2024-03-29T14:17:45Z
https://zenodo.org/oai2d
oai:zenodo.org:3471723
2020-01-20T17:17:11Z
user-omj
Areen Al-Khateeb
2019-07-01
<p>In this article, we study some new functions (namely Γ ̃_(p,q) (z)=Γ_(q/p) (z) and B ̃_(p,q) (s,t)=Γ_(q/p) (s,t)) and we will show how these functions are relevant to (p,q)-Gamma function and (p,q)-Beta function.</p>
https://doi.org/10.5281/zenodo.3471723
oai:zenodo.org:3471723
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.3471722
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 01(03), 1-14, (2019-07-01)
(p,q)-Gamma function
(p,q)-Beta function
Relevant Functions to (p,q)-Gamma Function and (p,q)-Beta Function
info:eu-repo/semantics/article
oai:zenodo.org:4595051
2021-03-11T00:27:24Z
user-omj
Reza Alizadeh
Ali Sameripour
2021-03-08
<p>The importance of studying non-self-adjoint differential operators is becoming more and more obvious to scientists. The non-self-adjoint operators appear in many branches of science. Today, these operators have many applications in kinetic theory and quantum mechanics to linearization of equations of mathematical physics. The spectrum of these operators is unstable and their resolvent is very unpredictable. In these operators, there is no general spectral theory and this causes problems in the study of these operators. In this paper, we consider a non-self-adjoint elliptic differential operator and study its resolvent.</p>
https://doi.org/10.5281/zenodo.4595051
oai:zenodo.org:4595051
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.4595050
info:eu-repo/semantics/openAccess
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Online Mathematics Journal, 03(01), 1–7, (2021-03-08)
resolvent
distribution of eigenvalues
non-self-adjoint operators
elliptic operators
On the Resolvent of a Non-Self-Adjoint Differential Operator in Hilbert Spaces
info:eu-repo/semantics/article
oai:zenodo.org:4743382
2021-05-08T13:48:07Z
user-omj
Reza Alizadeh
Ali Sameripour
2021-05-09
<p>The study of non-self-adjoint differential operators is a historical issue. Before and until now, most studies of operator theory have been about self-adjoint operators. But non-self-adjoint operators have recently found many applications in other sciences. These operators have received much attention in thermodynamics and quantum mechanics. Because there is no general spectral theory for these operators, it is more difficult to study these operators than the self-adjoint type. The spectrum of these operators is usually unstable and their resolvent is unpredictable. In this paper by use of Weyl’s law for asymptotic distribution of eigenvalues of elliptic self adjoint operators on bounded domain, we consider a second-order non-self-adjoint differential operator and study its distribution of eigenvalues. Our goal is to find an asymptotic formula for the Dirichlet eigenvalue counting function on the open interval (0,1).</p>
https://doi.org/10.5281/zenodo.4743382
oai:zenodo.org:4743382
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.4743381
info:eu-repo/semantics/openAccess
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Online Mathematics Journal, 03(02), 01–08, (2021-05-09)
resolvent
distribution of eigenvalues
non-self-adjoint operators
elliptic operators
asymptotic distribution of eigenvalues
Asymptotic Distribution of Eigenvalues of Non-Self Adjoint Differential Operators
info:eu-repo/semantics/article
oai:zenodo.org:3234186
2021-03-10T22:56:19Z
user-mathscicu
user-omj
Hend Dawood
Yasser Dawood
2019-07-01
<p>Interval arithmetic has been proved to be very subtle, reliable, and most fundamental in addressing uncertainty and imprecision. However, the theory of classical interval arithmetic and all its alternates suffer from algebraic anomalies, and all have difficulties with interval dependency. A theory of interval arithmetic that seems promising is the theory of parametric intervals. The theory of parametric intervals is presented in the literature with the zealous claim that it provides a radical solution to the long-standing dependency problem in the classical interval theory, along with the claim that parametric interval arithmetic, unlike Moore's classical interval arithmetic, has additive and multiplicative inverse elements, and satisfies the distributive law. So, does the theory of parametric intervals accomplish these very desirable objectives? Here it is argued that it does not.</p>
https://doi.org/10.5281/zenodo.3234186
oai:zenodo.org:3234186
eng
Zenodo
https://doi.org/10.5281/zenodo.3234184
https://doi.org/10.5281/zenodo.2656089
https://doi.org/10.5281/zenodo.2702404
https://doi.org/10.4018/978-1-4666-4991-0.ch001
https://zenodo.org/communities/mathscicu
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.3234185
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Online Mathematics Journal, 01(03), 37-54, (2019-07-01)
Interval mathematics
Classical interval arithmetic
Parametric interval arithmetic
Constrained interval arithmetic
Overestimation-free interval arithmetic
Interval dependency
Functional dependence
Dependency predicate
Interval enclosures
S-semiring
Uncertainty
Reliability
Parametric Intervals: More Reliable or Foundationally Problematic?
