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Journal articles on the topic 'Pseudotensore'

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Author: Grafiati

Published: 10 March 2023

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1

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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2

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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3

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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4

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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5

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.

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Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "Compatibility of strong discontinuities in micropolar thermoelastic media. A pseudotensor formulation." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 2(44) (December 14, 2020): 155–60. http://dx.doi.org/10.37972/chgpu.2020.44.2.015.

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В статье рассматривается процедура вывода условий совместности на поверхностях сильных разрывов в микрополярных термоупругих средах. Условия совместности сильных разрывов 4-тензора Пиолы-Кирхгофа и 4-тензора энергии-импульса выводятся из принципа наименьшего действия. Приведена определяющая форма микрополярного термоупругого потенциала для изотропных и гемитропных сред. Развиваемая псевдотензорная формулировка условий совместности сильных разрывов может быть применена при моделировании динамики изотропных и гемитропных микрополярных термоупругих сред. The paper deals with the regular procedures for deriving compatibility conditions on the surfaces of strong discontinuities in thermoelastic micropolar media. The jump conditions of the Piola-Kirchhoff 4-pseudotensor and the energy-momentum 4-pseudotensor are derived from the principle of least action. The compatibility conditions on the propagating strong discontinuity surface are explicitly formulated for a micropolar thermoelastic continuum. The developed pseudotensor formulation of the compatibility conditions for strong discontinuities can be applied to the dynamic problems for isotropic and hemitropic micropolar thermoelastic media.

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Chang, Chia-Chen, James M. Nester, and Chiang-Mei Chen. "Pseudotensors and Quasilocal Energy-Momentum." Physical Review Letters 83, no. 10 (September 6, 1999): 1897–901. http://dx.doi.org/10.1103/physrevlett.83.1897.

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13

Nester, James M. "General pseudotensors and quasilocal quantities." Classical and Quantum Gravity 21, no. 3 (January 13, 2004): S261—S280. http://dx.doi.org/10.1088/0264-9381/21/3/016.

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Nahmad-Achar, E., and B. F. Schutz. "Pseudotensors in asymptotically curvilinear coordinates." General Relativity and Gravitation 19, no. 7 (July 1987): 655–63. http://dx.doi.org/10.1007/bf00766272.

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15

Crothers, Stephen J. "Proof that Einstein’s field equations are invalid: Exposition of the unimodular defect." Physics Essays 34, no. 4 (December 17, 2021): 420–28. http://dx.doi.org/10.4006/0836-1398-34.4.420.

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Albert Einstein first presented his gravitational field equations in unimodular coordinates. In these coordinates, the field equations can be written explicitly in terms of the Einstein pseudotensor for the energy-momentum of the gravitational field. Since this pseudotensor produces, by contraction, a first-order intrinsic differential invariant, it violates the laws of pure mathematics. This is sufficient to prove that Einstein’s unimodular field equations are invalid. Since the unimodular form must hold in the general theory of relativity, it follows that the latter is also physically and mathematically unsound, lacking a proper mathematical foundation.

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KIM, WON T., and JULIAN LEE. "ADM MASS, BONDI MASS, AND ENERGY CONSERVATION IN TWO-DIMENSIONAL DILATON GRAVITIES." International Journal of Modern Physics A 11, no. 03 (January 30, 1996): 553–61. http://dx.doi.org/10.1142/s0217751x96000250.

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We show how a stress-energy pseudotensor can be constructed in two-dimensional dilaton gravity theories (classical, CGHS and RST) and derive from it the expression for the ADM mass in these theories. We compare this expression with the ones in the literature obtained by other methods. We define the Bondi mass for these theories by using the pseudotensor formalism. The resulting expression is the generalization of the expression for the ADM mass. The boundary condition needed for the energy conservation is also investigated. It is shown that under appropriate boundary conditions, our definition of the Bondi mass is exactly the ADM mass minus the matter radiation energy at null infinity.

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Frauendiener, J. "Geometric description of energy-momentum pseudotensors." Classical and Quantum Gravity 6, no. 12 (December 1, 1989): L237—L241. http://dx.doi.org/10.1088/0264-9381/6/12/001.

