013494   Shrivastava S (Mathematics Dep, Indian Institute of Science Education and Research, Bhopal-462 066, Email: saurabhk@iiserb.ac.in) : Weighted and vector-valued inequalities for one-sided maximal functions. Proc Math Sci 2016, 126(3), 359-80.

In this paper, we study weighted and vector-valued inequalities for one-sided maximal functions. In particular, we give a new proof of lr-valued extension of weighted L^p-inequalities for one-sided maximal functions. In the process, we prove an analogue of the well-known Fefferman-Stein's weighted lemma in the context of one-sided maximal functions. Further, we also study l_r-valued extension of the lemma.

17 ref

013493   Shattuck M (Mathematics Dep, , Tennessee, 37996 Knoxville, TN, USA, Email: shattuck@math.utk.edu) : Generalized r-Lah numbers. Proc Math Sci 2016, 126(4), 461-78.

In this paper, we consider a two-parameter polynomial generalization, denoted by G_a,b(n,k;r), of the r-Lah numbers which reduces to these recently introduced numbers when a=b=1. We present several identities for G_a,b(n,k;r) that generalize earlier identities given for the r-Lah and r-Stirling numbers. We also provide combinatorial proofs of some earlier identities involving the r-Lah numbers by defining appropriate sign-changing involutions. Generalizing these arguments yields orthogonality-type relations that are satisfied by G_a,b(n,k;r).

20 ref

013492   Sareen J K;Rana M (School of Mathematics, Thapar Univ, Patiala, Punjab-147 001, Email: mrana@thapar.edu) : Combinatorics of tenth-order mock theta functions. Proc Math Sci 2016, 126(4), 549-56.

In this paper, we provide the combinatorial interpretations of two tenth order mock theta functions which appeared in some identities given in Ramanujan's lost notebook ((1988) Narosa Publishing House, New Delhi).

1 table, 11 ref

013491   Sahoo B K (School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, Jatni-752 050, Email: bksahoo@niser.ac.in) : Existence of non-abelian representations of the near hexagon Q(5, 2) ⊗ Q(5, 2). Proc Math Sci 2016, 126(2), 143-51.

In [5], a new combinatorial model with four types of points and nine types of lines of the slim dense near hexagon Q(5, 2) ⊗ Q(5, 2) was provided and it was then used to construct a non-abelain representation of Q(5, 2) ⊗ Q(5, 2) in the extraspecial 2-group 2¹⁺¹⁸_-. In this paper, we give a direct proof for the existence of a non-abelian representation of Q(5, 2) ⊗ Q(5, 2) in 2_-¹⁺¹⁸.

11 ref

013490   Saha B (NO, Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600 113, Email: biswajyoti@imsc.res.in) : Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions. Proc Math Sci 2016, 126(3), 295-303.

For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the sum ∑_n≤N f(n) with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan's totient functions.

16 ref

013489   Roy A;Zaharescu A;Zaki M (Mathematics Dep, Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA, Email: roy22@illinois.edu) : Some indentities involving convolutions of dirichlet characteras and the mobius function. Proc Math Sci 2016, 126(1), 21-33.

In this paper, here is to present some identities involving convolutions of Dirichlet characters and the Mobius function, which are related to a well known identity of Ramanujan, Hardy and Littlewood.

1 table, 16 ref

013488   Raza M A;Rehman N U (Mathematics Dep, Aligarh Muslim Univ, Aligarh-202 002, Email: arifraza03@gmail.com) : On prime and semiprime rings with generalized derivations and non-commutative banach algebras. Proc Math Sci 2016, 126(3), 389-98.

R is supposed to be a prime ring of characteristic different from 2 and mm a fixed positive integer. If RR admits a generalized derivation associated with a nonzero deviation dd such that [F(x),d(y)]_m=[x,y] for all x, y in some appropriate subset of R, then R is commutative. Moreover, we also examine the case R is a semiprime ring. Finally, we apply the above result to Banach algebras, and we obtain a non-commutative version of the Singer-Werner theorem.

28 ref

013487   Rao T S S R K (Theoretical Statistics and Mathematics Div, Indian Statistical Institute, R. V. College P.O., Bangalore-560 059, Email: srin@fulbrightmail.org) : Extremely strict ideals in banach spaces. Proc Math Sci 2016, 126(3), 381-7.

