A composition of an integer constrained to have decreasing then increasing parts is called concave. We prove that the generating function for the number of concave compositions, denoted v(q), is a mixed mock modular form in a more general sense than is typically used. We relate v(q) to generating functions studied in connection with “Moonshine of the Mathieu group” and the smallest parts of a p...

In this paper we show that for discrete concave functions, a local maximum need not be a global maximum. We also provide examples of discrete concave functions where this coincidence holds. As a direct consequence of this, we can establish the equivalence of local and global profit maximizers for an equivalent well-behaved production function that is generated by a (not necessarily discrete con...

Zeldes (1989), Carroll (1992; 1993), and others have shown that optimal consumption behavior for consumers facing income uncertainty can be remarkably di erent from the certainty-equivalent case. Carroll (1992; 1993) observes that many of the di erences can be attributed to the concavity of the consumption function under uncertainty, but he does not describe the conditions under which the consu...

In this paper we prove that the linear transformation

We establish uniform estimates for order statistics: Given a sequence of independent identically distributed random variables ξ1, . . . , ξn with log-concave distribution and scalars x1, . . . , xn, for every k ≤ n we provide estimates for E kmin1≤i≤n |xiξi| and E k-max1≤i≤n |xiξi| in terms of the value k and the appropriate Orlicz norm ‖(1/x1, . . . , 1/xn)‖M , associated with the distribution...

Under margin assumptions, we prove several risk bounds, represented via the distribution depen-dent local entropies of the classes or the sizes of specific sample compression schemes. In somecases, our guarantees are optimal up to constant factors for families of classes. We discuss limi-tations of our approach and give several applications. In particular, we provide a new tight...

The paper provides shape derivative analysis for the wave equation with mixed boundary conditions on a moving domain Ωs in the case of non smooth neumann boundary datum. The key ideas in the paper are (i) bypassing the classical sensitivity analysis of the state by using parameter differentiability of a functional expressed in the form of Min-Max of a convex-concave Lagrangian with saddle point...

Do low interest rate environments lead to greater bank risk-taking? We show that, when banks can adjust their capital structures, reductions in real interest rates lead to greater leverage and higher risk for any downward sloping loan demand function. However, if the capital structure is fixed, the effect depends on the degree of leverage: following a decrease in interest rates, well capitalize...

The method of Quasilinearization which was developed by Bellman and Kalaba covers the situation when the forcing function is either convex or concave. Here, we describe the process of the Quasilinearization method being extended, refined and generalized so as to include forcing functions which are the sum of a convex and concave function. This includes many special cases which are extensions of...