Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Analysis of end point vibrations of a two-link manipulator by integrated CAD/CAE procedures

In this work, the effect of flexibility on the trajectory of a planar two-link manipulator is studied using integrated computer-aided design/analysis (CAD/CAE) procedures. The solid models and finite element models of the parts of the manipulator are created by using the CAD/CAE software I-DEAS. The assembly is defined, and knowing the payload and the end point trajectory, the velocities and accelerations of the parts, joint forces and driving torques are calculated using the rigid body dynamics. All the time dependent nodal forces acting on the parts including distributed gravity and inertia forces are created in files with the I-DEAS program file format. The finite element vibration analysis of the parts is performed by I-DEAS. The end point vibrations and the deviations from the rigid-body trajectory are analyzed for different types of end point acceleration curves. A circular trajectory is considered as an example. It is observed that the precision of the manipulator can be increased by testing different end point acceleration curves without changing the trajectory and the duration of the end point work. The procedure explained in this work can be used for this purpose successfully.     

Dynamic boundary stabilization of a Reissner–Mindlin plate with Timoshenko beam

This paper is concerned with well‐posedness results for a mathematical model for the transversal vibrations of a two‐dimensional hybrid elastic structure consisting of a rectangular Reissner–Mindlin plate with a Timoshenko beam attached to its free edge. The model incorporates linear dynamic feedback controls along the interface between the plate and the beam. Classical semigroup methods are employed to show the unique solvability of the coupled initial‐boundary‐value problem. We also show that the energy associated with the system exhibits the property of strong stability. Copyright © 2004 John Wiley & Sons, Ltd.     

Uniformity in Computable Structure Theory

We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously studied by Kudinov and by Ventsov. We discuss some of their results and establish new ones, while also exploring the connections with the relative computable structure theory of Ash, Knight, Manasse, and Slaman and Chisholm and with previous work of Ash, Knight, and Slaman on uniformity in a general computable structure-theoretical setting.     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.     

Space time-index plots for probing dynamical nonstationarity

We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated.     

The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

An analysis of the different philosophic and scientific visions of Henri Poincaré and Federigo Enriques relative to qualitative analysis provides us with a complex and interesting image of the “essential tension” between “tradition” and “innovation” within the history of science. In accordance with his scientific paradigm, Poincaré viewed qualitative analysis as a means for preserving the nucleus of the classical reductionist program, even though it meant “bending the rules” somewhat. To Enriques's mind, qualitative analysis represented the affirmation of a synthetic, geometrical vision that would supplant the analytical/quantitative conception characteristic of 19th-century mathematics and mathematical physics. Here, we examine the two different answers given at the turn of the century to the question of the relationship between geometry and analysis and between mathematics, on the one hand, and mechanics and physics, on the other.Copyright 1998 Academic Press.Un'analisi delle diverse posizioni filosofiche e scientifiche di Henri Poincaré e Federigo Enriques nei riguardi dell'analisi qualitativa fornisce un'immagine complessa e interessante della “tensione essenziale” tra “tradizione” e “innovazione” nell'ambito della storia della scienza. In linea con il proprio paradigma scientifico, Poincaré vedeva nell'analisi qualitativa un mezzo per preservare il nucleo del programma riduzionista calssico, anche se cio comportava una lieve “distorsione delle regole”. Nella mente di Enriques, l'analisi qualitativa rappresentava l'affermazione di un punto di vista sintetico e geometrico che avrebbe soppiantato la concezione analitico-quantitativa caratteristica della matematica e della fisica matematica del 19° secolo. Il nostro scopo principale è di esaminare due diverse risposte date a cavallo del secolo alla questione dei rapporti tra geometria e analisi e tra matematica da un lato e meccanica e fisica dall'altro.Copyright 1998 Academic Press.AMS subject classification: 01A55     

SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

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Assignment of conformation-sensitive near-infrared bands in high-spin ferrous haemoproteins. Low-temperature magnetic circular dichroism data

An assignment of the near-infrared bands in the 600–800 nm spectral region observed in magnetic circular dichroism (MCD) spectra of high-spin ferrous haemoproteins is presented. The assignment is based on a relative energy level scheme for iron d-electrons, a comparison of predicted and measured temperature dependences of MCD intensity, a sign of MCD bands and a group theoretical analysis of allowed transitions. The proposed assignment is consistent with the ∼15-nm red shift of the ∼760 nm band on breakage of the Fe-His bond in deoxy-myoglobin at low pH, with low-temperature photolysis experiments available for CO complexes of several haemoproteins. In accordance with the observations, the intensity of the MCD bands for proteins with a sulphur anion of cysteine as proximal haemligand (cytochrome P450 and chloroperoxidase) is predicted to be diminished by at least one order of magnitude compared to that for proteins with an imidazole of a histidine as a protein-derived haemligand (i.e. myoglobin, haemoglobin and horseradish peroxidase). Received: 4 February 1997 / Accepted: 1 May 1997     

Über die Magnetischen Eigenschaften der Cobaltate Na6CoS4, Na6CoSe4 und K6CoS4

Magnetic Properties of the Cobaltates Na₆CoS₄, Na₆CoSe₄, and K₆CoS₄ The alkali metal cobalt chalcogenides Na₆CoS₄, Na₆CoSe₄, and K₆CoS₄ crystallize in the space group P6₃mc with Z = 4. The structure is characterized by isolated [CoX₄]-tetrahedra. The magnetic susceptibilities show Curie-Weiss behaviour. The deviations at low temperatures are caused by antiferromagnetic interactions. The magnetic moments are discussed with regard to ligand-field parameters.