Motivated by the notion of an ideal introduced by Godefroy et al. (Studia Math.) 104 (1993) 13-59), in this article, we introduce and study the notion of an extremely strict ideal. For a Poulsen simplex KK, we show that the space of affine continuous functions on KK is an extremely strict ideal in the space of continuous functions on KK. For injective tensor product spaces, we prove a cancelation theorem for extremely strict ideals. We also exhibit non-reflexive Banach spaces which are not strict ideals in their fourth dual.

12 ref

013486   Rani R;Rakesh Kumar;Nagaich R K (Mathematics Dep, College Univ, Ghanur, Punjab-148 033, Email: nagaich58rakesh@gmail.com) : Axioms of spheres in lightlike geometry of submanifolds. Proc Math Sci 2016, 126(4), 613-21.

The authors prove that if an indefinite Kaehler manifold M with lightlike submanifolds satisfies the axioms of holomorphic 2r-spheres, axioms of holomorphic 2r-planes, axioms of transversal r-spheres and axioms of transversal r-planes, then it is an indefinite complex space form.

10 ref

013485   Prasad P (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: prasad@math.iisc.ernet.in) : Ray equations of a weak shock in a hyperbolic system of conservation laws in multi-dimensions. Proc Math Sci 2016, 126(2), 199-206.

In this paper we give a complete proof of a theorem, which states that 'for a weak shock, the shock ray velocity is equal to the mean of the ray velocities of nonlinear wavefronts just ahead and just behind the shock, provided we take the wavefronts ahead and behind to be instantaneously coincident with the shock front. Similarly, the rate of turning of the shock front is also equal to the mean of the rates of turning of such wavefronts just ahead and just behind the shock'. A particular case of this theorem for shock propagation in gasdynamics has been used extensively in applications. Since it is useful also in other physical systems, we present here the theorem in its most general form.

9 ref

013484   Pathak R S;Singh A (DST Centre for Interdisciplinary Mathematical Sciences, Faculty of Sci, Banaras Hindu Univ, Varanasi-221 005, Email: mathdras@gmail.com) : Wavelet transform of generlized functions in K'{M_p} spaces. Proc Math Sci 2016, 126(2), 213-26.

Using convolution theory in K{M_p}K{Mp} space we obtain bounded results for the wavelet transform. Calderon-type reproducing formula is derived in distribution sense as an application of the same. An inversion - 27 - formula for the wavelet transform of generalized functions is established.

14 ref

013483   Okagbue H I;Adamu M O;Opanuga A A;Oguntunde P E (Mathematics Dep, Convenant Univ, Canaanland, Ota, Nigeria, Email: hilary.okagbue@convenantuniversity.edu.ng) : Boundary properties of bounded interval support probability distributions. Far East J mathl Sci 2016, 99(9), 1309-23.

This paper explores the properties of probability distributions as the random variables that defined those distributions approaching their bounded interval support. The models under study are: Kumaraswamy, Kumaraswamy Kumaraswamy, Kumaraswamy (1, b) with beta (1, b), and Kumaraswamy (a, 1) with beta (a, 1) distributions. The behavior of the probability density function of the random variables differs greatly at both the lower and the upper boundary points of the support. The results displayed in this research are the same for all the aforementioned pdfs and their cumulative distribution functions, survival functions and hazard functions. The results agreed with some well-known results in the literature. The probability density function, cumulative distribution function, survival function and hazard function approximate to the different values at the boundary points as the support approaches the boundary points.

9 table, 23 ref

013482   Moghaddam M R R;Motaghi E;Rostamyari M A (Centre of Excellence in Analysis on Algeraic Structures, Ferodowsi Univ of Mashhad and Dep of Mathematics, Khayyam Univ, Mashhad, Iran) : Probability that a pair of group elements are autoconjugate. Proc Math Sci 2016, 126(1), 61-8.

Let g and h be arbitrary elements of a given finite group G. Then g and h are said to be autoconjugate if there exists some automorphism α of G such that h = g^α. In this article, we construct some sharp bounds for the probability that two random elements of G are autoconjugate, denoted by P_a(G). It is also shown that P_a(G)|G| depends only on the autoisoclinism class of G.

17 ref

013481   Mehta V B;Subramanian S (School of Mathematics, Tata Institute of Fundamental Research, Navy Nagar, Mumbai-400 005, Email: subramnn@math.tifr.res.in) : Non-properness of the functor of F-trivial bundles. Proc Math Sci 2016, 126(2), 179-86.

