Weak Monotonicity Research Articles

Stability of non-linear observers for dissipative ODEs

Conditions are given under which dissipative non-linear ordinary differential equations that have associated with them dynamic observers may be ‘observed’ with asymptotically zero error. The emphasis is on conditions under which the error equation is globally asymptotically stable. It is shown that if the error equation is dissipative, then observability implies a stable observer. Two different approaches are then taken to ensure that the error equation be dissipative: one approach is independent of observability but imposes strong conditions on the non-linearity; the other approach assumes a very strong observability condition while retaining only a very weak monotonicity property for the non-linear part of the system

On Levi-Like Properties and some of Their Applications in Riesz Space Theory

AbstractLet (L, λ) be a locally solid Riesz space. (L, λ) is said to have the Levi property if for every increasing λ-bounded net (xα) ⊂ L+, sup xα exists. The Levi property, appearing in literature also as weak Fatou property (Luxemburg and Zaanen), condition (B) or monotone completeness (Russian terminology), is a classical object of investigation. In this paper we are interested in some variations of the property, their mutual relationships and applications in the theory of topological Riesz spaces. In the first part of the paper we clarify the status of two problems of Aliprantis and Burkinshaw. In the second part we study ideal-injective Riesz spaces.

A parallel rule firing fuzzy production system with resolution of memory conflicts by weak fuzzy monotonicity, applied to the classification of multiple objects characterized by multiple uncertain features

A fuzzy production system shell is described characterized by parallel rather than sequential rule firing. All fireable rules are fired in effect concurrently. Since there is no unfired-rule stack, no backtracking can take place, and no rule conflict algorithm is necessary; instead, a memory conflict algorithm is invoked when more than one rule modifies the same datum. Memory conflicts are resolved by weakly monotonie fuzzy logic; i.e. the value or truth value of an attribute may be replaced if the new truth value is equal to or greater than the old truth value. The system depends heavily on the use of fuzzy logic and on confidence levels, fuzzy numbers and fuzzy sets as explicit data types, and on the generation of rules from a data base of expert knowledge. Fuzzy sets are used to store contradictory and ambiguous information and results. If a problem is suitable for parallel processing, substantial reductions in system overhead are achieved, together with substantial economy in the number of rules which must be written; if a problem is not suitable for parallel processing, no economy is achieved. We suggest that problems which yield to deductive reasoning constitute a class which is suitable for sequential rule firing, and problems which yield to inductive reasoning constitute a class suitable for parallel processing. A successful application of the system to the unsupervised analysis of a time sequence of noisy echocardiogram images is described.

How to examine construct validity of item banks

In this study data is brought to support an approach for assuring the content validity of item banks and for examining their construct validity. The method is an application of Guttman's concept of using mapping sentences for theory construction in the domain of “simple fraction’. The construct validity of the theory used for the creation of the item bank was tested by selecting two samples of items which are referenced in the same structuple (criterion). The Yule weak monotonicity coefficients of the items' connections were calculated and represented in two different matrices and in two different space diagrams. The results show clearly a similarity in both the structure of the space diagrams of any two parallel samples and in the partition of the points into regions, i.e., regions according to the classification of the items represented by them on the basis of the facets defined by the mapping sentences. Consequently, it may be concluded that the results support the construct validity of the theory on the basis of which the bank has been created.

Connected Maps and Essentially Connected Spaces

AbstractThe paper discusses some consequences of weak monotonicity for connected maps in relation to essential connectedness of a space. The first main result gives conditions under which the image by a connected map of an essentially connected space is essentially connected. The second is that, for a connected mapping of a connected, 1 .c. space to a WLOTS-wise and essentially connected space, w-monotonicity implies monotonicity. The remainder of the paper discusses continuity properties of connected, w-monotone mappings with WLOTS-wise and essentially connected range.

The cylindrical structure of political involvement

This research is devoted to a methodological study of interrelations among varieties of involvement in political issues, utilizing data designed and gathered in the context of the Israel election campaign for the Seventh Knesset in 1969. The observations on political involvement were defined by means of a mapping sentence. The interrelations were studied by calculating a weak monotonicity coefficient between each pair of variables. This correlation matrix was submitted to a smallest space analysis (SSA-I) in order to help ascertain the correspondence between the structure of the matrix and the facets of political issues in the mapping sentence. It is hypothesized that the regression of one form of involvement on another should be monotone and of positive sign. Such a ‘first law’ of involvement does hold empirically here. Furthermore, the structure of the intercorrelation matrix can be represented geometrically by a cylindrical interpretation of the SSA space which corresponds to the facet design of the varieties of involvement. The axis of the cylinder distinguishes between instrumental and cognitive involvement, while the circularity within strata of the cylinder corresponds to the facet of political issues which are the objects of the involvement.

