In this paper, some sharp inequalities for certain multilinear operators related to the Littlewood-Paley operator and the Marcinkiewicz operator are obtained. As an application, we obtain the (L p , L q)-norm inequalities and Morrey spaces boundedness for the multilinear operators.

Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. L norm inequalities are established for multilinear integral operators of Calderón-Zygmund type which incorporate oscillatory factors e iP , where P is a real-valued polynomial. A related problem concerning upper bounds for measures of sublevel sets is solved.

In this research, we will do a survey on multilinear maps and analyze some parameters in the recent implementations. The student will compare the two implementations, in particular their similarities and improvements made by the more recent work. The student will then analyze some possible applications of multilinear maps for cryptography.

Abstract The paper introduces a subclass of nonlinear differential-algebraic models interest for applications. By restricting the nonlinearities to multilinear polynomials, it is possible use modern tensor methods. This opens door new approximation and complexity reduction methods large scale systems with relevant behavior. modeling procedures including composition, decomposition, normalization...

In this paper, we consider a class of n-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix game where the utility function of every player is given by a quadratic form defined by the payoff matrix of that player. We will call such a problem the mult...

Multilinear maps enable homomorphic computation on encoded values and a public procedure to check if the computation on the encoded values results in a zero. Encodings in known candidate constructions of multilinear maps have a noise component, which is crucial for security. However, this noise grows (gets accumulated) with homomorphic computations and must remain below the maximal noise suppor...

BACKGROUND To estimate the age by evaluating the area and length of dentin translucency in single-rooted ground sections of extracted teeth using digital Vernier caliper and stereomicroscope. MATERIALS AND METHODS Ground sections of single rooted permanent anterior teeth were made and stained with 1% methylene blue. The area and length of dentin translucency were measured using digital Vernie...