Authors study the properness of the functor of F-trivial bundles by relating it to the base change question for the fundamental group scheme of Nori.

18 ref

013480   Mckibben M A (Mathematics Dep, West Chester Univ of Pennsylvania, West chester, PA 19383, U.S.A, Email: mmckibben@wcupa.edu) : General existence results for abstract McKean -Vlasov stochastic equations with variable delay. Far East J mathl Sci 2016, 99(9), 1335-70.

Results concerning the global existence and uniqueness of mild solutions for a class of first-order abstract stochastic integro-differential equations with variable delay in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state - 26 - of the solution at time t, but also on the corresponding probability distribution at time t are established. The classical Lipschitz is replaced by a weaker so-called Caratheodory condition under which we still maintain uniqueness. The time-dependent case is discussed, as well as an extension of the theory to the case of a nonlocal initial condition. Two examples illustrating the applicability of the general theory are provided.

40 ref

013479   Manadee P;Viriyapong C;Boonpok C (Mathematics and Applied Research Unit, Mathematics Dep, Mahasarakham Univ, Maha Sarakham-44150, Thailand, Email: alchemist_ph@hotmail.com) : Regular weakly closed sets in generalised topological spaces. Far East J mathl Sci 2016, 99(9), 1371-82.

The aim of this article is to introduce the concept of μ-regular weakly closed (briefly, μrw-closed) sets in generalized topological spaces and investigate some of their properties. In particular, a characterization of a μrw-T_1/2 space, i.e., every μrw-closed set in X is μ-closed, have been given. Furthermore, the notion of μ-regular weakly closed sets with respect to an ideal in a generalized topological space have been studied here.

15 ref

013478   Loc N Q (Faculty of Mathematics and Computer Science, Hanoj National Univ of Education, 136 Xuan Thuy Road, Honoi, Vietnam, Email: nqloc@hnue.edu.vn) : On the normality of orbit closures which are hypersurfaces. Proc Math Sci 2016, 126(1), 35-42.

Let N be a quiver representation with non-zero admissible annihilator. In this paper, we prove the normality of the orbit closure O_N when it is a hypersurface. The result thus gives new examples of normal orbit closures of quiver representations.

9 ref

013477   Lee M Y (Mathematics Dep, Dankook Univ, Cheonan 330-714, Korea, Email: leemy@dankook.ac.kr) : Characterizations of the power distribution by record values. Proc Math Sci 2016, 126(2), 283-7.

Let {X_n,n ≥ 1} be a sequence of i.i.d. random variables which has absolutely continuous distribution function F(x) with probability density function f(x) and F(0)=0. Assume that X_n belongs to the class C*₁ or C₂. Then X_k has the power distribution if and only if X_k and X_L(n+1)/X_L(n) or X_L(n+1)/X_L(n) and X_L(n)/X_L(n-1) are identically distributed, respectively. Suppose that X_n belongs to the class C₃. Also, X_k has the power distribution if and only if X_L(n+1) and X_L(n). V are identically distributed, where V is independent of X_L(n) and X_L(n+1) and is distributed as X_n's.

4 ref

013476   Kusmayadi T A;Kuntari S;Rahmadi D;Lathifah F A (Mathematics Dep Faculty of Mathematics and Natural Sciences, Sebelas Market Univ, Surakarta-57126, Indonesia, Email: kuntari.uns@gmail.com) : On the strong metric dimension of some related wheel graph. Far East J mathl Sci 2016, 99(9), 1325-34.

Let G be a connected simple graph with vertex set K(G) = {ν₁, ν₂, ..., ν_n} and edge set E(G) = {e₁, e₂, ..., e_n}. A vertex s is said to strongly resolve a pair of - 25 - vertices u and v if there exists some shortest v - s path containing u or some shortest u - s path containing v. A set S is called a strong resolving set for G if some vertices of S strongly resolve every pair of distinct vertices from G. Strong metric dimension is the smallest cardinality of a strong resolving set denoted by s dim(G). In this paper, we determine the strong metric dimensions of some graphs, namely, sunflower, t-fold wheel, helm, and friendship.

4 illus, 8 ref

013475   Kuang M;Huang G;Deng H (College of Mathematics and Computer Science, Hunan Normal Univ, Changsha, Hunan 410081, People's Republic of China, Email: hydeng@hunnu.edu.cn) : Some sufficient conditions for Hamiltonian property in terms of Wiener-type invariants. Proc Math Sci 2016, 126(1), 1-9.

