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A greater use of recycled wastepaper would preserve virgin forests as well as reducing the amount of wastepaper going to landfills. Theseenvironmental goals depend critically on the elasticity of substitution between pulp and wastepaper in producing paper and paperboard. Since most of the pulp consumed by U.S. paper mills and paperboard mills is transferred internally from vertically integrated pulp mills, the price data on pulp is not available. This paper constructs an econometric model which enables us to estimate the substitution possibility between unpriced pulp and wastepaper in the U.S. paper and paperboard industry. Empirical results show that the elasticity of substitution between unpriced pulp and wastepaper is positive, but not statistically significant. [ABSTRACT FROM AUTHOR]

The article examines the ideal dimensions of rectangular paper used in folding origami in the U.S. It explores the author's experience of allowing his students to investigate the different paper sizes, learn mathematical knowledge through problem solving and employ geometric modeling, number theory and algebraic concepts. It is noted that students manage to prove their conjectures and find the importance of minimizing repeated squares in obtaining the desired rectangle.

Purpose -- The motivation for this study is triggered by the fact that lately contract manufacturers in China have to deal with a number of unprecedented cost pressures such as currency fluctuations, the VAT rebate reduction, and minimum wage enforcement. As cost pressures in China continue to mount, this paper aims to analyze whether the US manufacturing outsourcing pendulum is swinging away from China and back to nearby Mexico, or towards emerging low-cost countries such as Vietnam, Indonesia, South Africa, Turkey or Argentina. Design/methodology/approach -- Analysis consists of comparing major cost drivers such as labor, currency, freight, and raw material and determined per unit price and the potential impact of currency fluctuations over the next five years. An example of Easle Pads (paper-based non-adhesive coated) is used to present the detailed analysis. Findings -- The outsourcing landscape today may change again in the near future as the VAT rebate is further reduced or eliminated or the impact of the Olympic Games finish. Assumptions will need to be updated to reflect any changes in the future. Though other countries such as Vietnam appear to be viable options, managers will need to take other factors into consideration when making outsourcing decisions. They will need to identify specific suppliers in a country and obtain quotes in order to finalize their decision. Research limitations -- The data analysis is supposedly very high-level. Many assumptions were applied lacking full detail, and duties and customs were not specifically addressed for each country. However, this organized approach is useful as a strategic decision tool in performing supplier searches to identify potential countries. Practical implications -- The paper helps shed light on the opportunities that exist in the emerging low-cost countries such as Vietnam and Indonesia. Other countries, such as Turkey and Argentina, also offer low labor costs, but may be better considered as regional sources of supply, rather than US outsourcing destinations. Originality/value -- The majority of studies on manufacturing outsourcing in relation to China concentrate on the reasons why one should choose China. The paper looks at manufacturing outsourcing away from China and identifies possible alternatives for contract manufacturing. [ABSTRACT FROM AUTHOR]

Opioid addiction in the United States is a national crisis. Various harm reduction strategies have been proposed, including safe injection sites, whose goals are to reduce deaths and improve the health of addicts. Many of these proposed strategies are controversial because their impact is unknown. In this paper we present a discrete time Markov model that captures essential probabilities in the description of the U.S. opioid epidemic, while remaining tractable to analysis. We use the model to analyze the impact of an overdose prevention site and other harm reduction strategies on the number of fatal overdoses and recovery rates, and make quantitative predictions about the consequences of implementing specific policies. [ABSTRACT FROM AUTHOR]

For homothetic time and state separable preferences, the coefficient of relative risk aversion (CRRA) is equal to the reciprocal of the elasticity of intertemporal substitution (EIS). This paper shows that when the growth rate of consumption is i.i.d., asset pricing models based upon preferences in which the CHRA and the EIS are no longer linked do not have more explanatory power. Further, in these stochastic environments, estimates of the CHRA in the standard preferences are measures of the true CHRA and not the EIS. These results are fairly accurate descriptions of economies calibrated using United States annual data. [ABSTRACT FROM AUTHOR]

