Academic literature on the topic 'Pseudotensore'
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Journal articles on the topic "Pseudotensore"
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Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "Algebraic algorithm for the systematic reduction of one-point pseudotensors to absolute tensors." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 1(51) (October 5, 2022): 19–28. http://dx.doi.org/10.37972/chgpu.2022.51.1.002.
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В настоящей работе предлагается алгебраический алгоритм систематического приведения одноточечных псевдотензоров произвольной валентности и веса к абсолютным тензорам. Вес псевдотензора полагается целым числом. Алгоритм основан на преобразовании одноточечного псевдотензора произвольной валентности и веса с использованием символов перестановок как ковариантных, так и контравариантных. Приводятся необходимые сведения из алгебры и анализа псевдотензоров. На основании предложенного алгебраического алгоритма преобразования предлагается реализация ковариантного дифференцирования одноточечного псевдотензорного поля произвольной валентности и веса, с помощью которой вводится определение градиента псевдотензорного поля. The paper is devoted to the an algebraic algorithm for the systematic reduction of one-point pseudotensors of an arbitrary valency and weight to absolute tensors. The weight of a pseudotensor is assumed to be an integer. The algorithm is based on the transformation of a one-point pseudotensor of an arbitrary valency and weight by the permutation symbols, both covariant and contravariant types. Notions and requisite equations from Algebra and the Analysis of pseudotensors are recalled and discussed. An implementation of covariant differentiation of a one-point pseudotensor field of an arbitrary valency and weight is manifested and derived by the proposed algebraic algorithm of pseudotensor transformation. The definition of the pseudotensor field gradient is introduced and discussed.
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Радаев, Юрий Николаевич, Евгений Валерьевич Мурашкин, and Тимофей Константинович Нестеров. "Pseudotensor formalism for neuber’s micropolar elasticity theory." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 4(50) (December 30, 2021): 73–81. http://dx.doi.org/10.37972/chgpu.2021.50.4.006.
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В настоящей работе рассматривается теория микрополярной упругости Нейбера в псевдотензорной формулировке. Приводятся минимально необходимые для понимания статьи сведения из алгебры и анализа псевдотензоров. Уравнения динамики микрополярного континуума представлены (наряду с абсолютной тензорной формой) в терминах псевдотензоров (относительных тензоров). Проведено сравнение динамических уравнений микрополярной теории упругости в псевдотензорной форме с абсолютной тензорной формой, предложенной Нейбером. То же самое сопоставление выполнено и для определяющих уравнений. Устранены недочеты в уравнениях динамики Нейбера и приведена их окончательная псевдотензорная форма. The paper deals with Neuber’s theory of micropolar elasticity in a pseudotensor formulation. The minimum notes and requisite equations from algebra and analysis of pseudotensors are given. The micropolar dynamic equations are presented in terms of pseudotensors (relative tensors). The pseudotensor form of dynamic equations is compared with the absolute tensor form of the Neuber dynamic equations. The refinements of Neuber’s dynamic equations are discussed.
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Murashkin, E. V., and Yu N. Radayev. "SCHOUTEN'S FORCE STRESS TENSOR AND AFFINOR DENSITIES OF POSITIVE WEIGHT." Problems of Strength and Plasticity 84, no. 4 (2022): 545–58. http://dx.doi.org/10.32326/1814-9146-2022-84-4-545-558.
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The paper deals with the concept of the force stress pseudotensor and the derivation of equilibrium equations in terms of the Schouten's stress pseudotensor being an affinor density. The definition of Schouten's force stress pseudotensor is mainly based on the notion of a pseudoinvariant element of area. The requisute equations and notions from algebra and the analysis of pseudotensors is revisited. A fundamental orienting pseudoscalar is introduced and discussed. Conventional and non-conventional definitions of the force stress tensor are given. A unit normal vector to a level surface of a pseudoscalar field is introduced. The exceptional importance of using the theory of orientable manifolds in modeling micropolar continua in mechanics of solids is noted. The notion of M-cell and its orientation algorithm are recalled. Algorithms for constructing the tensor elements of the area of M-manifold immersed in N-dimensional space are discussed. The notions of vector, pseudovector, invariant and pseudoinvariant elements of surface area in three-dimensional space are revisited. The possibility of using pseudotensor volume elements of a given integer weight due to the formula for a pseudotensor field transformation to an absolute tensor field by a fundamental orienting pseudoscalar is discussed. Various realisations of covariant differentiation of pseudotensors are considered. Covariant derivatives are given for a pseudoscalar and a contravariant pseudotensor of the second rank of an arbitrary integer weight. The principle of virtual displacements is formulated in terms of pseudo-invariant volume and area elements. The hypothesis of the absolute invariance of the virtual work is assumed, i.e. insensitive to rotations, 3D inversion and mirror reflections. Equations of equilibrium and dynamics are derived in terms of the affinor density of Schouten's force stresses. Equilibrium equations are obtained for the case of using pseudo-invariant volume and area elements of an arbitrary integer weight.
