2016
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Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
2
2
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
1

1
13


F. M.
Yaghoobi
Department of Mathemetics, College of Science, Hamedan Branch, Islamic Azad University, Hamedan, Iran
Department of Mathemetics, College of Science,
Iran
fm.yaghoobi@gmail.com


J.
Shamshiri
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Department of Mathematics, Mashhad Branch,
Iran
jamileshamshiri@gmail.com
Critical point
Semilinear elliptic system
Nonlinear boundary value problem
Fibering map
Nehari manifold
[[1] A. Aghajani and J. Shamshiri and F. M. Yaghoobi, Existence and multiplicity of positive solutions for a class of nonlinear elliptic problems, Turk. J. Math (2012) doi:10.3906/mat110723. ##[2] A. Aghajani and J. Shamshiri, Multilicity of positive solutions for quasilinear elliptic pLaplacian systems, E. J. D. E. 111 (2012) 116. ##[3] A. Aghajani and F.M. Yaghoobi and J. Shamshiri, Multiplicity of positive solutions for a class of quasilinear elliptic pLaplacian problems with nonlinear boundary conditions, Journal of Information and computing Science 8 (2013) 173182. ##[4] Y. Bozhkov and E. Mitidieri, Existence of multiple solutions for quasilinear systems via fibering method, Journal of Differential Equations 190 (2003) 239267. ##[5] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2010. ##[6] K. J. Brown and T.F.Wu, A semilinear elliptic system involving nonlinear boundary condition and signchanging weight function, J. Math.Anal. Appl. 337 (2008) 13261336. ##[7] K. J. Brown and Y. Zhang, The Nehari manifold for a semilinear elliptic problem with a sign changing weight function, J. Differential Equations 193 (2003) 481499. ##[8] C. M. Chu and C. L. Tang, Existence and multiplicity of positive solutions for semilinear elliptic systems with Sobolev critical exponents, Nonlinear Anal 71 (2009) 51185130. ##[9] P. Drabek and S. I. Pohozaev, Positive solutions for the pLaplacian: application of the fibering method, Proc. Royal Soc. Edinburgh Sect. A 127 (1997) 703726. ##[10] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974) 324353. ##[11] H. Fan, Multiple positive solutions for a critical elliptic system with concave and convex nonlinearities, Nonlinear Anal. Real World Appl. 18 (2014) 1422. ##[12] M. F. Furtado a and J. P. P. da Silva, Multiplicity of solutions for homogeneous elliptic systems with critical growth, J.Math. Anal. Appl. 385 (2012) 770785. ##[13] T. s. Hsu, Multiple positive solutions for a quasilinear elliptic system involving concaveconvex nonlinearities and sign changing weight functions, Internat. J. Math. Math. Sci. (2012) doi:10.1155 (2012) 109214. ##[14] FengYun Lu, The Nehari manifold and application to a semilinear elliptic system, Nonlinear Analysis 71 (2009) 34253433 ##[15] Y. Shen and J. Zhang, Multiplicity of positive solutions for a semilinear pLaplacian system with Sobolev critical exponent, Nonlinear Analysis 74 (2011) 10191030. ##[16] M. Struwe, Variational methods, Springer, Berlin, 1990. ##[17] T. F. Wu, The Nehari manifold for a semilinear elliptic system involving signchanging weight functions, Nonlin. Analysis 68 (6) (2008), 17331745.##]
Subcategories of topological algebras
2
2
In addition to exploring constructions and properties of limits and colimits in categories of topological algebras, we study special subcategories of topological algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with topological structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective subcategories.
1