Grid point pooling is a commonly used method to account for hurricane track variability in extreme value analysis. This paper presents a simplified mathematical interpretation of grid point pooling. Through logical arguments and numerical experiments, some general guidelines are then developed for a selection of grid points to include in the statistical pool. [ABSTRACT FROM AUTHOR]

In this paper we focus on a patch occupancy 4-dimensional model of barnacle-algae-mussel interactions with external periodic seasonal forcing proposed by Benincà et al. [Proc. Natl. Acad. Sci. USA, 112 (2015), pp. 6389--6394]. In order to understand the mechanism of the species fluctuation sustained by a cyclic succession at the edge of chaos, we investigate the corresponding system without seasonal forcing. When the mussel is absent, we give a complete description of the global asymptotic behavior of the solutions. If the mussel is present, we provide an amenable sufficient and necessary condition for the uniform persistence for the 4-dimensional system. Our analytic results on the uniform persistence provide useful necessary information for the chaotic dynamics of the periodically forced system Benincà et al. [ABSTRACT FROM AUTHOR]

Curiously and in spite of its name, very few business cycle theories actually treat it as a cycle. Mainstream economists, for example, model all macroeconomic fluctuations as a function of exogenous forces. In their view, the economy remains at full employment indefinitely unless impacted by some external event. Post Keynesian economists disagree strongly with this characterization, arguing instead that business-cycle fluctuations are endogenously generated. The goal of this paper is to compare the explanatory power of four business cycle models - three mainstream and one Post Keynesian - for the U.S. economy since 1971. While the test employed is a simple one, the results are very clear: no model's performance comes even close to that of the one based on Keynes's seventy-year old analysis. [ABSTRACT FROM AUTHOR]

A target is hidden in one of several possible locations, and the objective is to find the target as fast as possible. One common measure of effectiveness for the search process is the expected time of the search. This type of search optimization problem has been addressed and solved in the literature for the case where the searcher has imperfect sensitivity (possible false negative results), but perfect specificity (no false positive detections). In this paper, which is motivated by recent military and homeland security search situations, we extend the results to the case where the search is subject to false positive detections. [ABSTRACT FROM AUTHOR]

In 1970, abortion on demand was legalized in several sections of the United States. Due to increased demand for abortions, free standing abortion clinics came into existence. This paper develops a methodology for determining the optimal design of a free standing abortion clinic, in order to maximize its profits. An example of a clinic which was actually designed employing the methodology is presented, and the results suggest that the methodology is relevant and useful. [ABSTRACT FROM AUTHOR]

In 1993, the Chicago Board of Options Exchange (CBOE) introduced the VXO, a volatility index based on implied volatilities on S&P 100 index. In 2003, the CBOE changed their volatility index design and introduced the VIX in order to enhance its economic significance and to facilitate hedging. In this paper, using data from the USA and the German stock markets, we compare the forecasting capability of the volatility indexes with that of historical volatility and conditional volatility models. Following this analysis, we have studied whether it may be the case that volatility indexes forecast the realized volatilities more accurately for a different period to 30 (or 45) days, attempting to answer the question: what time horizon is the informational content of volatility indexes best adjusted for? The optimal prediction period of each volatility index (VXO, VIX, VDAX and V1X) in terms of coefficient of determination is analysed. The results identify a difference between the observed optimal forecasting period and the theoretical one. This could be explained from different perspectives such as the index's design, investor cognitive bias or overreaction. [ABSTRACT FROM AUTHOR]

Abstract: Social capital is a person or group''s sympathy or sense of obligation for another person or group. The objects of sympathetic feelings have social capital. Those holding sympathetic feelings for others provide social capital. Because social capital providers internalize the consequences of their choices on the objects of their social capital, they trade with each other on different terms and at different levels than would occur in arm''s length transactions, all other things equal. Furthermore, changes in the distribution of social capital alter the terms and level of trade which in turn alter the distribution of income. This paper demonstrates mathematically the connection between changes in social capital and income distributions and then tests empirically the influence of social capital on household income distributions in the 50 U.S. states for the census years 1980, 1990, and 2000. The mathematical and empirical findings of this paper support the proposition that social capital measured by social capital indicator variables have important influences on the distribution of household incomes. [Copyright &y& Elsevier]

