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Artykuły w czasopismach na temat „Algebraic law”

Autor: Grafiati

Data publikacji: 2 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Nowak, Piotr, and Olgierd Hryniewicz. "On MV-Algebraic Versions of the Strong Law of Large Numbers." Entropy 21, no. 7 (2019): 710. http://dx.doi.org/10.3390/e21070710.

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Many-valued (MV; the many-valued logics considered by Łukasiewicz)-algebras are algebraic systems that generalize Boolean algebras. The MV-algebraic probability theory involves the notions of the state and observable, which abstract the probability measure and the random variable, both considered in the Kolmogorov probability theory. Within the MV-algebraic probability theory, many important theorems (such as various versions of the central limit theorem or the individual ergodic theorem) have been recently studied and proven. In particular, the counterpart of the Kolmogorov strong law of larg

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2

Radisavljevic, V., and H. Baruh. "Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates." Journal of Dynamic Systems, Measurement, and Control 121, no. 4 (1999): 594–98. http://dx.doi.org/10.1115/1.2802521.

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A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to

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3

Schlather, Achim, and Martin Schlather. "Depicting Falsifiability in Algebraic Modelling." J 8, no. 3 (2025): 23. https://doi.org/10.3390/j8030023.

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This paper investigates how algebraic structures can encode epistemic limitations, with a focus on object properties and measurement. Drawing from philosophical concepts such as underdetermination, we argue that the weakening of algebraic laws can reflect foundational ambiguities in empirical access. Our approach supplies instruments that are necessary and sufficient towards practical falsifiability. Besides introducing this new concept, we consider, exemplarily and as a starting point, the following two fundamental algebraic laws in more detail: the associative law and the commutative law. We

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4

Sun, Yi, Ben Yong Chen, and Jing Li Fu. "Lie Algebraic Structure and Poisson Conservation Law for One Class of Multi-Dimensional Coupled Oscillators." Applied Mechanics and Materials 597 (July 2014): 388–92. http://dx.doi.org/10.4028/www.scientific.net/amm.597.388.

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This paper researches Lie algebraic structure and Poisson conservation law for one class of multi-dimensional coupled oscillators. The equations of motion are established, and the coupled terms in the equations of motion are eliminated by introducing normal transformations. The Lie algebraic structure and Poisson conservation law are given. Finally, an example is given to illustrate the results.

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5

Gaggioli, R. A., and Y. M. El-Sayed. "A Critical Review of Second Law Costing Methods—II: Calculus Procedures." Journal of Energy Resources Technology 111, no. 1 (1989): 8–15. http://dx.doi.org/10.1115/1.3231402.

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The following article completes the review of the development and state of engineering economic applications of the Second Law of Thermodynamics, which was begun in Part I (El-Sayed and Gaggioli, 1989). We began with a historical review, followed by a brief discussion of the relevant cost accounting concepts and, in turn, general descriptions of the different exergy costing methods which are in existence. Then, the various algebraic techniques of exergy costing were analyzed and critiqued, generally by considering successive publications developing and/or based on a technique. This paper, on t

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6

Lindahl, Lars, and Jan Odelstad. "An Algebraic Analysis of Normative Systems." Ratio Juris 13, no. 3 (2000): 261–78. http://dx.doi.org/10.1111/1467-9337.00155.

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7

Bernatska, Julia. "Abelian Function Fields on Jacobian Varieties." Axioms 14, no. 2 (2025): 90. https://doi.org/10.3390/axioms14020090.

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The aim of this paper is an exposition of fields of multiply periodic, or Kleinian, ℘-functions. Such a field arises on the Jacobian variety of an algebraic curve, providing natural algebraic models for the Jacobian and Kummer varieties, possessing the addition law, and accommodating dynamical equations with solutions. All of this will be explained in detail for plane algebraic curves in their canonical forms. Examples of hyperelliptic and non-hyperelliptic curves are presented.

