Rank 2 intersection types for local definitions and conditional expressions

Interaction nets have proved to be a useful tool for the study of computational aspects of various formalisms (e.g. λ-calculus, term rewriting systems), but they are also a programming paradigm in themselves, and this is actually how they were introduced by Lafont. In this paper we consider semi-simple interaction nets as a programming language, and present a type assignment system using intersection types. First we show that interactions preserve types (i.e., the system enjoys subject reduction), and we compare this type assignment system with the intersection systems for λ-calculus and term rewriting systems. Then we define a recursion scheme that ensures termination of all interaction sequences. By relaxing the scheme and using the type assignment system, we derive another sufficient condition for termination of interaction nets. Finally, we show that although the type system based on general intersection types is not decidable, its restriction to rank 2 types is, and we give an algorithm that computes principal types for nets.

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A family of rank-{2} mathematical instanton bundles on {${\bf P}\sb 3$}

Publications of the Research Institute for Mathematical Sciences ◽

10.2977/prims/1195145148 ◽

1997 ◽

Vol 33 (4) ◽

pp. 573-598

Author(s):

Valery Vedernikov

Keyword(s):

Instanton Bundles ◽

Rank 2

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The motion of the particles volume corresponding to invariant solution of rank 2 submodel of hydrodynamic type

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2016.2.030 ◽

2016 ◽

Vol 11 (2) ◽

pp. 205-209

Author(s):

D.T. Siraeva

Keyword(s):

Equation Of State ◽

Invariant Solution ◽

Hydrodynamic Type ◽

Lagrangian Coordinates ◽

Hydrodynamic Equations ◽

Rank 2 ◽

Invariant Submodel ◽

Entropy Functions

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.

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Powerfully nilpotent groups of rank 2 or small order

Journal of Group Theory ◽

10.1515/jgth-2020-0016 ◽

2020 ◽

Vol 23 (4) ◽

pp. 641-658

Author(s):

Gunnar Traustason ◽

James Williams

Keyword(s):

Detailed Analysis ◽

Special Kind ◽

Nilpotent Groups ◽

Nilpotency Class ◽

Central Series ◽

Rank 2 ◽

Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

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Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

Journal of High Energy Physics ◽

10.1007/jhep12(2020)021 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Mario Martone

Keyword(s):

Partition Function ◽

Central Charge ◽

Singular Locus ◽

Companion Paper ◽

Coulomb Branch ◽

Energy Limit ◽

Superconformal Field Theories ◽

Rank 2 ◽

Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

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