Journal articles: 'Rank one generated'

1

Barile, Margherita. "On Ideals Generated by Monomials and One Binomial." Algebra Colloquium 14, no. 04 (December 2007): 631–38. http://dx.doi.org/10.1142/s1005386707000582.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Hobson, Natalie L. F. "Quantum Kostka and the rank one problem for 𝔰𝔩2m." Advances in Geometry 19, no. 1 (January 28, 2019): 71–88. http://dx.doi.org/10.1515/advgeom-2017-0037.

Full text

Abstract:

Abstract We give necessary and sufficient conditions to specify vector bundles of conformal blocks for 𝔰𝔩2m with rectangular weights which have ranks 0, 1, and larger than 1. We show that the first Chern classes of such rank one bundles determine a finitely generated subcone of the nef cone.

APA, Harvard, Vancouver, ISO, and other styles

3

Wang, Yu, Zhihua Wang, and Libin Li. "Ideals of Finite-Dimensional Pointed Hopf Algebras of Rank One." Algebra Colloquium 28, no. 02 (May 11, 2021): 351–60. http://dx.doi.org/10.1142/s1005386721000274.

Full text

Abstract:

Let [Formula: see text] be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero. In this paper we show that any finite-dimensional indecomposable [Formula: see text]-module is generated by one element. In particular, any indecomposable submodule of [Formula: see text] under the adjoint action is generated by a special element of [Formula: see text]. Using this result, we show that the Hopf algebra [Formula: see text] is a principal ideal ring, i.e., any two-sided ideal of [Formula: see text] is generated by one element. As an application, we give explicitly the generators of ideals, primitive ideals, maximal ideals and completely prime ideals of the Taft algebras.

APA, Harvard, Vancouver, ISO, and other styles

4

Conn, A. R., N. I. M. Gould, and Ph L. Toint. "Convergence of quasi-Newton matrices generated by the symmetric rank one update." Mathematical Programming 50, no. 1-3 (March 1991): 177–95. http://dx.doi.org/10.1007/bf01594934.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Dudkin, M. E., and O. Yu Dyuzhenkova. "Singularly perturbed rank one linear operators." Matematychni Studii 56, no. 2 (December 26, 2021): 162–75. http://dx.doi.org/10.30970/ms.56.2.162-175.

Full text

Abstract:

The basic principles of the theory of singularly perturbed self-adjoint operatorsare generalized to the case of closed linear operators with non-symmetric perturbation of rank one.Namely, firstly linear closed operators are considered that coincide with each other on a dense set in a Hilbert space.The theory of singularly perturbed self-adjoint operators arose from the need to consider differential expressions in such terms as the Dirac $\delta$-function.Since it is important to consider expressions given not only by symmetric operators, the generalization (transfer) of the basic principles of the theory of singularly perturbed self-adjoint operators in the case of non-symmetric ones is important problem. The main facts of the theory include the definition of a singularly perturbed linear operator and the resolvent formula in the cases of ${\mathcal H}_{-1}$-class and ${\mathcal H}_{-2}$-class.The paper additionally describes the possibility of the appearance a point of the point spectrum and the construction of a perturbation with a predetermined point.In comparison with self-adjoint perturbations, the description of perturbations by non-symmetric terms is unexpected.Namely, in some cases, when the perturbed by a vectors from ${\mathcal H}_{-2}$ operator can be conveniently described by methods of class ${\mathcal H}_{-1}$, that is impossible in the case of symmetric perturbations of a self-adjoint operator. The perturbation of self-adjoint operators in a non-symmetric manner fully fits into the proposed studies.Such operators, for example, generalize models with nonlocal interactions, perturbations of the harmonic oscillator by the $\delta$-potentials, and can be used to study perturbations generated by a delay or an anticipation.

APA, Harvard, Vancouver, ISO, and other styles

6

BISCHI, GIAN-ITALO, LAURA GARDINI, and CHRISTIAN MIRA. "BASIN FRACTALIZATIONS GENERATED BY A TWO-DIMENSIONAL FAMILY OF (Z1–Z3–Z1) MAPS." International Journal of Bifurcation and Chaos 16, no. 03 (March 2006): 647–69. http://dx.doi.org/10.1142/s0218127406015039.

Full text

Abstract:

Two-dimensional (Z1–Z3–Z1) maps are such that the plane is divided into three unbounded open regions: a region Z3, whose points generate three real rank-one preimages, bordered by two regions Z1, whose points generate only one real rank-one preimage. This paper is essentially devoted to the study of the structures, and the global bifurcations, of the basins of attraction generated by such maps. In particular, the cases of fractal structure of such basins are considered. For the class of maps considered in this paper, a large variety of dynamic situations is shown, and the bifurcations leading to their occurrence are explained.

APA, Harvard, Vancouver, ISO, and other styles

7

Shusterman, Mark. "Groups with positive rank gradient and their actions." Mathematica Slovaca 68, no. 2 (April 25, 2018): 353–60. http://dx.doi.org/10.1515/ms-2017-0106.

Full text

Abstract:

Abstract We show that given a finitely generated LERF group G with positive rank gradient, and finitely generated subgroups A, B ≤ G of infinite index, one can find a finite index subgroup B0 of B such that [G : 〈A ∪ B0〉] = ∞. This generalizes a theorem of Olshanskii on free groups. We conclude that a finite product of finitely generated subgroups of infinite index does not cover G. We construct a transitive virtually faithful action of G such that the orbits of finitely generated subgroups of infinite index are finite. Some of the results extend to profinite groups with positive rank gradient.

APA, Harvard, Vancouver, ISO, and other styles

8

LIN, HUAXIN. "UNITARIES IN A SIMPLE C*-ALGEBRA OF TRACIAL RANK ONE." International Journal of Mathematics 21, no. 10 (October 2010): 1267–81. http://dx.doi.org/10.1142/s0129167x10006446.

Full text

Abstract:

Let A be a unital separable simple infinite dimensional C*-algebra with tracial rank not more than one and with the tracial state space T(A) and let U(A) be the unitary group of A. Suppose that u ∈ U0(A), the connected component of U(A) containing the identity. We show that, for any ϵ > 0, there exists a self-adjoint element h ∈ As.a such that [Formula: see text] We also study the problem when u can be approximated by unitaries in A with finite spectrum. Denote by CU(A) the closure of the subgroup of unitary group of U(A) generated by its commutators. It is known that CU(A) ⊂ U0(A). Denote by [Formula: see text] the affine function on T(A) defined by [Formula: see text]. We show that u can be approximated by unitaries in A with finite spectrum if and only if u ∈ CU(A) and [Formula: see text] for all n ≥ 1. Examples are given for which there are unitaries in CU(A) which cannot be approximated by unitaries with finite spectrum. Significantly these results are obtained in the absence of amenability.

