Vector Measures Research Articles

Financial performance of Polish energy companies in the pre-COVID-19 pandemic decade

The energy sector plays a crucial role for the socio-economic development all over the world. The aim of this study is to synthetically assess the financial efficiency of public energy companies (in this study represented mostly by state-owned companies or their subsidiaries) and compare them with other non-financial public companies (usually private) in the relatively stable decade of 2010–2019 which preceded the COVID-19 pandemic. Our analysis focused on nine energy companies in Poland listed continuously throughout the study period whose complete financial data was available in the Notoria Serwis database. The annual financial performance of each of them was measured by a custom synthetic vector measure of financial efficiency, constructed using 14 financial ratios describing liquidity, leverage, efficiency, profitability and market values as discriminant variables. The results demonstrate that energy companies in Poland do not belong to the cluster of the most financially efficient companies in terms of the applied vector measures. The performance of Lotos and Kogeneracja was improving in the analysed 10-year period, whereas in the case of Tauron, Enea and PGE, it was gradually deteriorating.

On spaces of integrable functions associated to vector measures and limiting real interpolation

We investigate which spaces are obtained when considering the limiting class of real interpolation spaces (0,q;J) for ordered Banach couples of spaces of (scalar) integrable functions with respect to a vector measure m, defined on a σ-algebra, with values in a Banach space. If m is in particular a finite positive scalar measure, previous known results are derived from ours. Furthermore, we study the interpolation of p-th power factorable operators by the extreme real interpolation method (1,q;K). We also deduce interpolation results for the (1,q;K)-method that apply to other related classes of operators to p-th power factorable operators, such as bidual (p,q)-power-concave operators and q-concave operators.

The Nemytskiĭ Operator and Vector Measure Solutions for Non-Linear Initial Value Problems

Abstract We define and study a Banach-space-valued Nemytskiĭ operator and we find vector measure solutions for associated non-linear initial value problems.

Fourier Transform for $$L^p$$-Functions with a Vector Measure on a Homogeneous Space of Compact Groups

Fourier Transform for $$L^p$$-Functions with a Vector Measure on a Homogeneous Space of Compact Groups

The modulus of a vector measure

It is known that if L is a Dedekind complete Riesz space and (Ω, Σ) is a measurable space, then the partially ordered linear space of all L-valued, finitely additive and order bounded vector measures m on Σ is also a Dedekind complete Riesz space (for the natural operations). In particular, the modulus |m| o of m exists in this space of measures and |m| o is given by a well known formula. Some 20 years ago L. Drewnowski and W. Wnuk asked the question (for L not Dedekind complete) if there is an m for which |m|o exists but, |m| o is not given by the usual formula? We show that such a measure m does indeed exist.

Managing investment attractiveness of a company during a period of high market volatility based on forecasting expectations

Evaluation of efficiency of economic and financial activities is primarily based on the financial performance of a company. In the context of the joint-stock companies’ activities, special importance belongs to timely or premature assessment of financial prospects of the activities for increasing the profit and potential of the company. To achieve the goals, it is extremely important to objectively evaluate the elements of innovative strategy of the company considering both internal and external influence as well as the company’s unique circumstances. While assessing a specific situation it is essential to take into account both innovative environment and position and its innovative potential. Financial coefficients which allow analysis of performance are used as the assessment criteria for financial condition. The study in hand suggests creation of a high-precision model based on the variability of statistical forecasting techniques followed by a thorough assessment to identify factors that objectively influence the company’s investment attractiveness. At the initial stage the authors calculated 40 financial indicators of the company quarterly over a seven-year period, and 10 factors of the external environment which were used later for conducting the multicorrelation analysis to select the most correlating with the leading one. This was the share price represented by binary code, where 0 indicates a decrease and 1 indicates an increase. A combination of approaches such as regression analysis, Gaussian processes, cumulative perspective theory and the method of constructing vector measures allowed increasing the accuracy of the model from 89 to 96.7% and identify the basic indicators which could be useful in forecasting the investment attractiveness of the company such as the share of net working capital in assets, the level of real income of the population and return on capital employed.

An effective framework of human abnormal behaviour recognition and tracking using multiscale dilated assisted residual attention network

