hakansabunis/tr-academic-research-agent-index huggingface dataset:
RESULTS ON THE COMPOSITION AND NEUTRIX COMPOSITION OF THE DELTA FUNCTION
RESULTS ON THE COMPOSITION AND NEUTRIX COMPOSITION OF THE DELTA FUNCTION
Yazar: Fisher, Brian; Jolevskatuneska, Biljana
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 43 No. 1, 2014
Anahtar kelimeler: distribution, dirac-delta function, composition of distributions, neutrix,neutrix limit.

The neutrix composition F (f (x))) of a distribution F (x) and a locallysummable function f (x) is said to exist and be equal to the distributionh(x) if the neutrix limit of the sequence {Fn (f (x))} is equal to h(x),where Fn (x) = F (x) ∗ δn (x) and {δn (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). It is proved that the neutrix composition δ(s) {[exp + (x) − 1]r } exists andδ (s) {[exp + (x) − 1]r } = rs+r−1k=0 (−1)s+k s!c rs+r−1,k2rk! δ (k) (x), for r = 1, 2, . . . and s = 0, 1, 2, . . .. Further results are also proved.

The neutrix composition F (f (x))) of a distribution F (x) and a locallysummable function f (x) is said to exist and be equal to the distributionh(x) if the neutrix limit of the sequence {Fn (f (x))} is equal to h(x),where Fn (x) = F (x) ∗ δn (x) and {δn (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). It is proved that the neutrix composition δ(s) {[exp + (x) − 1]r } exists andδ (s) {[exp + (x) − 1]r } = rs+r−1k=0 (−1)s+k s!c rs+r−1,k2rk! δ (k) (x), for r = 1, 2, . . . and s = 0, 1, 2, . . .. Further results are also proved.
ON STRONGLY AND SEPARABLY ω1-pω+n-PROJECTIVE ABELIAN p-GROUPS
ON STRONGLY AND SEPARABLY ω1-pω+n-PROJECTIVE ABELIAN p-GROUPS
Yazar: Danchev, Peter
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 43 No. 1, 2014
Anahtar kelimeler: C-decomposable groups, pω+n-projective groups, strongly n-simply presented groups, ω-p ω+n-projective groups, strongly ω-p ω+n-projective groups, boundedsubgroups, countable subgroups, nice subgroups, Ulm subgroups, Ulm factors.

Let n ≥ 0 be an arbitrary integer. We prove some results for stronglyn-simply presented abelian p-groups with C-decomposable property, extending classical achievements due to Keef in Commun. Algebra (1990).As applications we define the classes of strongly ω-p ω+n -projective andseparably ω-p ω+n -projective abelian p-groups which are also properlycontained in all ω-p ω+n -projectives, recently defined by Keef in J. Alg.Numb. Th. Acad. (2010). Moreover, some principal descriptions concerning these new objects are obtained as well.

Let n ≥ 0 be an arbitrary integer. We prove some results for stronglyn-simply presented abelian p-groups with C-decomposable property, extending classical achievements due to Keef in Commun. Algebra (1990).As applications we define the classes of strongly ω-p ω+n -projective andseparably ω-p ω+n -projective abelian p-groups which are also properlycontained in all ω-p ω+n -projectives, recently defined by Keef in J. Alg.Numb. Th. Acad. (2010). Moreover, some principal descriptions concerning these new objects are obtained as well.
GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS
GENERALIZED SKEW DERIVATIONS ON MULTILINEAR POLYNOMIALS IN RIGHT IDEALS OF PRIME RINGS
Yazar: Albaş, E.; Argaç, N.; Filippis, V. De; Demir, Ç.
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 43 No. 1, 2014
Anahtar kelimeler: Identity, generalized skew derivation, automorphism, (semi-)prime ring.

