Article Information

Identifiers and Pagination:
Year:2016
Volume:1
First Page:1
Last Page:2
Publisher Id:.1:1.2016
Article History:
Received:December 11, 2016
Accepted:December 17, 2016
Collection year:2016
First Published:December 23, 2016

The importance of analysis in mathematics cannot be overestimated. Many areas of modern mathematics may be seen as parts of analysis while, at the same time, many areas of mathematics heavily rely on analysis to built on and further comment on their problems.

Indeed many mathematicians, who consider themselves to be analysts, work on differential equations and prove numerous and powerful results regarding their behavior (enumerating these results, one could begin by mentioning the existence theorem of solutions in the O.D.E's case, and various results concerning solutions of boundary value problems in the P.D.E.'s case).

Such was the success of analysis in geometry, that the term \global analysis" was coined to describe the work of those mathematicians who use analytical techniques to study geometrical and topological properties \in the large". The proof of the Geometrization and Poincare conjectures is probably the most famous result of using analytical tools (properties of the Ricci flow) to achieve a geometrical result (classifi
cation of manifolds).

Algebra is not beyond the limits of analysis either. In number theory p-adic functional analysis provides us with results on the Weyl conjectures, while one cannot overlook the work of Hormander and its consequences in commutative algebra and complex algebraic geometry (the effective Nullstellensatz" easily comes to mind).

On the other hand, all these require concrete estimates. Norms have to be calculated, operators must be inverted and various types of constants should be explicitly constructed. Furthermore, for some time now, computers have become important not only as computational tools, but as valuable \coworkers" as well. Computer assisted proofs are here to stay, allowing us to draw de
finite conclusions on problems dicult to attack from a more \old fashioned" viewpoint.

The four color map theorem and the existence of a strange attractor in the Lorenz system were proved by mathematicians using computers to perform calculations unattainable by hand.

All these are but a few examples of the effectiveness of analysis, along with reliable calculations, on various problems arising in all areas of mathematics. We hope that this journal will serve as a widely respected forum for communicating techniques and results that will further broaden our understanding of the mathematical and physical universe.


© 2016 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. You are free to: Share — copy and redistribute the material in any medium or format Adapt — remix, transform, and build upon the material for any purpose, even commercially. The licensor cannot revoke these freedoms as long as you follow the license terms. Under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. No additional restrictions You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits
Editor in Chief
Zhilin Li (Ph.D. (Applied Mathematics))
Professor of Mathematics, Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205 USA

Bibliography

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.

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Subject & Scope
  • Applied mathematics
  • Bioinformatics
  • Statistical analysis
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  • Compartment and module analysis
  • Algebraic Topology
  • BCK Algebra
  • Semi Rings
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  • Fied Point Theory
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  • Group Theory and Algebraic Modeling
  • Industrial Mathematics
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  • 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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