's inner content, the cytoplasm, where it diffuses in the symplast to the chloroplasts for photosynthesis. In the roots, ions diffuse into the apoplast of the epidermis before diffusing into the symplast, or in some cases being taken up by specific ion channels, and being pulled by the plant's transpiration stream, which also occurs completely within the boundaries of the apoplast. Similarly, all gaseous molecules emitted and received by plants such as oxygen must pass through the apoplast.
Inverse problem for Lagrangian mechanics Summary Helmholtz_condition In mathematics, the inverse problem for Lagrangian mechanics is the problem of determining whether a given system of ordinary differential equations can arise as the Euler–Lagrange equations for some Lagrangian function. There has been a great deal of activity in the study of this problem since the early 20th century. A notable advance in this field was a 1941 paper by the American mathematician Jesse Douglas, in which he provided necessary and sufficient conditions for the problem to have a solution; these conditions are now known as the Helmholtz conditions, after the German physicist Hermann von Helmholtz.
Differential calculus Derivative Differential_calculus > Derivative We have thus succeeded in properly defining the derivative of a function, meaning that the 'slope of the tangent line' now has a precise mathematical meaning. Differentiating a function using the above definition is known as differentiation from first principles.
Principal quantum numbers Derivation Principal_quantum_level > Derivation In the notation of the periodic table, the main shells of electrons are labeled: based on the principal quantum number. The principal quantum number is related to the radial quantum number, nr, by: where ℓ is the azimuthal quantum number and nr is equal to the number of nodes in the radial wavefunction. The definite total energy for a particle motion in a common Coulomb field and with a discrete spectrum, is given by: where a B {\displaystyle a_{B}} is the Bohr radius. This discrete energy spectrum resulted from the solution of the quantum mechanical problem on the electron motion in the Coulomb field, coincides with the spectrum that was obtained with the help application of the Bohr–Sommerfeld quantization rules to the classical equations. The radial quantum number determines the number of nodes of the radial wave function R ( r ) {\displaystyle R(r)} .
Non-commuting formal power series Formal differentiation Formal_power_series > Operations on formal power series > Formal differentiation For example, the product rule is valid: D ( f g ) = f ⋅ ( D g ) + ( D f ) ⋅ g , {\displaystyle D(fg)\ =\ f\cdot (Dg)+(Df)\cdot g,} and the chain rule works as well: D ( f ∘ g ) = ( D f ∘ g ) ⋅ D g , {\displaystyle D(f\circ g)=(Df\circ g)\cdot Dg,} whenever the appropriate compositions of series are defined (see above under composition of series). Thus, in these respects formal power series behave like Taylor series. Indeed, for the f defined above, we find that ( D k f ) ( 0 ) = k ! a k , {\displaystyle (D^{k}f)(0)=k!a_{k},} where Dk denotes the kth formal derivative (that is, the result of formally differentiating k times).
Period (periodic table) Period 2 Second-row_transition_metal > Periods > Period 2 Period 2 elements involve the 2s and 2p orbitals. They include the biologically most essential elements besides hydrogen: carbon, nitrogen, and oxygen. Lithium (Li) is the lightest metal and the least dense solid element. In its non-ionized state it is one of the most reactive elements, and so is only ever found naturally in compounds.
Molecular cell biology Cell types Cellular_Biology > Cell types The four eukaryotic kingdoms are Animalia, Plantae, Fungi, and Protista. They both reproduce through binary fission. Bacteria, the most prominent type, have several different shapes, although most are spherical or rod-shaped.
Elementary Calculus: An Infinitesimal Approach Textbook Elementary_Calculus:_An_Infinitesimal_Approach > Textbook The usual definitions in terms of ε–δ techniques are provided at the end of Chapter 5 to enable a transition to a standard sequence. In his textbook, Keisler used the pedagogical technique of an infinite-magnification microscope, so as to represent graphically, distinct hyperreal numbers infinitely close to each other. Similarly, an infinite-resolution telescope is used to represent infinite numbers.