The Wiener-type invariants of a simple connected graph G = (V, E) can be expressed in terms of the quantities W_f=Σ_{u,v}⊆V f(d_G(u,v)) for various choices of the function f(x), where d_G(u, v) is the distance between vertices u and v in G. In this paper, we give some sufficient conditions for a connected graph to be Hamiltonian, a connected graph to be traceable, and a connected bipartite graph to be Hamiltonian in terms of the Wiener-type invariants.

18 ref

013474   Krishnakumari B;Venkatakrishnan Y B; Krzywkowski M (Mathematics Dep, Sastra Univ, Tanjore-613 401, Email: marcin.krzywkowski@gmail.com) : On trees with total domination number equal to edge-vertex domination number plus one. Proc Math Sci 2016, 126(2), 153-7.

An edge e ∈ E(G) dominates a vertex v ∈ V(G) if e is incident with v or e is incident with a vertex adjacent to v. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is edge-vertex dominated by an edge of D. The edge-vertex domination number of a graph G is the minimum cardinality of an edge-vertex dominating set of G. A subset D ⊆ V(G) is a total dominating set of GG if every vertex of G has a neighbor in D. The total domination number of G is the minimum cardinality of a total dominating set of G. We characterize all trees with total domination number equal to edge-vertex domination number plus one.

4 ref

013473   Kodiyalam V;Tupurani S (NO, The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, Email: stupurani@gmail.com) : Generators for finite depth subfactor planar algebras. Proc Math Sci 2016, 126(2), 235-40.

Authors show that a subfactor planar algebra of finite depth k is generated by a single s-box, for s ≤ min{k+4,2k}.

3 ref

013472   Khosravi B;Khosravi B;Khosravi B (Pure Math. Dep, Faculty of Math. and Computer Sci., Amirkabir Univ of Technology (Tehr, 424, Hafez Ave., Tehran 15914, Iran, Email: khosravibbb@yahoo.com) : New characterization for some extensions of PSL (2, q) for some q by some character degrees. Proc Math Sci 2016, 126(1), 49-59.

In [22] (Tong-Viet H P, Simple classical groups of Lie type are determined by their character degrees, J. Algebra, 357 (2012) 61-68), the following question arose: Which groups can be uniquely determined by the structure of their complex group algebras? The authors in [12] (Khosravi B et al., Some extensions of PSL(2, p²) are uniquely determined by their complex group algebras, Comm. Algebra, 43(8) (2015) 3330-3341) proved that each extension of PSL(2, p²) of order 2|PSL(2, p²)| is uniquely determined by its complex group algebra. In this paper we continue this work. Let p be an odd prime number and q = p or q = p³. Let M be a finite group such that |M| = h|PSL(2,q), where h - 24 - is a divisor of |Out(PSL(2, q))|. Also suppose that M has an irreducible character of degree q and 2p does not divide the degree of any irreducible character of M. As the main result of this paper we prove that M has a unique nonabelian composition factor which is isomorphic to PSL(2, q). As a consequence of our result we prove that M is uniquely determined by its order and some information on its character degrees which implies that M is uniquely determined by the structure of its complex group algebra.

26 ref

013471   Kharisudin I;Rosadi D;Abdurakhman;Suhartono (Mathematics Dep, Gadjah Mada Univ, Indonesia, Email: dedirosadi@ugm.ac.id ) : The asymptotic property of the sample generalized codifference function of stable MA (1). Far East J mathl Sci 2016, 99(9), 1297-1308.

In this paper, we obtain certain results related to the generalized codifference function of symmetric α-stable moving average, of order 1 (SαS MA(1)). Generalized codifference function as a dependence measure for stationary processes with infinite variance has been proposed as a generalization of the autocorrelation function. We derive the limiting distribution of the sample codifference function, when underlying model is MA(1) with symmetric α-stable innovation.

8 ref

013470   Kathuria L;Raka M (NO, Centre for Advanced in Mathematics, Panjab Univ, Chandigarh-160 014, Email: mraka@pu.ac.in) : On conjectures of Minkowski and Woods for n = 9. Proc Math Sci 2016, 126(4), 501-48.

