Log in

Relevant bibliographies by topics / Dimension theorem / Journal articles

To see the other types of publications on this topic, follow the link: Dimension theorem.

Journal articles on the topic 'Dimension theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Dimension theorem.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

FENG, ZHIGANG, and GANG CHEN. "ON THE MINKOWSKI DIMENSION OF FUNCTIONAL DIGRAPH." Fractals 11, no. 01 (March 2003): 87–92. http://dx.doi.org/10.1142/s0218348x03001616.

Full text

Abstract:

Functional digraphs are sometimes fractal sets. As a special kind of fractal sets, the dimension properties of the functional digraph are studied in this paper. Firstly, the proof of a Minkowski dimension theorem is discussed and a new proof is given. Secondly, according to this dimension theorem, the Minkowski dimensions of the digraphs of the sum, deviation, product and quotient of two functions are discussed. And the relations between these Minkowski dimensions and the Minkowski dimensions of the digraphs of the two functions are established. In the conclusion, the maximum Minkowski dimension of the two functional digraphs plays a decisive part in the Minkowski dimensions of the digraphs of the sum, deviation, product and quotient of two functions.

APA, Harvard, Vancouver, ISO, and other styles

2

LIMA, YURI, and CARLOS GUSTAVO MOREIRA. "A Marstrand Theorem for Subsets of Integers." Combinatorics, Probability and Computing 23, no. 1 (October 25, 2013): 116–34. http://dx.doi.org/10.1017/s0963548313000461.

Full text

Abstract:

We propose a counting dimension for subsets of $\mathbb{Z}$ and prove that, under certain conditions on E,F ⊂ $\mathbb{Z}$, for Lebesgue almost every λ ∈ $\mathbb{R}$ the counting dimension of E + ⌊λF⌋ is at least the minimum between 1 and the sum of the counting dimensions of E and F. Furthermore, if the sum of the counting dimensions of E and F is larger than 1, then E + ⌊λF⌋ has positive upper Banach density for Lebesgue almost every λ ∈ $\mathbb{R}$. The result has direct consequences when E,F are arithmetic sets, e.g., the integer values of a polynomial with integer coefficients.

APA, Harvard, Vancouver, ISO, and other styles

3

Zhang, N. L., and T. Kocka. "Effective Dimensions of Hierarchical Latent Class Models." Journal of Artificial Intelligence Research 21 (January 1, 2004): 1–17. http://dx.doi.org/10.1613/jair.1311.

Full text

Abstract:

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are latent. There are no theoretically well justified model selection criteria for HLC models in particular and Bayesian networks with latent nodes in general. Nonetheless, empirical studies suggest that the BIC score is a reasonable criterion to use in practice for learning HLC models. Empirical studies also suggest that sometimes model selection can be improved if standard model dimension is replaced with effective model dimension in the penalty term of the BIC score. Effective dimensions are difficult to compute. In this paper, we prove a theorem that relates the effective dimension of an HLC model to the effective dimensions of a number of latent class models. The theorem makes it computationally feasible to compute the effective dimensions of large HLC models. The theorem can also be used to compute the effective dimensions of general tree models.

APA, Harvard, Vancouver, ISO, and other styles

4

GHOSHAL, DEBASHIS, and SUDIPTA MUKHERJI. "NO GHOST THEOREM AND COHOMOLOGY THEOREM FOR STRINGS IN ARBITRARY STATIC BACKGROUNDS." Modern Physics Letters A 06, no. 10 (March 28, 1991): 939–47. http://dx.doi.org/10.1142/s0217732391000981.

Full text

Abstract:

We consider a string moving in an arbitrary time-independent background given by an arbitrary conformal field theory of appropriate central charge (e.g., c=25 for bosonic string) and one flat time-like dimension. We show that the physical subspace of the Hilbert space is positive semi-definite (no ghost theorem) and that the cohomology of the BRST operator is trivial except for the ghost number one (for open bosonic string) sector (cohomology theorem). Both the proofs are reductio ad absurdum proofs based on the corresponding theorems for the strings moving in flat background. In cases where there is an extra flat space-like dimension (besides the flat time-like one), the transverse subspace with positive-definite norm can be constructed.