The prevention of certain unwanted crime events and eliminating them even before their execution can be done by automatic identification of abnormal behavior in humans. Hence automatic prediction of abnormal human behavior is a difficult task to perform. Some of the automated model has been implemented and provided the most promising results. The manual intervention is being the greatest approach in earlier time, yet it brings with numerous errors, consumes more time and more cost effective. Henceforth, the automated model is suggested for identifying the activities. As the scholar focus on machine and deep learning, this classifier may extract the hand-crafted features. But it fails to yield the appropriate solution for finding the activities. Since it belongs to the video frames, the object detection is highly Ineffective feature vector and inadequate scale measures of the learning model paves the way for performance degradation. This issue can be resolved by including an attention mechanism in the deep learning model for both monitoring and classification purposes. The recommended Human Abnormal Behavior Recognition and Tracking (HABRT) model performs the following operations, such as the collection of video, categorizing the behavior in the video as normal or abnormal, monitoring, extraction of the object, and classification of the abnormality. The input video with such frames is initially gathered from publically available databases. By using these frames, the abnormal behavior classification is done by Multiscale Dilated assisted Residual Attention Network (MD-RAN), For further enhancement, the hyper-parameters in the MD-RAN are optimally selected by novel Modified Random Parameter-based Chimp Optimization Algorithm (MRP-ChOA). Once the abnormal frames are obtained, the activity tracking is achieved by Adaptively Modified You Only Look Once (YOLO) V3 (AM-YOLO V3). This model encompasses with multiple layers, so that utilized number of layers are determined optimally using MRP-ChOA. Consequently, the objects are extracted from the abnormal frames with the help of AM-YOLO V3. Finally, the abnormalities are classified by using the same MD-RAN. At last, the performance is analyzed and validated with diverse parameters, which are then compared with other algorithms. While implementing the dataset 1, the accuracy value attains maximum in contrast with 3.14% of DTCN, 2.308% of CNN-RNN and 13.7% of ResAttenConvLSTM, correspondingly. Thus, the findings reveal that it has the potential to deliver extensive results for abnormal recognition and tracking.

On vector measures with values in $\ell_\infty $

On vector measures with values in $\ell_\infty $

Geometry of Banach algebra [formula omitted] and the bidual of [formula omitted

This article is intended towards the study of the bidual of generalized group algebra L1(G,A) equipped with two Arens products, where G is any locally compact group and A is a Banach algebra. We show that the left topological center of (L1(G)⊗ˆA)⁎⁎ is a Banach L1(G)-module if G is abelian. Further it also holds permanence property with respect to the unitization of A. We then use this fact to extend the remarkable result of A.M. Lau and V. Losert [7], about the topological center of L1(G)⁎⁎ being just L1(G), to the reflexive Banach algebra valued case using the theory of vector measures. We further explore pseudo-center of L1(G,A)⁎⁎ for non-reflexive Banach algebras A and give a partial characterization for elements of pseudo-center using the Cohen's factorization theorem. In the running we also observe few consequences when A holds the Radon-Nikodym property and weak sequential completeness.

Version [1.2]- [pyrepo-mcda - Reference Objects based MCDA Software Package

This paper presents an update of the pyrepo-mcda Python package, providing a broad set of multi-criteria methods and methods supporting decision analysis, such as determining compromise rankings, criteria weights, distance metrics, and performing sensitive analysis. The pyrepo-mcda package was extended with the Vector Measure Construction Method (VMCM). This update expands the scope of multi-criteria analysis approaches offered by the proposed package. Several features of the VMCM method, such as considering non-typical objects, the possibility of individual defining patterns, and classifying evaluated objects, are sought by decision-makers in many decision-making problems, especially sustainability assessment.

Local vector measures

Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean space. In more general curved contexts, the same objects can be perfectly understood via charts. However, charts are often unavailable in the less regular setting of metric geometry, where still the questions make sense.In this paper we propose a way to deal with this sort of problems and, more generally, to give a meaning to a concept of ‘measure acting in duality with sections of a given bundle’, loosely speaking. Despite the generality, several classical results in measure theory like Riesz's and Alexandrov's theorems have a natural counterpart in this setting. Moreover, as we are going to discuss, the notions introduced here provide a unified framework for several key concepts in nonsmooth analysis that have been introduced more than two decades ago, such as: Ambrosio-Kirchheim's metric currents, Cheeger's Sobolev functions and Miranda's BV functions.Not surprisingly, the understanding of the structure of these objects improves with the regularity of the underlying space. We are particularly interested in the case of RCD spaces where, as we will argue, the regularity of several key measures of the type we study nicely matches the known regularity theory for vector fields, resulting in a very effective theory.We expect that the notions developed here will help creating stronger links between differential calculus in Alexandrov spaces (based on Perelman's DC charts) and in RCD ones (based on intrinsic tensor calculus).

Convergence aspects for sets of measures with divergences and boundary conditions

In this paper we study set convergence aspects for Banach spaces of vector-valued measures with divergences (represented by measures or by functions) and applications. We consider a form of normal trace characterization to establish subspaces of measures that directionally vanish in parts of the boundary, and present examples constructed with binary trees. Subsequently we study convex sets with total variation bounds and their convergence properties together with applications to the stability of optimization problems.

Challenge and opportunity for vector control strategies on key mosquito-borne diseases during the COVID-19 pandemic.

Mosquito-borne diseases are major global health problems that threaten nearly half of the world's population. Conflicting resources and infrastructure required by the coronavirus disease 2019 (COVID-19) global pandemic have resulted in the vector control process being more demanding than ever. Although novel vector control paradigms may have been more applicable and efficacious in these challenging settings, there were virtually no reports of novel strategies being developed or implemented during COVID-19 pandemic. Evidence shows that the COVID-19 pandemic has dramatically impacted the implementation of conventional mosquito vector measures. Varying degrees of disruptions in malaria control and insecticide-treated nets (ITNs) and indoor residual spray (IRS) distributions worldwide from 2020 to 2021 were reported. Control measures such as mosquito net distribution and community education were significantly reduced in sub-Saharan countries. The COVID-19 pandemic has provided an opportunity for innovative vector control technologies currently being developed. Releasing sterile or lethal gene-carrying male mosquitoes and novel biopesticides may have advantages that are not matched by traditional vector measures in the current context. Here, we review the effects of COVID-19 pandemic on current vector control measures from 2020 to 2021 and discuss the future direction of vector control, taking into account probable evolving conditions of the COVID-19 pandemic.

