Lifting Lagrangian immersions in CPn−1\mathbb{C} P^{n-1} to Lagrangian cones in Cn\mathbb{C}^n

In this paper we show how to lift Lagrangian immersions in $\mathbb{C} P^{n-1}$ to produce Lagrangian cones in $\mathbb{C} ^n$, and use this process to produce several families of examples of Lagrangian cones and special Lagrangian cones. Moreover we show how to produce Lagrangian cones, isotopic to the Harvey-Lawson and trivial cones, whose projections to $\mathbb{C} P^{n-1}$ are immersions with few transverse double points.Comment: 28 Pages, 7 figure

The Foster Parents Dilemma Who Can I Turn to When Somebody Needs Me?

One cannot help but feel compassion for foster parents who merely try to do what they feel is best for a child they love. The rights in this regard and chances of success in asserting these rights in court will be explored in this Article

Anaerobic Soil Disinfestation: Evaluation of Anaerobic Soil Disinfestation (ASD) for Warm-Season Vegetable Production in Tennessee

Anaerobic soil disinfestation (ASD) is a non-chemical, pre-plant soil treatment recently developed for control of pests such as soilborne plant pathogens, plant-parasitic nematodes, and weeds in specialty crop systems. Soil treatment by ASD includes incorporating a labile carbon (C) source, tarping with plastic, and irrigation of the topsoil to saturation to facilitate the development of strongly anaerobic soil conditions driven by soil microbes. Processes occurring during the anaerobic decomposition of the added C source have been reported control plant pests. The goal of this project was to evaluate and adapt the ASD procedure to environmental conditions and production systems in Tennessee and examine the potential for on-farm implementation. To meet this goal, study objectives were to 1) evaluate both cover crop and off-farm C inputs for ASD treatment for production of bell pepper and tomato in a research station field experiment, 2) evaluate cool-season cover crop and off-farm inputs as C sources for ASD treatment in a growth chamber pot experiment with introduced sclerotia of Sclerotium rolfsii and propagules of key weed species, and 3) demonstrate and evaluate on-farm implementation of ASD on a commercial tomato farm. Data collection included soil properties, pest assessment, and crop performance. Results indicated no differences in total marketable fruit yields between treatments in any of the studies, likely due to low disease pressure, plant-parasitic nematode populations, and weed populations apparent in all studies. Accumulation of anaerobic soil conditions generally did not differ among treatments, possibly due to the generally low C amendment rates and the soil properties in study locations. Treatment by ASD did impact a number of soil properties, including levels if inorganic soil nitrogen, which will need to be addressed when developing best management practices for ASD implementation. Additional studies are needed on sites with high existing pest pressure to further evaluate the feasibility of ASD for commercial production systems

