File Boundaryvalueproblem en.svg thumb right Shows a region where a differential equation is valid ... valueproblem is a differential equation together with a set of additional restraints, called the boundary conditions . A solution to a boundaryvalueproblem is a solution to the differential equation which also satisfies the boundary conditions. Boundaryvalue problems arise in several branches ... in applications, a boundaryvalueproblem should be well posed problem well posed . This means ... that boundaryvalue problems arising from scientific and engineering applications are in fact well posed. Among the earliest boundaryvalue problems to be studied is the Dirichlet problem , of finding ... . Initial valueproblem main Initial valueproblem A more mathematical way to picture the difference between an initial valueproblem and a boundaryvalueproblem is that an initial valueproblem ... and that value is at the lower boundary of the domain, thus the term initial value . On the other hand, a boundaryvalueproblem has conditions specified at the extremes of the independent variable ... of water would be a boundaryvalueproblem. Concretely, an example of a boundaryvalue in one spatial ... y x 2 sin x . , math Types of boundaryvalue problems Image Bounday valueproblem for a rod.PNG frame right The boundaryvalueproblem for an idealised Dimension 2D rod If the boundary gives a value to the normal ... temperature would not be known. If the boundary gives a value to the problem then it is a Dirichlet ... that gives a value to the normal derivative and the problem itself then it is a Cauchy boundary ... boundaryvalueproblem s. For an hyperbolic operator , one discusses hyperbolic boundaryvalue problems ... The World of Mathematical Equations. scholarpedia title Boundaryvalueproblem urlname Boundary ... , such as the determination of normal mode s, are often stated as boundaryvalue problems. A large class of important boundaryvalue problems are the Sturm Liouville theory Sturm Liouville problems ... more details
File Boundaryvalueproblem en.svg thumb right Shows a region where a differential equation is valid and the associated boundary values In mathematics , an elliptic boundaryvalueproblem is a special kind of boundaryvalueproblem which can be thought of as the stable state of an evolution problem . For example, the Dirichlet problem for the Laplacian gives the eventual distribution of heat in a room ... u in mathbb R n math . An elliptic boundaryvalueproblem is then a system of equations like math Lu f text in Omega math the PDE and math u 0 text on partial Omega math the boundaryvalue . This particular ... trace operator , one can construct the boundaryvalueproblem math Lu f text in Omega math and math ... step to cast the boundaryvalueproblem as in the language of Sobolev spaces is to rephrase it in its ... one being regularity . Regularity A regularity theorem for a linear elliptic boundaryvalueproblem ... references DEFAULTSORT Elliptic BoundaryValueProblem Category Mathematical analysis Category ... describing the physical universe in a relativistic way. Although all these equations are boundaryvalue ... must be analyzed using different techniques. The present article deals with the category of boundaryvalue problems known as linear elliptic problems. Boundaryvalue problems and partial differential ... does not change over time, there is no time variable. Elliptic boundaryvalue problems are a class ... to discuss elliptic boundaryvalue problems in more detail without referring to calculus ... that math Delta u nabla cdot nabla u math . The main example for boundaryvalue problems is the Laplace ... has the same essential properties as all other elliptic boundaryvalue problems. The solution math .... General linear elliptic boundaryvalue problems of the second degree Let math x 1,...,x n ... . Sobolev spaces The analysis of elliptic boundaryvalue problems requires some fairly sophisticated ... solvers for linear elliptic boundaryvalue problems see finite element method , finite difference ... more details
editor others title Elementary Differential Equations and BoundaryValue Problems origdate origyear ... John Wiley & Sons location New York isbn 0 471 31999 6 oclc 64431691 doi id chapter BoundaryValue ... more details