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Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "Covariantly constant tensors in Euclid spaces. Applications to continuum mechanics." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 2(52) (December 12, 2022): 118–27. http://dx.doi.org/10.37972/chgpu.2022.52.2.013.

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В настоящей работе обсуждаются вопросы использования в механике сплошных сред ковариантно постоянных тензоров и псевдотензоров (в том числе, двухточечных) произвольной валентности и целого веса в Евклидовых пространствах. В работе продемонстрировано, что тензоры дистории и обратной дисторсии не являются ковариантно постоянными двухточечными тензорами, в противовес указаниям на их ковариантное постоянство, встречающееся в литературных источниках по нелинейной механике континуума. Приводится общая форма упругого потенциала для линейного анизотропного микрополярного континуума. На основе неконвенционального определения полуизотропного тензора приводятся координатные представления определяющих тензоров и псевдотензоров четвертого ранга в терминах дельт Кронекера и метрических тензоров. Показывается ковариантное постоянство определяющих линейный анизотропный микрополярный континуум тензоров и псевдотензоров четвертого ранга. The present paper is devoted to applications of covariantly constant tensors and pseudotensors (including two-point ones) of arbitrary valency and integer weight in Euclidean spaces to continuum mechanics. The tensors of distortion and inverse distortion are not covariantly constant two-point tensors, in contrast to their covariant constancy mentions found in the literature on nonlinear continuum mechanics. The general form of the elastic potential for a linear anisotropic micropolar continuum is given. Based on the non-conventional definition of a semi-isotropic tensor, coordinate representations of constitutive tensors and pseudotensors of the fourth rank are given in terms of Kronecker deltas and metric tensors. The covariant constancy of the constitutive tensors and pseudotensors of the fourth rank for the linear anisotropic micropolar continuum is shown.

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Sharif, M., and M. Jamil Amir. "Energy-momentum of the Friedmann models in General Relativity and the teleparallel theory of gravity." Canadian Journal of Physics 86, no. 11 (November 1, 2008): 1297–302. http://dx.doi.org/10.1139/p08-073.

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This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used Møller’s pseudotensor prescription in General Relativity and a certain energy-momentum density developed from Møller’s teleparallel formulation. We show that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius ρ = 2[Formula: see text]. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between Møller’s pseudotensor for General Relativity and teleparallel theory. Further, we show that the results are independent of the free dimensionless coupling constant of the teleparallel gravity.PACS No.: 04.20.–q

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Rabinowitch, A. S. "Energy‐Momentum Pseudotensor of the Gravitational Field." Physics Essays 6, no. 4 (December 1993): 572–75. http://dx.doi.org/10.4006/1.3029095.

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21

Евгений Валерьевич, Мурашкин,, and Радаев, Юрий Николаевич. "On two base natural forms of asymmetric force and couple stress tensors of potential in mechanics of hemitropic solids." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(53) (December 31, 2022): 86–100. http://dx.doi.org/10.37972/chgpu.2022.53.3.010.

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В работе обсуждаются некоторые вопросы моделирования гемитропных упругих сред. Вводятся две основные квадратичные энергетические формы потенциала напряжений в терминах псевдотензоров. Указанные энергетические формы полагаются абсолютными инвариантами по отношению к произвольным преобразованиям трехмерного Евклидова пространства (в том числе, при зеркальных отражениях). В результате применения специальных координатных представлений полуизотропных (гемитропных) псевдотензоров четвертого ранга можно определить все 9 ковариантно постоянных определяющих псевдоскаляров, характеризующих гемитропную упругую среду. Выделены симметричные и антисимметричные части асимметричных тензоров и псевдотензоров деформаций и напряжений. Выполнено сравнение и получены соотношения, связывающие определяющие скаляры и псевдоскаляры первой и второй основных естественных энергетических форм, в том числе, с конвенционально используемыми гемитропными псевдоскалярами: модулем сдвига, коэффициентом Пуассона, характерной микродлиной (являющейся псевдоскаляром отрицательного веса, чувствительным к отражениям трехмерного пространства), и шестью безразмерными псевдоскалярами. The paper is devoted to some problems concerning modeling hemitropic elastic media. Two main quadratic energy forms of a stress potential are introduced in terms of pseudotensors. These energy forms are assumed to be absolute invariants with respect to arbitrary transformations of the three-dimensional Euclidean space (including mirror reflections). As a result of applying special coordinate representations of semi-isotropic (hemitropic) pseudotensors of the fourth rank, it is possible to determine 9 covariantly constant constitutive pseudoscalars characterizing a hemitropic elastic medium. Symmetric and antisymmetric parts of asymmetric tensors and pseudotensors of strains and stresses are discriminated. The first and second base natural energy forms are compared and equations are derived for constitutive scalars and pseudoscalars, including the conventional hemitropic pseudoscalars: shear modulus, Poisson’s ratio, characteristic microlength (a pseudoscalar of negative weight, sensitive to reflections of three-dimensional space), and six dimensionless pseudoscalars.

