35 results
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2. Coverings and crossed modules of topological groups with operations
- Author
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Osman Mucuk and Tunçar Şahan
- Subjects
Large class ,Pure mathematics ,Fundamental group ,General Mathematics ,Crossed module ,Morphism ,18D35, 22A05, 57M10 ,Simply connected space ,FOS: Mathematics ,Algebraic Topology (math.AT) ,Mathematics - Algebraic Topology ,Topological group ,Algebraic number ,Equivalence (formal languages) ,Covering groups,universal cover,crossed module,group with operations,topological groups with operations ,Mathematics - Abstract
It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic group $G$. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also give the cover of crossed modules within topological groups with operations., Comment: 15 pages, research paper, LaTeX2e, xypic
- Published
- 2015
3. On Condition $(PWP)_{w}$ for $S$-posets
- Author
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Xingliang Liang and Yanfeng Luo
- Subjects
Combinatorics ,Mathematics::Combinatorics ,Condition $(PWP)_{w}$,$S$-poset,Rees factor $S$-poset,direct product ,General Mathematics ,Algebra over a field ,Arithmetic ,Direct product ,Mathematics - Abstract
Golchin and Rezaei (Commun Algebra 2009; 37: 1995--2007) introduced the weak version of Condition $(PWP)$ for $S$-posets, called Condition $(PWP)_{w}$. In this paper, we continue to study this condition. We first present a necessary and sufficient condition under which the $S$-poset $A(I)$ satisfies Condition $(PWP)_{w}$. Furthermore, we characterize pomonoids $S$ over which all cyclic (Rees factor) $S$-posets satisfy Condition $(PWP)_{w}$, and pomonoids $S$ over which all Rees factor $S$-posets satisfying Condition $(PWP)_{w}$ have a certain property. Finally, we consider direct products of $S$-posets satisfying Condition $(PWP)_{w}$.
- Published
- 2015
4. The geometry of hemi-slant submanifolds of a locally product Riemannian manifold
- Author
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Fatma Özdemir and Hakan Mete Taştan
- Subjects
Mathematics - Differential Geometry ,Mean curvature ,Integrable system ,Locally product manifold,hemi-slant submanifold,slant distribution ,General Mathematics ,Mathematics::History and Overview ,Geometry ,Riemannian manifold ,Submanifold ,Computer Science::Computers and Society ,Statistical manifold ,Differential Geometry (math.DG) ,Primary 53B25, Secondary 53C55 ,Product (mathematics) ,Computer Science::Computer Vision and Pattern Recognition ,FOS: Mathematics ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,Ricci curvature ,Distribution (differential geometry) ,Mathematics - Abstract
In the present paper, we study hemi-slant submanifolds of a locally product Riemannian manifold. We prove that the anti-invariant distribution involved in the definition of hemi-slant submanifold is integrable and give some applications of this result. We get a necessary and sufficient condition for a proper hemi-slant submanifold to be a hemi-slant product. We also study these types of submanifolds with parallel canonical structures. Moreover, we give two characterization theorems for the totally umbilical proper hemi-slant submanifolds. Finally, we obtain a basic inequality involving Ricci curvature and the squared mean curvature of a hemi-slant submanifold of a certain type of locally product Riemannian manifolds.
