The divide-and-conquer principle is a majoi paradigm of algorithms design. Corresponding cost functions satisfy recurrences that directly reflect the decomposition mechanism used in the algorithm. This work shows that periodicity phenomena, often of a fractal nature, are ubiquitous in the performances of these algorithms. Mellin transforms and Dirichlet series are used to attain precise asympto...

introduction nowadays, many studies were performed about noise source and its type and effects related to duration of sound emission. most of these researches just report sound pressure level in frequency or time domain. these researches should be continued in order to find better absorber material in noise pollution. use of fractal geometry is a new method in this filed. wave fractal dimension...

In this paper we have defined two functions that have been used to construct different fractals having fractal dimensions between 1 and 2. More precisely, we can say that one of our defined functions produce the fractals whose fractal dimension lies in [1.58, 2) and rest function produce the fractals whose fractal dimension lies in (1, 1.58]. Also we tried to calculate the amount of increment o...

introduction: advanced oxidation processes (aops) suggest a highly reactive, nonspecific oxidant namely hydroxyl radical (oh•), that oxidize a wide range of pollutants fast and non-selective in wastewater and water. materials and methods: in this work, the nitrogen-doped titanium dioxide nanoparticles were primed by sol-gel method, characterized by x-ray diffraction and scanning electron micros...

In modeling using diffusion equations, the relationship between fractal geometry and fractional calculus arises by modeling the conditions of the medium as a fractal whose fractional dimension determines the order of this equation. For this reason, it is very useful to have numerical methods that solve them and discretization of the domain is not determinant for the efficiency of the algorithm....

Introduction: Two main theories of gully formation on Mars exist depending on the source of water. One holds that water was released from the subsurface [1]. The other proposes that water is deposited as nearsurface ice or snow from the atmosphere and is subsequently melted by insolation [2-4]. In this paper we applied fractal theory to study a gully's head alcove in different orientations of a...

Fractals and multifractals are used to model hierarchical, inhomogeneous structures in several areas of astrophysics, notably the distribution of matter at various scales in the universe. Current analysis techniques used to assert fractality or multifractality and extract scaling exponents from astrophysical data, however, have significant limitations and caveats. It is pointed out that some of...

ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...

In this study a parasitological investigation on 238 samples of Neogobius species from the south-east of Caspian Sea was carried out. The samples including Neogobius melanostomus (35), N. fluviatilis pallasi (103), N. kessleri gorlap (70) and N. bathybius (30) were seasonally seined by beach net during one year (summer 2006-spring 2007), fixed in 10 % buffer formalinand transferred to the labor...

Trying to combine fractal geometry and solid modeling seems to be a contradiction in itself, In this paper a new type of 3D objects is presented that accomplishes this combination in a specific way. Objects with a fractal macro structure and a 3D solid micro structure can be specified and rendered efficiently by using context free, attribute, geometric grammars. This new object type can be inco...