Getting OWA weights under given orness level is an active topic in the OWAoperator research. The paper proposes a series of weights generating methods in equidiﬀerent forms. Similar to the geometric (maximum entropy) OWAoperator, we propose a parameterized OWAoperator called equidiﬀerent OWAoperator, which consist the adjacent weighes with a common diﬀerence. The maximum spread equidiﬀerent OWA (MSEOWA) operator is equivalent to the minimum variance OWAoperator, but is more computational eﬃcient. Some properties associated with the orness level are discussed. One of them is that the aggregation value for any elements set is always increasing with the orness level, which can used as a parameterized aggregation method with orness as its control parameter. These properties similar to that of the geometric (maximum entropy) OWAoperator, which can also be seen as the discrete case of equidiﬀerent RIM (regular increasing monotone) quan- tiﬁers. The general forms of equidiﬀerent OWAoperator are proposed, and the weights generating methods are also extended in a similar way.
As a generalization of Yager’s OWAoperator, T1OWA operators provide an efficient tool to aggregate uncertain information modelled by fuzzy sets in soft decision making. By appropriately selecting fuzzy sets for the weights, various forms of T1OWA operators can be created to fulfill different tasks under multi-granular linguistic contexts. This has been demonstrated in the above case study of diabetic diagnosis, which is an imbalanced data problem. By appropriately selecting the uncertain weights to favour the rare class, such as
In this paper, in order to facilitate the assessing process, a two-level assessing model, including fuzzy model and OWAoperator-based decision-making model is developed, which benefits from the fuzzy properties and the capabilities of OWAoperator combination . Consider of the fundamental and commonly used means to evaluate transformer conditions. Employed are the transformer preventive tests including the electrical test, oil test, oil chromatographic analysis and other indicators. A OWAoperator-based decision-making procedure for condition assessments is then presented to illustrate how to use the model to address an assessing issue. The case study shows that the model is capable of providing a meaningful and effective condition assessment.
We have analyzed the use of the OWAoperator in the index of maximum and minimum level. As a result, we have obtained a new aggregation operator: the OWAIMAM operator. This operator is very useful because it provides a parameterized family of aggregation operators in the IMAM operator that includes the maximum, the minimum and the average. The main advantage of the OWAIMAM is that we can manipulate the neutrality of the aggregation so the decision maker can be more or less optimistic according to his interests. We have studied some of its main properties.
These properties are displayed in Fig. 2 , which shows the forward citations received by A. Let A be a patent published in 2000 and B, D and F be patents published around 2006, and citing A. The links between A and B, A and D, and A and F are direct citations. If C cites B without citing A this is an indirect citation. C also cites D, indicated by the grey line, which means that although it might appear to be another indirect citation it is not considered as such because of the previous direct rela- tion between D and A. In other words, as there are two or more indirect citations, but all refer to the same original node, we count them only once. While it is straightforward to identify direct citations, indirect citations require that each node in the network is counted only once and, more speciﬁcally, on its ﬁrst appearance. Studies on citation networks consider indirect citations in terms of co-citation and bibliographic coupling [33,67,49] . Co-citation is deﬁned as the edge between two nodes cited by the same node(s). In Fig. 2 , nodes B and D are cited by C. As Boyack and Klavans  noted, co-citation analysis is used in mapping science to identify the research front within a discipline. Bibliographic coupling is deﬁned as the edge between two nodes citing the same node(s). In Fig. 2 , there is bibliographic coupling between F and G, as they both cite D. Recent studies have validated the performance of these methods to detect emerging research front [66,12] and investi- gated citation networks with combinational types of citations, such as including direct citations and co-citations to exploit new possibilities of detecting research fronts  . The concept of indirect citations proposed in this paper differs from these studies, as described in our example referring to Fig. 2 .
