LOWER TYPE DIMENSIONS OF SOME MORAN SETS

Fractals ◽  
2019 ◽  
Vol 27 (05) ◽  
pp. 1950082
Author(s):  
JIAOJIAO YANG
Keyword(s):  
Large Class ◽  
The Other ◽  
Moran Set ◽  
Lower Type ◽  
Fractal Sets ◽  
Lipschitz Mappings ◽  
Other Hand ◽  
Lower Spectrum

In this paper, we discuss the lower type dimensions for some Moran sets. On one hand, for Moran set [Formula: see text] with [Formula: see text], we prove that [Formula: see text], where the supremum is taken over all quasi-Lipschitz mappings [Formula: see text]. On the other hand, we obtain the lower spectrum formula for homogeneous Moran sets. In the proof a lower spectrum formula for a large class of fractal sets is established.

Arithmetic functions monotonic at consecutive arguments

2014 ◽  
Vol 51 (2) ◽  
pp. 155-164
Author(s):  
Jean-Marie Koninck ◽  
Florian Luca
Keyword(s):  
Large Class ◽  
The Other ◽  
Arithmetic Functions ◽  
Arbitrary Integer ◽  
Other Hand ◽  
Positive Integers

For a large class of arithmetic functions f, it is possible to show that, given an arbitrary integer κ ≤ 2, the string of inequalities f(n + 1) < f(n + 2) < … < f(n + κ) holds for in-finitely many positive integers n. For other arithmetic functions f, such a property fails to hold even for κ = 3. We examine arithmetic functions from both classes. In particular, we show that there are only finitely many values of n satisfying σ2(n − 1) < σ2 < σ2(n + 1), where σ2(n) = ∑d|nd2. On the other hand, we prove that for the function f(n) := ∑p|np2, we do have f(n − 1) < f(n) < f(n + 1) in finitely often.

scholarly journals Explicit isogenies in quadratic time in any characteristic

2016 ◽  
Vol 19 (A) ◽  
pp. 267-282 ◽  
Author(s):  
Luca De Feo ◽  
Cyril Hugounenq ◽  
Jérôme Plût ◽  
Éric Schost
Keyword(s):  
Finite Field ◽  
Elliptic Curves ◽  
Large Class ◽  
The Other ◽  
Base Field ◽  
Other Hand ◽  
Previous Algorithm ◽  
The Cost ◽  
Interesting Alternative ◽  
Refined Version

Consider two ordinary elliptic curves$E,E^{\prime }$defined over a finite field$\mathbb{F}_{q}$, and suppose that there exists an isogeny$\unicode[STIX]{x1D713}$between$E$and$E^{\prime }$. We propose an algorithm that determines$\unicode[STIX]{x1D713}$from the knowledge of$E$,$E^{\prime }$and of its degree$r$, by using the structure of the$\ell$-torsion of the curves (where $\ell$ is a prime different from the characteristic $p$of the base field). Our approach is inspired by a previous algorithm due to Couveignes, which involved computations using the$p$-torsion on the curves. The most refined version of that algorithm, due to De Feo, has a complexity of $\tilde{O} (r^{2})p^{O(1)}$base field operations. On the other hand, the cost of our algorithm is$\tilde{O} (r^{2})\log (q)^{O(1)}$, for a large class of inputs; this makes it an interesting alternative for the medium- and large-characteristic cases.

Situational Irony

2017 ◽  
Author(s):  
G. R. F. Ferrari
Keyword(s):  
Large Class ◽  
The Other ◽  
Other Hand

When a situation feels like a story, we call it ironic. It seems audience-directed, though we know it is not. On the other hand, a large class of situations that strike people as ironic are simple incongruities, with no apparent connection to how stories work. This chapter therefore proposes a model that applies equally to ironies of simple incongruity and story-like ironies of peripety. It is the play of the mundane against the surprising (and not surprise alone) that makes a situation ironic. This characteristic of situational irony bears comparison with how, in stories, surprises that a plot holds in store must emerge from a plausible nexus of events, rather than springing from nowhere. It turns out, however, that ironies of simple incongruity manifest the same pattern: what makes their incongruity exquisite is that it shows up against a mundane background. Situational ironies ‘speak’ to their audiences, then, in the manner of a three-quarters-on intimation.

scholarly journals On the Exponent of the NK0-Groups of Virtually Infinite Cyclic Groups

