In 1937, Mears [Ann. Math., 38 (1937), 594–601] studied absolutely regular matrices for single sequences. In this paper, we define the absolutely almost conservative and absolutely almost regular matrices for double sequences and establish the necessary and sufficient conditions to characterize them.

Almost bounded variation of double sequences and some four dimensional summability matrices

Rapid variable-step computation of dynamic convolutions and Volterra-type integro-differential equations: RK45 Fehlberg, RK4

Anisotropic Noncommutative Schwarzschild Metamaterial

We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a system of partial differential equations with a fixed domain by using logarithm transformation and taking additional derivatives. With the addition of an intermediate function with a fixed free boundary, a quadratic formula is derived to compute the velocity of the optimal exercise boundary analytically. Furthermore, we implement an extrapolation method to ensure that at least, a third-order accuracy in space is maintained at the boundary point when computing the optimal exercise boundary from its derivative. As such, it enables us to employ fourth-order spatial and temporal discretization with Dirichlet boundary conditions for obtaining the numerical solution of the asset option, option Greeks, and the optimal exercise boundary. The advantage of the Runge-Kutta-Fehlberg method is based on error control and the adjustment of the time step to maintain the error at a certain threshold. By comparing with some existing methods in the numerical experiment, it shows that the present method has a better performance in terms of computational speed and provides a more accurate solution.

An Adaptive and Explicit Fourth Order Runge-Kutta-Fehlberg Method Coupled with Compact Finite Differencing for Pricing American Put Options

Rapid Variable-Step Computation of Dynamic Convolutions and Volterra-Type Integro-Differential Equations: Rk45 Fehlberg, Rk4

In 1939 Agnew presented a series of conditions that characterized the oscillation of ordinary sequences using ordinary square conservative matrices and square multiplicative matrices. The goal of this paper is to present multidimensional analogues of Agnew’s results. To accomplish this goal we begin by presenting a notion for double oscillating sequences. Using this notion along with square RH-conservative matrices and square RH-multiplicative matrices, we will present a series of characterization of this sequence space, i.e. we will present several necessary and sufficient conditions that assure us that a square RH-multiplicative(square RH-conservative) be such that 

$$ P - \mathop {limsup}\limits_{(m,n) \to \infty ;(\alpha ,\beta ) \to \infty } \left| {\sigma _{m,n} - \sigma _{\alpha ,\beta } } \right| \leqslant P - \mathop {limsup}\limits_{(m,n) \to \infty ;(\alpha ,\beta ) \to \infty } \left| {s_{m,n} - s_{\alpha ,\beta } } \right| $$

for each double real bounded sequences {sk;l} where 

$$ \sigma _{m,n} = \sum\limits_{k,l = 1,1}^{\infty ,\infty } {a_{m,n,k,l,} s_{k,l} } . $$

In addition, other implications and variations are also presented.

Four dimensional matrix characterization of double oscillation via RH-conservative and RH-multiplicative matrices

The Abel-type matrix Aα,t was introduced and studied as a mapping intoby Lemma (1999). The purpose of this paper is to study these transformations as mappings into Gw . The necessary and sufficient conditions for Aα,t to be Gw -Gw are established. The strength of Aα,t in the Gw -Gw setting is investigated. Also, it is shown that Aα,t is translative in the Gw -Gw senses for certain sequences. 2000 Mathematics Subject Classification. 40A05, 40D25.

/pdf/the-abel-type-transformations-into-gw-2sful2h9m1.pdf

THE ABEL-TYPE TRANSFORMATIONS INTO Gw

Recently the author introduced the logarithmic matrix L t and studied as it mappings into l. In this paper, we study L t as mappings into G. The necessary and sufficient conditions for L t to be G-G is proved. The strengths of L t in the G-G is settings is investigated. Also, it is shown that L t is translative in the G-G senses for certain sequences.

Logarithmic Transformations into G

In (1), Friday introduced and studied the Abel Matrix ll method, − l translativity, and Abel matrix ψ

/pdf/a-note-on-special-abel-matrices-into-l-2x8dn119qa.pdf

A Note on Special Abel Matrices into λ

We will learn the central roles that the Sylow Theorems play in the theory of finite groups. The arts of problem Solving using the three Slow the theorems are investig

Note On the arts of problem Solving Using The Three SYLOW THEOREMS

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Mulatu Lemma

Author Tools

Chat about Author