APA, Harvard, Vancouver, ISO, and other styles

9

Wang, Zhihua. "The corepresentation ring of a pointed Hopf algebra of rank one." Journal of Algebra and Its Applications 17, no. 12 (December 2018): 1850236. http://dx.doi.org/10.1142/s0219498818502365.

Full text

Abstract:

Let [Formula: see text] be an arbitrary pointed Hopf algebra of rank one and [Formula: see text] the group of group-like elements of [Formula: see text]. In this paper, we give the decomposition of a tensor product of finite dimensional indecomposable right [Formula: see text]-comodules into a direct sum of indecomposables. This enables us to describe the corepresentation ring of [Formula: see text] in terms of generators and relations. Such a ring is not commutative if [Formula: see text] is not abelian. We describe all nilpotent elements of the corepresentation ring of [Formula: see text] if [Formula: see text] is a finite abelian group or a particular Hamiltonian group. In this case, all nilpotent elements of the corepresentation ring form a principal ideal which is either zero or generated by a nilpotent element of degree 2.

APA, Harvard, Vancouver, ISO, and other styles

10

Ferenczi, Sébastien. "Rank and symbolic complexity." Ergodic Theory and Dynamical Systems 16, no. 4 (August 1996): 663–82. http://dx.doi.org/10.1017/s0143385700009032.

Full text

Abstract:

AbstractWe investigate the relation between the complexity function of a sequence, that is the number p(n) of its factors of length n, and the rank of the associated dynamical system, that is the number of Rokhlin towers required to approximate it. We prove that if the rank is one, then lim , but give examples with lim for any prescribed function G with G (n) = 0(an) for every a > 1. We give exact computations for examples of the ‘staircase’ type, which are strongly mixing systems with quadratic complexity. Conversely, for minimal sequences, if p(n) < an + b for some a ≥ 1, the rank is at most 2[a], with bounded strings of spacers, and the system is generated by a finite number of substitutions.

APA, Harvard, Vancouver, ISO, and other styles

11

Hossain, Tanjim, Mengze Shi, and Robert Waiser. "Measuring Rank-Based Utility in Contests: The Effect of Disclosure Schemes." Journal of Marketing Research 56, no. 6 (August 25, 2019): 981–94. http://dx.doi.org/10.1177/0022243719853289.

Full text

Abstract:

This article studies how the incentive structures and disclosure schemes of a contest affect the contestants’ intrinsic motivations. Specifically, the authors measure the effects of these design decisions on two types of nonmonetary rank-based utility: self-generated and peer-induced. They run a set of laboratory experiments involving contests under various reward spreads and disclosure schemes. First, they find that virtually all commonly adopted disclosure schemes generate positive peer-induced rank-based utility. However, the relative performances of alternative disclosure schemes can depend on the spread of contest rewards and the number of contestants. Second, being recognized as a winner confers positive peer-induced rank-based utility; moreover, being recognized as the sole first-place winner or as one among multiple winners does not produce significantly different peer-induced utility. Third, “shaming” by disclosing the identity of contestants ranked at the bottom leads to negative peer-induced rank-based utility, but the effect is marginally insignificant. Finally, a smaller spread of contest rewards consistently results in higher levels of self-generated rank-based utility. These results underscore the importance of jointly choosing incentive structures and disclosure schemes.

APA, Harvard, Vancouver, ISO, and other styles

12

Shneerson, L. M. "On the axiomatic rank of varieties generated by a semigroup or monoid with one defining relation." Semigroup Forum 39, no. 1 (December 1989): 17–38. http://dx.doi.org/10.1007/bf02573281.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Pettet, Martin R. "Finitely generated groups with virtually free automorphism groups." Proceedings of the Edinburgh Mathematical Society 38, no. 3 (October 1995): 475–84. http://dx.doi.org/10.1017/s0013091500019271.

Full text

Abstract:

It is shown that the full automorphism group of a finitely generated group G is virtually free if and only if the center Z(G) is finitely generated of torsion-free rank r at most two and, depending on the value of r, the central quotient G/Z(G) belongs to one of three precisely defined classes of virtually free groups. Some consequences and special cases are also discussed.

APA, Harvard, Vancouver, ISO, and other styles

14

Sun, Junzhe, Sergey Fomel, and Lexing Ying. "Low-rank one-step wave extrapolation for reverse time migration." GEOPHYSICS 81, no. 1 (January 1, 2016): S39—S54. http://dx.doi.org/10.1190/geo2015-0183.1.

Full text

Abstract:

Reverse time migration (RTM) relies on accurate wave extrapolation engines to image complex subsurface structures. To construct such operators with high efficiency and numerical stability, we have developed a one-step wave extrapolation approach using complex-valued low-rank decomposition to approximate the mixed-domain space-wavenumber wave extrapolation symbol. The low-rank one-step method involves a complex-valued phase function, which is more flexible than a real-valued phase function of two-step schemes, and thus it is capable of modeling a wider variety of dispersion relations. Two novel designs of the phase function leads to the desired properties in wave extrapolation. First, for wave propagation in inhomogeneous media, including a velocity gradient term assures a more accurate phase behavior, particularly when the velocity variations are large. Second, an absorbing boundary condition, which is propagation-direction-dependent, can be incorporated into the phase function as an anisotropic attenuation term. This term allows waves to travel parallel to the boundary without absorption, thus reducing artificial reflections at wide incident angles. Using numerical experiments, we revealed the stability improvement of a one-step scheme in comparison with two-step schemes. We observed the low-rank one-step operator to be remarkably stable and capable of propagating waves using large time step sizes, even beyond the Nyquist limit. The stability property can help to minimize the computational cost of seismic modeling or RTM. The low-rank one-step wave extrapolation also handles anisotropic wave propagation accurately and efficiently. When applied to RTM in anisotropic media, the proposed method generated high-quality images.

APA, Harvard, Vancouver, ISO, and other styles

15

Baldwin, John T., and Kitty Holland. "Constructing ω-stable structures: rank 2 fields." Journal of Symbolic Logic 65, no. 1 (March 2000): 371–91. http://dx.doi.org/10.2307/2586544.

Full text

Abstract:

AbstractWe provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from ‘primitive extensions’ to the natural numbers a theory Tμ of an expansion of an algebraically closed field which has Morley rank 2. Finally, we show that if μ is not finite-to-one the theory may not be ω-stable.

