faculty of science universiti putra … of science universiti putra malaysia faculty of science...

FACULTY OF SCIENCEUNIVERSITI PUTRA

MALAYSIA

FACULTY OF SCIENCE

WIZARD OF SCIENCE

HABSAH MIDI

Prof. Dr.Department of Mathematics

Faculty of ScienceTel-Office: 03 89466606

Fax: 03 [email protected]

Prof. Dr. Habshah Midi is a Deputy Dean of the Development, Finance & Industry andCommunity Relations, Faculty of Science, UPM. Her field of specialization includescomputational and Applied Robust Statistics, Regression Diagnostics and OutlierDetection. Her active participation in research has earned her awards at university,national and international levels. Nine PhD students and five Masters students havegraduated under her supervision. Currently she is supervising fourteen PhD students(main-8, Co- Supervisor-6). She has published more than 200 research papers(journals and proceedings) in international and local citation-indexed journals. DrHabshah is in the Editorial Board of local and international journals and has beenappointed as referee for many scientific papers for local and international journals.She is a committee member of the Malaysian Institute of Statistics and has organizedmany statistical workshops as speaker. Dr Habshah is very active in research,extension and also serves as a statistics consultant to several organizations includingMajlis Peperiksaan Malaysia.

Current research Interest:

Robust estimation techniques and Outlier Detection in Logistic Regression.

Robust Estimation and Outliers Detection in Response Surface Model.

Robust Estimation and outlier detection in Fixed Effect Panel Data.

Diagnostics and bootstrapping techniques in Logistic Regression.

Robust Diagnostics and Estimation in Autocorrelated Regression Model in thePresence of High Leverage Points.

Robust Estimation Method and Outlier Detection for regression model with errors ofmeasurements.

Robust variables selection technique in the presence of outliers.

Application of Statistical Methods to real life problems.

IBRAGIMOV GAFURJAN

Assoc. Prof. Dr.Department of Mathematics



Assoc. Prof. Dr. Gafurjan Ibragimov major research areas include linear pursuit andevasion differential games, linear discrete pursuit games, and simultaneous games.Major sponsors of Gafurjan Ibragimov’s research include Research University GrantScheme (RUGS) and Fundamental Research Grant Scheme (FRGS). He is currentlythe Coordinator of the Pure Mathematics program at the Department of Mathematics.In 1991, he received his PhD (Title: Optimal Pursuit in Some Differential Games)degree and in 2006, he received his DSc (Title: Differential Games of Many Personswith Different Constraints on Control Parameters). He has also been active inresearch. He has published more than 60 papers in national and internationaljournals. He is also an associate researcher of the Institute for MathematicalResearches (INSPEM), UPM.

Current Research Interest

Pursuit and Evasion Differential Games in Finite Dimensional SpacesHere we study linear pursuit-evasion differential games with integral constraints,differential games with phase constraints, multi person differential games, evasiondifferential games. The main problem is to construct optimal strategies of players andfind the value of the game (or optimal pursuit time).

Differential Games described by Infinite System of Differential EquationsControl and differential game problems are also of increasing interest for systemsdescribed by partial differential equations. Such problems by using the decompositionmethod can be reduced to the ones described by infinite systems of ordinarydifferential equations. Therefore, there is a significant relationship between the controlproblems described by partial differential equations and those described by infinitesystems of differential equations. The latter is of independent interest and can beinvestigated within one theoretical framework. However, in this we have to prove theexistence-uniqueness theorem for infinite system of differential equations, and thenstudy control and differential game problems. For such game problems manymethods developed for differential game problems in finite dimensional spaces do notwork and hence we need new approaches, methods to solve them.

Linear Discrete Pursuit GamesMany real life problems can be modeled as the linear pursuit games. Moreover, lineardiscrete pursuit games can be obtained if we discretize the linear differential games.Here, the main problem is to construct the strategy of the pursuer to complete thegame.

Simultaneous GamesLet A and B be given convex closed restricted non-empty subsets of a Hilbert space.The first player chooses points from the set A and the second one chooses pointsfrom the set B. Payoff function is expected value of the distances between thesepoints. The aim of the first player is to minimize of the expected value and that of thesecond player is to maximize it. We investigate the structure of optimal mixedstrategies and find the value of the game.

