On uniform continuous dependence of solution of Cauchy problem on a parameter

Suppose that an $n$-dimensional Cauchy problem \frac{dx}{dt}=f(t,x,\mu) (t \in I, \mu \in M), x(t_0)=x^0 satisfies the conditions that guarantee existence, uniqueness and continuous dependence of solution x(t,t_0,\mu) on parameter \mu in an open set M. We show that if one additionally requires that family \{f(t,x,\cdot)\}_{(t,x)} is equicontinuous, then the dependence of solution x(t,t_0,\mu) on parameter \mu \in M is uniformly continuous. An analogous result for a linear n \times n-dimensional Cauchy problem \frac{dX}{dt}=A(t,\mu)X+\Phi(t,\mu) (t \in I, \mu \in M), X(t_0,\mu)=X^0(\mu) is valid under the assumption that the integrals \int_I\|A(t,\mu_1)-A(t,\mu_2)\|dt and \int_I \|\Phi(t,\mu_1)-\Phi(t,\mu_2)\|dt can be made smaller than any given constant (uniformly with respect to \mu_1, \mu_2 \in M) provided that \|\mu_1-\mu_2\| is sufficiently small

Electrostatically controlled heat shutter

A heat transfer assembly for conducting thermal energy is described. The assembly includes a hermetically sealed container enclosing a quantity of inert gas such as nitrogen. Two opposed walls of the container have high thermal conducting characteristics while the connecting walls have low thermal conducting characteristics. Electrodes are positioned adjacent to the high thermal conducing walls and biased relative to the conducting walls to a corona potential for creating an ionic gas wind which must contact the conducting walls to be neutralized. The contact of the gas molecules permits the maximum thermal energy transfer between the walls. Baffles can be positioned adjacent to the electrodes to regulate gas flow between the high thermal conducting surfaces

Heated bimetal strip prevents damage of bearings by vibration

Strip of bimetal is shaped as split ring; when properly fabricated from thin sheet, width of strip increases when it is heated. When width of strip increases, outer races are forced apart, thus pressing balls tightly against inner races. Strip applies axial load to bearing, amount of load being function of temperature to which strip is heated

Distributions with dynamic test functions and multiplication by discontinuous functions

As follows from the Schwartz Impossibility Theorem, multiplication of two distributions is in general impossible. Nevertheless, often one needs to multiply a distribution by a discontinuous function, not by an arbitrary distribution. In the present paper we construct a space of distributions where the general operation of multiplication by a discontinuous function is defined, continuous, commutative, associative and for which the Leibniz product rule holds. In the new space of distributions, the classical delta-function $\delta_\tau$ extends to a family of delta-functions $\delta_\tau^\alpha$, dependent on the \textit{shape} $\alpha$. We show that the various known definitions of the product of the Heaviside function and the delta-function in the classical space of distributions $\mathcal D'$ become particular cases of the multiplication in the new space of distributions, and provide the applications of the new space of distributions to the ordinary differential equations which arise in optimal control theory. Also, we compare our approach of the Schwartz distribution theory with the approach of the Colombeau generalized functions algebra, where the general operation of multiplication of two distributions is defined

Shear flow-interchange instability in nightside magnetotail causes auroral beads as a signature of substorm onset

A geometric wedge model of the near-earth nightside plasma sheet is used to derive a wave equation for low frequency shear flow-interchange waves which transmit $\vec{E} \times \vec{B}$ sheared zonal flows along magnetic flux tubes towards the ionosphere. Discrepancies with the wave equation result used in Kalmoni et al. (2015) for shear flow-ballooning instability are discussed. The shear flow-interchange instability appears to be responsible for substorm onset. The wedge wave equation is used to compute rough expressions for dispersion relations and local growth rates in the midnight region of the nightside magnetotail where the instability develops, forming the auroral beads characteristic of geomagnetic substorm onset. Stability analysis for the shear flow-interchange modes demonstrates that nonlinear analysis is necessary for quantitatively accurate results and determines the spatial scale on which the instability varies

Contra Epstein, Good Explanations Predict

Epstein has argued that an explanation\'s capacity to make predictions should play a minor role in its evaluation . This view contradicts centuries of scientific practice and, at least, decades of philosophy of science. We argue that the view is not only unfounded but seems to arise from a mistaken fear that ABM models are in need of defense against the criticism that they don\'t necessarily forecast events in the natural or social world.ABM, Agent Based Model, Modeling, Prediction, Explanation, Philosophy of Science

SAVI Community Information System

poster abstractSAVI helps organizations and researchers make data-informed decisions by 1) providing reliable data about Central Indiana communities; 2) creating actionable information; 3) developing tools for data analysis; and 4) building capacity, especially for nonprofit and community-based organizations, to use data effectively. The SAVI Community Information System is the nation’s largest spatially-enabled system of its type, providing detailed, geographically precise information needed to make data-informed decisions. SAVI contains a wealth of free data about the social, physical, and economic conditions of Central Indiana communities from counties to neighborhoods and census tracts, as well as information on thousands of non-profit and community-based organizations and programs. SAVI is a donor-supported, web-based system (www.savi.org) that allows users to create custom maps, graphs, charts, and data profiles of over 2,000 Central Indiana communities. SAVI supports research: selecting appropriate study area; identifying community-based research partners; identifying and managing nurse-led community health activities; understanding health effects of neighborhood poverty; identifying health disparities; environmental health/environmental justice; identifying socio-spatial health knowledge networks; and understanding social and physical neighborhood context and influences on obesity, leukemia treatment adherence, cancer screening rates, asthma, diabetes, and STDs. SAVI also supports community research: identifying community assets, assessing needs, planning and evaluating programs, identifying collaborators, supporting grant applications, strategic planning, and visualizing patterns and trends. This hands-on exhibit will showcase SAVI and the ways in which it can support community and researcher decisionmaking needs. We will present a poster and have live demonstrations of our interactive website that provides a wealth of data and analysis tools

The SAVI Community Information System

poster abstractThe SAVI Community Information System (www.savi.org) is a dynamic and interactive resource for local, spatially-enabled data and information about Central Indiana. It provides local data about the social, economic, and physical conditions of neighborhoods, townships, and counties, and other geographic areas such as school districts which is then summarized into community profiles and allows users to view and analyze detailed data in interactive maps, charts, and tables