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Academic literature on the topic 'Transformation Equations To Two Fermat's Equations'

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Published: 7 June 2025

Last updated: 16 July 2025

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Journal articles on the topic "Transformation Equations To Two Fermat's Equations"

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P.N, Seetharaman. "An Alternative Elementary Proof for Fermat's Last Theorem." International Journal of Basic Sciences and Applied Computing (IJBSAC) 11, no. 8 (2025): 11–16. https://doi.org/10.35940/ijbsac.H0534.11080425.

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<strong>Abstract:</strong> Fermat’s Last Theorem states that the equation x n + y n = z n has no solution for x, y and z as positive integers, where n is any positive integer > 2. Taking the proofs of Fermat and Euler for the exponents n = 4 and n = 3, it would suffice to prove the theorem for the exponent n = p, where p is any prime > 3. We hypothesize that r, s and t are positive integers satisfying the equation r p + s p = t p and establish a contradiction in this proof. We include another Auxiliary equation x 3 + y 3 = z 3 and connect these two equations by using transformation

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P., N. Seetharaman. "A Proof for Fermat's Last Theorem using an Auxiliary Fermat's Equation." Indian Journal of Advanced Mathematics (IJAM) 4, no. 2 (2024): 19–24. https://doi.org/10.54105/ijam.A1182.04021024.

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<strong>Abstract:</strong> Fermat’s Last Theorem states that there exists no three positive integers x, y and z satisfying the equation x n + y n = z n , where n is any integer > 2. Fermat and Euler had already proved the theorem for the exponents n = 4 and n = 3 in the equations x 4 + y 4 = z 4 and x 3 + y 3 = z 3 respectively. Hence taking into account of the same, it is enough to prove the theorem for the exponent n = p, where p is any prime > 3. In this proof, we have hypothesized that r, s and t are positive integers in the equation r p + s p = t p where p is any prime >3 a

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P. N Seetharaman. "A Proof for Fermat's Last Theorem using an Auxiliary Fermat's Equation." Indian Journal of Advanced Mathematics 4, no. 2 (2024): 19–24. https://doi.org/10.54105/ijam.a1182.04021024.

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Fermat’s Last Theorem states that there exists no three positive integers x, y and z satisfying the equation xn + yn = zn, where n is any integer > 2. Fermat and Euler had already proved the theorem for the exponents n = 4 and n = 3 in the equations x4 + y4 = z4 and x3 + y3 = z3 respectively. Hence taking into account of the same, it is enough to prove the theorem for the exponent n = p, where p is any prime > 3. In this proof, we have hypothesized that r, s and t are positive integers in the equation rp + sp = tp where p is any prime >3 and prove the theorem by the method of contradi

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P., N. Seetharaman. "In Search of an Elementary Proof for Fermat's Last Theorem." Indian Journal of Advanced Mathematics (IJAM) 4, no. 1 (2024): 35–39. https://doi.org/10.54105/ijam.A1190.04010424.

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<strong>Abstract:</strong> Fermat’s Last Theorem states that the equation x n + y n = z n has no solution for x, y and z as positive integers, where n is any positive integer > 2. Taking the proofs of Fermat and Euler for the exponents n = 4 and n = 3, it would suffice to prove the theorem for the exponent n = p, where p is any prime > 3. We hypothesize that r, s and t are positive integers satisfying the equation r p + s p = t p and establish a contradiction in this proof. We include another Auxiliary equation x 3 + y 3 = z 3 and connects these two equations by using the transform

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5

P.N Seetharaman. "An Alternative Elementary Proof for Fermat's Last Theorem." International Journal of Basic Sciences and Applied Computing 11, no. 8 (2025): 11–16. https://doi.org/10.35940/ijbsac.h0534.11080425.

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Abstract:

Fermat’s Last Theorem states that the equation x n + y n = z n has no solution for x, y and z as positive integers, where n is any positive integer > 2. Taking the proofs of Fermat and Euler for the exponents n = 4 and n = 3, it would suffice to prove the theorem for the exponent n = p, where p is any prime > 3. We hypothesize that r, s and t are positive integers satisfying the equation r p + s p = t p and establish a contradiction in this proof. We include another Auxiliary equation x 3 + y 3 = z 3 and connect these two equations by using transformation equations. On solving the transf

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6

P.N. Seetharaman. "In Search of an Elementary Proof for Fermat's Last Theorem." Indian Journal of Advanced Mathematics 4, no. 1 (2024): 35–39. https://doi.org/10.54105/ijam.a1190.04010424.

