University of Missouri-St. Louis
University of Nebraska-Lincoln
University of New Mexico
Shawnee State University
University of South Florida
Trinity University
Minnesota State University Moorhead
Energy Extraction, Or Lack Thereof,
2023
Clark University
Energy Extraction, Or Lack Thereof, Nishanth Gudapati
Mathematics
The problem of stability of rotating black holes is the subject of a long standing research program since the 1960s and remains an unresolved problem in general relativity. A major obstacle in the black hole stability problem is that the energy of waves propagating through rotating black holes spacetimes is not necessarily positive-definite, due to the so called ergo-region. This is a serious complication that limits the efficacy of most mathematical techniques. In this expository article, we report that, despite the ergo-region, there exists a positive-definite total energy for axisymmetric Maxwell, gravitational and electrovacuum perturbations of Kerr and Kerr–Newman black …
Characterization Of The Long-Distance Dispersal Kernel Of White-Tailed Deer And Evaluating Its Impact On Chronic Wasting Disease Spread In Wisconsin,
2023
Utah State University
Characterization Of The Long-Distance Dispersal Kernel Of White-Tailed Deer And Evaluating Its Impact On Chronic Wasting Disease Spread In Wisconsin, Mennatallah Gouda
All Graduate Theses and Dissertations, Fall 2023 to Present
Chronic Wasting Disease (CWD) is a fatal, untreatable neurodegenerative disease that infects deer and related species. It is highly contagious and caused by abnormal malfunction and assembly of normal cellular proteins into aggregation-prone proteins. The Centers for Disease Control and prevention report that the prevalence of CWD in free-ranging deer in the US is still relatively low. However, in several states the infection rates exceed 1 deer in 10. Deer may uptake CWD from direct interaction with infected individuals or from the environment. Infected individuals shed CWD into the environment through feces, urine, saliva or carcasses, and long-distance dispersal of …
Math 115: College Algebra For Pre-Calculus,
2023
CUNY Queens College
Math 115: College Algebra For Pre-Calculus, Seth Lehman
Open Educational Resources
OER course syllabus for Math 115, College Algebra, at Queens College
On The Second Case Of Fermat's Last Theorem Over Cyclotomic Fields,
2023
The Graduate Center, City University of New York
On The Second Case Of Fermat's Last Theorem Over Cyclotomic Fields, Owen Sweeney
Dissertations, Theses, and Capstone Projects
We obtain a new simpler sufficient condition for Kolyvagin's criteria, regarding the second case of Fermat's last theorem with prime exponent p over the p-th cyclotomic field, to hold. It covers cases when the existing simpler sufficient conditions do not hold and is important for the theoretical study of the criteria.
Soundness And Completeness Results For The Logic Of Evidence Aggregation And Its Probability Semantics,
2023
The Graduate Center, City University of New York
Soundness And Completeness Results For The Logic Of Evidence Aggregation And Its Probability Semantics, Eoin Moore
Dissertations, Theses, and Capstone Projects
The Logic of Evidence Aggregation (LEA), introduced in 2020, offers a solution to the problem of evidence aggregation, but LEA is not complete with respect to the intended probability semantics. This left open the tasks to find sound and complete semantics for LEA and a proper axiomatization for probability semantics. In this thesis we do both. We also develop the proof theory for some LEA-related logics and show surprising connections between LEA-related logics and Lax Logic.
Differential Calculus: From Practice To Theory,
2023
Pennsylvania State University
Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers
Milne Open Textbooks
Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …
Double Barrier Backward Doubly Stochastic Differential Equations,
2023
Pension Fund Management Division, Mitsubishi UFJ Trust and Banking Corporation, 1-4-5, Marunouchi, Chiyoda-ku, Tokyo, 100-8212, Japan
Double Barrier Backward Doubly Stochastic Differential Equations, Tadashi Hayashi
Journal of Stochastic Analysis
No abstract provided.
Euler Archive Spotlight: Translations Of Euler's Works To Languages Other Than English,
2023
St. Edward's University
Euler Archive Spotlight: Translations Of Euler's Works To Languages Other Than English, Michael P. Saclolo
Euleriana
The Euler Archive is home to almost all of Euler’s original publications and roughly a quarter of them have accompanying translations to English. A small number of Euler’s works also have translations to a handful of other languages, namely, Dutch, French, German, Italian, Portuguese, and Turkish that are available in the archive. We put a spotlight on these non-English translations in this issue.
Perfect Numbers,
2023
Johann Wolfgang Goethe Universitat Frankfurt am Main
Perfect Numbers, Uwe Hassler
Euleriana
We provide a selected review of results known or conjectured before Euler entered and changed the quest for perfect numbers. Then we discuss his contributions to the determination of Mersenne primes that fueled research on primality tests.
Euler’S Variational Approach To The Elastica,
2023
University of São Paulo
Euler’S Variational Approach To The Elastica, Sylvio R. Bistafa
Euleriana
The history of the elastica is examined through the works of various contributors, including those of Jacob and Daniel Bernoulli, since its first appearance in a 1690 contest on finding the profile of a hanging flexible cord. Emphasis will be given to Leonhard Euler’s variational approach to the elastica, laid out in his landmark 1744 book on variational techniques. Euler’s variational approach based on the concept of differential value is highlighted, including the derivation of the general equation for the elastica from the differential value of the first kind, from which nine shapes adopted by a flexed lamina under different …
Euler’S First Proof Of Stirling’S Formula,
2023
Johannes Gutenberg Universitat, Mainz
Euler’S First Proof Of Stirling’S Formula, Alexander Aycock
Euleriana
We present a proof given by Euler in his paper “De serierum determinatione
seu nova methodus inveniendi terminos generales serierum” [4] (E189:“On
the determination of series or a new method of finding the general terms
of series”) for Stirling’s formula. Euler’s proof uses his theory of difference
equations with constant coefficients. This theory outgrew from his ear-
lier considerations on inhomogeneous differential equations with constant
coefficients of finite order that he tried to extend to the case of infinite
order.
