On the weak non-finite cover property and the n-tuples of simple structures

2005 ◽  
Vol 70 (1) ◽  
pp. 235-251 ◽  
Author(s):  
Evgueni Vassiliev
Keyword(s):  
Direct Proof ◽  
Simple Theory ◽  
Finite Cover ◽  
Stable Case ◽  
Combinatorial Condition ◽  
The Way

AbstractThe weak non-finite cover property (wnfcp) was introduced in [1] in connection with “axiomatizability” of lovely pairs of models of a simple theory. We find a combinatorial condition on a simple theory equivalent to the wnfcp, yielding a direct proof that the non-finite cover property implies the wnfcp, and that the wnfcp is preserved under reducts. We also study the question whether the wnfcp is preserved when passing from a simple theory T to the theory Tp of lovely pairs of models of T (true in the stable case). While the question remains open, we show, among other things, that if (for a T with the wnfcp) Tp is low, then TP has the wnfcp. To study this question, we describe “double lovely pairs”, and, along the way, we develop the notion of a “lovely n-tuple” of models of a simple theory, which is an analogue of the notion of a beautiful tuple of models of stable theories [2].

scholarly journals ON UNIFORM DECISION PROBLEMS AND ABSTRACT PROPERTIES OF SMALL OVERLAP MONOIDS

2011 ◽  
Vol 21 (01n02) ◽  
pp. 217-233
Author(s):  
MARK KAMBITES
Keyword(s):  
Isomorphism Problem ◽  
Decision Problems ◽  
Asymptotic Estimates ◽  
Case Complexity ◽  
Abstract Structure ◽  
Combinatorial Condition ◽  
Necessary And Sufficient ◽  
Small Overlap ◽  
The Way

We study the way in which the abstract structure of a small overlap monoid is reflected in, and may be algorithmically deduced from, a small overlap presentation. We show that every C(2) monoid admits an essentially canonical C(2) presentation; by counting canonical presentations we obtain asymptotic estimates for the number of non-isomorphic monoids admitting a-generator, k-relation presentations of a given length. We demonstrate an algorithm to transform an arbitrary presentation for a C(m) monoid (m at least 2) into a canonical C(m) presentation, and a solution to the isomorphism problem for C(2) presentations. We also find a simple combinatorial condition on a C(4) presentation which is necessary and sufficient for the monoid presented to be left cancellative. We apply this to obtain algorithms to decide if a given C(4) monoid is left cancellative, right cancellative or cancellative, and to show that cancellativity properties are asymptotically visible in the sense of generic-case complexity.

On types of CB-rank 1 in simple theories

2008 ◽  
Vol 7 (4) ◽  
pp. 895-899 ◽  
Author(s):  
Anand Pillay
Keyword(s):  
Recent Result ◽  
Simple Theory ◽  
Countable Model ◽  
Stable Case ◽  
Simple Theories ◽  
Complete Type ◽  
Special Case

AbstractWe prove that if M0 is a model of a simple theory, and p(x) is a complete type of Cantor–Bendixon rank 1 over M0, then p is stationary and regular. As a consequence we obtain another proof that any countable model M0 of a countable complete simple theory T has infinitely many countable elementary extensions up to M0-isomorphism. The latter extends earlier results of the author in the stable case, and is a special case of a recent result of Tanovic.

scholarly journals A Specialisation of the Bump–Friedberg L-function

2015 ◽  
Vol 58 (3) ◽  
pp. 580-595
Author(s):  
Nadir Matringe
Keyword(s):  
Integral Representation ◽  
Number Field ◽  
Direct Proof ◽  
Automorphic Representation ◽  
Simple Theory ◽  
Cuspidal Automorphic Representation