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Crothers, Stephen J. "The Einstein and Landau‐Lifshitz pseudotensors—A mathematical note on existence." Physics Essays 33, no. 3 (September 17, 2020): 268–70. http://dx.doi.org/10.4006/0836-1398-33.3.268.
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For a closed system, the conservation of energy and momentum has been affirmed through a vast array of experiments. In an attempt to reconcile the General Theory of Relativity with these findings, Einstein constructed, ad hoc, his so-called pseudotensor [A. Einstein, Ann. Phys. 49, 769 (1916)]. Yet this solution fell outside the tensorial mathematical structure of his theory. Landau and Lifshitz also constructed, ad hoc, an even more complex pseudotensor, as a proposed improvement upon the work of Einstein [The Classical Theory of Fields (Addison-Wesley Press, Inc., Cambridge, MA, 1951)]. Their pseudotensor is symmetric, unlike that proposed by Einstein. They advance that their pseudotensor yields a conservation law which also included angular momentum. However, once again, this approach leads to a mathematical construct which is not a tensor and thereby falls outside the very mathematical structure of Einstein’s theory. Both pseudotensors, whether that advanced by Einstein or by Landau and Lifshitz, violate the rules of pure mathematics and therefore can hold no place in physics.
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Capozziello, Salvatore, Maurizio Capriolo, and Maria Transirico. "The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity." International Journal of Geometric Methods in Modern Physics 15, supp01 (November 2018): 1850164. http://dx.doi.org/10.1142/s0219887818501645.
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We derive the gravitational energy–momentum pseudotensor [Formula: see text] in metric [Formula: see text] gravity and in teleparallel [Formula: see text] gravity. In the first case, [Formula: see text] is the Ricci curvature scalar for a torsionless Levi-Civita connection; in the second case, [Formula: see text] is the curvature-free torsion scalar derived by tetrads and Weitzenböck connection. For both classes of theories the continuity equations are obtained in presence of matter. [Formula: see text] and [Formula: see text] are non-equivalent, but differ for a quantity [Formula: see text] containing the torsion scalar [Formula: see text] and a boundary term [Formula: see text]. It is possible to obtain the field equations for [Formula: see text] and the related gravitational energy–momentum pseudotensor [Formula: see text]. Finally we show that, thanks to this further pseudotensor, it is possible to pass from [Formula: see text]–[Formula: see text] and vice versa through a simple relation between gravitational pseudotensors.
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Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "The generalized stokes integral theorem for a covariant pseudotensor field." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(49) (December 29, 2021): 66–74. http://dx.doi.org/10.37972/chgpu.2021.49.3.010.
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Ориентируемые континуумы играют важную роль в микрополярной теории упругости, все реализации которой возможны только в рамках псевдотензорного формализма и представления об ориентируемом многообразии. Особенно это касается теории микрополярных гемитропных упругих сред. В настоящей работе рассматриваются различные формулировки интегральной теоремы Стокса для асимметричного ковариантного пседотензорного поля, заданного веса. Тем самым достигается распространение известной интегральной формулы Стокса на случай псевдотензоров. Последнее обстоятельство позволяет использовать, указанное обобщение для микрополярных континуумов. Исследование существенно опирается на класс специальных координатных систем. Oriented continua play an important role in the micropolar theory of elasticity, all realizations of which are possible only within the framework of the pseudotensor formalism and the orientable manifold concept. This especially concerns the theory of micropolar hemitropic elastic media. In this paper, we consider various formulations of the Stokes integral theorem for an asymmetric covariant pseudotensor field of a given weight. This extends the well-known Stokes integral formula to the case of pseudotensors. The latter circumstance makes it possible to use the manifistated generalization for micropolar continua. The study relies heavily on the class of special coordinate systems.