The subject of fractional calculus (integral and derivative of any arbitrary real or com- plex order) has acquired significant popularity and major attention from several authors in various science due mainly to its direct involvement in the problems of differential equations in mathematics, physics, engineering and others for example Baskonus and Bulut (2015), Yin et al. (2015) and Bulut (2016). The fractional calculus has gained an interesting area in mathematical research and generalization of the (derivative and inte- gral) operators and its useful utility to express the mathematical problems which often leads to problems to be solved see Yao et al. (2015), Baskonus (2016) and Kumar et al. (2016). Specifically, it utilized to define new classes and generalized many geometric properties and inequalities in complex domain. In another words, these operators are play an important role in geometric function theory to define new generalized sub- classes of analytic univalent and then study their properties. By using the technique of convolution or Hadamard product, Sălăgean (1981) defined the differential operator D n of the class of analytic functions and it is well known as S a ˇ l a ˇ gean operator. Followed by Al-Oboudi differential operator see Al-Oboudi (2004). Several authors have used the S a ˇ l a ˇ gean operator to define and consider the properties of certain known and new classes of analytic univalent functions. We refer here some of them in recent years. Najafzadeh (2010) investigated a new subclass of analytic univalent functions with negative and fixed finitely coefficient based on S a ˇ l a ˇ gean and Ruscheweyh differential operators. Aouf et al. (2012) gave some results for certain subclasses of analytic functions based on the defi- nition for S a ˇ l a ˇ gean operator with varying arguments. El-Ashwah (2014) used S a ˇ l a ˇ gean operator to define a new subclass of analytic functions and derived some subordination
It is well known that the Helmholtz equation is an elliptic partial diﬀerential equation describing the electromagnetic wave, which has important applications in geophysics, medicine, engineering application, and many other ﬁelds. Many problems associated with the Helmholtz equation have been studied by many scholars, for example [–]. The boundary value problem for partial diﬀerential equations is an important and meaning- ful research topic. The singular integral operator is the core component of the solution of the boundary value problem for a partial diﬀerential system. The Teodorescu operator is a generalized solution of the inhomogeneous Dirac equation, which plays an important role in the integral representation of the general solution for the boundary value problem. Many experts and scholars have studied the properties of the Teodorescu operator. For ex- ample, Vekua  ﬁrst discussed some properties of the Teodorescu operator on the plane and its application in thin shell theory and gas dynamics. Hile  and Gilbert  stud- ied some properties of the Teodorescu operator in n-dimensional Euclid space and high complex space, respectively. Yang  and Gu  studied the boundary value problem associated with the Teodorescu operator in quaternion analysis and Cliﬀord analysis, re- spectively. Wang [–] studied the properties of many Teodorescu operators and related boundary value problems.
Based on the elaborate research, Yoshida ( and ) has considered the subharmonic function deﬁned on a cone or a cylinder which is dominated on the boundary by a certain function and generalized the classical Phragmén-Lindelöf theorem by making a harmonic majorant. Later Yoshida  proved the property of a harmonic function deﬁned on a half-space which is represented by the generalized Poisson integral with a slowly growing continuous function on the boundary. In  or  Yoshida and Miyamoto generalized some theorems (from ) to the conical case and extended the results (from  and ) given particular solutions and a type of general solutions of the Dirichlet problem on a cone by introducing conical generalized Poisson kernels and Poisson integrals. On the other hand, Qiao and Deng  extended Yoshida’s results (from ) to the situa- tion for the stationary Schrödinger operator; for the relevant research on the stationary Schrödinger operator, we may refer to Bramanti , Kheyﬁts [–] and Levin et al. [, ]. However, we ﬁnd a falsehood in  and have to make a correction. In  or  we also know the Green function associated with the stationary Schrödinger operator. Dependent on the related statement above, we are to be concerned with the solutions of the Dirichlet problem for the stationary Schrödinger operator L a on C n () and with their
good properties and important applications, it has been a much studied and signiﬁcant topic. Vekua  ﬁrst discussed some properties of the Teodorescu operator detailedly, and Hile  studied some properties of the Teodorescu operator in R n . Then Gilbert et al.  and Meng  studied its many properties in high dimensional complex space. Gürlebeck and Sprössig , and Yang  discussed its properties and the corresponding boundary value problems in the real quaternion analysis. Wang and Gong  discussed the stabilities of the singular integral operators when the boundary curve of integral do- main is perturbed. Recently, Brackx et al.  studied some properties of the Teodorescu operator which is related to the Hermitian regular functions. Wang et al. [, ] showed some properties of the Teodorescu operator and corresponding boundary value problems. In this paper, we deﬁne a kind of generalized Teodorescu operator which is related to the k-regular functions in real Cliﬀord analysis. First, we discuss the boundedness and Hölder continuity for the generalized Teodorescu operator in a nonempty open bounded connected domain in R n . Second, we discuss the stability and give the error estimate of the generalized Teodorescu operator when the boundary surface of the integral domain is perturbed. These results make the theory of Cliﬀord analysis more perfect and also lay a theoretical foundation for studying the properties of singularity integral operator in Cliﬀord analysis.
