Calculation method for the unsteady air supply in mine ventilation networks

The problem on one-dimensional unsteady compressed air flow in an arbitrary topology mine is solved using a mathematical model, including one-dimensional equations and pressure-velocity continuity condition, the method of characteristics, difference scheme and the AEROSET software.     

Simulation of scattering processes of optical radiation by nanodimensional structures

Mathematical simulation of the process of scattering of an optical wave by micro- or nano-scale structure on the basis of the vector equations of the electromagnetic field is performed. A rigorous analytic solution is obtained and the scattering problem solved by means of the method of finite elements.     

Perceived trustworthiness of knowledge sources: The moderating impact of relationship length.

Prior meta-analytic evidence has indicated no association between relationship length and perceived trustworthiness. Viewing trustors as information processors, the authors propose a model in which relationship length, although having no direct effect on perceived trustworthiness, moderates the association between perceived trustworthiness and the basis on which people decide to trust each other. Specifically, as trustors learn about others, they base their trust on different kinds of information (demographic similarity, trustworthy behavior, and shared perspective). Hierarchical multiple regression analyses of a field survey of supervisors and subordinates from 3 companies (N = 88) provide evidence consistent with this prediction: Perceived trustworthiness is associated with demographic similarity in newer relationships, with trustworthy behavior in relationships that are neither brand new nor old but in-between, and with shared perspective in older relationships. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Approximation Algorithms for Quickest Spanning Tree Problems

Let $G=(V,E)$ be an undirected multigraph with a special vertex ${\it root} \in V$, and where each edge $e \in E$ is endowed with a length $l(e) \geq 0$ and a capacity $c(e) > 0$. For a path $P$ that connects $u$ and $v$, the {\it transmission time} of $P$ is defined as $t(P)=\mbox{\large$\Sigma$}_{e \in P} l(e) + \max_{e \in P}\!{(1 / c(e))}$. For a spanning tree $T$, let $P_{u,v}^T$ be the unique $u$--$v$ path in $T$. The {\sc quickest radius spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max _{v \in V} t(P^T_{root,v})$ is minimized. In this paper we present a 2-approximation algorithm for this problem, and show that unless $P =NP$, there is no approximation algorithm with a performance guarantee of $2 - \epsilon$ for any $\epsilon >0$. The {\sc quickest diameter spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max_{u,v \in V} t(P^T_{u,v})$ is minimized. We present a ${3 \over 2}$-approximation to this problem, and prove that unless $P=NP$ there is no approximation algorithm with a performance guarantee of ${3 \over 2}-\epsilon$ for any $\epsilon >0$.     

Rate design for a decarbonizing grid

The Western U.S. electric grid has undergone vast changes since the pre-renewables era. For example, renewables now comprise nearly 30% of California’s electric supply portfolio, and recent CA legislation mandates 50% renewables by 2030. As a consequence, intra-day variation in hourly net loads is rapidly steepening, as shown by the California Independent System Operator (CAISO)’s now famous ‘Duck Curve”. In 2015, CAISO recommended a four-season TOU pricing period design, with peak hours between 4?PM and 9?PM on summer weekdays, and a “super-off-peak” period in spring mid-day hours. We present an aggressive four-season time-of-use (TOU) rate design based on CAISO’s recommended TOU periods, and some illustrative impacts of implementing such TOU rates.In Western U.S. energy markets, high wholesale prices generally correspond to high marginal carbon emissions, and conversely. Properly designed TOU rates can help reduce GHG emissions by discouraging energy use during times of high marginal carbon emissions. However, demand charges, a feature of many commercial rate designs, can negate the benefits of TOU rates if applied during off-peak hours. We show that overuse of non-coincident demand charges can discourage customer investments that would benefit both the customer and the grid if rates were correctly aligned with cost. We recommend the following pricing strategies to support long-term efforts toward decarbonization of the electric grid: (1) More widespread use of aggressive 3- or 4-season TOU rates (or RTP where feasible); and (2) Reduced dependence on demand charges that apply during off-peak hours. Widespread utilization of retail rates that are aligned with temporal variation in carbon intensity, by both residential and nonresidential customers, is essential, for achievement of decarbonization goals.

Mathematical theory of interval comparison and its application to measurement problems

We state the fundamental problem of measurement— comparison of quantities determined with accuracy up to an interval. We construct a mathematical theory of comparison for such quantities; for this theory we introduce interval relations similar to numerical relations, and we study their properties. Our results make it possible to solve measurement and control problems in interval form. Translated from Izmeritel'naya Tekhnika, No. 5, pp. 3–8, May, 1998.