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Abstract:

Fermat’s Last Theorem states that the equation x n + y n = z n has no solution for x, y and z as positive integers, where n is any positive integer > 2. Taking the proofs of Fermat and Euler for the exponents n = 4 and n = 3, it would suffice to prove the theorem for the exponent n = p, where p is any prime > 3. We hypothesize that r, s and t are positive integers satisfying the equation r p + s p = t p and establish a contradiction in this proof. We include another Auxiliary equation x 3 + y 3 = z 3 and connects these two equations by using the transformation equations. On solving the t

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P.N, Seetharaman. "An Elementary Proof for Fermat's Last Theorem using Three Distinct Odd Primes F, E and R." Indian Journal of Advanced Mathematics (IJAM) 5, no. 1 (2025): 22–26. https://doi.org/10.54105/ijam.A1191.05010425.

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<strong>Abstract:</strong> In number theory, Fermat’s Last Theorem states that no three positive integers a, b and c satisfy the equation a n + b n = c n where n is any integer > 2. Fermat and Euler had already proved that there are no integral solutions to the equations x 3 + y3 = z3 and x4 + y4 = z4 . Hence it would suffice to prove the theorem for the index n = p, where p is any prime > 3. In this proof, we have hypothesized that r, s and t are positive integers in the equation r p + sp = tp where p is any prime >3 and prove the theorem using the method of contradiction. We h

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P.N Seetharaman. "An Elementary Proof for Fermat's Last Theorem using a Transformation Equation to Fermat's Equation." Indian Journal of Advanced Mathematics 5, no. 1 (2025): 27–31. https://doi.org/10.54105/ijam.a1192.05010425.

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Fermat’s Last Theorem states that there are no positive integers x, y and z satisfying the equation x n + y n = z n, where n is any integer > 2. Around 1637 Fermat proved that there are non-zero solutions to the above equation with n = 4. In the 18th century Euler treated the case n = 3, thereby reducing the proof for the case of a prime exponent ≥ 5 in this proof we hypothesize that r, s and t are positive integers satisfying the equation rp + sp = tp , where p is any prime >3 and establish a contradiction. We use an Auxiliary equation x 3 + y3 = z3 and create transformation equations.

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P.N, Seetharaman. "An Elementary Proof for Fermat's Last Theorem using a Transformation Equation to Fermat's Equation." Indian Journal of Advanced Mathematics (IJAM) 5, no. 1 (2025): 27–31. https://doi.org/10.54105/ijam.A1192.05010425.

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<strong>Abstract: </strong>Fermat’s Last Theorem states that there are no positive integers x, y and z satisfying the equation x n + y n = z n , where n is any integer > 2. Around 1637 Fermat proved that there are non-zero solutions to the above equation with n = 4. In the 18th century Euler treated the case n = 3, thereby reducing the proof for the case of a prime exponent ≥ 5 in this proof we hypothesize that r, s and t are positive integers satisfying the equation rp + sp = tp , where p is any prime >3 and establish a contradiction. We use an Auxiliary equation x 3 + y3 = z3

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P. N Seetharaman. "A Comprehensible Proof for Fermat's Last Theorem." Indian Journal of Advanced Mathematics 4, no. 1 (2024): 29–34. https://doi.org/10.54105/ijam.a1181.04010424.

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Fermat’s Last Theorem states that it is impossible to find positive integers A, B and C satisfying the equation An + Bn = Cn where n is any integer > 2. Taking the proofs of Fermat for the index n = 4, and Euler for n = 3, it is sufficient to prove the theorem for n = p, any prime > 3. We hypothesize that all r, s and t are non-zero integers in the equation r p + sp = tp and establish contradiction. Just for supporting the proof in the above equation, we have another equation x 3 + y3 = z3 Without loss of generality, we assert that both x and y as non-zero integers; z3 a non-zero integer

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Dissertations / Theses on the topic "Transformation Equations To Two Fermat's Equations"

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William, James Pringle. "Two-way Coupled Multiscale Tsunami Modelling from Generation to Coastal Zone Hydrodynamics." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215503.

