On reduction to a symmetric relation

1952 ◽  
Vol 17 (3) ◽  
pp. 188-188 ◽  
Author(s):  
William Craig ◽  
W. V. Quine
Keyword(s):  
Present Note ◽  
Current Paper ◽  
Natural Numbers ◽  
Symmetric Relation ◽  
Dyadic Relation ◽  
A Current

In a current paper, Church and Quine show how any dyadic relation of natural numbers can be defined in terms of a symmetric dyadic relation of natural numbers together with the truth functions and quantification over natural numbers. The purpose of the present note is to extend their result to the following: Where R1, R2, …, ad infinitum are any classes or relations (of any degree) of natural numbers, they can all be defined in terms of a single symmetric dyadic relation of natural numbers together with the truth functions and quantification over natural numbers.Let pi, for each i, be the tth prime > 1. Let the degree of Ri, for each i, be di. Let R be the dyadic relation which each number x bears to each number y such that either x is a factor of y or else x is 0 and y is for some such that . Since R is dyadic, we know from Church and Quine's result that R is definable in terms of a symmetric dyadic relation. Moreover, as seen in the incidental constructions in §1 of Church and Quine, ‘y = x + 1’ is expressible on the same basis.

Methamphetamine and psychiatry: A story of the colourless substance of abuse

2017 ◽  
Vol 25 (3) ◽  
pp. 254-256 ◽  
Author(s):  
Shuichi Suetani ◽  
Jill Reddan ◽  
Carrick Anderson
Keyword(s):  
Clinical Experience ◽  
Animal Studies ◽  
Essential Role ◽  
Historical Context ◽  
Current Paper ◽  
Current Understanding ◽  
Multiple Levels ◽  
A Current

Objective: The current paper aims to provide an overview of methamphetamine in its historical context, integrated with a current understanding derived from animal studies and clinical experience. Conclusion: Despite over a century of clinical experience, methamphetamine remains a troublesome substance. There remains an urgent need at multiple levels from various sectors to combat this ongoing problem, and psychiatry has an essential role in this endeavour.

Publishing Trends of the Journal of Human Factors from 1997–2004

2005 ◽  
Vol 49 (10) ◽  
pp. 946-950
Author(s):  
Michael Curtis ◽  
Thomas Fincannon
Keyword(s):  
Human Factors ◽  
Trend Analysis ◽  
Previous Analysis ◽  
Collaborative Work ◽  
Current Paper ◽  
Current Analysis ◽  
Total Data ◽  
Human Factors Research ◽  
Publication Period ◽  
A Current

Following up on previous analysis of characteristics of articles in the Journal of Human Factors, the current paper is intended to present a current analysis of articles published from 1997-2004. The paper examines all published articles across the following characteristics: year of publication, period of publication, general affiliation of authors, specific affiliation of 1st author, country of origin of authors, technical group, and collaboration comparisons. This information illustrates the important contributors to research in the field, how much research is done within each technical group, and the characteristics of collaborative work produced. By making comparisons within the eight year period and comparing total data to previous trend analysis (Zavod & Hitt, 2000) this paper will illustrate the direction of human factors research. The information reported can provide a reference for professionals, students, and prospective researchers in identifying where research is taking place and burgeoning topics of interest.

Some theorems on definability and decidability

1952 ◽  
Vol 17 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Alonzo Church ◽  
W. V. Quine
Keyword(s):  
Number Theory ◽  
Functional Calculus ◽  
Natural Numbers ◽  
Quantification Theory ◽  
First Order ◽  
Dyadic Relation ◽  
Truth Value ◽  
Individual Variables

In this paper a theorem about numerical relations will be established and shown to have certain consequences concerning decidability in quantification theory, as well as concerning the foundation of number theory. The theorem is that relations of natural numbers are reducible in elementary fashion to symmetric ones; i.e.:Theorem I. For every dyadic relation R of natural numbers there is a symmetric dyadic relation H of natural numbers such that R is definable in terms of H plus just truth-functions and quantification over natural numbers.To state the matter more fully, there is a (well-formed) formula ϕ of pure quantification theory, or first-order functional calculus, which meets these conditions:(a) ϕ has ‘x’ and ‘y’ as sole free individual variables;(b) ϕ contains just one predicate letter, and it is dyadic;(c) for every dyadic relation R of natural numbers there is a symmetric dyadic relation H of natural numbers such that, when the predicate letter in ϕ is interpreted as expressing H, ϕ comes to agree in truth-value with ‘x bears R to y’ for all values of ‘x’ and ‘y’.