15
28


V. L.
Gompa
Department of Mathematics, Troy University, Dothan, AL 36304, USA
Department of Mathematics, Troy University,
United States
vgompa@jsu.edu
Monotopolocial category
topological category
topological functors
Universal algebra
topological algebra
reflective subcategory
coreflective subcategory, epireflective subcategory
[[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, John Wiley & Sons, Inc., New York, 1990. ##[2] H. L. Bentley, H. Herrlich and R. G. Ori, Zero sets and complete regularity for nearness spaces, In: Categorical Topology, World Scientific, Teaneck, New Jersey (1989), 446461. ##[3] P. M. Cohn, Universal Algebra, Harper and Row, Publishers, New York, 1965. ##[4] T. H. Fay, An axiomatic approach to categories of topological algebras, Quaestiones Mathematicae 2 (1977), 113137. ##[5] V. L. Gompa, Essentially algebraic functors and topological algebra, Indian Journal of Mathematics, 35, (1993), 189195. ##[6] H. Herrlich, Essentially algebraic categories, Quaest. Math. 9 (1986), 245262. ##[7] Y. H. Hong, Studies on categories of universal topological algebras, Doctoral Dissertation, McMaster University, 1974. ##[8] H. Herrlich and G. E. Strecker, Category Theory, Allyn and Bacon, Boston, 1973. ##[9] J. Koslowski, Dual adjunctions and the compatibility of structures, In: Categorical Topology, Heldermann Verlag, Berlin (1984), 308322. ##[10] J. D. Lawson and B. L. Madison, On congruences and cones, Math. Zeit. 120 (1971), 1824. ##[11] L. D. Nel, Universal topological algebra needs closed topological categories, Topology and its Applications 12 (1981) 321330. ##[12] L. D. Nel, Initially structured categories and cartesian closedness, Canad. J. Math. 27 (1975) 13611377. ##[13] M. Petrich, Lectures in Semigroups, John Wiley & Sons, New York, 1977. ##[14] W. Tholen, On Wyler’s taut lift theorem, General Topology and its Applications 8 (1978), 197206. ##[15] O. Wyler, On the categories of general topology and topological algebras, Arc. Math. (Basel) 22 (1971), 717.##]
Common fixed point results on vector metric spaces
2
2
In this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for three mappings in this space. Obtained results extend and generalize wellknown comparable results in the literature.
1

29
39


G.
Soleimani Rad
Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Young Researchers and Elite club, Central
Iran
gh.soleimani2008@gmail.com


I.
Altun
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey

King Saud University, College of Science, Riyadh, Saudi Arabia
Department of Mathematics, Faculty of Science
Turkey
ialtun@kku.edu.tr
Vector metric space
Riesz space
common fixed point
Weakly compatible pairs
[[1] M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416420. ##[2] M. Abbas, B.E. Rhoades and T. Nazir, Common fixed points for four maps in cone metric spaces, Appl. Math. Comput. 216 (2010), 8086. ##[3] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, SpringerVerlag, Berlin, 1999. ##[4] I. Altun, Common fixed point theorems for weakly increasing mappings on ordered uniform spaces, Miskolc Math. Notes. 12 (1) (2011), 310. ##[5] I. Altun and C. Cevik, Some common fixed point theroems in vector metric spaces, Filomat. 25 (1) (2011), 105113. ##[6] M. Arshad, A. Azam and P. Vetro, Some common fixed point results in cone metric spaces, Fixed Point Theory Appl. (2009), Article ID 493965. ##[7] C. Cevik and I. Altun, Vector metric space and some properties, Topol. Met. Nonlin. Anal. 34 (2) (2009), 375382. ##[8] A.S. Cvetkovi´c, M.P. Stani´c, S. Dimitrijevi´c and S. Simi´c, Common fixed point theorems for four mappings on cone metric type space, Fixed Point Theory Appl. (2011), Article ID 589725. ##[9] B. Fisher, Four mappings with a common fixed point, J. Univ. Kuwait Sci. 8 (1981), 131139. ##[10] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 14671475. ##[11] S. Jankovi´c, Z. Kadelburg and S. Radenovi´c, On cone metric spaces; a survey, Nonlinear Anal. 74 (2011), 25912601. ##[12] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Am. Math. Soc. 103 (1988), 977983. ##[13] G. Jungck and B.E. Rhoades, Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory. (7) (2) (2006), 287296. ##[14] H. Rahimi, B.E. Rhoades, S. Radenovi´c and G. Soleimani Rad, Fixed and periodic point theorems for Tcontractions on cone metric spaces, Filomat. 27 (5) (2013), 881888. ##[15] H. Rahimi and G. Soleimani Rad, Common fixed point theorems and cdistance in ordered cone metric spaces, Ukrainian Mathematical Journal. 65 (12) (2014), 18451861. ##[16] H. Rahimi, P. Vetro and G. Soleimani Rad, Some common fixed point results for weakly compatible mappings in cone metric type space, Miskolc Math. Notes. 14 (1) (2013), 233243. ##[17] S. Rezapour and R. Hamlbarani, Some note on the paper cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008), 719724. ##[18] P.P. Zabreiko, Kmetric and Knormed linear spaces: survey, Collect. Math. 48 (1997), 825859.##]
A note on quasi irresolute topological groups
2
2
In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semiconnected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semiopen neighborhood of $e_G$, then $G$ is generated by $V$. Moreover it is proven that a subgroup $H$ of a quasi irresolute topological group $(G,*,tau)$ is semidiscrete if and only if it has a semiisolated point.
1