cleanup section date June 2008 Portal Software Testing Boundaryvalue analysis is a software testing technique in which tests are designed to include representatives of boundary values. Values on the minimum and maximum edges of an equivalence partitioning equivalence partition are tested. The values could be either input or output ranges of a software component. Since these boundaries are common locations for errors that result in software fault technology faults they are frequently exercised in test case s. Application The expected input and output values to the software component should be extracted from the component specification. The values are then grouped into sets with identifiable boundaries. Each set, or partition, contains values that are expected to be processed by the component in the same way. Partitioning of test data ranges is explained in the equivalence partitioning test ... partition 1 valid partition invalid partition 2 The boundary between two partitions is the place where the behavior of the application changes and is not a real number itself. The boundaryvalue is the minimum or maximum value that is at the boundary. The number 0 is the maximum number in the first partition, the number 1 is the minimum value in the second partition, both are boundary ..., but the input was a decimal with 2 places then it would be .01. In the example above there are boundary values at 0,1 and 12,13 and each should be tested. Boundaryvalue analysis does not require ... side of each boundary, which results in two cases per boundary. The test cases on each side of a boundary ... or colder. There are two partitions temperature 10, temperature 10 and two boundary values to be tested temperature 10, temperature 11 . Where a boundaryvalue falls within the invalid partition the test case is designed to ensure the software component handles the value in a controlled manner. Boundaryvalue analysis can be used throughout the testing cycle and is equally applicable at all testing ... more details
the value g on the boundary. In the obstacle problem, we impose an additional constraint we minimize ...In mathematics , a free boundaryproblem is a partial differential equation to be solved for both an unknown function u and an unknown domain . The segment of the boundary of which is not known at the outset of the problem is the free boundary . The classic example is the melting of ice. Given a block of ice, one can solve the heat equation given appropriate initial and boundary conditions to determine ... famous free boundaryproblem is the obstacle problem , which bears close connections to the classical ... set N C as the region where u is not equal to , and the free boundary as the interface between the two. Then u satisfies the free boundaryproblem math nabla 2 u f text in N, quad u g math on the boundary ... Note that the set of all functions v such that v is convex. Where the Poisson problem corresponds to minimization of a quadratic functional over a linear subspace of functions, the free boundaryproblem ... boundaryvalue problems. Regularity of free boundaries In the theory of elliptic operator elliptic ... must also demonstrate the regularity of the free boundary itself. For example, for the Stefan problem ... is a Stefan problem for the temperature field T , which is formulated as follows. Consider a medium ... cdot alpha 2 nabla T Q. math This is subject to appropriate conditions on the known boundary of ... we mean the limit of the gradient as x approaches sub t sub from the region T 0. In this problem, we ... the Stefan problem we not only have to solve the heat equation in each region, but we must also track the free boundary . The one phase Stefan problem corresponds to taking either sub 1 sub or sub 2 sub to be zero it is a special case of the two phase problem. In the direction of greater complexity ... free boundary problems can profitably be viewed as variational inequality variational inequalities for the sake ... must be zero if x is on the boundary of C , the gradient of F at x must be perpendicular to the boundary ... more details
of spatial statistics. Geographical Analysis 12, 325 339. Griffith, D. 1983 The boundaryvalueproblem ...A boundaryproblem in spatial analysis refers to a phenomenon in which geographical patterns are differentiated ... purposes. This is distinct from and must not be confused with the boundaryproblem in the philosophy of science that is used as a synonym for the demarcation problem . Definition In spatial analysis , four major problems interfere with an accurate estimation of the statistical parameter the boundaryproblem, scale problem, pattern problem or spatial autocorrelation , and modifiable areal unit problem Barber 1988 . The boundaryproblem occurs because of the loss of neighbours in analyses that depend ... the boundaryproblem was discussed in relation to artificial and arbitrary boundaries, the effect ... at sites on the natural boundary such as streams are likely to differ from those at sites within the boundary Martin 1989 . The boundaryproblem occurs with regard not only to horizontal boundaries ... fHD7C68ZqPM S VBeClLMcI AAAAAAAAARc Fg3kytstuUg s640 BP.jpg Boundaryproblem urban sprawl in central ... rural areas. In spatial analysis, the boundaryproblem has been discussed along with the modifiable ... problemboundaryproblem in the philosophy of science Fuzzy architectural spatial analysis Generalized ... a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data. In analysis with point data, dispersion is evaluated as dependent of the boundary. In analysis with areal data, statistics should be interpreted based upon the boundary. In geographical research, two types of areas are taken into consideration in relation to the boundary ... boundaries e.g., an air pollution boundary in modeling studies or an urban boundary in population ..., such an approach leads to a significant model misspecification problem Upton and Fingleton 1985 ... been reported that the difference in the way of drawing the boundary significantly affects identification ... more details
