Periodic solutions of systems with asymptotically even nonlinearities

New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate ... next order ... terms are obtained for the 2 Pi-periodic problem for the scalar equation x'' +n2x=g(|x|)+f(t,x)+b(t) with bounded g(u) and f(t,x) -> 0 as |x| -> 0. The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory. AMS subject classifications: 47Hll, 47H30

Microparticle impact sensor measures energy directly

Construction of a capacitor sensor consisting of a dielectric layer between two conductive surface layers and connected across a potential source through a sensing resistor permits measurement of energy of impinging particles without degradation of sensitivity. A measurable response is produced without penetration of the dielectric layer

Finitely dependent coloring

We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently well-separated locations are independent; it is a block-factor if it can be expressed as an equivariant finite-range function of independent variables. The problem of finding non-block-factor finitely dependent processes dates back to 1965. The first published example appeared in 1993, and we provide arguably the first natural examples. More precisely, Schramm proved in 2008 that no stationary 1-dependent 3-coloring of the integers exists, and conjectured that no stationary k-dependent q-coloring exists for any k and q. We disprove this by constructing a 1-dependent 4-coloring and a 2-dependent 3-coloring, thus resolving the question for all k and q. Our construction is canonical and natural, yet very different from all previous schemes. In its pure form it yields precisely the two finitely dependent colorings mentioned above, and no others. The processes provide unexpected connections between extremal cases of the Lovasz local lemma and descent and peak sets of random permutations. Neither coloring can be expressed as a block-factor, nor as a function of a finite-state Markov chain; indeed, no stationary finitely dependent coloring can be so expressed. We deduce extensions involving d dimensions and shifts of finite type; in fact, any non-degenerate shift of finite type also distinguishes between block-factors and finitely dependent processes

Integrals, Partitions, and Cellular Automata

We prove that $$\int_0^1\frac{-\log f(x)}xdx=\frac{\pi^2}{3ab}$$ where $f(x)$ is the decreasing function that satisfies $f^a-f^b=x^a-x^b$, for $0<a<b$. When $a$ is an integer and $b=a+1$ we deduce several combinatorial results. These include an asymptotic formula for the number of integer partitions not having $a$ consecutive parts, and a formula for the metastability thresholds of a class of threshold growth cellular automaton models related to bootstrap percolation.Comment: Revised version. 28 pages, 2 figure

Higgs Boson Decays to Dark Photons through the Vectorized Lepton Portal

Vector-like fermions charged under both the Standard Model and a new dark gauge group arise in many theories of new physics. If these fermions include an electroweak doublet and singlet with equal dark charges, they can potentially connect to the Higgs field through a Yukawa coupling in analogy to the standard neutrino portal. With such a coupling, fermion loops generate exotic decays of the Higgs boson to one or more dark vector bosons. In this work we study a minimal realization of this scenario with an Abelian dark group. We investigate the potential new Higgs decays modes, we compute their rates, and we study the prospects for observing them at the Large Hadron Collider and beyond given the other experimental constraints on the theory. We also discuss extensions of the theory to non-Abelian dark groups.Comment: 32 pages, 5 figures, updated to match JHEP versio

Groundwater Use under Incomplete Information

In this paper, we introduce a game theoretic model of groundwater extraction in a two-cell aquifer under incomplete information. A novel assumption is that individual users have incomplete knowledge of the speed of lateral flows in the aquifer: although a user is aware that his neighbor's water use has some influence on their future water stock, they are uncertain about the degree of this impact. We find that the lack of information may either increase or decrease the rate of water use and welfare. In a two-period framework, the relevant characteristic is the ratio of the periodic marginal benefits of water use. Depending on whether this ratio is convex or concave, the average speed with which the aquifer is depleted decreases or increases when users learn more about the local hydrologic properties of groundwater. We also show that the effect of better information on the welfare of the average producer may be negative even in the situations when, on average, groundwater is allocated more efficiently across irrigation seasons.Resource /Energy Economics and Policy,

A major crustal feature in the southeastern United States inferred from the MAGSAT equivalent source anomaly field

The MAGSAT equivalent-source anomaly field evaluated at 325 km altitude depicts a prominent anomaly centered over southeast Georgia, which is adjacent to the high-amplitude positive Kentucky anomaly. To overcome the satellite resolution constraint in studying this anomaly, conventional geophysical data were included in analysis: Bouguer gravity, seismic reflection and refraction, aeromagnetic, and in-situ stress-strain measurements. This integrated geophysical approach, infers more specifically the nature and extent of the crustal and/or lithospheric source of the Georgia MAGSAT anomaly. Physical properties and tectonic evolution of the area are all important in the interpretation

Groundwater Pumping by Heterogeneous Users

Farm size is a significant determinant of both groundwater irrigated farm acreage and groundwater irrigation application rates per acre. This paper analyzes the patterns of groundwater exploitation when resource users in the area overlying a common aquifer are heterogeneous. In the presence of user heterogeneity, the common resource problem consists of inefficient dynamic and spatial allocation of groundwater because it impacts income distribution not only across periods but also across farmers. Under competitive allocation, smaller farmers pump groundwater faster if farmers have a constant marginal periodic utility of income. However, it is possible that larger farmers pump faster if the Arrow-Pratt coefficient of relative risk-aversion is sufficiently decreasing in wealth. A greater farm-size inequality may either moderate or amplify income inequality among farmers. Its effect on welfare depends on the curvature properties of the agricultural output function and the farmer utility of income. Also, it is shown that a flat-rate quota policy that limits the quantity of groundwater extraction per unit land may have unintended consequences for the income distribution among farmers.common property resource, groundwater, majorization, Resource /Energy Economics and Policy,