Axiom Schemes for m-Valued Functional Calculi of First Order. Part II. Deductive Completeness.

1951 ◽  
Vol 16 (4) ◽  
pp. 269
Author(s):  
Burton Spencer Dreben ◽  
J. B. Rosser ◽  
A. R. Turquette
Keyword(s):  
First Order ◽  
Order Part

scholarly journals First order normalization in the generalized photo gravitational non-planar restricted three body problems

2015 ◽  
Vol 3 (2) ◽  
pp. 46
Author(s):  
Nirbhay Kumar Sinha
Keyword(s):  
Oblate Spheroid ◽  
Second Order ◽  
Elliptic Motion ◽  
First Order ◽  
Short Period ◽  
Order Part ◽  
Three Body

<p>In this paper, we normalised the second-order part of the Hamiltonian of the problem. The problem is generalised in the sense that fewer massive primary is supposed to be an oblate spheroid. By photogravitational we mean that both primaries are radiating. With the help of Mathematica, H<sub>2</sub> is normalised to H<sub>2</sub> = a<sub>1</sub>b<sub>1</sub>w<sub>1</sub> + a<sub>2</sub>b<sub>2</sub>w<sub>2</sub>. The resulting motion is composed of elliptic motion with a short period (2p/w<sub>1</sub>), completed by an oscillation along the z-axis with a short period (2p/w<sub>2</sub>).</p>

scholarly journals Numerical description of mode coupled waves in inhomogeneous magnetized plasmas

2019 ◽  
Vol 203 ◽  
pp. 01011
Author(s):  
Kota Yanagihara ◽  
Shin Kubo ◽  
Toru Tsujimura
Keyword(s):  
Ray Tracing ◽  
Electron Cyclotron Resonance ◽  
Numerical Approach ◽  
Geometrical Optics ◽  
Order Theory ◽  
Complex Amplitude ◽  
First Order ◽  
First Order Theory ◽  
Full Wave Analysis ◽  
Order Part

Geometrical optics (GO) ray tracing has been widely used for a description of electron cyclotron resonance waves in inhomogeneous magnetized fusion plasmas. However, this reduced approach is not correct in sufficient low density plasmas with a sheared magnetic field, where mode coupling between two electromagnetic-like cold plasma modes can occur. Here, we extend a ray tracing method based on the first-order theory of extended geometrical optics (XGO), which captures mode coupled complex amplitude between O and X mode along the ray trajectory. In our approach, reference ray is calculated with ray equation to satisfy the lowest-order part of XGO theory and an evolution of complex amplitude profile along the reference ray is calculated with partial differential equation derived from first-order terms. Calculation results performed by extended ray tracing are in good agreement with 1D full wave analysis. By introducing second-order terms into our numerical approach, diffraction will be treated.

A NOTE ON THE ASYMPTOTIC PROBABILITIES OF EXISTENTIAL SECOND-ORDER MINIMAL GÖDEL SENTENCES WITH EQUALITY

1995 ◽  
Vol 06 (04) ◽  
pp. 339-351
Author(s):  
WIESŁAW SZWAST
Keyword(s):  
Dense Subset ◽  
Unit Interval ◽  
Second Order ◽  
Existential Quantifier ◽  
First Order ◽  
Order Part ◽  
Universal Quantifiers

The minimal Gödel class is the class of first-order prenex sentences whose quantifier prefix consists of two universal quantifiers followed by just one existential quantifier. We prove that asymptotic probabilities of existential second-order sentences, whose first-order part is in the minimal Gödel class, form a dense subset of the unit interval.

3D Interlock Composite Preforming Simulation

2012 ◽  
Vol 504-506 ◽  
pp. 261-266 ◽  
Author(s):  
Jean Guillaume Orliac ◽  
Adrien Charmetant ◽  
Fabrice Morestin ◽  
Philippe Boisse ◽  
Stephane Otin
Keyword(s):  
Virtual Work ◽  
Experimental Testing ◽  
Second Order ◽  
Beam Model ◽  
Forming Simulation ◽  
First Order ◽  
Material Stiffness ◽  
Material Formulation ◽  
Order Part ◽  
Continuous Material

In order to simulate 3D interlock composite reinforcement behavior in forming processes like Resin Transfer Molding (RTM), it is necessary to predict yarns positions in the fabric during the preforming stage of the process. The present paper deals about thick 3D interlock fabric forming simulation using a specific hexahedral semi-discrete finite elements simulation tool : Plast4. Using the virtual work principle, we distinguish the virtual internal work due to tensions in yarns from other internal virtual works. The part of material stiffness relative to yarns tension is described as "first order stiffness" by a 3D discrete beam model. The rest of the rigidities - like transverse compression, shear strains or friction between yarns - are depicted by a continuous quad-based discretization designated in our work as "second order stiffness". A combination of this "first order" discrete model and a continuous orthotropic hyperelastic "second order" material formulation will enables us to simulate interlock preforming process. Jointly to the simulation work, we also had to specify and perform experimental testing identification of material's parameters. Thoses parameters concern both parts of the model. A bilinear tension approach for the yarns discrete modelization and an orthotropic continuous material for the "second order" part.

scholarly journals Normalisation of Hamiltonian in photogravitational elliptic restricted three body problem with Poynting-Robertson drag

2015 ◽  
Vol 3 (1) ◽  
pp. 42
Author(s):  
Vivek Mishra ◽  
Bhola Ishwar
Keyword(s):  
Normal Form ◽  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Lagrangian Function ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
First Order ◽  
Order Part ◽  
Three Body

<p>In this paper, we have performed first order normalization in the photogravitational elliptic restricted three body problem  with Poynting-Robertson drag. We suppose that bigger primary as radiating and smaller primary is an oblate spheroid. We have found the Lagrangian and the Hamiltonian of the problem. Then, we have expanded the Lagrangian function in power series of x and y, where (x, y) are the coordinates of the triangular equilibrium points. Using Whittaker (1965) method, we have found that the second order part H<sub>2</sub> of the Hamiltonian is transformed into the normal form.</p>

Asymptotic probabilities of existential second-order Gödel sentences

1991 ◽  
Vol 56 (2) ◽  
pp. 427-438 ◽  
Author(s):  
Leszek Pacholski ◽  
WiesŁaw Szwast
Keyword(s):  
Second Order ◽  
First Order ◽  
Existential Sentences ◽  
Order Part

In [9] and [10] P. Kolaitis and M. Vardi proved that the 0-1 law holds for the second-order existential sentences whose first-order parts are formulas of Bernays-Schonfinkel or Ackermann prefix classes. They also provided several examples of second-order formulas for which the 0-1 law does not hold, and noticed that the classification of second-order sentences for which the 0-1 law holds resembles the classification of decidable cases of first-order prenex sentences. The only cases they have not settled are the cases of Gödel classes with and without equality.In this paper we confirm the conjecture of Kolaitis and Vardi that the 0-1 law does not hold for the existential second-order sentences whose first-order part is in Gödel prenex form with equality. The proof we give is based on a modification of the example employed by W. Goldfarb [5] in his proof that, contrary to the Gödel claim [6], the class of Gödel prenex formulas with equality is undecidable.

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