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2. Industry 4.0 Maturity and Readiness Models: A Systematic Literature Review and Future Framework.
- Author
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Hajoary, Pinosh Kumar
- Subjects
INDUSTRY 4.0 ,PREPAREDNESS ,CORPORATE culture ,COMPUTER software quality control ,PUBLIC officers ,BUSINESS models ,THEMATIC analysis ,TECHNOLOGY assessment - Abstract
Over the last five years, Industry 4.0 (I4.0) has gained a lot of attention from industry leaders, policymakers, and government officials worldwide. In an era where new concepts and techniques are introduced continuously, there is a lack of systematic literature review (SLR) on identifying main dimensions, levels, methods to assess the maturity and readiness level toward I4.0. To address this gap, we have chosen our primary objective to provide a critical review of existing literature on dimensions, methods, levels, and current trends to evaluate the I4.0 maturity and readiness models. A Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) methodology was adopted to make sure that there is no replication and to maintain complete transparency in the review process. A total of 53 papers were deemed relevant for thematic analysis. From the literature, we have found and proposed 10 main dimensions — Strategy and Organization, Manufacturing and Operations, Supply Chain, Business Model, IT, People, Customers, Product, Services, and Culture, to assess the I4.0 maturity and readiness levels of an organization. Further, a conceptual framework was proposed for the same. This study contributes theoretically to the development of I4.0 maturity and readiness models. So far, this is the first review paper on dimensions of I4.0 maturity and readiness models and is expected to give future researchers and practitioners a holistic guideline to design and develop I4.0 maturity and readiness models. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
3. A NEW PERSPECTIVE ON THE NONLINEAR DATE–JIMBO–KASHIWARA–MIWA EQUATION IN FRACTAL MEDIA.
- Author
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SUN, JIANSHE
- Subjects
- *
NONLINEAR equations , *DIFFERENTIAL calculus , *FRACTIONAL calculus , *VARIATIONAL principles , *PARTIAL differential equations , *FRACTALS , *DIMENSIONS - Abstract
In this paper, we first created a fractal Date–Jimbo–Kashiwara–Miwa (FDJKM) long ripple wave model in a non-smooth boundary or microgravity space recorded. Using fractal semi-inverse skill (FSIS) and fractal traveling wave transformation (FTWT), the fractal variational principle (FVP) was derived, and the strong minimum necessary circumstance was attested with the He Wierstrass function. We have discovered two distinct solitary wave solutions, the square form of the hyperbolic secant function and the hyperbolic secant function form. Then, soliton solutions are cultivated through FVP and the minimum steady state condition. Finally, the influences of non-smooth boundaries on solitons were tackled, and the properties of the solution were demonstrated through three-dimensional contour lines. Fractal dimension can impact waveforms, but cannot affect their vertex values. The presentation of soliton solutions (SWS) using techniques is not only laudable but also noteworthy. The technique employed can also be used to investigate solitary wave solutions of other local fractional calculus partial differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. KMD Quest-SW: A Diagnosis of Knowledge Management Addressed to Software Industry SMEs.
- Author
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Pinto, Danieli, Tenório, Nelson, Bortolozzi, Flávio, and Menegassi, Cláudia Herrero Martins
- Subjects
COMPUTER software industry ,KNOWLEDGE management ,SMALL business ,INFORMATION sharing ,CONSUMER expertise - Abstract
The software industry depends intensively on its actor's knowledge to develop its products. This knowledge is crucial to leverage innovation and market sustainability within the software industry companies. Knowledge Management (KM) processes are accomplished in the small- and medium-sized software industry companies daily, however, sometimes not formally. This paper proposes a questionnaire aimed to diagnose KM in small- and medium-sized enterprises (SME) of the software industry, namely, KMD Quest-SW. The KMD Quest-SW was designed to fill up the gap of KM diagnosis in SME in the software industry. The KMD Quest-SW has 46 statements distributed in six dimensions: so-called creation process, registration process, knowledge sharing, knowledge use, innovation process, and knowledge in the software industry. From the software industry perspective, our proposal appears as a promising tool to diagnose and map the knowledge flow in SMEs. From a scientific perspective, the questionnaire breaks new grounds for KM theoretically and practitioners to be adapted for other SME companies interested in KM. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. QUASISYMMETRIC PACKING-MINIMALITY OF MORAN SETS.
- Author
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LI, YANZHE, QIAO, YU, and LOU, MANLI
- Subjects
DIMENSIONS - Abstract
In this paper, we prove that a large class of Moran sets on the line with packing dimension 1 is quasisymmetrically packing-minimal. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
6. CONSTRUCTION AND ANALYSIS OF A SPECIAL ONE-DIMENSIONAL CONTINUOUS FUNCTION.
- Author
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WANG, J. and YAO, K.
- Subjects
CONTINUOUS functions ,DIMENSIONS ,LEBESGUE measure ,FUNCTIONS of bounded variation ,OSCILLATIONS - Abstract
In this paper, the definition of unbounded variation point is introduced firstly. Then, we construct a continuous function containing uncountable unbounded variation points on the basis of Devil stair function. Finally, a mass of meaningful properties have been proved, such as Box dimension of continuous function constructed in the paper is 1 and the continuous function has infinite length on [0,1]. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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7. INTERMEDIATE ASSOUAD-LIKE DIMENSIONS FOR MEASURES.
