Search

A novel bivariate interval function decomposition method is proposed and applied to predict the bounds of structural response with large-range interval parameters. When the existing interval methods solve large uncertainty problems, either the calculation accuracy is poor or better accuracy is often achieved at the cost of more computational effort. To overcome this drawback, the bivariate interval function decomposition (BIFD) is first constructed for the approximation of the original response function. The univariate and the bivariate points are substituted into the second-order Taylor expansion to derive BIFD; thus, the expression of BIFD contains only the one- and two-dimensional functions. Particularly, the response function is decomposed into the sum of multiple low-dimensional functions, and solving the bounds of multi-dimensional original response can be transformed into solving those of low-dimensional interval functions. Then, the sensitivity information of structural response with respect to uncertain parameters is utilized to save computational consumption. Finally, the precision and effectiveness of the method are validated by comparing it with the other six existing interval analysis methods through several numerical examples and engineering applications.

This paper introduces the theory of ϕ-Jensen variance. Our main motivation is to extend the connotation of the analysis of variance and facilitate its applications in probability, statistics and higher education. To this end, we first introduce the relevant concepts and properties of the interval function. Next, we study several characteristics of the log-concave function and prove an interesting quasi-log concavity conjecture. Next, we introduce the theory of ϕ-Jensen variance and study the monotonicity of the interval function $\operatorname{JVar}_{\phi}\varphi ( {{X _{ [ {a,b} ] }}} )$ by means of the log concavity. Finally, we demonstrate the applications of our results in higher education, show that the hierarchical teaching model is ‘normally’ better than the traditional teaching model under the appropriate hypotheses, and study the monotonicity of the interval function $\operatorname{Var} \mathscr{A} (X _{ [ {a,b} ] } )$ .

The fundamentals of mathematical chaotic theory used to analyze sequences formed by a randomly choosing elements from an event set are formulated. Their inherent and mutual interval characteristics (interval functions) are introduced. Analogs to probability characteristics are introduced within the framework of the set-theoretic approach. They are represented as a particular case, when similar features are exhibited only under certain conditions in the analysis of limiting cases of numerical sequences.

It is proved that a setH inR n has Lebesgue null measure if any function which is the restriction toH of a Baire function defined inR n is the restriction toH of a derivative of an interval function.

In this paper, we analyze the problem of the optimal (narrowest) approximation (enclosure) of a quadratic interval function \(y(x_1 ,...,x_n ) = [y(x_1 ,...,x_n ) \bar y(x_1 ,...x_n )]\) (i.e., an interval function for which both endpoint functions \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{y} (x_1 ,...,x_n ) {\text{and}} \bar y(x_1 ,...x_n )\), ..., xn) are quadratic) by a linear interval function. show that in general, this problem is computationally intractable (NP-hard). For a practically important 1D case (n = 1), we present an efficient algorithm.

This paper presents algorithms evaluating sharper bounds for interval functionsF(X) :IR n →IR. We revisit two methods that use partial derivatives of the function, and develop four other inclusion methods using the set of slopesS f (x, z) off atx eX with respect to somez eIR n . All methods can be implemented using tools that automatically evaluate gradient and slope vectors by using a forward strategy, so the complex management of reverse accumulation methods is avoided. The sharpest methods compute each component of gradients and slopes separately, by substituting each interval variable at a time. Backward methods bring no great advantage in the sharpest algorithms, since object-oriented forward implementations are easy and immediate.

One of the main sources of destruction during earthquake is resonance. Therefore, the following idea has been proposed. We design special control linkages between floors that are normally unattached to the building but can be attached if necessary. They are so designed that adding them changes the building's characteristic frequency. We continuously monitor displacements within the structure, and when they exceed specified limits, the linkages are engaged in a way to control structural motion. This idea can also be applied to avoid vibrational destruction of large aerospace structures.

We prove a general criterion for the lower semicontinuity of Burkill-Cesari integral in abstract setting. The basic idea, which is inspired by a classical Menger's conjecture, consists on reducing this result to a suitable adaptation of the semicontinuity of the length of a curve. Some noteworthy applications to the Weierstrass functionals of the Calculus of Variations in BV setting are also presented.

It is proved that for a functionf defined inRk, and for every derivation baseD, there exists an additive interval function wich is a primitive off onD. This generalizes a result of Sierpinski.

An interval function as «universal primitive» in the sense of Marcinkiewicz is constructed for measurable functions defined in a compact interval of R n .

Adrenalectomy and dexamethasone blocking of adrenocorticotropin (ACTH) release in adrenalectomized and sham-operated rats did not affect time-dependent changes in performance following discriminated avoidance conditioning. Adrenalectomized rats also yielded the U-shaped intersession interval function characteristic of the Kamin effect in shuttlebox conditioning. The use of Sprague-Dawley rats precluded the possibility that time-dependent performance changes following aversive conditioning in adrenalectomized rats are the product of postoperatively developed accessory adrenal tissue. The Kamin effect occurs independent of pituitary-adrenal function.

Acquisition rates for the classically conditioned nictitating membrane response of the rabbit were determined, using one paired presentation of tone and shock per day for 12 days, in Ss trained at a CS-US interval of either 250 or 1,250 msec. Although both groups displayed substantial conditioning, the 1,250-msec group was significantly superior to the 250-msec group, in marked contrast to the usual findings of experiments dealing with the CS-US interval parameter. Results are interpreted primarily in terms of the role of the orienting response in CR acquisition.