APA, Harvard, Vancouver, ISO, and other styles

16

Dong, Zhe. "A note on tensor products of reflexive algebras." Bulletin of the Australian Mathematical Society 66, no. 1 (August 2002): 25–31. http://dx.doi.org/10.1017/s0004972700020645.

Full text

Abstract:

In this short note, we obtain a concrete description of rank-one operators in Alg(ℒ1 ⊗…⊗ ℒn). Based on this characterisation, we give a simple proof of the tensor product formula: if Alg(ℒ1 ⊗…⊗ ℒn) is weakly generated by rank-one operators in itself and ℒi(i = 1,…,n) are subspace lattices.

APA, Harvard, Vancouver, ISO, and other styles

17

KURDACHENKO, LEONID A., JAVIER OTAL, and IGOR YA SUBBOTIN. "SOME CRITERIA FOR EXISTENCE OF SUPPLEMENTS TO NORMAL SUBGROUPS AND THEIR APPLICATIONS." International Journal of Algebra and Computation 20, no. 05 (August 2010): 689–719. http://dx.doi.org/10.1142/s0218196710005844.

Full text

Abstract:

We established several new criteria for existence of complements and supplements to some normal abelian subgroups in groups. In passing, as one of the many useful applications and corollaries of these results, we obtained a description of some finitely generated soluble groups of finite Hirsch–Zaitsev rank. As another application of our results, we obtained a D.J.S. Robinson's theorem on structure of finitely generated soluble groups of finite section rank. The original proof of this theorem was homological, but all proofs in this paper, including this one, are purely group-theoretical.

APA, Harvard, Vancouver, ISO, and other styles

18

Howie, John M., and Robert B. McFadden. "Idempotent rank in finite full transformation semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 114, no. 3-4 (1990): 161–67. http://dx.doi.org/10.1017/s0308210500024355.

Full text

Abstract:

SynopsisThe subsemigroup Singn of singular elements of the full transformation semigroup on a finite set is generated by n(n − l)/2 idempotents of defect one. In this paper we extend this result to the subsemigroup K(n, r) consisting of all elements of rank r or less. We prove that the idempotent rank, defined as the cardinality of a minimal generating set of idempotents, of K(n, r) is S(n, r), the Stirling number of the second kind.

APA, Harvard, Vancouver, ISO, and other styles

19

LANGE, H., and P. E. NEWSTEAD. "Lower bounds for Clifford indices in rank three." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 1 (October 8, 2010): 23–33. http://dx.doi.org/10.1017/s0305004110000502.

Full text

Abstract:

AbstractClifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in previous papers by the authors. In this paper, we establish lower bounds for the Clifford indices for rank 3 bundles. As a consequence we show that, on smooth plane curves of degree at least 10, there exist non-generated bundles of rank 3 computing one of the Clifford indices.

APA, Harvard, Vancouver, ISO, and other styles

20

Porter, D., and D. S. G. Stirling. "Finitely-generated solutions of certain integral equations." Proceedings of the Edinburgh Mathematical Society 37, no. 2 (June 1994): 325–45. http://dx.doi.org/10.1017/s0013091500006106.

Full text

Abstract:

Recent work has shown that the solutions of the second-kind integral equation arising from a difference kernel can be expressed in terms of two particular solutions of the equation. This paper establishes analogous results for a wider class of integral operators, which includes the special case of those arising from difference kernels, where the solution of the general case is generated by a finite number of particular cases. The generalisation is achieved by reducing the problem to one of finite rank. Certain non-compact operators, including those arising from Cauchy singular kernels, are amenable to this approach.

APA, Harvard, Vancouver, ISO, and other styles

21

Burns, R. G., A. Karrass, and D. Solitar. "A note on groups with separable finitely generated subgroups." Bulletin of the Australian Mathematical Society 36, no. 1 (August 1987): 153–60. http://dx.doi.org/10.1017/s0004972700026393.

Full text

Abstract:

An example is given of an infinite cyclic extension of a free group of finite rank in which not every finitely generated subgroup is finitely separable. This answers negatively the question of Peter Scott as to whether in all finitely generated 3-manifold groups the finitely generated subgroups are finitely separable. In the positive direction it is shown that in knot groups and one-relator groups with centre, the finitely generated normal subgroups are finitely separable.

APA, Harvard, Vancouver, ISO, and other styles

22

ROMAN'KOV, VITALY. "ON THE AUTOMORPHISM GROUP OF A FREE METABELIAN LIE ALGEBRA." International Journal of Algebra and Computation 18, no. 02 (March 2008): 209–26. http://dx.doi.org/10.1142/s0218196708004408.

Full text

Abstract:

Let K be a field of any characteristic. We prove that a free metabelian Lie algebra M3 of rank 3 over K admits wild automorphisms. Moreover, the subgroup I Aut M3 of all automorphisms identical modulo the derived subalgebra [Formula: see text] cannot be generated by any finite set of IA-automorphisms together with the sets of all inner and all tame IA-automorphisms. In the case if K is finite the group Aut M3 cannot be generated by any finite set of automorphisms together with the sets of all tame, all inner automorphisms and all one-row automorphisms. We present an infinite set of wild IA-automorphisms of M3 which generates a free subgroup F∞ modulo normal subgroup generated by all tame, all inner and all one-row automorphisms of M3.

APA, Harvard, Vancouver, ISO, and other styles

23

Bougacha, Aymen, Jihene Boughariou, Ines Njeh, Omar Kammoun, Kheireddine Ben Mahfoudh, Mariem Dammak, Chokri Mhiri, and Ahmed Ben Hamida. "A RANK-TWO NMF CLUSTERING: APPLICATION TO GLIOBLASTOMAS CHARACTERIZATION AND COMPARATIVE STUDY." Biomedical Engineering: Applications, Basis and Communications 31, no. 03 (May 27, 2019): 1950019. http://dx.doi.org/10.4015/s1016237219500194.

