We present new estimates for sums of the divisor function and other similar arithmetic functions in short intervals over fields. (When are long, one obtains a good estimate from Riemann hypothesis.) obtain an that approaches square-root cancellation as long characteristic finite field is relatively large. This done by geometric method, inspired work Hast Matei, where we calculate singular locus...

Jouberts syndrome is an uncommon autosomal recessive neurodevelopmental disorder involving cerebellar vermis and brain stem. We report a case of 5 year old male boy presented with global developmetal delay, abnormal eye moments and abnormal respiratory moments. On examination decreased muscle tone, nystagmus, and gait ataxia is present. Magnetic resonance imaging (MRI) revealed characteristic M...

Capturing the image of shadow cast by event horizon an illuminated black hole is, at most basic level, experiment extreme light deflection in a strongly curved spacetime. As such, properties imaged can be used to probe general relativistic Kerr nature astrophysical holes. example this prospect, it is commonly asserted that test validity theory's famous ``no hair theorem'' for hole's mass and sp...

We calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the nth moment of the partition function is given by the ground-state energy of a quantum problem of n interacting particles on a ring of length L, we write an integral equation allowing to expand these moments in powers of the streng...

The influence of local magnetic moment formation around three kinds of vacancies on the electron conduction through metallic single-wall carbon nanotubes is studied by use of the Landauer formalism within the coherent regime. The method is based on the single-band tight-binding Hamiltonian, a surface Green function calculation, and the mean-field Hubbard model. The numerical results show that t...

We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in te...

A weighted version of Lindley Distribution has been presented in this paper, offering a new single-parameter lifetime distribution. The expressions for the moment generating function (mgf), cumulant (cgf), characteristic function, moments, reliability and hazard rate functions distribution have also obtained. Tierney Kadane approximation method used to derive Bayes estimators its parameter (θ),...

Understanding moments of families of L-functions has long been an important subject with many number theoretic applications. Quite often, the application is to bound the error term in an asymptotic expression of the average of an arithmetic function. Also, a good bound for a moments can be used to obtain a point-wise bound for an individual L-function in the family; strong enough bounds of this...

We introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. These kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. We construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...