Abstract: This paper formally derives the class of multiple discrete-continuous generalized extreme value (MDCGEV) models, a general class of multiple discrete-continuous choice models based on generalized extreme value (GEV) error specifications. Specifically, the paper proves the existence of, and derives the general form of, closed-form consumption probability expressions for multiple discrete-continuous choice models with GEV-based error structures. In addition to deriving the general form, the paper derives a compact and readily usable form of consumption probability expressions that can be used to estimate multiple discrete-continuous choice models with general cross-nested error structures. The cross-nested version of the MDCGEV model is applied to analyze household annual expenditure patterns in various transportation-related expenses using data from a Consumer Expenditure Survey in the United States. Model estimation results and predictive log-likelihood based validation tests indicate the superiority of the cross-nested model over the mutually exclusively nested and non-nested model specifications. Further, the cross-nested model was amenable to the accommodation of socio-demographic heterogeneity in inter-alternative covariance across decision-makers through a parameterization of the allocation parameters. [Copyright &y& Elsevier]

The US National High Magnetic Field Laboratory constructed and tested a stand-alone 80 T prototype magnet. The activity was in support of the insert magnet development project for the US-DOE-NSF 100 Tesla Multi-Pulse Magnet Program. The 80 T magnet assembly was developed to simulate the physical conditions an insert magnet would encounter during peak field operations at 105 T… The design incorporated further improvements to the engineering template developed from the 65 T and 75 T pulsed magnets now in use at the NHMFL Pulsed Field Facility at Los Alamos National Laboratory. Two coaxially nested solenoid coils comprised the 80 T prototype magnet design. The windings are in series electrically. The inner coil is constructed with materials & techniques identical to those in use for the 100 T insert program. The outer coil is a conventional winding. The prototype was successfully trained to a peak field of ~80.4 T. 80 T pulsed operations were repeated until the coil assembly faulted after 10 full-field pulses. Post-fault inspection of the magnet assembly indicated that the outer magnet winding failed structurally. This paper will present an overview of the 80 T prototype's design, construction, and performance. A review of the magnets failure mode will be presented. Additionally, we will discuss new design criteria for stand alone high-field pulsed magnet based upon the 80 T prototype experience. [ABSTRACT FROM AUTHOR]

The article presents a practical way of studying wave propagation in the U.S. Accordingly, wave propagation is a phenomenon of fundamental importance to a wide variety of problems involving disordered media. In connection with this, the paper presents a further discussion on numerical simulation which is the only practical way of studying it.

Research on modelprocedure selection has focused on selecting a single model globally. In many applications, especially for high-dimensional or complex data, however, the relative performance of the candidate procedures typically depends on the location, and the globally best procedure can often be improved when selection of a model is allowed to depend on location. We consider localized model selection methods and derive their theoretical properties.This research was supported by U.S. National Science Foundation CAREER Grant DMS0094323. We thank three referees and the editors for helpful comments on improving the paper. [ABSTRACT FROM AUTHOR]

This paper presents the validation of a numerical model based on the full-scale broken insulator tests on a 138-kV high-voltage steel transmission line. The University of Wisconsin and the Electric Power Research Institute performed these tests in 1978. A finite-element model of the line is developed to perform incremental nonlinear dynamic analysis, carried out in the time domain. Upon validation of the numerical model with the test results, a sensitivity study is carried out for various insulator lengths, ice thicknesses, and initial tensions to determine the effects of these parameters on the impact loads on the tower cross arm. Results of the study show that the impact loads are less sensitive to the change in insulator length but they do vary significantly when the ice loads and the initial tensions are increased. Studies of this type are now possible and are cost effective because of the use of commercial software not available at the time of the original research. [ABSTRACT FROM AUTHOR]

