15 results
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2. On Some Multipliers and the Relative Completion in Amalgam Spaces
- Author
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Cihan Unal and Ünal, Cihan
- Subjects
Physics ,Relative completion ,Mühendislik ,Rölatif tamlanış ,General Medicine ,Space (mathematics) ,Linear subspace ,Combinatorics ,Engineering ,Homeomorphism (graph theory) ,İzomorfizma ,Amalgam space ,Amalgam uzayı ,Isomorphism ,Locally compact space ,Amalgam uzayı,Banach modül,Rölatif tamlanış,İzomorfizma ,Abelian group ,Algebraic number ,Banach modül ,Amalgam space,Banach module,Relative completion,Isomorphism ,Banach module ,Haar measure - Abstract
G, $\mu $ Haar ölçümüne sahip yerel tıkız değişmeli bir grup olsun. Bu çalışmada ilk olarak, $\left( L^{p},\ell ^{q}\right) (G)$ amalgam uzayı tanıtıldı ve bazı temel özellikleri verildi. Ayrıca $\left( L^{p},\ell ^{q}\right) (G)$ amalgam uzayının doğrusal bir A alt uzayı için bir $\overset{\sim }{A}$ rölatif tamlanış tanımlandı ve bu tamlanışın bazı özellikleri ele alındı. Son olarak; $Hom_{L^{1}(G)}\left( L^{1}(G),A\right) $ ile $\overset{\sim }{A}$ arasında cebirsel bir izomorfizma ve homeomorfizma olduğu ispatlandı., Let G be a locally compact abelian group with Haar measure $\mu $. First of all, in this paper, the amalgam space $\left( L^{p},\ell ^{q}\right) (G)$ is introduced and some basic properties of amalgam space are given. Moreover, a relative completion $\overset{\sim }{A}$ for a linear subspace A of amalgam space $\left( L^{p},\ell ^{q}\right) (G)$ is defined, and is considered several properties of it. Finally, it is proved that there is an algebraic isomorphism and homeomorphism between $Hom_{L^{1}(G)}\left( L^{1}(G),A\right) $ and $\overset{\sim }{A}$ .
- Published
- 2020
3. Polinom Denklemlerin Mutlak Değerce En Büyük Reel Kökünü Veren Bir Metot
- Author
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Özlem Moğol and Arif Kerem Dayi
- Subjects
Sequence ,Polynomial ,Matematik ,Recurrence relation ,Fibonacci number ,Degree (graph theory) ,Characteristic equation ,General Medicine ,Combinatorics ,Quadratic equation ,Limit (mathematics) ,Recursive sequence,Polynomial equations,The Fibonacci sequence ,Mathematics ,İndirgemeli diziler,Polinom denklemler,Fibonacci tavşan problemi - Abstract
The solution to the Rabbit Problem is the famous Fibonacci sequence. When this sequence is analyzed, it is found that the characteristic equation of this sequence is a quadratic equation. Furthermore, the ratio of the consecutive terms of the sequence converges to one of the roots of the characteristic equation. So why does it converge to the number of phi? Is it just because it is a positive root? In this study, some data in the rabbit problem have been changed. The changed data are “The time that the creature reaches adulthood“ and “At what intervals the creature gives birth after reaching adulthood”. According to the values of these variables, different recurrence relations emerged. It has been observed that the characteristic equations of these recurrence relations are polynomials of higher order than the 2nd degree. It has been shown that one of the roots of the polynomial equations, which are the characteristic equation of these sequences, can be found with the “Limit of the rates of consecutive terms” as in the algorithm applied in the Fibonacci sequence. “In this case, does the limit value of the rate of consecutive terms of the resulting array always converge to a root? Which root does it converge? Under what conditions is this method provided?” questions were answered. This paper suggests a new method to find the dominant root –the root with the largest modulus- of a polynomial equation. The method also helps to find lower and upper bounds for the roots., Fibonacci Tavşan Problemi önemli bir sayı dizisi olan Fibonacci dizisini vermektedir. Bu dizi incelendiğinde