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Journal articles on the topic 'Homogenization algebra'

Author: Grafiati

Published: 28 June 2021

Last updated: 29 July 2025

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1

Heckenberger, István, and Volkmar Welker. "A Deformation of the Orlik-Solomon Algebra." MATHEMATICA SCANDINAVICA 118, no. 2 (2016): 183. http://dx.doi.org/10.7146/math.scand.a-23686.

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A deformation of the Orlik-Solomon algebra of a matroid $\mathfrak{M}$ is defined as a quotient of the free associative algebra over a commutative ring $R$ with $1$. It is shown that the given generators form a Gröbner basis and that after suitable homogenization the deformation and the Orlik-Solomon have the same Hilbert series as $R$-algebras. For supersolvable matroids, equivalently fiber type arrangements, there is a quadratic Gröbner basis and hence the algebra is Koszul.

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2

Ballico, E., B. Callander, and E. Gasparim. "Compactifications of adjoint orbits and their Hodge diamonds." Journal of Algebra and Its Applications 17, no. 06 (2018): 1850099. http://dx.doi.org/10.1142/s0219498818500998.

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A recent theorem of [E. Gasparim, L. Grama and L. A. B. San Martin, Lefschetz fibrations on adjoint orbits, Forum Math. 28(5) (2016) 967–980.] showed that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We investigate the behavior of their fiberwise compactifications. Expressing adjoint orbits and fibers as affine varieties in their Lie algebra, we compactify them to projective varieties via homogenization of the defining ideals. We find that their Hodge diamonds vary wildly according to the choice of homogenization, and that extensions of the p

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3

MARTÍNEZ-VILLA, ROBERTO. "ON THE HOMOGENIZED ENVELOPING ALGEBRA OF THE LIE ALGEBRA Sℓ(2,ℂ) II". Glasgow Mathematical Journal 59, № 1 (2016): 189–219. http://dx.doi.org/10.1017/s0017089516000112.

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AbstractIn a previous paper, we studied the homogenized enveloping algebra of the Lie algebrasℓ(2,ℂ) and the homogenized Verma modules. The aim of this paper is to study the homogenization$\mathcal{O}$Bof the Bernstein–Gelfand–Gelfand category$\mathcal{O}$of sℓ(2,ℂ), and to apply the ideas developed jointly with J. Mondragón in our work on Groebner basis algebras, to give the relations between the categories$\mathcal{O}$Band$\mathcal{O}$as well as, between the derived categories$\mathcal{D}$b($\mathcal{O}$B) and$\mathcal{D}$b($\mathcal{O}$).

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4

Woukeng, Jean Louis. "Homogenization in algebras with mean value." Banach Journal of Mathematical Analysis 9, no. 2 (2015): 142–82. http://dx.doi.org/10.15352/bjma/09-2-12.

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5

Sandrakov, G. V. "Homogenization of variational inequalities for obstacle problems." Sbornik: Mathematics 196, no. 4 (2005): 541–60. http://dx.doi.org/10.1070/sm2005v196n04abeh000891.

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6

Zhikov, V. V. "Connectedness and homogenization. Examples of fractal conductivity." Sbornik: Mathematics 187, no. 8 (1996): 1109–47. http://dx.doi.org/10.1070/sm1996v187n08abeh000150.

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7

Gadyl'shin, R. R. "Analogues of the Helmholtz resonator in homogenization theory." Sbornik: Mathematics 193, no. 11 (2002): 1611–38. http://dx.doi.org/10.1070/sm2002v193n11abeh000691.

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8

Pastukhova, S. E. "Homogenization of elasticity problems on periodic composite structures." Sbornik: Mathematics 196, no. 7 (2005): 1033–73. http://dx.doi.org/10.1070/sm2005v196n07abeh000947.

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9

Sirazhudinov, M. M. "G-convergence and homogenization of generalized Beltrami operators." Sbornik: Mathematics 199, no. 5 (2008): 755–86. http://dx.doi.org/10.1070/sm2008v199n05abeh003941.

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10

Zhikov, V. V., and S. E. Pastukhova. "Homogenization for elasticity problems on periodic networks of critical thickness." Sbornik: Mathematics 194, no. 5 (2003): 697–732. http://dx.doi.org/10.1070/sm2003v194n05abeh000735.