Let R be a prime ring, f (x, . . . , xn ) a multilinear polynomial over Cin n noncommuting indeterminates, I a nonzero right ideal of R, andF : R → R be a nonzero generalized skew derivation of R.Suppose that F (f (r, . . . , rn ))f (r, . . . , rn ) ∈ C, for all r, . . . , rn ∈ I.If f (x, . . . , xn ) is not central valued on R, then either char(R) = 2and R satisfies sor one of the following holds:(i ) f (x, . . . , xn )x n+1 is an identity for I;(ii ) F (I)I = (0);(iii ) [f (x, . . . , xn ), x n+1 ]x n+2 is an identity for I, there existb, c, q ∈ Q with q an invertible element such that F (x) =bx − qxq−1 c for all x ∈ R, and q−1 cI ⊆ I.Moreover, inthis case either (b − c)I = (0) or b − c ∈ C and f (x, . . . , xn ) is central valued on R.

Let R be a prime ring, f (x, . . . , xn ) a multilinear polynomial over Cin n noncommuting indeterminates, I a nonzero right ideal of R, andF : R → R be a nonzero generalized skew derivation of R.Suppose that F (f (r, . . . , rn ))f (r, . . . , rn ) ∈ C, for all r, . . . , rn ∈ I.If f (x, . . . , xn ) is not central valued on R, then either char(R) = 2and R satisfies sor one of the following holds:(i ) f (x, . . . , xn )x n+1 is an identity for I;(ii ) F (I)I = (0);(iii ) [f (x, . . . , xn ), x n+1 ]x n+2 is an identity for I, there existb, c, q ∈ Q with q an invertible element such that F (x) =bx − qxq−1 c for all x ∈ R, and q−1 cI ⊆ I.Moreover, inthis case either (b − c)I = (0) or b − c ∈ C and f (x, . . . , xn ) is central valued on R.
GENERALIZED NOTION OF WEAK MODULE AMENABILITY
GENERALIZED NOTION OF WEAK MODULE AMENABILITY
Yazar: Bodaghi, Abasalt
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 43 No. 1, 2014
Anahtar kelimeler: Banach modules; Module derivation; Weak amenability; Weak moduleamenability; Inverse semigroup.

In the present paper, we introduce a new notion of weak moduleamenability for Banach algebras which is related to module homomorphisms. Among other results, we investigate the relationship betweenthis concept for a Banach algebraA which is a Banach A-bimodule withcompatible actions, and the quotient Banach algebraA/J where J isthe closed ideal ofA generated by elements of the form (a·α)b−a(α·b)for a ∈A and α ∈ A. We then study this concept for an inversesemigroup S, where some examples on(S) and C∗ (S) are given.

In the present paper, we introduce a new notion of weak moduleamenability for Banach algebras which is related to module homomorphisms. Among other results, we investigate the relationship betweenthis concept for a Banach algebraA which is a Banach A-bimodule withcompatible actions, and the quotient Banach algebraA/J where J isthe closed ideal ofA generated by elements of the form (a·α)b−a(α·b)for a ∈A and α ∈ A. We then study this concept for an inversesemigroup S, where some examples on(S) and C∗ (S) are given.
A NEW CLASS OF EXPONENTIAL REGRESSION CUM RATIO ESTIMATOR IN TWO PHASE SAMPLING
A NEW CLASS OF EXPONENTIAL REGRESSION CUM RATIO ESTIMATOR IN TWO PHASE SAMPLING
Yazar: Ozgul, Nilgun; Cingi, Hulya
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 43 No. 1, 2014
Anahtar kelimeler: Two phase sampling, Auxiliary variable, Exponential estimation, Efficiency.

In this paper, we propose a new class of exponential regression cumratio estimator using the auxiliary variable for the estimation of thefinite population mean under two phase sampling scheme. The Biasand Mean Square Error (MSE) equations of the proposed estimatorare obtained and compared with the MSE equations of some existingestimators in two phase sampling. We find theoretically the proposedestimator is always more efficient than classical ratio and regression estimators, Singh and Vishwakarma [17] ratio type exponential estimatorin two phase sampling. In addition, theoric results are supported by anumerical example using original data sets.