info:eu-repo/semantics/article
oai:zenodo.org:4609709
2021-03-17T12:27:18Z
user-omj
Boris B. Stefanov
2021-03-17
<p>This paper proposes a new two-parameter generalization T_{b,s}(x) of the Z -> Z Collatz function T(x) and restates the eponymous conjecture in terms of the proposed function. The generalization obviates some of the conditions for emergence of terminal cycles for the Collatz T(x) function over the integers. The stopping behavior of the T_{b,s}(x) is qualitatively similar to that of the T(x). The paper presents theoretical discussion of the generalization and computational results on the terminal cycles and stopping times of T_{b,s}(x). The {1,2} cycle of T(x) is shown to be a case of coincidence of three independent cycle categories of T_{b,s}(x).</p>
https://doi.org/10.5281/zenodo.4609709
oai:zenodo.org:4609709
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.4609708
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
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Online Mathematics Journal, 03(01), 19–25, (2021-03-17)
Collatz conjecture
3x+1 problem
iteration
convergence
terminal cycles
Two-Parameter Generalization of the Collatz Function: Characterization of Terminal Cycles and Empirical Results
info:eu-repo/semantics/article
oai:zenodo.org:4743395
2021-05-08T13:48:07Z
user-omj
Pasunoori Srinivasulu
V. Srinivas
2021-05-09
<p>In this paper, we present and carefully examine a new subclass of analytic functions characterized by a differential operator. Moreover, we derive coefficient estimates, extreme points, starlikeness, and radii of close-to-convexity for the aforementioned class. Furthermore, we investigate the integral means inequalities thereof.</p>
https://doi.org/10.5281/zenodo.4743395
oai:zenodo.org:4743395
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.4743394
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
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Online Mathematics Journal, 03(02), 09–15, (2021-05-09)
analytic functions
univalent functions
Mittag-Leffler function
coefficient bounds
starlikeness
distortion
On Univalent Functions with Negative Coefficients Defined by Mittag-Leffler Function
info:eu-repo/semantics/article
oai:zenodo.org:2656089
2020-01-20T15:11:06Z
user-mathscicu
user-omj
Hend Dawood
2019-04-01
<p>Interval arithmetic is a fundamental and reliable mathematical machinery for scientific computing and for addressing uncertainty in general. In order to apply interval mathematics to real life uncertainty problems, one needs a computerized (machine) version thereof, and so, this article is devoted to some mathematical notions concerning the algebraic system of machine interval arithmetic. After formalizing some purely mathematical ingredients of particular importance for the purpose at hand, we give formal characterizations of the algebras of real intervals and machine intervals along with describing the need for interval computations to cope with uncertainty problems. Thereupon, we prove some algebraic and order-theoretic results concerning the structure of machine intervals.</p>
https://doi.org/10.5281/zenodo.2656089
oai:zenodo.org:2656089
eng
Zenodo
https://doi.org/10.5281/zenodo.2702404
https://zenodo.org/communities/mathscicu
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.2656088
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 01(02), 1–13, (2019-04-01)
Interval mathematics
Machine interval arithmetic
Outward rounding
Floating-point arithmetic
Machine monotonicity
Dense orders
Orderability of intervals
Orderability of intervals
Singletonicity
Subdistributive semiring
S-semiring
On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic
info:eu-repo/semantics/article
oai:zenodo.org:3234184
2020-01-20T17:23:55Z
user-mathscicu
user-inclosure
user-omj
Hend Dawood
Yasser Dawood
2019-07-01
<p>Progress in scientific knowledge discloses an increasingly paramount use of quantifiable properties in the description of states and processes of the real-world physical systems. Through our encounters with the physical world, it reveals itself to us as systems of uncertain quantifiable properties. One approach proved to be most fundamental and reliable in coping with quantifiable uncertainties is interval mathematics. A main drawback of interval mathematics, though, is the persisting problem known as the "interval dependency problem". This, naturally, confronts us with the question: Formally, what is interval dependency? Is it a meta-concept or an object-ingredient of interval and fuzzy computations? In other words, what is the fundamental defining properties that characterize the notion of interval dependency as a formal mathematical object? Since the early works on interval mathematics by John Charles Burkill and Rosalind Cecily Young in the dawning of the twentieth century, this question has never been touched upon and remained a question still today unanswered. Although the notion of interval dependency is widely used in the interval and fuzzy literature, it is only illustrated by example, without explicit formalization, and no attempt has been made to put on a systematic basis its meaning, that is, to indicate formally the criteria by which it is to be characterized. Here, we attempt to answer this long-standing question. This article, therefore, is devoted to presenting a complete systematic formalization of the notion of interval dependency, by means of the notions of Skolemization and quantification dependence. A novelty of this formalization is the expression of interval dependency as a logical predicate (or relation) and thereby gaining the advantage of deducing its fundamental properties in a merely logical manner. Moreover, on the strength of the generality of the logical apparatus we adopt, the results of this article are not only about classical intervals, but they are meant to apply also to any possible theory of interval arithmetic. That being so, our concern is to shed new light on some fundamental problems of interval mathematics and to take one small step towards paving the way for developing alternate dependency-aware interval theories and computational methods.</p>