Realizability and recursive mathematics

Section 1: Philosophy, logic and constructivityPhilosophy, formal logic and the theory of computation all bear on problems in the foundations of constructive mathematics. There are few places where these, often competing, disciplines converge more neatly than in the theory of realizability structures. Uealizability applies recursion-theoretic concepts to give interpretations of constructivism along lines suggested originally by Heyting and Kleene. The research reported in the dissertation revives the original insights of Kleene—by which realizability structures are viewed as models rather than proof-theoretic interpretations—to solve a major problem of classification and to draw mathematical consequences from its solution.Section 2: Intuitionism and recursion: the problem of classificationThe internal structure of constructivism presents an interesting problem. Mathematically, it is a problem of classification; for philosophy, it is one of conceptual organization. Within the past seventy years, constructive mathematics has grown into a jungle of fullydeveloped "constructivities," approaches to the mathematics of the calculable which range from strict finitism through hyperarithmetic model theory. The problem we address is taxonomic: to sort through the jungle, set standards for classification and determine those features which run through everything that is properly "constructive."There are two notable approaches to constructivity; these must appear prominently in any proposed classification. The most famous is Brouwer's intuitioniam. Intuitionism relies on a complete constructivization of the basic mathematical objects and logical operations. The other is classical recursive mathematics, as represented by the work of Dekker, Myhill, and Nerode. Classical constructivists use standard logic in a mathematical universe restricted to coded objects and recursive operations.The theorems of the dissertation give a precise answer to the classification problem for intuitionism and classical constructivism. Between these realms arc connected semantically through a model of intuitionistic set theory. The intuitionistic set theory IZF encompasses all of the intuitionistic mathematics that does not involve choice sequences. (This includes all the work of the Bishop school.) IZF has as a model a recursion-theoretic structure, V(A7), based on Kleene realizability. Since realizability takes set variables to range over "effective" objects, large parts of classical constructivism appear over the model as inter¬ preted subsystems of intuitionistic set theory. For example, the entire first-order classical theory of recursive cardinals and ordinals comes out as an intuitionistic theory of cardinals and ordinals under realizability. In brief, we prove that a satisfactory partial solution to the classification problem exists; theories in classical recursive constructivism are identical, under a natural interpretation, to intuitionistic theories. The interpretation is especially satisfactory because it is not a Godel-style translation; the interpretation can be developed so that it leaves the classical logical forms unchanged.Section 3: Mathematical applications of the translation:The solution to the classification problem is a bridge capable of carrying two-way mathematical traffic. In one direction, an identification of classical constructivism with intuitionism yields a certain elimination of recursion theory from the standard mathematical theory of effective structures, leaving pure set theory and a bit of model theory. Not only are the theorems of classical effective mathematics faithfully represented in intuitionistic set theory, but also the arguments that provide proofs of those theorems. Via realizability, one can find set-theoretic proofs of many effective results, and the set-theoretic proofs are often more straightforward than their recursion-theoretic counterparts. The new proofs are also more transparent, because they involve, rather than recursion theory plus set theory, at most the set-theoretic "axioms" of effective mathematics.Working the other way, many of the negative ("cannot be obtained recursively") results of classical constructivism carry over immediately into strong independence results from intuitionism. The theorems of Kalantari and Retzlaff on effective topology, for instance, turn into independence proofs concerning the structure of the usual topology on the intuitionistic reals.The realizability methods that shed so much light over recursive set theory can be applied to "recursive theories" generally. We devote a chapter to verifying that the realizability techniques can be used to good effect in the semantical foundations of computer science. The classical theory of effectively given computational domains a la Scott can be subsumed into the Kleene realizability universe as a species of countable noneffective domains. In this way, the theory of effective domains becomes a chapter (under interpre¬ tation) in an intuitionistic study of denotational semantics. We then show how the "extra information" captured in the logical signs under realizability can be used to give proofs of classical theorems about effective domains.Section 4: Solutions to metamathematical problems:The realizability model for set theory is very tractible; in many ways, it resembles a Boolean-valued universe. The tractibility is apparent in the solutions it offers to a number of open problems in the metamathematics of constructivity. First, there is the perennial problem of finding and delimiting in the wide constructive universe those features that correspond to structures familiar from classical mathematics. In the realizability model, it is easy to locate the collection of classical ordinals and to show that they form, intuitionistically, a set rather than a proper class. Also, one interprets an argument of Dekker and Myhill to prove that the classical powerset of the natural numbers contains at least continuum-many distinct cardinals.Second, a major tenet of Bishop's program for constructivity has been that constructive mathematics is "numerical:" all the properties of constructive objects, including the real numbers, can be represented as properties of the natural numbers. The realizability model shows that Bishop's numericalization of mathematics can, in principle, be accomplished. Every set over the model with decidable equality and every metric space is enumerated by a collection of natural numbers

Geometric Graphs with Unbounded Flip-Width

We consider the flip-width of geometric graphs, a notion of graph width recently introduced by Toru\'nczyk. We prove that many different types of geometric graphs have unbounded flip-width. These include interval graphs, permutation graphs, circle graphs, intersection graphs of axis-aligned line segments or axis-aligned unit squares, unit distance graphs, unit disk graphs, visibility graphs of simple polygons, $\beta$-skeletons, 4-polytopes, rectangle of influence graphs, and 3d Delaunay triangulations.Comment: 10 pages, 7 figures. To appear at CCCG 202

THE IMPACT OF CURRENT COTTON PRICE AND PRODUCTION COSTS ON SKIP-ROW COTTON

According to conventional wisdom, low prices favor skip-row planting patterns while high prices favor solid planted cotton. Production costs have been trending upward for many years. Current high production costs have redefined the point at which a low price becomes a high price relative to skip-row versus solid planting pattern decisions. Growers considering a shift from solid to skip-row cotton must be able to produce high yields, more than 90% of the solid yield on a land acre basis.cotton, no-till yields, returns, Production Economics,

Using an Adventure Therapy Activity to Assess the Adlerian Lifestyle

The lifestyle is a central concept in Adlerian theory necessary for understanding a client and the purpose of behavior. Although there are a variety of methods counselors can employ to explore the lifestyle, to date, no literature addressing the use of Adventure Therapy (AT) exists. Adventure Therapy is a creative and interactive mode of counseling consistent with Adlerian theory that uses creativity and experiential activities to foster insight, awareness, and growth in clients. This article introduces a creative way to explore the client’s lifestyle using an AT activity called Ubuntu Cards©. The authors provide an overview of Adlerian theory, define Adlerian lifestyle, and explore traditional methods of assessing the lifestyle. The article also includes a detailed outline for using Ubuntu Cards© to assess a client’s lifestyle