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Journal articles on the topic 'Differential transformations'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

Kainz, Gerd, and Peter W. Michor. "Natural transformations in differential geometry." Czechoslovak Mathematical Journal 37, no. 4 (1987): 584–607. http://dx.doi.org/10.21136/cmj.1987.102187.

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2

Florian, H., J. Püngel, and W. Tutschke. "Matrix differential transformations." Applicable Analysis 65, no. 1-2 (1997): 103–17. http://dx.doi.org/10.1080/00036819708840552.

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3

Zagirnyak, Valentina, Boris Nevzlin, and Veronika Zahorulko. "DETERMINATION OF THE CONDITIONS FOR THE EXISTENCE OF HIGHER-ORDER DIFFERENTIAL ELECTROMAGNETIC INVARIANTS." Journal of Energy Technology 8, no. 2 (2024): 11–16. https://doi.org/10.18690/jet.8.2.11-16.2015.

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A four-element dipole representation by first-order electromagnetic invariants according to differential transformation and increments is well known. The paper deals with a most general description of the conditions of existence of an electromagnetic invariant for a four-element dipole with active-reactive components in a differential form and as increments of any order. It is shown analytically that invariants exist at mutual transformations of increments into differentials and differentials into increments.

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4

Tachoire, H., and V. Torra. "New trends in differential scanning calorimetry." Canadian Journal of Chemistry 67, no. 6 (1989): 983–90. http://dx.doi.org/10.1139/v89-150.

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Recent applications of differential scanning calorimetry in the study of solid–solid transformations are presented. The importance of the deconvolution of the thermograms and of the modelling of the calorimetric equipment is stressed.Investigations of the phase transformations of the martensitic type in shape-memory alloys have made clear the influence of thermomechanical treatment of the material and have evaluated the influence of defects on the dynamics of transformation. A combination of calorimetric and acoustical observations has demonstrated irreversibilities, even in the so-called ther

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5

Ustinov, N. V. "Transformations of ordinary differential equations via Darboux transformation technique." Reports on Mathematical Physics 46, no. 1-2 (2000): 279–86. http://dx.doi.org/10.1016/s0034-4877(01)80033-1.

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6

Ata, Enes, and I. Onur Kıymaz. "New generalized Mellin transform and applications to partial and fractional differential equations." International Journal of Mathematics and Computer in Engineering 1, no. 1 (2023): 45–66. http://dx.doi.org/10.2478/ijmce-2023-0004.

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Abstract In this paper, we introduce a generalized Mellin transformation in a general form that encompasses the generalized Mellin transformations found in the literature. Then, we give the fundamental properties of this new integral transformation and apply it to some elementary functions. Furthermore, we obtain the solutions of partial and fractional differential equations by means of this new integral transformation. Finally, we examine the relations between generalized Mellin transformations in the literature and the new generalized Mellin transformation and present a table showing the new

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7

Putz, V., and R. Wulkenhaar. "Seiberg–Witten Map for Noncommutative Super Yang–Mills Theory." International Journal of Modern Physics A 18, no. 19 (2003): 3325–34. http://dx.doi.org/10.1142/s0217751x03015246.

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In this paper we derive the Seiberg–Witten map for noncommutative super Yang–Mills theory in Wess–Zumino gauge. Following (and using results of) hep-th/0108045 we split the observer Lorentz transformations into a covariant particle Lorentz transformation and a remainder which gives directly the Seiberg–Witten differential equations. These differential equations lead to a θ-expansion of the noncommutative super Yang–Mills action which is invariant under commutative gauge transformations and commutative observer Lorentz transformation, but not invariant under commutative supersymmetry transforma

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8

Spivak L. V., Kirchanov V. S., and Shchepina N. E. "Polymorphic transformations in iodine titanium." Physics of the Solid State 64, no. 11 (2022): 1784. http://dx.doi.org/10.21883/pss.2022.11.54208.400.

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Based on the analysis of differential scanning calorimetry data, the possibility of classifying the observed endothermic or exothermic transformations as phase transformations of the first oder is considered. Two approaches have been implemented. The first is based on the correspondence between the temperatures of the maximum conversion rate and the temperatures of the extrema on the second derivative of the differential scanning calorimetry signal with respect to temperature. In the second approach, the phase transformation is considered as a kind of kinetic reaction of a chemical process wit

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9

Kadham, Shaymaa Maki, and Mohammed Ahmed Mustafa. "Medical applications of the new-transform." Journal of Interdisciplinary Mathematics 26, no. 6 (2023): 1341–53. http://dx.doi.org/10.47974/jim-1632.