41
46


T.
Oner
Department of Mathematics, Faculty of Science Mugla Sitk Kocman University, Mugla 48000, Turkey
Department of Mathematics, Faculty of Science
Turkey
onertarkan@gmail.com


A.
Ozek
Department of Mathematics, Graduate School of Natural and Applied Sciences Mugla Sitki Kocman University, Mugla 48000, Turkey
Department of Mathematics, Graduate School
Turkey
alperozek88@gmail.com
Semiopen set
semiclosed set
irresolute mapping
semihomeomorphism
quasi irresolute topological group
FClosedness in Bitopological Spaces
2
2
The purpose of this paper is to introduce the concept of pairwise Fclosedness in bitopological spaces. This space contains both of pairwise strongcompactness and pairwise Sclosedness and contained in pairwise quasi Hclosedness. The characteristics and relationships concerning this new class of spaces with other corresponding types are established. Moreover, several of its basic and important properties are discussed.
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47
53


A. A.
Nasef
Department of Physics and Engineering Mathematics, Faculty of Engineering, KafrElSheikh University, Kafr ElSheikh, Egypt
Department of Physics and Engineering Mathematics,
Egypt
nasefa50@yahoo.com


A.
Azzam
Department of Mathematics, Faculty of Science, Assuit University,
New Valley, Egypt
Department of Mathematics, Faculty of Science,
Egypt
azzam0911@yahoo.com
Fclosed
pairwise Fclosed
pairwise Sclosed
pairwise strongly compact
pairwise quasi Hclosed
pairwise almost cocompact
[[1] G. K. Banerjee, On Pairwise Almost Strongly θcontinuous mappings, Bull. Cal. Math. Soc. 79 (1987), 314 320. ##[2] V. R. Caroll, Hclosure for bitopological spaces, Kyungpook Math. J. 18 (2) (1978), 159165. ##[3] G. I. Chae, D. W. Lee and H. W. Lee, Feebly irresolute functions, Sung Shin W. Univ. Report, 21 (1985), 273280. ##[4] G. I. Chae and D. W. Lee, Fclosed spaces, Kyungpook Math. J. 27 (2) (1987), 127134. ##[5] G. Di. Maio, Bitopological Hclosedness and Sclosedness, Rend. Circ. Mat. Palermo(2) Supp1. No. 12(1986), 231243. ##[6] P. Flether, H. B. Hoyle and W. C. Patty, The comparison of topologies, Duke Math. J., 36 (1969) 325331. ##[7] M. Ganster and A. Kanibir, On Pairwise Sclosed spaces, R and A in General topology, Vol. 15(1997), 129136. ##[8] M. Jeli´c, A decomposition of pairwise continuity, J. Inst. Math. and Comp. Sci. (Math. Ser.), 3(1990), 2529. ##[9] M. Jeli´c, Feebly pcontinuous mappings, Suppl. Rend. Circ. Mat. Palermo(2). 24 (1990), 387397. ##[10] J. C. Kelly, Bitopological spaces, Proc. London Math. Soc., 3 (13) (1963), 7189. ##[11] F. H. Khedr, Properties of pairwise Sclosed spaces, Delta J. Sci., 8 (1984), 18. ##[12] F. H. Khedr, T. Noiri, On pairwise Sclosed spaces, Inst, Math. and Comp. Sci., 4 (1991), 367371. ##[13] Y. W. Kim, Pairwise compactness, Pub. Math. Debrecea 15 (1968), 8790. ##[14] S. S. Kumar, Pairwise αopen, αclosed and αirresolute functions in bitopological spaces, Bull. Inst. Math. Acad. Sinice 21 (1993), 5972. ##[15] S. N. Maheshwari, R. Prasad, Semiopen sets and semicontinuous function in bitopological spaces, Math. Notae, 26 (1977/78), 2937. ##[16] S. N. Maheshwari, U. D. Tapi, Note on some applications of feebly open sets, M. B. J. Univ. of Saugar, (1979). ##[17] A. S. Mashhour, F. H. Khedr, I. A. Hasanein and A. A. Allam, Sclosedness in bitopological