Full text

Abstract:

This paper explores a novel clustering approach for multimodal Glioblastomas (GBM) characterization using the magnetic resonance image (MRI) modality. We define our segmentation problem as a linear mixture model (LMM). In every segmentation process, we generate a non-negative matrix with GLCM features from every MRI slice and a rank-two NMF (Non Negative Matrix Factorization) is applied. Our method process in four levels of segmentation. In the first one, the LMM matrix for the whole brain was generated from FLAIR modality to extract whole tumor region, which considered as the region of Interest (ROI). In the second level, we extract the ROI from T1c modality and the LMM matrix was generated from only this ROI to extract necrosis region. The principle will be the same for the other two levels to extract the enhanced and the non-enhanced region. Quantitative and qualitative assessment over the publicly dataset from MICCAI 2015 challenge (BRATS 2015) demonstrated that the proposed method could generate a competitive efficiency for high grade Glioblastomas characterization among several competing method. In order to highlight the performance of our method, we propose a comparative study with unsupervised segmentation methodologies (K-means, fuzzy C-means (FCM), gaussian mixture model (GMM) and hierarchical non-negative factorization (hNMF)) over the publicly BRATS 2015 dataset by computing validation metrics (the sensitivity, the dice and the specificity). The obtained results could attest the performance of the proposed algorithm compared to the unsupervised segmentation methodologies.

APA, Harvard, Vancouver, ISO, and other styles

24

Imam, A. T., M. Balarabe, and M. J. Ibrahim. "Rank of the Subsemigroup of the Semigroup of Finite Full Contraction Maps Generated by Elements of Defect One." Journal of Advances in Mathematics and Computer Science 30, no. 5 (February 12, 2019): 1–7. http://dx.doi.org/10.9734/jamcs/2019/41513.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

BUENGER, C. DAVIS, and CHENG ZHENG. "Non-divergence of unipotent flows on quotients of rank-one semisimple groups." Ergodic Theory and Dynamical Systems 37, no. 1 (December 28, 2015): 103–28. http://dx.doi.org/10.1017/etds.2015.43.

Full text

Abstract:

Let$G$be a semisimple Lie group of rank one and$\unicode[STIX]{x1D6E4}$be a torsion-free discrete subgroup of$G$. We show that in$G/\unicode[STIX]{x1D6E4}$, given$\unicode[STIX]{x1D716}>0$, any trajectory of a unipotent flow remains in the set of points with injectivity radius larger than$\unicode[STIX]{x1D6FF}$for a$1-\unicode[STIX]{x1D716}$proportion of the time, for some$\unicode[STIX]{x1D6FF}>0$. The result also holds for any finitely generated discrete subgroup$\unicode[STIX]{x1D6E4}$and this generalizes Dani’s quantitative non-divergence theorem [On orbits of unipotent flows on homogeneous spaces.Ergod. Th. & Dynam. Sys.4(1) (1984), 25–34] for lattices of rank-one semisimple groups. Furthermore, for a fixed$\unicode[STIX]{x1D716}>0$, there exists an injectivity radius$\unicode[STIX]{x1D6FF}$such that, for any unipotent trajectory$\{u_{t}g\unicode[STIX]{x1D6E4}\}_{t\in [0,T]}$, either it spends at least a$1-\unicode[STIX]{x1D716}$proportion of the time in the set with injectivity radius larger than$\unicode[STIX]{x1D6FF}$, for all large$T>0$, or there exists a$\{u_{t}\}_{t\in \mathbb{R}}$-normalized abelian subgroup$L$of$G$which intersects$g\unicode[STIX]{x1D6E4}g^{-1}$in a small covolume lattice. We also extend these results to when$G$is the product of rank-one semisimple groups and$\unicode[STIX]{x1D6E4}$a discrete subgroup of$G$whose projection onto each non-trivial factor is torsion free.

APA, Harvard, Vancouver, ISO, and other styles

26

MIRA, CHRISTIAN, and ANDREY SHILNIKOV. "SLOW–FAST DYNAMICS GENERATED BY NONINVERTIBLE PLANE MAPS." International Journal of Bifurcation and Chaos 15, no. 11 (November 2005): 3509–34. http://dx.doi.org/10.1142/s0218127405014192.

Full text

Abstract:

The present paper focuses on the two time scale dynamics generated by 2D polynomial noninvertible maps T of (Z0 - Z2) and (Z1 - Z3 - Z1) types. This symbolism, specific to noninvertible maps, means that the phase plane is partitioned into zones Zk, where each point possesses the k real rank-one preimages. Of special interest here is the structure of slow and fast motion sets of such maps. The formation mechanism of a stable invariant close curve through the interaction of fast and slow dynamics, as well as its transformation into a canard are studied. A few among the plethora of chaotic attractors and chaotic transients produced by such maps are described as well.

APA, Harvard, Vancouver, ISO, and other styles

27

Hyman, Richard. "The Sound of One Hand Clapping: A Comment on the “Rank and Filism” Debate." International Review of Social History 34, no. 2 (August 1989): 309–26. http://dx.doi.org/10.1017/s0020859000009287.

Full text

Abstract:

The issue of “spontaneity versus organisation” has provoked constant controversy within labour movements, at least since the polemic between Lenin and Luxemburg in the first years of this century. The rise of mass social-democratic parties and national industrial unions generated a familiar dilemma for the left: an apparent contradiction between direct, localised and immediate collective expressions of working-class experience and aspirations – with the virtues of authenticity and self-activity – and the centralised, co-ordinated and disciplined institutions which strategic efficacy seemingly required. Experience of the particularly bureaucratic and authoritarian German movement helped inspire Michels' eloquent thesis that hierarchical organisational structures were unavoidable, yet inevitably resulted in conservative and anti-democratic outcomes. Others – most notably, perhaps, the Webbs – insisted that oligarchy could be avoided by appropriate organisational engineering; yet others, implicitly endorsing Michels' equation, proposed syndicalist strategies for avoiding institutional discipline. Subsequently the Third International, with its concept of “democratic centralism”, sought to dissolve the whole issue by what critics regarded as a definitional sleight-of-hand.

APA, Harvard, Vancouver, ISO, and other styles

28

EAST, JAMES. "ON THE SINGULAR PART OF THE PARTITION MONOID." International Journal of Algebra and Computation 21, no. 01n02 (February 2011): 147–78. http://dx.doi.org/10.1142/s021819671100611x.

Full text

Abstract:

We study the singular part of the partition monoid [Formula: see text]; that is, the ideal [Formula: see text], where [Formula: see text] is the symmetric group. Our main results are presentations in terms of generators and relations. We also show that [Formula: see text] is idempotent generated, and that its rank and idempotent-rank are both equal to [Formula: see text]. One of our presentations uses an idempotent generating set of this minimal cardinality.

APA, Harvard, Vancouver, ISO, and other styles

29

SILVA, PEDRO V., and PASCAL WEIL. "AUTOMORPHIC ORBITS IN FREE GROUPS: WORDS VERSUS SUBGROUPS." International Journal of Algebra and Computation 20, no. 04 (June 2010): 561–90. http://dx.doi.org/10.1142/s0218196710005790.

