We consider the problem of finding a subgraph given graph minimizing sum functions at vertices evaluated their degrees. While is NP-hard already for bipartite graphs when are convex on one side and concave other, we have that all convex, can be solved in polynomial time any graph. also provide solutions with fixed arbitrary functions, but number either nondecreasing or nonincreasing. note gener...

The paper investigates the enumeration of the set AP(n) of partitions of a positive integer n in which the nondecreasing sequence of parts form an arithmetic progression. We establish formulas for such partitions, and characterize a class of integers n with the property that the length of every member of AP(n) divides n. We prove that the number of such integers is small.

where G(u) is a bounded, nondecreasing function with G(— °o)=0 and where 7 is a real-valued constant. Below it is shown that for certain processes of this type the measure of the Hilbert neighborhood of the origin is related to the solution of a certain differential system. In fact, (A) if {x(t), 0fkt< °° } is a separable stochastic process with symmetric, stationary, and independent increments...

The Bakry-Émery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive or nonnegative Ricci tensor are also valid for the Bakry-Émery tensor. We show that the Bakry-Émery tensor is nondecreasing under a Riemannian submersion whose fiber transport preserves measures up to constants. We giv...

Consider the first-order linear delay differential equation x′(t) + p(t)x(τ(t)) = 0, t ≥ t0, and the second-order linear delay equation x′′(t) + p(t)x(τ(t)) = 0, t ≥ t0, where p and τ are continuous functions on [t0,∞), p(t) > 0, τ(t) is nondecreasing, τ(t) ≤ t for t ≥ t0 and limt→∞ τ(t) = ∞. Several oscillation criteria are presented for the first-order equation when

The paper primarily revolves around the convex and V-shaped finite sequences and the inequalities that govern them. We give an elementary proof that a convex sequence is also V-shaped. We prove an inequality that involves an arbitrary nondecreasing function that depends on ceiling functions, thereby establishing the convexity of the corresponding sequence. We present various interpretations and...

We prove L1{contraction principle and uniqueness of solutions for quasilinear elliptic{parabolic equations of the form @t[b(u)] div[a(ru; b(u))] + f(b(u)) = 0 in (0; T ) ; where b is monotone nondecreasing and continuous. We only assume that u is a weak solution of nite energy (see [1]). In particular, we do not suppose that the distributional derivative @t[b(u)] is a bounded Borel measure or a...

Abstract We study the existence and the properties of the reduced measures for the parabolic equations ∂tu−∆u+ g(u) = 0 in Ω× (0,∞) subject to the conditions (P ): u = 0 on ∂Ω× (0,∞), u(x, 0) = μ and (P ′): u = μ′ on ∂Ω × (0,∞), u(x, 0) = 0 where μ and μ′ are positive Radon measures and g a continuous nondecreasing function. 1991 Mathematics Subject Classification. 35K60, 34.

Selection models are appropriate when the probability that a potential datum enters the sample is a nondecreasing function of the numeric value of the datum. It is rarely justiiable to model this function, called the weight function, with a speciic parametric form, but is appealing to model with a nonparametric prior centered around a parametric form. The Bayesian analysis with Dirichlet proces...

We consider a portfolio-choice problem with one risky and one safe asset, where the utility function exhibits decreasing absolute risk aversion (DARA). We show that the indirect utility function of the portfolio-choice problem need not exhibit DARA. However, if the (optimal) marginal propensity to invest is positive for both assets, which is true when the utility function exhibits nondecreasing...