Let Rⁿ be the n-dimensional Euclidean space with O as the origin. Let Λ be a lattice of determinant 1 such that there is a sphere |X|<60>R which contains no point of Λ other than O and has nn linearly independent points of Λ on its boundary. A well known conjecture in the geometry of numbers asserts that any closed sphere in RnRn of radius √n/4 contains a point of Λ. This is known to be true for n ≤ 8. Here we prove a more general conjecture of Woods for n=9 from which this conjecture follows in R⁹. Together with a result of McMullen (J. Amer. Math. Soc. 18 (2005) 711-734), the long standing conjecture of Minkowski follows for n=9.

1 table, 21 ref

013469   Kasilingam R (Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata-700 108, Email: rameshkasilingam.iitb@gmail.com) : Classification of smooth structures on a homotopy complex projective space. Proc Math Sci 2016, 126(2), 277-81.

This is to classify, up to - 23 - diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective nn-space CPⁿ, where n=3 and 4. Let M²ⁿ be a closed smooth 2n-manifold homotopy equivalent to CPⁿ. We show that, up to diffeomorphism, M⁶ has a unique differentiable structure and M⁸ has at most two distinct differentiable structures. We also show that, up to concordance, there exist at least two distinct differentiable structures on a finite sheeted cover N²ⁿ of CPⁿ for n = 4, 7 or 8 and six distinct differentiable structures on N¹⁰.

10 ref

013468   Karzywkowski M;Mojdeh D A;Raoofi M (Pure and Applied Mathematics Dep, Johannesburg Univ, Johannesburg, South Africa, Email: krzywkowski@gmail.com) : Outer-2-independent domination in graphs. Proc Math Sci 2016, 126(1), 11-20.

We initiate the study of outer-2-independent domination in graphs. An outer-2-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a neighbor in D and the maximum vertex degree of the subgraph induced by V(G)D is at most one. The outer-2-independent domination number of a graph G is the minimum cardinality of an outer-2-independent dominating set of G. We show that if a graph has minimum degree at least two, then its outer-2-independent domination number equals the number of vertices minus the 2-independence number. Then we investigate the outer-2-independent domination in graphs with minimum degree one. We also prove the Vizing-type conjecture for outer-2-independent domination and disprove the Vizing-type conjecture for outer-connected domination.

4 ref

013467   Jee D J;Lee T Y;Zhi-Wei Leon N (Mathematics Dep, Statics and Computing, NUS High School of Mathematics and Science, 20 Clementi Avenue 1, Singapore 129957, Republic of Singapore, Email: h0910083@nhsingh.edu.sg) : Summation due to ramanujan revisited. Proc Math Sci 2016, 126(2), 207-12.

We employ Hardy's regularly convergent double series to refine an argument of Nanjundiah [7]. In particular, we evaluate some alternating series.

9 ref

013466   Itokawa Y;Shiohama K;Tiwari B (Information and Communication Engineering Dep, Fukuoka Institute of Technology, Fukuoka 811-0295, Japan, Email: itokawa@fit.ac.jp) : Strictly convex functions on complete finsler manifolds. Proc Math Sci 2016, 126(4), 623-7.

The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.

12 ref

013465   He X;Yang Y (Mathematics Dep, Kunming Univ, Kunming, Yunnan-650 214, P.R. China, Email: hexiumei2004@163.com) : Existence of sign changing solutions for generalized Quasilinear - 22 - Schrodinger equations. Far East J mathl Sci 2016, 99(9), 1283-95.

In this paper, we study the following generalized quasilinear Schrodinger equations: -div(g²(u)∇u) + g(u)g'(u)|∇u|² = f(x,u) in Ω, and u = 0 on ∂∇, where ∇ is a bounded smooth domain of R^N, g : R → R⁺ is a C¹ even function, g(0) = 1 and g'(s) ≥ 0 for all s ≥ 0. Under some suitable conditions, we prove that the equation is sign-changing by using variational methods.

12 ref

013464   Hancl J;Haddley A;Lertchoosakul P;Nair R (Mathematics and Center for Excellence IT4Innovation Dep, UO Div, Institute of Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic, Email: nair@liv.ac.uk) : Quantitative metric theory of continued fractions. Proc Math Sci 2016, 126(2), 167-77.

Quantitative versions of the central results of the metric theory of continued fractions were given primarily by C. De Vroedt. In this paper we give improvements of the bounds involved.