Full text

Abstract:

We show that the following problems are decidable in a rank 2 free group F2: Does a given finitely generated subgroup H contain primitive elements? And does H meet the orbit of a given word u under the action of G, the group of automorphisms of F2? Moreover, decidability subsists if we allow H to be a rational subset of F2, or alternatively if we restrict G to be a rational subset of the set of invertible substitutions (a.k.a. positive automorphisms). In higher rank, the following weaker problem is decidable: given a finitely generated subgroup H, a word u and an integer k, does H contain the image of u by some k-almost bounded automorphism? An automorphism is k-almost bounded if at most one of the letters has an image of length greater than k.

APA, Harvard, Vancouver, ISO, and other styles

30

Barron, Katrina, Karina Batistelli, Florencia Orosz Hunziker, Veronika Pedić Tomić, and Gaywalee Yamskulna. "On rationality of C-graded vertex algebras and applications to Weyl vertex algebras under conformal flow." Journal of Mathematical Physics 63, no. 9 (September 1, 2022): 091706. http://dx.doi.org/10.1063/5.0117895.

Full text

Abstract:

Using the Zhu algebra for a certain category of [Formula: see text]-graded vertex algebras V, we prove that if V is finitely Ω-generated and satisfies suitable grading conditions, then V is rational, i.e., it has semi-simple representation theory, with a one-dimensional level zero Zhu algebra. Here, Ω denotes the vectors in V that are annihilated by lowering the real part of the grading. We apply our result to the family of rank one Weyl vertex algebras with conformal element ω μ parameterized by [Formula: see text] and prove that for certain non-integer values of μ, these vertex algebras, which are non-integer graded, are rational, with a one-dimensional level zero Zhu algebra. In addition, we generalize this result to appropriate [Formula: see text]-graded Weyl vertex algebras of arbitrary ranks.

APA, Harvard, Vancouver, ISO, and other styles

31

LIRIANO, SAL. "ALGEBRAIC GEOMETRIC INVARIANTS OF PARAFREE GROUPS." International Journal of Algebra and Computation 17, no. 01 (February 2007): 155–69. http://dx.doi.org/10.1142/s0218196707003494.

Full text

Abstract:

Given a finitely generated (fg) group G, the set R(G) of homomorphisms from G to SL2ℂ inherits the structure of an algebraic variety known as the representation variety of G in SL2ℂ. This algebraic variety is an invariant of fg presentations of G. Call a group G parafree of rank n if it shares the lower central sequence with a free group of rank n, and if it is residually nilpotent. The deviation of a fg parafree group is the difference between the minimum possible number of generators of G and the rank of G. So parafree groups of deviation zero are actually just free groups. Parafree groups that are not free share a host of properties with free groups. In this paper algebraic geometric invariants involving the number of maximal irreducible components (mirc) of R(G), and the dimension of R(G) for certain classes of parafree groups are computed. It is shown that in an infinite number of cases these invariants successfully discriminate between ismorphism types within the class of parafree groups of the same rank. This is quite surprising, since an n generated group G is free of rank n if and only if Dim (R(G)) = 3n. In fact, a trivial consequence of Theorem 1.8 in this paper is that given an arbitrary positive integer k, and any integer r ≥ 2, there exist infinitely many non-isomorphic fg parafree groups of rank r and deviation 1 with representation varieties of dimension 3r, having more than k mirc of dimension 3r. This paper also introduces many novel and surprising dimension formulas for the representation varieties of certain one-relator groups.

APA, Harvard, Vancouver, ISO, and other styles

32

IVANOV, S. V. "ON THE INTERSECTION OF FINITELY GENERATED SUBGROUPS IN FREE PRODUCTS OF GROUPS." International Journal of Algebra and Computation 09, no. 05 (October 1999): 521–28. http://dx.doi.org/10.1142/s021819679900031x.

Full text

Abstract:

A subgroup H of a free product [Formula: see text] of groups Gα, α∈ I, is called factor free if for every [Formula: see text] and β ∈ I one has S H S-1∩ Gβ = {1} (by Kurosh theorem on subgroups of free products, factor free subgroups are free). If K is a finitely generated free group, denote [Formula: see text], where r(K) is the rank of K. It is proven that if H, K are finitely generated factor free subgroups of a free product [Formula: see text] then [Formula: see text]. It is also shown that the inequality [Formula: see text] of Hanna Neumann conjecture on subgroups of free groups does not hold for factor free subgroups of free products.

APA, Harvard, Vancouver, ISO, and other styles

33

Benson, D. J., Jon F. Carlson, and J. Rickard. "Complexity and varieties for infinitely generated modules, II." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 4 (November 1996): 597–615. http://dx.doi.org/10.1017/s0305004100001584.

Full text

Abstract:

It has now been almost twenty years since Alperin introduced the idea of the complexity of a finitely generated kG-module, when G is a finite group and k is a field of characteristic p > 0. In proving one of the first major results in the area [1], Alperin and Evens demonstrated the connection of the study of complexity for modules to the group cohomology. That connection eventually led to the categorization of modules according to their associated varieties in the maximal ideal spectrum of the cohomology ring H*(G, k). In all of the work that has followed, two principles have proved to be extremely important. The first is that the associated variety of a module is directly related to the structure of the module through the rank variety which is defined by the matrix representation of the module. The second major result is the tensor product theorem which says that the variety associated to a tensor product M ⊗kN is the intersection of the varieties associated to the modules M and N. In this paper we generalize these results to infinitely generated kG-modules.

APA, Harvard, Vancouver, ISO, and other styles

34

Bergs, Rolf. "Spatial dependence in the rank-size distribution of cities – weak but not negligible." PLOS ONE 16, no. 2 (February 9, 2021): e0246796. http://dx.doi.org/10.1371/journal.pone.0246796.

Full text

Abstract:

Power law distributions characterise several natural and social phenomena. Zipf’s law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities. For that purpose, a typical Zipfian rank-size distribution of cities is generated with random numbers. This distribution is then cast into two different settings of spatial coordinates. For the estimation, the variables rank and size are supplemented by considerations of spatial dependence within a spatial econometric approach. Results suggest that distance potentially matters. This finding is further corroborated by four country analyses even though estimates reveal only modest effects.

APA, Harvard, Vancouver, ISO, and other styles

35

Lemmer, A. A., and G. Naudé. "A glance back at the Quillen-Suslin theorem and the recent status o f the Bass-Quillen conjecture." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 8, no. 1 (March 14, 1989): 3–8. http://dx.doi.org/10.4102/satnt.v8i1.859.