IPCC Second Assessment Report Chapter 8: Detection of Climate Change and Attribution of Causes IPCC_Second_Assessment_Report > Chapter 8: Detection of Climate Change and Attribution of Causes The summary at the start of the accepted version of the chapter stated that "these results indicate that the observed trend in global mean temperature over the past 100 years is unlikely to be entirely natural in origin. More importantly, there is evidence of an emerging pattern of climate response to forcings by greenhouse gases and sulphate aerosols in the observed climate record. Taken together, these results point towards a human influence on global climate."
Adrenal insufficiency Summary Adrenal_insufficiency Deficiency of these hormones leads to symptoms ranging from abdominal pain, vomiting, muscle weakness and fatigue, low blood pressure, depression, mood and personality changes (in mild cases) to organ failure and shock (in severe cases). Adrenal crisis may occur if a person having adrenal insufficiency experiences stresses, such as an accident, injury, surgery, or severe infection; this is a life-threatening medical condition resulting from severe deficiency of cortisol in the body. Death may quickly follow.Adrenal insufficiency can be caused by dysfunction of the adrenal gland itself, whether by destruction (e.g. Addison's disease), failure of development (e.g. adrenal dysgenesis), or enzyme deficiency (e.g. congenital adrenal hyperplasia). Adrenal insufficiency can also occur when the pituitary gland or the hypothalamus do not produce adequate amounts of the hormones that assist in regulating adrenal function. This is called secondary adrenal insufficiency (when caused by lack of production of adrenocorticotropic hormone (ACTH) in the pituitary gland) or tertiary adrenal insufficiency (when caused by lack of corticotropin-releasing hormone (CRH) in the hypothalamus).
Pathological science N-rays Pathological_science > Langmuir's examples > N-rays After a time, American physicist Robert W. Wood decided to visit Blondlot's lab, which had moved on to the physical characterization of N-rays. An experiment passed the rays from a 2 mm slit through an aluminum prism, from which he was measuring the index of refraction to a precision that required measurements accurate to within 0.01 mm. Wood asked how it was possible that he could measure something to 0.01 mm from a 2 mm source, a physical impossibility in the propagation of any kind of wave.
SMAW (welding) Power supply MMAW > Equipment > Power supply Reversing the polarity so that the electrode is positively charged (DCEP) and the workpiece is negatively charged increases the weld penetration. With alternating current the polarity changes over 100 times per second, creating an even heat distribution and providing a balance between electrode melting rate and penetration.Typically, the equipment used for SMAW consists of a step-down transformer and for direct current models a rectifier, which converts alternating current into direct current. Because the power normally supplied to the welding machine is high-voltage alternating current, the welding transformer is used to reduce the voltage and increase the current.
Circuit element Types Circuit_element > Types They can be used to represent ideal batteries and power supplies. Dependent sources – These are two-port elements with a voltage or current source proportional to the voltage or current at a second pair of terminals.
Carboxylate ion Resonance stabilization of the carboxylate ion Carboxylate_group > Resonance stabilization of the carboxylate ion Hence acetic acid is a much stronger acid than ethanol. This in turn means that for equimolar solutions of a carboxylic acid or an alcohol in water, the carboxylic acid would have a much lower pH. : 263–7
Stomatogastric nervous system Summary Stomatogastric_nervous_system The STNS contains a set of distinct but interacting motor circuits. The understanding of this multifunctional network contributed importantly to the general understanding of neural circuit operation. The value of this system has resulted from its accessibility, the use of several innovative techniques, and the combined research effort of around 15 laboratories over the past ~30 years.
DD-transpeptidase Biological Function DD-transpeptidase > Biological Function All bacteria possess at least one, most often several, monofunctional serine DD-peptidases.
