modern research physics

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Some boundary value problems for the Cauchy-Riemann equation with non-local boundary conditions in several regions of plane have been investigated and solved by authors. In this paper, by making use of fundamental solutions of Cauchy-Riemann equations and by presenting analytic solutions to the above-mentioned boundary value problems, we try to present an analytic expression for the solution of Cauchy-Riemann equation in the first semi-quarter.

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Shewhart control charts are widely accepted as standard tools monitoring manufacturing statistical processes. The control charts have not applied, when the process distribution is not normal. The bootstrap is one of the resampling methods that can be used in statistical quality control without normality assumption. In most of papers, only the percentile bootstrap confidence interval is used for control limits. In this paper, we apply percentile bootstrap, bootstrap-t, bias corrected accelerated (BCa) and approximate bootstrap confidence interval (ABC) for mean control limits of statistical process. Then, the bootstrap confidence intervals are used and compared for mean control limits in simulation study. Finally, the bootstrap control limits are used for mean of CO2 data in Isfahan Zamzam factory.

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By using the Berwald connection, we show that there is a linear connection &nabla such that these are projectively equivalent and belong to the same projective structure on TM. We find a condition for the geodesics of the berwald connection under which &nabla is complete.

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In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) for analytic treatment of nonlinear Volterra integral equations, and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations.

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We introduce quasi-cofaithful ideals which is a generalization of cofaithful ideals, and investigate their
properties. We say a faithful ideal $I$ is textit{quasi-cofaithful} if $I$ contains a finitely generated
faithful ideal $I_1$. We show that every faithful ideal of $R$ is quasi-cofaithful if and only if every faithful ideal of $M_n(R)$ is quasi-cofaithful. We show that if $R$ has the descending chain condition on right annihilators of right ideals, then each faithful ideal of $R$ is quasi-cofaithful. For a u.p.-monoid $M$, it is shown that if $R$ is a quasi-Baer ring, then each faithful ideal of $R$ is quasi-cofaithful if and only if each faithful ideal of monoid ring $R[M]$ is quasi-cofaithful.

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Let R be a commutative ring with non-zero identity and M be a unital R-module. Then the concept of quasi-secondary submodules of M is introduced and some results concerning this class of submodules is obtained

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هدف اصلی در این مقاله حل معادلات انتگرال- دیفرانسیل فردهلم خطی با تأخیر زمانی از مراتب بالا است. روش مبتنی بر بسط لژاندر با استفاده از نقاط هم محلی گاوس- لژاندر می باشد. در این روش سری لژاندر قطع شده جواب معادله را در نظر گرفته و معادله انتگرال- دیفرانسیل خطی و شرایط داده شده را به یک معادله ماتریسی تبدیل می کنیم، سپس با استفاده از نقاط هم محلی گاوس- لژاندر، معادله ماتریسی تبدیل به یک دستگاه از معادلات جبری خطی با ضرایب مجهول بسط لژاندر می شود که از حل دستگاه، ضرایب بسط لژاندر تابع جواب به دست می آید. در آخر کارایی روش را با مثال هایی مورد تجزیه و تحلیل قرار می دهیم.

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Mortality forecasts are nowadays widely used to create and modify retirement pension schemes, disability insurance systems and other social security programmers. Experience shows that static life tables overestimate death probabilities. The reason for this overestimation is that static life tables, through being computed for a specific period of time, cannot take into account the decreasing mortality trend over time. Dynamic life tables overcome this problem by incorporating the influence of the calendar when graduating mortality.
In this paper, we first apply the Lee-Carter model for estimation of mortality rate. Then, we use parametric and semi parametric bootstrap prediction intervals for mortality trend. Finally, these methods are applied for analysis of mortality data of Iran.

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Spatial generalized linear mixed models are usually used for modeling non-Gaussian and discrete spatial responses. In these models, spatial correlation of the data can be considered via latent variables. Estimation of the latent variables at the sampled locations, the model parameters and the prediction of the latent variables at un-sampled locations are of the most important interest in SGLMM. Often the normal assumption for latent variables is considered just for convenient in practice. Although this assumption simplifies the calculations, in practice, it is not necessarily true or possible to be tested. In this paper, a closed skew normal distribution is proposed for the spatial latent variables. This distribution includes the normal distribution and also remains closed under linear conditioning and marginalization. In these models, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, for maximum likelihood estimation of the model parameters and predictions of latent variables, an approximate algorithm is introduced that is faster than the former method. The performance of the proposed model and algorithm are illustrated through a simulation study.