KAMEL ARIFFIN MOHD ATAN

Prof. Dato' Dr.Department of Mathematics


[email protected]

Professor Dato’ Dr. Kamel Ariffin research area includes Number Theory,Cryptography and topics in Philosophy and History of Mathematics. He has publishedseveral papers in national and international journals. Presently he is the Director ofthe Institute for Mathematical Research (INSPEM) of the university, and a member ofthe Cryptography, Analysis and Structure research laboratory of the institute. Over theyears he has completed a number of research projects funded by grants obtainedfrom various agencies. Several of his research products have won prizes nationallyand internationally. He has been a member of editorial board of some nationaljournals, and currently the chief editor of the Journal of Mathematical Sciences, anational publication. He is the founding president of the Malaysian Society forCryptology Research, the post he holds currently. He is also the president of thenewly-formed Malaysian Academy of Mathematical Scientists.

Current research Interest

Estimation of Multi-Variable Exponential Sums. Much research has been conductedto arrive at a good estimate of the exponential sums associated with a multi-variablepolynomial over the ring of integers. Currently research which we carry out is to find agood estimate of the sum associated with polynomials over the ring Zp. This estimatefinds application in the determination of the number of solutions in integers of a multi-variable polynomial. More recently, it has found application in the field ofCryptography.

NOOR AKMA IBRAHIM




Professor Dr. Noor Akma Ibrahim is a Deputy Director of Institute for MathematicalResearch, UPM. Her major research areas include survival analysis and diagnosticsinfluence in regression. Her active participation in research has earned her awards atuniversity, national and international levels. Seven PhD students and three Mastersstudents have graduated under her supervision. Currently she is supervising eightpostgraduate students (PhD-6, M.S-2). She has published more than 150 researchpapers in journals and proceedings. She is a life-member of ISOSS and PERSAMA,and an active member of ISM and ASA. She is in the Editorial Board of local andinternational journals and has been appointed as referee for many scientific papersfor local and international journals.


Generalized Log-Rank Tests for partly interval-censored data.

Cure models for interval-censored data.

Bayesian estimation for right censored data with covariates under Jeffreys’ andExtension Jeffreys’ prior.

Bayesian estimation for interval-censored data.

LEONG WAH JUNE




Assoc. Prof. Dr. Leong Wah June major research areas include numerical methodsfor unconstrained and large-scale optimization, and Newton-like methods fornonlinear systems. He is a recipient of the 2008 Chinese Academy of Sciences (CAS)Postdoctoral Fellowship and the 2008 Academy of Sciences for Developing Countries(TWAS) Fellowship. Major sponsors of Wah June’s research include the ScienceFund(Ministry of Science and Innovation of Malaysia (MOSTI), Research University GrantScheme (RUGS) and Fundamental Research Grant Scheme (FRGS).


Unconstrained OptimizationEfforts have been targeted to improve existing methods for solving unconstrainedoptimization problems include the gradient methods, quasi-Newton methods andconjugate gradient methods.Development of efficient codes is also an active activity within the group.

Large-scale OptimizationApart from small and medium scale optimization problems, the group also works onlarge-scale optimization problems. Various low memory methods are derived includethe improved gradient methods and memoryless quasi-Newton methods. Thesemethods are particularly important to be used as the solvers for large-scale problemswhere the calculation of Hessian matrix is unreachable.

Nonlinear SystemsOur group also works on the development of efficient solvers for nonlinear systems.Research on methods for solving system of nonlinear equations has very promisingfuture and since many physical problems can be reduced to find numerical solution ofa nonlinear systems.

MAHENDRAN SHITAN



[email protected]

Assoc. Prof. Dr. Mahendran Shitan is the Head of the Laboratory of ComputationalStatistics and Operations Research in the Institute for Mathematical Research(INSPEM). His research interest is in Time Series and Spatial Models.


Properties of estimators and hypothesis testing for Generalised ARMA time seriesmodels.Properties of Spatial Integer-Valued Autoregressive Models.