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Books on the topic "Transformation Equations To Two Fermat's Equations"

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F, Thompson Joe, and United States. National Aeronautics and Space Administration., eds. Semi-annual status report for the period November 15, 1985 through May 14, 1986 ... entitled Transformation of two and three-dimensional regions by elliptic systems. Mississippi State University, Dept. of Aerospace Engineering, 1986.

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F, Thompson Joe, and United States. National Aeronautics and Space Administration, eds. Semi-annual status report for the period November 15, 1985 through May 14, 1986 ... entitled Transformation of two and three-dimensional regions by elliptic systems. Mississippi State University, Dept. of Aerospace Engineering, 1986.

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Deruelle, Nathalie, and Jean-Philippe Uzan. The two-body problem: an effective-one-body approach. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0056.

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This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Ke

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Jaëck, Frédéric. Generality and structures in functional analysis: the influence of Stefan Banach. Edited by Karine Chemla, Renaud Chorlay, and David Rabouin. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198777267.013.7.

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This article examines Stefan Banach’s contributions to the field of functional analysis based on the concept of structure and the multiply-flvored expression of generality that arises in his work on linear operations. More specifically, it discusses the two stages in the process by which Banach elaborated a new framework for functional analysis where structures were bound to play an essential role. It considers whether Banach spaces, or complete normed vector spaces, were born in Banach’s first paper, the 1922 doctoral dissertation On operations on abstract spaces and their application to inte

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Book chapters on the topic "Transformation Equations To Two Fermat's Equations"

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Xu, Liu-Jun, and Ji-Ping Huang. "Theory for Thermoelectric Effect Control: Transformation Nonlinear Thermoelectricity." In Transformation Thermotics and Extended Theories. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-5908-0_4.

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AbstractTemperature-dependent (nonlinear) transformation thermotics provides a powerful tool for designing multifunctional, switchable, or intelligent metamaterials in diffusion systems. However, its extension to multiphysics remains studied, in which the temperature dependence of intrinsic parameters is ubiquitous. Here, we theoretically establish a temperature-dependent transformation method for controlling multiphysics. Taking thermoelectric transport as a typical case, we prove the form invariance of its temperature-dependent governing equations and formulate the corresponding transformation rules. Our finite-element simulations demonstrate robust thermoelectric cloaking, concentrating, and rotating performance in temperature-dependent backgrounds. We further design two practical applications with temperature-dependent transformation: an ambient-responsive cloak-concentrator thermoelectric device that can switch between cloaking and concentrating; an improved thermoelectric cloak with nearly-thermostat performance inside. Our theoretical frameworks and application designs may provide guidance for efficiently controlling temperature-related multiphysics and enlighten subsequent intelligent multiphysical metamaterial research.

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Hausmann, Daniel, and Lutz Schröder. "Quasipolynomial Computation of Nested Fixpoints." In Tools and Algorithms for the Construction and Analysis of Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72016-2_3.

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AbstractIt is well-known that the winning region of a parity game with n nodes and k priorities can be computed as a k-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $$\mathcal {O}(n^{\frac{k}{2}})$$ O ( n k 2 ) iterations of the function. Calude et al.’s recent quasipolynomial-time parity game solving algorithm essentially shows how to compute the same fixpoint in only quasipolynomially many iterations by reducing parity games to quasipolynomially sized safety games. Universal graphs have been used to modularize this transformation of parity games to equivalent safety games that are obtained by combining the original game with a universal graph. We show that this approach naturally generalizes to the computation of solutions of systems of any fixpoint equations over finite lattices; hence, the solution of fixpoint equation systems can be computed by quasipolynomially many iterations of the equations. We present applications to modal fixpoint logics and games beyond relational semantics. For instance, the model checking problems for the energy $$\mu $$ μ -calculus, finite latticed $$\mu $$ μ -calculi, and the graded and the (two-valued) probabilistic $$\mu $$ μ -calculus – with numbers coded in binary – can be solved via nested fixpoints of functions that differ substantially from the function for parity games but still can be computed in quasipolynomial time; our result hence implies that model checking for these $$\mu $$ μ -calculi is in $$\textsc {QP}$$ QP . Moreover, we improve the exponent in known exponential bounds on satisfiability checking.