2t 1 & 6e 3t 2 6e 3t 6t 3 & 6t 5. end align math See also Boundaryvalueproblem Constant of integration ...In mathematics , in the field of differential equation s, an initial valueproblem also called the Cauchy problem by some authors is an ordinary differential equation together with a specified value, called the initial condition , of the unknown function at a given point in the domain of the solution. In physics or other sciences, modeling a system frequently amounts to solving an initial valueproblem in this context, the differential equation is an evolution equation specifying how, given initial conditions, the system will time evolution evolve with time . Definition An initial valueproblem is a differential equation math y t f t, y t , math with math f Omega subset mathbb R times mathbb R n to mathbb R n math where math Omega , math is an open set, together with a point in the domain of math t 0, y 0 in Omega, math called the initial condition . A solution to an initial valueproblem is a function y that is a solution to the differential equation and satisfies math y t 0 y 0. , math ... that there exists a unique fixed point, which is the solution of the initial valueproblem. An older ... of the integral equation, and thus, the solution of the initial valueproblem. Such a construction ... and sufficient condition for the solution of an initial valueproblem to be unique. This condition ... For a large class of initial value problems, the existence and uniqueness of a solution can be illustrated ... proceeds by reformulating the problem as an equivalent integral equation . The integral ... in time the problem is that there is no guarantee of uniqueness. The result may be found in Coddington ... initial value there are several methods. like we use these two formulas br math y 0 left frac ... a value for math C math . Use math y 0 19 math as given at the start and substitute 0 for math t math ... Boundary conditions cs Po te n podm nky el it Problema ai valori iniziali nl Beginvoorwaarde ... more details
In mathematics , some boundaryvalueproblem s can be solved using the methods of stochastic processes stochastic analysis . Perhaps the most celebrated example is Shizuo Kakutani s 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion . However, it turns out that for a large class of semi elliptic operator semi elliptic second order partial differential equations the associated Dirichlet boundaryvalueproblem can be solved using an It process that solves an associated stochastic differential equation . Introduction Kakutani s solution to the classical Dirichlet problem Let D be a domain an open set open and connected space connected set in R sup n sup . Let &Delta be the Laplace operator , let g be a bounded function on the boundary topology boundary &part D , and consider the problem math begin cases Delta u x 0, & x in D displaystyle lim y to x u y g x , & x in partial D. end cases math It can be shown that if a solution u exists, then u x is the expected value of g x at the random first exit point from D for a canonical Brownian motion starting at x . See theorem 3 in Kakutani 1944, p. 710. The Dirichlet Poisson problem Let D be a domain in R sup n sup and let L be a semi elliptic differential operator on C sup 2 sup R sup n sup R of the form math L sum i 1 n b i x frac partial partial x i sum i, j 1 n a ij x frac partial 2 partial x i , partial x j , math where the coefficients b sub i sub and a sub ij sub are continuous function s and all the eigenvalue s of the matrix mathematics matrix a x a sub ij sub x are non negative. Let f &isin C D R and g &isin C &part D R . Consider the Poisson equation Poisson problem math begin cases L u x f x , & x in D displaystyle lim y to x u y g x , & x in partial D. end cases quad mbox P1 math The idea of the stochastic method for solving this problem ... isbn 3 540 04758 1 See Section 9 Category Boundary conditions Category Partial differential equations ... more details