17 ref

013463   Hadijirezaei S (Mathematics Dep, Valir-e-Asr Univ of Rafsanjan, P.O.Box 7718897111, Rafsanjan, Iran, Email: s.hajirezaei@vru.ac.ir) : When does the torsion submodule split off?. Far East J mathl Sci 2016, 99(9), 1409-20.

Let (R, P) be a Noetherian local ring and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M. The main result of this paper asserts that when I(M) = P, T(M) is a direct summand of M if and only if T(M) ⊆ PM. Also, we show that if T(M) ⊆ PM, then there exists some positive integer k such that T(P^kM] is a direct summand of P^kM.

17 ref

013462   Gao P (School of Mathematics and Statistics, and Center for Mathematics and I, Northeast Normal Univ, Changchun 130024, People's Republic of China, Email: gaopengjilindaxue@126.com) : Null controllability of the viscous Camassa-Holm equation with moving control. Proc Math Sci 2016, 126(1), 99-108.

In this paper, here is to study the null controllability of the viscous Camassa-Holm equation on the one-dimensional torus. By using a moving distributed control, we obtain that the system is null controllable for a given data with certain regularity.

17 ref

013461   Gadgil S;Kulkarni D (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: gadgil@math.iisc.ernet.in) : Relative symplectic caps, 4-genus and fibered knots. Proc Math Sci 2016, 126(2), 261-75.

This is to prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterion for Stein fillability and use these to study the 4-genus of knots. More precisely, suppose we have a symplectic 4-manifold X with convex boundary and a symplectic surface Σ in X such that ∂Σ is a transverse knot in ∂X. In this paper, we prove that there is a closed symplectic 4-manifold Y with a closed symplectic surface S such that (X, Σ) embeds into (Y, S) symplectically. As a consequence we obtain a relative version of the symplectic Thom conjecture. We also prove a relative version of the sufficiency part of Giroux's criterion for Stein fillability, namely, we show that a fibered knot whose mondoromy is a product of positive Dehn twists bounds a symplectic surface in a Stein filling. We use this to study 4-genus of fibered knots in S³. Further, we give a criterion for quasipositive fibered knots to be strongly quasipositive.

4 illus, 21 ref

013460   Fu B (Applied Mathematics Dep, Shanghai Finance Univ, Shanghai-201 209, Email: fuby@shfe.edu.cn) : Approximation properties of fine hyperbolic graphs. Proc Math Sci 2016, 126(2), 227-34.

In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa's to prove that a fine hyperbolic graph has the metric invariant translation approximation property.

12 ref

013459   Farahani M R;PradeepKumar R;kanna M R R;Wang S (Applied Mathematics Dep, Iran Univ of Science and Technology (IUST) Narmak, Tehran, Iran, Email: mrfarahani88@gmail.com) : Vertec szeged index of titania carbon nanotubes Tio₂ (m,n). Int J pharm Sci Res 2016, 7(9), 3734-41.

Let G = (V,E) be a simple connected molecular graph in chemical graph theory, where the vertex set and edge set of G denoted by V(G) and E(G) respectively and its vertices correspond to the atoms and the edges correspond to the bonds. A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. In this paper, the vertex Szeged index of Titania carbon Nanotubes TiO2(m,n) is computed.

32 ref

013458   Eskal C;Ekici N (Mathematics Dep, Osmaniye Korkut Ata Univ, 80000 Osmaniye, Turkey, Email: nekici@cu.edu.tr) : Test element of direct sums and free products of free lie algebras. Proc Math Sci 2016, 126(1), 43-8.

Here is to give a characterization of test elements of a direct sum of free Lie algebras in terms of test elements of the factors. In addition, we construct certain types of test elements and we prove that in a free product of free Lie algebras, product of the homogeneous test elements of the factors is also a test element.

13 ref

013457   Duan N (School of Science, Jiangnan Univ, Wuxi, 21422, China, Email: 123332453@qq.com) : Optimal control problem for the extended Fisher-Kolmogorov equation. Proc Math Sci 2016, 126(1), 109-23.

In this paper, the optimal control problem for the extended Fisher-Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.

26 ref

013456   Dolai D R;Mallick A (NO, The Institute of Mathematical Sciences, Taramani, Chennai-600 113, Email: anishm@imsc.res.in) : Eigenfunction statistics for anderson model with holder continuous single site potential. Proc Math Sci 2016, 126(4), 577-89.