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Chen, Chiang-Mei, Jian-Liang Liu, and James M. Nester. "Gravitational energy is well defined." International Journal of Modern Physics D 27, no. 14 (October 2018): 1847017. http://dx.doi.org/10.1142/s021827181847017x.
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The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy–momentum is now regarded as quasi-local (associated with a closed 2-surface). We consider the pseudotensor and quasi-local proposals in the Lagrangian–Noether–Hamiltonian formulations. There are two ambiguities: (i) many expressions, (ii) each depends on some nondynamical structure, e.g. a reference frame. The Hamiltonian approach gives a handle on both problems. Our remarkable discovery is that with a 4D isometric Minkowski reference, a large class of expressions — those that agree with the Einstein pseudotensor’s Freud superpotential to linear order — give a common quasi-local energy value. With a best-matched reference on the boundary, this value is the nonnegative Wang–Yau mass.
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Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "On a pseudotensor generalization of the Hugoniot-Hadamard linking boundary conditions." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 2(48) (October 29, 2021): 104–14. http://dx.doi.org/10.37972/chgpu.2021.48.2.013.
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В представляемой работе исследуются особенности связывающих двусторонних граничных условий на поверхностях разрывов, распространяющихся в сплошных средах (в частности, в микрополярных континуумах). Теория Югонио-Адамара, существенно развитая Г.И. Быковцевым, распространения поверхностей разрывов физических полей обобщена на случай псевдотензорного полевого описания. Вводятся понятия фундаментального ориентирующего псевдоскаляра и псевдоскалярного времени. Исследуется геометрия поверхностей уровня псевдоскалярного поля, представляющих интерес для механики наращиваемых тел. Вводится понятие псевдонормали к поверхности. Обсуждаются вопросы дифференцирования по псевдоскалярному времени и его преобразования при зеркальных отражениях и инверсиях пространства. Получены геометрические и кинематические условия совместности первого порядка в терминах псевдотензоров. Выведены условия совместности для слабых разрывов перемещений и микровращений в микрополярном континууме. The present work deals with the linking boundary conditions formulated on the both sides of a propagating wave surface (in particular, in micropolar continua). The Hugoniot-Hadamard theory of physical fields wave surfaces propagation, essentially developed by G.I. Bykovtsev, is generalized to the case of a pseudotensor field description. The concepts of fundamental orienting pseudoscalar and pseudoscalar time are introduced and discussed. The geometry of level surfaces of a given pseudoscalar field is studied. The concept of a pseudovector normal to a surface is introduced. The pseudoscalar time derivative is proposed and discussed. Geometric and kinematic first order compatibility conditions are obtained in terms of pseudotensors. The compatibility conditions are derived for weak discontinuities of displacements and microrotations due to defromations of the micropolar solid.
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Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "Covariantly constant tensors in Euclid spaces. Elements of the theory." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 2(52) (December 12, 2022): 106–17. http://dx.doi.org/10.37972/chgpu.2022.52.2.012.
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В настоящей работе обсуждаются вопросы ковариантного постоянства тензоров и псевдотензоров (в том числе, двухточечных) произвольной валентности и веса в Евклидовом пространстве. Приводятся минимально необходимые сведения из алгебры и анализа псевдотензоров в пространствах Евклида. Выясняются общие условия ковариантного постоянства псевдотензоров. Рассматриваются примеры ковариантно постоянных тензоров и псевдотензоров из многомерной геометрии. Речь, в частности, идет о фундаментальном ориентирующем псевдоскаляре, целые степени которого удовлетворяет условию ковариантного постоянства. Обсуждаются свойства и способы координатного представления тензоров ковариантно постоянных тензоров ипсевдотензоров четвертого ранга. На основе неконвенционального определения полуизотропного тензора четвертого ранга приводится координатное представление в терминах дельт Кронекера и метрических тензоров. Устанавливаются условия ковариантного постоянства полуизотропных тензоров четвертого ранга. In this paper, we discuss the covariant constancy of tensors and pseudotensors (including two-point ones) of arbitrary valency and weight in Euclidean space. The requisite notions and equations from algebra and analysis of pseudotensors in Euclidean spaces are given. The general conditions for the covariant constancy of pseudotensors are highlighted. Examples of covariantly constant tensors and pseudotensors from multidimensional geometry are considered. In particular, a fundamental orienting pseudoscalar whose integer powers satisfy the condition of covariant constancy is introduced. The properties and methods of coordinate representation of covariantly constant tensors and pseudotensors of the fourth rank are discussed. Based on an unconventional definition of a semi-isotropic tensor of the fourth rank, a coordinate representation in terms of Kronecker deltas and metric tensors is given. Conditions for the covariant constancy of semi-isotropic tensors of the fourth rank are derived.