- Author
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HARE, KATHRYN E. and HARE, KEVIN G.
- Subjects
DIMENSIONS - Abstract
The upper and lower Assouad dimensions of a metric space are local variants of the box dimensions of the space and provide quantitative information about the 'thickest' and 'thinnest' parts of the set. Less extreme versions of these dimensions for sets have been introduced, including the upper and lower quasi-Assouad dimensions, 𝜃 -Assouad spectrum, and Φ -dimensions. In this paper, we study the analogue of the upper and lower Φ -dimensions for measures. We give general properties of such dimensions, as well as more specific results for self-similar measures satisfying various separation properties and discrete measures. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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8. Positive curvature and symmetry in small dimensions.
- Author
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Amann, Manuel and Kennard, Lee
- Subjects
SYMMETRY ,CURVATURE ,TORUS ,MANIFOLDS (Mathematics) ,DIFFEOMORPHISMS ,DIMENSIONS - Abstract
Extending existing work in small dimensions, Dessai computed the Euler characteristic, signature, and elliptic genus for 8 -manifolds of positive sectional curvature in the presence of torus symmetry. He also computes the diffeomorphism type by restricting his results to classes of manifolds known to admit non-negative curvature, such as biquotients. The first part of this paper extends Dessai's calculations to even dimensions up to 1 6. In particular, we obtain a first characterization of the Cayley plane in such a setting. The second part studies a closely related family of manifolds called positively elliptic manifolds, and we prove a conjecture of Halperin in this context for dimensions up to 1 6 or Euler characteristics up to 1 6. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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9. Asymptotic behavior of normalized dimensions of standard and strict Young diagrams - growth and oscillations.
- Author
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Duzhin, V. S. and Vasilyev, N. N.
- Subjects
YOUNG tableaux ,DIMENSIONS ,GROUP theory ,MATHEMATICAL sequences ,OSCILLATION theory of difference equations ,FINITE differences - Abstract
In this paper, we present the results of a computer investigation of asymptotics for maximum dimensions of linear and projective representations of the symmetric group. This problem reduces the investigation of standard and strict Young diagrams of maximum dimensions. We constructed some sequences for both standard and strict Young diagrams with extremely large dimensions. The conjecture that the limit of normalized dimensions exists was proposed by Vershik 30 years ago [A. M. Vershit and S. V. Kerov, Funktsional Anal. i Prilozhen 19(1) (1985) 25-36] and has not been proved yet. We studied the growth and oscillations of the normalized dimension function in sequences of Young diagrams. Our approach is based on analyzing finite differences of their normalized dimensions. This analysis also allows us to give much more precise estimation of the limit constants. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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10. Exact optical solutions of the (2+1) dimensions Kundu–Mukherjee–Naskar model via the new extended direct algebraic method.
- Author
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Günerhan, Hatıra, Khodadad, Farid Samsami, Rezazadeh, Hadi, and Khater, Mostafa M. A.
- Subjects
EQUATIONS ,DIMENSIONS - Abstract
In this work, the researchers for computing an exact solution of the (2 + 1) dimensions Kundu–Mukherjee–Naskar (KMN) equation used a newly developed technique, namely, the new extended direct algebraic method. This powerful method gives an exact solution to the KMN equation considered in this paper. The results are new and attest to the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
11. Low energy configurations of topological singularities in two dimensions: A Γ-convergence analysis of dipoles.
- Author
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De Luca, Lucia and Ponsiglione, Marcello
- Subjects
MODELS & modelmaking ,MEASURE theory ,VORTEX motion ,CALCULUS of variations ,MATHEMATICAL decoupling ,DIMENSIONS - Abstract
This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg–Landau energy. Denoting by 𝜀 the length scale parameter in such models, we focus on the | log 𝜀 | energy regime. It is well known that, for configurations whose energy is bounded by c | log 𝜀 | , the vorticity measures can be decoupled into the sum of a finite number of Dirac masses, each one of them carrying π | log 𝜀 | energy, plus a measure supported on small zero-average sets. Loosely speaking, on such sets the vorticity measure is close, with respect to the flat norm, to zero-average clusters of positive and negative masses. Here, we perform a compactness and Γ -convergence analysis accounting also for the presence of such clusters of dipoles (on the range scale 𝜀 s , for 0 < s < 1), which vanish in the flat convergence and whose energy contribution has, so far, been neglected. Our results refine and contain as a particular case the classical Γ -convergence analysis for vortices, extending it also to low energy configurations consisting of just clusters of dipoles, and whose energy is of order c | log 𝜀 | with c < π. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