APA, Harvard, Vancouver, ISO, and other styles

5

Temur, Faruk. "A quantitative Balian–Low theorem for higher dimensions." Georgian Mathematical Journal 27, no. 3 (September 1, 2020): 469–77. http://dx.doi.org/10.1515/gmj-2018-0046.

Full text

Abstract:

AbstractWe extend the quantitative Balian–Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor–Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor–Riesz basis generators, two properties for which dimension reduction is possible.

APA, Harvard, Vancouver, ISO, and other styles

6

PANTILIE, RADU. "Harmonic morphisms with one-dimensional fibres on conformally-flat Riemannian manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 1 (July 2008): 141–51. http://dx.doi.org/10.1017/s0305004108001060.

Full text

Abstract:

AbstractWe classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four (Theorem 3.1), and (2) between conformally-flat Riemannian manifolds of dimensions at least three (Corollaries 3.4 and 3.6).Also, we prove (Proposition 2.5) an integrability result for any real-analytic submersion, from a constant curvature Riemannian manifold of dimensionn+2 to a Riemannian manifold of dimension 2, which can be factorised as ann-harmonic morphism with two-dimensional fibres, to a conformally-flat Riemannian manifold, followed by a horizontally conformal submersion, (n≥4).

APA, Harvard, Vancouver, ISO, and other styles

7

Duggan, John. "May’s theorem in one dimension." Journal of Theoretical Politics 29, no. 1 (July 9, 2016): 3–21. http://dx.doi.org/10.1177/0951629815603694.

Full text

Abstract:

This paper provides three versions of May’s theorem on majority rule, adapted to the one-dimensional model common in formal political modeling applications. The key contribution is that single peakedness of voter preferences allows us to drop May’s restrictive positive responsiveness axiom. The simplest statement of the result holds when voter preferences are single peaked and linear (no indifferences), in which case a voting rule satisfies anonymity, neutrality, Pareto, and transitivity of weak social preference if and only if the number of individuals is odd and the rule is majority rule.

APA, Harvard, Vancouver, ISO, and other styles

8

Brodsky, N., and A. Chigogidze. "Hurewicz theorem for extension dimension." Topology and its Applications 129, no. 2 (March 2003): 145–51. http://dx.doi.org/10.1016/s0166-8641(02)00144-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

BONNIN, MICHELE, FERNANDO CORINTO, and MARCO GILLI. "DILIBERTO'S THEOREM IN HIGHER DIMENSION." International Journal of Bifurcation and Chaos 19, no. 02 (February 2009): 629–37. http://dx.doi.org/10.1142/s0218127409023251.

Full text

Abstract:

The study of the local behavior of nonlinear systems in the neighborhood of a periodic orbit is a classical problem in nonlinear dynamics. Most of our knowledge stems from simulations or the numerical integration of the variational equation. Only in the case of planar oscillators, the solution of the variational equation can be found analytically, provided that an explicit expression for the periodic trajectory is available. The aim of this paper is to extend a classical theorem due to S. P. Diliberto to higher dimensional systems. In doing so, we show how the fundamental matrix solution to the variational equation of higher order differential equations can be obtained in a closed analytical form. To obtain this result, the knowledge of the periodic trajectory is not sufficient anymore, and a specific set of orthogonal vectors has to be determined. The analysis of some examples reveals that finding these vectors may be easier than solving the variational equations.

APA, Harvard, Vancouver, ISO, and other styles

10

Cliff, G., and B. Hartley. "Sjogren's theorem on dimension subgroups." Journal of Pure and Applied Algebra 47, no. 3 (1987): 231–42. http://dx.doi.org/10.1016/0022-4049(87)90048-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Lötscher, Roland. "A fiber dimension theorem for essential and canonical dimension." Compositio Mathematica 149, no. 1 (December 4, 2012): 148–74. http://dx.doi.org/10.1112/s0010437x12000565.

Full text

Abstract:

AbstractThe well-known fiber dimension theorem in algebraic geometry says that for every morphism f:X→Y of integral schemes of finite type the dimension of every fiber of f is at least dim X−dim Y. This has recently been generalized by Brosnan, Reichstein and Vistoli to certain morphisms of algebraic stacks f:𝒳→𝒴, where the usual dimension is replaced by essential dimension. We will prove a general version for morphisms of categories fibered in groupoids. Moreover, we will prove a variant of this theorem, where essential dimension and canonical dimension are linked. These results let us relate essential dimension to canonical dimension of algebraic groups. In particular, using the recent computation of the essential dimension of algebraic tori by MacDonald, Meyer, Reichstein and the author, we establish a lower bound on the canonical dimension of algebraic tori.