MOHD RIZAM ABU BAKAR




Assoc. Prof. Dr. Mohd Rizam Abu Bakar, obtained his PhD in Applied Statistics(“Multivariate Survival Analysis for Split Populations with Application to Patterns ofDomestic Violence”) from University of Bradford, United Kingdom. His researchinterest includes: Survival data analysis, data envelopment analysis and epidemicmodelling. Currently he is an associate professor in the Department of Mathematicsat Universiti Putra Malaysia (UPM). He is also an associate researcher of Institute forMathematical Researches (INSPEM), UPM. Recently is head of the programme ofSurvival Analysis in Computational Statistics and Operations Research Laboratory ofINSPEM.


Survival analysis models typically assume that everybody in the study population issusceptible to the event under study and will eventually experience this event withsufficient follow-up. However, there are situations when a group of individuals are notexpected to experience the event of interest; that is, those individuals are cured orinsusceptible. For example, researchers may be interested in analyzing therecurrence of a disease. Many individuals may never experience a recurrence;therefore, a cured fraction of the population exists.

Data Envelopment Analysis (DEA) is an increasingly popular management tool. It isused to empirically measure productive efficiency of decision (or DMUs). Non-parametric approaches have the benefit of not assuming a particular functionalform/shape for the frontier; however they do not provide a general relationship(equation) relating output and input. There are also parametric approaches in whichrequires that the shape of the frontier be guessed beforehand by specifying aparticular function relating output to input. One can also combine the relativestrengths from each of these approaches in a hybrid method where the frontier unitsare first identified by DEA and then a smooth surface is fitted to these. This allows abest-practice relationship between multiple outputs and multiple inputs to beestimated. It is also useful because it takes into consideration returns to scale incalculating efficiency, allowing for the concept of increasing or decreasing efficiencybased on size and output levels.

The outbreak and spread of disease has been questioned and studied for manyyears. The ability to make predictions about diseases could enable scientists toevaluate inoculation or isolation plans and may have a significant effect on themortality rate of a particular epidemic.Analysis of the structure of epidemic models isvital because of (1) the scarcity of good data and (2) the sensitive dependence ofresults on assumptions. In evaluating model dynamics, we need to look carefully attheir dependence, not only on parameters, but also on the structure of the model: forinstance, whether the population is treated as stochastic or deterministic, discrete orcontinuous, and how the timing and distribution of infectious contacts within thepopulation is modelled. The practical target is to identify those parts of models thathave most effect on dynamics: a few key parameters can drive a model.

MOHAMAD RUSHDAN MD SAID




Assoc. Prof. Dr. Mohamad Rushdan Md Said is the Head of Laboratory ofCryptography, Analysis and Structure at the Institute for Mathematical Research(INSPEM), UPM. He received his PhD in cryptography from Macquarie University,Sydney. His research interest is in public key cryptography and number theory. Hisprofessional affiliation includes the International Association for Cryptologic Research(IACR) and the Malaysian Society for Cryptology Research (MSCR) and is currentlythe chief editor of the MSCR journal, International Journal of Cryptology Research.


Public Key Cryptography: Designing public key cryptosystems

Efficiency and security aspects of the RSA-type cryptosystems

Finite Fields and Discrete Log Problem in Elliptic Curve Cryptography (ECC)

Public Key Systems Based on Iterated Function Systems

ANWAR FITRIANTO

Lecturer (Dr.) .Department of Mathematics



Dr. Anwar Fitrianto is a senior lecturer of Department of Mathematics, Universiti PutraMalaysia. He is also an associate researcher at the Institute for MathematicalResearch, UPM. His B.Sc (Hons), M.Sc (Research), and Ph.D are all majoringStatistics. He has excellent capability in Computational Statistics on major statisticssofwares, includes SAS, Mintab, SPSS, Statistica, Genstat, etc. He is also a CertifiedMinitab Trainer, His research areas include survival analysis, experimental designs,statistical quality control, robust statistics, mediation analysis and statistical modeling.


Robust Mediation Models, Optimization of Experimental Designs, Multiple ResponsesOptimizations, Statistical Quality Analysis

FADZILAH MD ALI

Lecturer (Dr.)Department of Mathematics



Dr. Fadzilah Md Ali is a lecturer in the Department of Mathematics, UPM. Her majorresearch areas include fluid mechanics and heat transfer in boundary layer. Majorsponsor research includes the ScienceFund (Ministry of Science and Innovation ofMalaysia (MOSTI), Research University Grant Scheme (RUGS) and FundamentalResearch Grant Scheme (FRGS).


