On the Betti numbers of monomial ideals and their powers

Let $S=\mathbb{K}[x_1,\ldots,x_n]$ the polynomial ring over a field $\mathbb{K}$. In this paper for some families of monomial ideals $I \subset S$ we study the minimal number of generators of $I^k$. We use this results to find some other Betti numbers of these families of ideals for special choices of $n$, the number of variables

The saturation number of monomial ideals

Let $S=\mathbb{K}[x_1,\ldots, x_n]$ be the polynomial ring over a field $\mathbb{K}$ and $\mathfrak{m}= (x_1, \ldots, x_n)$ be the irredundant maximal ideal of $S$. For an ideal $I \subset S$, let $\mathrm{sat}(I)$ be the minimum number $k$ for which $I \colon \mathfrak{m}^k = I \colon \mathfrak{m}^{k+1}$. In this paper, we compute the saturation number of irreducible monomial ideals and their powers. We apply this result to find the saturation number of the ordinary powers and symbolic powers of some families of monomial ideals in terms of the saturation number of irreducible components appearing in an irreducible decomposition of these ideals. Moreover, we give an explicit formula for the saturation number of monomial ideals in two variables

The saturation number of \cb-bounded stable monomial ideals and their powers

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. In this paper, we compute the socle of \cb-bounded strongly stable ideals and determine that the saturation number of strongly stable ideals and of equigenerated \cb-bounded strongly stable ideals. We also provide explicit formulas for the saturation number \sat(I) of Veronese type ideals $I$. Using this formula, we show that \sat(I^k) is quasi-linear from the beginning and we determine the quasi-linear function explicitly

The critical analysis of the master signifier and the interaction of the floating signifiers in the discourse of "Cloud Years" novel based on Laclau’s Approach and Van Dijk's ideological square

This study aimed to measure the articulation of the floating signifiers considering the master signifier of the discourse of "Cloud Years" novel using Ernesto Laclau’s and Theon Van Dijk's theories based on structuralist perspective. This novel written by Ali Ashraf Darvishian is a meaningful collection of linguistic and metalinguistic signs. Considering this issue, in order to explain the discourse of this novel, the authors analyze its components and described the relationship between the floating signifiers and the master signifier; then examined the transformation of "social inequality" into the master signifier and consequently the growth of socialism discourse. The main question of the present study is that how the floating signifiers of the discourse have been formed based on the master signifier with the aim of stabilizing and giving meaning to it? Based on the descriptive-analytical method, the authors have examined the novel in question at three levels.  The findings show that in this work, social inequality is considered as a master signifier in the formation of its discourse elements. Also, the floating signifiers, that the discourse of this novel is filled with, are articulated in the form of concepts such as "Social equality", all of which serve the master signifier. According to Theon Van Dijk's theory, polarization, irony, implication, metaphor, modality, comparison, agent, dramatization, explanation, repetition, and distancing are the most salient categories of ideological analysis in this discourse

Development and application of a social accountability assessment tool at the Shahid Beheshti University of Medical Sciences

Background: One of the critical needs of governmental agencies and educational institutions is meeting community needs. Organizations and governmental systems that rely on social capital are considered inefficient and vulnerable if they are unable to meet the needs of society. Thus, accountability is a critical pillar of government management that leads to effective actions and better service delivery. Methods: Critical review methodology was used in the first phase to review texts and documents available in the field of social accountability and to collect items used to develop the social accountability assessment tool. The Delphi method was then used to finalize and approve the model and assessment tool. University processes were investigated and evaluated based on the social accountability tool in the second phase. Result: In all, 422 university processes were investigated and evaluated to determine their accountability in different fields. The mean score of the evaluated processes was 11.9 out of 100. Conclusion: The results show that social accountability is a relatively new topic that has received considerable attention in medical education in Iran. Given the relative newness of this topic, these results could be expected; social accountability should try and be expected to improve in the coming years

Game-Based Privacy Analysis of RFID Security Schemes for Confident Authentication in IoT

Recently, Radio Frequency Identification (RFID) and Near Field Communication systems are found in various user-friendly services that all of us deal with in our daily lives. As these systems are ubiquitously deployed in different authentication and identification applications, inferring information about our behavior will be possible by monitoring our use of them. In order to provide privacy and security requirements of RFID users in novel authentication applications, lots of security schemes have been proposed which have tried to provide secure and untraceable communication for end-users. In this paper, we investigate the privacy of three RFID security schemes which have been proposed recently. For privacy analysis, we use the well-known RFID formal privacy model proposed by Ouafi and Phan. We show that all the studied protocols have some privacy drawbacks, making them vulnerable to various traceability attacks. Moreover, in order to overcome all the reported weaknesses and prevent the presented attacks, we apply some modifications in the structures of the studied protocols and propose an improved version of each one. Our analyses show that the modified protocols are more efficient than their previous versions and new modifications can omit all the existing weaknesses on the analyzed protocols. Finally, we compare the modified protocols with some new-found RFID authentication protocols in the terms of security and privacy

Breaking Anonymity of Some Recent Lightweight RFID Authentication Protocols

Due to their impressive advantages, Radio Frequency IDentification (RFID) systems are ubiquitously found in various novel applications. These applications are usually in need of quick and accurate authentication or identification. In many cases, it has been shown that if such systems are not properly designed, an adversary can cause security and privacy concerns for end-users. In order to deal with these concerns, impressive endeavors have been made which have resulted in various RFID authentications being proposed. In this study, we analyze three lightweight RFID authentication protocols proposed in Wireless Personal Communications (2014), Computers & Security (2015) and Wireless Networks (2016). We show that none of the studied protocols provides the desired security and privacy required by the end-users. We present various security and privacy attacks such as secret parameter reveal, impersonation, DoS, traceability, and forward traceability against the studied protocols. Our attacks are mounted in the Ouafi–Phan RFID formal privacy model which is a modified version of the well-known Juels–Weis privacy model