Measure preserving actions of affine semigroups and patterns

2016 ◽  
Vol 38 (2) ◽  
pp. 473-498 ◽  
Author(s):  
VITALY BERGELSON ◽  
JOEL MOREIRA
Keyword(s):  
Ergodic Theorem ◽  
Affine Group ◽  
General Situation ◽  
Finite Partition ◽  
Integral Domains ◽  
New Approach ◽  
Ring Of Integers ◽  
Affine Semigroups ◽  
Multiplicative Groups ◽  
Measure Preserving Actions

Ergodic and combinatorial results obtained in Bergelson and Moreira [Ergodic theorem involving additive and multiplicative groups of a field and$\{x+y,xy\}$patterns.Ergod. Th. & Dynam. Sys.to appear, published online 6 October 2015, doi:10.1017/etds.2015.68], involved measure preserving actions of the affine group of a countable field$K$. In this paper, we develop a new approach, based on ultrafilter limits, which allows one to refine and extend the results obtained in Bergelson and Moreira,op. cit., to a more general situation involving measure preserving actions of thenon-amenableaffine semigroups of a large class of integral domains. (The results and methods in Bergelson and Moreira,op. cit., heavily depend on the amenability of the affine group of a field.) Among other things, we obtain, as a corollary of an ultrafilter ergodic theorem, the following result. Let$K$be a number field and let${\mathcal{O}}_{K}$be the ring of integers of$K$. For any finite partition$K=C_{1}\cup \cdots \cup C_{r}$, there exists$i\in \{1,\ldots ,r\}$such that, for many$x\in K$and many$y\in {\mathcal{O}}_{K}$,$\{x+y,xy\}\subset C_{i}$.

scholarly journals Ergodic theorem involving additive and multiplicative groups of a field and patterns

2015 ◽  
Vol 37 (3) ◽  
pp. 673-692 ◽  
Author(s):  
VITALY BERGELSON ◽  
JOEL MOREIRA
Keyword(s):  
Finite Field ◽  
Ergodic Theorem ◽  
Finite Fields ◽  
Correspondence Principle ◽  
Combinatorial Problems ◽  
Alternative Proof ◽  
Large Set ◽  
Sidon Sets ◽  
New Variant ◽  
Multiplicative Groups

We establish a ‘diagonal’ ergodic theorem involving the additive and multiplicative groups of a countable field $K$ and, with the help of a new variant of Furstenberg’s correspondence principle, prove that any ‘large’ set in $K$ contains many configurations of the form $\{x+y,xy\}$. We also show that for any finite coloring of $K$ there are many $x,y\in K$ such that $x,x+y$ and $xy$ have the same color. Finally, by utilizing a finitistic version of our main ergodic theorem, we obtain combinatorial results pertaining to finite fields. In particular, we obtain an alternative proof for a result obtained by Cilleruelo [Combinatorial problems in finite fields and Sidon sets. Combinatorica32(5) (2012), 497–511], showing that for any finite field $F$ and any subsets $E_{1},E_{2}\subset F$ with $|E_{1}|\,|E_{2}|>6|F|$, there exist $u,v\in F$ such that $u+v\in E_{1}$ and $uv\in E_{2}$.

scholarly journals ElGamal Public-Key cryptosystem in multiplicative groups of quotient rings of polynomials over finite fields

2005 ◽  
Vol 2 (1) ◽  
pp. 63-77 ◽  
Author(s):  
A.N. El-Kassar ◽  
Ramzi Haraty
Keyword(s):  
Finite Fields ◽  
Multiplicative Group ◽  
Quotient Ring ◽  
Classical Case ◽  
Irreducible Polynomials ◽  
Gaussian Integers ◽  
Ring Of Integers ◽  
Elgamal Encryption ◽  
Multiplicative Groups ◽  
Quotient Rings