APA, Harvard, Vancouver, ISO, and other styles

12

Soltanifar, Mohsen. "A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals." Mathematics 9, no. 13 (July 1, 2021): 1546. http://dx.doi.org/10.3390/math9131546.

Full text

Abstract:

How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure. We prove the existence of aleph-two of virtual fractals with a Hausdorff dimension of a bi-variate function of them and the given Lebesgue measure. The question remains unanswered for other fractal dimensions.

APA, Harvard, Vancouver, ISO, and other styles

13

Xie, Heping, and Hongquan Sun. "The Study on Bivariate Fractal Interpolation Functions and Creation of Fractal Interpolated Surfaces." Fractals 05, no. 04 (December 1997): 625–34. http://dx.doi.org/10.1142/s0218348x97000504.

Full text

Abstract:

In this paper, the methods of construction of a fractal surface are introduced, the principle of bivariate fractal interpolation functions is discussed. The theorem of the uniqueness of an iterated function system of bivariate fractal interpolation functions is proved. Moreover, the theorem of fractal dimension of fractal interpolated surface is derived. Based on these theorems, the fractal interpolated surfaces are created by using practical data.

APA, Harvard, Vancouver, ISO, and other styles

14

Zhou, Xiangyu, and Langfeng Zhu. "Subadditivity of generalized Kodaira dimensions and extension theorems." International Journal of Mathematics 31, no. 12 (September 30, 2020): 2050098. http://dx.doi.org/10.1142/s0129167x20500986.

Full text

Abstract:

In this paper, we introduce the notion of generalized Kodaira dimension with multiplier ideal sheaves, and prove the subadditivity of these generalized Kodaira dimensions for certain Kähler fibrations, which was originally obtained for Kodaira dimensions of algebraic fiber spaces by Kawamata and Viehweg. Our method is analytic and based on some new results in recent years. The crucial step in our proof is to prove an [Formula: see text] extension theorem for twisted pluricanonical sections on compact Kähler manifolds. Moreover, we also discuss the relation between two previous optimal [Formula: see text] extension theorems with singular weights on weakly pseudoconvex Kähler manifolds.

APA, Harvard, Vancouver, ISO, and other styles

15

Sharif, Tirdad, and Siamak Yassemi. "Special homological dimensions and intersection theorem." MATHEMATICA SCANDINAVICA 96, no. 2 (June 1, 2005): 161. http://dx.doi.org/10.7146/math.scand.a-14950.

Full text

Abstract:

Let $(R,m)$ be commutative Noetherian local ring. It is shown that $R$ is Cohen-Macaulay ring if there exists a Cohen-Macaulay finite (i.e. finitely generated) $R$-module with finite upper Gorenstein dimension. In addition, we show that, in the Intersection Theorem, projective dimension can be replaced by quasi-projective dimension.

APA, Harvard, Vancouver, ISO, and other styles

16

Sahandi, Parviz, Tirdad Sharif, and Siamak Yassemi. "Complete Intersection Flat Dimension and the Intersection Theorem." Algebra Colloquium 19, spec01 (October 31, 2012): 1161–66. http://dx.doi.org/10.1142/s1005386712000934.

Full text

Abstract:

Any finitely generated module M over a local ring R is endowed with a complete intersection dimension CI-dim RM and a Gorenstein dimension G-dim RM. The Gorenstein dimension can be extended to all modules over the ring R. This paper presents a similar extension for the complete intersection dimension, and mentions the relation between this dimension and the Gorenstein flat dimension. In addition, we show that in the intersection theorem, the flat dimension can be replaced by the complete intersection flat dimension.

APA, Harvard, Vancouver, ISO, and other styles

17

Çelikler, Y. Firat. "Dimension theory and parameterized normalization for D-semianalytic sets over non-Archimedean fields." Journal of Symbolic Logic 70, no. 2 (June 2005): 593–618. http://dx.doi.org/10.2178/jsl/1120224730.