Sugeno-Like Operators in Preference and Uncertain Environments

Sugeno-like operators are binary operations based generalization of Sugeno integral and are still defined on real valued fuzzy measures. This work discusses the aggregation methods in the situation where both inputs and fuzzy measures are attached with numerical uncertainties. That is, when an input vector and a fuzzy measure are given, each of the entries of the vector and the measure value on each subset can be attached with numerical uncertainty degrees. To fulfill this meaningful aim of performing Sugeno-like aggregation with numerical uncertainties, it needs two parts of work. We firstly formally define basic uncertain vector and basic uncertain fuzzy measure. Then we discuss the methods to construct or adjust basic uncertain vector and basic uncertain fuzzy measure in two situations, the general fuzzy measure situation and the probability measure only situation, respectively. With uncertain input and uncertain fuzzy measure, we then accordingly propose the corresponding restricted Sugeno-like operator, for which some different logic restrictions are analyzed. All the proposals also have full consistency for they can immediately degenerates into Sugeno-like operator when the attached uncertainties disappear.

The metric-valued Lebesgue differentiation theorem in measure spaces and its applications

We prove a version of the Lebesgue differentiation theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation basis induced by a von Neumann lifting. As a consequence, we obtain a lifting theorem for the space of sections of a measurable Banach bundle and a disintegration theorem for vector measures whose target is a Banach space with the Radon–Nikodým property.

The second-order Cauchy problem in a scale of Banach spaces with vector-valued measures of noncompactness and an application to Kirchhoff equations

The second-order Cauchy problem in a scale of Banach spaces with vector-valued measures of noncompactness and an application to Kirchhoff equations

Application of multi-criteria Vector Measure Construction Method (VMCM) to assess importance of foreign direct investment (FDI) to host country's regional economy

Foreign Direct Investment (FDI) is an important element supporting the growth of national economies. Through competitive advantage and innovation, foreign-invested enterprises can become an important agent of beneficial structural change and have a positive impact on the host economy as a whole. In general, through the provision of external capital, FDI can contribute to the economic growth of a country hosting the investment and plays a particular role in the regional economy which encompasses all activities of an economic nature pursued in a given area. The article examine the role that foreign-invested companies play in the economy at the regional level. The significance of the foreign direct investment for the regional economy was conducted using the example of sixteen Polish voivodships. For the purpose of the study the Vector Measure Construction Method (VMCM) was used to determine the importance of FDI for the economies of each Polish provinces (voivodships) and to produce their ranking and classification. According to the study findings, voivodships where the examined problem was of a similar nature were assigned to particular classes. A definite leader was the Mazowieckie voivodship, which was the only one to be included in Class I. The most numerous Class II included 11 voivodships, which constituted approximately 70% of the total number of provinces. Four voivodships fell in Class III, comprising entities with the lowest aggregate measures. This means that Polish regions are mostly homogeneous in terms of the importance of foreign direct investment to the performance of their economies.

Nuclear operators and Baire vector measures

Let $C_b(X)$ be the Banach lattice of all bounded continuous real functions on a completely regular Hausdorff space $X$ and let $(E,\|\cdot\|_E)$ be a real Banach space. A linear operator $T:C_b(X)\to E$ is said to be $\sigma$-additive if $\|T(u_n)\|_E\to 0$ whenever $(u_n)$ is a sequence in $C_b(X)$ such that $u_n(x)\downarrow 0$ for each $x\in X$. We characterize $\sigma$-additive nuclear operators $T:C_b(X)\to E$ in terms of their representing Baire vector measures. The formula for the trace of $\sigma$-additive nuclear operators $T:C_b(X)\to C_b(X)$ is derived.

Bivariate Cumulative Tsallis Past Entropy: Properties and Applications

In the present study, we extend the cumulative Tsallis entropy in the past life to its bivariate case. We can use the proposed measure for determining the uncertainty associated with two-component systems in the past lifetime. Some important properties of these measures are studied along with the characterization results of some essential bivariate lifetime models. We also examine specific applications of the vector-valued measure based on the non-parametric methods of estimation and illustrated their performances using simulated and real data sets.

About Some Monge–Kantovorich Type Norm and Their Applications to the Theory of Fractals

If X is a Hilbert space, one can consider the space cabv(X) of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich type norm. Our first goal was to introduce a Monge–Kantorovich type norm on cabv(X), where X is a Banach space, but not necessarily a Hilbert space. Thus, we introduced here the Monge–Kantorovich type norm on cabvLq([0,1]),(1<q<∞). We obtained some properties of this norm and provided some examples. Then, we used the Monge–Kantorovich norm on cabvKn(K being R or C) to obtain convergence properties for sequences of fractal sets and fractal vector measures associated to a sequence of iterated function systems.