Tuesday, August 21, 2012

Mission Statement

The Math Khipu Program is an genuine project of general mathematical research, including Mathematical Modeling focusing on research related to the mathematical concepts, design of algorithms and computational implementation of several complex and pathological processes in mathematics and its applications, with current emphasis on but not limited to following fields:
i) Algebraic Combinatorics (constructing non-linear functions defined over a Finite Field F2n with special features, such as a high resistance against Differential Attacks) and its iteractions with Analysis.
ii) Systems of Elliptic Partial Differential Equations.
A great project which seeks to identify prolific trends.

Roberto C Reyes Carranza
Research Assistant
roberto.reyes@upr.edu  
"Because we know that is what is sought in mathematics and its applications, we are heirs of the responsibility to generate and manage sophisticated mathematical directions"

Current Research

"Fundamental Properties of Almost Perfect Nonlinear Functions, a Way to Measure its Nonlinearity and to construct Highly Nonlinear Functions", paper in preparation, with Moisés Delgado (at an advanced stage, to be submitted 2014).
"APN Functions in Differential cryptanalysis", with Moisés Delgado and Heeralal Janwa.
http://tuvalu.santafe.edu/events/workshops/index.php/Roberto_Reyes_Carranza

Education

PhD Candidate in Mathematics (expected- Dec 2014) 
University of Puerto Rico at Rio Piedras, Mathematical- Research Campus,
American Mathematical Society Member 
ANALYSIS PhD Qualifying Exam, already passed on my first year 2011-12, the considerably more
challenging exam of the Mathematics Department.

One of the selected participants to the Complex Systems School at Santa Fe Institute, New Mexico, USA. Selected participants (graduate students, postdoctoral fellows, and faculty) come from all over the world and represent a wide range of disciplines.

MS Applied Mathematics
University of Puerto Rico at Mayaguez
Thesis: “Comparison of Elastic Plate Theories for Micro-polar Materials”
https://library.villanova.edu/Find/Summon/Record?id=FETCH-proquest_dll_22361122611
Qualifying Exam in Real Analysis, the considerably more challenging exam of the Math Dept.

BS Mathematical Sciences
National University of Trujillo, Perú
Additionally: I attended twelve advanced Math courses and two of Physics as a "Visiting Student"
Thesis: “Decomposition and Reconstruction of a Signal through Semi-orthogonal Wavelet Transform” A formalization for mathematicians, of several concepts and methods that are used in departments of electrical engineering as well as in recent progresses in electromagnetic research (PIERS), and IEEE Microwave Theory and Technique (IEEE-MTT).
Science-Aptitude Exam of Admission UNT
Thinking all the time about fascinating abstract mathematical models. I always remember having been highly congratulated by my professors from school to PhD, highest scores in the courses of the profession of mathematician and I had the support of my professors to achieve teaching jobs. Right now, I'm using these analytical faculties to do research.

Scholar of The Select Mathematics Group at GUE An Own Initiative of GUE Faculty, GUE Highly Competitive Public School, Perú.

My UPR (some professors):

My advisor Prof Heeralal Janwa 
http://www.cims.nyu.edu/~hjanwa/  http://aaecc.free.fr/A17-board.htm
My adv. Lev Steinberg http://math.uprm.edu/people/peoplefind.php?person=Steinberg,%20Lev
Prof Krzysztof Rozga http://math.uprm.edu/people/peoplefind.php?person=Rozga, Krzysztof
Prof Italo Dejter http://home.coqui.net/dejterij/
http://en.wikipedia.org/wiki/Italo_Jose_Dejter
My Math Dept. http://math.uprrp.edu/english/research/ma_res.php
Prof Guihua Gong
http://archive.sciencewatch.com/dr/erf/2011/11augerf/11augerfElli/
Prof Liangqing Li http://math.uprrp.edu/personal/profinfo_es.php?id=60
Prof Moisés Delgado http://bsidespr.org/?page_id=147  http://arxiv.org/abs/1207.5528
http://www.informatik.uni-trier.de/~ley/pers/hd/d/Delgado:Moises.html 

Contact (current specific projects): roberto.reyes@upr.edu

Refereed Papers

1. Moisés Delgado O. and Roberto Reyes (Submitted 2012)
APN Functions for Electronic Commerce Security International Journal of Information and Computer Security IJICS.