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- 2015
5. On ampleness and pseudo-Anosov homeomorphisms in the free group
- Author
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Rizos Sklinos
- Subjects
Pure mathematics ,Sequence ,Mathematics::Dynamical Systems ,General Mathematics ,Free groups,pseudo-Anosov homeomorphisms,geometric stability theory ,Mathematical analysis ,Free group ,FOS: Mathematics ,Order (group theory) ,Preprint ,Mathematics - Logic ,Logic (math.LO) ,Mathematics - Abstract
We use pseudo-Anosov homeomorphisms of surfaces in order to prove that the first order theory of non abelian free groups, $T_{fg}$, is $n$-ample for any $n\in\omega$. This result adds to the work of Pillay, that proved that $T_{fg}$ is non CM -trivial. The sequence witnessing ampleness is a sequence of primitive elements in $F_{\omega}$. Our result provides an alternative proof to the main result of a preprint by Ould Houcine-Tent. We also add an appendix in which we make a few remarks on Sela's paper on imaginaries in torsion free hyperbolic groups. In particular we give alternative transparent proofs concerning the non-elimination of certain imaginaries., Comment: 22 pages, 2 figures. To appear in the Turkish Journal of Mathematics. Replaces arXiv:1205.4662
- Published
- 2015
6. On separating subadditive maps
- Author
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Vesko Valov
- Subjects
Surjective function ,Combinatorics ,Function spaces,separating maps,supports,subadditive maps ,Continuous map ,Function space ,General Mathematics ,Tychonoff space ,Additive function ,Subadditivity ,Bijection ,Type (model theory) ,Mathematics - Abstract
Recall that a map T \colon C(X,E) \to C(Y,F), where X, Y are Tychonoff spaces and E, F are normed spaces, is said to be separating, if for any 2 functions f,g \in C(X,E) we have c(T(f)) \cap c(T(g))= \varnothing provided c(f) \cap c(g) = \varnothing. Here c(f) is the co-zero set of f. A typical result generalizing the Banach--Stone theorem is of the following type (established by Araujo): if T is bijective and additive such that both T and T-1 are separating, then the realcompactification n X of X is homeomorphic to n Y. In this paper we show that a similar result is true if additivity is replaced by subadditivity (a map T is called subadditive if ||T(f+g)(y)|| \leq ||T(f)(y)||+ ||T(g)(y)|| for any f,g \in C(X,E) and any y \in Y). Here is our main result (a stronger version is actually established): if T \colon C(X,E) \to C(Y,F) is a separating subadditive map, then there exists a continuous map SY\colon b Y \rightarrow b X. Moreover, SY is surjective provided T(f)=0 iff f=0. In particular, when T is a bijection such that both T and T-1 are separating and subadditive, b X is homeomorphic to b Y. We also provide an example of a biseparating subadditive map from C(R) onto C(R), which is not additive.
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- 2015
7. Notes on the tangent bundle with deformed complete lift metric
- Author
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Mustafa Özkan and Aydin Gezer
- Subjects
Tangent bundle ,General Mathematics ,Mathematical analysis ,Geometry ,Levi-Civita connection ,Tensor field ,symbols.namesake ,Mathematics::Algebraic Geometry ,Unit tangent bundle ,Almost complex structure,holomorphic tensor field,Kähler-Norden metric,Killing vector field,Riemannian curvature tensors ,symbols ,Hermitian manifold ,Curvature form ,Mathematics::Differential Geometry ,Exponential map (Riemannian geometry) ,Metric connection ,Mathematics - Abstract
In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.
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- 2015
8. Covers and preenvelopes by V-Gorenstein flat modules
- Author
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Xiaoyan Yang
- Subjects
Class (set theory) ,Pure mathematics ,Mathematics::Algebraic Geometry ,Mathematics::Commutative Algebra ,General Mathematics ,Mathematics::Rings and Algebras ,Dualizing module,V-Gorenstein flat module,precover,preenvelope ,Mathematics - Abstract
In this paper, we introduce and study V -Gorenstein at modules and show the stability of the category of V -Gorenstein at modules. We investigate the existence of V -Gorenstein at covers and V -Gorenstein at preenvelopes for any left R -module. Also we prove that ( V - GF ;V - GF ? ) is a perfect hereditary cotorsion pair in B l ( R) , where V - GF stands the class of V -Gorenstein at left R -modules and B l ( R) is the left Bass class. Some applications are given.