12. Bounds on the sum of broadcast domination number and strong metric dimension of graphs.
- Author
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Yi, Eunjeong
- Subjects
GRAPH connectivity ,GEOMETRIC vertices ,GEODESICS ,DIMENSIONS ,BROADCASTING industry - Abstract
Let G be a connected graph of order at least two with vertex set V (G). For x , y ∈ V (G) , let d (x , y) denote the length of an x − y geodesic in G. A function f : V (G) → ℤ + ∪ { 0 } is called a dominating broadcast function of G if, for each vertex x ∈ V (G) , there exists a vertex y ∈ V (G) such that f (y) > 0 and d (x , y) ≤ f (y) , and the broadcast domination number, γ b (G) , of G is the minimum of ∑ z ∈ V (G) f (z) over all dominating broadcast functions f of G. For u , v ∈ V (G) , let S { u , v } denote the set of vertices w ∈ V (G) such that either u lies on a v − w geodesic or v lies on a u − w geodesic of G. Let g : V (G) → { 0 , 1 } be a function and, for any U ⊆ V (G) , let g (U) = ∑ α ∈ U g (α). We say that g is a strong resolving function of G if g (S { u , v }) ≥ 1 for every pair of distinct vertices u , v ∈ V (G) , and the strong metric dimension, sdim (G) , of G is the minimum of ∑ z ∈ V (G) g (z) over all strong resolving functions g of G. For any connected graph G , we show that 2 ≤ γ b (G) + sdim (G) ≤ | V (G) | ; we characterize G satisfying γ b (G) + sdim (G) equals two and three, respectively, and characterize unicyclic graphs achieving γ b (G) + sdim (G) = | V (G) |. For any tree T of order at least three, we show that γ b (T) + sdim (T) ≤ | V (T) | − 1 , and characterize trees achieving equality. Moreover, for a tree T of order n ≥ 2 , we obtain the results that γ b (T) + sdim (T) ≤ n − rad (T) if T is central, and that γ b (T) + sdim (T) ≤ n − rad (T) + 1 if T is bicentral; in each case, we characterize trees achieving equality. We conclude this paper with some remarks and an open problem. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
13. ON THE DECOMPOSITION OF CONTINUOUS FUNCTIONS AND DIMENSIONS.
- Author
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LIU, JIA and LIU, DEZHI
- Subjects
FRACTAL dimensions ,REAL numbers ,CONTINUOUS functions ,DIMENSIONS - Abstract
In this paper, we consider decomposition of continuous functions in C ([ 0 , 1 ]) in terms of Hausdorff dimension and lower box dimension. Precisely, we show that, given real numbers 1 ≤ α ≤ β ≤ 2 , any real-valued continuous function in C ([ 0 , 1 ]) can be decomposed into a sum of two real-valued continuous functions each having a graph of Hausdorff dimension α and lower box dimension β. This generalizes a theorem of Wingren, also Wu and the present author. We also consider the arbitrary decomposition of continuous functions in terms of Hausdorff dimension and lower box dimension. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
14. The metric dimension of the enhanced power graph of a finite group.
- Author
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Ma, Xuanlong and She, Yanhong
- Subjects
FINITE groups ,COMMUTATIVE rings ,DIMENSIONS ,QUATERNIONS - Abstract
The enhanced power graph of a finite group G is the graph whose vertex set is G , and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this paper, we establish an explicit formula for the metric dimension of an enhanced power graph. As an application, we compute the metric dimension of the enhanced power graph of an elementary abelian p -group, a dihedral group and a generalized quaternion group. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
15. The Cauchy problem for an Oldroyd-B model in three dimensions.
- Author
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Wang, Wenjun and Wen, Huanyao
- Subjects
CAUCHY problem ,SOBOLEV spaces ,NAVIER-Stokes equations ,DIMENSIONS ,MATHEMATICS ,EQUATIONS - Abstract
We consider an Oldroyd-B model which is derived in Ref. 4 [J. W. Barrett, Y. Lu and E. Süli, Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model, Commun. Math. Sci.15 (2017) 1265–1323] via micro–macro-analysis of the compressible Navier–Stokes–Fokker–Planck system. The global well posedness of strong solutions as well as the associated time-decay estimates in Sobolev spaces for the Cauchy problem are established near an equilibrium state. The terms related to η , in the equation for the extra stress tensor and in the momentum equation, lead to new technical difficulties, such as deducing L t 2 L x 2 -norm dissipative estimates for the polymer number density and its spatial derivatives. One of the main objectives of this paper is to develop a way to capture these dissipative estimates via a low–medium–high-frequency decomposition. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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16. Homology and Cohomology of the Super Schrödinger Algebra S(1/1) with Coefficients in the Trivial Module*.
- Author
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He, Yan, Wu, Yuezhu, and Zhu, Linsheng
- Subjects
ALGEBRA ,SPACETIME ,DIMENSIONS - Abstract
In this paper we study the homology and cohomology groups of the super Schrödinger algebra S (1 / 1) in (1 + 1)-dimensional spacetime. We explicitly compute the homology groups of S (1 / 1) with coefficients in the trivial module. Then using duality, we finally obtain the dimensions of the cohomology groups of S (1 / 1) with coefficients in the trivial module. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
17. Sobolev spaces with respect to a weighted Gaussian measure in infinite dimensions.
- Author
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Ferrari, S.
