scholarly journals String factorisations with maximum or minimum dimension

2020 ◽  
Vol 842 ◽  
pp. 65-73
Author(s):  
A. Monti ◽  
B. Sinaimeri
Keyword(s):  
Minimum Dimension

scholarly journals Application of Offshore HDPE Pipes Route Design in North Maluku Indonesia

2021 ◽  
Vol 26 (1) ◽  
pp. 45-56
Author(s):  
Franto Novico ◽  
Indra Kurniawan ◽  
Andi Egon ◽  
Davide Merli
Keyword(s):  
Concrete Block ◽  
Hydrodynamic Conditions ◽  
Seabed Sediment ◽  
Single Beam ◽  
Drag Forces ◽  
Route Design ◽  
Minimum Dimension ◽  
The Right ◽  
Alternative Routes ◽  
Hdpe Pipes

The lack of fresh water for the inhabitants of Maitara island is a very urgent problem to be solved. Two main factors at least must be taken into account to deliberate the right of way of subsea High-density polyethylene (HDPE) pipes, namely the hydrodynamic conditions and of a block analysis. This paper presents the study to justify the best route of subsea HDPE pipes based on hydrodynamic model analysis and concrete block strategy. The method used to analyze the best route includes 2 aspects. Firstly, the investigation method consisting of a bathymetric survey conducted by a single beam echosounder, 15 days tidal observations and seabed sediment sampling. Secondly, the hydrodynamic modelling analysis using Mike 21 FMHD and concrete block analysis, all these studies have been completed in August 2018. In the morphological behaviour analysis, three alternative routes are considered for the subsea HDPE pipes from Tidore Island to Maitara Island. The outcome of the analysis shows that the second track line option has the smallest impact by the hydrodynamic conditions, with a current speed of less than 0,5m/sec and a significant wave height of fewer than 1.2 meters. Furthermore, the uniformity of the lithology along the route is the other reason to select the second route. Finally, the concrete block analysis generated a minimum dimension of 75cm x 60cm x 30cm, and a free span of 3 meters is safe to absorb the uplift and drag forces acting on the pipe.

scholarly journals The minimum dimension of a residual ANR

1976 ◽  
Vol 36 (1) ◽  
pp. 97-99 ◽  
Author(s):  
D. A. Moran
Keyword(s):  
Minimum Dimension

scholarly journals A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION

2006 ◽  
Vol 04 (02) ◽  
pp. 325-330 ◽  
Author(s):  
B. V. RAJARAMA BHAT
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Product Formula ◽  
Maximal Dimension ◽  
Maximum Dimension ◽  
Dimension Formula ◽  
Finite Dimensional ◽  
Minimum Dimension ◽  
Orthogonal Product ◽  
Product Vector

Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

scholarly journals Representations of Polycrystalline Microstructure by n-Point Correlation Tensors

1993 ◽  
Vol 21 (1) ◽  
pp. 17-37 ◽  
Author(s):  
Pavel Etingof ◽  
Brent L. Adams
Keyword(s):  
Representation Theory ◽  
Crystal Lattice ◽  
Spatial Coherence ◽  
Central Problem ◽  
Important Class ◽  
Lower Dimension ◽  
Lattice Orientation ◽  
Minimum Dimension ◽  
Point Correlation ◽  
Polycrystalline Microstructure

An important class of representations of polycrystalline microstructure consists of the n-point correlation tensors. In this paper the representation theory of groups is applied to a consideration of symmetries in the n-point correlation tensors. Three sources of symmetry are included in the development: indicial symmetry in the coefficients of tensors, symmetry associated with the crystal lattice, and statistical symmetries in the microstructure induced by processing. The central problem discussed here is the “residence space”, or the space of minimum dimension occupied by correlation tensors possessing such symmetries. In addition to the general case of correlation tensors possessing such symmetries, a model microstructure is also considered which embodies an assumption of no spatial coherence of lattice orientation between neighboring grains or crystallites. It is shown that the model microstructure generally results in residence spaces of lower dimension.

scholarly journals Creation of the spatial metric for the image of an agricultural object

2021 ◽  
Vol 51 (1) ◽  
pp. 99-109
Author(s):  
P. K. Kutsenogii ◽  
V. K. Kalichkin
Keyword(s):  
Vector Space ◽  
Coordinate System ◽  
Predictive Power ◽  
Correct Choice ◽  
Real Object ◽  
Agricultural Activity ◽  
Modeling And Analysis ◽  
Minimum Dimension ◽  
Image Creation ◽  
External Conditions

The analysis of various approaches to forecasting complex multifactorial systems in conditions of uncertainty of external conditions is presented. It is necessary to develop these approaches in order to create adequate models of agricultural activities for their effective planning and management. A distinctive feature of agricultural production is a critical dependence on environmental factors, which cannot be accurately predicted. Regression modeling and analysis of time series used at present to solve this problem in difficult cases do not result in an adequate forecast of the dynamics of an agricultural object. As an approach, it is proposed to use the construction of the "image" of the system. This approach is classified as "nature-like", as it simulates a way of decision-making by a specialist on the basis of accumulated experience and intuition. The key parameter of this construction will be the correct choice of the metric (coordinate system). This approach is illustrated by an example of creating an image of a two-dimensional phenomenon in a one-dimensional coordinate system. As a result, an image is understood as an image of reality in a vector space of a certain dimension. The image in the authors' view is a reflection of reality in an artificially created metric, more suitable for understanding and analysis, but retaining the main (important) features and functions of the original object. Artificial intelligence techniques can be seen as tools for image creation and analysis. An important characteristic of an image is its predictive power, i.e. the ability to use the image in order to predict the state of a real object in the future period. An image retains its predictive power if the forecast obtained using this image corresponds to the data obtained when observing a real object. The image is formed in a suitable metric for solving a specific problem. The key metric parameter of the image of agricultural activity, suitable for forecasting purposes, is the minimum dimension of the vector space used, at which the predictive power of the image is retained to solve the problem.

Nonlinear Modeling of Flexible Multibody Systems Dynamics Subjected to Variable Constraints

1989 ◽  
Vol 56 (2) ◽  
pp. 444-450 ◽  
Author(s):  
S. K. Ider ◽  
F. M. L. Amirouche
Keyword(s):  
Nonlinear Modeling ◽  
Equations Of Motion ◽  
Body Motion ◽  
Matrix Formulation ◽  
Closed Loops ◽  
Elastic Bodies ◽  
Minimum Dimension ◽  
Geometric Stiffening ◽  
Angular Velocities ◽  
Constrained Multibody Dynamics

This paper presents the geometric stiffening effects and the complete nonlinear interaction between elastic and rigid body motion in the study of constrained multibody dynamics. A recursive formulation (or direct path approach) of the equations of motion based on Kane’s equations, finite element method and modal analysis techniques is presented. An extended matrix formulation of the partial angular velocities and partial velocities for flexible (elastic) bodies is also developed and forms the basis for our analysis. Closed loops and kinematical constraints (specified motions) are allowed and their corresponding Jacobian matrices are fully developed. The constraint equations are appended onto the governing equations of motion by representing them in a minimum dimension form using an innovative method called the Pseudo-Uptriangular Decomposition method. Examples are presented to illustrate the method and procedures proposed.

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