AbstractWe study the restriction of Bump–Friedberg integrals to affine lines {(s + α, 2s), s ∊ ℂ}. It has simple theory, very close to that of the Asai L-function. It is an integral representation of the product L(s + α, π)L(2s, Λ2, π), which we denote by Llin(s, π, α) for this abstract, when π is a cuspidal automorphic representation of GL(k, 𝔸) for 𝔸 the adeles of a number field. When k is even, we show that the partial L-function Llin,S(s, π, α) has a pole at 1/2 if and only if π admits a (twisted) global period. This gives a more direct proof of a theorem of Jacquet and Friedberg, asserting that π has a twisted global period if and only if L(α + 1/2, π) ≠ 0 and L(1, Λ2 , π) = ∞. When k is odd, the partial L-function is holmorphic in a neighbourhood of Re(s) ≥ 1/2 when Re(α) is ≥ 0.

scholarly journals WINNING THE HEARTS OF THE MALAYS: THE PERSPECTIVE OF THE AUTHOR OF SYAIR TUAN HAMPRIS TOWARDS THE COLONIALISTS

2020 ◽  
Vol 2 (5) ◽  
pp. 01-15
Author(s):  
Rahimah Hamdan
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century ◽  
Text Analysis ◽  
Local Community ◽  
Direct Proof ◽  
Indigenous Communities ◽  
The Other ◽  
Patriarchal System ◽  
Colonial Government ◽  
The Way

This study was aimed at identifying the author’s perspective of the colonialists, and to analyse her relationship with one of them in her poem. The British colonisation of the Malay world in the nineteenth century gave rise to various reactions and attitudes among the indigenous communities, the majority of whom were opposed to colonisation, as recorded in traditional Malay literary works. Most of these works expressed the anxiety and hardships they encountered in life under the colonial government. Therefore, it would have been disturbing if any Malay writer were to heap praises on the British colonialists, more so if the writer happened to be a female, as according to the patriarchal system that dominated the conventional Malay literary world, women should be ‘silent’. Nevertheless, this tradition was broken by Hajah Wok Aisyah Nik Idris from Terengganu with her writing of Syair Tuan Hampris, in the early twentieth century. Ironically, in her poem, the author appears to have forgotten the miserable state of the Malays in the other states under the British administration. As such, did Hajah Wok Aisyah have her own reasons for writing the way she did? Was the author of Syair Tuan Hampris captivated by the British administrator? Did the British administrator, J. L. Humphreys, succeed in winning the hearts of the Malays in Terengganu? The method of text analysis was employed in this study, guided by the eight ways proposed by the first British Resident-General of the Federation of Malaya, Sir Frank Swettenham, to Syair Tuan Hampris. This study found that Syair Tuan Hampris invites its readers to savour the unique spectrum of relationships that existed between the colonised people, and the colonialists. The colonialists are no longer regarded as individuals who brought ruin and destruction to the local community, but instead, all their actions are held as being honourable. Thus, the author, being a woman, was able to perfectly explain her closeness to one such colonialist in the verses of her poem. In conclusion, Syair Tuan Hampris is strong and direct proof that women had a voice in the community at that time, even though they had to go against the conventions of Malay literature.

Estimating ionospheric cross-modulation

1976 ◽  
Vol 351 (1665) ◽  
pp. 277-293 ◽  
Keyword(s):  
Radio Wave ◽  
Time Of Day ◽  
Simple Theory ◽  
Cross Modulation ◽  
Radio Engineer ◽  
The Way

A method of predicting the modulation imposed on a wanted radio wave by a powerful disturbing transmitter is described. It is shown that there are five general cases, depending on the positions of the receiver and the wanted and disturbing transmitters, their frequencies, the time of day and some other factors. Each case is examined in detail and it is decided whether the simple theory of Huxley & Ratcliffe is applicable for the situation. If not, then some modifications are suggested to this theory. More elaborate refinements are also described, but generally they need not be used by the radio engineer who is concerned only with achieving a rough guideline to indicate cross-modulation as a possible source of interference in communications. Some examples of the way in which the simple theory can be easily amended to produce more reliable results are given.