The UIVOWA operator, however, needs not be an interval-valued aggre- gation function, since, for instance, the output may not be an interval. For this reason, we study which conditions allow us to ensure that the result is an interval. We do not do this for the general case of admissible orders, but just for the specific case of the lexicographical orders, since the whole analysis would be too long for this paper.
o Shared or Unsecured: Select this option if you are working from a non- secure computer, or one that multiple people have access to (such as at a public library). This will cause your OWA session to automatically timeout after only a short period of inactivity to prevent non-authorized people from accessing your account.
Proposition . (see ) Let E be a real Banach space, V ⊂ E be a cone, and U ⊂ V be a bounded open subset of V . If the completely continuous operator B : U → V has no ﬁxed point on ∂U, then there exists an integer i(B, U, V ), which is regarded as the ﬁxed point index, and the following statements hold:
The theory of stability is important since stability plays a central role in the structural theory of operators such as semigroup of linear operator, contraction semigroup, invariant subspace theory and to mention but few. The theory of stability is rich in which concerns the methods and ideas, and this shall be one of the main points of this paper. The recent advances deeply interact with modern topics from complex function theory, harmonic analysis, the geometry of Ba- nach spaces, and spectra theory .
Abstract: In this paper, we introduce the class S α,λ n,s (β ), consisting of analytic functions defined by a generalized operator. We derive coefficient inequalities, growth and distortion theorem, extreme points and Fekete-Szeg¨ o problem for functions in this class.
First check the settings of the upper level – Exchange. In the IIS Manager, under Default Web site, locate the Exchange virtual directory. In its Properties window on the Directory Security tab click Edit in Authentication and Access control section. These are settings for OWA itself:
You can access your mailbox through any browser. To access your mailbox, enter your “OWA” web address/url that was provided to you by your network specialist or navigate to www.outlook.com (Outlook Live). On the “Sign In” page, enter your Domain\user name and password.
The above results gave a procedure for constructing eigenfunctions when the point spectrum dominated the rest of the spectrum. Unfortunately, this situation does not hold in a number of cases of interest. Consider a dynamical system with an attractor. In this setting, the spectrum on the unit circle corresponds to the attractor. Since the system is asymptotically stable, eigenvalues corresponding to eigenfunctions supported off-attractor are contained strictly inside the unit circle. In this system, the point spectrum may not dominate the spectrum since there may be parts of the continuous spectrum contained in the unit circle. If we wish to project onto the off- attractor, stable eigenspaces, we need to modify the above GLA procedure which was valid in the presence of a dominating point spectrum. The general idea is to consider the inverse operator U −1 . If U has point spectrum inside the unit circle, then U −1 has point spectrum outside the unit circle via the spectral mapping theorem. The GLA theorems of the last section can then be applied to U −1 to obtain projections onto the stable directions of the attractor. Proposition III.3.8 formalizes this.