Resolving Crystallites in Zirconium Oxide Films

1969 ◽  
Vol 27 ◽  
pp. 140-141
Author(s):  
R.A. Ploc
Keyword(s):  
Electron Microscope ◽  
Inelastic Scattering ◽  
Zirconium Oxide ◽  
Oxide Films ◽  
Optic Axis ◽  
Objective Lens ◽  
Microscope Objective ◽  
Linear Optic ◽  
A Current ◽  
Microscope Objective Lens

The optic axis of an electron microscope objective lens is usually assumed to be straight and co-linear with the mechanical center. No reason exists to assume such perfection and, indeed, simple reasoning suggests that it is a complicated curve. A current centered objective lens with a non-linear optic axis when used in conjunction with other lenses, leads to serious image errors if the nature of the specimen is such as to produce intense inelastic scattering.

Structure of Palladium Single-Crystal Films Prepared by Flash Evaporation onto (001) NaCl Substrates

1970 ◽  
Vol 28 ◽  
pp. 456-457
Author(s):  
L. E. Murr ◽  
G. Wong
Keyword(s):  
Single Crystal ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
High Rate ◽  
Flash Evaporation ◽  
Optimum Load ◽  
Single Crystal Films ◽  
Crystal Films ◽  
A Current

Palladium single-crystal films have been prepared by Matthews in ultra-high vacuum by evaporation onto (001) NaCl substrates cleaved in-situ, and maintained at ∼ 350° C. Murr has also produced large-grained and single-crystal Pd films by high-rate evaporation onto (001) NaCl air-cleaved substrates at 350°C. In the present work, very large (∼ 3cm2), continuous single-crystal films of Pd have been prepared by flash evaporation onto air-cleaved (001) NaCl substrates at temperatures at or below 250°C. Evaporation rates estimated to be ≧ 2000 Å/sec, were obtained by effectively short-circuiting 1 mil tungsten evaporation boats in a self-regulating system which maintained an optimum load current of approximately 90 amperes; corresponding to a current density through the boat of ∼ 4 × 104 amperes/cm2.

Novel magneto-optical recording materials: Bi-substituted garnet films

1991 ◽  
Vol 49 ◽  
pp. 776-777
Author(s):  
Takao Suzuki ◽  
Hossein Nuri
Keyword(s):  
Grain Size ◽  
Amorphous Film ◽  
Nitrogen Atmosphere ◽  
Optical Recording ◽  
Garnet Film ◽  
Media Noise ◽  
Garnet Films ◽  
Order Of Magnitude ◽  
A New Technique ◽  
A Current

For future high density magneto-optical recording materials, a Bi-substituted garnet film ((BiDy)3(FeGa)5O12) is an attractive candidate since it has strong magneto-optic effect at short wavelengths less than 600 nm. The signal in read back performance at 500 nm using a garnet film can be an order of magnitude higher than a current rare earth-transition metal amorphous film. However, the granularity and surface roughness of such crystalline garnet films are the key to control for minimizing media noise.We have demonstrated a new technique to fabricate a garnet film which has much smaller grain size and smoother surfaces than those annealed in a conventional oven. This method employs a high ramp-up rate annealing (Γ = 50 ~ 100 C/s) in nitrogen atmosphere. Fig.1 shows a typical microstruture of a Bi-susbtituted garnet film deposited by r.f. sputtering and then subsequently crystallized by a rapid thermal annealing technique at Γ = 50 C/s at 650 °C for 2 min. The structure is a single phase of garnet, and a grain size is about 300A.