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- 2015
9. The Ext-strongly Gorenstein projective modules
- Author
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Jie Ren
- Subjects
Strongly Gorenstein projective modules,precovers,Ext-strongly Gorenstein projective modules,projectively resolving ,Class (set theory) ,Pure mathematics ,Mathematics::Algebraic Geometry ,Mathematics::Commutative Algebra ,Mathematics::K-Theory and Homology ,General Mathematics ,Mathematics::Rings and Algebras ,Projective cover ,Projective test ,Arithmetic ,Mathematics::Representation Theory ,Mathematics - Abstract
In this paper, we introduce and study Ext-strongly Gorenstein projective modules. We prove that the class of Ext-strongly Gorenstein projective modules is projective resolving. Moreover, we consider Ext-strongly Gorenstein projective precovers.
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- 2015
10. General rotational surfaces in the 4-dimensional Minkowski space
- Author
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Velichka Milousheva and Georgi Ganchev
- Subjects
Minimal surface ,Basis (linear algebra) ,Euclidean space ,General Mathematics ,Minkowski space ,Mathematical analysis ,Surfaces in the 4-dimensional Minkowski space,general rotational surfaces,minimal surfaces,flat surfaces,surfaces with flat normal connection ,Invariant theory ,Connection (mathematics) ,Mathematics - Abstract
General rotational surfaces as a source of examples of surfaces in the 4-dimensional Euclidean space were introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the basis of our invariant theory of spacelike surfaces we study general rotational surfaces with special invariants. We describe analytically the flat general rotational surfaces and the general rotational surfaces with flat normal connection. We classify completely the minimal general rotational surfaces and the general rotational surfaces consisting of parabolic points.
- Published
- 2015
11. On p-schemes with the same degrees of thin radical and thin residue
- Author
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Fatemeh Raei Barandagh and Amir Rahnamai Barghi
- Subjects
Combinatorics ,Residue (complex analysis) ,Association scheme ,genetic structures ,Wreath product ,General Mathematics ,Prime number ,Valency ,sense organs ,Association scheme,p-scheme,thin radical,thin residue ,eye diseases ,Mathematics - Abstract
Let p and n>1 be a prime number and an integer, respectively. In this paper, first we show that any p-scheme whose thin radical and thin residue are equal is isomorphic to a fission of the wreath product of 2 thin schemes. In addition, we characterize association p-schemes whose thin radical and thin residue each have degree equal to p. We also characterize association p-schemes on pn points whose thin radical and thin residue each have degree equal to pn-1, and whose basis relations each have valency 1 or pn-1. Moreover, we show that such schemes are Schurian.
- Published
- 2015
12. On 4-dimensional almost para-complex pure-Walker manifolds
- Author
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Sibel Turanli, Hilmi Sarsilmaz, and Murat Iscan
- Subjects
Pure mathematics ,General Mathematics ,Injective metric space ,Mathematical analysis ,Structure (category theory) ,Fubini–Study metric ,Mathematics::Geometric Topology ,Manifold ,Almost para-complex structure,pure metric,neutral metric,Walker metric,Kähler structure ,Metric (mathematics) ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,Fisher information metric ,Mathematics - Abstract
This paper is concerned with almost para-complex structures on Walker 4-manifolds. For these structures, we study some problems of Kahler manifolds. We also give an example of a flat almost para-complex manifold, which consists of a nonintegrable almost para-complex structure on Walker 4-manifolds.
- Published
- 2015
13. Factorization of composite polynomials over finite fields
- Author
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Rasim İlker Gökbulut, Turhan Korkmaz, and Berk Yıldız
- Subjects
Corporate finance ,Leverage (finance) ,Actuarial science ,Galois fields,irreducible polynomial,composition method ,Free cash flow ,General Mathematics ,Dividend payout ratio ,Dividend yield ,Dividend ,Dividend policy ,Monetary economics ,Market liquidity ,Mathematics - Abstract
Dividend policy is a significant concern of corporate finance. Even though there is an extensive amount of research about determinants of the companies’ dividend policy, there is still no uniform result. This study investigates the determinants of dividends policy of 118 industrial companies listed in the Istanbul stock exchange for a period of 8 years from 2003 to 2010. The paper was basically modeled to examine the effects of profitability, growth opportunities, firm size, financial leverage, free floating rate, tax, investment, liquidity, board independence, free cash flow and operational risk on the cash dividend payout decisions of firms listed in industrial sector, using the panel regression analysis method. The study provides evidence that taxes, profitability, growth opportunities, firm size, leverage and liquidity are the most important considerations of dividend payout decisions for Turkish firms. It is found that only leverage has a negative effect on the dividend policy.