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8

Letychevskyi, O. O., V. S. Peschanenko, and M. Yu Poltorackiy. "Algebraic approach to the analysis of legal documents." PROBLEMS IN PROGRAMMING, no. 3-4 (December 2022): 117–27. http://dx.doi.org/10.15407/pp2022.03-04.117.

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In this study, problems regarding the analysis of law articles and their conformance to legal documents are considered. The algebraic approach is used for the formal verification of legal texts that is presented as specification of behavior algebra. Having a formal presen- tation of legal texts allows for the application of algebraic methods, such as symbolic modeling, automatic proving of statements and algebraic matching. The approach was implemented for Ukrainian-language legal documents to detect inconsistency, incompleteness, and prove conformance. The analysis of legal texts has been imp

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9

Milosevic, Jovana. "Hartwig’s triple reverse order law in C*-algebras." Filomat 32, no. 12 (2018): 4229–32. http://dx.doi.org/10.2298/fil1812229m.

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In this paper Hartwig?s triple reverse order law for the Moore-Penrose inverse is proved for C*-algebras. A very simple algebraic proof for Hartwig?s triple reverse order law for operators on Hilbert spaces is given.

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10

Kotsios, Stelios. "Feedback Control Techniques for a Discrete Dynamic Macroeconomic Model with Extra Taxation: An Algebraic Algorithmic Approach." Mathematics 11, no. 19 (2023): 4213. http://dx.doi.org/10.3390/math11194213.

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In this paper, a model matching feedback law design technique is applied to a macroeconomical model. We calculate, using computational algebra methodology, which paths of government expenditure and extra taxation will lead the system to a desired dynamic behavior. The solution is based on algebraic methods and the development, in computer algebra software, of appropriate symbolic algorithms that produce a class of feedback laws as solutions. A method for solving a linear algebraic system of polynomials equations is provided, as well as its application to the feedback law design.

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11

Vakil, Ravi. "Murphy’s law in algebraic geometry: Badly-behaved deformation spaces." Inventiones mathematicae 164, no. 3 (2006): 569–90. http://dx.doi.org/10.1007/s00222-005-0481-9.

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12

Adigu¨zel, E., and H. O¨z. "Direct Optimal Control of Nonlinear Systems Via Hamilton’s Law of Varying Action." Journal of Dynamic Systems, Measurement, and Control 117, no. 3 (1995): 262–69. http://dx.doi.org/10.1115/1.2799115.

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Based on direct application of Hamilton’s Law of Varying Action in conjunction with an assumed-time-modes approach for both the generalized coordinates and input functions, a direct optimal control methodology is developed for the control of nonlinear, time varying, spatially discrete mechanical systems. Expansion coefficients of admissible time modes for the dependent variables of the dynamic system and those for the inputs constitute the states and controls, respectively. This representation permits explicit a priori integration in time of the energy expressions in Hamilton’s law and leads t

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13

Liu, Xiaoyan, Feng Feng, and Hui Zhang. "On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/192957.

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Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov’s soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold

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14

Muhafzan. "Positive Stabilization of Linear Differential Algebraic Equation System." International Journal of Differential Equations 2016 (2016): 1–3. http://dx.doi.org/10.1155/2016/6346780.

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We study in this paper the existence of a feedback for linear differential algebraic equation system such that the closed-loop system is positive and stable. A necessary and sufficient condition for such existence has been established. This result can be used to detect the existence of a state feedback law that makes the linear differential algebraic equation system in closed loop positive and stable.

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15

Dai, Shouxin, and Marc Levine. "Connective Algebraic K-theory." Journal of K-Theory 13, no. 1 (2014): 9–56. http://dx.doi.org/10.1017/is013012007jkt249.