Self-sacrifice for in-group's history: A diachronic perspective

2018 ◽  
Vol 41 ◽  
Author(s):  
Maria Babińska ◽  
Michal Bilewicz
Keyword(s):  
Clinical Psychology ◽  
Historical Events ◽  
Emotional Events ◽  
Reciprocal Process ◽  
The Way

AbstractThe problem of extended fusion and identification can be approached from a diachronic perspective. Based on our own research, as well as findings from the fields of social, political, and clinical psychology, we argue that the way contemporary emotional events shape local fusion is similar to the way in which historical experiences shape extended fusion. We propose a reciprocal process in which historical events shape contemporary identities, whereas contemporary identities shape interpretations of past traumas.

What is the purpose of cognition?

2020 ◽  
Vol 43 ◽  
Author(s):  
Aba Szollosi ◽  
Ben R. Newell
Keyword(s):  
Infinite Number ◽  
Human Cognition ◽  
The Way

Abstract The purpose of human cognition depends on the problem people try to solve. Defining the purpose is difficult, because people seem capable of representing problems in an infinite number of ways. The way in which the function of cognition develops needs to be central to our theories.

Peculiarity Parameters

1976 ◽  
Vol 32 ◽  
pp. 233-254
Author(s):  
H. M. Maitzen
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Theoretical Work ◽  
Observational Evidence ◽  
Rotator Model ◽  
Peculiar Behaviour ◽  
Field Spectrum ◽  
Oblique Rotator ◽  
Ap Stars ◽  
The Way

Ap stars are peculiar in many aspects. During this century astronomers have been trying to collect data about these and have found a confusing variety of peculiar behaviour even from star to star that Struve stated in 1942 that at least we know that these phenomena are not supernatural. A real push to start deeper theoretical work on Ap stars was given by an additional observational evidence, namely the discovery of magnetic fields on these stars by Babcock (1947). This originated the concept that magnetic fields are the cause for spectroscopic and photometric peculiarities. Great leaps for the astronomical mankind were the Oblique Rotator model by Stibbs (1950) and Deutsch (1954), which by the way provided mathematical tools for the later handling pulsar geometries, anti the discovery of phase coincidence of the extrema of magnetic field, spectrum and photometric variations (e.g. Jarzebowski, 1960).

The mensuration of interfaces

1992 ◽  
Vol 50 (1) ◽  
pp. 216-217
Author(s):  
W.M. Stobbs
Keyword(s):  
Electron Microscopy ◽  
50Th Anniversary ◽  
Numerical Data ◽  
Industrial Applications ◽  
Dynamical Theory ◽  
Large Strains ◽  
Reasonable Approach ◽  
Lattice Resolution ◽  
Analogue To Digital ◽  
The Way

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.

Convergent-bceam diffraction studies on lead zirconate titanate Ceramics

1986 ◽  
Vol 44 ◽  
pp. 482-483
Author(s):  
M.L.A. Dass ◽  
T.A. Bielicki ◽  
G. Thomas ◽  
T. Yamamoto ◽  
K. Okazaki
Keyword(s):  
Lead Zirconate Titanate ◽  
Direct Proof ◽  
Lead Zirconate ◽  
Subsolidus Phase ◽  
Pzt Ceramics ◽  
Subsolidus Phase Diagram ◽  
Zirconate Titanate ◽  
Two Phases ◽  
Cbd Method ◽  
Titanate Ceramics

Lead zirconate titanate, Pb(Zr,Ti)O3 (PZT), ceramics are ferroelectrics formed as solid solutions between ferroelectric PbTiO3 and ant iferroelectric PbZrO3. The subsolidus phase diagram is shown in figure 1. PZT transforms between the Ti-rich tetragonal (T) and the Zr-rich rhombohedral (R) phases at a composition which is nearly independent of temperature. This phenomenon is called morphotropism, and the boundary between the two phases is known as the morphotropic phase boundary (MPB). The excellent piezoelectric and dielectric properties occurring at this composition are believed to.be due to the coexistence of T and R phases, which results in easy poling (i.e. orientation of individual grain polarizations in the direction of an applied electric field). However, there is little direct proof of the coexistence of the two phases at the MPB, possibly because of the difficulty of distinguishing between them. In this investigation a CBD method was found which would successfully differentiate between the phases, and this was applied to confirm the coexistence of the two phases.

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