Full text

Abstract:

AbstractWe develop a dimension theory for D-semianalytic sets over an arbitrary non-Arehimedean eomplete field. Our main results are the equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in characteristic 0. We also prove a parameterized version of normalization for D-semianalytic sets.

APA, Harvard, Vancouver, ISO, and other styles

18

SIMON, KÁROLY, and BORIS SOLOMYAK. "ON THE DIMENSION OF SELF-SIMILAR SETS." Fractals 10, no. 01 (March 2002): 59–65. http://dx.doi.org/10.1142/s0218348x02000963.

Full text

Abstract:

We extend a theorem of Falconer to give a complete result on the dimension and Lebesgue measure of typical self-similar attractors on the line. Further, we present some examples to point out that in higher dimensions, one cannot expect the same result in this generality.

APA, Harvard, Vancouver, ISO, and other styles

19

Mishra, Ratnesh Kumar, Shiv Datt Kumar, and Srinivas Behara. "On Projective Modules and Computation of Dimension of a Module over Laurent Polynomial Ring." ISRN Algebra 2011 (July 3, 2011): 1–12. http://dx.doi.org/10.5402/2011/926165.

Full text

Abstract:

We give a procedure and describe an algorithm to compute the dimension of a module over Laurent polynomial ring. We prove the cancellation theorems for projective modules and also prove the qualitative version of Laurent polynomial analogue of Horrocks' Theorem.

APA, Harvard, Vancouver, ISO, and other styles

20

Robert, Gerardo Gonzalez. "Good’s theorem for Hurwitz continued fractions." International Journal of Number Theory 16, no. 07 (March 17, 2020): 1433–47. http://dx.doi.org/10.1142/s1793042120500761.

Full text

Abstract:

Good’s Theorem for regular continued fraction states that the set of real numbers [Formula: see text] such that [Formula: see text] has Hausdorff dimension [Formula: see text]. We show an analogous result for the complex plane and Hurwitz Continued Fractions: the set of complex numbers whose Hurwitz Continued fraction [Formula: see text] satisfies [Formula: see text] has Hausdorff dimension [Formula: see text], half of the ambient space’s dimension.

APA, Harvard, Vancouver, ISO, and other styles

21

Myjak, Jozef, and Tomasz Szarek. "Szpilrajn type theorem for concentration dimension." Fundamenta Mathematicae 172, no. 1 (2002): 19–25. http://dx.doi.org/10.4064/fm172-1-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Carrillo, S. A., and F. Sanz. "Briot-Bouquet’s Theorem in high dimension." Publicacions Matemàtiques EXTRA (April 1, 2014): 135–52. http://dx.doi.org/10.5565/publmat_extra14_07.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Pflug, Peter, and Viêt-Anh Nguyên. "Boundary cross theorem in dimension 1." Annales Polonici Mathematici 90, no. 2 (2007): 149–92. http://dx.doi.org/10.4064/ap90-2-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Acquistapace, F., F. Broglia, and E. Fortuna. "A separation theorem in dimension 3." Nagoya Mathematical Journal 143 (September 1996): 171–93. http://dx.doi.org/10.1017/s0027763000005973.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Barton, G. "Levinson's theorem in one dimension: heuristics." Journal of Physics A: Mathematical and General 18, no. 3 (February 21, 1985): 479–94. http://dx.doi.org/10.1088/0305-4470/18/3/023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Ruiz, Jesús M. "A dimension theorem for real spectra." Journal of Algebra 124, no. 2 (August 1989): 271–77. http://dx.doi.org/10.1016/0021-8693(89)90129-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Blot, Joël. "The rank theorem in infinite dimension." Nonlinear Analysis: Theory, Methods & Applications 10, no. 10 (October 1986): 1009–20. http://dx.doi.org/10.1016/0362-546x(86)90085-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

David, Guy, Joseph Feneuil, and Svitlana Mayboroda. "Dahlberg's theorem in higher co-dimension." Journal of Functional Analysis 276, no. 9 (May 2019): 2731–820. http://dx.doi.org/10.1016/j.jfa.2019.02.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Nyman, A. "Noncommutative Tsen's theorem in dimension one." Journal of Algebra 434 (July 2015): 90–114. http://dx.doi.org/10.1016/j.jalgebra.2015.03.029.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Jakobsche, W., and D. Repovš. "An exotic factor of S3 × ℝ." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 2 (March 1990): 329–44. http://dx.doi.org/10.1017/s0305004100068596.

