scholarly journals A functorial approach to monomorphism categories for species I

2021 ◽  
Author(s):  
Nan Gao ◽  
Julian Külshammer ◽  
Sondre Kvamme ◽  
Chrysostomos Psaroudakis
Keyword(s):  
General Result ◽  
Path Algebra ◽  
Preprojective Algebra ◽  
Adjoint Functors ◽  
Almost Split Sequences ◽  
Functorial Approach

We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalized species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor send almost split sequences over the path algebra and the preprojective algebra to split or almost split sequences in the monomorphism category. We derive this from a general result on preservation of almost split morphisms under adjoint functors whose counit is a monomorphism. Despite of its generality, our monomorphism categories still allow for explicit computations as in the case of Ringel and Schmidmeier.

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

scholarly journals NEUTRINO OSCILLATIONS AND THE EXACT PARITY MODEL

1994 ◽  
Vol 09 (02) ◽  
pp. 169-179 ◽  
Author(s):  
R. FOOT
Keyword(s):  
Neutrino Mass ◽  
General Result ◽  
Neutrino Oscillations ◽  
Mass Matrix ◽  
Atmospheric Neutrino ◽  
Solar Neutrinos ◽  
Specific Model ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Significant Deficit

We re-examine neutrino oscillations in exact parity models. Previously it was shown in a specific model that large neutrino mixing angles result. We show here that this is a general result of neutrino mixing in exact parity models provided that the neutrino mass matrix is real. In this case, the effects of neutrino mixing in exact parity models is such that the probability of a given weak eigenstate remaining in that eigenstate averages to less than half when averaged over many oscillations. This result is interesting in view of the accumulating evidence for a significant deficit in the number of solar neutrinos. It may also be of relevance to the atmospheric neutrino anomaly.

scholarly journals On the geometrical representation of the powers of quantities, whose indices involve the square roots of negative quantities

1833 ◽  
Vol 2 ◽  
pp. 382-382
Keyword(s):  
General Result ◽  
Geometric Representation ◽  
Square Roots ◽  
Geometrical Representation

The author, in a former paper, read to the Society in February last, had discussed various objections which had been raised against his mode of geometric representation of the square roots of negative quantities. At that time he had only discovered geometrical repre­sentations for quantities of the form a + b √‒1, of geometrically adding and multiplying such quantities, and also of raising them to powers either whole or fractional, positive or negative; but he was at that time unable to represent geometrically quantities raised to powers, whose indices involve the square roots of negative quantities (such as a + b √‒1 m + n ). His attention has since been drawn to this latter class of quantities by a passage in M. Mourey’s work on this subject, which implied that that gentleman was in posses­sion of methods of representing them geometrically, but that he was at present precluded by circumstances from publishing his discoveries. The author was therefore induced to pursue his own investigations, and arrived at the general result stated by M. Mourey, that all algebraic quantities whatsoever are capable of geometrical representation by lines all situated in the same plane. The object of the present paper is to extend the geometrical representations stated in his former treatise, to the powers of quantities, whose indices involve the square roots of negative quantities. With this view he investigates Various equivalent formulæ suited to the particular cases, and employs a peculiar notation adapted to this express purpose ; but the nature of these investigations is such as renders them incapable of abridgement.

scholarly journals The twofold way of super holonomy

2016 ◽  
Vol 28 (6) ◽  
Author(s):  
Josua Groeger
Keyword(s):  
Comparison Theorem ◽  
Wilson Loops ◽  
Holonomy Algebra ◽  
Functorial Approach

AbstractThere are two different notions of holonomy in supergeometry, the supergroup introduced by Galaev and our functorial approach motivated by super Wilson loops. Either theory comes with its own version of invariance of vectors and subspaces under holonomy. By our first main result, the Twofold Theorem, these definitions are equivalent. Our proof is based on the Comparison Theorem, our second main result, which characterises Galaev’s holonomy algebra as an algebra of coefficients, building on previous results. As an application, we generalise some of Galaev’s results to

3. Laboratory Notes by Professor Tait (a.) Measurement of the Potential, required to produce Sparks of various lengths, in Air at different pressures, by a Holtz Machine

1878 ◽  
Vol 9 ◽  
pp. 332-333
Author(s):  
Messrs Macfarlane ◽  
Paton
Keyword(s):  
General Result ◽  
The Other ◽  
Considerable Distance ◽  
Image Position

The general result of these strictly preliminary experiments appears to show that for sparks not exceeding a decimetre in length (L), taken in air at different pressures (P), between two metal balls of 7mm·5 radius, the requisite potential (V), is expressed by the formulaThe Holtz machine employed is a double one, made by Ruhmkorff, and it was used with its small Leyden jars attached. The measurements had to be made with a divided-ring electrometer, so that two insulated balls, at a considerable distance from one another, were connected, one with the machine, the other with the electrometer.

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