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Solving differential equations by integral transformations is a highly general method. Using these powerful methods, mainly intractable problems may be conquered relatively easily. Because of the difficulty of solving ordinary differential equations, this study employs a novel integral transformation called the h-transform Related ideas, characteristics, and methods for evaluating significance are also elaborated upon. Due to the precision of the necessary transformations, the study of differential equations has inspired a new way of thinking called HA-fuzzy transformation, which is used to so

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10

Moazzam, Ali, Emad Kuffi, Zain Abideen, and Ayza Anjum. "Two parametric SEE transformation and its applications in solving differential equations." Al-Qadisiyah Journal for Engineering Sciences 16, no. 2 (2023): 116–20. http://dx.doi.org/10.30772/qjes.v16i2.891.

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Transformation plays a much more important role in every science. In this research article, two parametric forms of SEE transformation have been explored and the fundamental properties of two parametric SEE transformations have been shown. Furthermore, the transformed function of some fundamental functions and their time derivative rule has been shown. The application of two parametric SEE transformations in solving differential equations has been shown. The radioactive decay problem in first-order linear differential equations has been solved in this article which has large applications in nu

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11

Čadek, Martin. "Form of general pointwise transformations of linear differential equations." Czechoslovak Mathematical Journal 35, no. 4 (1985): 617–24. http://dx.doi.org/10.21136/cmj.1985.102052.

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12

Gear, C. W. "Differential-Algebraic Equation Index Transformations." SIAM Journal on Scientific and Statistical Computing 9, no. 1 (1988): 39–47. http://dx.doi.org/10.1137/0909004.

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13

Sitko, Patryk, and Ivan Tsyfra. "Extended symmetry of the Witten-Dijkgraaf-Verlinde-Verlinde equation of Monge-Ampere type." Opuscula Mathematica 45, no. 2 (2025): 251–74. https://doi.org/10.7494/opmath.2025.45.2.251.

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We construct the Lie algebra of extended symmetry group for the Monge-Ampere type Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation. This algebra includes novel generators that are unobtainable within the framework of the classical Lie approach and correspond to non-point group transformation of dependent and independent variables. The expansion of symmetry is achieved by introducing new variables through second-order derivatives of the dependent variable. By integrating the Lie equations, we derive transformations that enable the generation of new solutions to the Witten-Dijkgraaf-Verlinde-V

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14

DERELİ, TEKİN, ADNAN TEĞMEN, and TUĞRUL HAKİOĞLU. "CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE." International Journal of Modern Physics A 24, no. 25n26 (2009): 4769–88. http://dx.doi.org/10.1142/s0217751x09044760.

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Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show th

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15

Kipreos, Edward T., and Riju S. Balachandran. "An approach to directly probe simultaneity." Modern Physics Letters A 31, no. 26 (2016): 1650157. http://dx.doi.org/10.1142/s0217732316501571.

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The theory of special relativity derives from the Lorentz transformation. The Lorentz transformation implies differential simultaneity and light speed isotropy. Experiments to probe differential simultaneity should be able to distinguish the Lorentz transformation from a kinematically-similar alternate transformation that predicts absolute simultaneity, the absolute Lorentz transformation. Here, we describe how published optical tests of light speed isotropy/anisotropy cannot distinguish between the two transformations. We show that the shared equations of the two transformations, from the per

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16

Azhar, Aurizan Himmi, Sugiyanto Sugiyanto, Muhammad Wakhid Musthofa, and Muhamad Zaki Riyanto. "Transformasi Fourier Multiplikatif Dan Aplikasinya Pada Persamaan Diferensial Multiplikatif." Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika 8, no. 2 (2021): 149–60. http://dx.doi.org/10.31316/j.derivat.v8i2.1996.

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This research is a development of multiplicative calculus. This study is about the Fourier multiplicative transformation and its application to the multiplicative differential equation. This study aims to determine the Fourier multiplicative transformation as well as the multiplicative differential equation. This study contains numerical simulations to solve the problem of ordinary multiplicative differential equations of the first order. The methods used in this research are descriptive research methods through the study of literature. The results of this study are the application of multipli

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17

Спивак, Л. В., В. С. Кирчанов та Н. Е. Щепина. "Полиморфные превращения в йодидном титане". Физика твердого тела 64, № 11 (2022): 1820. http://dx.doi.org/10.21883/ftt.2022.11.53341.400.

