In this paper, we investigate and characterize the effects of multi-channel and rendezvous protocols on the connectivity of dynamic spectrum access networks using percolation theory. In particular, we focus on the scenario where the secondary nodes have plenty of vacant channels to choose from a phenomenon which we define as channel abundance. To cope with the existence of multi-channel, we use two types of rendezvous protocols: naive ones which do not guarantee a common channel and advanced ones which do. We show that, with more channel abundance, even with the use of either type of rendezvous protocols, it becomes difficult for two nodes to agree on a common channel, thereby, potentially remaining invisible to each other. We model this invisibility as a Poisson thinning process and show that invisibility is even more pronounced with channel abundance. Following the disk graph model, we represent the multiple channels as parallel edges in a graph and build a multi-layered graph (MLG) in R2. In order to study the connectivity, we show how percolation occurs in the MLG by coupling it with a typical discrete percolation. Using a Boolean model and the MLG, we study both cases of primaries' absence and presence. For both cases, we define and characterize connectivity of the secondary network in terms of the available number of channels, deployment densities, number of simultaneous transmissions per node, and communication range. When primary users are absent, we derive the critical number of channels which maintains supercriticality of the secondary network. When primary users are present, we characterize and analyze the connectivity for all the regions: channel abundance, optimal, and channel deprivation. For each region we show the requirement and the outcome of using either type of rendezvous techniques. Moreover, we find the tradeoff between deployment-density versus rendezvous probability which results in a connected network. Our results can be used to decide on the goodness of any channel rendezvous algorithm by computing the expected resultant connectivity. They also provide a guideline for achieving connectivity using minimal resources.
Iraqi calcium bentonite was activated via acidification to study its structural and electrical properties. The elemental analysis of treated bentonite was determined by using X-ray fluorescence while the unit crystal structure was studied through X-ray diffraction showing disappearance of some fundamental reflections due to the treatment processes. The surface morphology, on the other hand, was studied thoroughly by Scanning Electron microscopy SEM and Atomic Force Microscope AFM showing some fragments of montmorillonite sheets. Furthermore, the electrical properties of bentonite were studied including: The dielectric permittivity, conductivity, tangent loss factor, and impedance with range of frequency (0.1-1000 KHz) at different temperatu
... Show MoreThe using of waste products as a recycled material was one of the most important studies for saving money and reduces the pollution. Mortar and concrete mixes with (10, 20 and 30)% of brick, glass and tile powder as replacement by weight of cement was investigated. The concrete mixes using brick or glass as 10%replacement of cement exhibited enhancement in compressive strength about (6, 4.7 and 2.0)% and (7.2, 5.6 and 2)% at age 7, 28 and 90 days respectively compared to reference mix. The 20% replacement of glass powder also showed an increase in the compressive strength up to (8, 6.3 and 4) %at age 7,28 and 90 days respectively compared to reference mix. Finally concrete mix using (10, 20 and 30) % tile powder as replacement of cement sho
... Show MoreGermination and field emergence are delayed and their duration is prolonged due to the declining soil temperature during the spring season, which is reflected in the subsequent stages of crop growth, therefore, this study aimed to improve germination. Under a wide range of environmental conditions, a laboratory factorial experiment was carried out to study the effect of seed stimulation with potassium nitrate (distilled water only (0), 2, 4, and 6 mg L-1) and with an aqueous extract of licorice roots (distilled water only (0), 3, 6, and 9 g L-1) on the seed viability and vigor. The laboratory experiment was carried out according to the Completely Randomized Design (CRD) with four repetitions. The results showed the superiority of the intera
... Show MoreNew twin compounds having four-, five-, and seven- membered heterocyclic rings were synthesized via Schiff bases (1a,b) which were obtained by the condensation of o-tolidine with two moles of 4- N,N-dimethyl benzaldehyde or 4- chloro benzaldehyde. The reaction of these Schiff bases with two moles of phenyl isothiocyanate, phenyl isocyanate or naphthyl isocyanate as in scheme(1) led to the formation of bis -1,3- diazetidin- 2- thion and bis -1,3- diazetidin -2-one derivatives (2-4 a,b). While in scheme (2) bis imidazolidin-4-one (5a,b) ,bistetrazole (6a,b) and bis thiazolidin-4-one (7a,b) derivatives were produced by reacting the mentioned Schiff bases(1a,b)with two moles of glycine, sodium azide or thioglycolic acid, respectively. The new b
... Show MoreThis study aims to apply the theory of "Text from Text and the Plus Dimension" in the analysis of the Prophetic discourse found in the section on the virtues of knowledge and scholars from Imam Sahih al-Bukhari's book. This section covers several topics, including the virtue of gathering for the sake of learning, the superiority of a scholar over a worshipper, the excellence of jurisprudence in the religion of Allah, the acquisition of knowledge through the passing away of scholars, the merit of inviting people to Allah, the continuing benefit of beneficial knowledge after a scholar's demise, the warning against seeking knowledge for purposes other than Allah, and the Prophet seeking refuge from knowledge tha
... Show MoreLanguages were not found in our life in a way utter coincidence , and it’s not flounce on people’s tongue randomly ‚ but laws are the controlling in languages‚ these laws could be lift to the same level of natural laws‚ phonetics form the main part in producing those languages‚ the Arabic language is one of those languages ‚ it’s largest dialects in Arabian Peninsula according to speakers number ‚ Arabic language link with these dialects through properties and phenomena sound and grammar‚ from this point my topic search is came Similar and different between Arabic and Arabian peninsula Accents balance linguistic–study voice of the Seine typically ) . and Similar and different of the ph
... Show MoreThe physicochemical behaviour of dodecyltrimethylammonium bromide (DTAB) in water and ethanol-water mixture in the presence and absence of ZnSO4 were studied by measuring the conductivity at 298.15 K. The pre-micellar (S1) and post-micellar slopes (S2) were obtained and calculated the degree of dissociation (α) and the critical micelle concentration (cmc). With an increase in ethanol content, the cmc and α of DTAB increased whereas, in the presence of ZnSO4, the cmc and α decreased. By using cmc and α, thermodynamic properties as the standard free energy of micellization ( ) were evaluated. With an increase in ethanol content, the negative values of are decreased indicating less spont
... Show MoreSummary:This article discusses the topic of phraseological units with the names of wild animals in the Russian and Arabic languages in the aspect of their comparative semantic and cultural analysis, since a comparative analysis of the meanings of phraseological units of the Arabic and Russian languages, detection of coincidences and differences in the compared languages, is an important method for studying linguoculturology, since phraseological units represent a reflection of culture in the language