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"Transformations of the The equation." In Heun’s Differential Equations, edited by A. Ronveaux. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780198596950.003.0024.

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Abstract According to the proposition 1.3.6, a THE with a singular point located at ∞ may only occur with one of the two forms, namely the THE 1 equation (1.2.1) and the THE 2 equation (1.2.3). The following proposition (see [6]) gives conditions under which a transformation combining multiplication by an exponential of a polynomial and a homography leaving ∞ fix preserves the THE 1 form.

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Hu, Xing-Biao, and Peter A. Clarkson. "Generalized Bäcklund transformation and new explicit solutions of the two-dimensional Toda equation." In Symmetries and Integrability of Difference Equations. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9780511569432.003.

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Alexeyeva, Lyudmila, and Yergali Kurmanov. "Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot’s Medium." In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92064.

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Here processes of wave propagation in a two-component Biot’s medium are considered, which are generated by arbitrary forces actions. By using Fourier transformation of generalized functions, a fundamental solution, Green tensor, of motion equations of this medium has been constructed in a non-stationary case and in the case of stationary harmonic oscillation. These tensors describe the processes of wave propagation (in spaces of dimensions 1, 2, 3) under an action of power sources concentrated at coordinates origin, which are described by a singular delta-function. Based on them, generalized solutions of these equations are constructed under the action of various sources of periodic and non-stationary perturbations, which are described by both regular and singular generalized functions. For regular acting forces, integral representations of solutions are given that can be used to calculate the stress-strain state of a porous water-saturated medium.

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Zong, Quanwei, Hua Lu, Zhuoya An, and Fudong Zhang. "A Simple Method for Position Analysis of Stephenson-III Spherical Six Bar Mechanism." In Advances in Transdisciplinary Engineering. IOS Press, 2022. http://dx.doi.org/10.3233/atde220211.

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Aiming at the position analysis of Stephenson III spherical six bar mechanism, a simple method to solve its input-output equation is given. The Stephenson III spherical six bar mechanism is regarded as composed of basic spherical four-bar chain and spherical two-bar group. The basic coordinate system and branch coordinate system are established respectively. The coordinates of each hinge point are solved with the help of geometric principle and displacement rotation theory. Based on the motion constraints of the basic spherical four-bar chain and the coupling constraints with the spherical two-bar group, the constraint equations of the spherical six bar mechanism are established by using spherical trigonometry. The constraint equations are simplified and eliminated by Sylvester’s resultant elimination method and triangular transformation formula, and then the constraint equations of the mechanism are obtained.

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Milonni, Peter W. "Atoms in Light: Semiclassical Theory." In An Introduction to Quantum Optics and Quantum Fluctuations. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199215614.003.0002.

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The atom-field interaction is treated in semiclassical radiation theory, starting from the transformation from the minimal coupling Hamiltonian to the electric dipole form used extensively in quantum optics. The Heisenberg and density matrix approaches are developed and applied to two-state atoms, Bloch equations, Rabi oscillations, Maxwell-Bloch equations, and transition rates for absorption and emission. Einstein’s theory of blackbody radiation based on momentum fluctuations and dissipation is reviewed. The Einstein fluctuation formula is derived and used to introduce wave-particle duality, Hanbury Brown-Twiss correlations, and photon bunching.

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Kobasko, N. I. "Generalized Equations for Determination of Cooling Time for Bodies of Any Shape during Quenching." In Intensive Quenching Systems: Engineering and Design. ASTM International100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, 2010. http://dx.doi.org/10.1520/mnl12070m.

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The generalized equation for cooling time calculation, based on regular thermal condition theory, was achieved and used in thermal engineering in [1] and is presented in this introduction below. It has been widely used in the heat-treating industry in the countries of the former Soviet Union to develop two-step quenching processes [1]. An analytical equation for cooling time calculation is also needed to develop a method for calculating ideal critical diameter, which is based on accurate CCT (continuous cooling transformation) diagram. The ideal critical diameter is used for optimization of the intensive quenching processes. In the last decade, the generalized equation has been used in the United States to develop recipes for intensive quenching—so-called IQ-3 technology—which explores direct intensive turbulent convection [2].

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Iles, Terence c. "Multiple regression." In Biological Data Analysis. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780199633401.003.0004.