Comparison of vector algebra and geometric algebra Translations between formalisms Comparison_of_vector_algebra_and_geometric_algebra > Translations between formalisms Here are some comparisons between standard R 3 {\displaystyle {\mathbb {R} }^{3}} vector relations and their corresponding exterior product and geometric product equivalents. All the exterior and geometric product equivalents here are good for more than three dimensions, and some also for two. In two dimensions the cross product is undefined even if what it describes (like torque) is perfectly well defined in a plane without introducing an arbitrary normal vector outside of the space. Many of these relationships only require the introduction of the exterior product to generalize, but since that may not be familiar to somebody with only a background in vector algebra and calculus, some examples are given.
Trans-activating crRNA Summary Trans-activating_crRNA There are several CRISPR system subtypes. Type II CRISPR-Cas systems require a tracrRNA which plays a role in the maturation of crRNA. The tracrRNA is partially complementary to and base pairs with a pre-crRNA forming an RNA duplex. This is cleaved by RNase III, an RNA-specific ribonuclease, to form a crRNA/tracrRNA hybrid. This hybrid acts as a guide for the endonuclease Cas9, which cleaves the invading nucleic acid.
Triple integral Mathematical definition Area_integral > Mathematical definition The Riemann integral of a function defined over an arbitrary bounded n-dimensional set can be defined by extending that function to a function defined over a half-open rectangle whose values are zero outside the domain of the original function. Then the integral of the original function over the original domain is defined to be the integral of the extended function over its rectangular domain, if it exists. In what follows the Riemann integral in n dimensions will be called the multiple integral.
Syndiotactic macromolecule Head/tail configuration Syndiotactic_macromolecule > Head/tail configuration In vinyl polymers the complete configuration can be further described by defining polymer head/tail configuration. In a regular macromolecule all monomer units are normally linked in a head to tail configuration so that all β-substituents are separated by three carbon atoms. In head to head configuration this separation is only by 2 carbon atoms and the separation with tail to tail configuration is by 4 atoms. Head/tail configurations are not part of polymer tacticity but should be taken into account when considering polymer defects.
Theory of heat Branches of thermodynamics Theory_of_heat > Branches of thermodynamics 1970s Biological evolution thermodynamics – 1978 Geochemical thermodynamics – c. 1980s Atmospheric thermodynamics – c. 1980s Natural systems thermodynamics – 1990s Supramolecular thermodynamics – 1990s Earthquake thermodynamics – 2000 Drug-receptor thermodynamics – 2001 Pharmaceutical systems thermodynamics – 2002Concepts of thermodynamics have also been applied in other fields, for example: Thermoeconomics – c. 1970s
Heat generation Potentials Heat_generation > Potentials The five most well known potentials are: where T {\displaystyle T} is the temperature, S {\displaystyle S} the entropy, p {\displaystyle p} the pressure, V {\displaystyle V} the volume, μ {\displaystyle \mu } the chemical potential, N {\displaystyle N} the number of particles in the system, and i {\displaystyle i} is the count of particles types in the system. Thermodynamic potentials can be derived from the energy balance equation applied to a thermodynamic system. Other thermodynamic potentials can also be obtained through Legendre transformation.
Call frame Subroutine entry processing Frame_pointer > Use > Subroutine entry processing If frame pointers are being used, the prologue will typically set the new value of the frame pointer register from the stack pointer. Space on the stack for local variables can then be allocated by incrementally changing the stack pointer. The Forth programming language allows explicit winding of the call stack (called there the "return stack").
Go (game) Boards Go_(game) > Equipment > Traditional equipment > Boards There are two main types of boards: a table board similar in most respects to other gameboards like that used for chess, and a floor board, which is its own free-standing table and at which the players sit. The traditional Japanese goban is between 10 and 18 cm (3.9 and 7.1 in) thick and has legs; it sits on the floor (see picture). It is preferably made from the rare golden-tinged Kaya tree (Torreya nucifera), with the very best made from Kaya trees up to 700 years old.