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22

Мурашкин, Евгений Валерьевич, and Юрий Николаевич Радаев. "Pseudovector hyperbolic differential operators of hemitropic micropolar elasticity." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 4(50) (December 30, 2021): 59–72. http://dx.doi.org/10.37972/chgpu.2021.50.4.005.

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В статье обсуждаются вопросы, связанные с выводом и преобразованиями дифференциальных операторов, соответствующих модели гемитропного микрополярного континуума, при изменении ориентации базисного репера. Приводятся необходимые сведения из алгебры псевдотензоров. В терминах псевдотензоров формулируются уравнения динамики гемитропного микрополярного упругого тела с 9-ю определяющими псевдоскалярами. Указываются формы псевдовекторных гиперболических дифференциальных операторов в специальных системах координат. Обсуждаются свойства дифференциальных операторов изотропной микрополярной упругости. Рассмотрены преобразования дифференциальных операторов в случае зеркального отражения относительно заданной плоскости. The paper deals with the derivations and transformations of differential operators related to the hemitropic micropolar elastic model under mirror reflections. The requisite equations from algebra of pseudotensors are given. Dynamic differential equations for a hemitropic micropolar elastic solid with 9 constituve pseudoscalars are derived in terms of pseudotensors. Pseudovector hyperbolic differential operator forms caused by different coordinate net orientations are obtained and discussed. The properties of differential operators for isotropic micropolar elasticity are discussed. Mirror reflection transformations of the differential operators are considered.

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23

Szabados, L. B. "On canonical pseudotensors, Sparling's form and Noether currents." Classical and Quantum Gravity 9, no. 11 (November 1, 1992): 2521–41. http://dx.doi.org/10.1088/0264-9381/9/11/017.

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24

Türkan, A., H. Dağ, J. Y. Süngü, and E. Veli Veliev. "Hot medium effects on pseudotensor K2(1820) meson." EPJ Web of Conferences 199 (2019): 03007. http://dx.doi.org/10.1051/epjconf/201919903007.

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The investigation of mesons in hot medium can give valuable information about the nature of QCD vacuum and deconfinement phase transitions. In this study, thermal properties of pseudotensor K2(1820) meson is examined via QCD sum rules at finite temperature. The mass and the decay constant of K2(1820) are estimated up to dimension-five by considering the new operators emerging at finite temperature. It is seen that after a certain temperature, the decay constant and the mass decrease significantly due to the hot medium effects.

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25

Banerjee, N., and S. Sen. "Einstein pseudotensor and total energy of the universe." Pramana 49, no. 6 (December 1997): 609–15. http://dx.doi.org/10.1007/bf02848334.

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26

Yang, I.-Ching, Rue-Ron Hsu, Ching-Tzung Yeh, and Chin-Rong Lee. "On the Energy of a Charged Dilaton Black Hole." International Journal of Modern Physics D 06, no. 03 (June 1997): 349–56. http://dx.doi.org/10.1142/s0218271897000194.

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Employing the energy–momentum pseudotensor of Einstein, we obtain the energy distribution of a dyonic dilaton black hole. The energy distribution of this black hole depends on mass M, electric charge Qe, magnetic charge Qm and the asymptotic value of the dilaton ϕ0. We also make some comparisons between the results of Virbhadra et. al. and ours.