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11

Sandrakov, G. V. "Homogenization of variational inequalities and equations defined by pseudomonotone operators." Sbornik: Mathematics 199, no. 1 (2008): 67–98. http://dx.doi.org/10.1070/sm2008v199n01abeh003911.

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12

Waurick, Marcus. "On the homogenization of partial integro-differential-algebraic equations." Operators and Matrices, no. 2 (2016): 247–83. http://dx.doi.org/10.7153/oam-10-15.

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13

Nguetseng, Gabriel, Hubert Nnang, and Nils Svanstedt. "G-convergence and homogenization of monotone damped hyperbolic equations." Banach Journal of Mathematical Analysis 4, no. 1 (2010): 100–115. http://dx.doi.org/10.15352/bjma/1272374674.

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14

CAPRIZ, G., та G. MAZZINI. "A σ-ALGEBRA AND A CONCEPT OF LIMIT FOR BODIES". Mathematical Models and Methods in Applied Sciences 10, № 06 (2000): 801–13. http://dx.doi.org/10.1142/s0218202500000410.

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Recent developments in mechanics of continua (the search for optimal shapes of bodies, homogenization theory, the study of the trabecular structure of bones, the dynamics of immiscible mixtures, etc.) render some of the introductory axioms of continuum mechanics inadequate. Not only does one need to give meaning to the join and meet of two bodies, but also to extend the consequent algebra so as to encompass the result of a countable sequence of operations of join or meet; and one should also be able to define the limit of a sequence of bodies. To achieve this goal we propose here to define a b

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15

Kamiński, Marcin. "Probabilistic Relative Entropy in Homogenization of Fibrous Metal Matrix Composites (MMCs)." Materials 16, no. 18 (2023): 6112. http://dx.doi.org/10.3390/ma16186112.

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The main aim of this work is to deliver uncertainty propagation analysis for the homogenization process of fibrous metal matrix composites (MMCs). The homogenization method applied here is based on the comparison of the deformation energy of the Representative Volume Element (RVE) for the original and for the homogenized material. This part is completed with the use of the Finite Element Method (FEM) plane strain analysis delivered in the ABAQUS system. The probabilistic goal is achieved by using the response function method, where computer recovery with a few FEM tests enables approximations

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16

Redman, Irmgard T. "The homogenization of the three dimensional skew polynomial algebras of type I." Communications in Algebra 27, no. 11 (1999): 5587–602. http://dx.doi.org/10.1080/00927879908826775.

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17

Vasilevskaya, E. S. "A periodic parabolic Cauchy problem: Homogenization with corrector." St. Petersburg Mathematical Journal 21, no. 1 (2009): 1–41. http://dx.doi.org/10.1090/s1061-0022-09-01083-8.

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18

Veniaminov, N. "Homogenization of periodic differential operators of high order." St. Petersburg Mathematical Journal 22, no. 5 (2011): 751–75. http://dx.doi.org/10.1090/s1061-0022-2011-01166-5.

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19

Nazarov, Sergei A., Guido H. Sweers, and Andrey S. Slutskij. "Homogenization of a thin plate reinforced with periodic families of rigid rods." Sbornik: Mathematics 202, no. 8 (2011): 1127–68. http://dx.doi.org/10.1070/sm2011v202n08abeh004181.

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20

Skrypnik, I. V. "Homogenization of non-linear Dirichlet problems in perforated domains of general type." Sbornik: Mathematics 187, no. 8 (1996): 1229–60. http://dx.doi.org/10.1070/sm1996v187n08abeh000154.

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21

Suslina, T. A. "Homogenization with corrector for a stationary periodic Maxwell system." St. Petersburg Mathematical Journal 19, no. 3 (2008): 455–95. http://dx.doi.org/10.1090/s1061-0022-08-01006-6.

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22

KRONE, ROBERT. "NUMERICAL ALGORITHMS FOR DUAL BASES OF POSITIVE-DIMENSIONAL IDEALS." Journal of Algebra and Its Applications 12, no. 06 (2013): 1350018. http://dx.doi.org/10.1142/s0219498813500187.