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Abstract The previous chapter covers methods of fitting equations to data where there is just one predictor variable x for the dependent variable y. Sometimes data are collected on two or more different predictor variables x, x, … xk and an equation is sought to calculate y from the set of measurements of x x, … x k. This chapter describes the fitting and interpretation of linear equations with such data sets. The choice of the variables that should be included in the prediction equation, and the possible transformation of variables, will also be discussed. The calculations required for multiple regression are usually too time-consuming to be done by hand so it is necessary to use a computer. Fortunately, most statistical packages have regression routines and these give the user a wide choice of statistics that help in finding suitable prediction equations. Many of these diagnostic statistics are most easily interpreted by the use of plots, so a package with built-in plotting routines should be used.

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Bethke, Craig M. "Automatic Reaction Balancing." In Geochemical Reaction Modeling. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195094756.003.0013.

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Conveniently, perhaps even miraculously, the equations developed in Chapter 4 to accomplish basis swaps can be used to balance chemical reactions automatically. Once the equations have been coded into a computer program, there is no need to balance reactions, compute equilibrium constants, or even determine equilibrium equations by hand. Instead, these procedures can be performed quickly and reliably on a small computer. To balance a reaction, we first choose a species to appear on the reaction’ s left side, and express that species’ composition in terms of a basis B. The basis might be a list of the elements in the species’ stoichiometry, or an arbitrary list of species that combine to form the left-side species. Then we form a second basis B´ composed of species that we want to appear on the reaction’ s right side. To balance the reaction, we calculate the transformation matrix relating basis B´ to B, following the procedures in Chapter 4. The transformation matrix, in turn, gives the balanced reaction and its equilibrium constant. Two methods of balancing reactions are of interest. We can balance reactions in terms of the stoichiometries of the species considered. In this case, the existing basis B is a list of elements and, if charged species are involved, the electron e–. Alternatively, we may use a dataset of balanced reactions, such as the LLNL database. Basis B, in this case, is the one used in the database to write reactions. We will consider each possibility in turn. A straightforward way to balance reactions is to use as the initial basis the stoichiometries of the species involved. If the species’ free energies of formation are known, the reaction’ s equilibrium constant can be determined as well. In the stoichiometric approach, basis B is the list of elements that will appear in the reaction, plus the electron if needed. We write swap reactions and calculate a transformation matrix as described in Section 3.1. The equations in Sections 3.2 and 3.3 give the balanced reaction and associated equilibrium constant.

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Conference papers on the topic "Transformation Equations To Two Fermat's Equations"

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Albinmousa, Jafar, Syed Haris Iftikhar, and Mustafa Al-Samkhan. "Modeling Multiaxial Fatigue Damage Using Polar Equations." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70998.

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It is estimated that more than 70% of failures in engineering components are associated with fatigue loading. Therefore, fatigue is a major design tool for mechanical components. These components are usually subjected to multiaxial cyclic loading. In fact, multiaxial state is very common as tension specimen is under triaxial strain state even though its stress state is uniaxial. There are three approaches to modeling fatigue damage: stress, strain and energy. Critical plane concept is established based on the fact that fatigue cracks initiate at specific plane(s), therefore, multiaxial fatigue

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Reddy, N. M., and R. K. Tulasiram. "Transformation of two phase nozzle flow equations into pure type by introducing virtural area and virtual Mach number." In Current topics in shock waves 17th international symposium on shock waves and shock tubes Bethlehem, Pennsylvania (USA). AIP, 1990. http://dx.doi.org/10.1063/1.39460.

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Meghdari, Ali, and Farbod Fahimi. "A Novel Approach for Decoupling of Dynamical Equations of Flexible Manipulators." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dac-8556.

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Abstract Recent advances in the study of dynamics of elastic multibody systems, specially the flexible manipulators, indicate the need and importance of decoupling the equations of motion. In this paper, an improved method for deriving elastic generalized coordinates is presented. In this regard, the Kane’s equations of motion for elastic multibody systems are considered. These equations are in the generalized form and may be applied to any desired holonomic system. Flexibility in choosing generalized speeds in terms of generalized coordinate derivatives in Kane’s method is used. It is shown t

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Brill, Michael H. "Direct linear transformation methods of triangulating from optical and SAR images." In OSA Annual Meeting. Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.fq9.

