scholarly journals Disjoint hypercyclicity equals disjoint supercyclicity for families of Taylor-type operators

2018 ◽  
Vol 16 (1) ◽  
pp. 597-606
Author(s):  
Yingbin Ma ◽  
Cui Wang
Keyword(s):  
Holomorphic Function ◽  
Taylor Expansion ◽  
Sufficient Condition ◽  
Partial Sum ◽  
Supercyclic Operators ◽  
Disjoint Hypercyclicity

AbstractWe characterize disjointness of supercyclic operators which map a holomorphic function to a partial sum of the Taylor expansion. In particular, we show that disjoint hypercyclicity equals disjoint supercyclicity for families of Taylor-type operators. Moreover, we give a sufficient condition to yield the disjoint supercyclicity for families of Taylor-type operators.

Random Dirichlet Functions: Multipliers and Smoothness

1993 ◽  
Vol 45 (2) ◽  
pp. 255-268 ◽  
Author(s):  
W. George Cochran ◽  
Joel H. Shapiro ◽  
David C. Ullrich
Keyword(s):  
Power Series ◽  
Holomorphic Function ◽  
Dirichlet Series ◽  
Dirichlet Space ◽  
General Setting ◽  
Sufficient Condition ◽  
Dirichlet Spaces ◽  
Random Series ◽  
Weighted Dirichlet Spaces ◽  
Almost All

AbstractWe show that if is a holomorphic function in the Dirichlet space of the unit disk, then almost all of its randomizations are multipliers of that space. This parallels a known result for lacunary power series, which also has a version for smoothness classes: every lacunary Dirichlet series lies in the Lipschitz class Lip1/2 of functions obeying a Lipschitz condition with exponent 1/2. However, unlike the lacunary situation, no corresponding “almost sure” Lipschitz result is possible for random series: we exhibit a Dirichlet function with norandomization in Lip1/2. We complement this result with a “best possible” sufficient condition for randomizations to belong almost surely to Lip1/2. Versions of our results hold for weighted Dirichlet spaces, and much of our work is carried out in this more general setting.

scholarly journals An application of parallel cut elimination in multiplicative linear logic to the Taylor expansion of proof nets

2021 ◽  
Vol Volume 17, Issue 4 ◽  
Author(s):  
Jules Chouquet ◽  
Lionel Vaux Auclair
Keyword(s):  
Arbitrary Number ◽  
Taylor Expansion ◽  
Linear Logic ◽  
Cut Elimination ◽  
Sufficient Condition ◽  
Weighted Sum ◽  
Combinatorial Properties ◽  
Proof Nets ◽  
Infinite Sums

We examine some combinatorial properties of parallel cut elimination in multiplicative linear logic (MLL) proof nets. We show that, provided we impose a constraint on some paths, we can bound the size of all the nets satisfying this constraint and reducing to a fixed resultant net. This result gives a sufficient condition for an infinite weighted sum of nets to reduce into another sum of nets, while keeping coefficients finite. We moreover show that our constraints are stable under reduction. Our approach is motivated by the quantitative semantics of linear logic: many models have been proposed, whose structure reflect the Taylor expansion of multiplicative exponential linear logic (MELL) proof nets into infinite sums of differential nets. In order to simulate one cut elimination step in MELL, it is necessary to reduce an arbitrary number of cuts in the differential nets of its Taylor expansion. It turns out our results apply to differential nets, because their cut elimination is essentially multiplicative. We moreover show that the set of differential nets that occur in the Taylor expansion of an MELL net automatically satisfies our constraints. Interestingly, our nets are untyped: we only rely on the sequentiality of linear logic nets and the dynamics of cut elimination. The paths on which we impose bounds are the switching paths involved in the Danos--Regnier criterion for sequentiality. In order to accommodate multiplicative units and weakenings, our nets come equipped with jumps: each weakening node is connected to some other node. Our constraint can then be summed up as a bound on both the length of switching paths, and the number of weakenings that jump to a common node.

The Current Situation in Chemical Stabilization of Biological Materials

1972 ◽  
Vol 30 ◽  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Osmium Tetroxide ◽  
Molecular Level ◽  
Cross Linking ◽  
Chemical Stabilization ◽  
Specimen Preparation ◽  
Sufficient Condition ◽  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

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