Consistency proof via pointwise induction

We show that the consistency of the first order arithmetic follows from the pointwise induction up to the Howard ordinal. Our proof differs from U. Schmerl [Sc]: We do not need Girard's Hierarchy Comparison Theorem. A modification on the ordinal assignment to proofs by Gentzen and Takeuti [T] is made so that one step reduction on proofs exactly corresponds to the stepping down in ordinals. Also a generalization to theories of finitely iterated inductive definitions is proved. Received May 30, 1996     

A simplified proof of the real-time recognizability of palindromes on turing machines

A comparatively short proof is given of the recognizability of palindromes in real time on multitape Turing machines. It is based on the same idea as the original proof by the author, and on Z. Galil's idea for simplifying the proof by using the Fischer-Paterson algorithm for finding all symmetric suffixes in linear time.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 68, pp. 123–139, 1977.     

Epsilon substitution for transfinite induction

We apply Mints technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.     

Spatial inhomogenity due to turing bifurcation in a system of Gierer-Meinhardt type

This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.     

A formal system for fuzzy reasoning

A formal system for fuzzy reasoning is described which is capable of dealing rationally with evidence which may be inconsistent and/or involve degrees of belief. The basic idea is that the meaning of each formal sentence should be given by a certain commitment or bet associated with it. Each item of evidence is first expressed in the form of such a (hypothetical) bet, which is then written as a formal sentence in a language related to ?ukasiewicz logic. The sentences may be weighted to express the relative reliability of the various informants. A sentence is considered to “follow” from the evidence if the bet it represents can be offered by a speaker without fear of loss, on the assumption that the bets representing various items of evidence have been offered to him. A detailed account, illustrated by concrete examples, is given of the procedures by which an arbitrary sentence in common language can be translated into a formal sentence. The treatment of inconsistency, degrees of belief, and weights is illustrated by a practical example which is solved in full. It is shown that in most practical cases the computations involved in the process of formal reasoning reduce to a problem in linear programming. In the last section the relation between this system and the procedures advocated by Zadeh is examined. It is shown that, subject to certain modifications in formulas, there is general agreement in the region of overlap.     

Consistency of a linear system of inequalities

A definition given in ref. 1 is corrected.     

Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

AgentGeom: a multiagent system for pedagogical support in geometric proof problems

This paper aims, first, to describe the fundamental characteristics and workings of the AgentGeom artificial tutorial system, which is designed to help students develop knowledge and skills related to problem solving, mathematical proof in geometry, and the use of mathematical language. Following this, we indicate the manner in which a secondary school student can appropriate these abilities through interactions with the system. Our system uses strategic messages of the agent tutor in an argumentative process that collaborates with a student in the construction of a proof.     

On a special type of stability of differential equations for induction machines with double squirrel-cage rotor

This paper puts forward a new mathematical model describing the dynamics of an induction machine with double squirrel cage rotor. The limit load problem for induction machines is considered. The nonlocal reduction method is applied to estimate the limit load. Estimates for the stability domain of the system of differential equations for inductions machines in question are obtained.     

A computer-assisted proof for the existence of horseshoe in a novel chaotic system

The dynamics of a novel chaotic system are studied, and a rigorous computer-assisted proof for existence of horseshoe in this system is given. A Poincaré section is properly chosen to obtain the Poincaré map, which is proved to be semi-conjugate to the 4-shift map by utilizing topological horseshoe theory. This implies the entropy of the system is no less than log 4, and the system definitely exhibits chaos.     

A convergence proof for an affine-scaling algorithm for convex quadratic programming without nondegeneracy assumptions

This paper presents a theoretical result on convergence of a primal affine-scaling method for convex quadratic programs. It is shown that, as long as the stepsize is less than a threshold value which depends on the input data only, Ye and Tse's interior ellipsoid algorithm for convex quadratic programming is globally convergent without nondegeneracy assumptions. In addition, its local convergence rate is at least linear and the dual iterates have an ergodically convergent property.Research supported in part by the NSF under grant DDM-8721709.     

A proof of a conjecture about a symmetric system of orthogonal polynomials

ABSTRACT

The purpose of this note is to give an affirmative answer to a conjecture appearing in Berg [Open problems. Integral Transforms Spec Funct. 2015;26(2):90–95].     

*系统的一种改进系统 0*

研究了王国俊教授建立的模糊命题演算的形式演绎系统T以及在语义上相关的修正的Kleene逻辑系统W,W,Wk,给出了T系统的一种改进系统T0,并证明了二者之间的等价性,为形式演绎系统T的研究和应用提供了一个有益的途径。     

A search method for optimal control of a flow shop system of traditional machines

We consider a convex and nondifferentiable optimization problem for deterministic flow shop systems in which the arrival times of the jobs are known and jobs are processed in the order they arrive. The decision variables are the service times that are to be set only once before processing the first job, and cannot be altered between processes. The cost objective is the sum of regular costs on job completion times and service costs inversely proportional to the controllable service times. A finite set of subproblems, which can be solved by trust-region methods, are defined and their solutions are related to the optimal solution of the optimization problem under consideration. Exploiting these relationships, we introduce a two-phase search method which converges in a finite number of iterations. A numerical study is held to demonstrate the solution performance of the search method compared to a subgradient method proposed in earlier work.     

Automatic differentiation for the optimization of a ship propulsion and steering system: a proof of concept

We describe the optimization of the Voith-Schneider-Propeller (VSP) which is an industrial propulsion and steering system of a ship combined in one module. The goal is to optimize efficiency of the VSP with respect to different design variables. In order to determine the efficiency, we have to use numerical simulations for the complex flow around the VSP. Such computations are performed with standard (partly commercial) flow solvers. For the numerical optimization, one would like to use gradient-based methods which requires derivatives of the flow variables with respect to the design parameters. In this paper, we investigate if Automatic Differentiation (AD) offers a method to compute the required derivatives in the described framework. As a proof of concept, we realize AD for the 2D-code Caffa and the 3D-code Comet, for the simplified model of optimizing efficiency with respect to the angle of attack of one single blade (like an airfoil). We show that AD gives smooth derivatives, whereas finite differences show oscillations. This regularization effect is even more pronounced in the 3D-case. Numerical optimization by AD and Newton’s method shows almost optimal convergence rates.