, as in the case of a manifold with boundaryBoundaryvalueproblem , a differential equation together with a set of additional restraints called the boundary conditions Boundary thermodynamic , the edge ...wiktionary Boundary plural boundaries may refer to any meaning below, also to border . Psychology main Psychology Personal boundaries Mathematics and Physics main Mathematics Physics Boundary topology ... in landscape history , the divide between areas of differing land use Boundary real estate , the legal boundary between units of real property Boundary cricket , the edge of the playing field, or a scoring ... , a 2008 television series Boundary critique , a concept about the meaning and validity of propositions Communication privacy management theory Boundary Turbulence , a break in expectation of how private information is held within a group of knowledge owners Place names Boundary, Derbyshire , a civil parish and hamlet in South Derbyshire, England Boundary, Leicestershire , a village in Leicestershire, England Boundary, Staffordshire , a village in Staffordshire, England Boundary Ranges , also known as the Boundary Range, a mountain range in British Columbia, Canada and Alaska, United States Boundary Country , a region of southern British Columbia, Canada Kootenay Boundary Regional District , a regional district in British Columbia West Kootenay Boundary , a provincial electoral district in British Columbia Okanagan Boundary , a former provincial electoral district in British Columbia Boundary Similkameen , a former provincial electoral district in British Columbia Boundary Falls, British Columbia , also known as Boundary, a former railway town in the Boundary Country of British Columbia Stikine, British Columbia , called Boundary from 1930 to 1964, a former customs post on the Stikine River at the Alaska British Columbia border Ships MV Boundary , a number of ships with this name See also Boundary line disambiguation disambig ar bg de Granica fa fr Boundary it Frontiera ... more details
Wiktionary Value or values may refer to Concepts of worth Value theory overview of approaches in various disciplines Value ethics Value personal and cultural Value economics Theory of value economics Value investing Value marketing Value law i.e. consideration Concepts of quantity, amount, or entity Value semiotics Value mathematics Value computer science Note value music Colour theory Lightness Values usually refers to Value ethics Value personal and cultural Value law Disambiguation af Waarde ar cs Hodnota de Valor es Valor fr Valeur it Valore he ja no Verdi pl Warto pt Valor ro Valoare sk Hodnota fi Arvo t smennyssivu sv V rde vi Gi tr ... more details
image Labeledcyclohexane.png thumb 400px right The A value for a methyl group is 1.74 as derived from the chemical equilibrium above. This means it costs 1.74 kcal mol of energy to have a methyl group in the axial position compared to the equatorial position. A Values are numerical values used in the determination of the most stable orientation of atoms in a molecule Conformational isomerism Conformational Analysis , as well as a general representation of steric bulk . A values are derived from energy ... axial substitution and the lower energy conformation equatorial substitution is the A value for that particular ... the substituent with the largest A value is equatorial is favored. image methyltbutyl cyclohexane.png thumb 600px center A methyl substituent has a significantly smaller A value than a tert butyl ... help predict the steric effect of a substituent. In general, the larger a substituent s A value, the larger the steric effect of that substituent. Methyl has an A value of 1.74 while butyl tert butyl has an A value of 5. Because the A value of tert butyl is higher, tert butyl has a larger steric effect ... conformations of ethyl cyclohexane, the A value is reduced from what would be predicted based ... Havinga first4 E. ref class wikitable style text align center Substituent A Value Substituent A Value Substituent A Value D 0.006 CH sub 2 sub Br 1.79 OSi CH sub 3 sub sub 3 sub 0.74 F 0.15 CH CH sub ... value of a favorable intramolecular hydrogen bond can be calculated. ref name HBondApprox cite journal .... This leads to a problem when there are possible stabilizing electronic factors in a different system. The carboxylic acid substituent shown below is axial in the ground state, despite a positive A Value ... effect. For example, the tert butyl group A value 4.9 has a larger A value than the trimethylsilyl group A value 2.5 , yet the tert butyl group actually occupies less space. This difference can be attributed ... effectively makes the trimethylsilyl group less sterically hindering, thus, lowering it s A value ... more details
Dablink T value can also refer to the Student s t test . The United States Department of Agriculture defines the T Value as the maximum average soil loss in tons per year that will still allow economical maintenance of the current level of production into the future. ref http agriculture.house.gov info glossary tu.htm USA Department of Agriculture ref References Reflist colwidth 40em references references Category United States Department of Agriculture ... more details