In this paper, we propose a new class of exponential regression cumratio estimator using the auxiliary variable for the estimation of thefinite population mean under two phase sampling scheme. The Biasand Mean Square Error (MSE) equations of the proposed estimatorare obtained and compared with the MSE equations of some existingestimators in two phase sampling. We find theoretically the proposedestimator is always more efficient than classical ratio and regression estimators, Singh and Vishwakarma [17] ratio type exponential estimatorin two phase sampling. In addition, theoric results are supported by anumerical example using original data sets.
TYPE I ERROR RATE FOR TWO-SAMPLE TESTS IN STATISTICAL SHAPE ANALYSIS
TYPE I ERROR RATE FOR TWO-SAMPLE TESTS IN STATISTICAL SHAPE ANALYSIS
Yazar: Ocakoglu, Gokhan; Ercan, İlker
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 43 No. 1, 2014
Anahtar kelimeler: Statistical shape analysis, two-sample tests, type I error rate.

Nowadays, with the help of advanced imaging techniques the image orshape of an organ or organism can be used as input data. Therefore,the statistical analysis of shape has recently become more importantin the medical and biological sciences. Methods related to two-sampletests have been developed for statistical shape analysis, giving rise toconsiderable interest in research that evaluates the performance of thesetests. In this study, two sample procedures are used to compare themean shapes from the statistical shape analysis literature according totype I error rate.

Nowadays, with the help of advanced imaging techniques the image orshape of an organ or organism can be used as input data. Therefore,the statistical analysis of shape has recently become more importantin the medical and biological sciences. Methods related to two-sampletests have been developed for statistical shape analysis, giving rise toconsiderable interest in research that evaluates the performance of thesetests. In this study, two sample procedures are used to compare themean shapes from the statistical shape analysis literature according totype I error rate.
ON THE PARALLEL SURFACES IN GALILEAN SPACE
ON THE PARALLEL SURFACES IN GALILEAN SPACE
Yazar: Dede, Mustafa; Ekici, Cumali; Çöken, A. Ceylan
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 6, 2014
Anahtar kelimeler: Parallel surfaces, Surface curvature, Galilean space

In this paper, first of all, the definition of parallel surfaces in Galileanspace is given. Then, the relationship between the curvatures of theparallel surfaces in Galilean space is determined. Moreover, the firstand second fundamental forms of parallel surfaces are found in Galileanspace. Consequently, we obtained Gauss curvature and mean curvatureof parallel surface in terms of those curvatures of the base surface.

In this paper, first of all, the definition of parallel surfaces in Galileanspace is given. Then, the relationship between the curvatures of theparallel surfaces in Galilean space is determined. Moreover, the firstand second fundamental forms of parallel surfaces are found in Galileanspace. Consequently, we obtained Gauss curvature and mean curvatureof parallel surface in terms of those curvatures of the base surface.
BAYESIAN UNIT-ROOT TESTING INSTOCHASTIC VOLATILITY MODELS WITHCORRELATED ERRORS
BAYESIAN UNIT-ROOT TESTING INSTOCHASTIC VOLATILITY MODELS WITHCORRELATED ERRORS
Yazar: Kalaylıoğlu, Zeynep İ.; Bozdemir, Burak; Ghosh, Sujit K.
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 6, 2014
Anahtar kelimeler: Contemporaneous financial correlation, Markov chain Monte Carlo, Gibbssampling, unit-root test, WinBUGS, financial data2000 AMS Classification:62M10, 62P20

A series of returns are often modeled using stochastic volatility models. Many observed financial series exhibit unit-root non-stationarybehavior in the latent AR(1) volatility process and tests for a unit-rootbecome necessary, especially when the error process of the returns iscorrelated with the error terms of the AR(1) process. In this paper, wedevelop a class of priors that assigns positive prior probability on thenon-stationary region, employ credible interval for the test, and showthat Markov Chain Monte Carlo methods can be implemented usingstandard software. Several practical scenarios and real examples areexplored to investigate the performance of our method.

A series of returns are often modeled using stochastic volatility models. Many observed financial series exhibit unit-root non-stationarybehavior in the latent AR(1) volatility process and tests for a unit-rootbecome necessary, especially when the error process of the returns iscorrelated with the error terms of the AR(1) process. In this paper, wedevelop a class of priors that assigns positive prior probability on thenon-stationary region, employ credible interval for the test, and showthat Markov Chain Monte Carlo methods can be implemented usingstandard software. Several practical scenarios and real examples areexplored to investigate the performance of our method.
EFFICIENT FAMILY OF EXPONENTIALESTIMATORS FOR THE POPULATIONMEAN
EFFICIENT FAMILY OF EXPONENTIALESTIMATORS FOR THE POPULATIONMEAN
Yazar: Yadav, Subhash Kumar; Kadılar, Cem
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 6, 2014
Anahtar kelimeler: Exponential estimator, auxiliary variable, bias, mean square error, efficiency.