spaces, Ann. Soc. Sci. Bruxelles, 96 (1982), 6976. ##[18] M. N. Mukherjee, On pairwise Sclosed bitopological spaces, Internat. J. Math. and Math. Sci. 8(4) (1985), 729745. ##[19] T. Noiri, A note on Fclosed spaces, Kyungpook Math. J. 31 (2) (1991), 269273. ##[20] T. Noiri, A. S. Mashhour, F. H. Khedr and I. A. Hasanein, Strongcompactness in bitopological spaces, Indian J. Math. 25 (1) (1983), 3339. ##[21] J. Porter, J. Thomas, On Hclosed and minimal Hausdroff spaces. Trans. Amer. Math. Soc. 138 (1969), 159170 ##[22] M. K. Singal, S. P. Arya, On almostregular spaces, Glasnik Mat. 4 (1969), 8999. ##[23] M. K. Singal, A. Mathur, On nearlycompact spaces, Boll. UnMatItal. 4 (2) (1969), 702710. ##[24] M. K. Singal, A. R. Singal, Some more separation axioms in bitopological spaces, Ann. Soc. Sci. Bruxelles 84 (1970), 207230. ##[25] T. Thompson, Sclosed spaces, Proc. Amer. Math. Soc. 60 (1976), 335338.##]
Probability of having $n^{th}$roots and ncentrality of two classes of groups
2
2
In this paper, we consider the finitely 2generated groups $K(s,l)$ and $G_m$ as follows:$$K(s,l)=langle a,bab^s=b^la, ba^s=a^lbrangle,\G_m=langle a,ba^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]rangle$$ and find the explicit formulas for the probability of having nthroots for them. Also, we investigate integers n for which, these groups are ncentral.
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55
62


M.
Hashemi
Faculty of Mathematical Sciences, University of Guilan, P.O.Box 4133519141, Rasht, Iran
Faculty of Mathematical Sciences, University
Iran
m_hashemi@guilan.ac.ir


M.
Polkouei
Faculty of Mathematical Sciences, University of Guilan, P.O.Box 4133519141, Rasht, Iran
Faculty of Mathematical Sciences, University
Iran
mikhakp@yahoo.com
Nilpotent groups
$n^{th}$roots
ncentral groups
[[1] C. M. Campbell, P. P. Campel, H. Doostie and E. F. Robertson, Fibonacci length for metacyclian groups. Algebra Colloq. 11 (2004), 215222. ##[2] C. M. Campbell, E. F. Robertson, On a group presentation due to Fox. Canada. Math. Bull. 19 (1967), 247248. ##[3] H. Doostie, M. Hashemi, Fibonacci lengths involving the Wall number K(n). J. Appl. Math. Computing. 20 (2006), 171180. ##[4] A. Sadeghieh, H. Doostie And M. Azadi, Certain numerical results on the Fibonacci length and n throots of Hamiltonian groups. International Mathematical Forum. 39 (2009), 19231938. ##[5] A. Sadeghieh, H. Doostie, The nth roots of elements in finite groups. Mathematical Sciences. 4 (2008), 347356. ##[6] C. Delizia, A. Tortora and A. Abdollahi, Some special classes of nabelian groups. International journal of Group Theory. 1 (2012), 1924.##]
Recognition by prime graph of the almost simple group PGL(2, 25)
2
2
Throughout this paper, every groups are finite. The prime graph of a group $G$ is denoted by $Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite group $H$ with $Gamma(H) = Gamma(G)$, we conclude that $Gcong H$. Until now, it is proved that if $k$ is an odd number and $p$ is an odd prime number, then $PGL(2,p^k)$ is recognizable by prime graph. So if $k$ is even, the recognition by prime graph of $PGL(2,p^k)$, where $p$ is an odd prime number, is an open problem. In this paper, we generalize this result and we prove that the almost simple group $PGL(2,25)$ is recognizable by prime graph.
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63
66