No Problem may refer to No Problem Sonny Rollins album No Problem Sonny Rollins album , a 1981 album No Problem Fann Wong album No Problem Fann Wong album , a 2000 album No Problem TV series No Problem TV series , a British television series No Problem film No Problem film , a 2010 Bollywood film disambig it No problem ... more details
other uses A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites ... or goal. A problem implies a desired outcome coupled with an apparent deficiency, doubt or inconsistency that prevents the outcome from taking place. Problem solving main Problem solving Every theoretical problem asks for an answer or solution. Trying to find a solution to a problem is known as problem solving . There are many standard techniques for problem solving, such as Proof by Contradiction ... Problem posed by Leonhard Euler . A problem is a gap between an actual and desired situation. The time it takes to solve a problem is a way of measuring complexity . ref cite book last first authorlink ... solution and are therefore classified as an open problem . See also List of unsolved problems ... to solve problems. Examples Mathematical problem is a question about mathematical objects and structures ... include Word problem mathematics education word problems at school level or deeper problems such as Four color theorem shading a map with only four colours . In society , a problem can refer to particular ..., and conversely diminished hostility and disruption. See also Wicked problem In business and engineering , a problem is a difference between actual conditions and those that are required or desired. Often, the causes of a problem are not known, in which case root cause analysis is employed to find the causes and identify corrective actions. In Chess problem chess , a problem is a puzzle ... Problem , regarding the Gospels relationship to each other. In academic discourse a problem is a challenge ... or idea. An optimization problem is finding the best solution from all feasible solutions. A good example of this type of problem is the travelling salesperson problem which is based on calculating the most efficient route between many places In computability theory a decision problem requires a simple yes or no answer. In rock climbing a problem is a series of Rock geology rock s that forces ... more details
Unreferenced date December 2009 The term boundary case is frequently used in software engineering to refer to the behavior of a system when one of its inputs is at or just beyond its maximum or minimum limits. It is frequently used when discussing software testing . For example, if an input field is meant to accept only integer values 0 100, entering the values 1, 0, 100, and 101 would represent the boundary cases. It is commonly thought that three cases should be used when boundary testing one on the boundary, and one on either side to it . However, the case on the valid side of the boundary is redundant, and so equivalence partitioning recommends skipping it. Dubious date March 2009 Citation needed date February 2009 . See also Portal Software Testing Black box testing Boundaryvalue analysis Corner case Edge case DEFAULTSORT Boundary Case Category Software testing ... more details
Boundary testing or boundaryvalue analysis , is where test case s are generated using the extremes of the input domain , e.g. maximum, minimum, just inside outside boundaries, typical values, and error values. It is similar to Equivalence Partitioning but focuses on corner cases . ref http www.aptest.com glossary.html bvatesting Software Testing and Quality Assurance Glossary Bot generated title ref ref http www.youtube.com watch?v wNMM8Bc0G3A Video Tutorial on YouTube ref References references Category Software testing ... more details
Unreferenced stub auto yes date December 2009 In a statistical classification statistical classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other side as belonging to the other class. If the decision surface is a hyperplane , then the classification problem is linear, and the classes are linearly separable . Decision boundaries are not always clear cut. That is, the transition from one class in the feature space to another is not discontinuous, but gradual. This effect is common in fuzzy logic based classification algorithms, where membership in one class or another is ambiguous. In ANNs and SVMs In the case of backpropagation based artificial neural network s or perceptron s, the type of decision boundary that the network can learn is determined by the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then it can learn problems with convex decision boundaries and some concave decision boundaries . The network can learn more complex problems if it has two or more hidden layers. In particular, support vector machine s find a hyperplane that separates the feature space into two classes with the maximum margin hyperplane maximum margin . If the problem is not originally linearly separable, the kernel trick is used to turn it into a linearly separable one, by increasing the number of dimensions. Thus a general hypersurface in a small dimension space is turned into a hyperplane in a space with much larger dimensions. Neural networks try to learn the decision boundary which minimizes the empirical error, while support vector machines try to learn the decision boundary which gives the best generalization. DEFAULTSORT Decision Boundary C ... more details