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AbstractWe examine the theory of connective algebraic K-theory, , defined by taking the −1 connective cover of algebraic K-theory with respect to Voevodsky's slice tower in the motivic stable homotopy category. We extend to a bi-graded oriented duality theory when the base scheme is the spectrum of a field k of characteristic zero. The homology theory may be viewed as connective algebraic G-theory. We identify for X a finite type k-scheme with the image of in , where is the abelian category of coherent sheaves on X with support in dimension at most n; this agrees with the (2n,n) part of the th

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16

Girko, Vyacheslav L., and Larissa D. Shevchuk. "The Inverse Tangent Law for the solutions of systems of linear algebraic equations with independent random coefficients." Random Operators and Stochastic Equations 26, no. 2 (2018): 125–30. http://dx.doi.org/10.1515/rose-2018-0010.

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17

Fujii, Kazuyuki, and Hiroshi Oike. "An Algebraic Proof of the Associative Law of Elliptic Curves." Advances in Pure Mathematics 07, no. 12 (2017): 649–59. http://dx.doi.org/10.4236/apm.2017.712040.

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18

Salmela, Antti. "An algebraic method for solving the SU(3) Gauss law." Journal of Mathematical Physics 44, no. 6 (2003): 2521. http://dx.doi.org/10.1063/1.1572198.

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19

Gheyi, Rohit, Tiago Massoni, and Paulo Borba. "Algebraic Laws for Feature Models." JUCS - Journal of Universal Computer Science 14, no. (21) (2008): 3573–91. https://doi.org/10.3217/jucs-014-21-3573.

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Software Product Lines (SPL) may be adopted by either bootstrapping existing software products into a SPL, or extending an existing SPL to encompass an additional software product. Program refactorings are usually applied for carrying out those tasks. The notion of SPL refactoring is an extension of the traditional definition of refactoring; it involves not only program refactorings, but also Feature Model (FM) refactorings, in order to improve configurability. However, FM refactorings are hard to define, due to the incompleteness of the refactoring catalogs developed as of today. In this pape

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20

Girko, Vyacheslav L. "The limit G-Law for the solutions of systems of linear algebraic equations with independent random coefficients under the G-Lindeberg condition." Random Operators and Stochastic Equations 27, no. 1 (2019): 65–73. http://dx.doi.org/10.1515/rose-2019-2006.

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21

Škoda, Zoran. "Some Equivariant Constructions in Noncommutative Algebraic Geometry." gmj 16, no. 1 (2009): 183–202. http://dx.doi.org/10.1515/gmj.2009.183.

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Abstract We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which provide affine examples. We introduce a compatibility of monoidal actions and localizations which is a distributive law. There are satisfactory notions of equivariant objects, noncommutative fiber bundles and quotients in this setup.

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22

Ketsaris, A. A. "Action as an algebraic vector magnitude." Izvestiya MGTU MAMI 7, no. 3-1 (2013): 82–88. http://dx.doi.org/10.17816/2074-0530-68015.

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The article shows that quantum phenomena can be explained by the algebraic structure of space of the fundamental physical value of action. The eigenvalue operator problem is obtained as a consequence of an algebraic action vector multiplication law, existence of which we conceded. Thus we come to the explanation of quantum phenomena by the algebraic structure of the space of action vectors. Also the authors planned the path for explanations of types of quantum operators in relation to classical differentiation operators: multipliers included into the structure constants can be transferred to t

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23

Athira, Satheesh, Kaliappan Kamaraj, and Packia Johnson. "ALGEBRAIC PROOFS OF CHARACTERIZING REVERSE ORDER LAW FOR CLOSED RANGE OPERATORS IN HILBERT SPACES." Eurasian Mathematical Journal 14, no. 3 (2023): 08–25. http://dx.doi.org/10.32523/2077-9879-2023-14-3-08-25.

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24

Kubota, Tomio, and Satomi Oka. "On the deduction of the class field theory from the general reciprocity of power residues." Nagoya Mathematical Journal 160 (2000): 135–42. http://dx.doi.org/10.1017/s0027763000007728.