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An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However the usual standard basis algorithms are not numerically stable. A numerically stable approach to describing the ideal is by finding the space of dual functionals that annihilate it, which reduces the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zero-dimensional ideals. We present a stopping criterion for positive-dimensional cases based on homogeni

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23

Pastukhova, S. E. "The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization." Sbornik: Mathematics 207, no. 3 (2016): 418–43. http://dx.doi.org/10.1070/sm8486.

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24

Monzner, Alexandra, Nicolas Vichery, and Frol Zapolsky. "Partial quasimorphisms and quasistates on cotangent bundles, and symplectic homogenization." Journal of Modern Dynamics 6, no. 2 (2012): 205–49. http://dx.doi.org/10.3934/jmd.2012.6.205.

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25

Dorodnyĭ, M. A. "Homogenization of periodic Schrödinger-type equations, with lower order terms." St. Petersburg Mathematical Journal 31, no. 6 (2020): 1001–54. http://dx.doi.org/10.1090/spmj/1632.

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26

Pastukhova, S. "Improved resolvent 𝐿²-approximations in homogenization of fourth order operators". St. Petersburg Mathematical Journal 34, № 4 (2023): 611–34. http://dx.doi.org/10.1090/spmj/1772.

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A divergent elliptic operator A ε A_\varepsilon of the fourth order with ε \varepsilon -periodic coefficients acting in the space R d \mathbb {R}^d is treated, where ε \varepsilon is a small parameter. For the resolvent ( A ε + 1 ) − 1 (A_\varepsilon +1)^{-1} , approximations are constructed in the operator ( L 2 → L 2 ) {(L^2\to L^2)} -norm with remainder of order ε 3 \varepsilon ^3 . The method of two-scale expansions with the use of smoothing is employed.

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27

Sakamoto, Kunimochi. "Spatial homogenization and internal layers in a reaction-diffusion system." Hiroshima Mathematical Journal 30, no. 3 (2000): 377–402. http://dx.doi.org/10.32917/hmj/1206124605.

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28

Ming, Pingbing, and Pingwen Zhang. "Analysis of the heterogeneous multiscale method for parabolic homogenization problems." Mathematics of Computation 76, no. 257 (2007): 153–78. http://dx.doi.org/10.1090/s0025-5718-06-01909-0.

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29

Coulibaly, A. "Coupling homogenization and large deviations, with applications to nonlocal parabolic partial differential equations." Journal of Nonlinear Sciences and Applications 16, no. 03 (2023): 168–79. http://dx.doi.org/10.22436/jnsa.016.03.03.

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30

Birman, M. Sh, and T. A. Suslina. "Operator error estimates in the homogenization problem for nonstationary periodic equations." St. Petersburg Mathematical Journal 20, no. 6 (2009): 873–928. http://dx.doi.org/10.1090/s1061-0022-09-01077-2.

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31

Pastukhova, S. E., and R. N. Tikhomirov. "On operator-type homogenization estimates for elliptic equations with lower order terms." St. Petersburg Mathematical Journal 29, no. 5 (2018): 841–61. http://dx.doi.org/10.1090/spmj/1518.

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32

Sango, M. "Homogenization of singular numbers for a non self-adjoint elliptic problem in a perforated domain." Integral Equations and Operator Theory 43, no. 2 (2002): 177–88. http://dx.doi.org/10.1007/bf01200252.

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33

Zhikov, V. V. "Estimates of Nash-Aronson type for a diffusion equation with asymmetric matrix and their applications to homogenization." Sbornik: Mathematics 197, no. 12 (2006): 1775–804. http://dx.doi.org/10.1070/sm2006v197n12abeh003822.

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34

HORIE, Kazuo, and Hitoshi ISHII. "Simultaneous Effects of Homogenization and Vanishing Viscosity in Fully Nonlinear Elliptic Equations." Funkcialaj Ekvacioj 46, no. 1 (2003): 63–88. http://dx.doi.org/10.1619/fesi.46.63.

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35

Senik, N. N. "Homogenization for a periodic elliptic operator in a strip with various boundary conditions." St. Petersburg Mathematical Journal 25, no. 4 (2014): 647–97. http://dx.doi.org/10.1090/s1061-0022-2014-01311-8.