- Subjects
GAUSSIAN measures ,SOBOLEV spaces ,BANACH spaces ,DIMENSIONS - Abstract
Let X be a separable Banach space endowed with a nondegenerate centered Gaussian measure μ and let w be a positive function on X such that w ∈ W 1 , s (X , μ) and log w ∈ W 1 , t (X , μ) for some s > 1 and t > s ′ . In this paper, we introduce and study Sobolev spaces with respect to the weighted Gaussian measure ν : = w μ. We obtain results regarding the divergence operator (i.e. the adjoint in L 2 of the gradient operator along the Cameron–Martin space) and the trace of Sobolev functions on hypersurfaces x ∈ X | G (x) = 0 , where G is a suitable version of a Sobolev function. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
18. The study of complexitons and periodic solitary-wave solutions with fifth-order KdV equation in (2+1) dimensions.
- Author
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Tahir, Muhammad and Awan, Aziz Ullah
- Subjects
EQUATIONS ,PAINLEVE equations ,BILINEAR forms ,DIMENSIONS - Abstract
In this paper, the generalized fifth-order (2 + 1)-dimensional KdV equation is scrutinized via the extended homoclinic test technique (EHTT) and extended transformed rational function (ETRF) method. With the aid of Hirota's bilinear form, various exact solutions comprising, periodic solitary-wave, kinky-periodic solitary-wave, periodic soliton and complexiton solutions are constructed. Moreover, the mechanical features and dynamic characteristics of the obtained solutions are presented by three-dimensional plots. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
19. Homological dimensions of skew group algebras.
- Author
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Xiang, Yueming and Ouyang, Lunqun
- Subjects
HOMOLOGICAL algebra ,GROUP algebras ,DIMENSIONS - Abstract
Let Λ be a finite dimensional algebra over a field k and H a subgroup of a finite group G. In this paper, we consider the Gorenstein global dimensions and representation dimensions of the skew group algebras Λ G and Λ H. Under the assumption that Λ G is a separable extension over Λ H , we show that Λ G and Λ H share the same Gorenstein global dimensions and representation dimensions. As an application, we give an affirmative answer for a conjecture raised in [Adjoint functors and representation dimensions, Acta Math. Sinica 22(2) (2006) 625–640]. Several known results are then obtained as corollaries. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
20. Metamaterial-based fuel sensor application with three rhombus slots.
- Author
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Tümkaya, Mehmet Ali, Ünal, Emin, and Sabah, Cumali
- Subjects
FUEL ,DETECTORS ,RESONATORS ,MICROWAVE heating ,MICROWAVES ,DIMENSIONS - Abstract
In this paper, a sensor structure operating in the microwave frequency band is used and it is aimed to determine whether fuel samples are branded or not. In the literature, the studies on the sensor applications of metamaterials (MTMs) have increased considerably in recent years. However, this study, unlike other studies, focuses on determining the changes in electromagnetic parameters of different fuel samples at X band frequencies. For this purpose, the electromagnetic properties of the branded and unbranded fuel samples are measured experimentally. Then, simulation studies are carried out using the experimental results and the dimensions of the resonators are optimized to determine the most suitable structure. Fabrication of MTM sensor structure is then performed using optimized dimensions. Finally, the experimental study is carried out using the sensor structure. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
21. A REVISIT TO α-FRACTAL FUNCTION AND BOX DIMENSION OF ITS GRAPH.
- Author
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VERMA, S. and VISWANATHAN, P.
- Subjects
APPROXIMATION theory ,FRACTALS ,FRACTAL analysis ,CONTINUOUS functions ,INTERPOLATION ,DIMENSIONS - Abstract
One of the tools offered by fractal geometry is fractal interpolation, which forms a basis for the constructive approximation theory for nondifferentiable functions. The notion of fractal interpolation function can be used to obtain a wide spectrum of self-referential functions associated to a prescribed continuous function on a compact interval in ℝ. These fractal maps, the so-called α -fractal functions, are defined by means of suitable iterated function system which involves some parameters. Building on the literature related to the notion of α -fractal functions, the current study targets to record the continuous dependence of the α -fractal function on parameters involved in its definition. Furthermore, the paper attempts to study the box dimension of the graph of the α -fractal function. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
22. Overlapping sliced inverse regression for dimension reduction.
- Author
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Zhang, Ning, Yu, Zhou, and Wu, Qiang
- Subjects
DIMENSIONS ,ALGORITHMS - Abstract
Sliced inverse regression (SIR) is a pioneer tool for supervised dimension reduction. It identifies the effective dimension reduction space, the subspace of significant factors with intrinsic lower dimensionality. In this paper, we propose to refine the SIR algorithm through an overlapping slicing scheme. The new algorithm, called overlapping SIR (OSIR), is able to estimate the effective dimension reduction space and determine the number of effective factors more accurately. We show that such overlapping procedure has the potential to identify the information contained in the derivatives of the inverse regression curve, which helps to explain the superiority of OSIR. We also prove that OSIR algorithm is n -consistent and verify its effectiveness by simulations and real applications. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
23. On dimensions supporting a rational projective plane.
- Author
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Kennard, Lee and Su, Zhixu
- Subjects
PROJECTIVE spaces ,BERNOULLI numbers ,DIMENSIONS ,QUADRATIC equations ,PROJECTIVE planes ,CONGRUENCES & residues - Abstract
A rational projective plane ( ℚ ℙ 2 ) is a simply connected, smooth, closed manifold M such that H ∗ (M ; ℚ) ≅ ℚ [ α ] / 〈 α 3 〉. An open problem is to classify the dimensions at which such a manifold exists. The Barge–Sullivan rational surgery realization theorem provides necessary and sufficient conditions that include the Hattori–Stong integrality conditions on the Pontryagin numbers. In this paper, we simplify these conditions and combine them with the signature equation to give a single quadratic residue equation that determines whether a given dimension supports a ℚ ℙ 2 . We then confirm the existence of a ℚ ℙ 2 in two new dimensions and prove several non-existence results using factorization of the numerators of the divided Bernoulli numbers. We also resolve the existence question in the Spin case, and we discuss existence results for the more general class of rational projective spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