Boundary Commission may refer to Boundary Commissions United Kingdom Boundary Commissions of the United Kingdom Boundary Commission Ireland Boundary Commission between the United Kingdom and Ireland Boundary Commission Pacific Northwest Boundary Commission of the Pacific Northwest Boundary Commission Maine Boundary Commission of Maine Boundary Commission Alaska Panhandle Boundary Commission of the Alaska Panhandle Boundary Commissions Netherlands Boundary Commission of Indonesia disambig ... more details
In science studies , boundary work comprises instances in which boundaries, demarcations, or other divisions between fields of knowledge are created, advocated, attacked, or reinforced. Academic scholarship on boundary work has emphasized that such delineations often have high stakes involved for the participants, and carries with it the implication that such boundaries are flexible and social construction socially constructed . The original use of the term boundary work for these sorts of issues has been attributed to Thomas F. Gieryn , a sociology sociologist , who initially used it to discuss the problem of demarcation , the philosophical difficulty of coming up with a rigorous delineation between what is science and what is non science . He defined boundary work as the attribution of selected characteristics to an institution i.e., to its practitioners, methods, stock of knowledge, values and work organization for purposes of constructing a social boundary that distinguishes some intellectual activities as outside that boundary . Philosophy of science Philosophers and sociology of science sociologists of science , notably Karl Popper and Robert K. Merton , long struggled to come up with a criterion which would distinguish science as unique from other knowledge generating activities .... Gieryn s 1983 paper on boundary work and demarcation emphasized that the very discussions of demarcation ... for wikt autonomy autonomy . Gieryn s paper looked specifically at instances of boundary work in 19th ... as well. Many other works by sociologists and historians have since looked at boundary work in many ... and intersocial interactions. Studies in boundary work have also focused on how individual ... they satisfy the needs of multiple social groups boundary object s . Examples An example of such boundary ... , Bucknell University Press See also Conflict thesis Demarcation problem Science wars References cite journal last Gieryn first Thomas F. title Boundary work and the demarcation of science from ... more details
with this problem is to suck the boundary layer away through a porous surface see Boundary layer ...for the anatomy anatomical structure Boundary layer of uterus Image Boundarylayer.png 320px thumb right Boundary layer visualization, showing transition from laminar to turbulent condition In physics and fluid mechanics , a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. In the Earth s atmosphere , the planetary boundary ... to or from the surface. On an aircraft wing the boundary layer is the part of the flow close to the wing ... . Laminar boundary layers can be loosely classified according to their structure and the circumstances ... of a Stokes boundary layer , while the Blasius boundary layer refers to the well known Similitude ... inertia , an Ekman layer forms. In the theory of heat transfer, a thermal boundary layer occurs. A surface can have multiple types of boundary layer simultaneously. Aerodynamics File Laminar boundary layer scheme.svg thumb 320px Laminar boundary layer velocity profile The Aerodynamics aerodynamic boundary ... flow by dividing the flow field into two areas one inside the boundary layer, dominated by viscosity and creating the majority of drag physics drag experienced by the boundary body and one outside the boundary layer, where viscosity can be neglected without significant effects on the solution. This allows ... within the boundary layer, again allowing the equations to be simplified in the flow field outside the boundary layer. The pressure distribution throughout the boundary layer in the direction normal to the surface such as an airfoil remains constant throughout the boundary layer, and is the same as on the surface itself. The thickness of the velocity boundary layer is normally defined as the distance ... that the boundary layer represents a deficit in mass flow compared to inviscid flow with slip at the wall .... The flow velocity will then increase rapidly within the boundary layer, governed by the boundary ... more details