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AbstractWe denote by (A) Artin’s reciprocity law for a general abelian extension of a finite degree over an algebraic number field of a finite degree, and denote two special cases of (A) as follows: by (AC) the assertion (A) where K/F is a cyclotomic extension; by (AK) the assertion (A) where K/F is a Kummer extension. We will show that (A) is derived from (AC) and (AK) only by routine, elementarily algebraic arguments provided that n = (K : F) is odd. If n is even, then some more advanced tools like Proposition 2 are necessary. This proposition is a consequence of Hasse’s norm theorem for a q

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25

Umemura, Hiroshi. "Minimal rational threefolds II." Nagoya Mathematical Journal 110 (June 1988): 15–80. http://dx.doi.org/10.1017/s0027763000002877.

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The Enriques-Fano classification ([E.F], [F]) of the maximal connected algebraic subgroups of the three variable Cremona group, despite of its group theoretic feature, seems to be the most significant result on the rational threefolds so far known. In this paper as in [MU] we interpret the Enriques-Fano classification from a geometric view point, namely the geometry of minimal rational threefolds. We explained in [MU] the link between the two objects; the maximal algebraic subgroups and the minimal rational threefolds. Let (G, X) be a maximal algebraic subgroup of three variable Cremona group.

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26

SAIGO, HAYATO. "A NEW LOOK AT THE ARCSINE LAW AND "QUANTUM-CLASSICAL CORRESPONDENCE"." Infinite Dimensional Analysis, Quantum Probability and Related Topics 15, no. 03 (2012): 1250021. http://dx.doi.org/10.1142/s021902571250021x.

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We prove that the arcsine law as the time-averaged distribution for classical harmonic oscillators emerges from the distributions for quantum harmonic oscillators in terms of noncommutative algebraic probability. This is nothing but a simple and rigorous realization of "Quantum-Classical Correspondence" for harmonic oscillators.

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27

Hill, Richard. "A geometric proof of a reciprocity law." Nagoya Mathematical Journal 137 (March 1995): 77–144. http://dx.doi.org/10.1017/s0027763000005080.

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In this paper we prove the reciprocity law for a Kummer extension of an algebraic number field K. The proof is similar to the proof of the same theorem by Kubota [14, 15]. Such methods were applied by Gauss [6, 7] to the cases K ═ Q, and by Habicht [8] to the case . We now discuss informally the structure of the proof. All definitions and statements made at this stage are only approximations to the truth, and shouldn’t be used as references for the later chapters.

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28

Caicedo, Xavier, and Roberto Cignoli. "An algebraic approach to intuitionistic connectives." Journal of Symbolic Logic 66, no. 4 (2001): 1620–36. http://dx.doi.org/10.2307/2694965.

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Abstract.It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting algebras, unless they are alre

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29

Miana, Pedro J. "Algebra Structure of Operator-Valued Riesz Means." Journal of Operators 2014 (May 18, 2014): 1–7. http://dx.doi.org/10.1155/2014/923616.

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We characterize operator-valued Riesz means via an algebraic law of composition and establish their functional calculus accordingly. With this aim, we give a new integral expression of the Leibniz derivation rule for smooth functions.

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30

Gu, Ying-Qiu. "Hypercomplex Numbers and Roots of Algebraic Equation." Journal of Geometry and Symmetry in Physics 64 (2022): 9–22. http://dx.doi.org/10.7546/jgsp-64-2022-9-22.

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By means of hypercomplex numbers, in this paper we discuss algebraic equations and obtain some interesting relations. A structure equation $A^2=nA$ of a group is derived. The matrix representation of a group constitutes the basis elements of a hypercomplex number system. By a canonical real matrix representation of a cyclic group, we define the cyclic number system, which is exactly the solution space of the higher order algebraic equations, and thus can be used to solve the roots of algebraic equations. Hypercomplex numbers are linear algebras with definition of multiplication and division, s

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31

Olteanu, Lucian. "Distributive law as object of learning through direct and inverse tasks." International Journal for Lesson and Learning Studies 6, no. 1 (2017): 56–65. http://dx.doi.org/10.1108/ijlls-05-2016-0014.