Boundary layer problem and heat transfer characteristics towards a stretching andshrinking sheet.

MOHD BAKRI ADAM




Dr. Mohd Bakri Adam is a young lecturer of statistics, UPM. He obtained his Ph.D.from Lancaster University specialized in Extreme Sports Modeling in 2007. His majorresearch areas include extreme value theory, non-parametric regression, extreme-environmental statistics, extreme-sports statistics, extreme missing data and extremedata mining.


Extreme Value Theory, EVTDealing with extreme phenomena i.e. maximum, minimum of precipitation, the fastestathlete performance in the world etc. EVT not just limited to the above applications.The blend of mix field applications are much popular. The combination applicationwith other branches statistics like spatial statistics, non-parametric regression, timeseries, Bayesian statistics, medical statistics, missing data analysis etc lead to a goodfuture researches.

Apart from that, the development of new/improved good-ness-of-fit also being study.Some improvement version by manipulating some characteristics of the GEV andGPD distributions.

Non-parametric regressionAlternative to parametric approaches in statistics field. It also involve many part ofstatistics such as kernel analysis, penalized statistics, generalized additive modelling,smoothing, etc. Usually the data speak for themselves. Model selection criteriasometimes being used to select the best model.

Bayesian ExtremeThe combination knowledge of EVT and Bayesian in modelling new group of data.Some inferential method will be introduced. Much work can be carried out as theseBayesian extreme need more exploration and results to be put forward.

Sports Statistics

More accurate and rigorous statistics will be introduced to Malaysia community. Moreadvanced method of statistics methodology should be used to improve theperformance of athletes. We also can do some predictions and forecasting of someevents that can lead to some new policy in selection of new-to-be-come athletes torepresent the country.

IDHAM ARIF HAJI ALIAS




Dr. Idham’s specialization is in Pure Mathematics, specifically in Group Theory.

Current research:

Group Theory, Educational Mathematics, Financial Mathematics, Etno-Mathematics

ISAMIDDIN S.RAKHIMOV


Faculty of ScienceUniversity Putra Malaysia

Tel-office: 03 [email protected]

Professor. Dr. Isamiddin S.Rakhimov graduated from Leningrad State University (nowSaint Petersburg State University) Russia, in 1979. He received his M.Sc. (Title: Thedecomposition of the Jacobian of the Fermat’s curve) and Phd (Title: Filtrations ofgroups generated by some Abelian Varieties) degrees from the Leningrad StateUniversity in 1979 and 1985, respectively. Currently he is an professor of theMathematical Department of the Sciences’ Faculty, University Putra Malaysia(contract). Dr. Isamiddin also is an associate researcher of Institute for MathematicalResearches (INSPEM), UPM.


•Structural theory of Associative and Nonassociative Algebras.• Lie and Leibniz algebras and related to them (co)homological problems.•Commutative algebras, Algebraic geometry.•Ordinary and Differential Invariant theory.•Elliptic Curves and their applications.•Applications of Lie and Leibniz algebras to the problems of Quantum Physics.

JAYANTHI ARASAN




Assoc. Prof. Dr. Jayanthi Arasan research areas include survival/ reliability analysisand computational statistics, which mostly focus on the modeling of parallel andrepairable system failures. Her research is sponsored by Research University GrantScheme (RUGS) and Fundamental Research Grant Scheme (FRGS).

Current research:

•Repairable System Model for Interval Censored, Grouped and Truncated Data withTime Varying Covariates.

•Survival model of the paired organ system with dependent failures and multiplecovariates

•Computational statistics and data analysis involving computer intensive techniquessuch as the bootstrap and jackknife.