- Published
- 2014
14. On harmonicity in some Moufang-Klingenberg planes
- Author
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SÜLEYMAN ÇİFTÇİ, ATİLLA AKPINAR, BASRİ ÇELİK, Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Çelik, Basri, Akpınar, Atilla, Çiftçi, Süleyman, ABB-9790-2020, and AAE-2600-2019
- Subjects
Local alternative ring ,Moufang-Klingenberg planes ,Mathematics::Group Theory ,Moufang-Klingenberg planes,local alternative ring,projective collineation,cross-ratio,harmonicity,harmonic position ,General Mathematics ,Cross-ratio ,Local Ring ,Projective Transformation ,Collineation ,Projective collineation ,Harmonic position ,Harmonicity ,6-figures ,Mathematics - Abstract
In this paper we study Moufang-Klingenberg planes M (A) defined over a local alternative ring A of dual numbers. We show that some collineations of M (A) preserve cross-ratio and thus establish a relation between harmonicity and harmonic position.
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- 2014
15. On transformations of index 1
- Author
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Osman Kelekci, Leyla Bugay, [Bugay, Leyla] Cukurova Univ, Dept Math, Adana, Turkey -- [Kelekci, Osman] Nigde Univ, Dept Math, Nigde, Turkey, 0-Belirlenecek, and Çukurova Üniversitesi
- Subjects
index ,period ,Matematik ,Pure mathematics ,Transformations ,Index (economics) ,Transformations,orbit,index,period ,Semigroup ,General Mathematics ,Element (category theory) ,orbit ,Mathematics - Abstract
WOS: 000335286000005, The index and the period of an element a of a finite semigroup are defined as the smallest values of m >= 1 and r >= 1 such that a(m+r) = a(m), respectively. If m = 1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in T-n, which we call transformations of index 1.
- Published
- 2014
16. Horizontally submersions of contact CR-submanifolds
- Author
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Tshikunguila Tshikuna-Matamba and Fortuné Massamba
- Subjects
Riemannian submersion ,General Mathematics ,Mathematical analysis ,Tangent ,Curvature ,Manifold ,CR-submanifold,almost Hermitian manifold,almost contact metric submersion,symplectic manifold,horizontal submersion ,symbols.namesake ,symbols ,Hermitian manifold ,Mathematics::Differential Geometry ,Complex manifold ,Mathematics::Symplectic Geometry ,Symplectic geometry ,Symplectic manifold ,Mathematics - Abstract
In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that the structures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are related to (1, 2)-symplectic structures. For horizontally submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds, we study the principal characteristics and prove that their total spaces are CR-product. Curvature properties between curvatures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds and the base spaces of such submersions are also established. We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf of an integrable horizontal distribution and a curve tangent to the normal distribution.
- Published
- 2014
17. Foliations and a class of metrics on tangent bundle
- Author
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Leila Nourmohammadi Far and Esmaeil Peyghan
- Subjects
Tangent bundle ,Pure mathematics ,General Mathematics ,Mathematical analysis ,Levi-Civita connection ,symbols.namesake ,Hyperbolic set ,Unit tangent bundle ,symbols ,Finsler manifold,foliation,constant curvature,Riemannian metric ,Hermitian manifold ,Mathematics::Metric Geometry ,Sectional curvature ,Finsler manifold ,Mathematics::Differential Geometry ,Exponential map (Riemannian geometry) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
Let M be a smooth manifold with Finsler metric F, and let TM° be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of (TM°,G) and study some of their geometric properties. Next we use this approach to obtain new characterizations of Finsler manifolds with positive constant curvature.