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Purpose The purpose of this paper is to report how the use of a direct and an inverse task gave students an opportunity to discern the structure of a distributive law that they could apply to expand or to factorise algebraic expressions. The paper discusses a teaching sequence (of about 40 minutes) in a Grade 8 (14-15 year-olds) algebra class and it focusses on how the use of inverse tasks opens the dimension of variation. For instance, if the distributive law has always been used as a(b+c), factorising the expressions ab+ac means opening up the dimension of distributive law. The analysis show

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Delpoux, Romain, Thierry Floquet, and Hebertt Sira-Ramírez. "Finite-Time Trajectory Tracking of Second-Order Systems Using Acceleration Feedback Only." Automation 2, no. 4 (2021): 266–77. http://dx.doi.org/10.3390/automation2040017.

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In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems such as positioning systems and force-position controllers in robotic systems and aerospace applications. Based on an algebraic approach, an on-line algebraic estimator is developed in order to estimate in finite time the unmeasured position and vel

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Griparić, Karlo. "Algebraic Connectivity Control in Distributed Networks by Using Multiple Communication Channels." Sensors 21, no. 15 (2021): 5014. http://dx.doi.org/10.3390/s21155014.

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The effectiveness of collaboration in distributed networks, such as sensor networks and multi-agent systems, relies on nodes’ ability to exchange information. The availability of various communication protocols with different technical properties opens the possibility to guarantee connectivity during a system’s operation in any condition. A communication network can be represented by a graph on which connectivity can be expressed by a well-known algebraic connectivity value or Fiedler value. It is one of the most important tools used in many applications where connectivity preservation is requ

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Chatterjee, A., and A. Ruina. "A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations." Journal of Applied Mechanics 65, no. 4 (1998): 939–51. http://dx.doi.org/10.1115/1.2791938.

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We present a geometric representation of the set of three-dimensional rigid-body collisional impulses that are reasonably permissible by the combination of non-negative post-collision separation rate, non-negative collisional compression impulse, non-negative energy dissipation and the Coulomb friction inequality. The construction is presented for a variety of special collisional situations involving special symmetry or extremes in the mass distribution, the friction coefficient, or the initial conditions. We review a variety of known friction laws and show how they do and do not fit in the pe

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Elkouh, A. F., and Der-Fa Yang. "Flow of a Power-Law Fluid in a Rayleigh Step." Journal of Tribology 113, no. 3 (1991): 428–33. http://dx.doi.org/10.1115/1.2920642.

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An exact solution of the lubrication equations of motion for flow in a Rayleigh step of infinite width is presented. The fluid is assumed to be incompressible, and the non-Newtonian behavior of the fluid is described by a power-law model. The dimensionless pressure gradient and load capacity are obtained by the solution of a system of six algebraic equations. Optimum dimensions and load capacity for Rayleigh step bearing are presented.

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Lindahl, Lars, and Jan Odelstad. "Normative Systems and their Revision: An Algebraic Approach." Artificial Intelligence and Law 11, no. 2/3 (2003): 81–104. http://dx.doi.org/10.1023/b:arti.0000046005.10529.47.

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Dzhalladova, Irada Agayevna, and Oleg Yevhenovych Kaminsky. "MATHEMATICAL MODELING AND ANALYSIS OF CONTROLLABILITY OF SINGULAR HYBRID SYSTEMS IN APPLIED PROBLEMS." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1(8) (July 23, 2025): 61–66. https://doi.org/10.20998/2222-0631.2025.01(8).07.