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Treml, T. F. "Dimensional regularization and the path-integral approach to photon mass in the Schwinger model." Canadian Journal of Physics 67, no. 5 (May 1, 1989): 515–18. http://dx.doi.org/10.1139/p89-094.
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The derivation of the photon mass in the Schwinger model (two-dimensional quantum electrodynamics) is studied in a path-integral approach that employs a coordinate-space form of dimensional regularization. The role of the antisymmetric epsilon pseudotensor in dimensional regularization is briefly discussed. It is shown that the correct photon mass may easily be recovered by a dimensionally regularized calculation in which the epsilon pseudotensor is taken to be a purely two-dimensional quantity.
Dissertations / Theses on the topic "Pseudotensore"
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Capriolo, Maurizio. "Lo pseudotensore energia-impulso in teorie estese della gravitazione." Doctoral thesis, Universita degli studi di Salerno, 2018. http://elea.unisa.it:8080/xmlui/handle/10556/4238.
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2016 - 2017The gravitational field’s energy and momentum definitions are treated in extensive gravitation theories, through the generalization of the energymomentum pseudotensor, defined by Einstein in general relativity. This extension was obtained by modifying the Lagrangian of Hilbert-Einstein or by using a different connection from the one of Levi- Civita as that of Weitzenböck for teleparallel theories. We have firstly obtained the gravitational energy-momentum pseudotensor for extended Lagrangians that depend on the metric gμ⌫ and on its derivatives up to nth order and then demonstrated, in general, its affine and non-covariant behavior. Then we applied the weak field limit to Euler-Lagrange equations associated to the Lagrangian which depends linearly on the ⇤R terms and derived the modified gravitational waves with six polarization states, three transverse and three not, with helicity 0 and 2. Subsequently we have obtained, through the Noether theorem for infinitesimal rigid translations, the relative energy-momentum pseudotensor and after having developed it to the order h2 and mediated on an suitable domain, we have calculated the power emitted from a possible gravitational radiant source. For gravity f (R) and f (T) we have obtained the respective energy-momentum pseudotensors and, via the border therm B which connects the curvature R to the torsion T, we have studied the relative pseudotensor ⌧↵ #|!(T,B) allowing us to link ⌧↵ #|f(R) and ⌧↵ #|f(T). Finallywehave obtained the equations for two theories of higher order telepallel gravity: in particular for the Lagrangian L⇤kT = h ! T + Pp k=0 akT⇤kT # and for the sixth order telepallel gravity equivalent to LR⇤R = p−g (−R + a0R2 + a1R⇤R). [edited by author]
XXX n.s.
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Du, Wenwen. "Material Tensors and Pseudotensors of Weakly-Textured Polycrystals with Orientation Measure Defined on the Orthogonal Group." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/22.
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Material properties of polycrystalline aggregates should manifest the influence of crystallographic texture as defined by the orientation distribution function (ODF). A representation theorem on material tensors of weakly-textured polycrystals was established by Man and Huang (2012), by which a given material tensor can be expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a number of undetermined material parameters. Man and Huang's theorem is based on the classical assumption in texture analysis that ODFs are defined on the rotation group SO(3), which strictly speaking makes it applicable only to polycrystals with (single) crystal symmetry defined by a proper point group. In the present study we consider ODFs defined on the orthogonal group O(3) and extend the representation theorem of Man and Huang to cover pseudotensors and polycrystals with crystal symmetry defined by any improper point group. This extension is important because many materials, including common metals such as aluminum, copper, iron, have their group of crystal symmetry being an improper point group. We present the restrictions on texture coefficients imposed by crystal symmetry for all the 21 improper point groups and we illustrate the extended representation theorem by its application to elasticity.
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Chang, Chia-Chen, and 張佳正. "The Localization of Gravitational Energy: Pseudotensors and." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/02593741591016480346.