The behavior of phase boundaries has been a developing subject of interest and an active research field in physics and mathematics for almost two centuries. One reason behind this is that phase matter phase boundaries naturally arise in many physical processes due to immiscibility of two or more substances with different physical properties. Hence, various phenomena such as capillarity effect , growth of grain boundary grain boundaries , physics of binary alloy s, formation of snow flake s fall under the category of interface science. One of the oldest problems in the area dates back to Lame and Clapeyron ref Lame ref who studied the freezing of the ground. Their goal was to determine the thickness of solid crust generated by the cooling of a liquid at constant temperature filling the half space . In 1889, Stefan, while working on the freezing of the ground developed these ideas further and formulated the two phase model which came to be known as the Stefan problem Stefan Problem . ref Stefan ref The proof of existence and uniqueness of a solution to the Stefan problem was done in many stages. Proving the general existence of the solutions turned out to be a difficult problem for math d geq 2 math Clarify date July 2011 see e.g. cite 3 that was finally solved by Enverbek Meirmenov. ref Meirmenov ref See also Literature of phase boundaries References Reflist Category Phase transitions Category Applied mathematics ... more details
The Pocock boundary is a method for determine whether to stop a clinical trial prematurely. The typical clinical trial compares two groups of patients. One group are given a placebo or conventional treatment, while the other group of patients are given the treatment that is being tested. The investigators running the clinical trial will wish to stop the trial early for ethical reasons if the treatment group clearly shows evidence of benefit. In other words, when early results proved so promising it was no longer fair to keep patients on the older drugs for comparison, without giving them the opportunity to change. ref cite news author Hall C title Heart attacks may be cut by half newspaper Daily Telegraph date 5 September 2005 page 1 url http www.telegraph.co.uk news uknews 1497648 Heart attacks may be cut by half.html ref The concept was introduced by the medical statistician Stuart Pocock ... 16264167 ref Details The Pocock boundary ref cite journal doi 10.1093 biomet 64.2.191 author Pocock ... journal Biometrika year 1977 volume 64 issue 2 pages 191&ndash 9 jstor 2335684 ref gives a p value p value threshold for each interim analysis which guides the data monitoring committee on whether to stop the trial. The boundary used depends on the number of interim analyses. class wikitable List of p values used at each interim analysis, assuming the overall p value for the trial is 0.05 Number of planned analyses Interim analysis p value threshold style background lightgrey 2 1 0.0294 style ... lightgrey 4 final 0.0182 5 1 0.0158 2 0.0158 3 0.0158 4 0.0158 5 final 0.0158 The Pocock boundary is simple to use in that the p value threshold is the same at each interim analysis. The disadvantages ... interim analyses planned, but the trial is stopped after the third interim analysis because the p value was 0.01, then the overall p value for the trial is still reported as < 0.05 and not as 0.01 ... pmid 15885299 ref See also Haybittle Peto boundary References Reflist Category Statistical methods ... more details
A number of motor vessel s have been named Boundary , including MV Boundary 1942 , a Panaminan ship in service 1970 72 MV Boundary 1993 , a Marshallese ship in current service shipindex ... more details
Boundary Peak may refer to Boundary Peak, the former name of Pope s Peak , an historic summit on the Canadian Rockies on the British Columbia border one of c. 1000 peaks forming the international boundary between the British Columbia and Yukon, Canada, and Alaska, United States, numbered in sequence see List of Boundary Peaks of the Alaska British Columbia border Boundary Peak Alaska , a summit in the Yakutat Alsek River area in Alaska One of eight summits elsewhere in the United States Boundary Peak California Boundary Peak Idaho County, Idaho Boundary Peak Shoshone County, Idaho Boundary Peak Maine Boundary Peak Nevada the highest point in the State of Nevada Boundary Peak Wilderness , Nevada Boundary Peak New Mexico Boundary Peak New York Boundary Peak Washington geodis Category Place name disambiguation pages de Boundary Peak ... more details
Boundary Road may refer to Boundary Road Vancouver Burnaby , British Columbia, Canada Boundary Road, Singapore Boundary Road Brewery, a craft beer brand produced by Beer in New Zealand Large breweries Independent Breweries NZ See also Boundary Street , Kowloon, Hong Kong Roadindex ... more details
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