Facet Topography and Dislocation Structure as a Possible Source for Electrical Heterogeneity in [001] TILT Bicrystals of YBa2Cu3O7-δ

1996 ◽  
Vol 54 ◽  
pp. 338-339
Author(s):  
I-Fei Tsu ◽  
D.L. Kaiser ◽  
S.E. Babcock
Keyword(s):  
Grain Boundary ◽  
Critical Current Density ◽  
Critical Current ◽  
Current Density ◽  
Electromagnetic Properties ◽  
Length Scale ◽  
Density Values ◽  
Current Densities ◽  
Applied Fields ◽  
A Current

A current theme in the study of the critical current density behavior of YBa2Cu3O7-δ (YBCO) grain boundaries is that their electromagnetic properties are heterogeneous on various length scales ranging from 10s of microns to ˜ 1 Å. Recently, combined electromagnetic and TEM studies on four flux-grown bicrystals have demonstrated a direct correlation between the length scale of the boundaries’ saw-tooth facet configurations and the apparent length scale of the electrical heterogeneity. In that work, enhanced critical current densities are observed at applied fields where the facet period is commensurate with the spacing of the Abrikosov flux vortices which must be pinned if higher critical current density values are recorded. To understand the microstructural origin of the flux pinning, the grain boundary topography and grain boundary dislocation (GBD) network structure of [001] tilt YBCO bicrystals were studied by TEM and HRTEM.

Rem Study of Current Effect on the Structure of Clean Si(111) Surface

1990 ◽  
Vol 48 (1) ◽  
pp. 306-307
Author(s):  
A. Yamanaka ◽  
H. Ohse ◽  
K. Yagi
Keyword(s):  
The Other ◽  
Current Direction ◽  
Clean Surface ◽  
Current Effect ◽  
Atomic Steps ◽  
Step Bunching ◽  
Terrace Width ◽  
Step Down ◽  
A Current

Recently current effects on clean and metal adsorbate surfaces have attracted much attention not only because of interesting phenomena but also because of practically importance in treatingclean and metal adsorbate surfaces [1-6]. In the former case, metals deposited migrate on the deposit depending on the current direction and a patch of the deposit expands on the clean surface [1]. The migration is closely related to the adsorbate structures and substrate structures including their anisotropy [2,7]. In the latter case, configurations of surface atomic steps depends on the current direction. In the case of Si(001) surface equally spaced array of monatom high steps along the [110] direction produces the 2x1 and 1x2 terraces. However, a relative terrace width of the two domain depends on the current direction; a step-up current widen terraces on which dimers are parallel to the current, while a step-down current widen the other terraces [3]. On (111) surface, a step-down current produces step bunching at temperatures between 1250-1350°C, while a step-up current produces step bunching at temperatures between 1050-1250°C [5].In the present paper, our REM observations on a current induced step bunching, started independently, are described.Our results are summarized as follows.(1) Above around 1000°C a step-up current induces step bunching. The phenomenon reverses around 1200 C; a step-down current induces step bunching. The observations agree with the previous reports [5].

A highly stable CoMo2S4/Ni3S2 heterojunction electrocatalyst for efficient hydrogen evolution

2021 ◽  
Author(s):  
Minmin Wang ◽  
Mengke Zhang ◽  
Wenwu Song ◽  
Weiting Zhong ◽  
Xunyue Wang ◽  
...  
Keyword(s):  
Hydrogen Evolution ◽  
Current Density ◽  
A Current

A CoMo2S4/Ni3S2 heterojunction is prepared with an overpotential of only 51 mV to drive a current density of 10 mA cm−2 in 1 M KOH solution and ∼100% of the potential remains in the ∼50 h chronopotentiometric curve at 10 mA cm−2.

Current Trends in the Training and Utilization of Paraprofessionals in Speech and Language Programs

1991 ◽  
Vol 22 (2) ◽  
pp. 51-59 ◽  
Author(s):  
Kathy L. Coufal ◽  
Allen L. Steckelberg ◽  
Stanley F. Vasa
Keyword(s):  
Selection Criteria ◽  
Job Descriptions ◽  
Paraprofessional Training ◽  
Language Programs ◽  
Program Administrators ◽  
Current Trends ◽  
Training And Supervision ◽  
Communicative Disorders ◽  
Supervision Practices ◽  
A Current

Administrators of programs for children with communicative disorders in 11 midwestern states were surveyed to assess trends in the training and utilization of paraprofessionals. Topics included: (a) current trends in employment, (b) paraprofessional training, (c) use of ASHA and state guidelines, and (d) district policies for supervision. Selection criteria, use of job descriptions, training programs, and supervision practices and policies were examined. Results indicate that paraprofessionals are used but that standards for training and supervision are not consistently applied across all programs. Program administrators report minimal training for supervising professionals.

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