The ElGamal encryption scheme is described in the setting of any finite cyclic group G. Among the groups of most interest in cryptography are the multiplicative group Zp of the ring of integers modulo a prime p, and the multiplicative groups F2m of finite fields of characteristic two. The later requires finding irreducible polynomials H(x) and constructing the quotient ring Z2[x]/ < h(x)>. El-Kassar et al. modified the ElGamal scheme to the domain of Gaussian integers. El-Kassar and Haraty gave an extension in the multiplicative group of Zp[x]/ < x2 >. Their major finding is that the quotient ring need not be a field. In this paper, we consider another extension employing the group of units of Z2[x]/ < h(x) >, where H(x) = h1(x)h2(x)..Hr(x)is a product of irreducible polynomials whose degrees are pairwise relatively prime. The arithmetic needed in this new setting is described. Examples, algorithms and proofs are given. Advantages of the new method are pointed out and comparisons with the classical case of F2m are made.

scholarly journals Effective anisotropic stresses of the relic gravitons

2020 ◽  
pp. 2050112
Author(s):  
Massimo Giovannini
Keyword(s):  
Coordinate System ◽  
Effective Action ◽  
Pressure Fluctuations ◽  
Normal Modes ◽  
General Situation ◽  
Conformal Time ◽  
Coordinate Systems ◽  
Gauge Invariant ◽  
New Approach ◽  
Anisotropic Stress

The effective anisotropic stresses induced by the scalar modes of the geometry depend on the coordinate system so that the comparison of the competing results is ultimately determined by the evolution of the pivotal variables in each particular gauge. After arguing that the only reasonable physical coordinate systems for this problem are the ones where the gauge freedom is completely fixed (like the longitudinal and the uniform curvature gauges), we propose a novel gauge-invariant strategy for the comparison of gauge-dependent results. Instead of employing the pivotal variables of a given coordinate system, the effective anisotropic stress is solely expressed in terms of the gravitating normal modes of the plasma and in terms of their conformal time derivatives. The new approach is explicitly gauge-invariant and when the wavelengths of the normal modes are either shorter or larger than the sound horizon, the physical limits of the anisotropic stresses are determined without relying on the specific details of the background evolution. The relevance of the proposed strategy is discussed in the general situation where the scalar anisotropic stress and the nonadiabatic pressure fluctuations are simultaneously present. We finally argue that the anisotropic stress can be most efficiently obtained from the second-order effective action of the curvature inhomogeneities.

The International Crisis of 1791: Poland Between the Triple Alliance and Russia

1975 ◽  
Vol 2 (1) ◽  
pp. 1-63
Author(s):  
Jerzy Łojek
Keyword(s):  
World War I ◽  
Political Development ◽  
General Situation ◽  
World War ◽  
International Crisis ◽  
New Approach ◽  
New Material ◽  
Basic Facts ◽  
New Research ◽  
Almost All

AbstractMost Polish historians have misinterpreted Poland's international situation during the general "Eastern Crisis" of 1787-1791, which coincided with the period of great internal Polish political development during the Four-Year Diet of 1788-1792, whose work was crowned with the declaration of the May Third Constitution of 1791. Among Polish historians only Szymon Askenazy, and among foreigners only the American, Robert Howard Lord, fully understood the situation and interpreted it in conformity with the facts, although many important developments were unknown when they wrote on this theme. The purpose of this study is to re-interpret many facts of Poland's international situation during the Eastern Crisis, while also offering a new approach to the problem on the basis of many new documents unavailable until now. Although my interpretation runs contrary to the opinions of most Polish historians, extensive research in Polish as well as foreign archives supports it under close examination. The most important point I wish to make is that Poland's general situation in the years preceding the Second Partition of 1793 was not as hopeless as has generally been considered, and there were opportunities for the country to avoid the mortal blows of 1792-1794. It is important to emphasize that almost all the facts concerning Poland's international position at the end of the eighteenth century had been established by scholars before World War I. Rather than adding to this basic factual storehouse, further studies only interpreted or discussed them. But new research indicates that the basic facts were not at all well known, and hence the interpretations were overhasty. This is, therefore, a fresh attempt to show one important aspect of Poland's chances during this period in the light of considerable new material.