Two years ago I implemented a basic outline of each class for my students to take notes on for Calculus II at the United States Military Academy. The outline provided students with a shell of the class material for each day of class. Their job was to fill in the shell as we went through the material. The outlines provided students an easy method to organize their own notes exactly how I organized the class. Space was provided to fill in pertinent definitions, label figures, or drawings that I provided, and to work step-by-step examples that I planned to go over in the class. The reason behind this approach was to help the student follow the flow of the class without having to think about what they should write down and what they should not write down. The things I wanted them to write down were on the outlines. Essentially the outlines represented the minimum material each student needed to take away from each class. Further, I chose difficult problems to include in the outline that were not in the text for students to work on their own. After executing this style of teaching for three semesters the following paper discusses my experience implementing this technique. [ABSTRACT FROM AUTHOR]

This paper presents a graph-theoretic construct called a fuzzy metagraph (FM) with the capability of describing the relationships between sets of fuzzy elements instead of only single fuzzy elements. The algebraic structure of FM and its properties are extensively investigated. Subsequently, the FM construct is applied to rule-based systems. First, we propose FM-based knowledge representation in both graphic and algebraic format. The representation is capable of identifying dependencies across compound propositions in the rules. In the algebraic representation, the FM closure matrix is considered a precompiled rule base enabling efficient query processing. An iterative approach is presented to facilitate the construction and expansion of the FM closure matrix, which is a key for real-world applications. Next, we introduce the concept of indexing, which was originally developed for information retrieval (IR), to enable an immediate extraction of relevant entries from the FM closure matrix. The indexing approach is applied in combination with the FM closure matrix. Based on the combination, corresponding inference mechanisms are introduced to achieve instant acquisition of relevant rules over a large collection of rules. The application in rule-based systems indicates that the combination of FM and IR techniques offers advantages for the mathematical analysis of systems. [ABSTRACT FROM AUTHOR]

Near the conclusion of their final term in the calculus sequence at The United States Military Academy, cadets are given a week long group project. At the end of the week, the project is briefed to their instructors, classmates, and superior officers. From a teaching perspective, the goal is to encapsulate as much of the course as possible in one coherent student endeavor. We (the authors) developed a project that asked cadets to redesign the shape of a wing to improve performance, yet maintain costs. What we learned while helping cadets complete the project, during their briefings, and from a post-project survey provided insights to help improve the project and the entire course. Cadet performance clearly revealed what course topics needed more time and which were learned thoroughly. This paper is an overview of the project, its administration and how the project was seen from both the instructor and cadet viewpoints. We also discuss lessons we learned to improve the project and integration of technology into calculus courses. [ABSTRACT FROM AUTHOR]

During the Great Recession, expenditures on unemployment insurance (UI) benefits increased, and the benefits were extended. This research deals with development of a mathematical model to calculate unemployment benefits. At a conceptual level, unemployment benefits can be considered as directly proportional to salary and the employment period of the worker prior to being laid off. It is also inversely proportional to factors such as other governmental benefits received in that period of unemployment. The approach in this paper presents the need to calculate the unemployment benefits to keep up with the capricious wages and changing regulations. This analysis will include state and federal government benefits. Each state should be able to adapt the new formula, so it can assess the proper baseline for calculating the unemployment benefits needed for their specific cost of living requirements. [ABSTRACT FROM AUTHOR]

This paper applies the test of operational meaningfulness to the many detection laws that have been formulated and used in the mathematical optimization of search, and given as generalizations of those first developed in the United States Navy during and immediately following World War II. The word "operational" is used both in the sense of practical O.R. and in that of P. W. Bridgman's well-known requirement: that in applying mathematics to the material world, the physical preconditions implied in the quantities used, the operations for measuring them, and their laws of consistency must be set forth explicitly. It is submitted that this criterion will orient O.R. work toward useful developments in the search theory and may serve to identify as such those theories that are of chief interest as developments in pure mathematics. Finally, we note that the requirement that every numerical assumption of probability distributions in a study of the outside world must be based on objective evidence is perfectly consistent with the "subjective" conception of probability, viz., that its meaning is apprehended intuitively--the former measures what the latter defines. [ABSTRACT FROM AUTHOR]

This paper presents evidence on the long-run trends in U S regional specialization and localization and examines which model of regional specialization is most consistent with the data Regional specialization in the United States rose substantially between 1860 and the turn of the twentieth century, flattened out during the interwar years, and then fell substantially and continuously since the 1930s. The analysis of the long-run trends in U. S regional specialization and localization supports explanations based on production scale economies and the Heckscher- Ohlin model but is inconsistent with explanations based on external economies [ABSTRACT FROM AUTHOR]