24. BOUNDARY DIMENSIONS OF FRACTAL TILINGS.
- Author
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OUYANG, PEICHANG, YI, HUA, DENG, ZHIYUN, HUANG, XUAN, and YU, TAO
- Subjects
BOUNDARY value problems ,DIMENSIONS ,FRACTAL analysis ,EUCLIDEAN distance ,MATHEMATICAL formulas - Abstract
A fractal tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. In this paper, we investigate the boundary dimension of - and -tilings. We first derive an explicit recursion formula for the boundary edges of - and -tilings. Then we present an analytical expression for their fractal boundary dimensions using matrix methods. Results indicate that, as increases, the boundaries of - and -tilings will degenerate into general Euclidean curves. The method proposed in this paper can be extended to compute the boundary dimensions of other kinds of fractal tilings. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
25. Global dimension of Harada rings and serial rings.
- Author
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Koike, Kazutoshi
- Subjects
DIMENSIONS ,RING theory ,MATHEMATICAL proofs ,MATHEMATICAL analysis ,NUMERICAL analysis - Abstract
Baba [On Harada rings and quasi-Harada rings with left global dimension at most 2. Comm. Algebra 28(6) (2000) 2671-2684] proved that every left Harada rings with global dimension at most 2 is a serial ring. In this paper, improving the result, we show that every left Harada ring with global dimension at most 3 is a serial ring. We also prove that if a left Harada ring A of finite global dimension is of type (*) or has homogeneous right socle, then A is serial. Finally, we give an example of a non-serial left Harada ring of finite global dimension. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
26. LOWER TYPE DIMENSIONS OF SOME MORAN SETS.
- Author
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YANG, JIAOJIAO
- Subjects
DIMENSIONS - Abstract
In this paper, we discuss the lower type dimensions for some Moran sets. On one hand, for Moran set E with c ∗ > 0 , we prove that dim q L E = sup f dim L f (E) , where the supremum is taken over all quasi-Lipschitz mappings f. On the other hand, we obtain the lower spectrum formula for homogeneous Moran sets. In the proof a lower spectrum formula for a large class of fractal sets is established. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
27. The finiteness of the Gorenstein dimension for Artin algebras.
- Author
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Marczinzik, René
- Subjects
GORENSTEIN rings ,ARTIN algebras ,ARTIN rings ,INDECOMPOSABLE modules ,FINITE, The ,DIMENSIONS ,ALGEBRA - Abstract
In [A. Skowronski, S. Smalø and D. Zacharia, On the finiteness of the global dimension for Artinian rings, J. Algebra251(1) (2002) 475–478], the authors proved that an Artin algebra A with infinite global dimension has an indecomposable module with infinite projective and infinite injective dimension, giving a new characterization of algebras with finite global dimension. We prove in this paper that an Artin algebra A that is not Gorenstein has an indecomposable A -module with infinite Gorenstein projective dimension and infinite Gorenstein injective dimension, which gives a new characterization of algebras with finite Gorenstein dimension. We show that this gives a proper generalization of the result in [A. Skowronski, S. Smalø and D. Zacharia, On the finiteness of the global dimension for Artinian rings, J. Algebra251(1) (2002) 475–478] for Artin algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
28. Graded Lie Algebras of Dimension Five and Some Artin–Schelter Regular Algebras.
- Author
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Shen, Yuan
- Subjects
LIE algebras ,UNIVERSAL algebra ,ALGEBRA ,ARTIN algebras ,AUTOMORPHISMS ,DIMENSIONS - Abstract
In this paper, we show that there are only seven graded Lie algebras of dimension 5 generated in degree 1 up to isomorphism. By parameterizing the relations of the universal enveloping algebras of three of those graded Lie algebras, we construct some new Artin–Schelter regular algebras of global dimension 5. We prove that those algebras are all strongly noetherian, Auslander regular and Cohen–Macaulay, and describe their Nakayama automorphisms. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
29. BOX DIMENSION OF WEYL–MARCHAUD FRACTIONAL DERIVATIVE OF LINEAR FRACTAL INTERPOLATION FUNCTIONS.
- Author
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PENG, WEN LIANG, YAO, KUI, ZHANG, XIA, and YAO, JIA
- Subjects
INTERPOLATION ,FRACTAL analysis ,DIMENSIONS ,BOXES - Abstract
This paper mainly explores Weyl–Marchaud fractional derivative of linear fractal interpolation functions (FIFs). We prove that Weyl–Marchaud fractional derivative of a linear FIF is still a linear FIFs. More generally, we get a conclusion that there exists some linear relationship between the order of Weyl–Marchaud fractional derivative and box dimension of linear FIFs. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
