In this paper, an alternative approach in operational Modal analysis is presented, utilizing image processing technique and transmissibility functions. Imaging sensors do not impose additional mass on the structure due to their non-contact nature, while transmissibility functions, independent of excitation type, can directly extract mode shapes. The innovation of this research lies in combining these two techniques to record dynamic responses and identify Modal properties. To capture the temporal response history from video signals, the block-matching method with sub-pixel accuracy was employed. Validation was conducted by recording the response of the tip of a cantilevered steel beam subjected to impact excitation, using a high-speed camera and a laser vibrometer, simultaneously. The RMSE plots in the time domain and the PSD in the frequency domain indicate high accuracy of this method. Using this approach, the displacement time histories of various points on the structure were extracted from the video signals, and the Modal properties, including natural frequencies, damping ratios, and mode shapes, were identified using the transmissibility matrix method. The results obtained from the proposed method were compared with the stochastic subspace identification (SSI) method and analytical solutions. The findings reveal the accuracy of the Modal identification approach introduced in this article. The highest relative error in estimating the natural frequencies of the first and second modes, compared to the values from the laser method, are 0.19% and 0.13%, respectively, and in comparison to the analytical values, they are 0.34% and 1.5%, respectively.

In this paper, we define and study the Modal operators on pseudo-BE algebras as special cases of closure operators on these structures. We prove that the composition of two Modal operators is a Modal operator if and only if they commute. For the particular case of a good pseudo-BCK algebra an equivalent definition of the Modal operators is given, and the notion of a strong Modal operator is introduced and studied. We also define the notions of Modal deductive systems and Modal homomorphisms on pseudo-BE algebras and we investigate their properties. It is proved that, if two Modal operators have the same image, then they coincide. Also, given a normal Modal deductive system H of a distributive Modal pseudo-BE algebra (A; f) we construct a Modal operator on the quotient pseudo-BE algebra A=H.

Abstract. Intuitionistic Fuzzy Modal operator was defined by Atanassov in [3] in 1999. In 2001, [4], he introduced the generalization of these Modal opera-tors. After this study, in 2004, Dencheva [14] defined second extension of these operators. In 2006, the third extension of these was defined in [6] by Atanassov. In 2007, [11], the author introduced a new operator over Intuitionistic Fuzzy Sets which is a generalization of Atanassov's and Dencheva's operators. At the same year, Atanassov defined an operator which is an extension of all the operators defined until 2007. The diagram of One Type Modal operators on Intuitionistic Fuzzy Sets was introduced first in 2007 by Atanassov [10]. In 2008, Atanassov defined the most general operator and in 2010 the author expanded the diagram of One Type Modal operators on Intuitionistic Fuzzy Sets with the operator Zwa,b Some relationships among these operators were studied by several researchers [5]-[8] [11], [13], [14]- [19]. The aim of this paper is to expand the diagram of one type Modal operators over intuitionistic fuzzy sets. For this purpose, we defined a new Modal oparator Zw,qa,b over intuitionistic fuzzy sets. It is shown that this oparator is the generalization of the operators Zwa,b, Ea,b,  oa,b, a,b.

The Schwarz inequality and Jensen’s one are fundamental in a Hilbert space. Regarding a sesquilinear map B(X, Y ) = Y*X as an operatorvalued inner product, we discuss operator versions for the above inequalities and give simple conditions that the equalities hold.

There is a famous idea in Modal epistemology according to which conceivability of a proposition is a good guide for its possibility. Yablo (1993) persents a model for justification of Modal beliefs, based on which Conceivability of a proposition is evidence for its possibility. Van Inwagen (1998) believes that if we accept Yablo’s model, we have to accept Modal skepticism. To argue for this, Van Inwagen examines the Modal status of the proposition that transparent iron exists on Yablo’s model. Van Inwagen claims that this proposition is undecidable on Yablo’s model. So we cannot have a justified belief that it is possible that transparent iron exists. If van Inwagen’s claim about the Modal status of the proposition that transparent iron exists is correct, Yablo’s model, one might think, faces a serious problem. For if we generalize van Inwagen’s analysis of the proposition that transparent iron exists, we have to count intuitively possible propositions, propositions the Modal status of which can be intuitively known as possible, as undecidable. But it is quite plausible that our beliefs about the possibility of some intuitively possible propositions are justified, so these propositions are not undecidable. I will, however, argue that van Inwagen’s analysis of Modal status of the proposition that transparent iron exists cannot be generalized to all (or most) intuitively possible propositions. And therefore it is possible to accept at the same time both Yablo’s justification model and van Inwagen’s analysis about the Modal status of propositions like transparent iron exist.

In this investigation, using Opoola differential operator ($D^{m}(\mu,\beta,t)f(z)$), a new integral operator: $I_{t,\beta,\mu}^{m,\sigma}(f_{1},...,f_{n})(z): A^{n}\rightarrow A$  is defined in the unit disk, $U=\left\lbrace z\in C:\left|z\right|<1\right\rbrace$; and we investigated the Univalence conditions of this generalized operator. Finally, a number of corollaries and remarks which show the extension of our results are presented.