Full text

Abstract:

Cannon's recognition problem [10] asks for a short list of topological properties that is reasonably easy to check and that characterizes topological manifolds. In dimensions below three the answer has been known for a long time: see [6, 24]. In dimensions above four it is now known, due to the work of J. W. Cannon [11], R. D. Edwards [14] (see also [12] and [18]), and F. S. Quinn [21], that topological n-manifolds (n ≥ 5) are precisely ENR ℤ-homology n-manifolds with Cannon's disjoint disc property (DDP) [11] and with a vanishing Quinn's local surgery obstruction [23]. In dimension four there is a resolution theorem of Quinn [22] (with the same obstruction as in dimensions ≥ 5) and a 1-LCC shrinking theorem of M. Bestvina and J. J. Walsh [5]. However, it is still an open problem to find an effective analogue of Cannon's DDP for this dimension, one which would yield a shrinking theorem along the lines of that of Edwards [14]. For more on the history of the recognition problem see the survey [24].

APA, Harvard, Vancouver, ISO, and other styles

31

Laskowski, Michael Chris. "Uncountable theories that are categorical in a higher power." Journal of Symbolic Logic 53, no. 2 (June 1988): 512–30. http://dx.doi.org/10.1017/s0022481200028437.

Full text

Abstract:

AbstractIn this paper we prove three theorems about first-order theories that are categorical in a higher power. The first theorem asserts that such a theory either is totally categorical or there exist prime and minimal models over arbitrary base sets. The second theorem shows that such theories have a natural notion of dimension that determines the models of the theory up to isomorphism. From this we conclude that I(T,ℵα,) = ℵ0 + ∣α∣ where ℵα = the number of formulas modulo T-equivalence provided that T is not totally categorical. The third theorem gives a new characterization of these theories.

APA, Harvard, Vancouver, ISO, and other styles

32

Matsumoto, Kazuko. "On the cohomological completeness of q-complete domains with corners." Nagoya Mathematical Journal 168 (2002): 105–12. http://dx.doi.org/10.1017/s0027763000008382.

Full text

Abstract:

AbstractWe prove the vanishing and non-vanishing theorems for an intersection of a finite number of q-complete domains in a complex manifold of dimension n. When q does not divide n, it is stronger than the result naturally obtained by combining the approximation theorem of Diederich-Fornaess for q-convex functions with corners and the vanishing theorem of Andreotti-Grauert for q-complete domains. We also give an example which implies our result is best possible.

APA, Harvard, Vancouver, ISO, and other styles

33

Erlich, Yossi, Dan Chazan, Scott Petrack, and Avraham Levy. "Lower Bound on VC-Dimension by Local Shattering." Neural Computation 9, no. 4 (May 1, 1997): 771–76. http://dx.doi.org/10.1162/neco.1997.9.4.771.

Full text

Abstract:

We show that the VC-dimension of a smoothly parameterized function class is not less than the dimension of any manifold in the parameter space, as long as distinct parameter values induce distinct decision boundaries. A similar theorem was published recently and used to introduce lower bounds on VC-dimension for several cases (Lee, Bartlett, & Williamson, 1995). This theorem is not correct, but our theorem could replace it for those cases and many other practical ones.

APA, Harvard, Vancouver, ISO, and other styles

34

Pąk, Karol. "Brouwer Invariance of Domain Theorem." Formalized Mathematics 22, no. 1 (March 30, 2014): 21–28. http://dx.doi.org/10.2478/forma-2014-0003.

Full text

Abstract:

Summary In this article we focus on a special case of the Brouwer invariance of domain theorem. Let us A, B be a subsets of εn, and f : A → B be a homeomorphic. We prove that, if A is closed then f transform the boundary of A to the boundary of B; and if B is closed then f transform the interior of A to the interior of B. These two cases are sufficient to prove the topological invariance of dimension, which is used to prove basic properties of the n-dimensional manifolds, and also to prove basic properties of the boundary and the interior of manifolds, e.g. the boundary of an n-dimension manifold with boundary is an (n − 1)-dimension manifold. This article is based on [18]; [21] and [20] can also serve as reference books.

