ORDERING CONTRACTION MAPPING PRINCIPLE AND APPLICATIONS

This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.

Understanding electricity prices beyond the merit order principle using explainable AI

Electricity prices in liberalized markets are determined by the supply and demand for electric power,which are in turn driven by various external influences that vary strongly in time.In perfect competition,the merit order principle describes that dispatchable power plants enter the market in the order of their marginal costs to meet the residual load,i.e.the difference of load and renewable generation.Various market models are based on this principle when attempting to predict electricity prices,yet the principle is fraught with assumptions and simplifications and thus is limited in accurately predicting prices.In this article,we present an explainable machine learning model for the electricity prices on the German day-ahead market which foregoes of the aforementioned assumptions of the merit order principle.Our model is designed for an ex-post analysis of prices and builds on various external features.Using SHapley Additive exPlanation(SHAP)values we disentangle the role of the different features and quantify their importance from empiric data,and therein circumvent the limitations inherent to the merit order principle.We show that load,wind and solar generation are the central external features driving prices,as expected,wherein wind generation affects prices more than solar generation.Similarly,fuel prices also highly affect prices,and do so in a nontrivial manner.Moreover,large generation ramps are correlated with high prices due to the limited flexibility of nuclear and lignite plants.Overall,we offer a model that describes the influence of the main drivers of electricity prices in Germany,taking us a step beyond the limited merit order principle in explaining the drivers of electricity prices and their relation to each other.

Formation Principles of Similar Systems

In this paper some new concepts, i.e, Ordered Structure of Systems, Universal Information, Strength of Information Field are proposed. Based on Similarity System Theory and Similology, five principles for investigating similarity formation, i.e., Principle of Ordered Structue, Information Principle, Consanguining Principle, Coadaptation Principle and Governing Principle are introduced. The origin of similar systems, and way of similarity formation are expounded. Thus, formation principles of similar systems is presented.

Generalized Gerstewitz's Functions and Vector Variational Principle for-Efficient Solutions in the Sense of Németh

In this paper, we first generalize Gerstewitz's functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle.J. Math. Anal. Appl., 419, 904–937(2014)]. By using the generalized Gerstewitz's functions and the partial order principle, we obtain a vector EVP for-efficient solutions in the sense of N′emeth, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results.

A Generalization of Caristi's Fixed Point Theorem and Its Applications

The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point theorem is equivalent to the generalized Ekeland variational principle.