30. Dimension on non-essential submodules.
- Author
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Davoudian, Maryam
- Subjects
NOETHERIAN rings ,ORDINAL numbers ,ASSOCIATIVE rings ,DIMENSIONS - Abstract
In this paper, we introduce and study the concepts of non-essential Krull dimension and non-essential Noetherian dimension of an R -module, where R is an arbitrary associative ring. These dimensions are ordinal numbers and extend the notion of Krull dimension. They respectively rely on the behavior of descending and ascending chains of non-essential submodules. It is proved that each module with non-essential Krull dimension (respectively, non-essential Noetherian dimension) has finite Goldie dimension. We also show that a semiprime ring R with non-essential Noetherian dimension is uniform. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
31. Dimension of noncommutative plane curves.
- Author
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Jøndrup, Søren
- Subjects
PLANE curves ,DIMENSIONS - Abstract
In this paper, we prove that an algebra of the form k 〈 x , y 〉 / (f) is never right (or left) artinian in case (f) is a proper ideal and k is an uncountable, algebraically closed field of characteristic 0. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
32. Solving systems of multi-term fractional PDEs: Invariant subspace approach.
- Author
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Choudhary, Sangita and Daftardar-Gejji, Varsha
- Subjects
INVARIANT subspaces ,PARTIAL differential equations ,SPACETIME ,FRACTIONAL calculus ,DIMENSIONS - Abstract
In the present paper, invariant subspace method has been extended for solving systems of multi-term fractional partial differential equations (FPDEs) involving both time and space fractional derivatives. Further, the method has also been employed for solving multi-term fractional PDEs in (1 + n) dimensions. A diverse set of examples is solved to illustrate the method. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
33. Cubulated moves for 2-knots.
- Author
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Díaz, Juan Pablo, Hinojosa, Gabriela, and Verjosvky, Alberto
- Subjects
KNOT theory ,FINITE fields ,GEOMETRIC series ,DIMENSIONS ,DISCRETE systems - Abstract
In this paper, we prove that given two cubical links of dimension two in ℝ 4 , they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister and Roseman moves for classical tame knots (links) of dimensions one and two, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
34. Betti numbers of the HOMFLYPT homology.
- Author
-
Wu, Hao
- Subjects
BETTI numbers ,HOMOLOGY theory ,POLYNOMIALS ,MODULE structure in Banach spaces ,DIMENSIONS - Abstract
In [Rasmussen, Khovanov–Rozansky homology of two-bridge knots and links, Duke Math. J.136 (2007) 551–583], Rasmussen observed that the Khovanov–Rozansky homology of a link is a finitely generated module over the polynomial ring generated by the components of this link. In the current paper, we study the module structure of the middle HOMFLYPT homology, especially, the Betti numbers of this module. For each link, these Betti numbers are supported on a finite subset of ℤ 4 . One can easily recover from these Betti numbers the Poincaré polynomial of the middle HOMFLYPT homology. We explain why the Betti numbers can be viewed as a generalization of the reduced HOMFLYPT homology of knots. As an application, we prove that the projective dimension of the middle HOMFLYPT homology is additive under split union of links and provides a new obstruction to split links. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
35. Constructions of rotated lattice constellations in dimensions power of 3.
- Author
-
Ferrari, Agnaldo José and de Andrade, Antonio Aparecido
- Subjects
LATTICE field theory ,DIMENSIONS ,INTEGERS ,REAL numbers ,HOPF algebras ,ISOMORPHISM (Mathematics) - Abstract
In this paper, we present the constructions of rotated ℤ 3 r − 1 -lattices, where r is a positive integer, via ℤ -modules of the ring of the integers ℤ [ ζ 3 r + ζ 3 r − 1 ]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. Lower bounds for the minimum product distances of such construction are also presented. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
36. Time fractional modified anomalous sub-diffusion equation with a nonlinear source term through locally applied meshless radial point interpolation.
- Author
-
Shivanian, Elyas and Jafarabadi, Ahmad
- Subjects
HEAT equation ,INTERPOLATION ,DIMENSIONS ,FRACTIONAL calculus ,MESHFREE methods - Abstract
In this paper, an alternative approach of spectral meshless radial point interpolation (SMRPI) is applied to the modified anomalous fractional sub-diffusion equation with a nonlinear source term in one and two dimensions. The time fractional derivative is described in the Riemann–Liouville sense. The applied approach is based on a combination of meshless methods and the spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct the shape functions which act as basis functions in the frame of the SMRPI. It is proved that the scheme is unconditionally stable with respect to the time variable in H 1 and convergent with the order of convergence 𝒪 ( δ t 1 + γ ) , 0 < γ < 1. In this work, the thin plate splines (TPS) are used as the radial basis functions. In order to eliminate the nonlinearity, a simple predictor–corrector (P–C) scheme is used. The results of numerical experiments are compared to the analytical solutions in order to confirm the accuracy and the efficiency of the presented scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
37. Definitions of solutions to the IBVP for multi-dimensional scalar balance laws.
- Author
-
Rossi, Elena
- Subjects
BOUNDARY value problems ,SCALAR field theory ,BALANCE laws (Mechanics) ,DIMENSIONS ,DIFFERENTIAL equations - Abstract
