Recent Publications

The immersed interface method (IIM) ?rst proposed in is an accurate numerical method for solving elliptic interface problems on Cartesian meshes. It is a sharp interface method that was intended to improve accuracy of the immersed boundary (IB) method. The IIM is second order accurate in the maximum norm (pointwise, strongest) while the IB method is ?rst order accurate. The ?rst IIM paper is one of the most downloaded one from the SIAM website and is one of the most cited papers. While IIM provided a way of accurate discretization of the partial differential equations (PDEs) with discontinuous coefficients, the augmented IIM ?rst proposed in made the IIM much more efficient and faster by utilizing existing fast Poisson solvers. More important is that the augmented IIM provides an efficient way for multi-physics models with different governing equations, problems on irregular domains, multi-scales and multi-connected domains. A brie?y introduction of the augmented strategy including some recently progress is presented in this article.

Review Article
Fatma Elarabi, Aya Aboelkhair, Alaa Mohammed, Ehab Morsy

In this paper, we consider the problem of storage and search in peer-to-peer networks. It is well known that all storage systems try to meet two conflict goals, increasing the success rate within reasonable response time and decreasing the worst case message complexity. In this result, we focus on designing an e?cient algorithms for storage and search in unstructured peer-to-peer networks. In the storage, we present an algorithm for storage in which we try to maintain a reasonable number of copies of each file such that these copies can be reached in almost the same time from all nodes. In the search algorithm, we initiate a reasonable number of messages from the node that requests the file such that they cover random parts of the system. We evaluate our algorithm by applying it to random networks with various sizes.

Stavros Anastassiou PhD (Dynamical Systems)

Regression analysis is a powerful tool to describe the relationship between response and predictors. In practice, parametric regression models such as linear regression models are widely used due to their simplicity and interpretability. When a parametric regression model is correctly fitted by the data, further statistical analysis can be easily and accurately elaborated with good explanations. However, such further analysis and interpretation could be misleading when the model does not fit the data well.

The branching random walk on integer lattices is shown to be monotone decreasing in ascending direction (MDAD) as a corollary of an observation in regard to the lineage of particles from antisymmetric initial states, and a related property of percolation paths on the usual oriented lattices is also given.

Editor in Chief
Zhilin Li (Ph.D. (Applied Mathematics))
Professor of Mathematics, Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205 USA


Prof. Dr. Zhilin Li is associated with Department of Mathematics, North Carolina State University, US since 1997. He was graduated from Nanking Normal University (Mathematics B.S.) in 1982. Whereas, he has completed his Master in Mathematics from University of Washington Applied in 1991. The University of Washington awarded him PhD in Applied Mathematics in 1994. He has published 127 quality manuscript since October 31, 2016. Moreover, he received the Research Grants Current and past from NSF, NIH, NSF/NIGMS, ARO, AFOSR, Oak Ridge, DOE/ARO etc. He is collaborated and affiliated with Juan Alvares, UAH, Spain; Philippe Angot, Aix-Marceille University, France; J. Chen & H. Ji, NNU, China; K Ito, SR Lubkin, NCSU; M-C Lai, Taiwan; R. Luo, UCI; J. Xia, Purdue; Hayk Mikayelyan, Nottingham. Moreover, he has advised and supervised more than 15 graduated students to complete their research projects.

Journal Highlights
Abbreviation: Adv Calc Anal
Current Volume: 2 (2017)
Next volume: December, 2018 (Volume 3)
Back volumes: 1
Starting year: 2016
Nature: Online
Submission: Online
Language: English

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Subject & Scope
  • Applied mathematics
  • Bioinformatics
  • Statistical analysis
  • Computation and regression
  • Compartment and module analysis
  • Algebraic Topology
  • BCK Algebra
  • Semi Rings
  • Control Theory
  • Fied Point Theory
  • Geo Mathematics
  • Group Theory and Algebraic Modeling
  • Industrial Mathematics
  • Radical Theory of Rings
  • Real Analysis, Algebra
  • Complete Analysis and Differential Geometry
  • Mechanics
  • Topology and Functional Analysis
  • Advanced Analysis
  • Methods of Mathematical Physics
  • Numerical Analysis
  • Mathematical Statistics
  • Computer Applications
  • Group Theory
  • Rings and Modules
  • Number Theory
  • Fluid Mechanics
  • Quantum Mechanics
  • Special Theory of Relatity and Analytical Mechanics
  • Electromagnetic Theory
  • Operations Research
  • Theory of Approimation and Splines
  • Advanced Functional Analysis
  • Solid Mechanics
  • Theory of Optimization

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