We study strictly convex Alexandrov solutions u of the real MongeAmpère equation det(∇2u) = f , where f is measurable, positive, and bounded away from 0 and ∞. Under only these assumptions we prove interior Wregularity of u.

Given an n× n× p cost array C we consider the problem p-P3AP which consists in finding p pairwise disjoint permutations φ1, φ2, . . . , φp of {1, . . . , n} such that ∑p k=1 ∑n i=1 ciφk(i)k is minimized. For the case p = n the planar 3-dimensional assignment problem P3AP results. Our main result concerns the p-P3AP on cost arrays C that are layered Monge arrays. In a layered Monge array all n×n...

We present an experimental method based on Ohm’s Law to calibrate the Keithley 6485 picoammeter with the calibration error less than 0.4 pico-ampere (pA), which is specified as the highest sensitivity of this instrument. The maximum calibration difference between the measurement current and the calibration current in the picoammeter’s 2 nano-ampere (nA) range is 0.25 pA. This difference is far ...

We consider the problem of designing a reflector that transforms a spherical wave front with a given intensity into an output front illuminating a prespecified region of the far-sphere with prescribed intensity. In earlier approaches, it was shown that in the geometric optics approximation this problem is reduced to solving a second order nonlinear elliptic partial differential equation of Mong...

We define the fractional powers Ls=(−aij(x)∂ij)s, 0<s<1, of nondivergence form elliptic operators L=−aij(x)∂ij in bounded domains Ω⊂Rn, under minimal regularity assumptions on coefficients aij(x) and boundary ∂Ω. show that these appear several applications such as Monge–Ampère equations, elasticity, finance. The solution u to nonlocal Poisson problem{(−aij(x)∂ij)su=finΩu=0on∂Ω is characterized ...

We present efficient data structures for submatrix maximum queries in Monge matrices and Monge partial matrices. For n× n Monge matrices, we give a data structure that requires O(n) space and answers submatrix maximum queries in O(logn) time. The best previous data structure [Kaplan et al., SODA‘12] required O(n logn) space and O(log n) query time. We also give an alternative data structure wit...

IR light guides based on crystals and ceramics of the AgBr-AgI system are transparent in mid-infrared range from 2 to 25 μm, which is demand for thermal imaging, laser technology spectroscopy. High photo- radiation resistance makes these materials particularly attractive. For design optical equipment, information needed electrical properties material, most fully characterized by current-voltage...

In this paper, we propose a scheme to generate tunable coherent X-ray radiation for future light source applications. This scheme uses an energy chirped electron beam, a laser modulator, a laser chirper and two bunch compressors to generate a prebunched kilo-Ampere current electron beam from a few tens Ampere electron beam out of a linac. The initial modulation energy wavelength can be compress...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...