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27

So, Lau Loi, James M. Nester, and Hsin Chen. "Energy–momentum density in small regions: the classical pseudotensors." Classical and Quantum Gravity 26, no. 8 (April 1, 2009): 085004. http://dx.doi.org/10.1088/0264-9381/26/8/085004.

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28

Mehdipour, S. Hamid. "Gravitational energy of a noncommutative Vaidya black hole." Canadian Journal of Physics 91, no. 3 (March 2013): 242–45. http://dx.doi.org/10.1139/cjp-2012-0485.

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In this paper we evaluate the components of the energy–momentum pseudotensors of Landau and Lifshitz for the noncommutative Vaidya space–time. The effective gravitational mass experienced by a neutral test particle present at any finite distance in the gravitational field of the noncommutative Vaidya black hole is derived. Using the effective mass parameter, one finds that the naked singularity is massless and this supports Seifert's conjecture.

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29

Hellmann, H. "Tenside und Pseudotenside in Oberflächengewässern und Abwässern." Tenside Surfactants Detergents 28, no. 2 (March 1, 1991): 111–17. http://dx.doi.org/10.1515/tsd-1991-280212.

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30

Radayev, Yu N., and E. V. Murashkin. "PSEUDOTENSOR FORMULATION OF THE MECHANICS OF HEMITROPIC MICROPOLAR MEDIA." Problems of strenght and plasticity 82, no. 4 (2020): 399–412. http://dx.doi.org/10.32326/1814-9146-2020-82-4-399-412.

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The possibility of applications of relative tensors concepts to the mechanics of micropolar continuum and, in particular, for the hemitropic micropolar continua is considered. The fundamental tensors and orienting relative scalars in three-dimensional space are introduced. Permutation symbols and absolute Levi-Civita tensors are investigated in further details. Algebraic and differential properties of the relative tensors are discussed. The weights of the fundamental kinematic tensors are determined. The wryness tensor and the asymmetric strain tensor are constructed in terms of the vectors of micro-rotation and displacements. Notions of force and couple traction vectors, associated force and associated couple stress vector, force and couple stresses tensors are discussed in the frameworks of relative tensors algebra. The weights of the basic micropolar elasticity tensors are determined and discussed. The constitutive form of the micropolar elastic potential is introduced as an absolute scalar in order to obtain micropolar constitutive equations. In the linear case, the elastic potential is a quadratic form whose coefficients are pseudoscalars. The weights of the constitutive pseudoscalars are calculated. The dimensionless constitutive micropolar constants and constitutive constants with physical dimensions are discriminated. Statics and dynamics of micropolar elastic continua are developed in terms of relative tensors. Dynamic equations involving displacements and microrotations in the case of semi-isotropic (hemitropic) symmetry are derived and represented by the pseudotensor technique. The paper can be considered as a script of fundamental formulas and concepts related to the algebra and differentiation of relative tensors of arbitrary rank.

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31

Khrapko, R. I. "The truth about the energy-momentum tensor and pseudotensor." Gravitation and Cosmology 20, no. 4 (October 2014): 264–73. http://dx.doi.org/10.1134/s0202289314040082.

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32

Hirashima, H. "A New Gravitational Energy-Momentum Pseudotensor in Tetrad Form." Progress of Theoretical Physics 96, no. 2 (August 1, 1996): 347–75. http://dx.doi.org/10.1143/ptp.96.347.

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33

DÍAZ-CRUZ, J. L., and G. LÓPEZ CASTRO. "INDUCED SECOND CLASS CURRENTS IN τ DECAYS." Modern Physics Letters A 06, no. 17 (June 7, 1991): 1605–10. http://dx.doi.org/10.1142/s0217732391001731.

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We present a calculation of second class (SC) effects in τ decays induced by QCD corrections to the weak vertex [Formula: see text]. We find that the induced SC form factors behave like (md − mu)/q2 (q the momentum transfer, and mq the q-quark mass), which give branching ratios of O(10−6) and O(10−8) for the scalar and pseudotensor SC decays, respectively.

