In Riemannian manifolds, there exists a canonical Riemannian metric on the product of them (Lee in Riemannian geometry an introduction to curvature, Springer, New York, 1997). But at the product of Finsler manifolds, the canonical Finsler metric has not been defined. In this paper, we are going to study the product of Finsler manifolds and give a canonical Finsler metric on it.

Urban form can be affected by diverse factors in different times. Socio- economic, political and physical factors are among the main contributors. So, one of the most important challenges of urban planners is measuring and identifying urban development pattern in order to direct and strengthen it to sustainable pattern and right direction. The case study of the present paper is the city of Yazd, a middle-sized city in the center of Iran, and the studied years are 1975, 1987, 2000 and 2010. To achieve the main objective of the paper, measuring Yazd growth and expansion by spatial METRICS, it has used remote sensing data and satellite imageries and ArcGIS software.The conclusion revealed that in four periods of study, complexity or irregularity of the urban patch shapes has increased, centrality or average distance of the dispersed parts to the city center has decreased, compactness or the number and area of patches their distance from each other has decreased, porosity or ratio of open space has increased and finally population density of city has decreased in a large amount. Therefore, all perimeters show that the temporal - spatial form of Yazd has moved from compact to sprawl. Due to many undesired impacts of urban sprawl, urban planners and authorities are required to use adherent techniques and policies to control urban sprawl and to direct it toward more sustainable directions.

The surge of facilitating the ever-growing number of service classes in the contemporary Internet backbone has persuaded researches worldwide to search for suitable underlying network topologies with desirable properties. Even in the presence of speedy optical technologies, the arrangement of nodes in a network can be highly influential in boosting network performance.Among all the topologies investigated so far, k-ary n-cubes have been reported to be widely adopted in the literature. However in a hybrid network, where the network comprises of a mixture of different types of topologies, the type and size of k-ary n-cubes can greatly influence the performance factor of the network. The objective of this paper is twofold. Firstly, we introduce a set of new METRICS that can be used to analyze the performance behavior of simple regular meshes with their wrap-around variants (2-D and 3-D torus) for the Optical Packet Switching (OPS) paradigm.We then propose a simple and yet efficient switch-level analytical model for service differentiation in OPS in the presence of wavelength converters (WCs). The proposed model is further extended to include the impact of Fiber Delay Lines (FDLs) as well. Simulations are conducted for both cases to corroborate the accuracy of the models presented.

Arab's system of prosody was altered by prosody scholars of other lands, and the process of basic combination and compiling made some prosodic and metrical adoption available, especially in Persian Dari poetry. Such adopted meters, then, spread over languages and dialects of territory of New Persian by Persian Dari poetry, particularly got in touch with Divan (court) poetry of Turkish Seljuks. One can detect all these creations in Mulamma' at of Rumi's collected Divan. The rhythm in every language is a phonological matter of that language which is concerned with quantity, tension or stress of sounds and syllables. Now, it is obvious that every single language mixed in Mulamma'at is a subfamily of Semitic, Indo-European, and Altaic languages with different morphological and phonological order. The problem is an inter-lingual dispersion of metrical patterns and prosodic system from Arabic poetry to Persian Dari poetry and then to Seljuk Turkish poetry. This article comparatively studies the prosody in Mulamma'at of Rumi's collected Divan, analyzing meters applied in it from a linguistic point of view. Also, it is examined how the altered prosody of the Persians provided a musical-grammatical combination of poetries of different language families, but forced some metrical-phonological maladjustment in destination languages. Because of the inter-lingual move based on the sacred register and the formal dominance of the first language, socio-linguistic factors must also be taken into account.

Land cover/use change induced by human activities, ignoring environmental constrains caused landscape degradation. The continuous land use change has also severe impacts on natural ecosystems. Therefore, in consideration with the negative effects of unsuitable use of land and land use change, knowledge and understanding about the changes is essential in environmental impact assessment for sustainable planning and land management .This study is for investigating the trends of changes in the landscape, in Neka Watershed. In order to provide land cover maps the satellite images of MSS 1972, TM 1992, ETM+2001 were applied and landscape METRICS of class area, largest patch index, number and mean patch size were used to quantify landscape patterns. The analysis of landscape METRICS revealed that the extensive replacement of agricultural lands and forests with rangelands and the results verified that increased patch number and decreased mean patch area were two important fragmentation indicators and the trend of degradation and fragmentation of the landscape was increasing. Therefore the results necessitated paying attention to the quality of land use and cover in the region for decreasing the natural resources degradation.

In addition to harmful effects on the physical health of people, noise pollution can also create annoyance conditions for those who are exposed to it. Therefore, in addition to evaluating the sound quantity parameters, it is absolutely essential to examine the sound qualitative parameters in the work environment. In this research, the sound qualitative METRICS of the HEPCO backhoe loader were evaluated. The acoustic annoyance model of the tested machine was determined using loudness, sharpness and fluctuation strength. The coefficient of determination of acoustic annoyance model and jury test was 0. 93. Also, the acoustic annoyance model from this study was compared with two unbiased and psychoacoustic annoyance models. The results of this comparison showed that the proposed model changes in the gear ratios are not identical with the other two models. Therefore, by measuring the sound of the machine and extracting its quality METRICS, it can calculate the acoustic annoyance inside the cabin.

In this paper, we consider a secure network coding problem in which some secret keys are shared among legitimate nodes, and there exists an eavesdropper which is able to hear a subset of links. We show the equivalency of secure network coding under weak and strong secrecy conditions. For linear network coding, we show a stronger result: equivalency of "perfect secrecy and zero-error constraints" to "weak secrecy and $\epsilon$-error constraints". This is a secure version of the result obtained by Langberg and Effros, on the equivalence of zero-error and $\epsilon$-error regions in the network coding problem with co-located sources. Jalali and Ho exploit extractor functions to prove the weak and strong rate region equivalency for this network; however, to prove this equivalency, we develop some tools in random binning and prove the equivalency in a slightly more general setting.