LEE LAI SOON

Assoc. Prof .Dr.Department of Mathematics



Assoc. Prof .Dr. Lee Lai Soon is the Head of Program in Laboratory of Applied andComputational Statistics, Institute for Mathematical Research (INSPEM), UPM. Hismajor research areas include applications of metaheuristics approaches specificallyon Genetic Algorithms, Tabu Search, Ant Colony Optimisation and Descent Method incombinatorial optimization problems such as Machine Scheduling Problems, Cuttingand Packing Problems, Travelling Salesmen Problems, and Vehicle RoutingProblems. His research also covers the areas in fuzzy logic and data envelopmentanalysis. He has contributed to more than 30 technical papers. Major sponsors of hisresearch include the ScienceFund (Ministry of Science and Innovation of Malaysia,MOSTI), and Fundamental Research Grant Scheme (FRGS) (Ministry of HigherEducation, MOHE).

Current research:

Genetic AlgorithmsEfforts have been targeted to develop new strains of genetic algorithms where thepotential of the crossover operators are fully exploited to optimise the performance ofthe genetic algorithm in solving well known combinatorial optimisation problems suchas Machine Scheduling Problems, Cutting and Packing Problems, Vehicle RoutingProblems, Bus Timetabling Problems, and Resource Allocation Problems. Othergenetic operators are also explored to further enhance the performance of thealgorithm.

Ant Colony OptimisationAnt Colony Optimisation is a population based metaheuristic in which a colony ofartificial ants cooperates in finding good solutions to difficult combinatorialoptimization problems. It is inspired by the real life behavior of a colony of ants whenlooking for food.

This approach has proven to be efficient at solving Vehicle Routing Problem and ableto produce better/reasonable solutions within very short runtime. Therefore, the futuredirection of this research would be to modify the approach in order to solve one of thevariants of the Vehicle Routing Problem, which is known as Vehicle Routing Problemwith Time Windows.

Another aim of this study is to use the approach to improve the existing solution forContainer Loading Problem either in terms of space utilization or computation time.This might be accomplished by hybridizing the heuristic and Ant Colony Optimisationor by employing some different methods in pheromone updating or transitionprobability evaluation.

NIK MOHD ASRI BIN NIK LONG

Assoc. Prof. DrDepartment of Mathematics



Assoc. Prof. Dr. Nik Mohd Asri Bin Nik Long is a Coordinator of PostgraduateProgram Faculty of Science and also member of Laboratory of ComputationalSciences and Informatics, Institute for Mathematical (INSPEM) UPM. His majorresearch areas include fracture mechanics (investigating the behavior of solution ofcrack in two and three dimension), numerical solution to the integral equations (withweak, Cauchy, strong/hypersinguler kernel). Major sponsors of research work includethe ScienceFund (Ministry of Science and Innovation of Malaysia (MOSTI), ResearchUniversity Grant Scheme (RUGS) and Fundamental Research Grant Scheme(FRGS).

Current research:

Cracks problem in plane elasticityThe crack problems in plane elasticity are formulated into hypersingular integralequations through complex potential method. These equations are then solvednumerically for the unknown coefficients, and subsequently, other physical propertiesof the crack can be determined.

Apart from numerical approach, analytical effort are also being made to solve theclosed curved crack problems. The main tool is the modified complex potentialmethod.

Integral equationsDevelop an approximate solution of the integral equations (with weak, Cauchy,strong/hypersingular kernel). These equations appear in many engineering problems,most of them have no analytical solutions, and therefore searching a goodapproximation solution becomes a vital work.

NORIHAN MD. ARIFINNORIHAN MD. ARIFIN




Assoc. Prof. Dr. Norihan Md. Arifin major research areas include fluid mechanics andheat transfer with application to the thermal convection and boundary-layer theory,heat transfer in Newtonian and non-Newtonian as well as in fluid saturated porousmedia and nanofluids. She has contributed to more than 60 technical papers. Majorsponsors of Norihan’s research include the ScienceFund (Ministry of Science andInnovation of Malaysia (MOSTI), Research University Grant Scheme (RUGS) andFundamental Research Grant Scheme (FRGS).

Current Research Interest:

Marangoni convection in micropolar fluids and porous mediumConvection has been the subject of many investigations as it is becoming important tothe industry as in crystal growth, weld penetration and in coating process. Thesurface tension gradients that are responsible for Marangoni convection can be dueto gradients of temperature and/or concentration. Our group focus on Marangoniconvection in a horizontal fluid layer due to imposed temperature gradients. We usethe linear stability theory to examine the onset of Marangoni convection in micropolarfluids and porous medium.