We consider random Schrodinger operators on l²(Z^d) with α-Holder continuous (0 <60> α ≤ 1) single site distribution. In localized regime, we study the distribution of eigenfunctions in space and energy simultaneously. In a certain scaling limit, we prove limit points are Poisson.

19 ref

013455   Dey R (NO, International Centre for Theoretical Sciences (ICTS)-TIFR, Survey No. 151, Shivakote, Hesaraghatta, Bangalore-560 089, Email: rukmini.dey@gmail.com) : Ramanujan's identities, minimal surfaces and solitons. Proc Math Sci 2016, 126(3), 421-31.

Using Ramanujan's identities and the Weierstrass--Enneper representation of minimal surfaces, and the analogue for Born--Infeld solitons, we derive further nontrivial - 20 - identities.

7 ref

013454   Deshpande P (NO, Chemical Mathematical Institute, H1 SIPCOT IT Park, Siruseri Chennai-603 103, Email: pdeshpande@cmi.ac.in) : On arrangements of pseudohyperplanes. Proc Math Sci 2016, 126(3), 399-420.

To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completely determined by the oriented matroid. In this paper we study arrangements of pseudohyperplanes; they correspond to non-realizable oriented matroids. These arrangements arise as a consequence of the Folkman--Lawrence topological representation theorem. We propose a generalization of the complexification process in this context. In particular we construct a space naturally associated with these pseudo-arrangements which is homeomorphic to the complexified complement in the realizable case. Further, we generalize the classical theorem of Salvetti and show that this space has the homotopy type of a cell complex defined in terms of the oriented matroid.

3 illus, 29 ref

013453   Chadwick E;Hatam A;Kazem S (School of Computing Sciences and Engineering, The Univ of Salford, Salford M5 4WT, United Kingdom, Email: SaeedKazem@aut.ac.ir) : Exponential function method for solving nonlinear ordinary differential equations with constant coefficients on a semi-infinite domain. Proc Math Sci 2016, 126(1), 79-97.

A new approach, named the exponential function method (EFM) is used to obtain solutions to nonlinear ordinary differential equations with constant coefficients in a semi-infinite domain. The form of the solutions of these problems is considered to be an expansion of exponential functions with unknown coefficients. The derivative and product operational matrices arising from substituting in the proposed functions convert the solutions of these problems into an iterative method for finding the unknown coefficients. The method is applied to two problems: viscous flow due to a stretching sheet with surface slip and suction; and mageto hydrodynamic (MHD) flow of an incompressible viscous fluid over a stretching sheet. The two resulting solutions are compared against some standard methods which demonstrates the validity and applicability of the new approach.

5 illus, 4 tables, 26 ref

013452   Caristi G;Stoka M (Economics Dep, Univ of Messina, Via dei verdi, 75 98122, Messina, Italy, Email: gcaristic@unime.it) : Problem of geometric probabilities for a rectangular lattice with obstacles and non uniform distribution. Far East J mathl Sci 2016, 99(9), 1391-8.

In this paper, we consider a lattice with cell represented in Figure 1 and we compute the probability that a segment with constant length and random direction of non-uniform distribution intersects a side of lattice.

2 illus, 9 ref

013451   Caristi G;Stoka M (Economics Dep, Univ of Messina, Via de Verdi, 75, 98122, Messina, Italy, Email: gcaristi@unime.it ) : Laplace type problems for a triangular lattice and non uniform distribution. Far East J mathl Sci 2016, 99(9), 1383-90.

In this paper, we consider a lattice with fundamental cell an isosceles triangle and we compute the probability that a random segment with exponential or γ (2) distribution of constant length intersects a side of the lattice.

2 illus, 5 ref

013450   Cardinali I;Sastry N S N (Information Engineering and Mathematics Dep, Siena Univ, Via Roma 56, I-53100, Siena, Italy, Email: nsastry@isibang.ac.in) : Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order. Proc Math Sci 2016, 126(4), 591-612.