Full text

Abstract:

In his famous FAC-article J.P. Serre asked whether all finitely generated projective modules over K[X1,...,Xn] (K a field) are free. This question soon became known in the mathematical society as “Serre’s Conjecture”. This conjecture was proved independently in 1976 by A. A. Suslin and D. Quillen. Important further developments followed from the ideas in Quillen’s proof. In this article we discuss the geometric motivation of the original problem as well as certain aspects of Quillen’s proof. Then we discuss further developments, in particular a proof that finitely generated projective modules over R[X1,...,Xn], R a Bezout domain, are free. We also give attention to new results on the existence of free summands in projective modules. In the case of polynomial rings, this work strengthens Serre’s famous free summand theorem: if R is a Noetherian ring and P is a finitely generated projective R-module such that rank P > dim R, then there exists a free rank one summand in P. Finally we discuss the present status of the most important open problem in this field, namely the Bass-Quillen Conjecture: if R is a regular local ring, is every finitely generated projective R[X1,...,Xn] module free?

APA, Harvard, Vancouver, ISO, and other styles

36

KYE, SEUNG-HYEOK. "On the convex set of completely positive linear maps in matrix algebras." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 1 (July 1997): 45–54. http://dx.doi.org/10.1017/s0305004196001508.

Full text

Abstract:

Let PI (respectively CPI) be the convex compact set of all unital positive (respectively completely positive) linear maps from the matrix algebra Mm([Copf ]) into Mn([Copf ]). We show that maximal faces of CPI correspond to one dimensional subspaces of the vector space Mm, n([Copf ]). Furthermore, a maximal face of CPI lies on the boundary of PI if and only if the corresponding subspace is generated by a rank one matrix.

APA, Harvard, Vancouver, ISO, and other styles

37

AKHAVAN-MALAYERI, MEHRI, and AKBAR RHEMTULLA. "PRODUCTS OF COMMUTATORS IN FREE GROUPS." International Journal of Algebra and Computation 13, no. 02 (April 2003): 231–40. http://dx.doi.org/10.1142/s0218196703001316.

Full text

Abstract:

Let F be the free group of rank 2, generated by x and y, and let w(x, y) ∈ F′ be a non-trivial word. We give elementary algebraic proofs and algorithms to (1) express [x, y]n as a product of [n/2] + 1 commutators and show this is the best possible; (2) show that (w(x, y))2 cannot be written as one w-word and if g ≠ 1 ∈ w(F) then show that the minimal number of w-words required to express gn as their product tends to infinity with n. Other results for free groups of higher rank are also presented.

APA, Harvard, Vancouver, ISO, and other styles

38

Bonelli, Giulio, Fabrizio Del Monte, and Alessandro Tanzini. "BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations." Annales Henri Poincaré 22, no. 8 (March 31, 2021): 2721–73. http://dx.doi.org/10.1007/s00023-021-01034-3.

Full text

Abstract:

AbstractWe study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with $$\tau $$ τ -functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and $$N_f=2$$ N f = 2 on a circle.

APA, Harvard, Vancouver, ISO, and other styles

39

Bieri, Robert, Yves Cornulier, Luc Guyot, and Ralph Strebel. "Infinite presentability of groups and condensation." Journal of the Institute of Mathematics of Jussieu 13, no. 4 (January 2, 2014): 811–48. http://dx.doi.org/10.1017/s1474748013000327.

Full text

Abstract:

AbstractWe describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We introduce here a larger class of condensation groups, called infinitely independently presentable groups, and establish criteria which allow one to infer that a group is infinitely independently presentable. In addition, we construct examples of finitely generated groups with no minimal presentation, among them infinitely presented groups with Cantor–Bendixson rank 1, and we prove that every infinitely presented metabelian group is a condensation group.

APA, Harvard, Vancouver, ISO, and other styles

40

Ma, Xiaojian, and Yinghong Ma. "The Local Triangle Structure Centrality Method to Rank Nodes in Networks." Complexity 2019 (January 2, 2019): 1–16. http://dx.doi.org/10.1155/2019/9057194.

Full text

Abstract:

Detecting influential spreaders had become a challenging and crucial topic so far due to its practical application in many areas, such as information propagation inhibition and disease dissemination control. Some traditional local based evaluation methods had given many discussions on ranking important nodes. In this paper, ranking nodes of networks continues to be discussed. A semilocal structures method for ranking nodes based on the degree and the neighbors’ connections of the node is presented. The semilocal structures are regarded as the number of neighbors of the nodes and the connections between the node and its neighbors. We combined the triangle structure and the degree information of the neighbors to define the inner-outer spreading ability of the nodes and then summed the node neighbors’ inner-outer spreading ability to be used as the local triangle structure centrality (LTSC). The LTSC avoids the defect “pseudo denser connections” in measuring the structure of neighbors. The performance of the proposed LTSC method is evaluated by comparing the spreading ability on both real-world and synthetic networks with the SIR model. The simulation results of the discriminability and the correctness compared with pairs of ranks (one is generated by SIR model and the others are generated by central nodes measures) show that LTSC outperforms some other local or semilocal methods in evaluating the node’s influence in most cases, such as degree, betweenness, H-index, local centrality, local structure centrality, K-shell, and S-shell. The experiments prove that the LTSC is an efficient and accurate ranking method which provides a more reasonable evaluating index to rank nodes than some previous approaches.

APA, Harvard, Vancouver, ISO, and other styles

41

Branco, Mário J. J., Gracinda M. S. Gomes, and Pedro V. Silva. "Takahasi semigroups." Forum Mathematicum 29, no. 5 (September 1, 2017): 1145–61. http://dx.doi.org/10.1515/forum-2015-0059.

Full text

Abstract:

AbstractTakahasi’s Theorem on chains of subgroups of bounded rank in a free group is generalized to several classes of semigroups. As an application, it is proved that the subsemigroups of periodic points are finitely generated and periodic orbits are bounded for arbitrary endomorphisms for various semigroups. Some of these results feature classes such as completely simple semigroups, Clifford semigroups or monoids defined by balanced one-relator presentations.

APA, Harvard, Vancouver, ISO, and other styles

42

Wang, Yishu, Dejie Yang, and Minghua Deng. "Low-Rank and Sparse Matrix Decomposition for Genetic Interaction Data." BioMed Research International 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/573956.