Boundary layer problem in nanofluidsA nanofluid is a colloidal mixture of nano-sized particles (< 100nm) in a base fluid. Itis known that nanofluids can tremendously enhance the heat transfer characteristicsof the original (base) fluid. Thus, nanofluids have many applications in industry suchas coolants, lubricants, heat exchangers, micro-channel heat sinks, etc. The study ofnanofluids is still at its early stage and it seems very difficult to have a precise idea onthe way the use of nanoparticles acts in heat transfer. We focus on the problem ofsteady, laminar convection boundary layer flow in nanofluids using different types ofnanoparticles, namely Cu, Al2O3, and TiO3 .

NORIHAN MD. ARIFINNORAZAK SENU




Dr. Norazak Senu is a senior lecturer in the Department of Mathematics at UniversitiPutra Malaysia. His research interest includes Numerical Analysis and Web BasedLearning and Teaching System. He is also an associate researcher of Institute forMathematical Research (INSPEM). He has also been active in research andsuccessfully completed several research projects (FRGS, RUG and ScienceFund).


Solution of Ordinary Differential Equations(ODEs)Dr. Norazak’s research is in the general area of numerical analysis; her specialtiesinclude the numerical solution of ordinary differential equations, focusing on first orderand higher order ordinary differential equations in which the solutions are in theoscillatory functions: The methods are includes Runge-Kutta methods, Runge-Kutta-Nystrom methods, block method, and parallel computing using MPI for solving largescale problem.

Web Based Learning and Teaching SystemThe research is focusing on developing very interactive, attractive and user friendlymathematics software based on wab based and stand alone basis. With this systemstudents or users can access or use the material of learning and teaching system atanywhere and anytime. User interface embedded in the website with the numericaland graphical output illustration are criteria of the software. The software developed iscalled Numerical Computations Laboratory(NCL).

SITI HASANA SAPAR




Dr. Siti Hasana Sapar is a Senior Lecturer, UPM. Her major research areas includeEstimation of exponential sums and Diophantine Equations and major sponsors ofher research are Research University Grant Scheme (RUGS) and FundamentalResearch Grant Scheme (FRGS).


Estimation of Exponential Sums

This research will concentrate on the problem of determining an estimation of theexponential sums for multi-variable polynomials, estimation of the multiple exponentialsums for two-variable polynomials of higher degree and also to find the p-adic sizesof factorial functions which involve Bernoulli functions, left Kurepa’s factorial functionsand other functions.

Diophantine Equations

This research will concentrate on the problem of finding an integral solution to varytypes of Diophantine equation.

MD SOHEL RANA




Dr. Md. Sohel Rana is a Senior Lecturer at the Department of Mathematics,Universiti Putra Malaysia. He is also a co-researcher at the Institute for mathematicalresearch, Universiti Putra Malaysia. His research interest comprises of developingnew robust techniques in the branch of Robust Statistics. In addition to researchoutputs, he has published several research articles in peer reviewed national andinternational journals and proceedings. Moreover, he is involved in several researchprojects and also supervising Master and PhD students.


Robust statistical methods in conjunction to Regression diagnostics, Detection ofoutlier, Volatility in regression and time series analysis, Econometrics, Missing dataanalysis, Inferential statistics, Multivariate analysis, Parametric and nonparametricmethods, Simulation and bootstrapping techniques, Environmental statistics,Statistical quality control.

ZAINIDIN ESHKUVATOV




Assoc. Prof. Dr. Zainidin K. Eshkuvatov is a associate researcher at the Laboratory ofComputational Sciences and Mathematical Physics, Institute for MathematicalResearch (INSPEM), UPM. His major research areas include area of Integrationproblems (such as approximating proper and improper integrals of the product typeintegrals, Cauchy and Hilbert type singular integrals as well as Hadamard typehypersingular integrals) and Integral Equations Problems (such as Fredholm andVolterra type integral equation of first and second kind, Singular integral equations ofCauchy type, nonlinear integral equations as well as Hypersingular integral equationsof the first and second kind). He won several awards and gold medals with his hardwork and distinguished efforts in research. He has Research Copyrights for thesoftware entitled: Different floating point rounding methods for singular integralequations, 2012. Major sponsors of research work include the Research UniversityGrant Scheme (RUGS) and Fundamental Research Grant Scheme (FRGS).