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Based on the analysis of differential scanning calorimetry data, the possibility of classifying the observed endothermic or exothermic transformations as phase transformations of the first oder is considered. Two approaches have been implemented. The first is based on the correspondence between the temperatures of the maximum conversion rate and the temperatures of the extrema on the second derivative of the differential scanning calorimetry signal with respect to temperature. In the second approach, the phase transformation is considered as a kind of kinetic reaction of a chemical process wit

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18

Mysik, Raisa K., Sergey V. Brusnitsyn, and Andrey V. Sulitsin. "Differential Thermal Analysis of Complex Alloyed Brass." Materials Science Forum 946 (February 2019): 282–86. http://dx.doi.org/10.4028/www.scientific.net/msf.946.282.

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Copper alloys are widely used in mechanical engineering. In the article it is shown that the requirements of consumers to properties of alloys are constantly increasing. Complex alloyed brasses have a high wear resistance and corrosion resistance. The wear resistance is a basic property of an alloy. This characteristic determines the operating life of parts working in the wear conditions. The wear resistance is supported by phase composition of alloy, uniformity of distribution of phase in the structure of alloy, their volume fraction, their morphology and their dimensions. At present time the

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19

Johnpillai, A. G., C. M. Khalique, and F. M. Mahomed. "Lie and Riccati Linearization of a Class of Liénard Type Equations." Journal of Applied Mathematics 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/171205.

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We construct a linearizing Riccati transformation by using an ansatz and a linearizing point transformation utilizing the Lie point symmetry generators for a three-parameter class of Liénard type nonlinear second-order ordinary differential equations. Since the class of equations also admits an eight-parameter Lie group of point transformations, we utilize the Lie-Tresse linearization theorem to obtain linearizing point transformations as well. The linearizing transformations are used to transform the underlying class of equations to linear third- and second-order ordinary differential equatio

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20

Sinkala, Winter. "Some Remarks on the Solution of Linearisable Second-Order Ordinary Differential Equations via Point Transformations." Journal of Mathematics 2020 (July 1, 2020): 1–5. http://dx.doi.org/10.1155/2020/2406961.

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Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on such transformations is the class of linearisable second-order ordinary differential equations (ODEs). There are various characterisations of such ODEs. We exploit a particular characterisation and the expanded Lie group method to construct a generic solution for all linearisable second-order ODEs. The general solution of any given equation from this class is

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21

Ali Moazzam, Hira Aslam, Naila Tabassum, and Emad A. Kuffi. "Solution of Population Growth Rate Linear Differential Model via Two Parametric SEE Transformation." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 2 (2023): 430–35. http://dx.doi.org/10.30526/36.2.3251.

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The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution

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22

Brunner, Hermann, and Stefano Maset. "Time transformations for delay differential equations." Discrete & Continuous Dynamical Systems - A 25, no. 3 (2009): 751–75. http://dx.doi.org/10.3934/dcds.2009.25.751.

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23

Pakdemirli, Mehmet, and Muhammet Yurusoy. "Similarity Transformations for Partial Differential Equations." SIAM Review 40, no. 1 (1998): 96–101. http://dx.doi.org/10.1137/s003614459631001x.

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24

Cătaş, Adriana, Georgia Irina Oros, and Gheorghe Oros. "Differential Subordinations Associated with Multiplier Transformations." Abstract and Applied Analysis 2008 (2008): 1–11. http://dx.doi.org/10.1155/2008/845724.

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The authors introduce new classes of analytic functions in the open unit disc which are defined by using multiplier transformations. The properties of these classes will be studied by using techniques involving the Briot-Bouquet differential subordinations. Also an integral transform is established.

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25

Kim, Yong Chan, Adam Lecko, Jae Ho Choi, and Megumi Saigo. "Differential subordinations for fractional-linear transformations." International Journal of Mathematics and Mathematical Sciences 23, no. 2 (2000): 109–17. http://dx.doi.org/10.1155/s0161171200001666.

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26

Podestá, Fabio. "Affine Transformations in Affine Differential Geometry." Results in Mathematics 16, no. 1-2 (1989): 155–61. http://dx.doi.org/10.1007/bf03322651.

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27

Sandu, Constantine, and Rakesh K. Singh. "Physical transformations in differential scanning calorimetry." Thermochimica Acta 132 (September 1988): 89–99. http://dx.doi.org/10.1016/0040-6031(88)87098-9.

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28

Van Casteren, Jan A. "Contact transformations for micro-differential operators." Communications in Algebra 14, no. 9 (1986): 1737–73. http://dx.doi.org/10.1080/00927878608823394.

