A locking differential , diff lock or locker is a variation on the standard automotive differential mechanics differential . A locking differential may provide increased traction engineering traction compared to a standard, or open differential by restricting each of the two wheels on an axle to the same ... wheel. A locking differential is designed to overcome the chief limitation of a standard open differential ... individually. When the differential is unlocked open differential , it allows each wheel to rotate at different ... of the merry go round , thus avoiding tire scuffing. An open or unlocked differential ..., a locked differential forces both left and right wheels on the same axle to rotate at the same ... apply to automatic lockers, discussed below. A locked differential can provide a significant traction advantage over an open differential, but only when the traction under each wheel differs significantly ... input from the driver. Some automatic locking differential designs ensure that engine power ... wheel to spin slower than the differential carrier or axle as a whole, but will permit a wheel to be over ... Detroit Locker, also known as the Detroit No Spin, which replaces the entire differential carrier assembly. Others, sometimes referred to as Lunchbox locker lunchbox lockers , employ the stock differential ... types of automatic lockers will allow for a degree of differential wheel speed while turning corners ... oversteer when traction is exceeded. Some other automatic lockers operate as an open differential until ... Lok. Some other automatic lockers operate as an open differential until high torque is applied and then they lockup ... lockers allow the driver to lock and unlock the differential at will from the driver s seat. This can ... ford super duty electric locker lowdown index.html ref Pros Allows the differential to perform as an open differential for improved driveability, maneuverability, provides full locking capability when .... Unskilled drivers often put massive stress on driveline components when leaving the differential ... more details
Differential hardening is a method used in forging sword s and knife knives to increase the hardness of the edge without making the whole blade brittle . To achieve this, the edge is cooled more rapidly than the spine by adding a heat insulator to the spine before quenching . Clay or another material is used for insulation. It can also be achieved by carefully pouring water perhaps already heated onto the edge of a blade as is the case with the manufacture of some kukri . Differential hardening technology was perfected in China and later spread to Korea and Japan. This technique is mainly used in the Chinese jian and the katana , the traditional Japan ese sword, and the khukuri , the traditional Nepal ese knife. Most blades made with this technique have visible temper lines. Another process, often referred to as differential hardening, but in reality differential tempering can also be obtained by quenching the object uniformly, then differentially tempering one part of it with a torch or some other directed heat source. The heated portion of the metal is softened by this process. http www.primitiveways.com pt knives 1.html See also Case hardening Shot peening External links http www.engnath.com claytemp.htm Claying blades Differential hardening with clay Category Metal heat treatments metalworking stub ... more details
Differential Staining is a general term that can refer to a number of specific processes. Generally, it is used to describe staining processes which use more than one chemical stain . Using multiple stains can better differentiate between different microorganisms or structures cellular components of a single organism. Differential Staining also describes medical process used to detect abnormalities in the proportion of different white blood cells in the blood . The process or results are called a WBC differential. This test is useful because many diseases alter the proportion of certain white blood cells . By analyzing these differences in combination with a clinical exam and other lab tests, medical professionals can diagnose disease. One commonly recognizable use of differential staining is the Gram stain . Gram staining uses two dyes Crystal violet and Fuchsin the counterstain to differentiate between Gram positive bacteria large Peptidoglycan layer on outer surface of cell and Gram negative bacteria. Further reading http www.mansfield.ohio state.edu sabedon black03.htm differential stain Detailed Overview of staining http www.uphs.upenn.edu bugdrug antibiotic manual Gram2.htm The Gram Stain Technique Category Medical tests pathology stub pt Colora o diferencial ... more details