Neutral mutation Summary Neutral_mutation That loss or fixation of the gene proceeds based on random sampling known as genetic drift. A neutral mutation that is in linkage disequilibrium with other alleles that are under selection may proceed to loss or fixation via genetic hitchhiking and/or background selection. While many mutations in a genome may decrease an organism’s ability to survive and reproduce, also known as fitness, those mutations are selected against and are not passed on to future generations.
Intercultural simulation Description Intercultural_simulation > Description Viewing games as systems of interaction, playing is a form of contact by interaction given the central role of play within games. Prior to exploring specific differences between digital and non-digital games and simulations, it is advisable to understand the simulation on a conceptual level. Simulations demand the use of rules.
Shannon theory Directed Information Shannon_theory > Quantities of information > Directed Information , X i ; Y i | Y 1 , Y 2 , . . .
Corticobasal syndrome Differential Corticobasal_syndrome > Diagnosis > Differential Other degenerative pathologies that can cause corticobasal syndrome include: Alzheimer's disease Pick's disease with Pick bodies Lewy body dementias Neurofilament inclusion body disease Creutzfeldt–Jakob disease Frontotemporal degeneration due to progranulin gene mutation Motor neuron disease‐inclusion dementia.The symptoms of classic CBS differ from CBD in that CBD also includes cognitive deficits in the executive functions.
Fizeau's measurement of the speed of light in air Summary Fizeau's_measurement_of_the_speed_of_light_in_air In 1848−49, Hippolyte Fizeau used a toothed wheel apparatus to perform an absolute measurement of the speed of light in air. Subsequent experiments performed by Marie Alfred Cornu in 1872–76 improved the methodology and made a more accurate measurement.
Hashcash Advantages and disadvantages Hashcash > Advantages and disadvantages Like hashcash, cryptocurrencies use a hash function as their proof-of-work system. The rise of cryptocurrency has created a demand for ASIC-based mining machines. Although most cryptocurrencies use the SHA-256 hash function, the same ASIC technology could be used to create hashcash solvers that are three orders of magnitude faster than a consumer CPU, reducing the computational hurdle for spammers.
Phenolphthalein pH indicator Phenolphthalein > Uses > pH indicator However, a later paper suggested that this color is due to sulfonation to phenolsulfonphthalein.The lactone form (HIn) is colorless between strongly acidic and slightly basic conditions. The doubly deprotonated (In2-) phenolate form (the anion form of phenol) gives the familiar pink color. In strongly basic solutions, phenolphthalein is converted to its In(OH)3− form, and its pink color undergoes a rather slow fading reaction and becomes completely colorless when pH is greater than 13. The pKa values of phenolphthalein were found to be 9.05, 9.50 and 12 while those of phenolsulfonphthalein are 1.2 and 7.70.
Turing Test Naïveté of interrogators Turing_Test > Weaknesses > Naïveté of interrogators It has been suggested that what interrogators expect as human responses is not necessarily typical of humans. As a result, some individuals can be categorised as machines. This can therefore work in favour of a competing machine. The humans are instructed to "act themselves", but sometimes their answers are more like what the interrogator expects a machine to say. This raises the question of how to ensure that the humans are motivated to "act human".
Mixing ratio Mole ratio Mixing_ratio > In atmospheric chemistry and meteorology > Mole ratio In atmospheric chemistry, mixing ratio usually refers to the mole ratio ri, which is defined as the amount of a constituent ni divided by the total amount of all other constituents in a mixture: r i = n i n t o t − n i {\displaystyle r_{i}={\frac {n_{i}}{n_{\mathrm {tot} }-n_{i}}}} The mole ratio is also called amount ratio. If ni is much smaller than ntot (which is the case for atmospheric trace constituents), the mole ratio is almost identical to the mole fraction.
