Suppose that $\varphi$ is an analytic self-map of the open unit disk $\mathbb{D}$ and $\psi$ is a bounded analytic function on $\mathbb{D}$. The WEIGHTED composition operator $C_{\psi,\varphi}$ is the operator on the WEIGHTED Bergman spaces $A_{\alpha}^{2}$ given by $C_{\psi,\varphi}f=\psi f\circ\varphi$ for any $f\in A_{\alpha}^{2}$. If $\varphi_1,\varphi_2,...,\varphi_n$ are linear fractional non-automorphisms and $\psi_{1},\psi_{2},...,\psi_{n} $ are bounded analytic functions, under some conditions, we obtain a subset of the numerical range of $C_{\psi_1,\varphi_1}+C_{\psi_2,\varphi_2}+...+C_{\psi_n,\varphi_n}$ on $A_{\alpha}^{2}$ and determine when zero lies in the interior of its numerical range.

Control charts are powerful tools of statistical process control (SPC) used for monitoring processes. Control charts are not only used to detect changes in process, but also enable the quality engineers to prepare the system for an appropriate response before production of the faulty products. The main objective of most researches on control charts is developing a favorable and cost-effective design as well as most appropriate sampling methods. In most of the researches that have been done in this field, the control charts are designed based on simple random sampling (SRS). However, there are many charts in the literature of statistical process control that are not based on SRS and use alternative methods such as ranked set sampling (RSS) or generalized methods. The RSS method is an alternative to SRS when taking actual measurement of the quality characteristic is costly or production of the faulty products is expensive. In this paper, in order to improve the performance of mixed EWMA-CUSUM (MEC) and mixed CUSUM-EWMA (MCE) control charts in estimating the population mean, ranked set sampling method rather than common simple random sampling method is used to design these mixed control charts. The performances of the proposed MEC-RSS and MCE-RSS control charts are evaluated through simulation studies using the average run length (ARL) criterion. Moreover, the performances of the proposed control charts are compared with those of CUSUM-SRS, CUSUM-RSS, EWMA-SRS, EWMA-RSS, MEC-SRS, and MCE-SRS control charts. The results revealed that RSS method improves control charts performance compared to SRS method because it provides an efficient estimation of the mean and variance of the population. In addition, using the ranked set sampling scheme makes the proposed mixed control charts more sensitive to detecting the small and moderate shifts in the process mean than the other corresponding classical control charts. Moreover, based on the same sampling methods, the performances of mixed control charts are better than those of the single CUSUM and EWMA control charts.

The aim of this study is Prioritization potential pathway to walking at the historical context of yazd city. the research is an applied research with descriptive analytical method . research indexes were obtained using theoretical framework of research and validation of criteria was confirmed by experts of group and urban traffic experts and experts . the final indices include security, access to public transportation, car traffic volume in the passage, the compatibility of pedestrian adjacent streets, visual landscape, access to roads, width and length of the passage. the indices were WEIGHTED using analytic hierarchy process, then, by using gis software, different layers that have a role in the site selection were created . then the weights assigned to each layer were placed in WEIGHTED SUM function . the results showed that in the old tissue of yazd city, the streets of northern imam khomeini, southern imam khomeini, and Giyam have the most talent. the innovation of this research is using WEIGHTED SUM function over linear layers.

The max+SUM spanning tree problem is to find a spanning tree T* which makes the combined weight “max w(e)+SUM c(e) time” as small as possible, in which a weight w(e) and a cost c(e) are prescribed for each e ͼT. The problem can be solved in O(mlog n) time. In an inverse max+SUM spanning tree problem, T0 is a given spanning tree of G, which is not an optimal max+SUM spanning tree. Then we modify the weight vector w to w̅ so that T0 becomes a max+SUM spanning tree. The goal is to minimize the modification cost ||w̅-w||under Hamming distance. This paper presents a new solution algorithm for the inverse max+SUM spanning tree problem under WEIGHTED SUM-type Hamming distance by modifying the max-weight vector with time complexity of O(mlog n). First, we formulate the problem and then present a new solution algorithm for the problem under investigation. Finally, we present a numerical example to illustrate the efficiency of the algorithm.

The max+SUM spanning tree problem is to find a spanning tree T* which makes the combined weight “, max w(e)+SUM c(e) time”,as small as possible, in which a weight w(e) and a cost c(e) are prescribed for each e ͼ, T. The problem can be solved in O(mlog n) time. In an inverse max+SUM spanning tree problem, T0 is a given spanning tree of G, which is not an optimal max+SUM spanning tree. Then we modify the weight vector w to w̅,so that T0 becomes a max+SUM spanning tree. The goal is to minimize the modification cost ||w̅,-w||under Hamming distance. This paper presents a new solution algorithm for the inverse max+SUM spanning tree problem under WEIGHTED SUM-type Hamming distance by modifying the max-weight vector with time complexity of O(mlog n). First, we formulate the problem and then present a new solution algorithm for the problem under investigation. Finally, we present a numerical example to illustrate the efficiency of the algorithm.

We survey some old and new results concerning WEIGHTED norm inequalities of SUM and product form and apply the theory to obtain limit point conditions for second order differential operators of Sturm-Liouville form defined in Lp spaces. We also extend results of Anderson and Hinton by giving necessary and sufficient criteria that perturbations of such operators be relatively bounded. Our work is in part a generalization of the classical Hilbert space theory of Sturm-Liouville operators to a Banach space setting.

This study discusses some variants of Ordered WEIGHTED Averaging (OWA) operators and related information aggrega-tion methods. In detail, we define the Extended Ordered WEIGHTED SUM (EOWS) operator and the Extended Ordered WEIGHTED Averaging (EOWA) operator, which are applied in scientometrics evaluation where the preference is over finitely many representative works. As contrast, we also define the Infinite Ordered WEIGHTED SUM (InOWS) opera-tor and the Infinite Ordered WEIGHTED Averaging (InOWA) operator, which are more suitable for the corresponding scientometrics evaluation where all of works of scholars are considered. We also define the family of Infinite Gaussian maxitive OWA weights function and the family of Infinite Gaussian OWA weights function, and discuss some of their mathematical properties. Some illustrative examples, comparisons and figures are provided to better expound their applicability in scientometrics evaluation.

Nowadays, development of tourism types is one of the most important research topics in the area of human geography. Because the tourism, on the one hand, has different types and on the other hand, it can have profound and positive effects on the mundane and spiritual dimensions of the human life and geography areas. Development of tourism types in each geography area may encounter with different driver and barriers. Alongside the management structures and physical and mundane prerequisites, dominant tourism pattern on area’s tourism system is one of the factors that has positive and negative effects on its tourism development. Halal tourism is the behavioral-functional pattern that the goal of present research is assessment of its effects on Iran' s tourism types. This article is fundamental and descriptive-analytical research.Method of gathering data is survey by the expert’s questionnaire. The sample consists of 25 tourism professors of Tehran universities. The method of data analysis is WEIGHTED SUM Model (WSM) and Shannon Entropy is used for weighting of indicators. Research findings indicate that the tourism Halal pattern can have different effects on the development, efficiency and affectivity of each type of the country' tourism and this pattern can be a driver factor for some forms of tourism and as a limitation factor for some. The results show the Halal pattern can lead to development of some types of tourism such as religious, cultural, historical, health tourism and ecotourism, while it considers as a limiting factor for development of leisure, marine, adventure tourism.