In mathematics, differential inclusions are a generalization of the concept of ordinary differential equation of the form math frac dx dt t in F t,x t , math where F t , x is a set rather than a single point in math scriptstyle Bbb R d math . Differential inclusions arise in many situations including differential variational inequality differential variational inequalities , projected dynamical system s, dynamic Coulomb friction problems and fuzzy set arithmetic. For example, the basic rule for Coulomb friction is that the friction force has magnitude N in the direction opposite to the direction of slip, where N is the normal force and is a constant the friction coefficient . However, if the slip is zero, the friction force can be any force in the correct plane with magnitude smaller than or equal to N Thus, writing the friction force as a function of position and velocity leads to a set valued function. Theory Existence theory usually assumes that F t , x is an hemicontinuous upper semi continuous function of x , measurable in t , and that F t , x is a closed, convex set for all t and x . Existence of solutions for the initial value problem math frac dx dt t in F t,x t , quad x t 0 x 0 math for a sufficiently small time interval t sub 0 sub , t sub 0 sub , 0 then follows. Global existence can be shown provided F does not allow blow ... math scriptstyle t math . Existence theory for differential inclusions with non convex F t , ... by Minty and Ha m Brezis . Applications Differential inclusions can be used to understand and suitably interpret discontinuous ordinary differential equations, such as arise for Coulomb friction ... of regularization was used by Nikolai Nikolaevich Krasovsky Krasovskii in the theory of differential game s. References Jean Pierre Aubin, Arrigo Cellina Differential Inclusions, Set Valued Maps And Viability .... Frankowska Set Valued Analysis , Birkh auser, Basel, 1990 Klaus Deimling Multivalued Differential ... more details
Refimprove date December 2008 File Differential linearity.svg thumb right Demonstrates A. Differential Linearity where a change in the input produces a corresponding change in output and B. Differential Non linearity, where the relationship is not directly linear Differential nonlinearity acronym DNL is a term describing the deviation between two analog values corresponding to adjacent input digital values. It is an important specification for measuring error in a digital to analog converter DAC the accuracy of a DAC is mainly determined by this specification. Ideally, any two adjacent digital codes correspond to output analog voltages that are exactly one Least significant bit Least Significant Bit LSB apart. Differential non linearity is a measure of the worst case deviation from the ideal 1 LSB step. For example, a DAC with a 1.5 LSB output change for a 1 LSB digital code change exhibits 1 2 LSB differential non linearity. Differential non linearity may be expressed in fractional bits or as a percentage of full scale. A differential non linearity greater than 1 LSB may lead to a non monotonic transfer function in a DAC. ref INL and DNL definitions A DNL error specification of less than or equal to 1LSB guarantees a monotonic transfer function with no missing codes. http www.maxim ic.com app notes index.mvp id 283 ref It is also known as a missing code . Differential linearity refers to a constant relation between the change in the output and input. For transducer s if a change in the input produces a uniform step change in the output the tranducer possess differential linearity. Differential linearity is desirable and is inherent to a system such as a single slope analog to digital convertor used in Particle detector nuclear instrumentation . Formula DNL Max V sub out sub i 1 V sub out sub i V sub ideal LSB step sub See also Integral nonlinearity References reflist External links http www.maxim ic.com appnotes.cfm an pk 283 INL DNL Measurements for High Speed Analog ... more details
during maturation Differential Signaling Hypothesis Differential signaling is a method of transmitting ... thumb upright 1.3 right Elimination of noise by using differential signaling. Advantages Tolerance of ground offsets Image Differential Signaling.png thumb 500px right In a system with a differential ... immunity . Differential signaling helps to reduce these problems because, for a given supply ... V V S math . Now consider a differential system with the same supply voltage. The voltage difference ... twice as much noise to cause an error with the differential system as with the single ended system ... is not actually due to differential signaling itself, but to the common practice of transmitting differential signals on balanced line s. ref cite web url http www.soundcraft.com support white ... would fail completely, the matching of the differential audio signals being irrelevant, though ... rejection property is independent of the presence of a desired differential signal. page 111 ... by a differential amplifier. See Balanced line for more details. Comparison with single ended signaling ... to operate at high speed. Examples Examples of differential signaling include LVDS , differential ... a common Ground electricity ground . Differential signaling is used with a balanced pair of conductors ... to behave as transmission line s. Use in computers Differential signaling is often used in computers ... into a small space, as on a typical PCB. High voltage differential signaling High voltage differential ... means 5 volts or more. SCSI 1 variations included a high voltage differential HVD implementation whose ... than the older HVD SCSI. The term high voltage differential signaling is a generic one that describes a variety of systems. Low voltage differential signaling or LVDS , on the other hand, is a specific system defined by a TIA EIA standard. See also Current mode logic CML Low voltage differential ... Transition Minimized Differential Signaling TMDS Longitudinal voltage Differential amplifier Differential ... more details