BPP (complexity) Definition BPP_(complexity) > Definition For example, if one defined the class with the restriction that the algorithm can be wrong with probability at most 1/2100, this would result in the same class of problems. The error probability does not even have to be constant: the same class of problems is defined by allowing error as high as 1/2 − n−c on the one hand, or requiring error as small as 2−nc on the other hand, where c is any positive constant, and n is the length of input. This flexibility in the choice of error probability is based on the idea of running an error-prone algorithm many times, and using the majority result of the runs to obtain a more accurate algorithm. The chance that the majority of the runs are wrong drops off exponentially as a consequence of the Chernoff bound.
Yu-Chi Ho Control theory and optimization Yu-Chi_Ho > Work > Control theory and optimization Kálmán developed the study of the time domain using state-space models. Joining Kálmán, Ho showed that the state-space representation provides a convenient and compact way to model and analyze dynamical systems with multiple inputs and outputs which would otherwise take multiple Laplace transforms to encode; further, the state-space representation can be extended into nonlinear systems. Their paper controllability of linear dynamic systems, developed the theory of controllability (then known as the "Kalman-Bertram condition"). Together with Ho's student Robert Lee at MIT, the paper A Bayesian approach to problems in stochastic estimation and control formulated a general class of stochastic estimation and control problems from a Bayesian Decision-Theoretic viewpoint.
Bohr atom Electron energy levels Sommerfeld–Wilson_quantization > Electron energy levels The total energy is half the potential energy, the difference being the kinetic energy of the electron. This is also true for noncircular orbits by the virial theorem.A quantum ruleThe angular momentum L = mevr is an integer multiple of ħ: m e v r = n ℏ . {\displaystyle m_{\mathrm {e} }vr=n\hbar .}
Classical Mechanics (Taylor) Summary Classical_Mechanics_(Taylor) Taylor has written several college-level physics textbooks. His bestselling book is An Introduction to Error Analysis, which has been translated into nine languages. His intermediate-level undergraduate textbook, Classical Mechanics, was well-reviewed.
Renewable energy policy Levelling the playing field Renewable_energy_commercialization > Public policy landscape > Levelling the playing field The IEA has identified three actions which will allow renewable energy and other clean energy technologies to "more effectively compete for private sector capital". "First, energy prices must appropriately reflect the "true cost" of energy (e.g. through carbon pricing) so that the positive and negative impacts of energy production and consumption are fully taken into account". Example: New UK nuclear plants cost £92.50/MWh, whereas offshore wind farms in the UK are supported with €74.2/MWh at a price of £150 in 2011 falling to £130 per MWh in 2022. In Denmark, the price can be €84/MWh. "Second, inefficient fossil fuel subsidies must be removed, while ensuring that all citizens have access to affordable energy". "Third, governments must develop policy frameworks that encourage private sector investment in lower-carbon energy options".
Super-recursive algorithm Summary Super-recursive_algorithm In computability theory, super-recursive algorithms are a generalization of ordinary algorithms that are more powerful, that is, compute more than Turing machines. The term was introduced by Mark Burgin, whose book "Super-recursive algorithms" develops their theory and presents several mathematical models. Turing machines and other mathematical models of conventional algorithms allow researchers to find properties of recursive algorithms and their computations. In a similar way, mathematical models of super-recursive algorithms, such as inductive Turing machines, allow researchers to find properties of super-recursive algorithms and their computations. Burgin, as well as other researchers (including Selim Akl, Eugene Eberbach, Peter Kugel, Jan van Leeuwen, Hava Siegelmann, Peter Wegner, and Jiří Wiedermann) who studied different kinds of super-recursive algorithms and contributed to the theory of super-recursive algorithms, have argued that super-recursive algorithms can be used to disprove the Church-Turing thesis, but this point of view has been criticized within the mathematical community and is not widely accepted.
Timeline of numerals and arithmetic 1000–1500 Timeline_of_numerals_and_arithmetic > 1000–1500 c. 1000 — Pope Sylvester II introduces the abacus using the Hindu–Arabic numeral system to Europe. 1030 — Ali Ahmad Nasawi writes a treatise on the decimal and sexagesimal number systems. His arithmetic explains the division of fractions and the extraction of square and cubic roots (square root of 57,342; cubic root of 3, 652, 296) in an almost modern manner.