Supplementary Material: http://doi.org/10.5281/zenodo.3466032
Download latest release of InCLosure via https://doi.org/10.5281/zenodo.2702404
https://doi.org/10.5281/zenodo.3234184
oai:zenodo.org:3234184
eng
Zenodo
https://doi.org/10.5281/zenodo.2702404
https://doi.org/10.5281/zenodo.3466032
https://doi.org/10.5281/zenodo.2656089
https://zenodo.org/communities/mathscicu
https://zenodo.org/communities/omj
https://zenodo.org/communities/inclosure
https://doi.org/10.5281/zenodo.3234183
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 01(03), 15-36, (2019-07-01)
Interval Mathematics
Interval Dependency
Functional Dependence
Skolemization
Guaranteed Bounds
Interval Enclosures
Interval Functions
Quantifiable Uncertainty
Scientific Knowledge
Reliability
Fuzzy Mathematics
InCLosure
Subdistributive Semiring
S-Semiring
Interval Computations
Interval Analysis
Interval Arithmetic
Universal Intervals
Rounding Error
Real Functions
A Logical Formalization of the Notion of Interval Dependency: Towards Reliable Intervalizations of Quantifiable Uncertainties
info:eu-repo/semantics/article
oai:zenodo.org:3046037
2020-01-20T17:41:38Z
user-omj
M. Awadalla
Y .Y. Yameni
K. Abuassba
2019-04-01
<p>In this article, a mathematical model for cancer treatment by radiotherapy is examined. The model is integrated into the Hadamard fractional derivative. First, we examine the existence of the solution. Then, the uniqueness of the solution is investigated.</p>
https://doi.org/10.5281/zenodo.3046037
oai:zenodo.org:3046037
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.3046036
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 01(02), 14-18, (2019-04-01)
Hadamard fractional derivative
Existence and uniqueness
fixed point theory
nonlinear fractional differential equation
A New Fractional Model for the Cancer Treatment by Radiotherapy Using the Hadamard Fractional Derivative
info:eu-repo/semantics/article
oai:zenodo.org:3047015
2020-01-20T14:59:04Z
user-omj
S. Alfaqeih
T. Ozis
2019-04-01
<p>In this study, we introduce definitions of a fractional double Aboodh transform of order α, where α ϵ [0, 1], for a functions which are fractional differentiable. We then establish some main properties of this transform. Furthermore, we prove some related theorems.</p>
https://doi.org/10.5281/zenodo.3047015
oai:zenodo.org:3047015
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.3047014
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 01(02), 19-25, (2019-04-01)
Fractional Laplace transform
Summudu transform
Double Aboodh transform
Mittag leffler function
Note on Double Aboodh Transform of Fractional Order and its Properties
info:eu-repo/semantics/article
oai:zenodo.org:4595454
2021-03-11T00:27:25Z
user-omj
B. Venkateswarlu
P. Thirupathi Reddy
S. Sridevi
Sujatha Tha
2021-03-08
<p>In this paper, we introduce a new subclass of uniformly convex functions defined by Gegenbauer polynomials with negative coefficients. For functions in the class TS, we attain coefficient bounds, growth distortion properties, extreme points and radii of close-to-convexity, starlikeness and convexity. For this class, we also produced modified Hadamard product, convolution, and integral operators.</p>
https://doi.org/10.5281/zenodo.4595454
oai:zenodo.org:4595454
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.4595453
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
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Online Mathematics Journal, 03(01), 8–18, (2021-03-08)
analytic
coefficient bounds
extreme points
convolution
polynomials
A Certain Subclass of Uniformly Convex Functions with Negative Coefficients Defined by Gegenbauer Polynomials
info:eu-repo/semantics/article
oai:zenodo.org:3466032
2020-01-24T19:24:29Z
user-mathscicu
user-inclosure
openaire_data
user-omj
Hend Dawood
Yasser Dawood
2019-07-01
<p>InCLosure Input and Output Files for Guaranteed Enclosures Under Interval Dependency: Supplementary Material for Article "A Logical Formalization of the Notion of Interval Dependency: Towards Reliable Intervalizations of Quantifiable Uncertainties", Online Mathematics Journal, July 2019. Download latest release of InCLosure via <a href="https://doi.org/10.5281/zenodo.2702404">https://doi.org/10.5281/zenodo.2702404</a></p>
https://doi.org/10.5281/zenodo.3466032
oai:zenodo.org:3466032
eng
Zenodo
https://doi.org/10.5281/zenodo.2702404
https://zenodo.org/communities/mathscicu
https://zenodo.org/communities/omj
https://zenodo.org/communities/inclosure
https://doi.org/10.5281/zenodo.3466031
info:eu-repo/semantics/openAccess
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InCLosure
Interval Mathematics
Interval Dependency
Functional Dependence
Interval Subdivision Method
Uncertainty
Reliability
Fuzzy Mathematics
Interval Arithmetic
Interval Functions
Interval Enclosures
InCLosure Code for Guaranteed Enclosures Under Interval Dependency: Supplementary Material for Article "A Logical Formalization of the Notion of Interval Dependency: Towards Reliable Intervalizations of Quantifiable Uncertainties"
info:eu-repo/semantics/other