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碩士國立中央大學
物理學系
86
We investigate the relation between pseudotensors and quasilocal expressionsin this thesis. The starting point is that energy and momentum should be consideredas the value of the Hamiltonian. By applying the covariant Hamiltonian analysis, wecome up with a set of covariant symplectic boundary expressions which depend ona reference configuration and a displacement vector field and determine the valueof quasilocal quantity. By adopting their vacuum GR formulations and choosing appropriatereference configurations and frames, these expressions will reduce to superpotentials.Conversely superpotentials are Hamiltonian boundary terms. The idea isthat since the integral of the divergence of a superpotential is the totalenergy-momentum, we may expression this as an integral of an ADM Hamiltonian witha boundary term which is the superpotential. The validity of this techniquedepends upon the fact that the variation of superpotentials can give thedesired asymptotically vanishing value at infinity which is required to guaranteethe correctness of the Hamiltonian field equation. With the help of thesymplectic idea, we can understand the boundary condition of eachsuperpotential by calculating their variation. Hence pseudotensors are reallyquasilocal and correspond to various boundary conditions.
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Chung-Chin, Tsai, and 蔡崇欽. "Landau-Lifshitz Pseudotensor Applied on Numerical Relativity." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/07587713576981367822.
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So, Lau-Loi, and 蘇樓來. "Quasi-local energy-momentum and pseudotensors for GR in small regions." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/35696956976231977181.
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博士國立中央大學
物理研究所
94
The localization of energy-momentum for gravitating systems has remained an important problem since the time of Einstein. Due to the equivalence principle there is no proper energy-momentum density. Traditional approaches led to a va- riety of reference frame dependent expressions, referred to as pseudotensors. A more modern idea is quasilocal energy-momentum. C.M. Chen, using a covariant Hamiltonian formalism, gave four preferred Hamiltonian boundary term quasilocal energy-momentum expressions. The classical pseudotenor expressions, as well as the quasilocal expressions generally agree for the total (i.e. global) values but give quite di®erent values locally. It is desirable to ‾nd some way to choose which expression gives a better description of the energy-momentum for a gravitating system. Here we shall test both the well-known classical pseudotensors (in particular, Einstein, Papapetrou, Landau-Lifshits ' Bergmann-Thomson, M¿ller (1958), M¿ller (1961), Weinberg) and the covariant Hamiltonian quasilocal boundary expressions in a dif- ferent regime, namely the small region limit|both inside matter and in vacuum. All of the expressions|except for M¿ller's 1958 expression|give the correct mate- rial limit. In small vacuum regions we found some interesting results which allows us to choose which expressions satisfy an important physical property: positive en- ergy. None of the classical pseudotensors satis‾es this positivity property, however there is a one-parameter set of linear combinations which, to lowest non-vanishing order is proportional to the Bel-Robinson tensor and hence is positive for small regions. Moreover, we have constructed an in‾nite set (with 10 constant parame- ters) of additional new holonomic pseudotensors which, although rather contrived, satisfy this important positive energy requirement. On the other hand we found that M¿ller's 1961 teleparallel-tetrad energy-momentum expression naturally has this Bel-Robinson property. For C.M. Chen's covariant-symplectic quasilocal ex- pressions we found that one, corresponding to the natural boundary choices, gives this desired Bel-Robinson positivity result in orthonormal frames. Moreover within a two parameters modi‾cation of the Chen-Nester four expressions, one gives an extra nice result in holonomic frames.
Book chapters on the topic "Pseudotensore"
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Man, Chi-Sing. "Tensor and Pseudotensor Representations of SO(3), O(3), and Their Finite Subgroups." In Crystallographic Texture and Group Representations, 337–59. Dordrecht: Springer Netherlands, 2023. http://dx.doi.org/10.1007/978-94-024-2158-3_16.
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Raychaudhuri, A. K., S. Banerji, and A. Banerjee. "The Energy—Momentum Pseudotensor of the Gravitational Field and Loss of Energy by Gravitational Radiation." In Astronomy and Astrophysics Library, 105–13. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2754-0_8.
Full textConference papers on the topic "Pseudotensore"
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Guo, Jia, Weiwei Jiang, and Zhu Benchao. "Einstein Energy-Momentum Pseudotensor in Generalized Covariant Equation." In 2016 International Conference on Education, Management and Computer Science. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icemc-16.2016.241.
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