We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
38. Stabilization in a higher-dimensional attraction-repulsion chemotaxis system if repulsion dominates over attraction.
- Author
-
Lin, Ke, Mu, Chunlai, and Zhou, Deqin
- Subjects
CHEMOTAXIS ,BOUNDARY value problems ,DOMINATING set ,DIMENSIONS ,THEORY of knowledge - Abstract
The long-time behavior of solutions to an attraction-repulsion chemotaxis system is considered in this paper in a bounded domain under zero-flux boundary conditions if repulsion dominates over attraction. It is known that under the assumption that repulsion balances/overbalances attraction in two or higher dimensions, for any suitably regular initial data all solutions of this system will be global and bounded. The present work further shows that if the degradation rate of a repulsive signal is smaller than the attractive one or the repulsion is suitably strong, this global solutions converge to the steady state for arbitrarily large initial data. To the best of our knowledge, these are the first results on the large time of large-data solutions in a higher-dimensional attraction-repulsion chemotaxis system. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
39. A note on (co)homologies of algebras from unpunctured surfaces.
- Author
-
Valdivieso-Díaz, Yadira
- Subjects
HOMOLOGY theory ,COHOMOLOGY theory ,GEOMETRIC vertices ,DIMENSIONS ,TRIANGULATED categories - Abstract
In a previous paper, the author computed the dimension of Hochschild cohomology groups of Jacobian algebras from (unpunctured) triangulated surfaces, and gave a geometric interpretation of those numbers in terms of the number of internal triangles, the number of vertices and the existence of certain kind of boundaries. The aim of this note is to compute the cyclic (co)homology and the Hochschild homology of the same family of algebras and to give an interpretation of those dimensions through elements of the triangulated surface. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
40. Very singular problems with critical nonlinearities in two dimensions.
- Author
-
Prashanth, S., Tiwari, Sweta, and Sreenadh, K.
- Subjects
MATHEMATICAL singularities ,NONLINEAR theories ,DIMENSIONS ,ELLIPTIC curves ,BIFURCATION theory ,EXISTENCE theorems - Abstract
In this paper, we consider the following singular elliptic problem involving an exponential nonlinearity in two dimensions: where is a bounded domain with smooth boundary, , , and . We show the existence and multiplicity of positive solutions globally with respect to the bifurcation parameter . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
41. AN INTERMEDIATE VALUE PROPERTY OF FRACTAL DIMENSIONS OF CARTESIAN PRODUCT.
- Author
-
JIANG, XIAOFANG, LIU, QINGHUI, and WEN, ZHIYING
- Subjects
METRIC spaces ,FRACTAL dimensions ,CARTESIAN coordinates ,DIMENSIONS ,FRACTALS - Abstract
Given two metric spaces , it is well known that, where , denote, respectively, the Hausdorff and packing dimension of . In this paper, we show that, for any , there exist such that the following equalities hold simultaneously: This complete the related results of Wei et al. [C. Wei, S. Y. Wen and Z. X. Wen, Remarks on dimensions of Cartesian product sets, Fractals 24(3) (2016) 1650031]. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
42. On dimension of Schur multiplier of nilpotent Lie algebras II.
- Author
-
Saeedi, F., Arabyani, H., and Niroomand, P.
- Subjects
NILPOTENT Lie groups ,DIMENSIONS ,SCHUR multiplier ,LIE algebras ,HEISENBERG model - Abstract
Let be a non-abelian nilpotent Lie algebra of dimension and put , where denotes the Schur multiplier of . Niroomand and Russo in 2011 proved that and that if and only if , in which is the Heisenberg algebra of dimension and is the abelian -dimensional Lie algebra. In the same year, they also classified all nilpotent Lie algebras satisfying or . In this paper, we obtain all nilpotent Lie algebras provided that . [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
43. Analytical solutions for fermions on a thick brane with a piecewise and smooth warp factor.
- Author
-
Landim, R. R., Tahim, M. O., Alencar, G., and Costa Filho, R. N.
- Subjects
FERMIONS ,DIMENSIONS ,MAGNETIC coupling ,RADIATION ,SPACETIME - Abstract
In this paper, we study analytical solutions for fermion localization in Randall-Sundrum (RS) models. We show that there exist special couplings between scalar fields and fermions giving us discrete massive localizable modes. Besides this we obtain resonances in some models by analytical methods. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
44. Subspace codes from Ferrers diagrams.
- Author
-
Gorla, Elisa and Ravagnani, Alberto
- Subjects
SUBSPACES (Mathematics) ,DIMENSIONS ,LINEAR systems ,PARAMETER estimation ,ALGEBRAIC geometry - Abstract
In this paper, we survey the main known constructions of Ferrers diagram rank-metric codes, and establish new results on a related conjecture by Etzion and Silberstein. We also give a sharp lower bound on the dimension of linear rank-metric anticodes with a given profile. Combining our results with the multilevel construction, we produce examples of subspace codes with the largest known cardinality for the given parameters. We also apply results from algebraic geometry to the study of the analogous problem over an algebraically closed field, proving that the bound by Etzion and Silberstein can be improved in this case, and providing a sharp bound for full-rank matrices. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