This paper deals with the estimation of the population mean with improved family of exponential estimators for the variable under studyusing some known population parameters of the auxiliary variable. Theexpressions for the bias and mean square error (MSE) of the estimatorsof the proposed family have been derived to the first degree of approximation. A comparison has been made with the exponential family ofestimators of Singh et al. [10]. An improvement has been shown overthe family of estimators of Singh et al. [10] through an empirical study.

This paper deals with the estimation of the population mean with improved family of exponential estimators for the variable under studyusing some known population parameters of the auxiliary variable. Theexpressions for the bias and mean square error (MSE) of the estimatorsof the proposed family have been derived to the first degree of approximation. A comparison has been made with the exponential family ofestimators of Singh et al. [10]. An improvement has been shown overthe family of estimators of Singh et al. [10] through an empirical study.
A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function
A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function
Yazar: Gülyaz, Selma; Karapınar, Erdal
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 4, 2014
Anahtar kelimeler: Coupled fixed point; Mixed monotone property; Implicit relation; Orderedpartial metric space2000

In this manuscript, we discuss the existence of coupled fixed points inthe context of partially ordered metric spaces through implicit relationsfor mappings F : X× X → X such that F has the mixed monotoneproperty. Our main theorem improves and extends various results inthe literature. We also state an example to illustrate our work.

In this manuscript, we discuss the existence of coupled fixed points inthe context of partially ordered metric spaces through implicit relationsfor mappings F : X× X → X such that F has the mixed monotoneproperty. Our main theorem improves and extends various results inthe literature. We also state an example to illustrate our work.
On &#960 - Morphic Modules
On &#960 - Morphic Modules
Yazar: Harmanci, A.; Kose, H.; Kurtulmaz, Y.
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 4, 2014
Anahtar kelimeler: Endomorphism rings; π-morphic rings; π-morphic modules; unit π-regularrings.

Let R be an arbitrary ring with identity and M be a right R-modulewith S = End(MR ). Let f∈ S. f is called π-morphic if M/fn (M ) ∼= r M (f n ) for some positive integer n. A module M is called π-morphicif every f∈ S is π-morphic. It is proved that M is π-morphic andimage-projective if and only if S is right π-morphic and M generates itskernel. S is unit-π-regular if and only if M is π-morphic and π-Rickartif and only if M is π-morphic and dual π-Rickart. M is π-morphic andimage-injective if and only if S is left π-morphic and M cogenerates itscokernel.

Let R be an arbitrary ring with identity and M be a right R-modulewith S = End(MR ). Let f∈ S. f is called π-morphic if M/fn (M ) ∼= r M (f n ) for some positive integer n. A module M is called π-morphicif every f∈ S is π-morphic. It is proved that M is π-morphic andimage-projective if and only if S is right π-morphic and M generates itskernel. S is unit-π-regular if and only if M is π-morphic and π-Rickartif and only if M is π-morphic and dual π-Rickart. M is π-morphic andimage-injective if and only if S is left π-morphic and M cogenerates itscokernel.
Greens Functional Concept for a Nonlocal Problem
Greens Functional Concept for a Nonlocal Problem
Yazar: Özen, Kemal; Oruçoğlu, Kamil
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 4, 2014
Anahtar kelimeler: Green’s function; loaded differential equation; nonlocal condition; adjointproblem.

In this work, by Green’s functional concept, in order to obtain Green’ssolution we concentrate on a new constructive technique by which alinear completely nonhomogeneous nonlocal problem for a second-orderloaded differential equation with generally variable coefficients satisfying some general properties such as p-integrability and boundedness istransformed into one and only one integral equation. A system of threeintegro-algebraic equations called the special adjoint system is obtainedfor this problem. A solution of this special adjoint system is Green’sfunctional which enables us to determine Green’s function and Green’ssolution for the problem. Two illustrative applications are provided.