The purpose of this paper is to offer an explanation as to why Eucidean distance serves as a reasonably good approximation of reality when it does not incorporate explicitly a consideration of the sides of the issue taken by the voter and candidate. The empirical evidence indicates quite clearly that Eucidean distance and side of issue are extremely highly correlated. Two general classes of explanation are offered. First, this powerful association can be seen as a function of the mathematical difficulty of actually being in close proximity to a preferred party while being on the opposite side of an issue on a 7-point scale. Second, even after this mathematical artifact is taken into account, the combined effects of assimilation, contrast, and negativity may bring favored candidates closer to the voter and drive the opposition further away, resulting in a strong correlation of Euclidean distance and side of the issue. [ABSTRACT FROM AUTHOR]

Traditional economic analysis using a crop production function approach has assumed that all variable factors, including irrigation water, are fully employed in the crop production process. However, this paper first demonstrates that economic benefits of irrigation water areoverestimated when the crop production function, and therefore the irrigation water demand function, is expressed in terms of irrigation water supplied, rather than consumptive irrigation water use. Second,the paper demonstrates that the magnitude of the estimation bias is proportional to the rate of irrigation water losses through leaching,runoff and evaporation. Consequently, the model misspecification problem would lead to increased irrigation water use and reduce incentives for farmers to adopt improved irrigation technologies. [ABSTRACT FROM AUTHOR]

Abstract: This paper provides a solution to address one of the requirements identified in the US Northwest 6th Power Plan, specifically, meeting an increase in the forecasted Pacific Northwest demand with renewable generation. A model is presented which evaluates one source of renewable generation, off-shore wind energy. The model analyzes different wind turbine design characteristics, assigns significance to potential synergistic effects of one design feature on another, and provides an optimized design relative to the cost, environment, robustness, and overall efficiency of an off-shore wind turbine. [Copyright &y& Elsevier]

Abstract: The United States Code (Code) is a document containing over 22 million words that represents a large and important source of Federal statutory law. Scholars and policy advocates often discuss the direction and magnitude of changes in various aspects of the Code. However, few have mathematically formalized the notions behind these discussions or directly measured the resulting representations. This paper addresses the current state of the literature in two ways. First, we formalize a representation of the United States Code as the union of a hierarchical network and a citation network over vertices containing the language of the Code. This representation reflects the fact that the Code is a hierarchically organized document containing language and explicit citations between provisions. Second, we use this formalization to measure aspects of the Code as codified in October 2008, November 2009, and March 2010. These measurements allow for a characterization of the actual changes in the Code over time. Our findings indicate that in the recent past, the Code has grown in its amount of structure, interdependence, and language. [Copyright &y& Elsevier]

Abstract: Many approaches have been proposed for decision criteria to judge whether or not transfer of bioanalytical methods has been successful. Many of these approaches involve mathematical and statistical complexities that limit their use routinely. The FDA accuracy criterion (±15%) without an allowance for imprecision may be used for method transfer and may result in a large numbers of method transfers being judged unacceptable when the method is valid under both conditions. An acceptance criterion should be based on the existing guidance, be convenient and be based on statistical principles that provide consistent and reasonable rejection rates. In the current paper, we propose a “fixed” range acceptance criteria based on the FDA bioanalytical guidance limits on precision and accuracy. While the proposed “fixed” range criteria shares the shortcomings of any other fixed criterion, there are advantages when compared to use of accuracy criterion alone. The proposed criterion is also more user-friendly. Data simulations were performed to assess the probabilities of successful transfer using the proposed criteria. With an experimental design consisting of 3 independent runs with 3 replicates per run, a fixed criterion of ±20% of the reference method mean is proposed. [Copyright &y& Elsevier]

In this paper we obtain a long time asymptotic behavior of the optimal exercise boundary for an American put option. This is done by analyzing an integral equation for the rescaled exercise boundary derived from the corresponding Black-Scholes partial differential equation with a free boundary. [ABSTRACT FROM AUTHOR]

Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software is free and multi-platform dynamic mathematics software for learning and teaching, awards in Europe and the USA. This paper describes some critical but constructive investigation using the platform for graph functions and dynamic geometry. [ABSTRACT FROM AUTHOR]

This paper investigates the computability problem of the existence of a vetoer and an oligarchy for quasi-transitive binary social choice rules (Mas-Colell and Sonnenschein in Rev Econ Stud 39:185–192, 1972) in a society with an infinite number of individuals (infinite society) according to the computable calculus (or computable analysis) by Aberth (Computable analysis, McGraw-Hill, New York, 1980; Computable calculus, Academic Press, Dublin, 2001). We will show the following results. The problem whether a quasi-transitive binary social choice rule which satisfies Pareto principle and independence of irrelevant alternatives (IIA) has a vetoer or has no vetoer in an infinite society is a nonsolvable problem, that is, there exists no ideal computer program for a quasi-transitive binary social choice rule which satisfies Pareto principle and IIA that decides whether it has a vetoer or has no vetoer. And it is equivalent to nonsolvability of the halting problem. We also show that if for any quasi-transitive binary social choice rule there exists an oligarchy in an infinite society, whether it is finite or infinite is a nonsolvable problem. A vetoer is an individual such that if he strictly prefers an alternative to another alternative, then the society prefers the former to the latter or is indifferent between them regardless of the preferences of other individuals, and an oligarchy is the minimal set of individuals which has dictatorial power and its each member is a vetoer. It will be shown that an oligarchy is a set of vetoers if it exists. [ABSTRACT FROM AUTHOR]

A critical issue related to the use of simulation environments in school-based learning is the relationship between the use of these environments and the structure of traditional curricula. Teachers are often caught in the bind of attempting to address significantly raised standards for what all students should know, yet receiving very little support to innovate in their use of simulations in their approaches to teaching. Particularly challenging for practitioners and school-based re- searchers alike is the expectation that students should first master "the basics" before engaging innovation related to learning advanced content such as calculus. This paper summarizes years of work related to the early learning of the mathematics of change. The goal is to resolve this tension by suggesting that advanced mathematics, embodied in an accessible simulation environment, helps situate and deepen students' understanding of the basics as they typically are encountered in the traditional mathematics curriculum. Selected episodes transcribed from work in economically challenged schools in the United States are used to illustrate the practical potential of this reconsideration of the relationships between basic and advanced topics. The delta-blocks approach to the mathematics of change, making use of widely available forms of technology and the Math Worlds simulation software, is introduced and illustrated. [ABSTRACT FROM AUTHOR]

One of the problems with proposals for substantial institutional change in water systems is that modification and irreversibility make the process slow, cautious and costly to society. In this paper, we discuss the role that experimental economics can play in evaluating proposed institutional changes to help facilitate a more rapid and smoothadoption of changes in the water system. Experimental economics yields a formal and replicable system for analyzing alternative market structures before they are actually implemented. For example, a water market can be developed and tested in the laboratory under supply and demand constraints that reflect drought conditions that might occur in California, or other arid regions in the world. We present a prototype of a California water transfer model and the results from a series of water market experiments. Results include realized market efficiency and surplus distribution, as well as an analysis of market pricevolatility. The implications of this research extend well beyond California water markets, not only to water markets in other arid regions, but also to the design of markets for other environmental goods, including tradable pollution permits and fishery ITQs. [ABSTRACT FROM AUTHOR]

In this paper, we develop a theoretically consistent framework to incorporate the environmental effects of agricultural production and the depletion of natural capital caused by agricultural production intothe existing income accounts. We apply the framework and adjust the income attributed to the agricultural sector and economy-wide net national product (NNP) for the United States. Estimated adjustments to the income attributed to agriculture are in the range of $4 billion and have declined as a percentage of net farm income since 1982. [ABSTRACT FROM AUTHOR]