APA, Harvard, Vancouver, ISO, and other styles

35

Brattka, Vasco, Stéphane Le Roux, Joseph S. Miller, and Arno Pauly. "Connected choice and the Brouwer fixed point theorem." Journal of Mathematical Logic 19, no. 01 (June 2019): 1950004. http://dx.doi.org/10.1142/s0219061319500041.

Full text

Abstract:

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes.

APA, Harvard, Vancouver, ISO, and other styles

36

Bavula, V. V., and T. H. Lenagan. "A Bernstein-Gabber-Joseph theorem for affine algebras." Proceedings of the Edinburgh Mathematical Society 42, no. 2 (June 1999): 311–32. http://dx.doi.org/10.1017/s0013091500020277.

Full text

Abstract:

Bernstein's famous result, that any non-zero module M over the n-th Weyl algebra An satisfies GKdim(M)≥GKdim(An)/2, does not carry over to arbitrary simple affine algebras, as is shown by an example of McConnell. Bavula introduced the notion of filter dimension of simple algebra to explain this failure. Here, we introduce the faithful dimension of a module, a variant of the filter dimension, to investigate this phenomenon further and to study a revised definition of holonomic modules. We compute the faithful dimension for certain modules over a variant of the McConnell example to illustrate the utility of this new dimension.

APA, Harvard, Vancouver, ISO, and other styles

37

Prasad, K., Nupur Nandini, and Divya Shenoy. "Rank and dimension functions." Electronic Journal of Linear Algebra 29 (September 20, 2015): 144–55. http://dx.doi.org/10.13001/1081-3810.2999.

Full text

Abstract:

In this paper, we invoke theory of generalized inverses and minus partial order on regular matrices over a commutative ring to define rankâfunction for regular matrices and dimensionâfunction for finitely generated projective modules which are direct summands of a free module. Some properties held by the rank of a matrix and the dimension of a vector space over a field are generalized. Also, a generalization of rank-nullity theorem has been established when the matrix given is regular.

APA, Harvard, Vancouver, ISO, and other styles

38

Crabb, Michael C., and Pedro L. Q. Pergher. "Limiting cases of Boardman's five halves theorem." Proceedings of the Edinburgh Mathematical Society 56, no. 3 (June 28, 2013): 723–32. http://dx.doi.org/10.1017/s0013091513000400.

Full text

Abstract:

AbstractThe famous five halves theorem of Boardman states that, if T: Mm → Mm is a smooth involution defined on a non-bounding closed smooth m-dimensional manifold Mm (m > 1) and ifis the fixed-point set of T, where Fj denotes the union of those components of F having dimension j, then 2m ≤ 5n. If the dimension m is written as m = 5k − c, where k ≥ 1 and 0 ≤ c < 5, the theorem states that the dimension n of the fixed submanifold is at least β(m), where β(m) = 2k if c = 0, 1, 2 and β(m) = 2k − 1 if c = 3, 4. In this paper, we give, for each m > 1, the equivariant cobordism classification of involutions (Mm, T), for which the fixed submanifold F attains the minimal dimension β(m).

APA, Harvard, Vancouver, ISO, and other styles

39

DOOLEY, ANTHONY H., and RIKA HAGIHARA. "Computing the critical dimensions of Bratteli–Vershik systems with multiple edges." Ergodic Theory and Dynamical Systems 32, no. 1 (April 5, 2011): 103–17. http://dx.doi.org/10.1017/s0143385710000969.

Full text

Abstract:

AbstractThe critical dimension is an invariant that measures the growth rate of the sums of Radon–Nikodym derivatives for non-singular dynamical systems. We show that for Bratteli–Vershik systems with multiple edges, the critical dimension can be computed by a formula analogous to the Shannon–McMillan–Breiman theorem. This extends earlier results of Dooley and Mortiss on computing the critical dimensions for product and Markov odometers on infinite product spaces.

APA, Harvard, Vancouver, ISO, and other styles

40

RI, SONG-IL. "BOX DIMENSION OF A NONLINEAR FRACTAL INTERPOLATION CURVE." Fractals 27, no. 03 (May 2019): 1950023. http://dx.doi.org/10.1142/s0218348x19500233.