- Published
- 2014
18. Products of conjugacy classes and products of irreducible characters in finite groups
- Author
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Sajjad Mahmood Robati and Mohammad Reza Darafsheh
- Subjects
Combinatorics ,Discrete mathematics ,Finite group ,Character (mathematics) ,Conjugacy class ,Character table ,General Mathematics ,Product (mathematics) ,Conjugacy classes,irreducible characters,products ,Upper and lower bounds ,Mathematics - Abstract
Let G be a finite group. If A and B are two conjugacy classes in G, then AB is a union of conjugacy classes in G and h(AB) denotes the number of distinct conjugacy classes of G contained in AB. If c and y are two complex irreducible characters of G, then cy is a character of G and again we let h(cy) be the number of irreducible characters of G appearing as constituents of cy. In this paper our aim is to study the product of conjugacy classes in a finite group and obtain an upper bound for h in general. Then we study similar results related to the product of two irreducible characters.
- Published
- 2014
19. Complete cotorsion pairs in the category of complexes
- Author
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Zhongkui Liu and Zhanping Wang
- Subjects
Combinatorics ,Class (set theory) ,Cover (topology) ,General Mathematics ,Completeness (order theory) ,Complete,cotorsion pair,cover,Gorenstein flat complex ,Coherent ring ,Mathematics - Abstract
In this paper, we study completeness of cotorsion pairs in the category of complexes of R-modules. Let (A, B) be a cotorsion pair in R-Mod. It is shown that the cotorsion pair (\widetilde{A}, dg\widetilde{B}) and (\overline{A}, \overline{A}\perp) are complete if A is closed under pure submodules and cokernels of pure monomorphisms, where in Gillespie's definitions \widetilde{A} is the class of exact complexes with cycles in A and dg\widetilde{B} is the class of complexes X with components in B such that the complex Hom(A, X) is exact for every complex A \in \widetilde{A}; and \overline{A} is the class of all complexes with components in A. Furthermore, they are perfect. As an application, we get that every complex over a right coherent ring has a Gorenstein flat cover, which generalizes the well-known results on the existence of Gorenstein flat covers.
- Published
- 2014
20. Generalized hypercenter of a finite group
- Author
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Mohammed M. Al-Shomrani and Mohamed Ezzat Mohamed
- Subjects
Finite group ,Pure mathematics ,Mathematics::Group Theory ,Group (mathematics) ,Locally finite group ,General Mathematics ,S-quasinormally embedded,generalized supersolvably embedded,super generalized supersolvably embedded,supersolvable ,Characterization (mathematics) ,Mathematics - Abstract
Let G be a finite group. In this paper, we introduce the concept of super generalized supersolvably embedded subgroup of a group G and give a new characterization of the generalized hypercenter of G.
- Published
- 2014
21. Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds
- Author
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Fereshteh Malek and Mohammad Bagher Kazemi Balgeshir
- Subjects
Pure mathematics ,Almost contact 3-structure manifold,semi-slant and bi-slant submanifold,3-Sasakian manifold ,General Mathematics ,Computer Science::Computer Vision and Pattern Recognition ,Mathematical analysis ,Mathematics::History and Overview ,Physics::Optics ,Mathematics::Differential Geometry ,Invariant (mathematics) ,Mathematics::Symplectic Geometry ,Manifold ,Computer Science::Computers and Society ,Mathematics - Abstract
In this paper we introduce the notions of semi-slant and bi-slant submanifolds of an almost contact 3-structure manifold. We give some examples and characterization theorems about these submanifolds. Moreover, the distributions of semi-slant submanifolds of 3-cosymplectic and 3-Sasakian manifolds are studied. ϕi)i=1;2;3 and the vector elds should be slant or invariant with respect to all of the ϕi's. Therefore, it is a generalization of invariant, anti-invariant, slant, semi-slant, and bi-slant submanifolds in almost contact metric 3-structures and we denote them by 3- semi-slant and 3-bi-slant submanifolds. Following the approaches of (3, 13), we characterized 3-bi-slant and 3-semi-slant submanifolds and studied geometric properties of distributions of these submanifolds where the ambient manifolds are 3-Sasakian or 3-cosymplectic. It should be noted that, in the denition of semi-slant
- Published
- 2014
22. Hölder regularity for weak solutions of diagonal divergence quasilinear degenerate elliptic systems
- Author
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Yan Dogn and Xuewei Cui
- Subjects
Class (set theory) ,Elliptic systems ,General Mathematics ,Degenerate energy levels ,Diagonal ,Mathematical analysis ,Lower order ,Vector field ,Divergence (statistics) ,Quasilinear degenerate elliptic system,Hölder regularity,Hörmander's vector fields,VMOX function,natural growth ,Mathematics - Abstract
In this paper, we establish Hölder regularity for weak solutions of a class of diagonal divergence quasilinear degenerate elliptic systems of Hörmander's vector fields when the coefficients belong to the class of VMOX functions with respect to x and uniformly with respect to u, and the lower order terms satisfy a natural growth condition.