Let Q₀ be the classical generalized quadrangle of order q = 2ⁿ(n≥2) arising from a non-degenerate quadratic form in a 5-dimensional vector space defined over a finite field of order q. We consider the rank two geometry <67> having as points all the elliptic ovoids of Q₀ and as lines the maximal pencils of elliptic ovoids of Q₀ pairwise tangent at the same point. We first prove that <67> is isomorphic to a 2-fold quotient of the affine generalized quadrangle QQ₀, where Q is the classical (q,q²)-generalized quadrangle admitting Q₀ as a hyperplane. Further, we classify the cliques in the collinearity graph Γ of X. We prove that any maximal clique in Γ is either a line of <67> or it consists of 6 or 4 points of <67> not contained in any line of X, accordingly as nn is odd or even. We count the number of cliques of each type and show that those cliques which are not contained in lines of <67> arise as subgeometries of Q defined over F₂.

6 illus, 12 ref

013449   Biswas I;Hogadi A (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400 005, Email: indranil@math.tifr.res.in) : Unitary representations of the fundamental group of orbifolds. Proc Math Sci 2016, 126(4), 557-75.

Let X be a smooth complex projective variety of dimension n and L an ample line bundle on it. There is a well known bijective correspondence between the isomorphism classes of polystable vector bundles E on X with c₁(E) = 0 = c₂(E). c₁(L)^n-2 and the equivalence classes of unitary representations of π₁(X). We show that this bijective correspondence extends to smooth orbifolds.

16 ref

013448   Bhosle U N;Singh S (NO, Indian Institute of Science, Bangalore-560 012, Email: usnabh07@gmail.com) : Weak point property and sections of picard bundles on a compactified Jacobian over a nodal curve. Proc Math Sci 2016, 126(3), 329-39.

We show that the compactified Jacobian (and its desingularization) of an integral nodal curve Y satisfies the weak point property and the Jacobian of Y satisfies the diagonal property. We compute some cohomologies of Picard bundles on the compactified Jacobian and its desingularization

12 ref

013447   Bhatt S J (Center for Interdisciplinary Studies in Science and Technology (CISST), Sardar Patel Univ, Vallabh Vidyanagar-388 120, Email: subhashbbhaib@gmail.com) : Smooth Frechet subalgebras of C-algebras defined by first order differential seminorms. Proc Math Sci 2016, 126(1), 125-41.

The differential structure in a C*-algebra defined by a dense Frechet subalgebra whose topology is defined by a sequence of differential seminorms of order 1 is investigated. This includes differential Arens-Michael decomposition, spectral invariance, closure under functional calculi as well as intrinsic spectral description. A large number of examples of such Frechet algebras are exhibited; and the smooth structure defined by an unbounded self-adjoint Hilbert space operator is discussed.

18 ref

013446   Basak B (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: biplab10@math.iisc.ernet.in) : Algorithmic approach to construct crystallizations of 3-manifolds from presentations of fundamental groups. Proc Math Sci 2016, 126(4), 629-53.

We have defined the weight of the pair (<193>S | R<209>, R) for a given presentation <193>S | R<209> of a group, where the number of generators is equal to the number of relations. We present an algorithm to construct crystallizations of 3-manifolds whose fundamental group has a presentation with two generators and two relations. If the weight of (<193>S | R<209>, R) is n, then our algorithm constructs all the nn-vertex crystallizations which yield (<193>S|R<209>,R). As an application, we have constructed some new crystallizations of 3-manifolds. We have generalized our algorithm for presentations with three generators and a certain class of relations. For m ≥ 3 and m ≥ n ≥ k ≥ 2, our generalized algorithm gives a 2(2m+2n+2k-6+δ²_n+δ²< v>k-vertex crystallization of the closed connected orientable 3-manifold M<193>m,n,k<209> having fundamental group <193>x₁,x₂,x₃ | x^m₁ = xⁿ₂ = x^k₃ = x₁ x₂ x₃<209>. These crystallizations are minimal and unique with respect to the given presentations. If 'n = 2' or 'k ≥ 3 and m ≥ 4' then our crystallization of M<193>m,n,k<209> is vertex-minimal for all the known cases.

8 illus, 19 ref

013445   Balodi M;Huang H L;Kumar S D (Mathematics Dep, Motilal Nehru National Institute of Technology, Allahabad-211 004, Email: mamta.balodi@gmail.com) : Diamond lemma for the group graded quasi-algebras. Proc Math Sci 2016, 126(3), 341-52.

Let G be a group. We prove that every expression in a G-graded quasialgebra can be reduced to a unique irreducible form and the irreducible words form abasis for the quasi-algebra. The result obtained is applied to some interesting classes of group graded quasi-algebras like generalized octonions.

11 ref