Collapse of a Volterra soliton into a weak monotone shock wave

Abstract The perturbation of the stationary solitary solution of a feeder-eater Volterra equation by a small linear dissipative-like term is studied both numerically and analytically and leads to the existence of “quasi-solitons” which are hybrid non-stationary profiles constituted each by a high amplitude, exponentially damped soliton followed by a small amplitude uniform residue left behind the advancing pulse and shown to be a stationary Burgers shock wave. These quasi-solitons appear as stable as unperturbed solitons and preserve their own identity despite nonlinear interactions. They seem to be a consequence of the finiteness of the initial condition norm (measured above the reference noise level).

The Effect of Personal Characteristics on Attitudes toward Risk

This paper examines the relationship between some personal characteristics of investors and investment advisors, and the degree of risk attributed by them to various types of financial investments. Personal characteristics investigated included the investors' age, education, investment experience, degree of concern for others, and the extent to which they use financial journals. The data were collected by interviews using questionnaires based on a comprehensive mapping sentence. For statistical analysis Guttman's weak monotonicity coefficient was used and the findings were further subjected to the technique of smallest space analysis. Three dimensional diagrams have been developed to facilitate visual examination of the findings. For both groups investigated, the degree of concern for others was significantly related to the degree of risk attributed to investments. The other characteristics exhibited varying degrees of relationships for the two groups. Risk can be described as a state in which more than one outcome is possible and where a probability distribution exists over possible results (outcomes) with different utilities for the decision maker. A riskless situation exists when the probability of an outcome is 1. The greater the dispersion of possible outcomes the larger is the risk.' The literature on the risk of securities has been well developed since Markowitz's [27] wellknown portfolio theory and its subsequent extensions by Sharpe [34], Lintner, [25, 26] and others [31]. According to currently accepted risk theory, the variances in stock price movements serve as the basis for measuring relative risk in securities investments. The widely used beta is a measure of systematic risk reflecting variance of the investment rate of return relative to the overall market rate of return. However, people are likely to have different attitudes toward risk.2 That a security whose

Aggregation of Preferences with Variable Electorate

IN THIS PAPER we consider procedures for going from several individual preferences among several alternatives, called candidates, to something which may be called a collective preference. The individual preferences take the form of (total) orderings of the alternatives, and the collective preference is to take the form of a (total) weak ordering (i.e., ties allowed). We consider certain properties which seem desirable in such and investigate which have these properties. The of view taken here differs from that of other work in this area (e.g., [1, 2, 3, 4]) chiefly in asking that the procedure work for all possible sizes of the voting population, rather than for a fixed population, given in advance. This permits us to require, for example, that if each of two bodies of voters prefers candidate A to candidate B under a given procedure, then the combination of these bodies should prefer A to B under the same procedure. In Section 1 we give the formal definitions of an aggregation procedure and discuss certain desirable features, namely neutrality (treats candidates symmetrically), (the condition mentioned above), monotonicity, and an Archimedean property which says, roughly, that a sufficiently large body with a given distribution of preferences can impose its will on any body of fixed size. In Section 2 we introduce certain procedures: point systems and systems (roughly, allowing infinitesimal points), which are neutral and separable. They are monotonic if and only if the points are arranged in the natural order, and the are, in addition, Archimedean. In Section 3 we prove a converse, namely that any neutral and separable procedure can be realized by a generalized system and, if it is Archimedean, by a system. This part requires some familiarity with the notions of least upper bound of a set of real numbers and bases of vector spaces. In Section 4 (which is largely independent of Section 3), we consider point which use in a succession of eliminations. Such are neither separable nor monotonic but do satisfy some very weak separability and monotonicity conditions. While these probably do not characterize runoff systems, we know of no other satisfying them.

Quasilinear elliptic problems in unbounded domains

This paper provides an existence theorem for the Dirichlet problem for a quasilinear partial differential equation of elliptic type in an unbounded domain. The principal new feature of this work is that the results are obtained under weaker monotonicity conditions on the coefficients of the equation than those employed in earlier work in this area.