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Given an optical photograph with images of six control points (whose three-space coordinates are known), and the two image coordinates of an unknown ground point, it is possible to determine the equation of the line of sight from the camera station to the unknown point via a direct linear transformation (DLT) approach.1 To do this requires writing the projective equations for the control points in a form that is linear in the unknowns containing camera position, orientation, and (assumed affine) film distortions. These equations are written so each image coordinate of each control point appear

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Attia, Hazem Ali, Tarek M. A. El-Mistikawy, and Adel A. Megahed. "Formulation of the Equations of Motion of RRPR Robot Manipulator." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/dac-14538.

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Abstract In this paper the dynamic analysis of RRPR robot manipulator is presented. The equations of motion are formulated using a two-step transformation. Initially, a dynamically equivalent system of particles that replaces the rigid bodies is constructed and then Newton’s second law is applied to derive their equations of motion. The equations of motion are then transformed to the relative joint variables. Use of both Cartesian and joint variables produces an efficient set of equations without loss of generality. For open chains, this process automatically eliminates all of the non-working

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Herrin, D. W., Y. Zhang, and J. Liu. "Exploiting the Complex Plane: The Moebius Transformation and Vibro-Acoustic Optimization." In ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ncad2012-1208.

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If a mechanical or acoustical impedance modification is introduced between two positions, the effect of that modification can be plotted in the complex plane at a given frequency. It has been shown that the mechanical or acoustical response will trace a circle in the complex plane for straight-line modifications to impedance in the complex plane. In that case, the equations relating the response to an impedance modification are in a form consistent with the Moebius transformation, which maps straight lines or circles in one complex domain into straight lines or circles in another complex plane

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Kang, Yaw-Hong, Feng-Chi Wu, Hong-Yih Cheng, and Hong-Sen Yan. "On the Surface Geometry of Variable Pitch Cylindrical Cams With Hyperboloidical Meshing Elements." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0249.

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Abstract The hyperpoloid of revolution is a kind of skew surface that has engineering applications. Based on differential geometry, theory of gearing, and coordinate transformation, this paper derive mathematical equations of the geometric profiles of a double threaded variable pitch cylindrical cams with four hyperboloidical meshing elements. And based on the developed surface equations, we develope a computer program for solid modeling to simulate the surface geometry. Two examples are given to prove the derived equations.

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Dimakopoulos, Aggelos S., and Athanassios A. Dimas. "Numerical Simulation of Two-Dimensional Free-Surface Flow and Wave Transformation Over Constant-Slope Bottom Topography." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37520.

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A numerical model is presented for the simulation of the two-dimensional, inviscid, free-surface flow developing by the propagation and breaking of water waves over a flat bottom of steep slope. The simulation is based on the numerical solution of the unsteady, two-dimensional, Euler equations subject to the fully-nonlinear free-surface boundary conditions, the non-penetration condition at the bottom and appropriate inflow and outflow conditions. A boundary-fitted transformation, which includes both the time-dependent free surface and the arbitrary bottom shape, is applied. For the numerical s

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Zargar, Yasir S., and Kambiz Farhang. "An Algorithm for Systematic Generation of Subscales With Application to a Two-Disk Friction System." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4166.

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Abstract In this paper we propound an algorithm for development of scale models of complex physical systems. The algorithm systematically treats the three sub-tasks of scaling, which includes creation of dimensionless parameters, application of scaling law and similitude requirements, and determination of scale factors. Optimum set of dimensionless parameters are obtained in which the pertinent variables with only integer powers appear. This is achieved by seeking integer solutions to appropriate set of linear algebraic equations in the powers, using a simple iterative technique. Application o

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Deshmukh, Venkatesh. "Stability Analysis and Computation of Solutions of Nonlinear Delay Differential Algebraic Equations With Time Periodic Coefficients." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35263.

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Abstract:

Stability theory of Nonlinear Delay Differential Algebraic Equations (DDAE) with periodic coefficients is proposed with a geometric interpretation of the evolution of the linearized system. First, a numerical algorithm based on direct integration by expansion in terms of Chebyshev polynomials is derived for linear analysis. The proposed algorithm is shown to have deeper connections with and computationally less cumbersome than the solution of the underlying semi-explicit system via a similarity transformation. The stability of time periodic DDAE systems is characterized by the spectral radius

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