The main purpose of the electronic differential is to replace the Differential mechanical device mechanical differential in multi drive systems, providing the required torque for each driving wheel and allowing different wheel speeds. When cornering, the inner and outer wheels rotate at different speeds, because the inner wheels describe a smaller turning radius. The electronic differential uses the steering wheel command signal and the motor speed signals to control the power to each wheel so that all wheels have the maximum torque they need. Functional description The classical automobile drive train is composed by a single Internal combustion engine motor providing torque to one or more driving wheels. The most common solution is to use a mechanical device to distribute torque to the wheels. This Differential mechanical device mechanical differential allows different wheel speeds when cornering. With the emergence of electric vehicle s new drive train configurations are possible. Multi drive systems become easy to implement due to the large power density of electric motor s. These systems, usually with one motor per driving wheel, need an additional top level controller which performs the same task as a mechanical differential. The ED scheme has several advantages over a mechanical differential ref cite web url http ieeexplore.ieee.org search srchabstract.jsp?arnumber 1339466&isnumber 29535&punumber 41&k2dockey 1339466 ieeejrns&query 28 uot 3Cin 3Emetadata 29&pos 1 title Future vehicle driven by electricity and Control research ref simplicity it avoids additional mechanical parts such as a gearbox or clutch independent torque for each wheel allows additional capabilities e.g., traction control system traction control , stability control reconfigurable it is reprogrammable ... differential. faster response times accurate knowledge of traction torque per wheel. Applications ... and reducing tire wear. The Eliica is also equipped with electronic differential this eight wheeled ... more details
Unreferenced date December 2009 Differential rotation is seen when different parts of a rotating object ... s usually show differential rotation and examples in our solar system include the Sun , Jupiter and Saturn ... at the poles and at the equator, in good agreement with modern values. The cause of differential rotation ... is induced. Differential rotation is caused by convection in stars. This is movement of mass, due ... angular velocity in stellar wind s. Differential rotation thus depends on temperature differences in adjacent regions. Measuring differential rotation There are many ways to measure and calculate differential rotation in stars to see if different latitudes have different angular velocities. The most ... measurements of solar p modes it is possible to deduce the differential rotation. The Sun has very ... also plot 2. Solar differential rotation is also seen in magnetograms, images showing the strength and location of solar magnetic fields. Effects of differential rotation Gradients in angular rotation ... differential rotation is one part of the mixing processes in stars, mixing the materials and the heat energy of the stars. Differential rotation affects stellar optical absorption line spectra through ... surface. Solar differential rotation causes shear at the so called tachocline. This is a region where rotation changes from differential in the convection zone to nearly solid body rotation in the interior, at 0.71 solar radii from the center. Calculating differential rotation For observed sunspots, the differential rotation can be calculated as math Omega Omega 0 Delta Omega sin 2 Psi math ... for the equator to do a full lap more than the poles. The relative differential rotation rate is the ratio ... measured from the poles . Differential rotation of the Sun File Tachocline.gif thumb right 200px Internal rotation in the Sun, showing differential rotation in the outer convective region and almost ... speed of 2 km s its differential rotation implies that the angular velocity decreases with increased ... more details
one source date December 2010 File Differential sticking.svg thumb 250px right A diagram showing forces at work during differential sticking. The small black arrows represent pressure exerted on the drill pipe from the wellbore, the red arrows represent pressure exerted on the pipe from the formation smaller than in the wellbore and the large black arrow represents the net force on the pipe, which is pushing it into the wall. Differential sticking is a problem that occurs when drilling a Oil well well with a greater well bore pressure than formation pressure, as is usually the case. The drill pipe is pressed against the wellbore wall so that part of its circumference will see only reservoir pressure, while the rest will continue to be pushed by wellbore pressure. As a result the pipe becomes stuck to the wall, and can require millions of pounds of force to remove, which may prove impossible. In many cases the drilling fluid mud weight is simply reduced, thus relieving the pressure difference and releasing the stuck pipe string. Should this option be unavailable, as in sour gas wells, a specialty fishing company is called to retrieve the stuck pipe or fish . Many options exist once a fishing company is on site oil or nitrogen may be pumped down the well, or the fish may be washed over using a carbide shoe on a string of washpipe. Jarring is not usually attempted with differential sticking due to the massive amount of pressure that holds the pipe in place. External links http www.glossary.oilfield.slb.com Display.cfm?Term differential 20sticking Schlumberger Oilfield Glossary about differential sticking petroleum stub Category Drilling technology br Petroleum industry ... more details
