Different types of contact, including contact between node pairs, any-contact of nodes, and contacts of the entire network, are used to characterize social relations in mobile social networks. Different modes of routing, from the point of view of message delivery semantics, encompass unicasting, multicasting, any-casting, and broadcasting. Studies have shown that using probability distribution functions of contact data, which is mainly assumed to be Homogeneous for nodes, improves the performance of these networks. However, there exists an important challenge in studies on distributions. A lot of works apply the distribution of one type of contact to other types. Hence in routing applications, it causes to use of the distribution of one type of contact for any mode of routing. This study provides a complete solution to model each type of Homogeneous contact data distribution and to use them in different modes of routing. We propose a routing algorithm that uses this new model. Results show that our solution improves the average latency of comparing methods Epidemic, TCCB, and DR about 3.5-times, 30%, and 45%, respectively. It achieves a delivery rate of about 5% and 6%, and average latency about 6% and 8% better than that of DR and TCCB, respectively.

Let G be a locally compact Hausdorff topological group and H be a compact subgroup of G. Then, the Homogeneous space G/H possesses a specific Radon measure, which is called a relatively invariant measure. We show that the concepts of convolution and involution can be extended to the integrable functions defined on this Homogeneous space. We study the properties of convolution and prove that the space of integrable functions is an involutive Banach algebra with an approximate identity. We also find a necessary and sufficient condition on a closed subspace of this Banach algebra to make it a left ideal.

A non-interactive (t; n)-publicly veri able secret sharing scheme (non-interactive (t; n)-PVSS scheme) is a (t; n)-secret sharing scheme in which anyone, not only the participants of the scheme, can verify the correctness of the produced shares without interacting with the dealer and participants. The (t; n)-PVSS schemes have found a lot of applications in cryptography because they are suitable for real-life scenarios in which an external veri er is required to check the correctness of the produced shares without interacting with the dealer and participants. In this paper, we propose a non-interactive (t; n)-PVSS scheme using the non-Homogeneous linear recursions (NHLRs), and prove its security with a formal method. We compare the computational complexity of our scheme with that of Schoenmakers's scheme and show that our non-interactive (t; n)-PVSS scheme runs faster than Schoenmakers's scheme when n  5 and n  t  d 2n+9 n e. The communicational complexity of our scheme is almost equal to that of Schoenmakers's scheme.

Let G be a locally compact non‐abelian group and H be a compact subgroup of G also let m be a G ‐invariant measure on the Homogeneous space G / H. In this article, we extend the linear operator TH: Cc (G) ® Cc (G/H) as a bounded surjective linear operator for all LP -spaces with p≥1. As an application of this extension, we show that each frame for L2 (G) determines a frame for L2 (G/H, m) and each frame for L2 (G/H, m), m arises from a frame in L2 (G) via the linear operator TH.

Background and Aim: Leukoplakia is one of the most common premalignant or potentially malignant lesions of the oral mucosa. It’s potential for malignant transformation is unpredictable. The aim of present study was to evaluate the expression of p53 and proliferation status of ki67 antigen in normal, Homogeneous and non-Homogeneous leukoplakia.Materials and Methods: The standard immunohistochemistry staining method (Biotin Streptavidin peroxidase) was used to study the expression of p53 and ki67 on formalin fixed, paraffin embedded blocks of 7 cases of Homogeneous leukoplakia, 10 cases of non-Homogeneous leukoplakia and 9 cases of normal oral epithelium. Data were analyzed using ANOVA, MC Nemar and Fisher’s exact tests.Results: No relationship was detected between p53 protein and Ki67 expression and clinical features of leukoplakia. The distribution patterns of p53 and ki67 were mainly localized in the basal layer of normal oral mucosa, while the expression of p53 and Ki67 were extended into suprabasal cell layer in leukoplakia lesions. Ki67 expression in dysplastic lesions was higher than non-dysplastic lesions. This study showed significant relationship between Ki67 and p53 protein.Conclusion: These findings showed that the expression of p53 and Ki67 in suprabasal cell layers in leukoplakia may be correlated with poor clinical outcome and alterations of p53 lead to increased cell proliferation.

In this paper we study hereditarily Homogeneous general-ized topological spaces. Various properties of hereditarily Homogeneous generalized topological spaces are discussed. We prove that a general-ized topological space is hereditarily Homogeneous if and only if every transposition of X is a -homeomorphism on X.

In this paper we give an overview of recent developments pertaining to the quantitative‎ ‎aspects of dynamics of group actions on Homogeneous spaces.

Please click on PDF to view the abstract