2002 ◽  
Vol 45 (2) ◽  
pp. 180-195 ◽  
Author(s):  
Francis X. Connolly ◽  
Stratos Prassidis
Keyword(s):  
Large Class ◽  
The Other ◽  
Main Difficulty ◽  
Cyclic Subgroups ◽  
Cyclic Groups ◽  
Other Hand

AbstractIt is known that the K-theory of a large class of groups can be computed from the K-theory of their virtually infinite cyclic subgroups. On the other hand, Nil-groups appear to be the obstacle in calculations involving the K-theory of the latter. The main difficulty in the calculation of Nil-groups is that they are infinitely generated when they do not vanish. We develop methods for computing the exponent of NK0-groups that appear in the calculation of the K0-groups of virtually infinite cyclic groups.

scholarly journals Branes, quivers and wave-functions

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Taro Kimura ◽  
Milosz Panfil ◽  
Yuji Sugimoto ◽  
Piotr Sułkowski
Keyword(s):  
Large Class ◽  
Wave Functions ◽  
The Other ◽  
Partition Functions ◽  
Other Hand ◽  
Generating Series

We consider a large class of branes in toric strip geometries, both non-periodic and periodic ones. For a fixed background geometry we show that partition functions for such branes can be reinterpreted, on one hand, as quiver generating series, and on the other hand as wave-functions in various polarizations. We determine operations on quivers, as well as SL(2,\mathbb{Z})SL(2,ℤ) transformations, which correspond to changing positions of these branes. Our results prove integrality of BPS multiplicities associated to this class of branes, reveal how they transform under changes of polarization, and imply all other properties of brane amplitudes that follow from the relation to quivers.

Sprung Rhythm

PMLA ◽  
1959 ◽  
Vol 74 (4-Part1) ◽  
pp. 418-425
Author(s):  
Paull F. Baum
Keyword(s):  
Large Class ◽  
The Other ◽  
English Poetry ◽  
Strong Case ◽  
Other Hand ◽  
The Right

In a long essay apropos of Yeats's Oxford Book of Modern Verse, G. M. Young works himself around to modern versification and to G. M. Hopkins. What should have been a development, he says, has turned out to be a catastrophe. “It is common, too, I find to look on Hopkins as the chief legislator of the new mode. For Hopkins as a poet I have the greatest admiration, but his theories on metre seem to me to be as demonstrably wrong as those of any speculator who has ever led a multitude into the wilderness to perish. Unfortunately they have been used as a justification for the cacophonies which naturally result when the metrically deaf write verse, and the metrically deaf are a very large class.” Young is not sure of the right meaning of counterpoint, but “using it as Hopkins did,” he says: “You must counterpoint to avoid monotony, but you must not silence the pattern. You can only work within limits, and if you go beyond them the result is prose. It is no use saying like the Pharisees: ‘It is Corban, a sprung rhythm’: it will not be verse.” That Young uses Hopkins as a stick to beat the moderns is merely amusing; they had their own bit of chaos and needed a form in which to express it. But when he casts a doubt on Hopkins' theories on meter and forth-rightly accuses Hopkins of “an ignorance of his subject so profound that he was not aware there was anything to know”—that is, as he would say, certainly a bone for the dog. And when, on the other hand, Sir Herbert Read, lending his authority to the defense, says that “Hopkins shows that he understood the technique of English poetry as no poet since Dryden had understood it,” it is time to apply a few tests. A beginning was made ten years ago by Yvor Winters, rather more extreme than what follows here. But granted that both Young and Winters have a strong case, it still seems best to deal patiently with Hopkins, if only because he was an impetuous novice in prosody, too impatient to think his theories through before he began to explain them.

scholarly journals Combinatorial analysis.—The foundations of a new theory

1900 ◽  
Vol 66 (424-433) ◽  
pp. 336-337
Keyword(s):  
Large Class ◽  
Finite Differences ◽  
The Other ◽  
Combinatorial Analysis ◽  
Infinitesimal Calculus ◽  
Other Hand ◽  
The One

The object of the paper is to exhibit the processes of the infinitesimal calculus and of the calculus of finite differences as combinatorial processes. A large class of problems can be dealt with by designing on the one hand a function, and on the other hand an operation, in such wise that when the operation is performed upon the function a number results which enumerates the combinations with which the problem is concerned.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

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