A.
Mahmoudifar
Department of Mathematics, TehranNorth Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, TehranNorth Branch,
Iran
alimahmoudifar@gmail.com
linear group
Almost simple group
prime graph
element order
Frobenius group
[[1] Z. Akhlaghi, M. Khatami and B. Khosravi, Characterization by prime graph of PGL(2, pk) where p and k are odd, Int. J. Algebra Comp. 20 (7) (2010), 847873. ##[2] A. A. Buturlakin, Spectra of Finite Symplectic and Orthogonal Groups, Siberian Advances in Mathematics, 21 (3) (2011), 176210. ##[3] G. Y. Chen, V. D. Mazurov, W. J. Shi, A. V. Vasil’ev and A. Kh. Zhurtov, Recognition of the finite almost simple groups P GL2(q) by their spectrum, J. Group Theory 10(1) (2007), 7185. ##[4] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Oxford University Press, Oxford, 1985. ##[5] M. A. Grechkoseeva, On element orders in covers of finite simple classical groups, J. Algebra, 339 (2011), 304319. ##[6] D. Gorenstein, Finite Groups, Harper and Row, New York, 1968. ##[7] M. Hagie, The prime graph of a sporadic simple group, Comm. Algebra 31(9) (2003), 44054424. ##[8] G. Higman, Finite groups in which every element has prime power order, J. London Math. Soc. 32 (1957), 335–342. ##[9] M. Khatami, B. Khosravi and Z. Akhlaghi, NCFdistinguishability by prime graph of P GL(2, p), where p is a prime, Rocky Mountain J. Math. (to appear). ##[10] B. Khosravi, nRecognition by prime graph of the simple group P SL(2, q), J. Algebra Appl. 7(6) (2008), 735748. ##[11] B. Khosravi, B. Khosravi and B. Khosravi, 2Recognizability of P SL(2, p2 ) by the prime graph, Siberian Math. J. 49(4) (2008), 749–757. ##[12] B. Khosravi, B. Khosravi and B. Khosravi, On the prime graph of P SL(2, p) where p > 3 is a prime number, Acta. Math. Hungarica 116(4) (2007), 295307. ##[13] R. KoganiMoghadam and A. R. Moghaddamfar, Groups with the same order and degree pattern, Sci. China Math. 55 (4) (2012), 701720. ##[14] A. S. Kondrat’ev, Prime graph components of finite simple groups, Math. USSRSB. 67(1) (1990), 235247. ##[15] A. Mahmoudifar and B. Khosravi, On quasirecognition by prime graph of the simple groups A + n (p) and A − n (p), J. Algebra Appl. 14(1) (2015), (12 pages). ##[16] A. Mahmoudifar and B. Khosravi, On the characterization of alternating groups by order and prime graph, Sib. Math. J. 56(1) (2015), 125131. ##[17] A. Mahmoudifar, On finite groups with the same prime graph as the projective general linear group PGL(2, 81), (to appear). ##[18] V. D. Mazurov, Characterizations of finite groups by sets of their element orders, Algebra Logic 36(1) (1997), 2332. ##[19] A. R. Moghaddamfar, W. J. Shi, The number of finite groups whose element orders is given, Beitr¨age Algebra Geom. 47(2) (2006), 463479. ##[20] D. S. Passman, Permutation groups, W. A. Bengamin, New York, 1968. ##[21] A. V. Zavarnitsine, Fixed points of large primeorder elements in the equicharacteristic action of linear and unitary groups, Sib. Electron. Math. Rep. 8 (2011), 333340.##]