On Euler's Solution Of The Simple Difference Equation,
2023
Johannes Gutenberg Universitat, Mainz
On Euler's Solution Of The Simple Difference Equation, Alexander Aycock
Euleriana
In this note we will discuss Euler's solution of the simple difference equation that he gave in his paper{\it ``De serierum determinatione seu nova methodus inveniendi terminos generales serierum"} \cite{E189} (E189:``On the determination of series or a new method of finding the general terms of series") and also present a derivation for the values of the Riemann $\zeta$-function at positive integer numbers based on Euler's ideas.
Euler And The Legendre Polynomials,
2023
Johannes Gutenberg Universitat, Mainz
Euler And The Legendre Polynomials, Alexander Aycock
Euleriana
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the Legendre polynomials was already written down by Euler in at least two different papers. Furthermore, we will demonstrate that some familiar expressions for the Legendre polynomials are corollaries of the before-mentioned works. Finally, we will show that Euler's ideas on continued fractions lead to an integral representation for the Legendre polynomials that seems to be less generally known.
Solution Of The Diophantine Equation (Maa+Nbb)=Cd(Mcc+Ndd) Using Rational Numbers,
2023
Oak Ridge National Laboratory
Solution Of The Diophantine Equation (Maa+Nbb)=Cd(Mcc+Ndd) Using Rational Numbers, Georg Ehlers
Euleriana
This paper (E716) was published in Nova acta Academiae scientiarum imperialis petropolitanae, Volume 13 (1795/96), pp. 45-63. It was also included in Commentationes Arithmeticae, Volume II, as Number LXVIII, pp. 281-293 (E791). Euler starts with Fermat's Last Theorem and mentions the proofs for the cases n=3 and n=4 which he had completed himself earlier. He then moves on to make the sum of powers conjecture, which was later disproved in the second half of the 20th century. In this context he discusses his discovery of 134^4+133^4=158^4+59^4, which he calls unexpected. Euler derives the title equation from A^4+B^4=C^4+D^4, generalizing it to …
On The Motion Of The Nodes Of The Moon And The Variation Of Its Inclination To The Ecliptic (An English Translation Of De Motu Nodorum Lunae Eiusque Inclinationis Ad Eclipticam Variatione),
2023
Gannon University
On The Motion Of The Nodes Of The Moon And The Variation Of Its Inclination To The Ecliptic (An English Translation Of De Motu Nodorum Lunae Eiusque Inclinationis Ad Eclipticam Variatione), Patrick T. Headley
Euleriana
In this paper Euler attempts to explain some features of the motion of the Moon using Newton’s inverse-square law of gravity. He describes the evidence in favor of Newton’s theory but also the lack of progress in the study of lunar motion due to the difficulty of the three-body problem, arising here since both the Sun and the Earth have large effects on the Moon. He proceeds to investigate the line of intersection between the planes of the Earth's orbit and the Moon's orbit, as well as the angle between the two planes.
The Wide Scope Of Euler’S Work,
2023
University of the Pacific
The Wide Scope Of Euler’S Work, Christopher Goff, Erik R. Tou
Euleriana
An introduction to the contents in Issue 2, Volume 3 of Euleriana.
The $\Gamma$-Signless Laplacian Adjacency Matrix Of Mixed Graphs,
2023
College of Engineering and Technology, American University of the Middle East, Kuwait
The $\Gamma$-Signless Laplacian Adjacency Matrix Of Mixed Graphs, Omar Alomari, Mohammad Abudayah, Manal Ghanem
Theory and Applications of Graphs
The $\alpha$-Hermitian adjacency matrix $H_\alpha$ of a mixed graph $X$ has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number $\alpha$. This enables us to define an incidence matrix of mixed graphs. Consequently, we define a generalization of line graphs as well as a generalization of the signless Laplacian adjacency matrix of graphs. We then study the spectral properties of the gamma-signless Laplacian adjacency matrix of a mixed graph. Lastly, we characterize when the signless Laplacian adjacency matrix of a mixed graph is …
Undetermined Coefficients With Hyperbolic Sines And Cosines,
2023
DEVCOM Armaments Center U.S. Army Armament Graduate S
Undetermined Coefficients With Hyperbolic Sines And Cosines, Laurie A. Florio, George L. Fischer
CODEE Journal
The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function is from a selected class of functions. Often the hyperbolic sine and cosine functions are not explicitly included in this list of functions. Through a set of guided examples, this work argues that the hyperbolic sine and cosine ought to be included in the select class of functions. Careful explanation is provided for the necessary treatment of the cases where the argument of the hyperbolic sine and/or cosine functions matches one or both of the roots of the characteristic …
Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices,
2023
Southern Illinois University, Carbondale, Illinois 62901, USA
Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver
Journal of Stochastic Analysis
No abstract provided.
Efficient And Secure Digital Signature Algorithm (Dsa),
2023
university mh'amed bougara of boumerdes
Efficient And Secure Digital Signature Algorithm (Dsa), Nissa Mehibel, M'Hamed Hamadouche
Emirates Journal for Engineering Research
The digital signature is used to ensure the integrity of messages as well as the authentication and non-repudiation of users. Today it has a very important role in information security. Digital signature is used in various fields such as e-commerce and e-voting, health, internet of things (IOT). Many digital signature schemes have been proposed, depending on the computational cost and security level. In this paper, we analyzed a recently proposed digital signature scheme based on the discrete logarithm problem (DLP). Our analysis shows that the scheme is not secure against the repeated random number attack to determine the secret keys …