Differential weathering is the difference in degree of discoloration , disintegration , of rocks of different kinds exposed to the same environment. Quartz deposits in basaltic flows will weather slower than the surrounding rock, while being exposed to the same forces of weathering. More simply, Differential weathering is the chemical or physical breakdown of different rock units at different rates. The rate of breakdown is determined by several factors the rocks mineral composition, surface area, climate, time, etc. Landforms created by differential weathering consist of balanced rocks, cliff and bench topography, natural arches, natural bridges, and fins. References Reynolds, Stephen, Julia Johnson, Paul Morin, and Charles Carter. Exploring Geology. 2nd. 1. New York City McGraw Hill, 2010. Print. Northern Kentucky University Geology Dept. reflist Category Geomorphology climate stub ja ... more details
Image Op amp symbol.svg frame right div style text align center Differential amplifier symbol div The inverting ... the diagram for simplicity, but of course must be present in the actual circuit. A differential amplifier ... not amplify the particular voltages. Theory Many electronic devices use differential amplifiers internally. The output of an ideal differential amplifier is given by math V text out A text d V text ... A text d math is the differential gain. br In practice, however, the gain is not quite equal for the two ... of a differential amplifier thus includes a second term. math V text out A text d V text in V ... mode gain of the amplifier. br As differential amplifiers are often used to null out noise or bias ... ratio CMRR , usually defined as the ratio between differential mode gain and common mode gain ... In a perfectly symmetrical differential amplifier, math A text c math is zero and the CMRR is infinite. Note that a differential amplifier is a more general form of amplifier than one with a single input by grounding one input of a differential amplifier, a single ended amplifier results. Long tailed ... Invented the Differential Amplifier? . IEEE Engineering in Medicine and Biology, May June 1996 .... Configurations A differential long tailed, ref group nb Long tail is a figurative name of high resistance ... length at differential mode this tail shortens up to zero . If additional emitter resistors ... negative feedback at differential mode , they can be figuratively represented by short tails . ref ... degeneration emitter , Common source source or Valve amplifier cathode degeneration. Differential output ... and two outputs, this forms a differential amplifier stage Fig. 2 . The two bases or grids or gates ... with a differential balanced input signal, or one input could be grounded to form a phase splitter circuit. An amplifier with differential output can drive floating load or another stage with differential input. Single ended output If the differential output is not desired, then only one output can ... more details
Differential Inheritance is a common Inheritance object oriented programming inheritance model used by Prototype based programming prototype based programming languages such as JavaScript , Io programming language Io and NewtonScript . It operates on the principle that most objects are derived from other, more general objects, and only differ in a few small aspects while usually maintaining a list of pointers internally to other objects which the object differs from. An Analogy To think of differential inheritance, you think in terms of what is different. So for instance, when trying to describe to someone how Dumbo looks, you could tell them in terms of elephants Think of an elephant. Now Dumbo is a lot shorter, has big ears, no tusks, a little pink bow and can fly. Using this method, you don t need to go on and on about what makes up an elephant, you only need to describe the differences anything not explicitly different can be safely assumed to be the same. External links http developer.mozilla.org en docs Differential inheritance in JavaScript Differential inheritance in JavaScript Mozilla Developer Center article See also Inheritance object oriented programming Single inheritance Category Object oriented programming soft eng stub es Herencia diferencial ... more details