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The article investigates singular hybrid systems (SHS), which combine differential-algebraic structures with hybrid dynamics involving mode switching. A mathematical model is presented, approaches to stability and controllability analysis are substantiated, and numerical simulation is performed. Such systems naturally arise in complex engineering applications – from energy systems to biomedical devices – where the system behavior changes due to faults, mode transitions, or internal structural variations. A mathematical model of SHS is proposed based on matrices, which depend on the discrete mo

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Bayen, Alexandre M., Alexander Keimer, and Nils Müller. "A proof of Kirchhoff's first law for hyperbolic conservation laws on networks." Networks and Heterogeneous Media 18, no. 4 (2023): 1799–819. http://dx.doi.org/10.3934/nhm.2023078.

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<abstract><p>In dynamical systems on networks, Kirchhoff's first law describes the local conservation of a quantity across edges. Predominantly, Kirchhoff's first law has been conceived as a phenomenological law of continuum physics. We establish its algebraic form as a property that is inherited from fundamental axioms of a network's geometry, instead of a law observed in physical nature. To this end, we extend calculus to networks, modeled as abstract metric spaces, and derive Kirchhoff's first law for hyperbolic conservation laws. In particular, our results show that hyperbolic

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Katragadda, Mohit, Nilanjan Chakraborty, and R. S. Cant. "A PrioriAssessment of Algebraic Flame Surface Density Models in the Context of Large Eddy Simulation for Nonunity Lewis Number Flames in the Thin Reaction Zones Regime." Journal of Combustion 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/794671.

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The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimensionDand inner cut-off scaleηihave been studied in detail. It has been found thatDis strongly affected by Lewis number and increases significantly with decreasing Le. By contrast,ηiremain

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Zhang, Sheng, En-Mi Yong, Yu Zhou, and Wei-Qi Qian. "Dynamic backstepping control for pure-feedback non-linear systems." IMA Journal of Mathematical Control and Information 37, no. 2 (2019): 674–97. http://dx.doi.org/10.1093/imamci/dnz019.

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Abstract A dynamic backstepping control method is proposed for non-linear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit non-linear algebraic equation. This method treats the implicit algebraic equation directly via a dynamic way, by augmenting the (virtual) controls as states during each recursive step. Compared with the traditional backstepping method, one more Lyapunov design is executed in each step. As new dynamics are included in the design, the resulting control law is in the dynamic feedback form. Under appropriate ass

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McClamroch, H., and D. Wang. "Linear Feedback Control of Position and Contact Force for a Nonlinear Constrained Mechanism." Journal of Dynamic Systems, Measurement, and Control 112, no. 4 (1990): 640–45. http://dx.doi.org/10.1115/1.2896189.

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A feedback control problem for a constrained mechanism is formulated and solved. The mechanism is controlled by forces applied to the mechanism which are to be adjusted according to a linear control law, based on feedback of the positions and velocities of the mechanism and feedback of the constraint force on the mechanism. The control objective is to achieve accurate and robust local regulation of the motion of the mechanism and of the constraint force on the mechanism. Derivation of a suitable control law is significantly complicated by the nonclassical nature of the differential-algebraic m

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Koo, Ja Kyung, Dong Hwa Shin, and Dong Sung Yoon. "Siegel families with application to class fields." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 4 (2018): 751–71. http://dx.doi.org/10.1017/s030821051700052x.

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We investigate certain families of meromorphic Siegel modular functions on which Galois groups act in a natural way. By using Shimura's reciprocity law we construct some algebraic numbers in the ray class fields of CM-fields in terms of special values of functions in these Siegel families.

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Pegler, Samuel S., John R. Lister, and M. Grae Worster. "Release of a viscous power-law fluid over an inviscid ocean." Journal of Fluid Mechanics 700 (April 17, 2012): 63–76. http://dx.doi.org/10.1017/jfm.2012.91.