In this work, by Green’s functional concept, in order to obtain Green’ssolution we concentrate on a new constructive technique by which alinear completely nonhomogeneous nonlocal problem for a second-orderloaded differential equation with generally variable coefficients satisfying some general properties such as p-integrability and boundedness istransformed into one and only one integral equation. A system of threeintegro-algebraic equations called the special adjoint system is obtainedfor this problem. A solution of this special adjoint system is Green’sfunctional which enables us to determine Green’s function and Green’ssolution for the problem. Two illustrative applications are provided.
On One Weighted Inequalities for Convolution Type Operator
On One Weighted Inequalities for Convolution Type Operator
Yazar: B, R. A.; -, -
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 3, 2014
Anahtar kelimeler: Weighted Lebesgue space, Singular integral, Kernel, Generalized H¨ormander’s condition, Boundedness.

In this paper we prove the boundedness of certain convolution operatorin a weighted Lebesgue space with kernel satisfying the generalizedH¨ ormander’s condition. The sufficient conditions for the pair of generalweights ensuring the validity of two-weight inequalities of a strong typeand of a weak type for convolution operator with kernel satisfying thegeneralized H¨ormander’s condition are found.

In this paper we prove the boundedness of certain convolution operatorin a weighted Lebesgue space with kernel satisfying the generalizedH¨ ormander’s condition. The sufficient conditions for the pair of generalweights ensuring the validity of two-weight inequalities of a strong typeand of a weak type for convolution operator with kernel satisfying thegeneralized H¨ormander’s condition are found.
Anti-Invariant &#958 &#8869 -Riemannian Submersions fromAlmost Contact Manifolds
Anti-Invariant &#958 &#8869 -Riemannian Submersions fromAlmost Contact Manifolds
Yazar: Lee, Jae Won
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 3, 2014
Anahtar kelimeler: Riemannian submersion, Sasakian manifold, Anti-invariant ξ⊥ -Riemannainsubmersion2000 AMS Classification:53C25, 53C40, 53C50

We introduce anti-invariant ξ⊥ -Riemannian submersions from almostcontact manifolds onto Riemannian manifolds. We give an example,investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of suchsubmersions. We also find necessary and sufficient conditions for a special anti-invariant ξ⊥ -Riemannian submersion to be totally geodesic.Moreover, we obtain decomposition theorems for the total manifold ofsuch submersions.

We introduce anti-invariant ξ⊥ -Riemannian submersions from almostcontact manifolds onto Riemannian manifolds. We give an example,investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of suchsubmersions. We also find necessary and sufficient conditions for a special anti-invariant ξ⊥ -Riemannian submersion to be totally geodesic.Moreover, we obtain decomposition theorems for the total manifold ofsuch submersions.
On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance
On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance
Yazar: Kesemen, Tülay
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 3, 2014
Anahtar kelimeler: Semi-Markovian random walk; a discrete interference of chance; Weibulldistribution; ergodic distribution; asymptotic expansion; ladder variables.

In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered.It is assumed that therandom variables {ζn } , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0. Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.

In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered.It is assumed that therandom variables {ζn } , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0. Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.
Z3-Graded Differential Calculus on the Quantum Space R3q
Z3-Graded Differential Calculus on the Quantum Space R3q
Yazar: Yasar, Ergün; Bakkaloglu, Ahmet
Dergi: Hacettepe Journal of Mathematics and Statistics, Vol. 42 No. 2, 2014
Anahtar kelimeler: Z -graded quantum 3d space, Lie algebra, inner derivation, Lie derivation

In this work, the Z-graded differential calculus of the extended quantum 3d space is constructed. By using this differential calculus, weobtain the algebra of Cartan-Maurer forms and the corresponding quantum Lie algebra. To give a Z-graded Cartan calculus on the extendedquantum 3d space, the noncommutative differential calculus on thisspace is extended by introducing inner derivations and Lie derivatives.

In this work, the Z-graded differential calculus of the extended quantum 3d space is constructed. By using this differential calculus, weobtain the algebra of Cartan-Maurer forms and the corresponding quantum Lie algebra. To give a Z-graded Cartan calculus on the extendedquantum 3d space, the noncommutative differential calculus on thisspace is extended by introducing inner derivations and Lie derivatives.