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34

Giacosa, Francesco. "Conventional mesons below 2 GeV." EPJ Web of Conferences 274 (2022): 03008. http://dx.doi.org/10.1051/epjconf/202227403008.

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We briefly review the status of various conventional quark-antiquark mesons below 2 GeV and outline some open questions: the status of the strangeantistrange orbitally excited vector meson, the status of the nonet of axial-tensor mesons (chiral partners of the well known tensor mesons), and the isoscalar mixing angle in the pseudotensor sector, which can eventually represent a novel manifestation of the chiral anomaly.

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35

Cvetkovic, Milica, and Milan Zlatanovic. "New Cartan’s tensors and pseudotensors in a generalized Finsler space." Filomat 28, no. 1 (2014): 107–17. http://dx.doi.org/10.2298/fil1401107c.

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In this work we defined a generalized Finsler space (GFN) as 2N-dimensional differentiable manifold with a non-symmetric basic tensor gij(x,x?), which applies that gij_?|m(x,x?)=0; ?=1,2. Based on non-symmetry of basic tensor, we obtained ten Ricci type identities, comparing to two kinds of covariant derivative of a tensor in Rund?s sense. There appear two new curvature tensors and fifteen magnitudes, we called ?curvature pseudotensors?.

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36

Nahmad-Achar, E., and B. F. Schutz. "Conserved quantities from pseudotensors and extremum theorems for angular momentum." Classical and Quantum Gravity 4, no. 4 (July 1, 1987): 929–42. http://dx.doi.org/10.1088/0264-9381/4/4/024.

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37

Mehdipour, S. Hamid. "Entropic gravity versus gravitational pseudotensors in static spherically symmetric spacetimes." Astrophysics and Space Science 352, no. 2 (April 18, 2014): 877–81. http://dx.doi.org/10.1007/s10509-014-1933-8.

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38

Kovalev, Vladimir Aleksandrovich, Eugenii Valeryevich Murashkin, and Yuri Nikolaevich Radayev. "On the Neuber theory of micropolar elasticity. A pseudotensor formulation." Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 24, no. 4 (2020): 752–61. http://dx.doi.org/10.14498/vsgtu1799.

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Рассматривается псевдотензорная формулировка теории микрополярной упругости Нейбера. Приведены и обсуждаются динамические уравнения микрополярного континуума в терминах относительных тензоров (псевдотензоров). Даны определяющие уравнения для линейного изотропного микрополярного твердого тела. Окончательные формы динамических уравнений для изотропного микрополярного континуума в терминах смещений и микровращений получены в терминах относительных тензоров. Устранены недочеты в окончательной форме динамических уравнений Нейбера. Получены динамические уравнения Нейбера в цилиндрической системе координат.

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39

Fatibene, L., M. Ferraris, M. Francaviglia, and L. Lusanna. "ADM pseudotensors, conserved quantities and covariant conservation laws in general relativity." Annals of Physics 327, no. 6 (June 2012): 1593–616. http://dx.doi.org/10.1016/j.aop.2012.02.010.

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40

Kuball, H. G., O. Türk, I. Kiesewalter, and E. Dorr. "A Non-Traceless Molecular Pseudotensor for a Description of the HTP." Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals 352, no. 1 (November 2000): 195–204. http://dx.doi.org/10.1080/10587250008023177.

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41

Virbhadra, K. S. "A comment on the energy-momentum pseudotensor of Landau and Lifshitz." Physics Letters A 157, no. 4-5 (July 1991): 195–97. http://dx.doi.org/10.1016/0375-9601(91)90050-i.

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42

Murashkin, E. V., and Yu N. Radayev. "On the Theory of Covariant Differentiation of Two Point Pseudotensor Fields." Mechanics of Solids 57, no. 6 (December 2022): 1365–73. http://dx.doi.org/10.3103/s0025654422060255.

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43

So, Lau Loi. "Gravitational energy from a combination of a tetrad expression and Einstein's pseudotensor." Classical and Quantum Gravity 25, no. 17 (August 15, 2008): 175012. http://dx.doi.org/10.1088/0264-9381/25/17/175012.