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بخش مهمی از مسائل قابل هدایت در مهندسی، از جمله مهندسی شیمی، مسائل کنترلی از نوع تنظیم‏کننده هستند. از طرفی روش‏های گرادیان مزدوج تعمیم یافته و روش نشاندن قابلیت‏های توانمندی در حل این مسائل دارند. این مقاله با معرفی الگوریتم آنها برای حل مسائل کنترل بهینه، به مقایسه این دو شیوه کارا، از نظر تحلیلی و عددی خواهد پرداخت. همچنین چگونگی کاربرد آنها در محاسبه مسیر و کنترل بهینه یک مخزن هم زده شده پیوسته راکتور شیمیایی را که تا کنون از این دو شیوه حل نشده‏اند، بیان و بررسی می‏نماید. در این راستا با بیان مثال‏های عددی، مقادیر بهینه همراه با مسیر و کنترل بهینه حاصل از این روش‏ها، مقایسه خواهند شد.

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An automorphism $theta$ of a group $G$ is pointwise inner if$theta(x)$ is conjugate to $x$ for any $xin G$. It is interesting and natural to discuss the question of ``finding necessary and sufficient conditions for a group $G$ such that certain subgroups of $text{Aut}(G)$ be equal''.
There are some well-known results in this regard for finite groups.
In this paper, we find a necessary and sufficient condition in certain finitely generatednilpotent groups of class 2 for which $mathrm{Aut}_{pwi}(G)simeq mathrm{Inn}(G)$. We also prove that
in a nilpotent group of class 2 with cyclic commutator subgroup $mathrm{Aut}_{pwi}(G)simeq mathrm{Inn}(G)$ and the quotient$mathrm{Aut}_{pwi}(G)/mathrm{Inn}(G)$ is torsion. In particular if $G'$ is a finite cyclic group then $mathrm{Aut}_{pwi}(G)= mathrm{Inn}(G)$.

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In this article‎, ‎the efficient numerical methods for finding solution of the linear and nonlinear Fredholm integral equations of the second kind on base of Bernstein multi scaling functions are being presented‎. ‎In the beginning the properties of these functions‎, ‎which are a combination of block-pulse functions on ‎, ‎and Bernstein polynomials with the dual operational matrix are presented‎. ‎Then these properties are used for the purpose of conversion of the mentioned integral equation to a matrix equation that are compatible to a algebraic equations system‎. ‎The imperative of the Bernstein multi scaling functions are‎, ‎for the proper quantitative value of and have a high accuracy and specifically the relative errors of the numerical solutions will be minimum‎. ‎The presented methods from the standpoint of computation are very simple and attractive and the numerical examples which were presented at the end shows the efficiency and accuracy of these methods‎.

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In this paper, we study the Arens regularity properties of module actions and we extend some proposition from Baker, Dales, Lau and others into general situations. We establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. In 1951 Arens shows that the second dual of Banach algebra endowed with the either Arens multiplications is a Banach algebra, see [1]. The constructions of the two Arens multiplications in lead us to definition of topological centers for with respect to both Arens multiplications. The topological centers of Banach algebras, module actions and applications of them were introduced and discussed in [3, 5, 6, 9, 15, 16, 17, 18, 19, 24, 25]. In this paper, we extend some problems from [3, 5, 6, 16, 22] to the general criterion on module actions with some applications in group algebras. Baker, Lau and Pym in [3] proved that for Banach algebra with bounded right approximate identity, is an ideal of right annihilators in and . In the following, for a Banach , we study the similar discussion on the module actions and for Banach , we show that

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Let ( R,m ) be a Noetherian local ring, a an ideal of R and M a finitely generated R- module. We investigate some properties of formal local cohomology modules with respect to a Serre subcategory. We provide a common language to indicate some properties of formal local cohomology modules. Let ( R,m ) be a Noetherian local ring, a an ideal of R and M a finitely generated R- module. We investigate some properties of formal local cohomology modules with respect to a Serre subcategory. We provide a common language to indicate some properties of formal local cohomology modules.

