Approximations of the Abstract Problem

Let the pair of self-adjoint operators {A≥0,W≤0} be such that: (a) there is a dense domain [Formula: see text] such that [Formula: see text] is semibounded from below (stability domain), (b) the symmetric operator [Formula: see text] is not essentially self-adjoint (singularity of the perturbation), (c) the Friedrichs extension [Formula: see text] of [Formula: see text] is maximal with respect to W, i.e., [Formula: see text]. [Formula: see text]. Let [Formula: see text] be a regularizing sequence of bounded operators which tends in the strong resolvent sense to W. The abstract problem of the right Hamiltonian is: (i) to give conditions such that the limit H of self-adjoint regularized Hamiltonians [Formula: see text] exists and is unique for any self-adjoint extension [Formula: see text] of [Formula: see text], (ii) to describe the limit H. We show that under the conditions (a)–(c) there is a regularizing sequence [Formula: see text] such that [Formula: see text] tends in the strong resolvent sense to unique (right Hamiltonian) [Formula: see text], otherwise the limit is not unique.

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ChemInform Abstract: PROBLEM OF THE EXISTENCE OF A CUBIC PYROCHLORE LEAD(II) ANTIMONATE(V)

Chemischer Informationsdienst ◽

10.1002/chin.197912038 ◽

1979 ◽

Vol 10 (12) ◽

Author(s):

G. BURCHARD ◽

W. RUEDORFF

Keyword(s):

Abstract Problem

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ChemInform Abstract: PROBLEM OF CATALYTIC HYDROGEN EVOLUTION DURING CHLORALKALI ELECTROLYSIS AFTER THE AMALGAMATION PROCESS

Chemischer Informationsdienst ◽

10.1002/chin.197849367 ◽

1978 ◽

Vol 9 (49) ◽

Author(s):

J. BALEJ ◽

I. PASEKA ◽

H. MATSCHINER

Keyword(s):

Hydrogen Evolution ◽

Abstract Problem ◽

Catalytic Hydrogen ◽

Catalytic Hydrogen Evolution

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ChemInform Abstract: Problem Solving in Organic Synthesis: The False Steps, Failed Pathways, and Ultimately Successful Route to the Bottom Half of Ivermectin

ChemInform ◽

10.1002/chin.199003332 ◽

1990 ◽

Vol 21 (3) ◽

Author(s):

M. E. JUNG

Keyword(s):

Problem Solving ◽

Organic Synthesis ◽

Abstract Problem

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The Solution of An Inferential Problem as a Function of Stimulus Materials

Quarterly Journal of Experimental Psychology ◽

10.1080/14640747408400437 ◽

1974 ◽

Vol 26 (3) ◽

pp. 480-488 ◽

Cited By ~ 28

Author(s):

R. J. Bracewell ◽

S. E. Hidi

Keyword(s):

Cognitive Load ◽

Significant Interaction ◽

Abstract Problem ◽

Stimulus Materials ◽

Problem Material

Stimulus materials were varied in three ways to assess the effect on performance of problems involving implicational rules. The three factors were natural versus arbitrary relationship between the terms of the problem, concrete versus abstract problem material and order of the presentation of the terms in the rules. The natural relationship condition facilitated performance compared with the arbitrary relationship condition. This difference was explained in terms of differential cognitive load. A significant interaction between materials and order factors was attributed to semantic differences in the rules.

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