نشریه پژوهشهای ریاضی
سال دهم شماره 4 (پیاپی 31، زمستان 1403)

Let AlgN be a nest algebras on Hilbert space and let φ:Alg N --> AlgN be an additive map. We prove that if Xφ(Y)+φ(X)Y=0 whenever X, Y in AlgN are such that XY = Y X = 0, then φ is a centralizer. By applying these results we obtain some corollaries concerning (Jordan) centralizers on nest algebras.

The homogeneity of variances test is a prerequisite for many statistical methods. In this article, a recently introduced test based on the jackknife approach is compared with common tests such as Levene's and Bartlett's tests, as well as two tests by James and Alexander-Govern, in terms of their ability to maintain the first type error rate and test power for several distributions. The permutation versions of these tests were also examined. The results indicate that the performance of the tests significantly improves in the permutation version. To evaluate the performance of the tests in the real world, the tests were applied to two real data sets, and the results are presented.

Suppose that (R, m) is a Noetherian complete local ring of dimension d ≥ 4. Let 2 ≤ k ≤ d−2 be an integer and assume that a1,…,ak is a part of a system of parameters for R. In this paper, it is shown that the category of all (a1,…,ak )R-cofinite modules is not an Abelian category.

In this paper, the probability density function of the process, its trend functions, the maximum likelihood estimate and the confidence interval of the parameters are calculated. This paper investigates a nonhomogeneous state of a diffusion process with a time-dependent velocity reduction coefficient. First, the process probability density function and trend functions are calculated and then, using discrete sampling, statistical inferences such as estimating the parameters by the maximum likelihood method, finding the distribution of the obtained estimators and the confidence interval of the parameters are performed. Finally, for the simulated data, the applications of this model are introduced. In this paper, from the point of view of statistical inference, stochastic differential equation models are studied. A heterogeneous case of a diffusion process with time-dependent deceleration coefficient and stochastic differential equation models with random effects are investigated and an approximation for the nonlinear stochastic differential equation is presented. Also, with the help of time series analysis and statistical methods, the parameters of stochastic differential equation models are estimated.At the end, the application of invariant copulas in the modeling of stochastic differential equations is expressed. In each of these cases, the process probability density function and trend functions are calculated, and statistical inferences such as point estimation, interval estimation, selection of the best model, and numerical analyzes and simulations are performed in stochastic differential equations.

Let (X‚ d) and (Y‚ ρ) be compact metric spaces‚ τ be a Lipschitz involution on (X‚ d) and η be Lipschitz involution on (Y‚ ρ). Suppose that  for all x∈X‚ for all y∈Y‚ , A is a real subalgebra of C(X‚ τ) which contains Lip(X‚ d‚ τ) and B is a real subalgebra of C(Y‚ η) which contains Lip(Y‚ ρ‚ η). We prove that if T:A→B is a surjetive -homogenous norm-additive in modulus map then there exists a unique bijection  such that  for all f∈A ‚ y∈Y and . Applying this fact‚ we show that if  (X‚d) and (Y‚ρ) are compact metric spaces and  is a surjective -homogenous norm-additive in modulus map then there exists a Lipschitz homeomorphism  from  to such that  for all  and y∈Ỵ

In this paper, generalized binomial edge ideals of corona product of two graphs have been considered. In particular, some explicit formulas for computing the height and the Krull dimension of such ideals in terms of the graphs participating in the corona product have been provided. Moreover, by adding certain special conditions on those graphs, some simpler formulas have been achieved.