The Bohr atom was a solar system in miniature. Despite many deep foundational questions related to the origin of quantized motion, rapid progress was made in its mathematical development and its apparently successful application to spectral line series. In United States, where celestial mechanics flourished throughout the 19th and well into the 20th century, mathematicians and physicists were well prepared for just this sort of problem and made it their own far faster than many areas of the new physics. This paper examines the link between classical problems of perturbation theory, three-body and N-body orbital trajectories, the Hamilton–Jacobi equation, and the old quantum theory. I discuss why it was comparatively easy for American applied mathematicians, astronomers, and mathematical physicists to make significant contributions quickly to quantum theory and why further progress toward quantum mechanics by the same cohort was, in contrast, so slow. [Copyright &y& Elsevier]

In this article, authors reply to the comment by Paul Swaim and Michael Podgursky on their research paper related to the distributional shape of unemployment duration. They remark that they are pleased to note that in the comment on their study Paul Swaim and Michael Podgursky provide results that are broadly consistent with their own. A further and important point of agreement concerns the utility of the flexible, three parameter extended generalized gamma distribution as a useful tool in sensitivity analysis. In this reply, authors argue that the criticism of their sample construction is misplaced, and that their solutions to the measurement difficulties they allude to are unconvincing. Authors remark that their equations are properly to be interpreted as conditional on benefit status. Authors specifically made reference to their separate analysis of the endogeneity issue. Authors conclude with some remarks on distributional assumptions and also by noting the limitations that should be borne in mind when deploying general parametric accelerated failure time.

The article illustrates how an elegant mathematical analysis may obscure the real world phenomena being investigated through oversimplification. The increased use of sophisticated mathematics in sociology appears to have two disadvantages. Mathematical reasoning per se seems to be accepted as more legitimate, or more scientific, than verbal reasoning. The mathematical analyst necessarily works with a very simplified model of the real world, and the shortcomings of this sort of simplification may not be recognized by many sociologists with limited mathematical facility. Sociologist S. Spilerman's analysis of probably models related to black urban riots in the United States and his empirical data support only the heterogeneity assumption. Spilerman argues that the riot distribution is not consistent with an explanation which locates the cause of rioting in community conditions, and that outside of the South, the only important factor determining a city's riot proneness is the size of its black population.

The article presents the author's reply to a critique by William Roberds of his paper "Budget Constraints and Time-Series Evidence on Consumption," published in the December 1991 issue. The author says that Roberds has questioned the validity of the Lemma, by providing an example which appears to violate it. He says that Roberds' counterexample does not satisfy the pair of continuity conditions that are necessary for the Lemma to go through. The author adds that the continuity conditions were not formally stated in the Lemma of the original paper, though they are necessary to guarantee a critical step in its proof. For completeness, he rewrites the proof of the Lemma in a way that highlights the key role of the continuity condition.

The objective of this paper is to study the performance of surge andcontinuous furrow irrigation based on field experiments. The experiments took place on two farms located in the State of New Mexico, U.S.A., cultivated with Beans and Alfalfa and having different types of soil. Each farm was divided into two parts, where the first was designed to practice surge and the second continuous irrigation. The analysis of the results showed that surge flow provides the desired crop water requirement at almost 40% saving in water and time as well as improving the distribution uniformity and application efficiency of irrigation to about 90%. [ABSTRACT FROM AUTHOR]

Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional problem-solving framework. We are particularly interested in students' evoked concept images for the mathematical concepts that play a role in the construction of the function whose minimum is needed. Data analysis revealed several gaps in students’ understanding of the optimization process. We highlight the mathematical concepts that play a role in these gaps, focusing on variables, function notation, function composition, properties of rectangles and the relationships between them, the role of the optimizing function, and the graphical representation of the function. [ABSTRACT FROM PUBLISHER]

This article is devoted to the analysis of electoral systems involving two step procedures. It appears that designers are able to manipulate the result of these type of elections by gerrymandering, except in a very few cases. When imposing an unanimity condition on every jurisdiction's voting rule, it is shown that, for any finite number of candidates, a two step voting rule that is gerrymander-proof necessarily gives every voter the power of overruling the unanimity. A characterization of the set of gerrymander proof rules is provided in the case of two candidates. [ABSTRACT FROM AUTHOR]