- Published
- 2014
23. A class of uniquely (strongly) clean rings
- Author
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Orhan Gürgün, Ayşe Çiğdem Özcan, and Matematik
- Subjects
Combinatorics ,Class (set theory) ,Ring (mathematics) ,Intersection ,Mathematics::Commutative Algebra ,General Mathematics ,Condensed Matter::Superconductivity ,Idempotence ,Element (category theory) ,Clean ring,strongly clean ring,uniquely clean ring,strongly J-clean ring ,Mathematics - Abstract
In this paper we call a ring R delta(r)-clean if every element is the sum of an idempotent and an element in delta(R-R) where delta(R-R) is the intersection of all essential maximal right ideals of R. If this representation is unique (and the elements commute) for every element we call the ring uniquely (strongly) delta(r)-clean. Various basic characterizations and properties of these rings are proved, and many extensions are investigated and many examples are given. In particular, we see that the class of delta(r)-clean rings lies between the class of uniquely clean rings and the class of exchange rings, and the class of uniquely strongly delta(r)-clean rings is a subclass of the class of uniquely strongly clean rings. We prove that R is delta(r)-clean if and only if R/delta(r)(R-R) is Boolean and R/Soc(R-R) is clean where Soc(R-R) is the right socle of R.
- Published
- 2014
24. Approximation by iterates of Beta operators
- Author
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Karunesh Kumar Singh, Vikas Kumar Mishra, and Purshottam Narain Agrawal
- Subjects
Modulus of smoothness ,Iterated function ,General Mathematics ,Mathematical analysis ,Applied mathematics ,Beta (velocity) ,Operator theory ,Mathematics ,Key words: Beta operators,iterative combination,modulus of smoothness - Abstract
In this paper, we study the degree of approximation by an iterative combination Tn,k of the beta operators introduced by Upreti [8].
- Published
- 2014
25. On 2 nonsplit extension groups associated with HS and HS:2
- Author
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Thekiso Trevor Seretlo and Jamshid Moori
- Subjects
Combinatorics ,Overline ,Clifford theory ,Character table ,Group extension ,Group (mathematics) ,General Mathematics ,Group extensions,Higman--Sims group,automorphism group,character table,Clifford theory,inertia groups,Fischer--Clifford matrices ,Order (ring theory) ,Outer automorphism group ,Higman–Sims group ,Mathematics - Abstract
The group HS:2 is the full automorphism group of the Higman--Sims group HS. The groups 24.S6 and 25.S6 are maximal subgroups of HS and HS:2, respectively. The group 24.S6 is of order 11520 and 25.S6 is of order 23040 and each of them is of index 3 850 in HS and HS:2, respectively. The aim of this paper is to first construct \overline{G} = 25.S6 as a group of the form 24.S6.2 (that is, \overline{G} = G1.2) and then compute the character tables of these 2 nonsplit extension groups by using the method of Fischer--Clifford theory. We will show that the projective character tables of the inertia factor groups are not required. The Fischer--Clifford matrices of \overline{G}1 and \overline{G} are computed. These matrices together with the partial character tables of the inertia factors are used to compute the full character tables of these 2 groups. The fusion of \overline{G}1 into \overline{G} is also given.