More footnotes date March 2009 Differential cryptanalysis is a general form of cryptanalysis applicable ... . History The discovery of differential cryptanalysis is generally attributed to Eli Biham and Adi ... and Shamir that DES is surprisingly resistant to differential cryptanalysis, in the sense that even ... stating that differential cryptanalysis was known to IBM as early as 1974, and that defending against differential cryptanalysis had been a design goal. ref name coppersmith cite journal doi 10.1147 ... ref According to author Steven Levy , IBM had discovered differential cryptanalysis on its own, and the NSA ... would reveal the technique of differential cryptanalysis, a powerful technique that could be used ... over other countries in the field of cryptography. ref name coppersmith Within IBM, differential ... to differential cryptanalysis in mind, other contemporary ciphers proved to be vulnerable ... round version of FEAL is susceptible to the attack. Attack mechanics Differential cryptanalysis is usually .... The resulting pair of differences is called a differential . Their statistical properties ... basic form of key recovery through differential cryptanalysis, an attacker requests the ciphertexts for a large number of plaintext pairs, then assumes that the differential holds for at least ... probable differences through the various stages of encryption, termed a differential characteristic . Since differential cryptanalysis became public knowledge, it has become a basic concern of cipher ... or known plaintext inputs suggests possible key values. For example, if a differential of 1 1 implying ... or 2 pairs of inputs is that differential possible. Suppose we have a non linear function where the key is XOR ed before evaluation and the values that allow the differential are 2,3 and 4,5 . If the attacker ... function one would ideally seek as close to 2 sup n 1 sup as possible to achieve differential uniformity . When this happens, the differential attack requires as much work to determine the key as simply ... more details
In mathematics , a differential operator is an Operator mathematics operator defined as a function of the derivative ..., which are the most common type. However, non linear differential operators, such as the Schwarzian derivative also exist. Notations The most common differential operator is the action of taking ... , who considered differential operators of the form math sum k 0 n c k D k math in his study of differential equation s. One of the most frequently seen differential operators is the Laplace operator ... Another differential operator is the operator, or theta operator, defined by ref cite web url http ... of applying the differential to the left Clarify date February 2012 and to the right Clarify date February 2012 , and the difference obtained when applying the differential operator to the left ... Main Del The differential operator del is an important Euclidean vector vector differential operator. It appears frequently in physics in places like the differential form of Maxwell s Equations . In three ... of an operator See also Hermitian adjoint Given a linear differential operator T math Tu sum k 0 n ... n sup , and P a differential operator on , then the adjoint of P is defined in Lp space L sup 2 ... example of a formal self adjoint operator. This second order linear differential operator L can be written ... of this operator are considered. Properties of differential operators Differentiation is linearity ..., and a is a constant. Any polynomial in D with function coefficients is also a differential operator. We may also compose differential operators by the rule math D 1 circ D 2 f D 1 D 2 f . , math ... another way it consists of the translation invariant operators. The differential operators also ... see symmetry of second derivatives . Coordinate independent description In differential geometry and algebraic geometry it is often convenient to have a coordinate independent description of differential ... to be a k th order linear differential operator if it factors through the jet bundle J sup k sup ... more details
about the concept from elementary differential calculus the generalized advanced mathematical concept from differential topology and differential geometry closed and exact differential forms Expert subject Physical Chemistry date March 2011 A mathematics mathematical differential infinitesimal differential is said to be exact , as contrasted with an inexact differential , if it is of the form dQ , for some ... a differential form. A differential form is exact on a domain D in space if A dx B ... to saying that the field is conservative. Overview For one dimension, a differential math dQ A x , dx math is always exact. For two dimensions, in order that a differential math dQ A x, y ,dx B x, y ,dy math be an exact differential in a simply connected region R of the xy plane, it is necessary ... y right x left frac partial B partial x right y math For three dimensions, a differential math dQ A x, y, z , dx B x, y, z , dy C x, y, z , dz math is an exact differential in a simply connected ... of the second derivatives. So, in order for a differential dQ , that is a function of four variables to be an exact differential, there are six conditions to satisfy. In summary, when a differential .... An exact differential is sometimes also called a total differential , or a full differential , or, in the study of differential geometry , it is termed an exact form . Partial differential relations ... math F x,y,z math , the following total differential s exist ref name Cengel1998 cite book last ... frac partial y partial z right x 1 math See also Closed and exact differential forms for a higher level treatment Differential mathematics Inexact differential Integrating factor for solving non exact differential equations by making them exact Exact differential equation References references Perrot ... Course in Differential Equations, 5th Ed. Boston PWS Kent Publishing Company. External links http mathworld.wolfram.com InexactDifferential.html Inexact Differential from Wolfram MathWorld http www.chem.arizona.edu ... more details