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29

Florack, L. M. J., B. M. Ter Haar Romeny, J. J. Koenderink, and M. A. Viergever. "General intensity transformations and differential invariants." Journal of Mathematical Imaging and Vision 4, no. 2 (1994): 171–87. http://dx.doi.org/10.1007/bf01249895.

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30

Gerlich, G. "Transformations of Variables for Differential Equations." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 66, no. 10 (1986): 501–2. http://dx.doi.org/10.1002/zamm.19860661023.

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31

Chandrasekar, V. K., M. Senthilvelan, and M. Lakshmanan. "On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2070 (2006): 1831–52. http://dx.doi.org/10.1098/rspa.2005.1648.

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We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle–Singer method. We describe a procedure to deduce all the integrals of motion associated with the given equation, so that the general solution follows straightforwardly from these integrals. The method is illustrated with several examples. Further, we propose a powerful method of identifying linearizing transformations. The proposed method not only unifies all the known linearizing transformations systematically but also introduces a new and generalized linearizin

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32

Özkan, Ozan. "Numerical implementation of differential transformations method for integro-differential equations." International Journal of Computer Mathematics 87, no. 12 (2010): 2786–97. http://dx.doi.org/10.1080/00207160902795627.

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33

Tryhuk, Václav. "Remark to transformations of linear differential and functional-differential equations." Czechoslovak Mathematical Journal 50, no. 2 (2000): 265–78. http://dx.doi.org/10.1023/a:1022414717364.

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34

Gordoa, Pilar Ruiz, and Andrew Pickering. "Novel Bäcklund Transformations for Integrable Equations." Mathematics 10, no. 19 (2022): 3565. http://dx.doi.org/10.3390/math10193565.

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In this paper, we construct a new matrix partial differential equation having a structure and properties which mirror those of a matrix fourth Painlevé equation recently derived by the current authors. In particular, we show that this matrix equation admits an auto-Bäcklund transformation analogous to that of this matrix fourth Painlevé equation. Such auto-Bäcklund transformations, in appearance similar to those for Painlevé equations, are quite novel, having been little studied in the case of partial differential equations. Our work here shows the importance of the underlying structure of dif

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35

ZHANG, DA-JUN, JIE JI, and XIAN-LONG SUN. "CASORATIAN SOLUTIONS AND NEW SYMMETRIES OF THE DIFFERENTIAL-DIFFERENCE KADOMTSEV–PETVIASHVILI EQUATION." Modern Physics Letters B 23, no. 17 (2009): 2107–14. http://dx.doi.org/10.1142/s0217984909020254.

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This paper first discusses the condition in which Casoratian entries satisfy for the differential-difference Kadomtsev–Petviashvili equation. Then from the Casoratian condition we find a transformation under which the differential-difference Kadomtsev–Petviashvili equation is invariant. The transformation, consisting of a combination of Galilean and scalar transformations, provides a single-parameter invariant group for the equation. We further derive the related symmetry, and the symmetry together with other two symmetries form a closed three-dimensional Lie algebra.

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36

Yahyazadeh, Hossein, Domairry Ganji, Arash Yahyazadeh, Taghi Khalili, Payam Jalili, and Mohsen Jouya. "Evaluation of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field by the differential transformation method." Thermal Science 16, no. 5 (2012): 1281–87. http://dx.doi.org/10.2298/tsci1205281y.

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In the present study, the convective flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of a magnetic field are investigated. The governing partial differential equations with the auxiliary conditions are reduced to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. The semi-analytical solutions of the resulting ordinary differential equations are obtained using differential transformation method coupled with Pade approximation. Comparison with published results is

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37

Zeshan Haider and Khalil Ahmad. "Novel Exact Solutions for a Biological Population Model Using the Power Index Method." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5936. https://doi.org/10.29020/nybg.ejpam.v18i2.5936.

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In this paper, we study a nonlinear biological population model that describes the spatiotemporal evolution of population density, incorporating nonlinear diffusion and reaction effects. Using the Power Index Method, we derive exact solutions for this model. In this approach, we select appropriate indexes for the independent variable in the similarity transformation, allowing the unknown functions to take polynomial, rational, or other elementary forms. These transformations reduce the nonlinear partial differential equation (NLPDE) to nonlinear ordinary differential equations (NLODEs). We the

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38

Liu, Yong Chang, F. Sommer, and Eric J. Mittemeijer. "Kinetics of the Austenite-Ferrite Transformation with and without Applied Stress." Solid State Phenomena 172-174 (June 2011): 1207–13. http://dx.doi.org/10.4028/www.scientific.net/ssp.172-174.1207.

