Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric h...

We define a generalized variant of the satisfiability problem (SAT) where each “clause” is an or -list of inequalities in n variables. The inequality satisfiability problem (I-SAT) is to find whether there exists a feasible point in <n that satisfies at least one inequality in each “clause”. We show that I-SAT is harder than SAT in that I-SAT is NP-complete even when restricted to contain only ...

In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.

Two new inequalities for Riemann--Stieltjes integral are introduced functions of bounded $p$-variation and H\"{o}lder continuous integrators.

In a celebrated work by Shao [13] several inequalities for negatively associated random variables were proved. In this paper we obtain some maximal inequalities for associated random variables. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].

in the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. in this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. two path inequalities for the node-only interdiction problem are represented. it has been proved that the integrality gap of relaxation of the maximum fl...

in this paper‎, ‎making use of a new identity‎, ‎we establish new‎ ‎inequalities of ostrowski type for the class of preinvex functions and‎ ‎gave some midpoint type inequalities‎.

In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...

-In this paper, we establish the equivalence between the generalized nonlinear variational inequalities and the generalized Wiener-Hopf equations. This equivalence is used to suggest and analyze a number of iterative algorithms for solving generalized variational inequalities. We also discuss the convergence analysis of the proposed algorithms. As a special case, we obtain various known results...

We obtain an e¤ective lower bound on the distance of sum of coadjoint orbits from the origin. Even when the distance is zero, thus the symplectic quotient is well-de…ned, our result give a nontrivial constraint on these co-adjoint orbits. In the particular case of unitary groups, we recover the quadratic inequality for eigenvalues of Hermitian matrices satisfying A+B = C: This quadratic inequal...