In the mathematics mathematical fields of differential geometry and tensor calculus , differential forms are an approach to multivariable calculus that is independent of coordinate s. Differential forms ... manifold s. The modern notion of differential forms was pioneered by lie Cartan . It has many ... algebra algebra of differential forms is organized in a way that naturally reflects the orientation mathematics orientation of the domain of integration. There is an operation d on differential forms ... extends the differential of a function , and the divergence and the curl mathematics curl of a vector ... way, this theorem relates the topology of the domain of integration to the structure of the differential ... of differential forms is on a differentiable manifold . Differential 1 forms are naturally ... to arbitrary differential forms by the interior product . The algebra of differential forms along with the exterior derivative defined on it is preserved by the pullback differential geometry pullback ... in terms of differential forms. As a particular example, the change of variables formula for integration becomes a simple statement that an integral is preserved under pullback. History Differential forms are part of the field of differential geometry, influenced by linear algebra. Although the notion of a differential is quite old, the initial attempt at an algebraic organization of differential ... www.numdam.org item?id ASENS 1899 3 16 239 0 year 1889 page 239 332 ref . Concept Differential forms ... set in R sup n sup . A differential 0 form zero form is defined to be a smooth function f on U ... n frac partial y i partial x j frac partial f partial y i math The first idea leading to differential ... derivative &mdash an example of a differential 1 form . Since any vector v is a linear combination ... , and so define differential 1 forms dx sup 1 sup , dx sup 2 sup , ..., dx sup n sup . Since ... sub i sub on U , we define the differential 1 form sub i sub g sub i sub dh sub i sub ... more details
Orphan date September 2008 Unreferenced date August 2008 Differential identification is a criminology criminological theory which states that crime and or Deviant behaviour deviance develops when the individual identifies more with the deviant group than with conforming members of society. For example, older criminals would serve as role models for younger criminals. The individual learns skills from an existent criminal. This criminal can be either real or imaginary such as a character from a movie , but is still affective in transferring the skills one would need to commit a crime. See also Daniel Glaser Differential opportunity crime stub sociology stub Category Criminology ... more details
differential have roots in the medieval controversy between the nominalist s and Philosophical realism ... differential . Use of adjectives The development of this instrument provides an interesting insight ... Osgood and his colleagues performed a factor analysis of large collections of semantic differential ... descriptive system of personality. Osgood s semantic differential measures these three factors ... of attitude psychology attitudes ref Himmelfarb 1993 p 56 ref . Usage The semantic differential ... on the development of the semantic differential is provided in the monumental book, Cross Cultural ... when using computerized graphic rating scale s. See also Thurstone scale Likert scale structural differential Structural Differential Notes Reflist References Heise, David R. 2010 . Surveying Cultures ..., C. E. 1969 Semantic Differential Technique A Sourcebook. Chicago Aldine. External links http www.writing.ws ... On line Semantic Differential Category Psychometrics Category General semantics cs S mantick ... more details
Compensating differential is a term used in labor economics to analyze the relation between the wage rate and the unpleasantness, risk, or other undesirable attributes of a particular job. A compensating differential, which is also called a compensating wage differential or an equalizing difference , is defined as the additional amount of income that a given worker must be offered in order to motivate them to accept a given undesirable job, relative to other jobs that worker could perform. ref cite book last Kaufman first Bruce E. first2 Julie L. last2 Hotchkiss year 2005 chapter Education, Training, and Earnings Differentials The Theory of Human Capital title The economics of labor markets edition 5th publisher Harcourt College Publishers location isbn 0324288794 ref ref cite book last Rosen first Sherwin year 1986 chapter The theory of equalizing differences editor1 first Orley editor1 last Ashenfelter editor2 first Richard editor2 last Layard title The Handbook of Labor Economics volume 1 pages 641 692 location New York publisher Elsevier isbn 0444878564 ref One can also speak of the compensating differential for an especially desirable job, or one that provides special benefits, but in this case the differential would be negative that is, a given worker would be willing to accept ... first Richard D., Jr. year 2004 title Estimating the compensating differential for employer provided ... risk and compensating differential in late nineteenth century New Jersey manufacturing work National ... title Sex workers and the cost of safe sex the compensating differential for condom use among Calcutta ... concepts The terms compensation differential , pay differential , and wage differential see ... last Bender first Keith A. year 1998 title The central government private sector wage differential ... So a compensation differential can be explained by many factors, such as differences in the skills ... of the jobs themselves. A compensating differential , in contrast, refers only ... more details
