scholarly journals A simple construction of exponential bases in L2 of the union of several intervals

1995 ◽  
Vol 38 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Kristian Seip
Keyword(s):  
Riesz Basis ◽  
Partial Result ◽  
Simple Construction ◽  
Real Numbers ◽  
Exponential Bases ◽  
Several Intervals

It is proved that every space L2 (I1, ∪ I2), where I1 and I2 are finite intervals, has a Riesz basis of complex exponentials , {λk} a sequence of real numbers. A partial result for the corresponding problem for n≧3 finite intervals is also obtained.

scholarly journals Three Problems on Exponential Bases

2019 ◽  
Vol 62 (1) ◽  
pp. 55-70
Author(s):  
Laura De Carli ◽  
Alberto Mizrahi ◽  
Alexander Tepper
Keyword(s):  
Lebesgue Measure ◽  
Riesz Basis ◽  
Unit Cube ◽  
Exponential Basis ◽  
Exponential Bases ◽  
Finite Lebesgue Measure

AbstractWe consider three special and significant cases of the following problem. Let $D\subset \mathbb{R}^{d}$ be a (possibly unbounded) set of finite Lebesgue measure. Let $E(\mathbb{Z}^{d})=\{e^{2\unicode[STIX]{x1D70B}ix\cdot n}\}\text{}_{n\in \mathbb{Z}^{d}}$ be the standard exponential basis on the unit cube of $\mathbb{R}^{d}$. Find conditions on $D$ for which $E(\mathbb{Z}^{d})$ is a frame, a Riesz sequence, or a Riesz basis for $L^{2}(D)$.

An exploration of target L2 morphemes in the oral production of young EFL learners in Croatia

2020 ◽  
Author(s):  
Jelena O'Reilly ◽  
Eva Jakupčević
Keyword(s):  
Foreign Language ◽  
Research Area ◽  
Simple Construction ◽  
L2 Acquisition ◽  
Efl Learners ◽  
Oral Production ◽  
The Past ◽  
Base Form ◽  
Production Study ◽  
Efl Students

Although the second language (L2) acquisition of morphology by late L2 learners has been a popular research area over the past decades, comparatively little is known about the acquisition and development of morphology in children who learn English as a foreign language (EFL). Therefore, the current study presents the findings from a longitudinal oral production study with 9/10-year-old L1 Croatian EFL students who were followed up at the age of 11/12. Our results are largely in line with the limited research so far in this area: young EFL learners have few issues using the be copula and, eventually, the irregular past simple forms, but had considerable problems with accurately supplying the 3rd person singular -s at both data collection points. We also observed a be + base form structure, especially at the earlier stage, which appears to be an emergent past simple construction.

DISTANCE EDUCATION IN FURTHER PROFESSIONAL TRAINING IN ENTERPRISES DURING PANDEMIC PERIOD

2020 ◽  
Author(s):  
Marta Matulčíková ◽  
Daniela Breveníková
Keyword(s):  
Distance Education ◽  
Empirical Research ◽  
Management System ◽  
Professional Training ◽  
Developmental Stages ◽  
Content Management ◽  
Partial Result ◽  
Corporate Education ◽  
Research Survey ◽  
Learning Management

Constraints on our personal and professional life imposed by the COVID 19 pandemic have radically influenced our approach to forms of education, including those used in further professional training of employees. This shift means the focus on distance education as a managed educational form, which is suitable for further professional training. The aim of the paper is to present the implementation of distance education in further professional training in enterprises and based on the empirical research propose ways of improving options of education. Distance education is characterised in terms of its principles and developmental stages. Its first generation was correspondence education. The Learning Management System (LMS) and Learning Content Management System (LCMS) are described as the systems applied in further professional training. The research was conducted by means of the questionnaire method, combined with the pre-research survey. Results of empirical research are presented in tables. Separate parts of the paper deal with ICT application in corporate education (correspondence education, Computer-based training (CBT), Web-based training (WBT), Technology Based Training (TBT) and with the utilisation of Learning Management Systems (LMS). Analysis of respondent opinions shows that respondents tend to prefer the face-to-face form of corporate education. The length of the pandemic is going to affect the spread of e-learning in corporate education and its role in education. The learners’ interest may be expected to be shifted to LCM and LCMS utilisation. The paper is a partial result of the research scheme VEGA No. 1/0309/18 “Social networks in human resource management” supported by the Ministry of Education, Science and Research and Sports, Slovakia

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

Dynamics of a family of orbitally continuous mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3507-3517
Author(s):  
Abhijit Pant ◽  
R.P. Pant ◽  
Kuldeep Prakash
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Real Numbers ◽  
Continuous Mappings ◽  
Non Linear

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5945-5953 ◽  
Author(s):  
İmdat İsçan ◽  
Sercan Turhan ◽  
Selahattin Maden
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Special Means ◽  
Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

On calculating extinction probabilities for branching processes in random environments

1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson
Keyword(s):  
Generating Functions ◽  
Infinite Sequence ◽  
Branching Processes ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Random Environments ◽  
Real Numbers ◽  
Discrete Time Markov Chain ◽  
Extinction Probabilities ◽  
Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

scholarly journals Some Properties Involving q-Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1168
Author(s):  
Cheon Seoung Ryoo ◽  
Jung Yoog Kang
Keyword(s):  
Differential Equations ◽  
Hermite Polynomials ◽  
Real Numbers ◽  
Different Types

Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations, we investigate some identities and properties of q-Hermite polynomials. We also find the position of the roots of these polynomials under certain conditions and their stacked structures. Furthermore, we locate the roots of various forms of q-Hermite polynomials according to the conditions of q-numbers, and look for values which have approximate roots that are real numbers.

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