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In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integro-differential equations (FVHIDEs) under mixed condition. This method of estimating the solution, transforms the nonlinear (FVHIDEs) to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results and comparisons demonstrate that our estimate has good degree of accuracy and this method is more valid and useful than other methods.In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integro-differential equations (FVHIDEs) under mixed condition. This method of estimating the solution, transforms the nonlinear (FVHIDEs) to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results and comparisons demonstrate that our estimate has good degree of accuracy and this method is more valid and useful than other methods.

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            Inverse time - dependent heat source   problems have an important role in many branches
     of science and  technology. The aim of this paper is to solve these classes of problems using a 
     variational  iteration  method(VIM). The method applied does not require discretization  of the
      region, as in the case  of classical methods based on the finite difference method,  the boundary
     element method  or the other methods.  Applying this method, we obtain a stable approximation
      to an  unknown source term  in an inverse heat equation   from  over-specified data  that the  source
      term is only time - dependent.  Some numerical examples using this approach are presented and
     discussed

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Copula functions are powerful tools for construction the multivariate distribution of dependent variables in terms of their marginal distributions. Each of these functions provide a model which represents all properties of the variables dependency. For spatial data analysis, the dependence structure of the data should be determined by using the multivariate distribution of the random field. In analysis of Spatio-temporal data it is also necessary to identify the relations between spatial and temporal structure of the data in terms of Spatio-temporal covariance function. Sometimes a separable Spatio-temporal covariance function is used for the ease of application, but in some applications this property is not realistic. In these cases it is required to use a non-separable Spatio-temporal covariance function. In this paper the role of copula functions in determination of joint distribution of a random field is considered and the properties of a valid spatial copula function are determined. Then a new valid spatial copula family is introduced. Next some spatial and nonseparable Spatio-temporal covariance functions are constructed by using these copula functions

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Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed models, such that the spatial correlation of the data can be introduced via normal latent variables. The model parameters and the prediction of the latent variables at unsampled locations are of the most important interest in SGLMM by estimating of the latent variables at sampled locations. In these models, since there are the latent variables and non-Gaussian spatial response variables, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, a new algorithm is introduced for maximum likelihood estimation of the model parameters and predictions, that is faster than the former method. This algorithm obtains to combine the pseudo maximum likelihood method, the Expectation maximization Gradient algorithm and an approximate method. The performance and accuracy of the proposed model are illustrated through a simulation study. Finally, the model and the algorithm are applied to a case study on rainfall data observed in the weather stations of Semnan in 2012.

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In this papear, we produce the method for formation and recognizing boundary layers in singular perturbation problems. This method involves four step for localization of non-local boundary conditions to local case.For the given problem some sufficient and necessary conditions are given for formation and non formation of boundary layers. Since the existence of boundary layers and their places has a direct relation with the structure of approximate solutions and uniform solutions, therefore the main purpose of this paper is recognition and formation of boundary layers in singular perturbation problems with non-local boundary conditions. This process will be done by using fundamental solution of adjoint given differential equation and necessary conditions.In fact by using these necessary conditions and given boundary conditions, we make an algebraic system.By solving this algebraic system by Cramer rule we obtain boundary values of unknown function.These values of unknown function are local boundary conditions.The mathematical model for this kind of problem usually is in the form
of either ordinary differential equations (O.D.E) or partial differential equations (P.D.E) in which the highest derivative is multiplied by some powers of as a positive small parameter.

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Monitoring process mean and variance simultaneously in a single control chart simplifies
the process monitoring. If in addition, a simultaneous control chart is capable of
recognizing the source of contamination, this capability leads to additional simplicity.
These are the reasons why simultaneous control charts have attracted many researchers and
manufacturers.
Recently, in the statistical process control literature some control charts have been
introduced which are based on the idea of Bayesian predictive density. This type of control
charts, not only brings into account the uncertainty concerning the estimation of unknown
parameters, but also do not need extensive simulations for computation of control limits.
These control charts have been introduced for mean and variance in both univariate and
multivariate situations.
Up to now, no simultaneous control chart has been introduced based on Bayesian predictive
density. In this paper, using the idea of Bayesian predictive density, we introduce a new
simultaneous control chart for monitoring univariate mean and variance. We illustrate the
important capabilities of this new chart through simulated data.
This new chart is applicable when parameters are unknown. In other words, it brings into
account the uncertainty concerning the unknown parameters. This chart is able to recognize
the source of contamination and is sensitive to small changes in the mean and variance. In
this chart the control limits, needless of simulation, can simply be obtained from normal
table.