Design of dynamically isotropic two radii Gough-Stewart platforms with arbitrary number of struts

2021 ◽  
Author(s):  
Yogesh Pratap Singh ◽  
Nazeer Ahmad ◽  
Ashitava Ghosal
Keyword(s):  
Arbitrary Number ◽  
Stewart Platforms

Kinematic analysis and deformation of a planar lattice with an arbitrary number of panels

2020 ◽  
pp. 15-19
Author(s):  
M.N. Kirsanov
Keyword(s):  
Exact Solution ◽  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Design Parameters ◽  
Lattice Deformation ◽  
Planar Lattice ◽  
Force Loading

Formulae are obtained for calculating the deformations of a statically determinate lattice under the action of two types of loads in its plane, depending on the number of panels located along one side of the lattice. Two options for fixing the lattice are analyzed. Cases of kinematic variability of the structure are found. The distribution of forces in the rods of the lattice is shown. The dependences of the force loading of some rods on the design parameters are obtained. Keywords: truss, lattice, deformation, exact solution, deflection, induction, Maple system. [email protected]

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Alessandro Torrielli
Keyword(s):  
Spectral Problem ◽  
Transfer Matrix ◽  
Arbitrary Number ◽  
Free Fermion ◽  
Nearest Neighbour ◽  
Bogoliubov Transformation ◽  
Free Fermions ◽  
New Models ◽  
Lower Dimensional

Abstract In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS3, mixed-flux relativistic AdS3 and massless AdS2. We also attack the class of models akin to AdS5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

scholarly journals Language Family Engineering with Product Lines of Multi-level Models

2021 ◽  
Author(s):  
Juan de Lara ◽  
Esther Guerra
Keyword(s):  
Software Engineering ◽  
Arbitrary Number ◽  
Formal Theory ◽  
The Other ◽  
Language Family ◽  
Top Down ◽  
Product Lines ◽  
Modelling Languages ◽  
Multi Level ◽  
Definition Of

AbstractModelling is an essential activity in software engineering. It typically involves two meta-levels: one includes meta-models that describe modelling languages, and the other contains models built by instantiating those meta-models. Multi-level modelling generalizes this approach by allowing models to span an arbitrary number of meta-levels. A scenario that profits from multi-level modelling is the definition of language families that can be specialized (e.g., for different domains) by successive refinements at subsequent meta-levels, hence promoting language reuse. This enables an open set of variability options given by all possible specializations of the language family. However, multi-level modelling lacks the ability to express closed variability regarding the availability of language primitives or the possibility to opt between alternative primitive realizations. This limits the reuse opportunities of a language family. To improve this situation, we propose a novel combination of product lines with multi-level modelling to cover both open and closed variability. Our proposal is backed by a formal theory that guarantees correctness, enables top-down and bottom-up language variability design, and is implemented atop the MetaDepth multi-level modelling tool.

On the Complexity of Deadlock Recovery

1986 ◽  
Vol 9 (3) ◽  
pp. 323-342
Author(s):  
Joseph Y.-T. Leung ◽  
Burkhard Monien
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Arbitrary Number ◽  
The Other ◽  
Np Hard ◽  
Total Cost ◽  
Other Hand ◽  
Input Parameters ◽  
Resource Type

We consider the computational complexity of finding an optimal deadlock recovery. It is known that for an arbitrary number of resource types the problem is NP-hard even when the total cost of deadlocked jobs and the total number of resource units are “small” relative to the number of deadlocked jobs. It is also known that for one resource type the problem is NP-hard when the total cost of deadlocked jobs and the total number of resource units are “large” relative to the number of deadlocked jobs. In this paper we show that for one resource type the problem is solvable in polynomial time when the total cost of deadlocked jobs or the total number of resource units is “small” relative to the number of deadlocked jobs. For fixed m ⩾ 2 resource types, we show that the problem is solvable in polynomial time when the total number of resource units is “small” relative to the number of deadlocked jobs. On the other hand, when the total number of resource units is “large”, the problem becomes NP-hard even when the total cost of deadlocked jobs is “small” relative to the number of deadlocked jobs. The results in the paper, together with previous known ones, give a complete delineation of the complexity of this problem under various assumptions of the input parameters.

scholarly journals Conjectures on Stably Newton Degenerate Singularities

2021 ◽  
Author(s):  
Jan Stevens
Keyword(s):  
Characteristic Zero ◽  
Arbitrary Number ◽  
Milnor Number ◽  
Plane Curves ◽  
Newton Diagram ◽  
Finite Characteristic ◽  
Vanishing Cycles

AbstractWe discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions.We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, $$x^p+x^q$$ x p + x q in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

scholarly journals Higher spins from exotic dualisations

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nicolas Boulanger ◽  
Victor Lekeu
Keyword(s):  
Infinite Number ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Young Tableaux ◽  
Spacetime Dimension ◽  
Massless Field ◽  
Free Level ◽  
Higher Spins

Abstract At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height hi by columns of height D − 2 − hi, where D is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of D − 2 extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in D = 5 and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in D = 3.

Collapse phase diagram of carbon nanotubes with arbitrary number of walls. Collapse modes and macroscopic analog

Carbon ◽  
2021 ◽  
Author(s):  
Y. Magnin ◽  
F. Rondepierre ◽  
W. Cui ◽  
D.J. Dunstan ◽  
A. San-Miguel
Keyword(s):  
Carbon Nanotubes ◽  
Phase Diagram ◽  
Arbitrary Number ◽  
Collapse Phase
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