scholarly journals Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1654
Author(s):  
Octav Olteanu
Keyword(s):  
Polynomial Approximation ◽  
Quadratic Forms ◽  
Existence And Uniqueness ◽  
Cartesian Product ◽  
Point Of View ◽  
Bounded Linear ◽  
Uniqueness Of The Solution ◽  
Markov Moment ◽  
Unbounded Intervals

This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under natural assumptions, the existence and uniqueness of the solution are deduced. The characterization of the existence of the solution is formulated by two inequalities, one of which involves only quadratic forms. This is the first aim of this work. Characterizing the positivity of a bounded linear operator only by means of quadratic forms is the second aim. From the latter point of view, one solves completely the difficulty arising from the fact that there exist nonnegative polynomials on ℝn, n≥2, which are not sums of squares.

scholarly journals Optimal consumption of multiple goods in incomplete markets

2018 ◽  
Vol 55 (3) ◽  
pp. 810-822
Author(s):  
Oleksii Mostovyi
Keyword(s):  
Closed Form ◽  
Incomplete Markets ◽  
Existence And Uniqueness ◽  
Dual Problem ◽  
Optimal Consumption ◽  
Closed Form Solutions ◽  
Uniqueness Of The Solution ◽  
Incomplete Models

Abstract We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for the existence and uniqueness of the solution, and provide a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models.

scholarly journals Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Bahar Ali Khan ◽  
Thabet Abdeljawad ◽  
Kamal Shah ◽  
Gohar Ali ◽  
Hasib Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Research Work ◽  
Sufficient Conditions ◽  
Point Of View ◽  
Uniqueness Of The Solution ◽  
Delay Differential ◽  
Ulam Type Stability

AbstractIn this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph. On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation. Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied. Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR). After the demonstration of our results, some pertinent examples are given.

Why Measuring Inequality by the Variance Makes Sense from a Theoretical Point of View

2001 ◽  
Author(s):  
Satya R. Chakravarty
Keyword(s):  
Quadratic Form ◽  
Quadratic Forms ◽  
Point Of View ◽  
Theoretical Point ◽  
Numerical Illustration ◽  
Absolute Inequality

The variance, which has many advantages as a measure of inequality, is a quadratic form in incomes. In this paper we develop a characterization of the variance by showing that among all quadratic forms in incomes, it is the only one that satisfies absolute inequality invariance, symmetry, the principle of transfers and the principle of population. A numerical illustration of several inequality indices, including the variance, is also presented in the paper.

scholarly journals Sturm–Liouville Differential Equations Involving Kurzweil–Henstock Integrable Functions

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1403
Author(s):  
Salvador Sánchez-Perales ◽  
Tomás Pérez-Becerra ◽  
Virgilio Vázquez-Hipólito ◽  
José J. Oliveros-Oliveros
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Integrable Functions ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville ◽  
Unbounded Intervals

In this paper, we give sufficient conditions for the existence and uniqueness of the solution of Sturm–Liouville equations subject to Dirichlet boundary value conditions and involving Kurzweil–Henstock integrable functions on unbounded intervals. We also present a finite element method scheme for Kurzweil–Henstock integrable functions.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

The Analyses of Learning Strategies in English as a Second Language: Theoretical Classification and Measurement Test

2020 ◽  
Vol 4 (2) ◽  
pp. 118-129
Author(s):  
Asti Gumartifa ◽  
◽  
Indah Windra Dwie Agustiani
Keyword(s):  
Language Learning ◽  
Learning Outcomes ◽  
Learning Strategies ◽  
Learning Process ◽  
English Learners ◽  
English Language ◽  
Point Of View ◽  
Effective Learning ◽  
The Impact

Gaining English language learning effectively has been discussed all years long. Similarly, Learners have various troubles outcomes in the learning process. Creating a joyful and comfortable situation must be considered by learners. Thus, the implementation of effective learning strategies is certainly necessary for English learners. This descriptive study has two purposes: first, to introduce the classification and characterization of learning strategies such as; memory, cognitive, metacognitive, compensation, social, and affective strategies that are used by learners in the classroom and second, it provides some questionnaires item based on Strategy of Inventory for Language Learning (SILL) version 5.0 that can be used to examine the frequency of students’ learning strategies in the learning process. The summary of this study explains and discusses the researchers’ point of view on the impact of learning outcomes by learning strategies used. Finally, utilizing appropriate learning strategies are certainly beneficial for both teachers and learners to achieve the learning target effectively.

The Algorithm of Characterization of an Action as a Jointly Committed Crime

2018 ◽  
pp. 37-44
Keyword(s):  
Criminal Code ◽  
Point Of View

The article discusses a sequence of activities to identify a crime as jointly committed. The requirements to the algorithm of such activities are formulated. Programme-based and targeted methods applied by the authors allowed detecting a range of stages of the algorithm. The first four stages aim at defining mandatory elements of a crime allowing to characterize it as a jointly committed action. The rest of the stages focus on identifying a type of criminal complicity. In the article, each stage is described. It is emphasized that in each stage there is a special objective. At the same time, all these stages, taken together, constitute a separate module of the program of criminal characterization of an action. From the authors’ point of view, algorithms are necessary not only for detection of crimes and their criminal characterization, but also for answering the question on existence of criminal complicity in each case. Also the authors give their opinions on interpretation of criminal complicity as a legal category. In particular, it is emphasized that not all of crimes merely committed with participation of two or more persons should be understood as jointly committed. It is joint participation that makes a crime jointly committed. Various forms of criminal complicity and types of co-offenders are considered in the article as well. In various crimes, criminal complicity manifests itself differently. Therefore the proposed algorithm can be applied only after identification a specific article of the Russian Criminal Code stipulating the responsibility for the crime committed.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

scholarly journals Processing Effect and Characterization of Olive Oils from Spanish Wild Olive Trees (Olea europaea var. sylvestris)

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1304
Author(s):  
Francisco Espínola ◽  
Alfonso M. Vidal ◽  
Juan M. Espínola ◽  
Manuel Moya
Keyword(s):  
Phenolic Compounds ◽  
Volatile Compounds ◽  
Olive Tree ◽  
Extraction Yield ◽  
Point Of View ◽  
Human Consumption ◽  
Analytical Point ◽  
Wild Olive ◽  
Olive Trees

Wild olive trees have important potential, but, to date, the oil from wild olives has not been studied significantly, especially from an analytical point of view. In Spain, the wild olive tree is called “Acebuche” and its fruit “Acebuchina”. The objective of this work is to optimize the olive oil production process from the Acebuchina cultivar and characterize the oil, which could be marketed as healthy and functional food. A Box–Behnken experimental design with five central points was used, along with the Response Surface Methodology to obtain a mathematical experimental model. The oils from the Acebuchina cultivar meet the requirements for human consumption and have a good balance of fatty acids. In addition, the oils are rich in antioxidants and volatile compounds. The highest extraction yield, 12.0 g oil/100 g paste, was obtained at 90.0 min and the highest yield of phenolic compounds, 870.0 mg/kg, was achieved at 40.0 °C, and 90.0 min; but the maximum content of volatile compounds, 26.9 mg/kg, was obtained at 20 °C and 30.0 min. The oil yield is lower than that of commercial cultivars, but the contents of volatile and phenolic compounds is higher.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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