- Published
- 2014
26. On Finsler metrics with vanishing S-curvature
- Author
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Hassan Sadeghi, Akbar Tayabi, and Esmaeil Peyghan
- Subjects
Pure mathematics ,General Mathematics ,Mathematical analysis ,Equivalence of metrics ,Fundamental theorem of Riemannian geometry ,Fubini–Study metric ,(a,b)-metric,Berwald metric,S-curvature ,Intrinsic metric ,Statistical manifold ,Metric signature ,Mathematics::Metric Geometry ,Information geometry ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,Fisher information metric ,Mathematics - Abstract
In this paper, we consider Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We study these metrics with vanishing S-curvature. We find some conditions under which such a Finsler metric is Berwaldian or locally Minkowskian.
- Published
- 2014
27. Characteristic classes on Grassmannians
- Author
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Jin Shi and Jianwei Zhou
- Subjects
General Mathematics ,Vector bundle ,Serre duality ,Cohomology ,Characteristic class ,Combinatorics ,symbols.namesake ,Grassmann number ,symbols ,Grassmann manifold,fibre bundle,characteristic class,homology group,Poincaré duality ,Geometry and topology ,Poincaré duality ,Singular homology ,Mathematics - Abstract
In this paper, we study the geometry and topology on the oriented Grassmann manifolds. In particular, we use characteristic classes and the Poincare duality to study the homology groups of Grassmann manifolds. We show that for k=2 or n \leq 8, the cohomology groups H*(G(k,n), R) are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles. In these cases, the Poincare duality: Hq(G(k,n), R) \to Hk(n-k)-q(G(k,n), R) can be expressed explicitly.
- Published
- 2014
28. Generalized derivations centralizing on Jordan ideals of rings with involution
- Author
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Lahcen Oukhtite and Abdellah Mamouni
- Subjects
Involution (mathematics) ,Pure mathematics ,Mathematics::Commutative Algebra ,General Mathematics ,Prime ring ,Semiprime ring ,Commutative property ,Rings with involution,generalized derivations,Jordan ideals ,Mathematics - Abstract
A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
- Published
- 2014
29. On the maximal operators of Vilenkin-Fejéer means
- Author
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George Tephnadze
- Subjects
Combinatorics ,symbols.namesake ,Series (mathematics) ,Vilenkin system,Fejéer means,martingale Hardy space ,General Mathematics ,Bounded function ,symbols ,Maximal operator ,Hardy space ,Space (mathematics) ,Mathematics - Abstract
The main aim of this paper is to prove that the maximal operator \overset{\sim}{s}\astf:=\underset{n \in P} \sup\frac{|s nf|}{\log2 (n+1)} is bounded from the Hardy space H1/2 to the space L1/2, where s nf are Fejer means of bounded Vilenkin-Fourier series.
- Published
- 2014
30. Slant submersions from almost product Riemannian manifolds
- Author
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Yılmaz Gündüzalp
- Subjects
Pure mathematics ,symbols.namesake ,Riemannian submersion ,Mathematics::Complex Variables ,General Mathematics ,symbols ,Totally geodesic ,Riemannian submersion,almost product Riemannian submersion,almost product Riemannian manifold,slant submersion ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,Submersion (mathematics) ,Mathematics - Abstract
In this paper, we define the concept of almost product Riemannian submersion between almost product Riemannian manifolds. We introduce slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give examples and investigate the geometry of foliations that arise from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a slant submersion to be totally geodesic.
- Published
- 2014
31. A characterization of Auslander category
- Author
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Juxiang Sun
- Subjects
Subcategory ,Semidualizing module,Auslander class,Bass class ,Pure mathematics ,Mathematics::Commutative Algebra ,General Mathematics ,Mathematics::Rings and Algebras ,Bijection ,Mathematics::Representation Theory ,Associative property ,Mathematics - Abstract
In this paper, we discuss the Bass class and the Auslander class with respect to a semidualizing module over an associative ring. Let SCR be a semidualizing module, we proved that the Bass class BC (R) is a right orthogonal subcategory of some right R-module; and that the Auslander class AC (S) is a left orthogonal subcategory of the character module of some left S-module. As an application, we introduce the notion of the minimal semidualizing module, and get a one to one correspondence between the isomorphism classes of minimal semidualizing R-modules and maximal classes among coresolving preenvelope classes of Mod R with the same Ext-projective generators in gen* R.