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36

Zhikov, V. V., and S. E. Pastukhova. "Homogenization and two-scale convergence in the Sobolev space with an oscillating exponent." St. Petersburg Mathematical Journal 30, no. 2 (2019): 231–51. http://dx.doi.org/10.1090/spmj/1540.

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37

Bertone, Cristina, Francesca Cioffi, and Margherita Roggero. "Macaulay-like marked bases." Journal of Algebra and Its Applications 16, no. 05 (2017): 1750100. http://dx.doi.org/10.1142/s0219498817501006.

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We define marked sets and bases over a quasi-stable ideal [Formula: see text] in a polynomial ring on a Noetherian [Formula: see text]-algebra, with [Formula: see text] a field of any characteristic. The involved polynomials may be non-homogeneous, but their degree is bounded from above by the maximum among the degrees of the terms in the Pommaret basis of [Formula: see text] and a given integer [Formula: see text]. Due to the combinatorial properties of quasi-stable ideals, these bases behave well with respect to homogenization, similarly to Macaulay bases. We prove that the family of marked

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38

Dorodnyi, M., та T. Suslina. "Homogenization of hyperbolic equations with periodic coefficients in ℝ^{𝕕}: Sharpness of the results". St. Petersburg Mathematical Journal 32, № 4 (2021): 605–703. http://dx.doi.org/10.1090/spmj/1664.

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In L 2 ( R d ; C n ) L_2(\mathbb {R}^d;\mathbb {C}^n) , a selfadjoint strongly elliptic second order differential operator A ε \mathcal {A}_\varepsilon is considered. It is assumed that the coefficients of A ε \mathcal {A}_\varepsilon are periodic and depend on x / ε \mathbf {x}/\varepsilon , where ε > 0 \varepsilon >0 is a small parameter. We find approximations for the operators cos ⁡ ( A ε 1 / 2 τ ) \cos (\mathcal {A}_\varepsilon ^{1/2}\tau ) and A ε − 1 / 2 sin ⁡ ( A ε 1 / 2 τ ) \mathcal {A}_\varepsilon ^{-1/2}\sin (\mathcal {A}_\varepsilon ^{1/2}\tau ) in the norm of operators actin

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39

Pakhnin, M. A., and T. A. Suslina. "Operator error estimates for homogenization of the elliptic Dirichlet problem in a bounded domain." St. Petersburg Mathematical Journal 24, no. 6 (2013): 949–76. http://dx.doi.org/10.1090/s1061-0022-2013-01274-x.

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40

Meshkova, Yu M., and T. A. Suslina. "Homogenization of the first initial boundary-value problem for parabolic systems: operator error estimates." St. Petersburg Mathematical Journal 29, no. 6 (2018): 935–78. http://dx.doi.org/10.1090/spmj/1521.

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41

Belyaev, A. G., and G. A. Chechkin. "Homogenization of a mixed boundary-value problem for the Laplace operator in the case of an insoluble 'limit' problem." Sbornik: Mathematics 186, no. 4 (1995): 511–25. http://dx.doi.org/10.1070/sm1995v186n04abeh000029.

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42

Nazarov, S. A. "Homogenization of Kirchhoff plates joined by rivets which are modeled by the Sobolev point conditions." St. Petersburg Mathematical Journal 32, no. 2 (2021): 307–48. http://dx.doi.org/10.1090/spmj/1649.

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43

Sokołowski, Damian, Marcin Kamiński, and Artur Wirowski. "Energy Fluctuations in the Homogenized Hyper-Elastic Particulate Composites with Stochastic Interface Defects." Energies 13, no. 8 (2020): 2011. http://dx.doi.org/10.3390/en13082011.

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The principle aim of this study is to analyze deformation energy of hyper-elastic particulate composites, which is the basis for their further probabilistic homogenization. These composites have some uncertain interface defects, which are modelled as small semi-spheres with random radius and with bases positioned on the particle-matrix interface. These defects are smeared into thin layer of the interphase surrounding the reinforcing particle introduced as the third component of this composite. Matrix properties are determined from the experimental tests of Laripur LPR 5020 High Density Polyure

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44

Cardone, G., A. Corbo Esposito, and S. A. Nazarov. "Homogenization of the mixed boundary-value problem for a formally selfadjoint elliptic system in a periodically punched domain." St. Petersburg Mathematical Journal 21, no. 4 (2010): 601–34. http://dx.doi.org/10.1090/s1061-0022-2010-01108-7.