Differential stress is the difference between the greatest and the least compressive stress experienced by an object. For both the geology geological and civil engineering convention math sigma 1 math is the greatest compressive stress and math sigma 3 math is the weakest, math sigma D sigma 1 sigma 3 math . In other engineering fields and in physics , math sigma 1 math is the greatest compressive stress and math sigma 3 math is the weakest, so math sigma D sigma 3 sigma 1 math . These conventions originated because geologists and civil engineers especially soil mechanics soil mechanicians are often concerned with failure in compression, while many other engineers are concerned with failure in tension physics tension . A further reason for the second convention is that it allows a positive stress to cause a Compressibility compressible object to increase in size, making the sign convention self consistent. In structural geology , differential stress is used to assess whether tensile failure tensile or shear failure will occur when a Mohr circle plotted using math sigma 1 math and math sigma 3 math touches the failure envelope of the rocks. If the differential stress is less than four times the tensile strength of the rock geology rock , then extensional failure will occur. If the differential stress is more than four times the tensile strength of the rock, then shear failure will occur. ref Cosgrove. J. W. 1998 The role of structural geology in reservoir characterization. Geological Society, London, Special Publications, v. 127 p. 1 13 ref References references DEFAULTSORT Differential Stress Category Geology Geology stub phys stub nl Differentiaalspanning ... more details
context date October 2008 Differential capacitance in physics , electronics , and electrochemistry is a measure of the voltage dependent capacitance of a nonlinear capacitor , such as an electrical double layer or a semiconductor diode . It is defined as the derivative of charge with respect to potential. ref cite book title Modern methods of pharmaceutical analysis, Volume 2 edition 2nd author Roger E. Schirmer publisher CRC Press year 1991 isbn 9780849352676 pages 17 18 url http books.google.com books?id 7NDrUh2HgxIC&pg PA17&dq electrical double layer differential capacitance&lr &num 20&as brr 3&ei JMU2S uYLpDqkQScp TRAQ&cd 2 v onepage&q electrical double layer 20differential capacitance&f false ref ref cite book title Semiconductor material and device characterization author Dieter K. Schroder edition 3rd publisher John Wiley and Sons year 2006 isbn 9780471739067 pages 61 62 url http books.google.com books?id OX2cHKJWCKgC&pg PA61&dq 22differential capacitance 22&lr &as drrb is q&as minm is 0&as miny is &as maxm is 0&as maxy is &num 20&as brr 0&ei 28I2S86 N5qIlQSZuLy5AQ&cd 2 v onepage&q 22differential 20capacitance 22&f false ref Description In electrochemistry differential capacitance is a parameter introduced for characterizing electrical double layer s math C frac d sigma d Psi math where is surface charge and is electric surface potential Capacitance is usually defined ... potential . The latter is called the differential capacitance, but usually the stored charge .... This type of differential capacitance may be called parallel plate capacitance, after the usual form ... No. 142,352, August 13, 1912. ref blockquote The differential capacitance between the spheres is obtained .... ref blockquote Another form of differential capacitance refers to single isolated conducting bodies ... reflist External links http www.answers.com topic differential capacitance McGraw Hill Dictionary of Scientific and Technical Terms definition of differential capacitance Category Electrochemistry Category ... more details
In mathematics, a N ron differential , named after Andr N ron , is an almost canonical choice of 1 form on an elliptic curve or abelian variety defined over a local field or global field that behaves well on the N ron minimal model s. For an elliptic curve of the form math y 2 a 1xy a 3 x 3 a 2x 2 2 a 4x a 6 math the N ron differential is math frac dx 2y a 1x a 3 math References Citation last1 Bosch first1 Siegfried last2 L tkebohmert first2 Werner last3 Raynaud first3 Michel author3 link Michel Raynaud title N ron models publisher Springer Verlag location Berlin, New York series Ergebnisse der Mathematik und ihrer Grenzgebiete 3 isbn 978 3 540 50587 7 id MathSciNet id 1045822 year 1990 volume 21 Citation last1 N ron first1 Andr author1 link Andr N ron title Mod les minimaux des vari tes ab liennes sur les corps locaux et globaux url http www.numdam.org item?id PMIHES 1964 21 5 0 id MathSciNet id 0179172 year 1964 journal Publications Math matiques de l IH S volume 21 pages 5 128 doi 10.1007 BF02684271 DEFAULTSORT Neron differential Category Elliptic curves mathematics stub ... more details
