scholarly journals Cyclic derivations, species realizations and potentials

2019 ◽  
Vol 53 (supl) ◽  
pp. 185-194
Author(s):  
Daniel López-Aguayo
Keyword(s):  
Finite Dimensional ◽  
New Construction ◽  
Quivers With Potential

In this paper we give an overview of a generalization, introduced by R. Bautista and the author, of the theory of mutation of quivers with potential developed in 2007 by Derksen-Weyman-Zelevinsky. This new construction allows us to consider finite dimensional semisimple F-algebras, where F is any field. We give a brief account of the results concerning this generalization and its main consequences.

Derived equivalences from cohomological approximations and mutations of Φ-Yoneda algebras

2013 ◽  
Vol 143 (3) ◽  
pp. 589-629 ◽  
Author(s):  
Wei Hu ◽  
Steffen Koenig ◽  
Changchang Xi
Keyword(s):  
Triangulated Categories ◽  
Endomorphism Rings ◽  
Infinite Dimensional ◽  
Derived Equivalences ◽  
Finite Dimensional ◽  
New Construction ◽  
Yoneda Algebras ◽  
Frobenius Categories ◽  
Finite Dimensional Algebras

A new construction of derived equivalences is given, which relates different endomorphism rings and, more generally, cohomological endomorphism rings, including higher extensions, of objects in triangulated categories. These objects need to be connected by certain universal maps that are cohomological approximations and that exist in very general circumstances. The construction turns out to be applicable to a wide variety of situations, covering finite-dimensional algebras as well as certain infinite-dimensional algebras, Frobenius categories and n-Calabi–Yau categories.

scholarly journals Selfinjective quivers with potential and 2-representation-finite algebras

2011 ◽  
Vol 147 (6) ◽  
pp. 1885-1920 ◽  
Author(s):  
Martin Herschend ◽  
Osamu Iyama
Keyword(s):  
Rich Source ◽  
Sufficient Condition ◽  
Finite Algebras ◽  
Finite Dimensional ◽  
Quivers With Potential ◽  
Nakayama Permutation

AbstractWe study quivers with potential (QPs) whose Jacobian algebras are finite-dimensional selfinjective. They are an analogue of the ‘good QPs’ studied by Bocklandt whose Jacobian algebras are 3-Calabi–Yau. We show that 2-representation-finite algebras are truncated Jacobian algebras of selfinjective QPs, which are factor algebras of Jacobian algebras by certain sets of arrows called cuts. We show that selfinjectivity of QPs is preserved under iterated mutation with respect to orbits of the Nakayama permutation. We give a sufficient condition for all truncated Jacobian algebras of a fixed QP to be derived equivalent. We introduce planar QPs which provide us with a rich source of selfinjective QPs.

Completeness of Graphical Languages for Mixed State Quantum Mechanics

2021 ◽  
Vol 2 (4) ◽  
pp. 1-28
Author(s):  
Titouan Carette ◽  
Emmanuel Jeandel ◽  
Simon Perdrix ◽  
Renaud Vilmart
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Monoidal Category ◽  
Quantum Information Processing ◽  
Quantum Circuits ◽  
Quantum Operations ◽  
Symmetric Monoidal Category ◽  
Finite Dimensional ◽  
General Quantum ◽  
New Construction

There exist several graphical languages for quantum information processing, like quantum circuits, ZX-calculus, ZW-calculus, and so on. Each of these languages forms a †-symmetric monoidal category (†-SMC) and comes with an interpretation functor to the †-SMC of finite-dimensional Hilbert spaces. In recent years, one of the main achievements of the categorical approach to quantum mechanics has been to provide several equational theories for most of these graphical languages, making them complete for various fragments of pure quantum mechanics. We address the question of how to extend these languages beyond pure quantum mechanics to reason about mixed states and general quantum operations, i.e., completely positive maps. Intuitively, such an extension relies on the axiomatisation of a discard map that allows one to get rid of a quantum system, an operation that is not allowed in pure quantum mechanics. We introduce a new construction, the discard construction , which transforms any †-symmetric monoidal category into a symmetric monoidal category equipped with a discard map. Roughly speaking this construction consists in making any isometry causal. Using this construction, we provide an extension for several graphical languages that we prove to be complete for general quantum operations. However, this construction fails for some fringe cases like Clifford+T quantum mechanics, as the category does not have enough isometries.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

Main Provisions Of The Concept Of Technology Of Diamond Cutting And Drilling Of Building Structures

2019 ◽  
pp. 59-63
Keyword(s):  
Combustion Engine ◽  
Front Surface ◽  
The Body ◽  
Building Structures ◽  
Diamond Cutting ◽  
Variable Diameter ◽  
Diamond Drilling ◽  
Single Structure ◽  
New Construction ◽  
Non Destructive

The main provisions of the concept of technology of diamond cutting and drilling of building structures are considered. The innovativeness of the technology, its main possibilities and advantages are presented. Carrying out works with the help of this technology in underwater conditions expands its use when constructing and reconstructing hydraulic structure. The use of diamond drilling equipment with motors equipped with an internal combustion engine is considered. Drilling holes with a variable diameter during the reconstruction of the runways of airfields makes it possible to combine the landing mats into a single structure. The ability to cut inside the concrete mass, parallel to the front surface, has no analogues among the methods of concrete treatment. The use of this technology for producing blind openings in the body of concrete without weakening the structure is also unique. Work with precision quality in cutting and diamond drilling of concrete and reinforced concrete was noted by architects and began to be implemented in the manufacture of inter-room and inter-floor openings. Non-destructive approach to the fragmentation of building structures allows them to be reused. The technology of diamond cutting and drilling is located at the junction of new construction, repair, reconstruction of buildings and structures, and dismantling of structures. Attention is paid to the complexity and combinatorial application of diamond technology. Economic efficiency and ecological safety of diamond technology are presented. The main directions of further research for the development of technology are indicated.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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