Full text

Abstract:

Background. Epistatic miniarray profile (EMAP) studies have enabled the mapping of large-scale genetic interaction networks and generated large amounts of data in model organisms. One approach to analyze EMAP data is to identify gene modules with densely interacting genes. In addition, genetic interaction score (Sscore) reflects the degree of synergizing or mitigating effect of two mutants, which is also informative. Statistical approaches that exploit both modularity and the pairwise interactions may provide more insight into the underlying biology. However, the high missing rate in EMAP data hinders the development of such approaches. To address the above problem, we adopted the matrix decomposition methodology “low-rank and sparse decomposition” (LRSDec) to decompose EMAP data matrix into low-rank part and sparse part.Results. LRSDec has been demonstrated as an effective technique for analyzing EMAP data. We applied a synthetic dataset and an EMAP dataset studying RNA-related processes inSaccharomyces cerevisiae. Global views of the genetic cross talk between different RNA-related protein complexes and processes have been structured, and novel functions of genes have been predicted.

APA, Harvard, Vancouver, ISO, and other styles

43

BAADER, SEBASTIAN, and ALEXANDRA KJUCHUKOVA. "Symmetric quotients of knot groups and a filtration of the Gordian graph." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 1 (April 10, 2019): 141–48. http://dx.doi.org/10.1017/s0305004119000136.

Full text

Abstract:

AbstractWe define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The nth subgraph of this family is generated by all knots whose fundamental groups surject to a symmetric group with parameter at least n, where all meridians are mapped to transpositions. Incidentally, we verify the Meridional Rank Conjecture for a family of knots with unknotting number one yet arbitrarily high bridge number.

APA, Harvard, Vancouver, ISO, and other styles

44

Oreshkina (Nikol’skaya), Olga V. "On the Hodge, Tate and Mumford-Tate Conjectures for Fibre Products of Families of Regular Surfaces with Geometric Genus 1." Modeling and Analysis of Information Systems 25, no. 3 (June 30, 2018): 312–22. http://dx.doi.org/10.18255/1818-1015-2018-3-312-322.

Full text

Abstract:

The Hodge, Tate and Mumford-Tate conjectures are proved for the fibre product of two non-isotrivial 1-parameter families of regular surfaces with geometric genus 1 under some conditions on degenerated fibres, the ranks of the N\'eron - Severi groups of generic geometric fibres and representations of Hodge groups in transcendental parts of rational cohomology.Let $\pi_i:X_i\to C\quad (i = 1, 2)$ be a projective non-isotrivial family (possibly with degeneracies) over a smooth projective curve $C$. Assume that the discriminant loci $\Delta_i=\{\delta\in C\,\,\vert\,\, Sing(X_{i\delta})\neq\varnothing\} \quad (i = 1, 2)$ are disjoint, $h^{2,0}(X_{ks})=1,\quad h^{1,0}(X_{ks}) = 0$ for any smooth fibre $X_{ks}$, and the following conditions hold:$(i)$ for any point $\delta \in \Delta_i$ and the Picard-Lefschetz transformation $ \gamma \in GL(H^2 (X_{is}, Q)) $, associated with a smooth part $\pi'_i: X'_i\to C\setminus\Delta_i$ of the morphism $\pi_i$ and with a loop around the point $\delta \in C$, we have $(\log(\gamma))^2\neq0$;$(ii)$ the variety $X_i \, (i = 1, 2)$, the curve $C$ and the structure morphisms $\pi_i:X_i\to C$ are defined over a finitely generated subfield $k \hookrightarrow C$.If for generic geometric fibres $X_{1s}$ \, and \, $X_{2s}$ at least one of the following conditions holds: $(a)$ $b_2(X_{1s})- rank NS(X_{1s})$ is an odd prime number, $\quad\,\,$ $b_2(X_{1s})- rank NS(X_{1s})\neq b_2(X_{2s})- rank NS(X_{2s})$; $(b)$ the ring $End_{ Hg(X_{1s})} NS_ Q(X_{1s})^\perp$ is an imaginary quadratic field, $\quad\,\, b_2(X_{1s})- rank NS(X_{1s})\neq 4,$ $\quad\,\, End_{ Hg(X_{2s})} NS_ Q(X_{2s})^\perp$ is a totally real field or $\,\, b_2(X_{1s})- rank NS(X_{1s})\,>\, b_2(X_{2s})- rank NS(X_{2s})$ ; $(c)$ $[b_2(X_{1s})- rank NS(X_{1s})\neq 4, \, End_{ Hg(X_{1s})} NS_ Q(X_{1s})^\perp= Q$; $\quad\,\,$ $b_2(X_{1s})- rank NS(X_{1s})\neq b_2(X_{2s})- rank NS(X_{2s})$,then for the fibre product $X_1 \times_C X_2$ the Hodge conjecture is true, for any smooth projective $k$-variety $X_0$ with the condition $X_1 \times_C X_2$ $\widetilde{\rightarrow}$ $X_0 \otimes_k C$ the Tate conjecture on algebraic cycles and the Mumford-Tate conjecture for cohomology of even degree are true.

APA, Harvard, Vancouver, ISO, and other styles

45

Garba, G. U. "Nilpotents in semigroups of partial order-preserving transformations." Proceedings of the Edinburgh Mathematical Society 37, no. 3 (October 1994): 361–77. http://dx.doi.org/10.1017/s001309150001885x.

Full text

Abstract:

In this paper we extend the results of Garba [1] on IOn, the semigroup of all partial one-one order-preserving maps on Xn = {1,…, n}, to POn, the semigroup of all partial order-preserving maps on Xn, A description of the subsemigroup of POn generated by the set N of all its nilpotent elements is given. The set {α∈POn:lim α/≦r and |Xn /dom α|≧r} is shown to be contained in 〈N〉 if and only if r≦½n. The depth of 〈N〉, which is the unique k for which 〈N〉 = N ∪ N2 ∪…∪ Nk and 〈N〉 ≠ N ∪ N2 ∪…∪Nk−1 is shown to be equal to 3 for all n≧3. The rank of the subsemigroup {α∈POπ|imα|≦/n − 2 and α∈〈N〉} is shown to be equal to 6(n − 2), and its nilpotent rank to be equal to 7n−15.

APA, Harvard, Vancouver, ISO, and other styles

46

SAMANTA, KALYAN SUNDAR. "User Generated Social Tags Versus Librarian Generated Subject Headings, A Comparative Study in the Domain of History." DESIDOC Journal of Library & Information Technology 40, no. 03 (May 26, 2020): 176–84. http://dx.doi.org/10.14429/djlit.40.03.15413.