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The formation of ferrite (α) from austenite (γ) and vice versa, upon thermo-mechanical processing of steels, are phase transformations of great technological importance. Often these transformations occur in the presence of externally or internally imposed stress. This paper provides an overview of recent research on the quantitative analysis of the transformation kinetics of the γ®a and a®g transformations subjected to uniaxial compressive stress below the yield stress of g and a, based on the application of the high-resolution differential dilatometry and the modular model of transformation k

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39

Krasil’shchik, Iosif. "Nonlocal Conservation Laws of PDEs Possessing Differential Coverings." Symmetry 12, no. 11 (2020): 1760. http://dx.doi.org/10.3390/sym12111760.

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In his 1892 paper, L. Bianchi noticed, among other things, that quite simple transformations of the formulas that describe the Bäcklund transformation of the sine-Gordon equation lead to what is called a nonlocal conservation law in modern language. Using the techniques of differential coverings, we show that this observation is of a quite general nature. We describe the procedures to construct such conservation laws and present a number of illustrative examples.

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40

Kaptsov, O. V. "Ideals of differential operators and transformations of linear partial differential equations." Programming and Computer Software 36, no. 2 (2010): 97–102. http://dx.doi.org/10.1134/s0361768810020076.

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41

Meftin, Dr Noor Kadhim. "Utilizing Dinesh Verma Transformation (DVT) and Differential Equations in a Cryptography Model." Webology 19, no. 1 (2022): 3184–91. http://dx.doi.org/10.14704/web/v19i1/web19210.

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The ever-expanding area of cryptography fostered the development of numerous cryptographic models utilizing a variety of mathematical and logical methodologies, and integral transformations were no exception. This paper proposes a cryptographic model based on the application of the Dinesh Verma integral Transformation (DVT) to the series produced by the production of a general polynomial P(t) of degree n with the Taylor series to increase the complexity of the resulting ciphertext, and in which key elements required for encryption and decryption are transmitted over channels of various securit

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42

Clarkson, P. A., A. S. Fokas, and M. J. Ablowitz. "Hodograph Transformations of Linearizable Partial Differential Equations." SIAM Journal on Applied Mathematics 49, no. 4 (1989): 1188–209. http://dx.doi.org/10.1137/0149071.

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43

Antonelli, P. L., and D. Hrimiuc. "Symplectic transformations of the differential geometry of." Nonlinear Analysis: Theory, Methods & Applications 36, no. 5 (1999): 529–57. http://dx.doi.org/10.1016/s0362-546x(98)00095-9.

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44

Anderson, I. M., and M. E. Fels. "Bäcklund transformations for Darboux integrable differential systems." Selecta Mathematica 21, no. 2 (2014): 379–448. http://dx.doi.org/10.1007/s00029-014-0159-5.

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45

Aminova, A. V. "Projective transformations and symmetries of differential equation." Sbornik: Mathematics 186, no. 12 (1995): 1711–26. http://dx.doi.org/10.1070/sm1995v186n12abeh000090.

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46

Garifullin, R. N., R. I. Yamilov, and D. Levi. "Non-invertible transformations of differential–difference equations." Journal of Physics A: Mathematical and Theoretical 49, no. 37 (2016): 37LT01. http://dx.doi.org/10.1088/1751-8113/49/37/37lt01.

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47

Hounkonnou, M. N., and A. Ronveaux. "On some differential transformations of hypergeometric equations." Journal of Physics: Conference Series 597 (April 13, 2015): 012044. http://dx.doi.org/10.1088/1742-6596/597/1/012044.

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48

Rybnikov, A. K. "Differential-geometric structures defining Lie-Bäcklund transformations." Doklady Mathematics 79, no. 2 (2009): 163–68. http://dx.doi.org/10.1134/s1064562409020057.

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49

Dattoli, G., V. Loreto, C. Mari, M. Richetta, and A. Torre. "Biunitary transformations and ordinary differential equations.—I." Il Nuovo Cimento B Series 11 106, no. 12 (1991): 1357–74. http://dx.doi.org/10.1007/bf02728366.

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Dattoli, G., V. Loreto, C. Mari, M. Richetta, and A. Torre. "Biunitary transformations and ordinary differential equations.—II." Il Nuovo Cimento B Series 11 106, no. 12 (1991): 1375–90. http://dx.doi.org/10.1007/bf02728367.

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