Integration problemsIntegration is an important concept in mathematics and, together with its inverse,differentiation, is one of the two main operations in calculus. Almost all area ofmathematics and physics encounters with different type of integration problems,however few problems can be solved in closed form. Numerical integration and itsconvergence is one of the major problem in computational mathematicsApart from numerical approach, analytical efforts are also being made to solve theintegrals with week, strong and hypersingular kernels. The main tool is to show theexactness of the quadrature or cubature formulas.

Integral equationsThe theory of integral equations has close contacts with many different areas ofmathematics. Many problems in the fields of ordinary and partial differential equationscan be recast as integral equations. Existence and uniqueness results can then bederived from the corresponding integral equations.Linear and nonlinear integral equations with kernel (smooth, weak singularity,logarithmic singularity, strong singularity, hypersingular) most of the time have noanalytical solutions, and developing an approximate solution of the integral equationsbecomes a vital work.

MUHAMMAD REZAL BIN DATO’ DR. KAMEL ARIFFIN




Assoc. Prof. Dr. Muhammad Rezal bin Dato’ Dr. Kamel Ariffin is Program Head forMathematical Cryptology at the Al-Kindi Cryptography Research Laboratory,Laboratory of Theoretical Studies, Institute for Mathematical Research, UPM. Hismajor area is related to mathematical cryptology, designing public key cryptographyprimitives as well as cryptanalyzing them. Since being appointed to the post ofLecturer (DS45) in 2005, he has published various 22 scientific writings, 3 researchgrants totaling more than RM300,000, 2 research product approved by UPM to bepatented in Malaysia and 1 in the United States of America, 5 innovation awards (4international), appointed as a paper reviewer for an international conference in China,invited to give presentations at local institutions of higher learning, giving expertopinions in designing security systems for classified Malaysian governmentorganizations, appointed as a member of International Journal of CryptologyResearch editorial board, General Chari of the 2nd International CryptologyConference 2010 (Cryptology2010), committee member of the Malaysian Society forCryptology Research (MSCR) and other academic activities in accordance to hisexpert area.


AAβ Public Key CryptosystemA new public key cryptosystem has been designed and has the potential to reducethe key size down to 128-bits. It is conjectured that a 128-bit AAβ Public KeyCryptosystem is equivalent to a 1024-bit RSA and a 160-bit elliptic curvecryptosystem.Efforts have been made to study the strength of the underlying mathematical conceptAAβ-function and it resistant to known types of cryptanalytic attacks.

Counting terms of an equivalent subset sum problem of the AAβ Public KeyCryptosystemA cryptosystem that is based upon a subset problem in known to be “provably”difficult. The AAβ Public Key Cryptosystem is based upon the AAβ-function which hasits equivalent subset sum problem. This research is to generalize the number of termsresiding within the subset sum problem of the AAβ-function. We intend to derive anasymptotic relation analogous to the Prime Number Theorem.

The Pollard-Rho type attack on the AAβ Public Key CryptosystemEfforts heve been made to study the feasibility (or infeasibility) to design a pollard-rhotype attack on the AAβ Public Key Cryptosystem. Research is conducted by studyingthe underlying mathematical concept that exists in the Diffie-Hellman key exchangeprocedure and the elliptic curve cryptosystem that exposes itself towards thepossibility of a pollard-rho type attack. Comparison on the underlying mathematicalconcepts will then be done with the AAβ Public Key Cryptosystem.

ZARINA BIBI IBRAHIM




Assoc. Prof. Dr. Zarina Bibi Ibrahim is a Assoc. Prof. Dr of Mathematics, UPM.PhD in Applied Mathematics (Numerical Analysis), UPM, 2006.Masters in Mathematics, California State Univ. Long Beach, United States of America,1985.Bachelor Degree in Mathematics, California State University Long Beach, UnitedStates of America, 1984.

