We survey a few concentration inequalities for submodular and fractionally subadditive functions of independent random variables, implied by the entropy method for self-bounding functions. The power of these concentration bounds is that they are dimension-free, in particular implying standard deviation O( √ E[f ]) rather than O( √ n) which can be obtained for any 1Lipschitz function of n variab...

The aim of this study is to solve the Fekete-Szeg? problem and define upper bound for Hankel determinant H2(1) in a novel class K analytical functions unit disc. Moreover, analytic on disc, assuming existence an angular limit boundary point, estimations from below modulus derivative have been obtained.

We show that the feasibility of a system of m linear inequalities over the cone of symmetric positive semideenite matrices of order n can be tested in mn O(minfm;n 2 g) arithmetic operations with ln O(minfm;n 2 g)-bit numbers, where l is the maximum binary size of the input coeecients. We also show that any feasible system of dimension (m; n) has a solution X such that log kXk ln O(minfm;n 2 g) .

Gomory’s and Chvátal’s cutting-plane procedure proves recursively the validity of linear inequalities for the integer hull of a given polyhedron. The number of rounds needed to obtain all valid inequalities is known as the Chvátal rank of the polyhedron. It is well-known that the Chvátal rank can be arbitrarily large, even if the polyhedron is bounded, if it is of dimension 2, and if its intege...

In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators (O(12 ) iterations), and for the operators with bounded variations (O( 1 22 ) iterations). Our technique can be applied for solving nonsmooth convex minimization problems with kn...

In the past three decades, incarceration has become an increasingly powerful force for reproducing and reinforcing social inequalities. A new wave of sociological research details the contemporary experiment with mass incarceration in the United States and its attendant effects on social stratification. This review first describes the scope of imprisonment and the process of selection into pris...

The definition of classical holomorphic function spaces such as the Hardy space or Dirichlet on Hartogs triangle is not canonical. In this paper we introduce a natural family which includes some weighted Bergman spaces, candidate and space. For study L p mapping properties Szeg? projection respectively, whereas for prove it isometric to bidisc.

In the current work, we use (M,N)-Lucas Polynomials to introduce a new family of holomorphic and bi-univalent functions which involve linear combination between Bazilevic ?-pseudo-starlike function defined in unit disk D establish upper bounds for second third coefficients belongs this family. Also, discuss Fekete-Szeg? problem

In this investigation, the q-difference operator and S?l?gean q-differential are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine general Taylor–Maclaurin coefficient functions in class using Faber polynomial method. demonstrate unpredictable behaviour initial coefficients a2, a3 investigate Fekete–Szeg? problem a3?a22 for To highlight connections ...