2. Reyes, RobertoComparison of Elastic Plate Theories for Micro- polar Materials 2011, ProQuest, ISBN: 9781124400891, Publication Number: AAT148756 http://search.proquest.com/docview/837356963#

3. (Author's Acknowledgments to Roberto Reyes for the computations related with the bending problem, pg 23) Steinberg, Lev Deformation of Micro- polar Plates of Moderate Thickness 2010 International Journal Applied Mathematics and Mechanics IJAMM e- Journal System http://ijamm.bc.cityu.edu.hk/ijamm/outbox/Y2010V6N17P1C57668704.pdf

Specialized Computational Libraries Produced  * Contain analytical work plus the implementation of one rich set of functions.
1. Library for Regularized Analytical Solutions for Steinberg-   Reissner and Eringen II Families of Elliptic PDE Systems with Mixed Boundary Conditions corresponding to the Bending Problem, written in Mathematica 4.0, presented at UPR.

2. Theorem of the Weighted Directed Graph as a Class of Polynomials, a Generalization, Properties and Implementation, programmed in wxMaxima- GNU, December 2011.

3. A Interactive Computer-Assisted Proof of Convergence and Homogeneity property of Solutions of Elastic Plate Theories for Micro-polar Materials on a Zero Neighborhood, written in Mathematica 4.0, presented at IX Annual Research Forum, TU, March 2011.

4. An Existence Lemma for Classical Differential Geometry Generated by Polynomials, implemented in Maxima and Mathematica, this work was produced in the Math PhD Students Office at UPR, Apr 2012.

Teaching Experience

Instructor on campuses of public and private US universities such as UPR, an AMS member, SUAGM System and Inter American University, an AMS member, with progressive Faculty responsibilities. I feel honored for the support and recommendations I have received from the Mathematics Departments to give extra tuition. Also, I have had the pleasure of welcoming several visiting students interested in my classes.
Math Research at UPR (AMS member):
Research at SUAMG University System:
http://srdc.suagm.edu/ http://ccce.suagm.edu/
Professional Activities:
Teacher Training Program, for Public Schools participants, UPR, US.
College Board Training at UPR, US.
Judge for the 22nd Annual Mathematics Olympiad, Education Department, UPR at Rio Piedras, Apr 16 2010.
Math Group SEPAS Federal Inc at Rep of Perú US Public School, 2011.
Advice for Teachers of Physics and Mathematics of Middle-High Schools. 

Selected Presentations

1. “On Necessary and Sufficient Conditions for Second-order Elliptic Field Equations of Elastic Plate Theories”. XII Congress of Research and Academic Development of UPR at Ponce, Committee of Research and Academic Development, Dean of Academic Affairs, UPR at Ponce, May 13, 2011 PR, https://sites.google.com/a/upr.edu/congresouprp/topics

2. “Homogeneity property of Maximum Micro- rotation Vector of Steinberg-Reissner and Eringen Models on a Neighborhood of Zero” IX Annual Research Forum, Doctoral Studies Center, University of Turabo at Gurabo, March 11, 2011 PR, US http://www.suagm.edu/utdoctoral/pdfs/Programa-IX-Encuentro-Investigadores-UT.pdf

3. “Comparison of Elastic Plate Theories for Micropolar Materials” SIDIMXXV Feb 2010 http://sidim.uprh.edu/Memorias/2010/libroSIDIM2010.pdf

4. “Method of Berlekamp for Factorization of Polynomials over the Field Zp” V Italian- Latin American Conference on Applied and Industrial Mathematics ITLA, Dec 15-18, 2004 http://www.mail-archive.com/notiamca@venus.ceride.gov.ar/msg00484.html

...Website under construction

Showing some lines of our code, a PRELIMINARY and SHORT VERSION, written in powerful Computer Algebra Systems (CAS):

 

Khipu ? Related Projects and Others

The Nasca Lines

How can I be sure that an article is peer reviewed?
http://www.library.unisa.edu.au/learn/FindPeerReviewedArticles.pdf


The largest gold mine in Peru
http://www.newmont.com/south-america

Centers for Computational Research

XSEDE Undergraduate and Graduate Internship Opportunities
https://www.xsede.org/for-pis  https://www.xsede.org/engagement  
https://www.xsede.org/web/guest/project-documents-archive

Open MPI
http://www.open-mpi.org/

Medical Imaging Simulation
http://dmip1.rad.jhmi.edu/xcat/

Friday, September 3, 2010

Mathematical Sciences

Education:

MS Applied Mathematics
University of Puerto Rico at Mayaguez

BS Mathematical Sciences
National University of Trujillo- Peru.