karşılaşılan indirgeme bağıntısının karakteristik denklemi 2. dereceden bir polinom denklem olduğu görülür. Bu dizinin ardışık terimlerinin oranının limiti ise bu 2. derece polinom denklemin köklerinden biri olan Fi sayısına yakınsar. Peki neden Fi sayısına yakınsar? Sadece pozitif kök olduğu için mi? Bu çalışmada tavşan problemindeki bazı veriler değiştirilmiştir. Değiştirilen veriler “Canlının yetişkinliğe ulaşma süresi” ve “Canlının yetişkinliğe ulaştıktan sonra hangi aralıklarla doğum yaptığı”dır. Bu değişkenlerin aldıkları değerlere göre ortaya, farklı indirgeme bağıntıları çıkmıştır. Bu indirgeme bağıntılarının karakteristik denklemlerinin 2. dereceden daha yüksek mertebelerde polinomlar oldukları görülmüştür. Bu dizilerin karakteristik denklemi olan Polinom denklemlerin köklerinden birinin Fibonacci dizisinde uygulanan algoritmada olduğu gibi “Dizinin ardışık terimlerin oranlarının limiti” ile bulunabileceği gösterilmiştir. “Bu durumda oluşan dizinin ardışık terimlerin oranının limit değeri her zaman bir köke yakınsar mı? Hangi köke yakınsar? Bu metot hangi koşullar altında sağlanır?” sorularına cevap verilmiştir. Bu çalışmada yüksek mertebeden polinom denklemlerin köklerinden mutlak değerce en büyük kök reel ise bu reel kökün bulunması için bir metot ortaya koyulmuştur. Bu metot aynı zamanda polinom denklemlerin reel kökleri için üst veya alt sınır bulunmasına da katkı sağlamaktadır.
- Published
- 2019
4. A Neo-Assyrian Docket from the Güray Museum
- Author
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Ömer Kahya
- Subjects
Cultural Studies ,Combinatorics ,History ,Arkeoloji ,Güray Museum,Neo-Assyrian,Barley Loan,Docket ,Archaeology ,C++ string handling ,Cylinder seal ,Güray Müze,Yeni Asurca,Hububat Borcu,Etiket ,Impression ,Mathematics - Abstract
Bu çalışmanın amacı Güray Müze’de bulunan üçken biçimli Yeni Asurca hububat borcu etiketini (G.M. 302) tanıtmaktır. Tabletin her iki yüzünde bir silindir mühür baskısı ve geniş kısmının köşelerinde ip deliği mevcuttur. 4+2+1 satırdan oluşmaktadır ve sağlam durumdadır. Etiketin yılı ve menşei/eyaleti bilinmemektedir., The aim of this paper is to introduce a Neo-Assyrian triangular shaped barley loan docket from the Güray Museum in Nevşehir. There is a cylinder seal impressionon its both sides and string holes on the corners of its large part. The docket which bears 4+2+1 lines, is substantially complete. Its date and province is unknown.
- Published
- 2018
5. Some relations among the largest eigenvalues of product matrix and graph matrices
- Author
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Kahraman Birgin, Sezer Sorgun, Hatice Topcu, Hakan Küçük, and Nevşehir Hacı Bektaş Veli Üniversitesi/fen-edebiyat fakültesi/matematik bölümü/matematiğin temelleri ve matematik lojik anabilim dalı
- Subjects
Physics ,Combinatorics ,Graph matrices ,Laplasyan ,Signless laplacian ,Adjacency ,Komşuluk ,Graf matrisleri ,Spektral yarıçap ,Laplacian ,İşaretsiz laplasyan ,Spectral radius - Abstract
( ) ve ( ) sırasıyla bir grafının komşuluk matrisi ve nokta derecelerinin bir köşegen matrisi olmak üzere ( ) ( ) ( ) matrisini tanımlarız. Bu makalede bu çarpım matrisinin spektral yarıçapı ile graf matrislerinin en büyük öz değerleri arasında bazı bağıntılar elde edilmiştir. Ayrıca nümerik sonuçlar da verilmiştir. We define product matrix as ( ) ( ) ( ) , where ( ) is an adjacency matrix and ( ) is a diagonal matrix of vertex degrees of a graph . In this paper, some relations among the spectral radius of product matrix and the largest eigenvalues of graph matrices are obtained. We also give numerical results for them.
- Published
- 2016
6. 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
7. 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.
- Published
- 2015
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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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