Full text

Abstract:

Social tagging allows users to assign any free-form keywords as tags to any digital resources through a decentralised way. Many information scientists find that there are similarities through their studies between usergenerated social tags and the librarian-generated subject headings for the libraries. The present study was conducted to identify the similarity and dissimilarity between user-generated social tags and librarian-generated subject terms of 1000 books in the domain of History. The study also conducted to identify whether social tags can replace controlled vocabularies. The study finds that only a small portion of terms overlaps with each other (3.54 % of social tags & 56.07 % of SLSH terms) and Spearman’s rank correlation proves that there is a good association between overlapping terms. Jaccard similarity coefficient highlights that users and the librarian use different terminologies (as J = 0.13, 0.12 & 0.11). Individual title wise comparison also defines that 90 per cent (88.4 %) of all book titles where users and the librarian use at least one common term. Users use the least subject & non-subject terms but use some personal tags for personal benefit whereas the librarian use only subject & non-subject terms. Matching with each book title clarifies that for describing resources users mostly use title based keywords (696) whereas the librarian use very little title based keywords (113). The study clearly defines that social tags can enhance the experience of library users. If it can be exploited properly it can complement to controlled vocabularies but can not replace the controlled vocabularies used for libraries a long time. Overall the study explicitly identifies the viability regarding the adoption of social tags into the library databases where the resources in the field of history will be accessed.

APA, Harvard, Vancouver, ISO, and other styles

47

SHLAPENTOKH, ALEXANDRA. "ELLIPTIC CURVE POINTS AND DIOPHANTINE MODELS OF ℤ IN LARGE SUBRINGS OF NUMBER FIELDS." International Journal of Number Theory 08, no. 06 (August 3, 2012): 1335–65. http://dx.doi.org/10.1142/s1793042112500789.

Full text

Abstract:

Let K be a number field such that there exists an elliptic curve E of rank one over K. For a set [Formula: see text] of primes of K, let [Formula: see text]. Let P ∈ E(K) be a generator of E(K) modulo the torsion subgroup. Let (xn(P), yn(P)) be the affine coordinates of [n]P with respect to a fixed Weierstrass equation of E. We show that there exists a set [Formula: see text] of primes of K of natural density one such that in [Formula: see text] multiplication of indices (with respect to some fixed multiple of P) is existentially definable and therefore these indices can be used to construct a Diophantine model of ℤ. We also show that ℤ is definable over [Formula: see text] using just one universal quantifier. Both the construction of a Diophantine model using the indices and the first-order definition of ℤ can be lifted to the integral closure of [Formula: see text] in any infinite extension K∞ of K as long as E(K∞) is finitely generated and of rank one.

APA, Harvard, Vancouver, ISO, and other styles

48

Ayu, Media A., Sony Surya Wijaya, and Teddy Mantoro. "An automatic lexicon generation for indonesian news sentiment analysis: a case on governor elections in Indonesia." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 3 (December 1, 2019): 1555. http://dx.doi.org/10.11591/ijeecs.v16.i3.pp1555-1561.

Full text

Abstract:

Sentiment analysis has been popularly used in analyzing data from the internet. One of the techniques used is lexicon based sentiment analysis. Generating lexicon is not an easy process, and lexicon in Bahasa Indonesia is rarely available. This paper proposes an automatic lexicon generation in Bahasa Indonesia for sentiment analysis purpose. Experiments were performed using the generated lexicon for doing sentiment analysis on Indonesian political news about the 2018 governor election in three provinces in Indonesia. The conducted experiments show promising results where it can predict the candidate’s rank, the election winner, and the percentage of votes for each candidate with better accuracy than the previous work which used manually generated lexicon.

APA, Harvard, Vancouver, ISO, and other styles

49

Rosenoer, Shlomo. "Trace-Class Operators in CSL Algebras." Canadian Mathematical Bulletin 35, no. 3 (September 1, 1992): 416–22. http://dx.doi.org/10.4153/cmb-1992-055-x.

Full text

Abstract:

AbstractIn this note we show that if 𝓛 is a commutative subspace lattice, then every trace-class operator in Alg 𝓛 lies in the norm-closure of the span of rank-one operators in Alg 𝓛. We also give an elementary proof of a recent result of Davidson and Pitts that if 𝓛 is a CSL generated by completely distributive lattice and finitely many commuting chains, then 𝓛 is compact in the strong operator topology if and only if 𝓛 is completely distributive.

APA, Harvard, Vancouver, ISO, and other styles

50

Arroyo-Rabasa, Adolfo. "Characterization of Generalized Young Measures Generated by $${\mathcal {A}}$$-free Measures." Archive for Rational Mechanics and Analysis 242, no. 1 (July 8, 2021): 235–325. http://dx.doi.org/10.1007/s00205-021-01683-y.

Full text

Abstract:

AbstractWe give two characterizations, one for the class of generalized Young measures generated by $${{\,\mathrm{{\mathcal {A}}}\,}}$$ A -free measures and one for the class generated by $${\mathcal {B}}$$ B -gradient measures $${\mathcal {B}}u$$ B u . Here, $${{\,\mathrm{{\mathcal {A}}}\,}}$$ A and $${\mathcal {B}}$$ B are linear homogeneous operators of arbitrary order, which we assume satisfy the constant rank property. The first characterization places the class of generalized $${\mathcal {A}}$$ A -free Young measures in duality with the class of $${{\,\mathrm{{\mathcal {A}}}\,}}$$ A -quasiconvex integrands by means of a well-known Hahn–Banach separation property. The second characterization establishes a similar statement for generalized $${\mathcal {B}}$$ B -gradient Young measures. Concerning applications, we discuss several examples that showcase the failure of $$\mathrm {L}^1$$ L 1 -compensated compactness when concentration of mass is allowed. These include the failure of $$\mathrm {L}^1$$ L 1 -estimates for elliptic systems and the lack of rigidity for a version of the two-state problem. As a byproduct of our techniques we also show that, for any bounded open set $$\Omega $$ Ω , the inclusions $$\begin{aligned} \mathrm {L}^1(\Omega ) \cap \ker {\mathcal {A}}&\hookrightarrow {\mathcal {M}}(\Omega ) \cap \ker {{\,\mathrm{{\mathcal {A}}}\,}}\,,\\ \{{\mathcal {B}}u\in \mathrm {C}^\infty (\Omega )\}&\hookrightarrow \{{\mathcal {B}}u\in {\mathcal {M}}(\Omega )\} \end{aligned}$$ L 1 ( Ω ) ∩ ker A ↪ M ( Ω ) ∩ ker A , { B u ∈ C ∞ ( Ω ) } ↪ { B u ∈ M ( Ω ) } are dense with respect to the area-functional convergence of measures.

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Rank one generated'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles