The 46 Annual Iranian Mathematics Conference Proceedings of the ...

The 46th Annual Iranian

Mathematics Conference

25-28 August 2015, Yazd University, Yazd, Iran

Proceedings of the Conference

Talk

Preface

The Annual Iranian Mathematics Conference (AIMC) has been held since 1970. It isthe oldest Iranian scientific gathering which takes place regularly each year at one ofIranian universities. The 36th annual Iranian mathematics conference was held at YazdUniversity and now we are pleased to organize the 46th conference. The 46th AIMC willbe held at Yazd University in Yazd (the most beautiful and historical city of Iran) fromAugust 25 until August 28, 2015. The Iranian Mathematical Society and Yazd Universityhave jointly sponsored the 46th AIMC. This conference is an international conference andincludes Keynote speakers, Invited speakers, Presentations of contributed research papers,and Poster presentations.

It is our pleasure to publish the Proceedings of the 46th AIMC. More than 700 math-ematicians from our country and abroad have taken part in the conference. By kindcooperation of contributors, more than 1100 papers were received. The scientific com-mittee put a considerable effort on referral process in order to arrange a conference ofexcellent scientific quality. We have 15 plenary speakers from universities of Iran, as wellas from Australia, South Korea, Canada, China, Czech Republic, India, Serbia and Spain.Moreover, our invited speakers are about 12.

The Scientific Committee of46th Annual Iranian Mathematics Conference

46th Annual Iranian Mathematics Conference, 25-28 August 2015, Yazd University, Iran

Scientific Committee

Akbari, Saieed Sharif University of TechnologyAlikhani, Saeid Yazd UniversityAshrafi, Ali Reza Kashan UniversityAzarpanah, Fariborz Shahid Chamran University of AhvazBabolian, Esmail Kharazmi UniversityBaridloghmani, Ghasem (Chair) Yazd UniversityBehzad, Mehdi Shahid Behashti UniversityBidabad, Behroz Amirkabir University of TechnologyDarafsheh, Mohammad Reza University of TehranDavvaz, Bijan (Scientific chair) Yazd UniversityDehghan Nezhad, Akbar Yazd UniversityDelavar Khalafi, Ali Yazd UniversityEslamzadeh, Gholamhossein Shiraz UniversityFarshi, Mohammad Yazd UniversityGhasemi Honary, Taher Kharazmi UniversityGooya, Zahra Shahid Behashti UniversityHooshmandasl, Mohammad Reza Yazd UniversityHosseini, Seyed Mohammad Mahdi Yazd UniversityIranmanesh, Ali Tarbiat Modares UniversityIranmanesh, Mohammad Ali Yazd UniversityKarbasi, Seyed Mahdi Yazd UniversityKhorshidi, Hossein Yazd UniversityMaalek Ghaini, Farid Yazd UniversityMaimani, Hamidreza Shahid Rajaee Teacher Training UniversityModarres Mosaddegh, Seyed Mohammad Sadegh Yazd UniversityMohseni Moghadam, Mahmoud Shahid Bahonar UniversityMolaei, Mohammad Reza Shahid Bahonar UniversityMoshtaghioun, Seyed Mohammad Yazd UniversityNadjafikhad, Mahdi Iran University of Science and TechnologyParsian, Ahmad University of TehranRejali, Ali Isfahan University of TechnologySafi, Mohammad Reza Semnan UniversitySal Moslehian, Mohammad Ferdowsi University of MashhadSalemi, Abbas Shahid Bahonar UniversityShahzadeh Fazeli, Seyed Abolfazl Yazd UniversitySharif, Habib Shiraz UniversityTorabi, Hamzeh Yazd UniversityVaezpour, Seyed Mansour Amirkabir University of TechnologyYassemi, Siamak University of TehranYousefi, Sohrab Ali Shahid Behashti UniversityZangeneh, Bijan Z. Sharif University of Technology

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Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Scientific Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Plenary Speakers

A medley of group actionsCheryl E. Praeger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

On Laplacian eigenvalues of graphsKinkar Ch. Das . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Partition of Unity Parametrics: A framework for meta-modeling in computer graph-icsFaramarz F. Samavati . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

An eigenvalue problemBehrouz Emamizadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Set-theoretic methods of homological algebra and their applications to module theoryJan Trlifaj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Biological NetworksS. Arumugam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Covering properties defined by starsLjubisa D.R. Kocinac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Some question on the reduction of elliptic curvesJorge Jimenez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Nonlinear Separation for Constrained OptimizationMehdi Chinaie, Jafar Zafarani . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Derived Algebraic Structures from Algebraic HyperstrutcturesR. Ameri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

A survey of simplicial cohomology for semigroup algebrasA. Pourabbas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Zero Divisors of Group Rings of Torsion-Free GroupsAlireza Abdollahi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Geometry and ArchitectureM. M. Rezaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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Cramers probabilistic model of primes and the Zeta functionKasra Alishahi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Invited Speakers

Semigroups with apartness: constructive versions of some classical theoremsMelanija Mitrovi, Sini, and Daniel Abraham Romano . . . . . . . . . . . . . . 64

On a conjecture of Richard StanleySeyed Amin Seyed Fakhari . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Steiner triple systems with forbidden configurationsEbrahim Ghorbani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

A new view of supremum, infimum, maximum and minimumMadjid Eshaghi Gordji . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

On enumeration of complete semihypergroups and M-P-Hs.Saeed Mirvakili . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Closed non-vanishing ideals in CB(X)M. R. Koushesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Second derivative general linear methods for the numerical solution of IVPsGholamreza Hojjati . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

On a sub-projective Randers geometryMehdi Rafie-Rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Derivations of direct limits of Lie superalgebrasMalihe Yousofzadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Local bifurcation control of nonlinear singularitiesMajid Gazor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Algebra

2-absorbing ideal in latticeAli Akbar Estaji, Toktam Haghdadi . . . . . . . . . . . . . . . . . . . . . . . 133

2-absorbing submodules and flat modulesSedigheh Moradi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

2-capability and 2-exterior center of a groupFarangis Johari, Mohsen Parvizi and Peyman Niroomand . . . . . . . . . . . . 141

A classification of cubic one-regular graphsMohsen Ghasemi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

A generalization of commutativity notionMehdi Kheradmand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

A new algorithm to compute secondary invariantsAbdolali Basiri, Sajjad Rahmany and Monireh Riahi . . . . . . . . . . . . . . 152

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A new result of the intersection graph of subgroups of a finite groupHadi Ahmadi and Bijan Taeri . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

A note on the graph of equivalence classes of zero divisors of a ringHamid Reza Dorbidi and Zahra Abyar . . . . . . . . . . . . . . . . . . . . . . 159

Annihilator conditions in noncommutative ring extensionsAbdollah Alhevaz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Baer invariants of certain class of groupsAzam Kaheni and Saeed Kayvanfar . . . . . . . . . . . . . . . . . . . . . . . . 167

Behavior of prime (ideals) filters of hyperlattices under the fundamental relationMohsen Amiri and Reza Ameri . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Capability of groups satisfying a certain bound for the index of the centerMarzieh Chakaneh, Azam Kaheni and Saeed Kayvanfar . . . . . . . . . . . . . 175

Characterizations of interior hyperideals of semihypergroups towards fuzzy pointsSaeed Azizpour and Yahya Talebi . . . . . . . . . . . . . . . . . . . . . . . . . 179

Class preserving automorphisms of finite p-groupsRasoul Soleimani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Congruence on a ternary monoid generated by a relationZahra Yazdanmehr and Nahid Ashrafi . . . . . . . . . . . . . . . . . . . . . . 186

Decomposing modules into modules with local endomorphism ringsTayyebeh Amouzegar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Divisibility Graph for some finite simple groupsAdeleh Abdolghafourian, Mohammad A. Iranmanesh and Alice C. Niemeyer . . 192

Domination number of the order graph of a groupHamid Reza Dorbidi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Extended annihilating-ideal graph of a ringEsmaeil Rostami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

First hochchild cohomology of square algebraNegin Salehi, Feisal Hasani . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Frobenius semirational groupsAshraf Daneshkhah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Group factorisations and associated geometriesSeyed Hassan Alavi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Independence graph of a vector spaceMohammad Ali Esmkhani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Large non-nilpotent subsets of finite general linear groupsAzizollah Azad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Lie structure of smash productsSalvatore Siciliano and Hamid Usefi . . . . . . . . . . . . . . . . . . . . . . . . 215

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Local dimension and direct sum of cyclic modulesAtefeh Ghorbani and Mahdieh Naji Esfahani . . . . . . . . . . . . . . . . . . . 219

Minimum size of intersetion for covering groups by subgroupsMohammad Javad Ataei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Monoids over which products of indecomposable acts are indecomposableMojtaba Sedaghatjoo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

On direct products of S-posetsRoghaieh Khosravi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

On graded generalized local cohomology modulesFatemeh Dehghani-Zadeh and Maryam Jahangiri . . . . . . . . . . . . . . . . 235

On hypergroups with trivial fundamental groupHossein Shojaei and Reza Ameri . . . . . . . . . . . . . . . . . . . . . . . . . 238

On prime submodules and hypergraphsFatemeh Mirzaei and Reza Nekooei . . . . . . . . . . . . . . . . . . . . . . . . 242

On split Clifford algebras with involution in characteristic twoA.H. Nokhodkar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

On strongly clean triangular matrix ringsA. Karimi Mansoub, A. Moussavi and M. Habibi . . . . . . . . . . . . . . . . 250

On subgroups with large relative commutativity degreesHesam Safa, Homayoon Arabyani and Mohammad Farrokhi . . . . . . . . . . . 254

On the n-c-nilpotent groupsAzam Pourmirzaei and Yaser Shakourie Jooshaghan . . . . . . . . . . . . . . . 256

On the number of minimal prime idealsMohammad Ali Esmkhani and Yasin Sadegh . . . . . . . . . . . . . . . . . . . 259

On weakly prime fuzzy submodulesRazieh Mahjoob and Shahin Qiami . . . . . . . . . . . . . . . . . . . . . . . . 263

Perfect dimensionMaryam Davoudian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

Positive implicative filters in triangle algebrasArsham Borumand Saeid, Esfandiar Eslami and Saeide Zahiri . . . . . . . . . . 271

Primary decomposition of ideals in MV -algebrasSimin Saidi Goraghani and Rajab Ali Borzooei . . . . . . . . . . . . . . . . . . 275

Representations of polygroups based on Krasner hypervector spacesKarim Ghadimi, Reza Ameri and Rajabali Borzooei . . . . . . . . . . . . . . . 279

Semi Factorization StructuresAzadeh Ilaghi Hosseini, Seyed Shahin Mousavi and Seyed Naser Hosseini . . . . 283

Some Properties Of n-almost Prime SubmodulesSedigheh Moradi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

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Some properties of the character graph of a solvable groupMahdi Ebrahimi and Ali Iranmanesh . . . . . . . . . . . . . . . . . . . . . . . 291

Some quotient graphs of the power graphsSeyed Mostafa Shaker, Mohammad A. Iranmanesh and Daniela Bubboloni . . . 294

Some results on complementable semihypergroupsGholamhossien Aghabozorgi and Morteza Jafarpour . . . . . . . . . . . . . . . 298

Some types of ideals in bounded BCK-algebrasSadegh Khosravi Shoar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

The subgroup generated by small conjugacy classesMahmoud Hassanzadeh and Zohreh Mostaghim . . . . . . . . . . . . . . . . . 306

Torsion theory cogenerated by a class of modulesBehnam Talaee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

Analysis

A convergence theorem by extragradient method for variational inequalities in Ba-nach spacesZeynab Jouymandi and Fridoun Moradlou . . . . . . . . . . . . . . . . . . . . 314

A generalized Hermite-Hadamard type inequality for h-convex functions via frac-tional integralMaryam Hosseini, Azizollah Babakhani and Hamzeh Agahi . . . . . . . . . . . 318

A note on composition operators between weighted Hilbert spaces of analytic func-tionsMostafa Hassanlou and Morteza Sohrabi-Chegeni . . . . . . . . . . . . . . . . 322

A note on composition operators on Besov type spacesEbrahim Zamani and Hamid Vaezi . . . . . . . . . . . . . . . . . . . . . . . . 326

A note on the transitive groupoid spacesHabib Amiri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

Abstract convexity of ICR-k functionsMohammad Hossein Daryaei . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

Amenability of vector valued group algebrasSamaneh Javadi and Ali Ghaffari . . . . . . . . . . . . . . . . . . . . . . . . . 337

Amenability of weighted semigroup algebras based on a characterMorteza Essmaili and Mehdi Rostami . . . . . . . . . . . . . . . . . . . . . . 341

An iterative method for nonexpansive mappings in Hilbert spacesZahra Solimani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

Best approximation in normed left modulesAli Reza Khoddami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

Best proximity points for cyclic generalized contractionsSajjad Karami and Hamid Reza Khademzade . . . . . . . . . . . . . . . . . . 353

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Block matrix operators and p-paranormalityZahra Moayyerizadeh and Mohammadreza Jabbarzadeh . . . . . . . . . . . . . 357

C*-algebras and dynamical systems, a categorical approachMassoud Amini, George A. Elliott and Yasser Golestani . . . . . . . . . . . . . 361

C*-algebras of Toeplitz and composition operatorsMassoud Salehi Sarvestani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

Chebyshevity and proximity in quotient spacesHamid Mazaheri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

Classification of frame graphs by dimensionAbdolaziz Abdollahi and Hashem Najafi . . . . . . . . . . . . . . . . . . . . . 372

Compact composition operators on real Lipschitz spaces of complex-valued boundedfunctionsDavood Alimohammadi and Sajedeh Sefidgar . . . . . . . . . . . . . . . . . . 375

Complex symmetric weighted composition operators on the weighted Hardy spaces.Mahsa Fatehi and Zahra Hosseini . . . . . . . . . . . . . . . . . . . . . . . . . 379

Composition operators on weak vector valued weighted Dirichlet type spacesSepideh Nasresfahani and Hamid Vaezi . . . . . . . . . . . . . . . . . . . . . . 383

Connectivity of idempotent graph of bounded linear operators on a Hilbert spacePandora Raja . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

Constructing dual and approximate dual fusion framesFahimeh Arabyani and Ali Akbar Arefijamaal . . . . . . . . . . . . . . . . . . 389

Convergence theorems for a broad class of nonlinear mappingsSattar Aalizadeh, Zeynab Jouymandi and Fridoun Moradlou . . . . . . . . . . 393

Convolution condition on n-starlike functionsE. Amini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

Derivations on the algebra of operators in Hilbert modules over locally C-algebrasKhadijeh Karimi and Kamran Sharifi . . . . . . . . . . . . . . . . . . . . . . . 401

Disjoint hypercyclicity of composition operators on the weighted Dirichlet spacesZahra Kamali and Marzieh Monfaredpour . . . . . . . . . . . . . . . . . . . . 405

Eigenvalues of Euclidean distance matrices and rs-majorization on R2Asma Ilkhanizadeh Manesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408

Existence of three solutions for a problem involving the p(x)-LaplacianFariba Fattahi and Mohsen Alimohammady . . . . . . . . . . . . . . . . . . . 412

Fekete-Szego problem for new subclasses of univalent functions with bounded posi-tive real partHormoz Rahmatan, Shahram Najafzadeh and Ali Ebadian . . . . . . . . . . . 415

Fixed point theorems in probabilistic metric space and intuitionistic probabilisticmetric spaceFatemeh mohmedi, Behnoosh Salimiyan and Maryam Shams . . . . . . . . . . 419

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Fixed point theory for Ciric-type-generalized -probabilistic contraction maps inprobabilistic Menger spacesHamid Shayanpour and Asiyeh Nematizadeh . . . . . . . . . . . . . . . . . . . 423

Fixed points of generalized contractions on intuitionistic fuzzy metric spacesAsieh Sadeghi Hafshejani and Seyed Mohammad Moshtaghioun . . . . . . . . . 427

Function-valued Gram-Schmidt process in L2(0,)Mohammad Ali Hasankhani Fard . . . . . . . . . . . . . . . . . . . . . . . . . 431

Fusion Riesz basisMitra Shamsabadi and Ali Akbar Arefijamaal . . . . . . . . . . . . . . . . . . 435

Fuzzy frame in fuzzy real inner product spaceA. Rostami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

G-ultrametric dynamics and some fixed point theoremsHamid Mamghaderi and Hashem Parvaneh Masiha . . . . . . . . . . . . . . . 442

Generalized cyclic contraction and convex structureT. Ahmady, T. D. Narang, S. A. M. Mohsennialhosseni, M. Asadi . . . . . . . 446

Generalized weighted composition operators between Zygmund spaces and BlochspacesMostafa Hassanlou and Amir H. Sanatpour . . . . . . . . . . . . . . . . . . . 450

Hausdorff measure of noncompactness for some paranormed -sequence spaces ofnon-absolute typeElahe Abyar and Mohammad Bagher Ghaemi . . . . . . . . . . . . . . . . . . 454

Higher nummerical ranges of basic Afactor block circulant matrixMohammad Ali Nourollahi Ravari . . . . . . . . . . . . . . . . . . . . . . . . 458

Homological properties of certain subspaces of L(G) on group algebrasSima Soltani Renani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

Inequalities for Keronecker product of matricesS. M. Manjegani and S. Moein . . . . . . . . . . . . . . . . . . . . . . . . . . 466

Iinfty-tuples of operators and HereditarilyMezban Habibi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

Integral operators and multiplication operators on F (p, q, s) spacesAmir H. Sanatpour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Mappings under asymptotic pointwise weaker Meir-Keeler-type contractive type con-ditionsM. Shakeri and A. Mahmoodi . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

Minimal description for the real interpolation in the case of quasi-Banach quaternionZahra Ghorbani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

Monotonicity and dominated best proximity pair in Banach lattices and some ap-plicationsHamid Reza Khademzadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

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Multilinear mappings on matrix algebrasMahdi Dehghani and Mohsen Kian . . . . . . . . . . . . . . . . . . . . . . . . 489

New reverse of continuous triangle inequalities type for Bochner integral in HilbertC*-modulesAmir Gahsem Ghazanfari and Marziyeh Shafiei . . . . . . . . . . . . . . . . . 493

Non-linear semigroups in Hadamard spacesBijan Ahmadi Kakavandi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

On a new notion of injectivity of Banach modulesMorteza Essmaili and Mohammad Fozouni . . . . . . . . . . . . . . . . . . . . 501

On a one-dimensional Laplacian-like problem via a local minimization principleGhasem A. Afrouzi and Saeid Shokooh . . . . . . . . . . . . . . . . . . . . . . 505

On best approximation in km fuzzy metric spacesNasser Abbasi and Hamid Mottaghi Golshan . . . . . . . . . . . . . . . . . . . 509

On chatterjea contractions in metric space with a graphKamal Fallahi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

On linear operators from a Banach space to analytic Lipschitz spacesA. Golbaharan and . Mahyar . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

On pseudospectrum of matrix polynomialsGholamreza Aghamollaei and Madjid Khakshour . . . . . . . . . . . . . . . . 521

On some means inequalities in matrix spasesMaryam Khosravi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

On the stability of Szasz-Mirakjan operatorsEhsan Anjidani and Samira Karany . . . . . . . . . . . . . . . . . . . . . . . . 527

On the zeroes of the elliptic operatorAli Parsian and Maryam Masoumi . . . . . . . . . . . . . . . . . . . . . . . . 530

On two types of approximate identitiesMohammad Fozouni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

Orthogonality preserving mappings in inner product C-modulesAli Zamani and Mohammad Sal Moslehian . . . . . . . . . . . . . . . . . . . . 538

Periodic point for the generalized (, )-contractive mapping in right complete gen-eralized quasimetric spacesNegar Gholami and Mohammad Javad Mehdipour . . . . . . . . . . . . . . . . 542

Phi-means of some Banach subspaces on a Banach algebraSamaneh Javadi and Ali Ghaffari . . . . . . . . . . . . . . . . . . . . . . . . . 546

PPF dependent fixed point results for c-admissible integral type mappings in Ba-nach spacesHossain Alaeidizaji, Farzaneh Zabihi and Vahid Parvaneh . . . . . . . . . . . . 550

Pseudonumerical range of matricesGholamreza Aghamollaei and Madjid Khakshour . . . . . . . . . . . . . . . . 554

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Real interpolation method of martingale spacesMaryam Mohsenipour and Ghadir Sadeghi . . . . . . . . . . . . . . . . . . . . 558

Real interpolation of quasi-Banach spacesZahra Ghorbani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562

Sobolev embedding theorem for weighted variable exponent Lebesgue spaceSomayeh Saiedinezhad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

Some C- algebraic results on expansion of semigroupsBahman Tabatabaie Shourijeh . . . . . . . . . . . . . . . . . . . . . . . . . . 569

Some equivalent condition to strong uniqueness in normed linear spaceNoha Eftekhari and Somayeh Rajabpoor . . . . . . . . . . . . . . . . . . . . . 573

Some fixed point results for the sum of two mappingsRoholla Keshavarzi and Ali Jabbari . . . . . . . . . . . . . . . . . . . . . . . . 576

Some fixed point results in non-Archimedean probabilistic Menger spaceShahnaz Jafari and Maryam Shams . . . . . . . . . . . . . . . . . . . . . . . . 579

Some fixed point theorems for C-algebra-valued -contractive mappingsNayereh Gholamian and Mahnaz Khanehgir . . . . . . . . . . . . . . . . . . . 583

Some inequalities for the numerical radius of operatorsMostafa Sattari and Mohammad Sal Moslehian . . . . . . . . . . . . . . . . . 587

Some new singular value inequalities for compact operatorsAli Taghavi and Vahid Darvish . . . . . . . . . . . . . . . . . . . . . . . . . . 591

Some properties of -spirallike functions with respect to 2k-symmetric conjugatepointsE. Amini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

Some results concerning 2-framesFarideh Monfared and Sedigheh Jahedi . . . . . . . . . . . . . . . . . . . . . . 599

Some results on t-remotest points and t-approximate remotest points in fuzzy normedspacesMarzieh Ahmadi Baseri and Hamid Mazaheri . . . . . . . . . . . . . . . . . . 603

Some results on almost L-DunfordPettis sets in Banach latticesHalimeh Ardakani and Manijeh Salimi . . . . . . . . . . . . . . . . . . . . . . 607

Some results on best proximity pairs in Banach lattice spacesMohammad Husein Labbaf Ghasemi Zavareh and Noha Eftekhari . . . . . . . . 611

Some sufficient conditions for subspace-hypercyclicityMansooreh Moosapoor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

Space of operatorsManijeh Bahreini Esfahani . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

Spectrum and eigenvalues of quaternion matricesS. M. Manjegani and A. Norouzi . . . . . . . . . . . . . . . . . . . . . . . . . 623

xiii


Starlikeness of a general integral operator on meromorphic multivalent functionsSaman Azizi, Ali Ebadian and Shahram Najafzadeh . . . . . . . . . . . . . . . 627

Sublinear operators on two-parameter martingale spacesMaryam Mohsenipour and Ghadir Sadeghi . . . . . . . . . . . . . . . . . . . . 630

Ternary (, , )-derivations on Banach ternary algebrasRazieh Farokhzad and Madjid Eshaghi . . . . . . . . . . . . . . . . . . . . . . 634

The BSE property of semigroup algebrasZeinab Kamali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638

The existence of efficient solutions for generalized systems and the properties of theirsolution setsMohammad Rahimi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642

The spectra of endomorphisms of analytic Lipschitz algebrasA. Golbaharan and . Mahyar . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

Two modes of limit in probabilistic normed spacesMahmood Haji Shaabani and Fateme Zeydabadi . . . . . . . . . . . . . . . . . 649

Universal metric space of dimension n and its application in clusteringHajar Beyzavi and Zohreh Hajizadeh . . . . . . . . . . . . . . . . . . . . . . . 653

Weak fixed point property in closed subspaces of some compact operator spacesMaryam Zandi and S.Mohammad Moshtaghioun . . . . . . . . . . . . . . . . . 657

Weighted composition operators on spaces of analytic vector-valued Lipschitz func-tionsK. Esmaeili . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661

Which commutators of composition operators with adjoints of composition operatorson weighted Bergman spaces are compact?Mahsa Fatehi and Roya Poladi . . . . . . . . . . . . . . . . . . . . . . . . . . 665

Combinatorics & Graph Theory

d-self center graphs and graph operationsYasser Alizadeh and Ehsan Estaji . . . . . . . . . . . . . . . . . . . . . . . . . 670

Bounds on some variants of clique cover numbersAkbar Davoodi, Ramin Javadi and Behnaz Omoomi . . . . . . . . . . . . . . . 674

Cospectral regular graphsMasoud Karimi and Ravindra B. Bapat . . . . . . . . . . . . . . . . . . . . . 678

Diameter of (M1 M2)Rezvan Varmazyar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681

Domination polynomial of generalized friendship graphsSomayeh Jahari and Saeid Alikhani . . . . . . . . . . . . . . . . . . . . . . . . 683

Notes on STP number of a graphMasoud Ariannejad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687

xiv


On the biclique Cover of GraphsFarokhlagha Moazami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690

On the construction of 3-way 3-homogeneous Steiner tradesHanieh Amjadi and Nasrin Soltankhah . . . . . . . . . . . . . . . . . . . . . . 694

On the cospectrality of graphsMohammad Reza Oboudi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697

On the signed Roman domination number of graphsAli Behtoei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701

On the Wiener index of Sierpinski graphsEhsan Estaji and Yasser Alizadeh . . . . . . . . . . . . . . . . . . . . . . . . . 705

One-solely balanced sets and related Steiner tradesSaeedeh Rashidi and Nasrin Soltankhah . . . . . . . . . . . . . . . . . . . . . 709

Permutation representation of graphsMoharram N. Iradmusa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713

Relations between some packing and covering parameters of graphsHamideh Hosseinzadeh and Nasrin Soltankhah . . . . . . . . . . . . . . . . . . 715

Roman k-domination number upon vertex and edge removalHamid Reza Golmohammadi, Lutz Volkmann, Seyed Mehdi Hosseini Moghad-dam and Arezoo N. Ghameshlou . . . . . . . . . . . . . . . . . . . . . . . . . 718

Roman entire domination in graphsKaram Ebadi and S. Arumugam . . . . . . . . . . . . . . . . . . . . . . . . . 722

Some new families of 2-regular self-complementary k-hypergraphs for k = 4, 5M. Ariannejad, M. Emami and O. Naserian . . . . . . . . . . . . . . . . . . . 726

Some Remarks of bipolar fuzzy graphsHossein Rashmanlou and R. A. Borzooei . . . . . . . . . . . . . . . . . . . . . 729

Some result about relative non-commuting graphSomayeh Ghayekhloo and Ahmad Erfanian . . . . . . . . . . . . . . . . . . . . 733

Some results on the annihilator graph of a commutative ringReza Nikandish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737

Total domination number of a family of graph productAdel P. Kazemi and Nasrin Malekzadeh . . . . . . . . . . . . . . . . . . . . . 741

Twin 2-rainbow dominating sets in graphsNahideh Asadi and Sepideh Norouzian . . . . . . . . . . . . . . . . . . . . . . 744

When the annihilator graphs are ring graph and outerplannerZohreh Rajabi, Kazem Khashyarmanesh and Mojgan Afkhami . . . . . . . . . 748

Computer Science

xv


A generalization of -dominating set and its complexityDavood Bakhshesh, Mohammad Farshi and Mahdieh Hasheminezhad . . . . . . 753

An approximation algorithm for a heterogeneous capacitated vehicle routing problemHaniyeh Fallah, Farzad Didehvar and Farhad Rahmati . . . . . . . . . . . . . 757

On the number of Doche-Icart-Kohel curves over finite fieldsReza Rezaeian Farashahi and Mehran Hosseini . . . . . . . . . . . . . . . . . . 761

Projection method combining preconditioners for solving large and sparse linearsystemsAzam Sadeghian and Azam Ghodratnema . . . . . . . . . . . . . . . . . . . . 765

Differential Equations & Dynamical Systems

A neurodynamic model for solving invex optimization problemsNajmeh Hosseinipour-Mahani and Alaeddin Malek . . . . . . . . . . . . . . . . 770

A new nonstandard finite difference scheme for Burger equationMehdi Zeinadini, Sadegh Zibaei and Mehran Namjoo . . . . . . . . . . . . . . 774

A numerical method for discrete fractionalorder Chen system derived from non-standard numerical schemeMehdi Zeinadini, Sadegh Zibaei and Mehran Namjoo . . . . . . . . . . . . . . 778

A reliable algorithm based on the Sumudu transform for solving partial differentialequationsMohsen Riahi, Esmail Hesameddini and Mehdi Shahbazi . . . . . . . . . . . . 782

A spectral method for the solution of KdV equation via orthogonal rational basisfunctionsSeyed Rouhollah Alavizadeh and Farid (Mohammad) Maalek Ghaini . . . . . . 786

An approximation of a two-dimensional Volterra-Fredholm integral equations viainverse multiquadric RBFsNasim Chamangard Khorram Abad and Mohammad Reza Ahmadi Darani . . . 790

Comparison between the Direct and local discontinuous Galerkin methods for thethird order kdv equationHajar Arebi , Esmaeil Hesameddini . . . . . . . . . . . . . . . . . . . . . . . . 794

Confidence interval for number of population in stochastic exponential populationgrowth models with mixture noiseRamzan Rezaeyan and Mohammad Ali Jafari . . . . . . . . . . . . . . . . . . 798

Continuous single-species population model with delayTayebe Waezizadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802

Direct meshless local Petrov-Galerkin (DMLPG) method for numerical solution of2D nonlinear Klein-Gordon equationAli Shokri and Erfan Bahmani . . . . . . . . . . . . . . . . . . . . . . . . . . 806

xvi


Discrete mollification method and its application to solving backward nonlinearcauchy problemSoheila Bodaghi and Ali Zakeri . . . . . . . . . . . . . . . . . . . . . . . . . . 810

Dynamic analysis of a fractional-order prey-predator modelZohreh Sadeghi and Reza Khoshsiar . . . . . . . . . . . . . . . . . . . . . . . 814

Existence and uniqueness of the mild solution for fuzzy fractional semilinear initialvalue problemsMonir Mirvakili, Marziyeh Alinezhad and Tofigh Allahviranloo . . . . . . . . . 818

Existence of infinitely many solutions for coupled system of Schrodinger-MaxwellsequationsGholamreza Karamali and Morteza Koozehgar Kalleji . . . . . . . . . . . . . . 822

Existence results for a k-dimensional system of multi-term fractional integro-differentialequations with anti-periodic boundary value problemsSayyedeh Zahra Nazemi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825

Greens function for fractional differential equation with Hilfer derivativeShiva Eshaghi and Alireza Ansari . . . . . . . . . . . . . . . . . . . . . . . . . 829

Hopf bifurcation in a general class of delayed BAM neural networksElham Javidmanesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833

Irreducible Smale spacesSarah Saeidi Gholikandi and Massoud Amini . . . . . . . . . . . . . . . . . . . 837

Isospectral matrix flows and numerical integrators on Lie groupsMahsa R. Moghaddam and Kazem Ghanbari . . . . . . . . . . . . . . . . . . . 841

Lie group classification of the Kuramoto-Sivashinsky equationMojtaba Sajjadmanesh and Parisa Vafadar . . . . . . . . . . . . . . . . . . . . 845

A mathematical model of hepatitis E virus transmission and its application for vac-cination strategy in a displaced persons camp in UgandaHossein Kheiri, Morteza Zereh Poush and Parvaneh Agha Mohammad Zadeh . 849

Nehari manifold approach to p-Laplacian eigenvalue problem with variable exponenttermsSomayeh Saiedinezhad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853

Positive solutions of nonlinear fractional differential inclusionsTahereh Haghi and Kazem Ghanbari . . . . . . . . . . . . . . . . . . . . . . . 857

Product integration method for numerical solution of a heat conduction problemBahman Babayar-Razlighi and Mehdi Solaimani . . . . . . . . . . . . . . . . . 861

Ratio-dependent functional response predator-prey model with threshold harvestingRazie Shafei and Dariush Behmardi Sharifabad . . . . . . . . . . . . . . . . . 865

Regularized Sinc-Galerkin method for solving a two-dimensional nonlinear inverseparabolic problemA. Zakeri, A. H. Salehi Shayegan and S. Sakaki . . . . . . . . . . . . . . . . . 869

xvii


Singular normal forms and computational algebraic geometryMajid Gazor and Mahsa Kazemi . . . . . . . . . . . . . . . . . . . . . . . . . 873

Solving linear fuzzy Fredholm integral equations system by triangular functionsElias Hengamian Asl and Afsane Hengamian Asl . . . . . . . . . . . . . . . . . 877

Some properties Sturm-Liouville problem with fractional derivativeTahereh Haghi and Kazem Ghanbari . . . . . . . . . . . . . . . . . . . . . . . 881

Spectral solutions of time fractional telegraph equationsHamed Bazgir and Bahman Ghazanfari . . . . . . . . . . . . . . . . . . . . . . 885

Steklov problem for a three-dimensional Helmholtz equation in bounded domainMojtaba Sajjadmanesh and Parisa Vafadar . . . . . . . . . . . . . . . . . . . . 889

Using Chebyshev polynomials zeros as mesh points for numerical solution of linearand nonlinear PDEs by differential quadrature method- based RBFsSajad Kosari . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893

Mathematical Finance

Arbitrage and curvatureMohammad Jelodari Mamaghani . . . . . . . . . . . . . . . . . . . . . . . . . 898

Numerical solution of stochastic optimal control problems: experiences from Mertonportfolio selection modelBehzad Kafash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 902

Risk measure in a financial marketElham Dastranj and Faeze Shokri . . . . . . . . . . . . . . . . . . . . . . . . . 906

Stochastic terminal times in G-backward stochastic differential equationsMojtaba Maleki, Elham Dastranj and Arazmohammad Arazi . . . . . . . . . . 909

The application of game theory in the real option (bond and convertible bond fi-nancing)Narges Hassani and Morteza Rahmani . . . . . . . . . . . . . . . . . . . . . . 913

Geometry & Topology

A generalization of contact metric manifoldsFereshteh Malek and Mahboobeh Samanipour . . . . . . . . . . . . . . . . . . 918

A note on an ideal of C(X) with - compact supportSimin Mehran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922

An extension of CF (X)Mehrdad Namdari and Somayeh Soltanpour . . . . . . . . . . . . . . . . . . . 926

Classification pseudosymmetric (, )-contact metric manifoldsNasrin Malekzadeh and Esmaiel Abedi . . . . . . . . . . . . . . . . . . . . . . 930

xviii


Complete CGC hypersurfaces in hyperbolic spaceSahar Masoudian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934

Containment problem for the ideal of fatted almost collinear closed points in P2Mohammad Mosakhani and Hassan Haghighi . . . . . . . . . . . . . . . . . . 938

Curvature of multisymplectic connections of order 3Masoud Aminizadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 942

Curvature properties and totally geodesic hypersurfaces of some para-hypercomplexLie groupsMansour Aghasi and Mehri Nasehi . . . . . . . . . . . . . . . . . . . . . . . . 945

Existence of extensions for generalized Lie groupsAbdo Reza Armakan and Mohammad Reza Farhangdoost . . . . . . . . . . . . 949

New results on induced almost contact structure on product manifoldsE. Abedi, G. H. Haghighatdoost and S. M. Mousavi . . . . . . . . . . . . . . . 953

On a subalgebra of C(X) containing Cc(X)Somayeh Soltanpour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956

On conservative generalized recurrent structuresMohammad Bagher Kazemi and Fatemeh Raei . . . . . . . . . . . . . . . . . . 960

On generalized covering subgroups of a fundamental groupS.Z. Pashaei, M. Abdullahi Rashid, B. Mashayekhy and H. Torabi . . . . . . . 964

On the flag curvature of bi-invariant Randers metricsMansour Aghasi and Mehri Nasehi . . . . . . . . . . . . . . . . . . . . . . . . 967

On the fundamental group of Yamabe solitonsBehroz Bidabad, Mohamad Yar Ahmadi . . . . . . . . . . . . . . . . . . . . . 971

On the space of Finslerian metricsNeda Shojaee, Morteza Mirmohammad Rezaii . . . . . . . . . . . . . . . . . . 974

On topologies generated by subrings of the algebra of all real-valued functionsMehdi Parsinia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978

Recurrent second fundamental form in submanifolds of Kenmotsu manifoldsMohammad Bagher Kazemi . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982

Ricci Codazzi homogeneous pseudo-Riemannian manifolds of dimension fourAmirhesam Zaeim and Ali Haji-Badali . . . . . . . . . . . . . . . . . . . . . . 985

Semi-symmetric four dimensional homogeneous pseudo-Riemannian manifoldsAli Haji-Badali and Amirhesam Zaeim . . . . . . . . . . . . . . . . . . . . . . 989

Some new subgroupoids of topological fundamental groupoidFereshteh Shahini and Ali Pakdaman . . . . . . . . . . . . . . . . . . . . . . . 993

Some properties of multi-Fedosove supermanifolds of order 3Masoud Aminizadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997

Some results on -reflexive propertyAkbar Dehghan Nezhad and Saman Shahriyari . . . . . . . . . . . . . . . . . .1000

xix


Topological classification of some orbit spaces arising from isometric actions on flatRiemannian manifoldsHamed Soroush, Reza Mirzaie and Hadi Hoseini . . . . . . . . . . . . . . . . .1004

Unique Path Lifting from Homotopy Point of View and FibrationsMehdi Tajik, Ali Pakdaman and Behrooz Mashayekhy . . . . . . . . . . . . . .1008

Web geometry of Lorentz dynamical systemRohollah Bakhshandeh-Chamazkoti . . . . . . . . . . . . . . . . . . . . . . . .1012

Numerical Analysis

A compact finite difference method without using Hopf-Cole transformation for solv-ing 1D Burgers equationRahman Akbari and Reza Mokhtari . . . . . . . . . . . . . . . . . . . . . . .1017

A computational algorithm for the inverse of positive definite tri-diagonal matricesT. Dehghn Niri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1021

A fast iterative method for solving first kind linear integral equationsMeisam Jozi and Saeed Karimi . . . . . . . . . . . . . . . . . . . . . . . . . .1025

A greedy meshless method for solving boundary value problemsYasin Fadaei and Mahmoud Mohseni Moghadam . . . . . . . . . . . . . . . . .1029

A method of particular solutions with Chebyshev basis functions for systems ofmulti-point boundary value problemsElham Malekifard and Esmail Babolian . . . . . . . . . . . . . . . . . . . . .1033

A new adaptive element free Galerkin algorithm based on the background meshMaryam Kamranian and Mehdi Dehghan . . . . . . . . . . . . . . . . . . . . .1037

A new iterative method for solving free boundary problemsMaryam Dehghan and Saeed Karimi . . . . . . . . . . . . . . . . . . . . . . .1041

A new method for Lane-Emden type equation in terms of shifted orthonormalBernestein polynomialZeinab Taheri and Shahnam Javadi . . . . . . . . . . . . . . . . . . . . . . . .1045

A non-standard finite difference method for HIV infection of CD4+T cells modelMorteza Bisheh Niasar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1049

A numerical study for the MHD Jeffery-Hamel problem based on orthogonal Bern-stein polynomialsAmir Reza Shariaty Nasab and Ghasem Barid Loghmani . . . . . . . . . . . .1053

A preconditioned method for approximating the generalized inverse of large matricesSaeed Karimi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1057

A preconditioner based on the shift-splitting method for generalized saddle pointproblemsDavod Khojasteh Salkuyeh, Mohsen Masoudi and Davod Hezari . . . . . . . .1061

A quick Numerical approach for Solving high order integro-differential equationsFariba Fattahzadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1065

xx


An algorithm for Jacobi inverse eigenvalue problemAzim Rivaz and Somayeh Zangoei Zadeh . . . . . . . . . . . . . . . . . . . . .1068

Bernoulli operational matrix for solving optimal control problemsNeda Aeinfar, Moosareza Shamsyeh Zahedi and Hassan Saberi Nik . . . . . . .1072

B-spline collocation method to solve the nonlinear fractional Burgers equationFateme Arjang and Khosro Sayehvand . . . . . . . . . . . . . . . . . . . . . .1076

Block pulse operational matrix for solving fractional partial differential equationS. Momtahan, M. Mohseni Moghadam and H. Saeedi . . . . . . . . . . . . . .1080

Complete pivoting strategy to compute the IULBF preconditionerA. Rafiei and Fatemeh Rezaei Fazel . . . . . . . . . . . . . . . . . . . . . . . .1084

Constructing an H-matrix via Randomized AlgorithmsMohammad Izadi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1088

Global CMRH method for solving general coupled matrix equationsToutounian Faezeh, Amini Saeide and Ramezani Zohreh . . . . . . . . . . . . .1092

How to recognize a fictitious signature?Fatemeh Zarmehi and Ali Tavakoli . . . . . . . . . . . . . . . . . . . . . . . .1096

Inverse eigenvalue problem for a matrix polynomialEsmaeil Kokabifar and Ghasem Barid Loghmani . . . . . . . . . . . . . . . . .1100

Inverse eigenvalue problem of nonnegative bisymmetric matrices of order 4Ali Mohammad Nazari and Atiyeh Nezami . . . . . . . . . . . . . . . . . . . .1104

Nested splitting conjugate gradient method for solving generalized Sylvester matrixequationMalihe Shaibani, Azita Tajaddini and Mohammad Ali Yaghoobi . . . . . . . .1108

Numerical solution for nth order linear Fredholm integro-differential equations byusing Chebyshev wavelets integration operational matrixR. Ezzati, A. Mashhadi Gholam and H. Nouriani . . . . . . . . . . . . . . . .1112

Numerical solution of an inverse source problem of the time-fractional diffusion equa-tion using a LDG methodSomayeh Yeganeh and Reza Mokhtari . . . . . . . . . . . . . . . . . . . . . .1116

Numerical solution of the time fractional Fokker-Planck equation using local discon-tinuous Galerkin methodJafar Eshaghi and Hojatollah Adibi . . . . . . . . . . . . . . . . . . . . . . . .1120

Numerical treatment of coupling of two hyperbolic conservation laws by local dis-continuous Galerkin methodsMohammad Izadi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1124

On existence, uniqueness and stability of solutions of a nonlinear integral equationHamid Baghani, Javad Farokhi Ostad and Omid Baghani . . . . . . . . . . . .1128

Parallelization of the adaptive wavelet galerkin method for elliptic BVPsNabi Chegini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1132

xxi


Pivoting strategy for an ILU preconditionerA. Rafiei, Mahdi Mohseni and Fatemeh Rezaei Fazel . . . . . . . . . . . . . . .1136

Reproducing kernel method for solving a class of Fredholm integral equationsAzizallah Alvandi, Mahmoud Paripour and Zahra Roshani . . . . . . . . . . .1140

Semiconvergence of the iterative Monte Carlo method for solving singular linearsystemsBehrouz Fathi-Vajargah and Zeinab Hassanzadeh . . . . . . . . . . . . . . . .1144

Septic B-spline solution of one dimensional Cahn-Hillird equationReza Mohammadi and Fatemeh Borji . . . . . . . . . . . . . . . . . . . . . . .1148

Sinc-Finite difference collocation method for time-dependent convection diffusionequationsZinat Taghipour and Jalil Rashidinia . . . . . . . . . . . . . . . . . . . . . . .1152

Sinc-Galerkin method for solving parabolic equationsZinat Taghipour and Jalil Rashidinia . . . . . . . . . . . . . . . . . . . . . . .1156

Solving a multi-order fractional differential equation using the method of particularsolutionsElham Malekifard and Jamshid Saeidian . . . . . . . . . . . . . . . . . . . . .1160

Solving large sparse linear systems by using QR-decomposition whit iterative refine-mentElias Hengamian Asl and Seyed Mehdi Karbassi . . . . . . . . . . . . . . . . .1164

Solving nonlinear fuzzy differential equations by the Adomian-Tau methodTayebeh Aliabdoli Bidgoli . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1168

Solving the Black-Scholes equation through a higher order compact finite differencemethodRahman Akbari and Mohammad Taghi Jahandideh . . . . . . . . . . . . . . .1172

Solving two-dimensional FitzHugh-Nagumo model with two-grid compact finite dif-ference (CFD) methodHamid Moghaderi and Mehdi Dehghan . . . . . . . . . . . . . . . . . . . . . .1176

The interval matrix equation AXB = CSomayeh Zangoei Zadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1180

The use of a tau method based on Bernstein polynomials for solving the viscoelasticsqueezing flow between two parallel platesS.Gh. Hosseini, M. Heydari and S.M. Hosseini . . . . . . . . . . . . . . . . . .1184

Two-stage waveform relaxation method for linear system of IVPs with non-constantHPD coefficientsDavod Khojasteh Salkuyeh and Zeinab Hassanzadeh . . . . . . . . . . . . . . .1188

Operation Research & Control Theory

A delayed-projection neural networks to solve bilevel programming problemsSoraya Ezazipour and Ahmad golbabai . . . . . . . . . . . . . . . . . . . . . .1193

xxii


A genetic algorithm for finding the semi-obnoxious (k,l)-core of a networkSamane Motevalli Ashkezari and Jafar Fathali . . . . . . . . . . . . . . . . . .1197

A Newton-type method for multiobjective optimization problemsNarges Hoseinpoor and Mehrdad Ghaznavi . . . . . . . . . . . . . . . . . . . .1201

A three-stage Data Envelopment Analysis model on fuzzy dataAmineh Ghazi, Farhad Hosseinzadeh Lotfi and Masoud Sanei . . . . . . . . . .1205

An efficient computational algebraic method for convex polynomial optimizationBenyamin M. Alizadeh, Sajjad Rahmany and Abdolali Basiri . . . . . . . . . .1209

An optimal algorithm for reverse obnoxious center location problems on graphsBehrooz Alizadeh and Roghayeh Etemad . . . . . . . . . . . . . . . . . . . . .1213

Control of fractional discrete-time linear systems by partial eigenvalue assignmentJavad Esmaeili and Hojjat Ahsani Tehrani . . . . . . . . . . . . . . . . . . . .1217

Decomposition algorithm for fuzzy linear programmingSohrab Effati and Azam Ebrahimi . . . . . . . . . . . . . . . . . . . . . . . .1221

Generalized KKT optimality conditions in an optimization problem with interval-valued objective function and linear-fractional constraintsM. R. Safi, T. Hoseini Khah and S. S. Nabavi . . . . . . . . . . . . . . . . . .1225

Multiwavelets Galerkin method for solving linear control systemsBehzad Nemati Saray, Farid Heidarpoor and Seyed Mahdi Karbasi . . . . . . .1229

Solving bi-level integer programming problems with multiple linear objectives atlower level by using particle swarm optimizationAkhtar Faramarzi, Maryam Zangiabadi and Hossein Mansouri . . . . . . . . .1233

Solving fuzzy LR interval linear systems using Ghanbari and Mahdavi-Amiris MethodMahnoosh Salari . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1237

Using Chebyshev wavelet in state-control parameterization method for solving timevarying systemZahra Rafiei and Behzad Kafash . . . . . . . . . . . . . . . . . . . . . . . . .1241

Vitality of nodes in networks carrying flows over timeShahram Morowati-Shalilvand and Mehdi Djahangiri . . . . . . . . . . . . . .1245

Statistics & Probability Theory

Directionally uniform distributions and their applicationsErfan Salavati . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1250

Improved ridge M-estimatorsMohammad Arashi and Mina Norouzirad . . . . . . . . . . . . . . . . . . . . .1254

Interval estimation for a general class of exponential distributions under progressivecensoringM. Abdi and A. Asgharzadeh . . . . . . . . . . . . . . . . . . . . . . . . . . .1258

xxiii


Matrix Variate Hypergeometric Gamma DistributionAnis Iranmanesh and Sara Shokri . . . . . . . . . . . . . . . . . . . . . . . . .1262

Preliminary test shrinkage estimator in the exponential distribution under progres-sively Type-II censoringAkbar Asgharzadeh and Mohammad Sharifi . . . . . . . . . . . . . . . . . . .1266

Robust mixture regression model fitting by slash distribution with application tomusical tonesHadi Saboori, Sobhan Shafiei and Afsaneh Sepahdar . . . . . . . . . . . . . . .1270

Testing Statistical Hypothesis of exponential populations with multiply sequentialorder statisticsMajid Hashempour and Mahdi Doostparast . . . . . . . . . . . . . . . . . . .1274

The Exponentiated G Family of Power Series DistributionsS. Tahmasebi, A. A. Jafari and B.Gholizadeh . . . . . . . . . . . . . . . . . .1278

Others (Applications of Mathematics in other Sciences)

A generalization of the Mertens formula and analogue to the Wallis product overprimesMohammadreza Esfandiari . . . . . . . . . . . . . . . . . . . . . . . . . . . .1283

A new approach for image compression using normal matricesEsmaeil Kokabifar and Alimohammad Latif . . . . . . . . . . . . . . . . . . .1287

Adaptive backstepping control of nonlinear systems based on singular perturbationtheoryMehrnoosh Asadi and Heydar Toossian Shandiz . . . . . . . . . . . . . . . . .1291

Algebraic structure of bags and fuzzy bagsFateme Kouchakinejad and Mashaallah Mashinchi . . . . . . . . . . . . . . . .1295

An edge detection scheme with legendre multiwaveletsNasser Aghazadeh, Yaser Gholizade Atani and Parisa Noras . . . . . . . . . . .1299

Coexistence of game theory in social scienceSaeed seyed agha Banihashemi, Hadi Ziaei and Tahereh Asadi . . . . . . . . .1303

Hunters lemma for forest algebrasSaeid Alirezazadeh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1307

L2-SVM problem and a new one-layer recurrent neural network for its primal Train-ingS. Hamid Mousavi, Majid Mohammadi and Sohrab Effati . . . . . . . . . . . .1311

New optimization algorithm via modified quantum genetic computationMajid Yarahmadi and Ameneh Arjmandzadeh . . . . . . . . . . . . . . . . . .1315

Nonbinary cycle codes by packing designMohammad Gholami and Masoumeh Alinia . . . . . . . . . . . . . . . . . . .1319

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On uniqueness of a spacewise-dependent heat source in a time-fractional heat diffu-sion processLeyli Shirazi and Mohammad Nili Ahmadabadi . . . . . . . . . . . . . . . . .1323

Open questions concerning Hindmans theoremAmir Khamseh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1326

Private quantum channels and higher rank numerical rangeNaser Hossein Gharavi and Sayyed Ahmad Mousavi . . . . . . . . . . . . . . .1330

Range of charged particle in matter: the Mellin transformAmir Pishkoo and Minoo Nasiri Hamed . . . . . . . . . . . . . . . . . . . . .1334

Schmidt rank-k numerical range and numerical radiusNaser Hossein Gharavi and Sayyed Ahmad Mousavi . . . . . . . . . . . . . . .1337

Shifted Legendre pseudospectral approach for solving population projection modelsAli Najafi Abrand Abadi, Habib Allah Zanjani . . . . . . . . . . . . . . . . . .1341

Uniqueness of solutions to fuzzy differential equations driven by Lius process withweak Lipschitz coefficientsSamira Siahmansouri, Somayeh Moghari and Somayeh Jalalipoo . . . . . . . .1345

Weighted Hermite-Hadamards inequality without symmetry condition for fractionalintegralAzizollah Babakhani and Hamzeh Agahi . . . . . . . . . . . . . . . . . . . . .1349

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Plenary Speakers

A medley of group actions

Cheryl E. Praeger

The University of Western Australia

Abstract

Most of my interaction and collaborative research with Iranian mathematicians hasbeen linked with symmetric structures, and has involved group actions. The lecturewill be a tribute to my Iranian colleagues.

Keywords: Group actions, symmetric structures, Iranian mathematicians

Mathematics Subject Classification [2010]: 20B25, 05C25

1 My first visit to Iran

My first mathematical colleague from Iran was Dr Akbar Hassani, who had been a graduatestudent with me in Oxford. His sabbatical leave spent at the University of WesternAustralia in 1986 led to my first visit to Tehran in 1994. Dr Hassani worked in Perth withme and Dr Luz Nochefranca on 2-arc transitive graphs.

Definition 1.1. A graph is (G, 2)-arc-transitive, for some subgroup G of automor-phisms, if G is transitive on all vertex triples (, , ) such that {, } and {, } areboth edges and 6= .

Previous work of mine had shown that every non-bipartite (G, 2)-arc transitive graphis a normal cover of a basic one where the group G has a special from. Hassani, Luz andI classified all possible basic examples for an infinite family of almost simple groups G.

Theorem 1.2. [1] All (G, 2)-arc-transitive graphs such that PSL(2, q) G PL(2, q)are known.

My lecture course in Tehran in 1994 was on the movement and separation of subsetsunder group actions, and some open problems on this theme became the topic of the PhDthesis for Mehdi Khayaty, now Professor Mehdi Alaeiyan.

Definition 1.3. Let G be a permutation group on a finite set such that G has no fixedpoints in , and let . The movement of is move() = maxgG |g \ |, and themovement of G is the maximum value of move() over all subsets .

Will be presented in EnglishSpeaker

Talk

46th Annual Iranian Mathematics Conference

25-28 August 2015

Yazd University

A medley of group actions pp.: 15

2

In earlier work I had shown that both the number of G-orbits in and the length ofeach G-orbit are bounded above by linear functions of the movement of G. In particular,if G is transitive on with movement m, and if G not a 2-group and p is the smallestodd prime dividing its order |G|, then I had shown that || b2mpp1 c. The main result ofMehdis thesis was a classification of all groups which attain this upper bound.

Theorem 1.4. [2] Let p be a prime, p 5, let m be a positive integer, and let G be atransitive permutation group on a set of size b2mpp1 c such that G has movement m, G isnot a 2-group and p is the least odd prime dividing |G|. Then either G is known explicitly,or G is a p-group of exponent bounded in terms of p only.

The second of Akbar Hassanis students who worked with me in the 1990s was AssociateProfessor Mohammadali Iranmanesh. Mohammadalis thesis topic was vertex-transitivenon-Cayley graphs, namely deciding whether such graphs exist of certain orders [3].

Definition 1.5. Let G be a group and S an inverse-closed subset of G such that 1G / S.The Cayley graph Cay(G,S) is the graph with vertex set G such that {x, y} is an edge ifand only if xy1 S. The group G acts by right multiplication as a regular subgroup ofautomorphisms (that is, G is transitive and only the identity fixes a vertex).

A graph is a Cayley graph (for some group) if and only if Aut() contains a regularsubgroup. As a result of Mohammadalis work (extending work of Brendan McKay, AliceMiller, Greg Gamble, Akos Seress, Akbar Hassani and myself) we know precisely whensuch graphs exist for a large class of orders. Mohammadali has worked on several otherresearch projects with me since this time [5, 6, 7, 16].

Theorem 1.6. [4] All integers n are known such that n has at most three distinct primedivisors, and there exists a vertex-transitive graph on n vertices which is not a Cayleygraph.

2 Professor Mehdi Behzad

In 2005 I participated in the Annual Iranian Mathematical Society Conference in Yazd.At that conference I met four Iranian mathematicians who have since visited me in Perth.The first is Professor Mehdi Behzad, with whom I wrote two papers [8, 9] jointly alsowith Professor Behzads son Arash. The most interesting one, for me, was the paper [9] inwhich we discussed nine different fundamental domination parameters for a graph . (Avertex/edge subset A dominates a graph if each vertex/edge is either in A or adjacentto an element of A.) We interpreted these parameters in terms of the total graph T () of introduced by Professor Behzad, namely, the vertices of T () are the vertices and edgesof , with two (vertices or edges) being adjacent in T () if they are either adjacent orincident in . We concluded that, arguably, the most fundamental of these parameters isthe vertex-vertex domination parameter.

In addition, I spent hundreds of hours editing an English version of Professor Behzadsplay The Legend of the King and the Mathematician [10]. Based on the puzzle of theWolf, Sheep and Cabbage, the play is a wonderful initiative of Professor Behzad aimed atinspiring young people to enjoy and engage with the mathematical strategies behind themain story.

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3 My work with younger Iranian colleagues

Dr Seyed Hassan Alavi worked with me and Dr John Bamberg on triple factorisations ofgroups of the form G = ABA (for proper subgroups A,B). A surprising equivalence isthat a triple factorisation is directly associated with a G-flag-transitive point-line incidencestructure in which each point-pair is incident with at least one line. If the latter propertyholds we say that the geometry is collinearly complete. Part of Hassans development, of atheory of these geometries, is his fundamental paper [11] which connects these geometrieswith primitive permutation groups, with restricted movement of point-subsets, and withflag-transitive symmetric designs. One very interesting class of examples arises for generallinear groups: note that, for given collections of points and lines there are often severalpossible notions of incidence. In [12], Hassan identifies all possibilities for subspace actions,producing new collinearly complete geometries. He also find new examples when the pointsor lines are subspace bisections.

Theorem 3.1. [12] Let G = GL(n, q), and V = GF(q)n, and consider the geometry withm-dimensional subspaces as points, k-dimensional subspaces as lines, and incidencebetween a point and a line when the intersection has dimension j. This geometry iscollinearly complete if and only if max{0,m+ k n} j k2 + max{0,m n2 .

Associate Professor Ashraf Daneshkhah worked with me and Associate Professor AliceDevillers in Perth on subdivision graphs S() of a given graph , that is, the graphobtained by adding a vertex in the middle of each edge of . Formally, the vertices ofS() are the vertices and edges of , and edges of S() are those vertex-edge pairs (, e)such that the vertex lies on the edge e. The paper [13] elucidates connections betweenvarious symmetry properties of and of its subdivision graph S(), in particular locals-arc-transitivity, and local s-distance transitivity.

Theorem 3.2. [13] Let be a connected graph, s a positive integer, and G Aut().Then S() is locally (G, s)-arc transitive if and only if is (G, d s+12 e)-arc transitive.Moreover, provided has diameter at least s+12 , either of these conditions holds if andonly S() is locally (G, s)-distance transitive.

Ashraf and Alice then extended this study further and obtained a complete classifica-tion of locally distance transitive subdivision graphs, which highlighted their connectionwith projective planes, generalised quadrangles and generalised hexagons.

Dr Moharram Iradmusa and I worked on a very interesting generalisation of Cayleygraphs, called 2-sided group digraphs. Start with a group G and two subsets L,R of G.

The corresponding 2-sided group digraphs2S(G;L,R) has vertex set G and an arc from

a vertex x to a vertex y if and only if y = `1xr for some ` L, r R. Despite thesimilarities to Definition 1.3, these digraphs need not be vertex-transitive, and we give in[14, Example 2.1] a surprising example with 12 vertices, and with connected components

of sizes 4 and 8 (see Figure 11). We also determine conditions under which2S(G;L,R) is

a graph (that is, the joining relation is symmetric), and conditions for it to be connected,and to be a Cayley graph or digraph. We pose several open problems about these digraphs.

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Figure 1: Disconnected two-sided group graph with non-isomorphic components

I have worked also with Dr Azizollah Azad on non-commuting graphs for general lineargroups [15, 16], and with Dr Marzieh Akbari on codes in Hamming graphs. I thank allmy Iranian colleagues for their great collaborations and their friendship.

Acknowledgement

I thank the University of Yazd for their generous support for my presence at this confer-ence. I also thank the University of Western Australia for granting my sabbatical leavewhich has allowed me to visit Iran this year.

References

[1] A. Hassani, L. Nochefranca and Cheryl E. Praeger, Two-arc transitive graphs admittinga two-dimensional projective linear group, J. Group Theory 2 (1999), 335353.

[2] A. Hassani, M. Khayaty, E. I. Khukhro and Cheryl E. Praeger, Transitive permutationgroups with bounded movement having maximal degree, J. Algebra 214 (1999), 317337.

[3] Akbar Hassani, Mohammad Ali Iranmanesh and Cheryl E. Praeger, On vertex-imprimitive graphs of order a product of three distinct odd primes, J. Combin. Math.and Combin. Computing 28 (1998), 187213.

[4] Mohammad A. Iranmanesh and Cheryl E. Praeger, On non-Cayley vertex-transitivegraphs of order a product of three primes, J. Combin. Theory (B) 81 (2001), 119.

[5] Mohammad A. Iranmanesh, Cheryl E. Praeger, and Sanming Zhou, Finite symmetricgraphs with two-arc transitive quotients, J. Combin. Theory Series B. 94 (2005), 7999.

[6] Daniela Bubboloni, Silvio Dolfi, Mohammadali A. Iranmanesh, and Cheryl E. Praeger,On bipartite divisor graphs for group conjugacy class sizes, J. Pure and Applied Algebra213 (2009), 17221734.

[7] Mohammad A. Iranmanesh and Cheryl E. Praeger, Bipartite divisor graphs for integersubsets, Graphs and Combin. 26 (2010), 95105.

[8] Mehdi Behzad, Arash Behzad, and Cheryl E. Praeger, On the domination number ofthe generalized Petersen graphs, Discrete Math. 308 (2008), 603610. [In the ScienceDi-rect Top 25 Hottest Articles, Discrete Math. Oct-Dec 2007.]

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[9] Mehdi Behzad, Arash Behzad, and Cheryl E. Praeger, Fundamental dominations ingraphs, Bulletin Inst. Math. Appl. 61 (2011), 616.

[10] Mehdi Behzad and Naghmeh Samini, The Legend of the King and the Mathematician,Candle and Fog, 2013. ISBN: 978-964-2667-67-3

[11] Seyed Hassan Alavi and Cheryl E. Praeger, On triple factorisations of finite groups,J. Group Theory 14 (2011), 341360.

[12] Seyed Hassan Alavi and Cheryl E. Praeger, Triple factorisations of the general lineargroup and their associated geometries, Linear Algebra Appn. 469 (2015), 169203.

[13] Ashraf Daneshkhah, Alice Devillers and Cheryl E. Praeger, Symmetry properties ofSubdivision Graphs, Discrete Math. 312 (2012), 8693.

[14] Moharram N. Iradmusa, Cheryl E. Praeger, Two-sided group digraphs and graphs,J. graph theory, accepted. (arXiv: 1401.2741)

[15] Azizollah Azad and Cheryl E. Praeger, Maximal subsets of pairwise non-commutingelements of finite three-dimensional general linear groups, Bull. Austral. Math. Soc. 80(2009), 91104.

[16] Azizollah Azad, Mohammadali Iranmanesh, Cheryl E. Praeger, and Pablo Spiga,Abelian coverings of finite general linear groups and an application to their non-commuting graphs, J. Alg. Combin. 34 (2011), 683710.

Email: [email protected]

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25-28 August 2015

Yazd University


6

On Laplacian eigenvalues of graphs

Kinkar Ch. Das

Department of Mathematics, Sungkyunkwan University,

Suwon 440-746, Republic of Korea

Abstract

Let G = (V, E) be a simple graph. Denote by D(G) the diagonal matrix of itsvertex degrees and by A(G) its adjacency matrix. Then the Laplacian matrix of G isL(G) = D(G) A(G). Denote the spectrum of L(G) by S(L(G)) = (1, 2, . . . , n),where we assume the eigenvalues to be arranged in nonincreasing order: 1 2 n1 n = 0. Let a be the algebraic connectivity of graph G. Then a = n1.Among all eigenvalues of the Laplacian matrix of a graph, the most studied is thesecond smallest, called the algebraic connectivity (a(G)) of a graph [5]. In this talkwe show some results on 1(G) and a(G) of graph G. We obtain some integer andreal Laplacian eigenvalues of graphs. Moreover, we discuss several relations betweenLaplacian eigenvalues and graph parameters. Finally, we give some conjectures on theLaplacian eigenvalues of graphs.

Keywords: Graph, Largest Laplacian eigenvalue, Algebraic connectivity, Diameter,Minimum degreeMathematics Subject Classification [2010]: 05C50

References

[1] M. Aouchiche, P. Hansen, A survey of automated conjectures in spectral graph theory,Linear Algebra Appl. 432 (2010) 22932322.

[2] K. C. Das, Conjectures on index and algebraic connectivity of graphs, Linear AlgebraAppl. 433 (2010) 16661673.

[3] K. C. Das, Proof of conjectures on adjacency eigenvalues of graphs, Discrete Math.313 (2013) 1925.

[4] K. C. Das, S.-G. Lee, G.-S. Cheon, On the conjecture for certain Laplacian integralspectrum of graphs, Journal of Graph Theory 63 (2010) 106113.

[5] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.

[6] R. Merris, Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197,198(1994) 143176.

Email: [email protected]: http://kinkardas.tripod.com

Speaker

Talk


25-28 August 2015

Yazd University

On Laplacian eigenvalues of graphs pp.: 11

7

Partition of Unity Parametrics: A framework for

meta-modeling in computer graphics

Faramarz F. Samavati

University of Calgary

In the past three decades, the field of Computer Graphics (CG) has experienced a rev-olution, benefiting from significant research and technical achievements. Creating detaileddigital content is a major task in CG related industries such as Game, Film, GIS and CAD,and requires well-constructed, high quality geometric models. However, even with sophis-ticated software packages, geometric modeling is still a challenging and time consumingtask. This challenge is due to the mathematical foundation of geometric models, our wayof interacting with them, and more specifically, the augmenting of these geometric modelswith respect to their macro- and microscopic character. Therefore, geometric modeling -as a main pillar of CG - still requires evaluation to rectify foundation issues.

We present Partition of Unity Parametrics (PUPs), a natural and more flexible ex-tension of NURBS (which are widely used in industry) that maintains affine invariance.NURBS inherit many useful properties from B-spline basis functions, and extend B-splinesby allowing a scalar weight to be associated with each control point, indicating its relativeimportance to the curve. For these reasons NURBS have emerged as the predominantchoice for modeling in computer graphics. Despite their widespread use, it is difficult tomodify the characteristics of NURBS models. In practice, it is complex to toggle betweensharp and smooth features, as well as to interpolate and approximate control points. Like-wise, it is difficult to control the local character of curves and surfaces, and not possibleto increase NURBS smoothness without increasing its support.

PUPs replace the weighted basis functions of NURBS with arbitrary weight-functions(WFs). By choosing appropriate WFs, PUPs yield a comprehensive geometric modelingframework, accounting for a variety of beneficial properties, such as local-support, speci-fied smoothness, arbitrary sharp features and approximating or interpolating curves. Thisserves as a basis for metamodeling systems where users model the tools used for modeling(ie. weight functions) in tandem with the model itself. PUPs allow common geometricrequirements and operations to be phrased succinctly, including: the addition of controlpoints, arbitrary sharp features, increasing smoothness without increasing support, ap-proximation and interpolation. For surfaces, PUPs permit non-tensor weight functionsand allow control points to be added anywhere (without introducing other control points).This facilitates simple methods for sketching features and converting a planar mesh intoa parametric surface of arbitrary smoothness.

As an important class of PUPs, we introduce CINAPCT-spline, based on bump-functions, which is C-infinity but with compact-support. The underlying weight functions

Speaker

Talk


25-28 August 2015

Yazd University

Partition of Unity Parametrics: A framework for meta-modeling in . . . pp.: 12

8

are similar in form to B-spline basis functions, and are parameterized by a degree-like shapeparameter. We examine approximating and interpolating curves created using CINAPCT-spline. Furthermore, we propose and demonstrate a method to specify the tangents andhigher order derivatives of the curve at control points for CINPACT and PUPs curves.

Talk


25-28 August 2015

Yazd University

Partition of Unity Parametrics: A framework for meta-modeling in . . . pp.: 22

9

An eigenvalue problem

Behrouz Emamizadeh

Department of Mathematical Sciences

University of NottinghamNingbo, China

Abstract

This talk is motivated by the following nonlinear Lorentz invariant wave equation:

2u+ 6u V (u) = 0, (1)

where

pu =

t

[(c2|u|2 |ut|2)p2ut

] c2

[(c2|u|2 |ut|2)p2u

],

and V is an appropriate function. In the last equation, u : R3+1 R4, u = u(x, t),x R3, t R, u denotes the Jacobian with respect to x, and ut is the derivativewith respect to t.

A static solution of (1) is a function Z : R3 R4 that satisfies

c2Z c10 10Z V (Z) = 0, (2)

where p = (|u|p2u) is the well-known p-Laplace operator. The differentialoperator in (2) is a linear combination of and 10.

