The purpose of this paper is to develop nonsmooth optimization problems (P) in which all emerging functions are assumed to be real-valued quasiconvex functions that are defined on a finite-dimensional Euclidean space. First, we introduce two linear optimization problems with the same optimal value of the considered problem. Then, we introduce a real-valued non-negative gap function for (P), and we provide some conditions which ensure that its null points are the same as the optimal solution of problem (P). The results are based on Incident subdifferential, which is an important concept in the analysis of quasiconvex functions.

In this paper, we deal with the subdifferential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and necessary and sufficient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdifferential in Hadamard spaces is addressed and some basic properties are highlighted. Finally, a density theorem for subdifferential set is established.

In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator function. Relation between weak subifferential and augmented normal cone and epigraph is also explored. We also obtain optimality conditions via weak subdifferential and augmented normal cone. Finally, we define the Stampacchia and Minty solution via weak subdifferential and investigate the relation between Stampacchia and Minty solution and the minimal point.

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz.Necessary optimality conditions and regularity conditions are given. Our approach are based on the Michel-Penot subdifferential.

We are interested in proposing the convex fuzzy functions from R into E to describe the concepts of left and right generalized derivatives. In this way, several properties of the concepts are discussed. As well, the notions of generalized subdifferential for these functions are studied and calculated. Finally, the properties of the concepts are illustrated and applied through some examples.

The Mena Incident in 2015, which resulted in the death of a large number of pilgrims of Kaaba, is considered by the Iranian poets as a historical context and led to the formation of a new flow in contemporary monody. A collection of these works has been published under the name of “ Mena minus many” by Literature County publishing. The high frequency of sonnet among the poems provided a ground for conducting a research on the correlation of its textual levels with the historical context. Accordingly, Mena's monodies in the format of sonnet were studied at three levels of music, rhetoric (traditional rhetoric) and theme. The results of textual investigations show that these sonnets are conceptual and contextual, and their three levels, having a reciprocal relationship, concentrate on transiting an explicit message to the reader; In a way that its two levels of music and rhetoric have been formed, using instruments such as the allegory to Ashura, avoiding of verbal figures, the frequency of sentences with a secondary motives of regret and grief, as well as limited metaphorical imagination, along with the main idea that is informing and describing Mena and its consequences. Other sub-motives also have been used by the poets such as “ sanctification of the dead” , “ content approximation with the event of Karbala” and “ rebuking and threatening the dealers of Mena” in order for thematization and making links between the text and the context.

Oncocytic cysts of the larynx are benign and rare lesions constituting a pathologically distinct sub-group of cysts. In this report, we present a case with dyspnea with two large masses on false vocal cord identified by video laryngoscopy. Fiberoptic nasotracheal intubation revealed oncocytic laryngeal cysts.