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We note a simple algebraic proof of Frolkina's result that ℝ 3 does not contain uncountably many pairwise disjoint copies of the Möbius band, and of a similar result in higher dimensions. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

Process discovery algorithms typically aim at discovering process models from event logs that best describe the recorded behavior. Often, the quality of a process discovery algorithm is measured by quantifying to what extent the resulting model can reproduce the behavior in the log, i.e. replay fitness. At the same time, there are other measures that compare a model with recorded behavior in terms of the precision of the model and the extent to which the model generalizes the behavior in the log. Furthermore, many measures exist to express the complexity of a model irrespective of the log. In this paper, we first discuss several quality dimensions related to process discovery. We further show that existing process discovery algorithms typically consider at most two out of the four main quality dimensions: replay fitness, precision, generalization and simplicity. Moreover, existing approaches cannot steer the discovery process based on user-defined weights for the four quality dimensions. This paper presents the ETM algorithm which allows the user to seamlessly steer the discovery process based on preferences with respect to the four quality dimensions. We show that all dimensions are important for process discovery. However, it only makes sense to consider precision, generalization and simplicity if the replay fitness is acceptable. [ABSTRACT FROM AUTHOR]

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]

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]

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]

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation-type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge $\hat{c}_j(\sigma) = 26f_j(\sigma)$, where fj(σ) is the length of cycle j in twisted sector σ. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge cj(σ) = 26. These tools are used to begin the study of the target space-time dimension $\hat{D}_j(\sigma)$ of cycle j in sector σ, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

With an enlighting analysis, Baskaran and Grishchuk have recently shown the presence and importance of the so-called "magnetic" components of gravitational waves (GWs), which have to be taken into account in the context of the total response functions of interferometers for GWs propagating from arbitrary directions. In this paper, more detailed angular and frequency dependences of the response functions for the magnetic components are given in the approximation of wavelength much larger than the linear dimensions of the interferometer, with a specific application to the parameters of the LIGO and Virgo interferometers. The results of this paper agree with the work of Baskaran and Grishchuk, in which it has been shown that the identification of "electric" and "magnetic" contributions is unambiguous in the long-wavelength approximation. At the end of this paper, the angular and frequency dependences of the total response functions of the LIGO and Virgo interferometers are given. In the high-frequency regime, the division on "electric" and "magnetic" components becomes ambiguous, thus the full theory of gravitational waves has to be used. Our results are consistent with the ones of Baskaran and Grishchuk for this case. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of solutions to the cubic and the quadratic nonlinear Schrödinger equations in one and two space dimensions, respectively. When the nonlinearity is of a form f = |u|[sup p-1]u, it is known that there exist scattered states if p > 1+2/n and there does not otherwise. Therefore we may consider the nonlinearities treated in the present paper to be of critical order for the existence of scattered states though their forms differ slightly from that given above. We prove, however, that there exist scattered states for these critical nonlinear Schrödinger equations, in other words, that the wave operators exist on a certain set of final states. Our proof is mainly based on the construction of suitable approximate functions that approach to solutions of nonlinear Schrödinger equations at t = ∞. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Over the past 20 years, a great deal of work has been done on the moduli spaces of coherent systems on algebraic curves. Until recently, however, there has been very little work on the fixed determinant case, except for the special case of rank 2 and canonical determinant. This situation has changed due to two papers of Osserman, who has obtained lower bounds for the dimensions of the fixed determinant moduli spaces in some cases. Our object in this paper is to show that some of Osserman's bounds are sharp. [ABSTRACT FROM AUTHOR]

In today's knowledge-based business, knowledge is the only source of competitive advantage for engineering industries. Knowledge sharing plays an important role in the success of knowledge management (KM). Knowledge sharing barriers (KSBs) become obstacles for KM to achieve the goals of the industries. In this paper, three categories of KSBs have been identified such as individual, organisational and technological. The main purpose of this research is to measure the effectiveness of individual, organisational and technological KSBs which helps the managers for taking decision to enhance the successful knowledge sharing strategy in the engineering industries. In this paper, an analytical network process (ANP) framework has been developed with the help of identified determinants, dimensions and enablers to evaluate the effectiveness of alternatives such as individual, organisational and technological KSBs. As per evaluation, the organisational KSBs have the maximum effect on knowledge sharing followed by technological and individual KSBs. [ABSTRACT FROM AUTHOR]

In this paper, we study in detail the multifractal features of the main matrices of an encryption system based on a rule-90 cellular automaton. For this purpose, we consider the scaling method known as the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). In addition, we analyze the multifractal structure of the matrices of different dimensions, and find that there are minimal differences in all the examined multifractal quantities such as the multi-fractal support, the most frequent singularity exponent, and the generalized Hurst exponent. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

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]