Here we are interested in a class of scalar equations similar to (2), in which thedifferential operator is a convex combination of p and . More precisely, weconsider the eigenvalue problem

{tpu (1 t)u = u in Du = 0 on D,

(p 6= 2) (3)

where D Rn is a smooth bounded domain. We will show that the set of eigenvaluesof (3) is continuous for t (0, 1]. In fact, if 1 is the first eigenvalue of , then wewill prove the striking result that the spectrum of (3) is ((1 t)1,), even whent is very close to zero. This result is surprising because when t approaches zero thedifferential operator

Ct := tp (1 t)approaches and the expectation would be that when t is very near zero the spec-trum (Ct) of Ct would be the union

Ii of some intervals Ii each containing the

ith-eigenvalue of . Recall that the spectrum of the Laplacian is a discrete set:

() = {j | j N} where 1 < 2 3 4 .Speaker

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25-28 August 2015

Yazd University

An eigenvalue problem pp.: 13

10

In other words, when the convex parameter t moves from 1 to 0 in the interval [0, 1],the spectrum (Ct) will keep containing the interval [1,) until t takes the exactvalue 0, in which case (Ct) suddenly snaps into the discrete set ().

The eigenvalue problems of type (3) are new in the mathematics literature. Re-cently, the following eigenvalue problem was investigated:

{puu = u in Du = 0 on D,

where denotes the unit outward normal to the boundary D. It was proved thatthe spectrum is {0} (N1 ,), where N1 denotes the first non-zero eigenvalue of with respect to the Neumann boundary condition. Our approach toward solving theeigenvalue problem (3) is different; our approach is based on the fibering method thatwas introduced in the early 1990s by the late S. Pohozaev. The fibering method is farmore powerful than the Nehari-manifold method as it is applicable to a much broaderrange of boundary value problems than we discuss here. To help with a geometricintuition of the material, we introduce the -plane, which we denote by . This planehas two axes, the p-axis and the -axis. The -plane is naturally equivalent toR2 in the sense that there exists a canonical map : R2 as follows:

(a, b) = ap b.

In particular, we haveCt = (t, 1 t),

which is a convex combination of p and .1The unit square S is the square with vertices at points O = (0, 0), A = (1, 0),

B = (1, 1), and C = (0, 1). The main diagonal of S, joining (0, 1) to (1, 0), iswhat we are interested in.

The following is a summary of what is known about the spectrum of some of theoperators in the -plane:

(i) ((0, 1)) = {j | j N} in which 1 < 2 3 4 , with respectto both Dirichlet and Neumann boundary conditions. In the latter case, 1 = 0and 2 < 3.

(ii) ((1, 1)) = {0} (N1 ,), with respect to the Neumann boundary conditions.(iii) ((1, 0)) = [0,), provided that p ( 2nn+2 ,) \ {2}.

Note that every operator in the first quadrant of the -plane (R+ R+) isa translate of one in S. The same goes with those in the third quadrant, since(a,b) = (a, b). Hence it makes sense to focus on S in this talk. On theother hand, the operators in the second and the fourth quadrants need to be treatedseparately.

The main result of this presentation is the following:

Theorem 0.1. Let p (1,) \ {2} and t (0, 1). Then the following hold:(i) If [0, (1 t)1], then / (Ct).

(ii) If ((1 t)1,), then (Ct).Here 1 denotes the first eigenvalue of with respect to the Dirichlet boundaryconditions on D.

1hence the use of the calligraphic C with a t subscript in Ct.

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25-28 August 2015

Yazd University


11

We prove the theorem using variational methods. For this purpose we will consideran energy functional associated with (3), and prove that the critical points of thisfunctional will give rise to non-trivial solutions of (3). The challenge is the parameterp. More precisely, for p > 2, the energy functional is coercive, hence the directmethod applies. However, for the case p < 2, the lack of coercivity will render thedirect method ineffective. Hence, we will apply the fibering method of Pohozaev.

We will derive a priori bounds and regularity results on the eigenfunctions. Wewill show that the behavior of the eigenfunctions are totally different between the caseof p (1, 2) and that of p > 2. More precisely, it turns out that when approachesthe threshold (1 t)1, then

{supD |u| 0, (p > 2)supD |u| , (1 < p < 2).

Key Words: Lorentz invariant wave equation, continuous eigenvalues, Laplacian, p-Laplacian, fibering method, coercivity, existence, bounds, regularity.

MSC 2010: 81Q05, 35J60, 35P30

Email: [email protected]

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25-28 August 2015

Yazd University


12

Set-theoretic methods of homological algebra and their

applications to module theory

Jan Trlifaj

Charles University, Prague

Abstract

We present some of the recent tools of set-theoretic homological algebra togetherwith their applications, notably to the approximation theory of modules, and to (in-finite dimensional) tilting.

Keywords: approximations of modules, set-theoretic homological algebra, infinitedimensional tilting theory

Mathematics Subject Classification [2010]: 16DXX, 18G25, 13D07, 03E75

1 Introduction

A major topic of module theory concerns existence and uniqueness of direct sum decom-positions. Positive results provided by the Krull-Remark-Schmidt-Azumaya theorems,the Faith-Walker Theorem, and Kaplansky theorems, form the cornerstones of the clas-sic theory. However, there are a number of important classes of (not necessarily finitelygenerated) modules to which the theory does not apply, because their modules do notdecompose into (possibly infinite) direct sums of indecomposable, or small, submodules.

While such direct sum decompositions are rare, there do exist more general structuraldecompositions that are almost ubiquitous. The point is to replace direct sums by transfi-nite extensions. For example, taking direct sums of copies of the group Zp, one obtains allZp-modules whose sole isomorphism invariant is the vector space dimension. In contrast,transfinite extensions of copies of Zp yield the much richer class of all abelian p-groupswhose isomorphism invariants are known basically only in the totally-projective case (theUlm-Kaplansky invariants).

Starting with the solution of the Flat Cover Conjecture [5], numerous classes C of mod-ules have been shown to be deconstructible, that is, expressible as transfinite extensionsof small modules from C. Basic tools for deconstruction come from set-theoretic homolog-ical algebra and originate in abelian group theory [6], but have since been expanded andgeneralized to module categories, and even beyond that setting.

Each deconstructible class is precovering, so it provides for approximations of modules.By choosing appropriately the class C, one can tailor these approximations to the needsof various particular structural problems, cf. [12].

Speaker

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25-28 August 2015

Yazd University

Set-theoretic methods of homological algebra and their applications to . . . pp.: 18

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Approximations can also be employed in developing relative homological algebra inmodule categories. In the case when minimal approximations exist, ones obtains newinvariants of modules, generalizing classic invariants such as the Betti numbers, or the(dual) Bass invariants, cf. [8]. Further applications in this direction involve model categorystructures associated to deconstructible classes in the setting of Grothendieck categories,such as the category of all unbounded chain complexes of modules, or the category of allquasi-coherent sheaves on a scheme. They yield new ways of computing cohomology ofquasi-coherent sheaves via the approach of Quillen and Hovey, cf. [9], [11], [15].

But deconstructibility has its limits. This has first been observed by Eklof and Shelah[7] who proved that it is consistent with ZFC that the class of all Whitehad groups is notprecovering. The latter fact, however, is not provable in ZFC, because it is also consistentthat all Whitehead groups are free. More recent results show that non-deconstructibilityis a phenomenon occuring in ZFC, and it is much more widespread than expected earlier.There is also a surprising connection to another important part of module theory: thetilting theory, [2], [14].

Our goal here is to explain these developments in more detail, and present some of thetechniques of set-theoretic homological algebra and approximation theory of modules thathave been developed over the past two decades. We will also consider several applications,notably to (infinite dimensional) tilting theory [1] and to representation theory [13].

2 Filtrations and approximations

2.1 Filtrations and the Hill Lemma

For an (associative, but not necessarily commutative) ring R with 1, we denote by Mod-Rthe category of all (unitary right R-) modules. Moreover, given an infinite cardinal and aclass of modules C, we will use the notation C

As mentioned in the Introduction, given a class of modules C and M C, it is rarelypossible to decompose M into a direct sum of small, or indecomposable, modules from C.Deconstructibility is much more feasible:

Definition 2.2. Let C be a class of modules and an infinite cardinal. Then C is -deconstructible provided that C =Filt(C

factorization through f :

Af

// M

A

g

OO

f

>>||||||||

The map f is called an A-precover of M (or a right A-approximation of M).(ii) An A-precover is special in case it is surjective, and its kernel K satisfies Ext1R(A,K) =

0 for each A A.(iii) Let A be precovering. Assume that in the setting of (i), if f = f then each factoriza-

tion g is an automorphism. Then f is an A-cover of M . A is called a covering classin case each module has an A-cover. We note that each covering class containing P0and closed under extensions is necessarily special precovering.

For example, the class P0 is easily seen to be precovering, while F0 is covering by [5].By a classic result of Bass, P0 is covering, iff P0 = F0, i.e., iff R is a right perfect ring.

Dually, we define (special) preenveloping and enveloping classes of modules. For ex-ample, I0, the class of all injective modules, is an enveloping class.

Precovering classes are ubiquitous because of the following

Theorem 2.6. Let S be a set of modules and C = Filt(S). Then C is precovering.Moreover, if C is closed under direct limits, then C is covering.

Example 2.7. The classes Pn (n < ) for any ring R, as well as GP, the class of allGorenstein projective modules for R IwanagaGorenstein, are special precovering. Theclasses Fn (n < ) over any ring, and GF of all Gorenstein flat modules for R IwanagaGorenstein, are covering. The classes In (n < ) for any ring R (resp. GI for R IwanagaGorenstein) are special preenveloping (resp. enveloping).

Precovering classes C, and preenveloping classes E , can be employed in developingrelative homological algebra similarly as the classes of all projective and injective modulesare used in the classic (absolute) case, cf. [8].

Besides the formal duality between the definitions of precovering and preenvelopingclasses, there is also an explicit duality discovered by Salce, mediated by complete cotorsionpairs:

Definition 2.8. Let R be a ring. A pair of cla

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