Full text

Abstract:

In this paper, we present a delightful method to estimate the lower and upper box dimensions of a special nonlinear fractal interpolation curve. We use Rakotch contractibility and monotone property of function in the estimation of upper box dimension, and we use Rakotch contractibility, noncollinearity of interpolation points, nondecreasing property of function, convex (or concave) property of function and differential mean value theorem in the estimation of lower box dimension. In particular, we propose a well-founded conjecture motivated by our results.

APA, Harvard, Vancouver, ISO, and other styles

41

Zhao, Yi-Bo, and Zhen-Qiang Yin. "Apply current exponential de Finetti theorem to realistic quantum key distribution." International Journal of Modern Physics: Conference Series 33 (January 2014): 1460370. http://dx.doi.org/10.1142/s2010194514603706.

Full text

Abstract:

In the realistic quantum key distribution (QKD), Alice and Bob respectively get a quantum state from an unknown channel, whose dimension may be unknown. However, while discussing the security, sometime we need to know exact dimension, since current exponential de Finetti theorem, crucial to the information-theoretical security proof, is deeply related with the dimension and can only be applied to finite dimensional case. Here we address this problem in detail. We show that if POVM elements corresponding to Alice and Bob's measured results can be well described in a finite dimensional subspace with sufficiently small error, then dimensions of Alice and Bob's states can be almost regarded as finite. Since the security is well defined by the smooth entropy, which is continuous with the density matrix, the small error of state actually means small change of security. Then the security of unknown-dimensional system can be solved. Finally we prove that for heterodyne detection continuous variable QKD and differential phase shift QKD, the collective attack is optimal under the infinite key size case.

APA, Harvard, Vancouver, ISO, and other styles

42

ELLIOTT, GEORGE A. "DIMENSION GROUPS WITH TORSION." International Journal of Mathematics 01, no. 04 (December 1990): 361–80. http://dx.doi.org/10.1142/s0129167x90000198.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Boege, Margareta, Jerzy Dydak, Rolando Jiménez, Akira Koyama, and Evgeny V. Shchepin. "Borsuk–Sieklucki theorem in cohomological dimension theory." Fundamenta Mathematicae 171, no. 3 (2002): 213–22. http://dx.doi.org/10.4064/fm171-3-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Yamaguchi, Tatao. "Collapsing and soul theorem in three-dimension." Séminaire de théorie spectrale et géométrie 15 (1997): 163–66. http://dx.doi.org/10.5802/tsg.188.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

ALONSO-GONZÁLEZ, CLEMENTA. "Infinitesimal Hartman-Grobman Theorem in Dimension Three." Anais da Academia Brasileira de Ciências 87, no. 3 (September 2015): 1499–503. http://dx.doi.org/10.1590/0001-3765201520140094.

Full text

Abstract:

ABSTRACTIn this paper we give the main ideas to show that a real analytic vector field in R3 with a singular point at the origin is locally topologically equivalent to its principal part defined through Newton polyhedra under non-degeneracy conditions.

APA, Harvard, Vancouver, ISO, and other styles

46

Heuberger, Clemens. "Hwang's Quasi-Power-Theorem in Dimension Two." Quaestiones Mathematicae 30, no. 4 (December 2007): 507–12. http://dx.doi.org/10.2989/16073600709486217.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

SCHOEN, TOMASZ, and ILYA D. SHKREDOV. "ADDITIVE DIMENSION AND A THEOREM OF SANDERS." Journal of the Australian Mathematical Society 100, no. 1 (October 22, 2015): 124–44. http://dx.doi.org/10.1017/s1446788715000324.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Hillman, Jonathan A. "A homotopy fibration theorem in dimension four." Topology and its Applications 33, no. 2 (October 1989): 151–61. http://dx.doi.org/10.1016/s0166-8641(89)80004-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Pasynkov, B. A. "On the subset theorem in dimension theory." Topology and its Applications 155, no. 17-18 (October 2008): 1909–18. http://dx.doi.org/10.1016/j.topol.2007.04.031.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Nurowski, Paweł, and Arman Taghavi-Chabert. "A Goldberg–Sachs theorem in dimension three." Classical and Quantum Gravity 32, no. 11 (May 12, 2015): 115009. http://dx.doi.org/10.1088/0264-9381/32/11/115009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!