Dablink For other uses of differential in mathematics, see differential mathematics . In calculus , the differential ... to changes in the independent variable. The differential dy is defined by math dy f x ,dx, math ... may take on a particular geometrical significance if the differential is regarded as a particular differential form , or analytical significance if the differential is regarded as a linear approximation ... to be very small infinitesimal . History and usage The differential was first introduced via ... Berkeley. Augustin Louis Cauchy CITEREFCauchy1823 1823 defined the differential without appeal to the atomism of Leibniz s infinitesimals. ref For a detailed historical account of the differential ... then defined in terms of it. That is, one was free to define the differential dy by an expression math ... y by the linear expression h&fnof x to construct a logically satisfactory definition of a differential ... and differential geometry , it became clear that the notion of the differential of a function could be extended in a variety of ways. In real analysis , it is more desirable to deal directly with the differential ... that the differential of a function at a point is linear functional of an increment x . This approach allows the differential as a linear map to be developed for a variety of more sophisticated ... . Likewise, in differential geometry , the differential of a function at a point is a linear function ..., which can themselves be put on a rigorous footing see differential infinitesimal . Definition File Sentido geometrico del diferencial de una funcion.png thumb The differential of a function &fnof x at a point x sub 0 sub . The differential is defined in modern treatments of differential ... include also harvnb Tolstov 2001 and harvnb Ito 1993 loc 106 . ref The differential of a function ..., i.e., one may see df x or simply df . If y x , the differential may also ... x , so that the following equality holds math df x f x , dx math This notion of differential is broadly ... more details
In mathematics, a Prym differential of a Riemann surface is a differential form on the universal covering space that transforms according to some complex character mathematics character of the fundamental group . Equivalently it is a section of a certain line bundle on the Riemann surface in the same component as the canonical bundle . Prym differentials were introduced by harvs txt authorlink Friedrich Prym last Prym year 1869 . The space of Prym differentials on a compact Riemann surface of genus g has dimension g 1, unless the character of the fundamental group is trivial, in which case Prym differentials are the same as ordinary differentials and form a space of dimension g . References Citation last1 Prym first1 F.E. title Zur Integration der gleichzeitigen Differentialgleichungen . url http resolver.sub.uni goettingen.de purl?GDZPPN002154129 year 1869 journal Journal f r die reine und angewandte Mathematik issn 0075 4102 volume 70 pages 354 362 Citation last1 Weyl first1 Hermann author1 link Hermann Weyl title The Concept of a Riemann Surface publisher Addison Wesley year 1964 Category Riemann surfaces ... more details
In mathematics , an n dimensional differential structure or differentiable structure on a set M makes M into an n dimensional differential manifold , which is a topological manifold with some additional structure that allows us to do differential calculus on the manifold. If M is already a topological ... differential structure ref Hirsch, Morris, Differential Topology , Springer 1997 , ISBN 0 387 90148 5. for a general mathematical account of differential structures ref is defined using a C sup k sup ... manifold is a C sup k sup atlas defining a C sup k sup differential manifold. Two atlases are C ... manifold is said to determine a C sup k sup differential structure on the topological manifold. The C sup k sup equivalence classes of such atlases are the distinct C sup k sup differential structures of the manifold . Each distinct differential structure is determined by a unique maximal atlas ... R4 exotic R sup 4 sup . Differential structures on spheres of dimension from 1 to 20 The following ... m from 1 up to 20. Spheres with a smooth, i.e. C sup sup differential structure not smoothly ... of the topological 4 disk or 4 ball . Differential structures on topological manifolds As mentioned above, in dimensions smaller than 4, there is only one differential structure for each topological manifold ... of smooth structures on a compact PL manifold is finite and agrees with the number of differential ... 7 This needs checking this number agrees with the number of differential structures on the sphere of the same dimension. Thus the table above lists also the number of differential structures for any ... math in a simply connected 4 manifold, one can use a surgery along a knot or link to produce a new differential structure. With the help of this procedure one can produce countably infinite many differential ... the construction of other differential structures. For non compact 4 manifolds there are many examples like math mathbb R 4,S 3 times mathbb R ,M 4 setminus ,... math having uncountably many differential ... more details
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