- Published
- 2014
32. Attractors for parabolic problems in weighted spaces
- Author
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Ying Tang and Xiaojun Li
- Subjects
Weak topology ,General Mathematics ,Mathematical analysis ,Attractor ,Attractor,parabolic equation,singular initial data,weighted space ,Boundary (topology) ,Parabolic partial differential equation ,Mathematics ,Exponential function ,Weighted space - Abstract
The purpose of this paper is to investigate the asymptotic behavior of the solutions of parabolic equations with singular initial data in weighted spaces Lrd(x)(W) where d(x) is the distance to the boundary. We first establish the existence of the attractor for that equation in Lrd(x)(W) and then show the existence of the exponential attractor in L2d(x)(W). In contrast to our previous results, we get the existence of attractors in weak topology spaces.
- Published
- 2014
33. Algorithm to solve certain ternary quartic Diophantine equations
- Author
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László Szalay
- Subjects
Polynomial ,Diophantine set ,General Mathematics ,Diophantine equation ,Cornacchia's algorithm ,Legendre's equation ,symbols.namesake ,Diophantine equation,Runge method,inhomogeneous ternary equation ,Integer ,Quartic function ,symbols ,Ternary operation ,Algorithm ,Mathematics - Abstract
In this paper, we develop an algorithm to solve completely the Diophantine equation F(x,y)=z2, where the quartic inhomogeneous polynomial F(x,y) with integer coefficients satisfies certain technical conditions. The procedure is an extension of the version of Runge's method given by Poulakis.
- Published
- 2014
34. Structure theory of central simple Zd-graded algebras
- Author
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Cemal Koç, Yosum Kurtulmaz, Doğuş Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, TR45948, and Kurtulmaz, Yosum
- Subjects
Pure mathematics ,Jordan algebra ,Unity ,General Mathematics ,Clifford Cebiri ,Clifford algebra ,Subalgebra ,ω-Clifford algebra ,Central simple graded algebra ,Graded Lie algebra ,Algebra ,Clifford Algebra ,Classification of Clifford algebras ,Teklik ,Differential graded algebra ,Aşmaçlı Cebir ,Algebra representation ,Graded Algebra ,Primitive dth root of unity ,Central simple algebra ,Central simple graded algebra,primitive dth root of unity,w-Clifford algebra ,Mathematics - Abstract
This paper investigates the structure theory of Zd-central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of Zd-central simple graded algebras.
- Published
- 2014
35. On the nilpotent graph of a ring
- Author
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S. Khojasteh and Mohammad Javad Nikmehr
- Subjects
Combinatorics ,Discrete mathematics ,Nilpotent ,Finite ring ,Nilpotent graph,diameter,girth ,General Mathematics ,Artinian ring ,Unipotent ,Graph ,Vertex (geometry) ,Mathematics - Abstract
Let R be a ring with unity. The nilpotent graph of R, denoted by GN(R), is a graph with vertex set ZN(R)* = {0 \neq x \in R \mid xy \in N(R) for some 0 \neq y \in R}; and two distinct vertices x and y are adjacent if and only if xy \in N(R), where N(R) is the set of all nilpotent elements of R. Recently, it has been proved that if R is a left Artinian ring, then diam(GN(R)) \leq 3. In this paper, we present a new proof for the above result, where R is a finite ring. We study the diameter and the girth of matrix algebras. We prove that if F is a field and n \geq 3, then diam(GN(Mn(F))) = 2. Also, we determine diam (GN (M2(F))) and classify all finite rings whose nilpotent graphs have diameter at most 3. Finally, we determine the girth of the nilpotent graph of matrix algebras.
- Published
- 2014
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