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44

Nakanishi, N. "De Donder Condition and the Gravitational Energy-Momentum Pseudotensor in General Relativity." Progress of Theoretical Physics 75, no. 6 (June 1, 1986): 1351–58. http://dx.doi.org/10.1143/ptp.75.1351.

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45

Noonan, Thomas W. "Remarks on the necessity and uniqueness of the gravitational stress-energy pseudotensor." Astrophysical Journal 313 (February 1987): 37. http://dx.doi.org/10.1086/164946.

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46

Iosifidis, Damianos. "Solving Linear Tensor Equations II: Including Parity Odd Terms in Four Dimensions." Universe 8, no. 6 (May 31, 2022): 312. http://dx.doi.org/10.3390/universe8060312.

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In this paper, focusing on 4-dimensional space, we extend our previous results of solving linear tensor equations. In particular, we consider a 30-parameter linear tensor equation for the unknown tensor component Nαμν in terms of the known component (source) Bαμν. The extension also included the parity even linear terms in Nαμν (and the associated traces), which are formed by contracting the latter with the 4-dimensional Levi-Civita pseudotensor. Assuming generic non-degeneracy conditions and following a step-by-step procedure, we show how to explicitly solve for the unknown tensor field component Nαμν and, consequently, derive its unique and exact solution in terms of the component Bαμν.

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47

Houra-Yaou, Ladonne, Paul Kessler, Joseph Parisi, Francesco Murgia, and Johan Hansson. "Production of meson pairs, involving tensor and pseudotensor mesons, in photon-photon collisions." Zeitschrift f�r Physik C Particles and Fields 76, no. 3 (November 1, 1997): 537–47. http://dx.doi.org/10.1007/s002880050576.

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48

Giacosa, Francesco. "Chiral anomaly and strange-nonstrange mixing." EPJ Web of Conferences 199 (2019): 05012. http://dx.doi.org/10.1051/epjconf/201919905012.

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As a first step, a simple and pedagogical recall of the η-η′ system is presented, in which the role of the axial anomaly, related to the heterochiral nature of the multiplet of (pseudo)scalar states, is underlined. As a consequence, η is close to the octet and η′ to the singlet configuration. On the contrary, for vector and tensor states, which belong to homochiral multiplets, no anomalous contribution to masses and mixing is present. Then, the isoscalar physical states are to a very good approximation nonstrange and strange, respectively. Finally, for pseudotensor states, which are part of an heterochiral multiplet (just as pseudoscalar ones), a sizable anomalous term is expected: η2(1645) roughly corresponds to the octet and η2(1870) to the singlet.

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49

Vyalova, A. V. "Curvature and torsion pseudotensors of coaffine connection in tangent bundle of hypercentred planes manifold." Differential Geometry of Manifolds of Figures, no. 51 (2020): 49–57. http://dx.doi.org/10.5922/0321-4796-2020-51-6.

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The hypercentered planes family, whose dimension coincides with dimension of generating plane, is considered in the projective space. Two principal fiber bundles arise over it. Typical fiber for one of them is the stationarity subgroup for hypercentered plane, for other — the linear group operating in each tangent space to the manifold. The latter bundle is called the principal bundle of linear coframes. The structural forms of two bundles are related by equations. It is proved that hypercentered planes family is a holonomic smooth manifold. In the principal bundle of linear coframes the coaffine connection is given. From the differential equations it follows that the coaffine connection object forms quasipseudotensor. It is proved that the curvature and torsion objects for the coaffine connection in the linear coframes bundle form pseudotensors.

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50

MATYJASEK, JERZY. "SOME REMARKS ON THE EINSTEIN AND MØLLER PSEUDOTENSORS FOR STATIC AND SPHERICALLY-SYMMETRIC CONFIGURATIONS." Modern Physics Letters A 23, no. 08 (March 14, 2008): 591–601. http://dx.doi.org/10.1142/s0217732308026558.

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It is shown that for the spherically-symmetric and static systems the hypotheses posed by Yang and Radinschi and by Vagenas can be related to the particular distribution of the source. Simple proofs are given and a number of examples are discussed with the special emphasis put on the quantum corrected Schwarzschild black hole.

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