45. ASSOUAD-MINIMALITY OF MORAN SETS UNDER QUASI-LIPSCHITZ MAPPINGS.
- Author
-
XI, LIFENG, DENG, JUAN, and WEN, ZHIYING
- Subjects
SET theory ,LIPSCHITZ spaces ,MATHEMATICAL mappings ,FRACTAL dimensions ,DIMENSIONS - Abstract
The quasi-Lipschitz mappings, weaker than the bi-Lipschitz mappings, preserve Hausdorff, packing and box dimensions, but change Assouad dimension . In this paper, for Moran fractals, we investigate the change of their Assouad dimension under the quasi-Lipschitz mappings. We study a class of Moran set which is quasi-Lipschitz Assouad-minimal, i.e. for any in the class, for all quasi-Lipschitz mappings defined on . For another class of Moran sets, we prove that for any in the class, where the infimum is taken over all quasi-Lipschitz mappings defined on , and is the quasi-Assouad dimension introduced in [F. Lü and L. F. Xi, Quasi-Assouad dimension of fractals, J. Fractal Geom. 3 (2016) 187-215]. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
46. A note on division algebras of dimension four.
- Author
-
Tvalavadze, Marina and Vickery, Patrick
- Subjects
DIVISION algebras ,DIMENSIONS ,MATHEMATICAL proofs ,QUATERNIONS ,DIMENSIONAL analysis ,PARAMETER estimation - Abstract
In this paper we consider a four-dimensional real algebra and prove that if the quaternion group acts on a certain subset of End transitively, then is a division algebra. We will also show that under certain technical conditions has no identity. Using these results we can explicitly construct a 16-parameter family of four-dimensional real division algebras. In addition, we will find a one-parameter family of such algebras with trivial derivation algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
47. Improved Approximation for Fréchet Distance on -Packed Curves Matching Conditional Lower Bounds.
- Author
-
Bringmann, Karl and Künnemann, Marvin
- Subjects
CURVES ,MATHEMATICAL bounds ,APPROXIMATION theory ,ALGORITHMS ,DIMENSIONS - Abstract
The Fréchet distance is a well studied and very popular measure of similarity of two curves. The best known algorithms have quadratic time complexity, which has recently been shown to be optimal assuming the Strong Exponential Time Hypothesis (SETH) [Bringmann, FOCS'14]. To overcome the worst-case quadratic time barrier, restricted classes of curves have been studied that attempt to capture realistic input curves. The most popular such class are -packed curves, for which the Fréchet distance has a -approximation in time [Driemel et al., DCG'12]. In dimension this cannot be improved to for any unless SETH fails [Bringmann, FOCS'14]. In this paper, exploiting properties that prevent stronger lower bounds, we present an improved algorithm with time complexity . This improves upon the algorithm by Driemel et al. for any . Moreover, our algorithm's dependence on , and is optimal in high dimensions apart from lower order factors, unless SETH fails. Our main new ingredients are as follows: For filling the classical free-space diagram we project short subcurves onto a line, which yields one-dimensional separated curves with roughly the same pairwise distances between vertices. Then we tackle this special case in near-linear time by carefully extending a greedy algorithm for the Fréchet distance of one-dimensional separated curves. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
48. Class dimension of association schemes in singular linear spaces.
- Author
-
Guo, Haixia and Gao, You
- Subjects
VECTOR spaces ,DIMENSIONS ,ASSOCIATION schemes (Combinatorics) ,MATHEMATICAL bounds ,SET theory ,INTEGERS - Abstract
A resolving set for an association scheme is a set of points such that, for all , the ordered list of relations uniquely determines , where denotes the relation containing the pair in . In this paper, we determine upper bounds on class dimension for a family of association schemes in singular linear spaces, and construct their resolving sets for a special case. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
49. Large random simplicial complexes, III the critical dimension.
- Author
-
Costa, A. and Farber, M.
- Subjects
RANDOM variables ,MATHEMATICAL complexes ,DIMENSIONS ,PARAMETER estimation ,ALGORITHMS - Abstract
In this paper, we study the notion of critical dimension of random simplicial complexes in the general multi-parameter model described in [Random simplicial complexes, preprint (2014), ; Large random simplicial complexes, I, preprint (2015), ; Large random simplical complexes, II, preprint (2015), ]. This model includes as special cases the Linial-Meshulam-Wallach model [Homological connectivity of random 2-complexes, Combinatorica 26 (2006) 475-487; Homological connectivity of random -complexes, Random Struct. Alogrithms 34 (2009) 408-417.] as well as the clique complexes of random graphs. We characterize the concept of critical dimension in terms of various geometric and topological properties of random simplicial complexes such as their Betti numbers, the fundamental group, the size of minimal cycles and the degrees of simplexes. We mention in the text a few interesting open questions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
50. REMARKS ON DIMENSIONS OF CARTESIAN PRODUCT SETS.
- Author
-
WEI, CHUN, WEN, SHENGYOU, and WEN, ZHIXIONG
- Subjects
CARTESIAN coordinates ,SET theory ,DIMENSIONS ,METRIC spaces ,MATHEMATICAL analysis - Abstract
Given metric spaces and , it is well known that and where , , , denote the Hausdorff, packing, lower box-counting, and upper box-counting dimension of , respectively. In this paper, we shall provide examples of compact sets showing that the dimension of the product may attain any of the values permitted by the above inequalities. The proof will be based on a study on dimension of products of sets defined by digit restrictions. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
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