Current research:

Developing Code For Solving Higher Order Ordinary Differential Equations (ODEs)Directly Using Implicit Block Methods

Solving Boundary Value Problems by Multiple Shooting using the multistep method inits Backward Difference Formulations

Block Multistep Formulas for Solving Ordinary Differential Equations (ODEs)

Parallel Partitioning Technique Using Multistep Formulas for Solving OrdinaryDifferential Equations (ODEs)

Developing Code For Solving Delay Differential Equations (DDEs) Using Multi StepBlock Methods

ZANARIAH ABDUL MAJID




Assoc. Prof. Dr Zanariah Abdul Majid is currently a lecturer in the Department ofMathematics at the University Putra Malaysia (UPM). She is also an associateresearcher at the Institute for Mathematical Research, UPM. She has publishedwidely in the area of parallel block method and the general area of numerical analysis.She won several awards and gold medals with her hard work and distinguishedefforts in research. She has three Research Copyrights for the software entitle:VSVO: Parallel and Sequential Two Point Block VSVO Code for Solving OrdinaryDifferential Equations, 2008, TPBC: Parallel and Sequential Two Point Block Code forSolving Higher Order Differential Equations Directly, 2008 and Parallel and SequentialFour Point Block Algorithm for Solving Ordinary Differential Equations (FPBA), 2009.Major sponsors of her research include the Research University Grant Scheme(RUGS) and Fundamental Research Grant Scheme (FRGS).

Current research:

Dr. Zanariah’s research is in the general area of numerical analysis; her specialtiesinclude the numerical solution of ordinary differential equations, with emphasis onhigher order ordinary differential equations, boundary value problem, delay differentialequations, multistep methods, Runge-Kutta methods, block method, and parallelcomputing using MPI for solving large scale problem.

ADEM KILICMAN


Faculty of ScienceTel-Office: 03 8946 6813

Fax: 03 8943 [email protected]

Professor Dr. Adem Kilicman is a professor in the Department of Mathematics atUniversity Putra Malaysia. His research interest includes Functional Analysis andTopology, Integral transforms, Special functions and differential equations. He haspublished several papers in national and international journals. He is an activemember also in several activities in the department and Institute of mathematicalresearch (INSPEM). He has also been active in research and succesfully completedseveral research projects (IRPA, ScienFund and FRGS). He is also member ofeditorial board of the several international journals and co editors of severalproceedings. Recently is head of the programme of Functional Analysis and topologyin Theoretical Laboratory, of INSPEM and a reviewer for American MathematicalSociety as well as reviewer for Zentralblatt Mathematik(Germany).

Current research:

Distributions and operationsDistributions also known as generalized functions are objects which generalizefunctions and probability distributions. They allow us to extend the concept ofderivative to all continuous functions and are used to formulate generalized solutionsof partial differential equations. They are important inseveral areas especially in physics and engineering where many non-continuousproblems that naturally lead to differential equations whose solutions are distributions,such as the delta distribution.

Distribution theory in its full scope is not only difficult but also requires a sophisticatedmathematical background. The elementary aspects of the theory, where we use ofgeneralized functions in differential equations and that adds considerably to theapplied mathematics and can be considered as an effective tool. Our main aim in thisresearch area is to extend the irregular operations to broader classes of distributions.

Covering properties in topological spacesSince compactness is a very important property in topology and analysis it is worth tostudy carefully, thus mathematician studied it widely. In compact spaces one dealswith open covers to get a finite subcover, e.g. A space is compact if every open coverof the space has a finite subcover.

Later compactness was generalized to countable compactness that is A space iscountably compact if every countable open cover of has a finite subcover and theidea of Lindelof property came later by dealing with open covers to get countablesubcover. Thus the idea of Lindelof property was first introduced from studyingcompactness property.

Therefore the relation between compactness and Lindelof property is very strong,where every compact space is Lindelof but not the converse, many properties ofcompact spaces were generalized onto Lindelof spaces. However generalizations ofLindelof spaces that depend on open covers and regularly open covers introducedand studied Lindelof spaces. Some of these generalizations depend on theirdefinitions.

The above covering properties can be extended to the bitopological spaces and studylindelof properties as well as mappings and decompositions of continuity.

faculty of science universiti putra … of science universiti putra malaysia faculty of science...

Documents