scholarly journals Three improvements to the HPSG model theory

2021 ◽  
Author(s):  
Adam Przepiórkowski
Keyword(s):  
Model Theory ◽  
Second Order ◽  
The Third ◽  
Order Extension

The aim of this paper is to propose three improvements to the HPSG model theory. The first is a solution to certain formal problems identified in Richter 2007. These problems are solved if HPSG models are rooted models of utterances and not exhaustive models of languages, as currently assumed. The proposed solution is compatible with all existing views on the nature of objects inhabiting models. The second improvement is a solution to “Höhle’s Problem”, i.e., the problem of massive spurious ambiguities in models of utterances. The third is a formalisation of Yatabe's (2004) analysis of the coordination of unlike categories, one that requires a second-order extension of the language for stating HPSG grammars.

scholarly journals B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 340-346
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Spline Function ◽  
Cubic Spline ◽  
Second Order ◽  
Third Order ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
The Third ◽  
New Procedures

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Models in sociocybernetics: A 20 year review at the ISA-RC51 on Sociocybernetics

2019 ◽  
Vol 67 (4) ◽  
pp. 527-543
Author(s):  
Luciano Gallón
Keyword(s):  
Systems Theory ◽  
Model Theory ◽  
Second Order ◽  
Theory And Practice ◽  
Integral Approach ◽  
Research Committee ◽  
Model Concept ◽  
International Sociological Association ◽  
Models And Modelling

What is a model? A frequently asked question by an observer when sharing the record of their work describing reality when communicating findings. However, there are other related questions: Has the model been validated? Is the model valid? Is the model useful? This article gives possible answers to these questions from the sociocybernetics paradigm. The second order, the observation of the observer, is an integral approach to the study of the model concept, but, above all, to the action involved: making a model. The text draws on systems theory and offers a reflection on the possibilities, alternatives, barriers and potentials of making models-based sociocybernetics and, also, sociocybernetics-based models. The reader will find a review of the approach to reality through models, the scales of observables and observers, an account of main works related to model theory and practice, and a review of tools available for making and simulating models and discussion on model value. The article concludes with a review of the last 20 years of the International Sociological Association (ISA) Research Committee 51 (RC51) on Sociocybernetics activity related to models and modelling.

The Baire category theorem in weak subsystems of second-order arithmetic

1993 ◽  
Vol 58 (2) ◽  
pp. 557-578 ◽  
Author(s):  
Douglas K. Brown ◽  
Stephen G. Simpson
Keyword(s):  
Functional Analysis ◽  
Model Theory ◽  
Baire Category ◽  
Second Order ◽  
Base System ◽  
Baire Category Theorem ◽  
Second Order Arithmetic ◽  
Category Theorem ◽  
Order Arithmetic

AbstractWorking within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call and , and , show that suffices to prove B.C.T.II. Some model theory of and its importance in view of Hilbert's program is discussed, as well as applications of our results to functional analysis.

Application of the Godunov method and its second-order extension to cascade flow modeling

AIAA Journal ◽  
1984 ◽  
Vol 22 (11) ◽  
pp. 1609-1615 ◽  
Author(s):  
Shmuel Eidelman ◽  
Phillip Colella ◽  
Raymond P. Shreeve
Keyword(s):  
Second Order ◽  
Godunov Method ◽  
Flow Modeling ◽  
Cascade Flow ◽  
Order Extension

WENO-TVD schemes for hyperbolic conservation laws

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Yousef Hashem Zahran
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Building Blocks ◽  
Second Order ◽  
Third Order ◽  
Weno Schemes ◽  
Hyperbolic Conservation ◽  
Systematic Assessment ◽  
The Third ◽  
Seventh Order

The purpose of this paper is twofold. Firstly we carry out a modification of the finite volume WENO (weighted essentially non-oscillatory) scheme of Titarev and Toro [14] and [15].This modification is done by using two fluxes as building blocks in spatially fifth order WENO schemes instead of the second order TVD flux proposed by Titarev and Toro [14] and [15]. These fluxes are the second order TVD flux [19] and the third order TVD flux [20].Secondly, we propose to use these fluxes as a building block in spatially seventh order WENO schemes. The numerical solution is advanced in time by the third order TVD Runge–Kutta method. A way to extend these schemes to general systems of nonlinear hyperbolic conservation laws, in one and two dimension is presented. Systematic assessment of the proposed schemes shows substantial gains in accuracy and better resolution of discontinuities, particularly for problems involving long time evolution containing both smooth and non-smooth features.

Contigious hyperquadrics of coequipped hyperbands sHm

2019 ◽  
pp. 126-132
Author(s):  
Yu. Popov
Keyword(s):  
Projective Space ◽  
Second Order ◽  
Third Order ◽  
Base Surface ◽  
The Third ◽  
Two Parameter ◽  
Order Contact

We consider hyperquadrics that are internally connected to coequipped hyperbands in the projective space. Specifically, a hyperquadric Qn1 tangent to a hyperplane at the point is called a contiguous hyper quadric of a hyperband if it has a second-order contact with the base surface of the hyperband. In a the third order differential neighborhood of the forming element of the hyperband, two two-parameter bundles of fields of adjoining hyperquadrics are internally invariantly joined, their equations are given in a dot frame. The set of hyperquadrics such that the plane and the plane of Cartan are conjugate with respect to hyperquadric Qn1 is considered. The condition is shown under which the normal of the 2nd kind and the Cartan plane are conjugate with respect to the hyperquadric Qn1 . In addition, the following theorem is proved: normalization of a coequipped regular hyperband has a semi-internal equipment if and only if its normals of the first and second kind are polarly conjugate with respect to the hyperquadric.

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

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