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AbstractWe consider the two- and three-dimensional spreading of a finite volume of viscous power-law fluid released over a denser inviscid fluid and subject to gravitational and capillary forces. In the case of gravity-driven spreading, with a power-law fluid having strain rate proportional to stress to the power $n$, there are similarity solutions with the extent of the current being proportional to ${t}^{1/ n} $ in the two-dimensional case and ${t}^{1/ 2n} $ in the three-dimensional case. Perturbations from these asymptotic states are shown to retain their initial shape but to decay relative

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BANERJEE, R. "COVARIANT ANOMALIES AND SCHWINGER TERMS IN ANOMALOUS GAUGE THEORIES." Modern Physics Letters A 05, no. 32 (1990): 2741–46. http://dx.doi.org/10.1142/s021773239000319x.

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The general relation connecting the divergence anomaly with the Schwinger terms in the commutator of Gauss law constraints is shown to be violated, in the algebraic approach, for the covariant anomaly. We discuss the origin of this violation and derive a modified relation valid for the covariant anomaly.

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Tierney, J. W., and J. W. Eischen. "Residual Stress Analysis of Bimaterial Strips Under Multiple Thermal Loading." Journal of Electronic Packaging 119, no. 4 (1997): 281–87. http://dx.doi.org/10.1115/1.2792250.

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The residual stress distribution in bimaterial beams induced by multiple thermal loadings has been investigated. Three models for the nonlinear stress-strain material behavior were considered: bilinear elastic-plastic, power law elastic-plastic, and power law purely plastic. The equations governing equilibrium, compatibility of strain, and stress-strain for the bimaterial configuration make up a system of nonlinear algebraic equations which is solved numerically. The elastic-plastic power law model leads to stress discontinuity in the layers. The other two models have been verified with a fini

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Semenič, Nikolaj, Andrej Sarjaš, Amor Chowdhury, and Rajko Svečko. "Quasipolynomial Approach to Simultaneous Robust Control of Time-Delay Systems." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/930697.

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A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law.

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OBERLACK, MARTIN. "A unified approach for symmetries in plane parallel turbulent shear flows." Journal of Fluid Mechanics 427 (January 25, 2001): 299–328. http://dx.doi.org/10.1017/s0022112000002408.

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A new theoretical approach for turbulent flows based on Lie-group analysis is presented. It unifies a large set of ‘solutions’ for the mean velocity of stationary parallel turbulent shear flows. These results are not solutions in the classical sense but instead are defined by the maximum number of possible symmetries, only restricted by the flow geometry and other external constraints. The approach is derived from the Reynolds-averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equatio

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Białecki, Mariusz, Mateusz Gałka, Arpan Bagchi, and Jacek Gulgowski. "Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton." Entropy 25, no. 5 (2023): 819. http://dx.doi.org/10.3390/e25050819.

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We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg–Richter law and Omori law with the waiting time distribution for earthquakes. In this work, we provide a general algebraic solution to the inverse problem for the model and apply the proposed procedure to seismic data recorded in the Legnica-Głogów Copper District in Poland, which demonstrate the adequacy of the method. The solution of the inverse problem enables adjustment of the model to localiz

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El-Sayed, Y. M., and R. A. Gaggioli. "A Critical Review of Second Law Costing Methods—I: Background and Algebraic Procedures." Journal of Energy Resources Technology 111, no. 1 (1989): 1–7. http://dx.doi.org/10.1115/1.3231396.

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The following report reviews the development and state of engineering economic applications of the second law of thermodynamics. It encompasses virtually all of the work carried out publicly in the United States, and to the best of our knowledge that done in other countries (but also see Tsatsaronis, 1987). The ultimate objective here is to provide direction for future research on the fundamentals and applications of this subject, and for the support thereof. We begin with a historical review, which is important for better comprehension of second law costing, its objectives, its state, and its

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Luo, Shao-Kai, Lin Li, and Yan-Li Xu. "Lie algebraic structure and generalized Poisson conservation law for fractional generalized Hamiltonian systems." Acta Mechanica 225, no. 9 (2014): 2653–66. http://dx.doi.org/10.1007/s00707-014-1101-9.

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