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45

Meshkova, Yu M. "Homogenization of periodic parabolic systems in the $L_2(\mathbb {R}^d)$-norm with the corrector taken into account." St. Petersburg Mathematical Journal 31, no. 4 (2020): 675–718. http://dx.doi.org/10.1090/spmj/1619.

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46

Rossi, Michele, and Lea Terracini. "Toric varieties and Gröbner bases: the complete $$\mathbb {Q}$$-factorial case." Applicable Algebra in Engineering, Communication and Computing 31, no. 5-6 (2020): 461–82. http://dx.doi.org/10.1007/s00200-020-00452-w.

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Abstract We present two algorithms determining all the complete and simplicial fans admitting a fixed non-degenerate set of vectors V as generators of their 1-skeleton. The interplay of the two algorithms allows us to discerning if the associated toric varieties admit a projective embedding, in principle for any values of dimension and Picard number. The first algorithm is slower than the second one, but it computes all complete and simplicial fans supported by V and lead us to formulate a topological-combinatoric conjecture about the definition of a fan. On the other hand, we adapt the Sturmf

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47

Suslina, T. A. "Homogenization in the Sobolev class $H^{1}(\mathbb R^{d})$ for second order periodic elliptic operators with the inclusion of first order terms." St. Petersburg Mathematical Journal 22, no. 1 (2011): 81. http://dx.doi.org/10.1090/s1061-0022-2010-01135-x.

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48

Sloushch, V., and T. Suslina. "Threshold approximations for the resolvent of a polynomial nonnegative operator pencil." St. Petersburg Mathematical Journal 33, no. 2 (2022): 355–85. http://dx.doi.org/10.1090/spmj/1704.

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In a Hilbert space H \mathfrak {H} , a family of operators A ( t ) A(t) , t ∈ R t\in \mathbb {R} , is treated admitting a factorization of the form A ( t ) = X ( t ) ∗ X ( t ) A(t) = X(t)^* X(t) , where X ( t ) = X 0 + X 1 t + ⋯ + X p t p X(t)=X_0+X_1t+\cdots +X_pt^p , p ≥ 2 p\ge 2 . It is assumed that the point λ 0 = 0 \lambda _0=0 is an isolated eigenvalue of finite multiplicity for A ( 0 ) A(0) . Let F ( t ) F(t) be the spectral projection of A ( t ) A(t) for the interval [ 0 , δ ] [0,\delta ] . For | t | ≤ t 0 |t| \le t^0 , approximation in the operator norm in H \mathfrak {H} for the proj

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49

Tsumoto, Shusaku, Shoji Hirano, Tomohiro Kimura, and Haruko Iwata. "Mining Clinical Process from Hospital Information System: A Granular Computing Approach." Fundamenta Informaticae 182, no. 2 (2021): 181–218. http://dx.doi.org/10.3233/fi-2021-2070.

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Data mining methods in medicine is a very important tool for developing automated decision support systems. However, since information granularity of disease codes used in hospital information system is coarser than that of real clinical definitions of diseases and their treatment, automated data curation is needed to extract knowledge useful for clinical decision making. This paper proposes automated construction of clinical process plan from nursing order histories and discharge summaries stored in hospital information system with curation of disease codes as follows. First, the system appli

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50

Gaddis, Jason. "PBW deformations of Artin–Schelter regular algebras." Journal of Algebra and Its Applications 15, no. 04 (2016): 1650064. http://dx.doi.org/10.1142/s021949881650064x.

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We consider properties and extensions of PBW deformations of Artin–Schelter regular algebras. PBW deformations in global dimension two are classified and the geometry associated to the homogenizations of these algebras is exploited to prove that all simple modules are one-dimensional in the non-PI case. It is shown that this property is maintained under tensor products and certain skew polynomial extensions.

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