Available energy Summary Exergy Exergy, often referred to as "available energy" or "useful work potential," is a fundamental concept in the field of thermodynamics and engineering. It plays a crucial role in understanding and quantifying the quality of energy within a system and its potential to perform useful work. Exergy analysis has widespread applications in various fields, including energy engineering, environmental science, and industrial processes. From a scientific and engineering perspective, second-law based exergy analysis is valuable because it provides a number of benefits over energy analysis alone.
Code property graph Machine learning on code property graphs Code_property_graph > Machine learning on code property graphs Code property graphs provide the basis for several machine-learning-based approaches to vulnerability discovery. In particular, graph neural networks (GNN) have been employed to derive vulnerability detectors.
Mathematical constants Simple representatives of sets of numbers Mathematical_constants > Mathematical curiosities and unspecified constants > Simple representatives of sets of numbers Some constants, such as the square root of 2, Liouville's constant and Champernowne constant: C 10 = 0. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 … {\displaystyle C_{10}=0. {\color {blue}{1}}2{\color {blue}{3}}4{\color {blue}{5}}6{\color {blue}{7}}8{\color {blue}{9}}10{\color {blue}{11}}12{\color {blue}{13}}14{\color {blue}{15}}16\dots } are not important mathematical invariants but retain interest being simple representatives of special sets of numbers, the irrational numbers, the transcendental numbers and the normal numbers (in base 10) respectively. The discovery of the irrational numbers is usually attributed to the Pythagorean Hippasus of Metapontum who proved, most likely geometrically, the irrationality of the square root of 2. As for Liouville's constant, named after French mathematician Joseph Liouville, it was the first number to be proven transcendental.
William Lipscomb Boron chemistry and the nature of the chemical bond William_Lipscomb > Scientific studies > Boron chemistry and the nature of the chemical bond The three-center two-electron bond is illustrated in diborane (diagrams at right). In an ordinary covalent bond a pair of electrons bonds two atoms together, one at either end of the bond, the diboare B-H bonds for example at the left and right in the illustrations. In three-center two-electron bond a pair of electrons bonds three atoms (a boron atom at either end and a hydrogen atom in the middle), the diborane B-H-B bonds for example at the top and bottom of the illustrations.
Unintended acceleration Resolution Unintended_acceleration > Resolution Ways of resolving sudden unintended acceleration are to apply the brakes and/or clutch, or shift into neutral if the car has an automatic transmission. In most cars, fully applied brakes are easily capable of stopping the car while the accelerator pedal is also fully applied. "Pumping the brakes" is strongly discouraged during an unintended acceleration event, as this can lead to a loss of braking power. Unresponsive (entrapped) pedals can be avoided by using car mat clips.
Square function In complex numbers Square_(algebra) > In complex numbers The absolute square of a complex number is always a nonnegative real number, that is zero if and only if the complex number is zero. It is easier to compute than the absolute value (no square root), and is a smooth real-valued function. Because of these two properties, the absolute square is often preferred to the absolute value for explicit computations and when methods of mathematical analysis are involved (for example optimization or integration).
Centre for Gene Regulation and Expression Research and discoveries Centre_for_Gene_Regulation_and_Expression > Research and discoveries Live cell imaging and proteomic studies have allowed researchers at the centre to gain fresh understanding of protein function and cell behaviour. The centre is studying many aspects of the cell cycle, including the way in which chromosomes replicate and separate during cell division and how DNA damage is detected. Failure of these events can lead to major faults within a genome, potentially leading to the rise of cancerous cells. The centre is also investigating how DNA is tightly wound and compacted so that it can fit into the nuclei of eukaryotic cells, as well as the protein-DNA complexes that are involved in this packaging. The controlled unravelling of DNA is an important step in the regulation of gene function.