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Processing Immunoperoxidase Labeled Cell Monolayers and Cryostat Sesctions For Electron Microscopy

1985 ◽  
Vol 43 ◽  
pp. 714-715
Author(s):  
K. Chien ◽  
R. Van de Velde ◽  
I.P. Shintaku ◽  
A.F. Sassoon
Keyword(s):  
Cell Monolayer ◽  
Cell Types ◽  
Surface Antigens ◽  
Immunoperoxidase Method ◽  
Reaction Step ◽  
Hot Plate ◽  
Air Drying ◽  
New Approach ◽  
Cell Monolayers ◽  
Glass Slides

Immunoelectron microscopy of neoplastic lymphoma cells is valuable for precise localization of surface antigens and identification of cell types. We have developed a new approach in which the immunohistochemical staining can be evaluated prior to embedding for EM and desired area subsequently selected for ultrathin sectioning.A freshly prepared lymphoma cell suspension is spun onto polylysine hydrobromide- coated glass slides by cytocentrifugation and immediately fixed without air drying in polylysine paraformaldehyde (PLP) fixative. After rinsing in PBS, slides are stained by a 3-step immunoperoxidase method. Cell monolayer is then fixed in buffered 3% glutaraldehyde prior to DAB reaction. After the DAB reaction step, wet monolayers can be examined under LM for presence of brown reaction product and selected monolayers then processed by routine methods for EM and embedded with the Chien Re-embedding Mold. After the polymerization, the epoxy blocks are easily separated from the glass slides by heatingon a 100°C hot plate for 20 seconds.

TEM study of a biofilm on copper corrosion

1996 ◽  
Vol 54 ◽  
pp. 220-221
Author(s):  
W. A. Chiou ◽  
N. Kohyama ◽  
B. Little ◽  
P. Wagner ◽  
M. Meshii
Keyword(s):  
Marine Bacterium ◽  
Culture Medium ◽  
Copper Alloys ◽  
Pure Copper ◽  
Localized Corrosion ◽  
Natural Seawater ◽  
Copper Corrosion ◽  
New Approach ◽  
The Past ◽  
Copper Tolerant

The corrosion of copper and copper alloys in a marine environment is of great concern because of their widespread use in heat exchangers and steam condensers in which natural seawater is the coolant. It has become increasingly evident that microorganisms play an important role in the corrosion of a number of metals and alloys under a variety of environments. For the past 15 years the use of SEM has proven to be useful in studying biofilms and spatial relationships between bacteria and localized corrosion of metals. Little information, however, has been obtained using TEM capitalizing on its higher spacial resolution and the transmission observation of interfaces. The research presented herein is the first step of this new approach in studying the corrosion with biological influence in pure copper.Commercially produced copper (Cu, 99%) foils of approximately 120 μm thick exposed to a copper-tolerant marine bacterium, Oceanospirillum, and an abiotic culture medium were subsampled (1 cm × 1 cm) for this study along with unexposed control samples.

High resolution at low voltage: A new approach

1989 ◽  
Vol 47 ◽  
pp. 76-77
Author(s):  
Arthur V. Jones
Keyword(s):  
Low Voltage ◽  
Emission Sources ◽  
New Approach ◽  
Design Concepts ◽  
Probe Diameter ◽  
Low Voltage Operation ◽  
Sufficient Intensity ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes ◽  
Immersion Type

With the introduction of field-emission sources and “immersion-type” objective lenses, the resolution obtainable with modern scanning electron microscopes is approaching that obtainable in STEM and TEM-but only with specific types of specimens. Bulk specimens still suffer from the restrictions imposed by internal scattering and the need to be conducting. Advances in coating techniques have largely overcome these problems but for a sizeable body of specimens, the restrictions imposed by coating are unacceptable.For such specimens, low voltage operation, with its low beam penetration and freedom from charging artifacts, is the method of choice.Unfortunately the technical dificulties in producing an electron beam sufficiently small and of sufficient intensity are considerably greater at low beam energies — so much so that a radical reevaluation of convential design concepts is needed.The probe diameter is usually given by

New approach to drawing in dental anatomy

1968 ◽  
Vol 32 (3) ◽  
pp. 279-282
Author(s):  
JI Mock ◽  
JW Grenfell ◽  
WA Richter
Keyword(s):  
New Approach ◽  
Dental Anatomy
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