On the degree of regularity of generalized van der Waerden triples

Let $1 \leq a \leq b$ be integers. A triple of the form $(x,ax+d,bx+2d)$, where $x,d$ are positive integers is called an {\em (a,b)-triple}. The {\em degree of regularity} of the family of all $(a,b)$-triples, denoted dor($a,b)$, is the maximum integer $r$ such that every $r$-coloring of $\mathbb{N}$ admits a monochromatic $(a,b)$-triple. We settle, in the affirmative, the conjecture that dor$(a,b) < \infty$ for all $(a,b) \neq (1,1)$. We also disprove the conjecture that dor($a,b) \in \{1,2,\infty\}$ for all $(a,b)$.Comment: 5 page

Session 11: Relationships and Conflict

All relationships have conflicts (even Norby) because conflict is simply a disagreement. With this in mind, students experience conflict with parents, professors, friends, and roommates. This session will introduce some basic relationship definitions and walk students through how to handle and resolve conflict. After this session, students will know what to do when they experience conflict and be challenged to see conflict as an opportunity to improve rather than damage their relationships

Dissolution of Marriage—Jurisdiction over Nondomiciliary Service Members: Time to Adopt a New Jurisdictional Analysis—In re Marriage of Ways, 85 Wn. 2d 693, 538 P.2d 1225 (1975); Wash. Rev. Code § 26.09.030 (1975)

On November 30, 1973, Raymond A. Ways, a member of the United States Navy on active military duty, filed a petition for dissolution of marriage in a Washington superior court. Ways had been stationed in Washington aboard the USS Enterprise (then undergoing repairs at the Puget Sound Naval Shipyard, Bremerton, Washington) since October 1973, but neither he nor his wife had ever been domiciled in Washington. Ways filed his petition in reliance upon R.C.W. § 26.09.030, a statute allowing members of the armed forces stationed in Washington to petition for dissolution of marriage in the state. On February 2, 1974, sixty-four days after the filing of Ways\u27 petition, the USS Enterprise departed for California, terminating Ways\u27 Washington station. Three days after the ship departed Washington, petitioner\u27s wife filed a motion to dismiss for lack of jurisdiction. The Superior Court for Kitsap County denied this motion. Respondent wife next petitioned the Washington Supreme Court for a writ of certiorari to review the order denying the motion to dismiss and for a writ of prohibition to bar further proceedings in the dissolution action. In a 5-4 decision, the Washington Supreme Court reversed. Held: Where a petitioning member of the armed forces fails to remain continuously stationed in Washington for ninety days after filing the petition pursuant to R.C.W. § 26.09.030, the superior court is without jurisdiction to enter a decree of dissolution. In re Marriage of Ways, 85 Wn. 2d 693, 538 P.2d 1225 (1975)

THE ROLES OF FOOD AND PREDATION IN SHAPING ADAPTIVE AND MALADAPTIVE BEHAVIORS IN POSTFIRE BIRD SPECIES

Most animals live in rapidly changing environments, and within-individual phenotypic plasticity can allow populations to track sources of selection that often vary dramatically in time and space. However, if conditions change too rapidly, the cues animals use to track environmental changes may become uncoupled from the ultimately important factors with which they have been historically correlated. Animals relying upon proximal cues to guide their behaviors may, in novel environments, consistently make errors. When these errors occur within the context of choosing a habitat, the organism is said to be caught in an ‘ecological trap’. Herein, I develop a conceptual model to explain how an ecological trap might work, outline the specific criteria that are necessary for demonstrating the existence of an ecological trap, and provide tools for researchers to use in detecting ecological traps. I then review the existing literature and summarize the state of empirical evidence for the existence of traps. My conceptual model suggests that there are two basic kinds of ecological traps and three mechanisms by which traps may be created. To this point in time, there are still only a few solid empirical examples of ecological traps in the published literature, although those examples suggest that both types of traps and all three of the predicted mechanisms do exist in nature. Next I examine habitat selection behavior and nest success of Olive-sided Flycatchers (Contopus cooperi) in naturally occurring burned forest and in an anthropogenically created habitat type—a selectively harvested forest. I show that Olive-sided Flycatchers preferred to settle in the selectively harvested forest despite the fact that estimated nest success in that habitat was roughly half that found in naturally burned forest. These results are consistent with the hypothesis that selectively harvested forest can act as an “ecological trap” by attracting Olive-sided Flycatchers to a poor-quality habitat type. Natural disturbances, such as wildfire, are important ecological processes in that they alter habitat structure and resource availability. I used the dramatic temporal and spatial variation in microclimatic conditions generated by variation in wildlife severity to examine the microclimatic consequences of nest site preferences and the fitness costs to parents and offspring in the Dark-eyed Junco (Junco hyemalis). Adults preferred to select nest sites with the most moderate microclimates. Nestlings reared in colder nest sites gained mass more slowly and experienced retarded skeletal growth while parents suffered costs associated with hot microclimates; incubating females reduced their nest attentiveness and doubled their nestling provisioning rate at hot nest sites. Nest site preference in junco appear to be an adaptive consequence of the costs of hot nest sites to parents and the costs of overly cool climates to developing young. Resource levels have been widely recognized to change over time as organisms recover from fire damage or recolonize a site after a wildfire. I report on the importance of food limitation versus nest predation on the expression of plastic life-history traits in Dark-eyed Junco (Junco hyemalis). Junco clutch size was primarily determined by habitat-specific and seasonal changes in food availability, while nest predation risk shaped egg laying decisions when food was extremely limited. Conversely, nestling growth rates were primarily determined by habitat-specific, seasonal changes in nest predation risk, but were mediated by food availability. Results illustrate that food is more important than environmental risk of nest predation in shaping the expression of clutch size. Overall, results demonstrate the birds assess and respond to variation in nest predation risk and food availability at fine temporal and spatial scales, and that that both factors play an important role in the expression of avian reproductive strategies

Individual cognitive-behavioural anger treatment for people with mild-borderline intellectual disabilities and histories of aggression: a controlled trial

Objectives - Anger is a significant predictor and activator of violent behaviour in patients living in institutional settings. There is some evidence for the value of cognitive-behavioural treatments for anger problems with people with intellectual disabilities. In this study, a newly designed treatment targeted at anger disposition, reactivity, and control was provided to intellectually disabled offenders with aggression histories living in secure settings. Design - About forty detained patients with mild-borderline intellectual disabilities and histories of serious aggression were allocated to specially modified cognitive-behavioural anger treatment (AT group) or to routine care waiting-list control (RC group) conditions. Methods - AT group participants received 18 sessions of individual treatment. The AT and RC groups were assessed simultaneously at 4 time points: screen, pre- and post-treatment, and at 4-month follow-up using a range of self- and staff-rated anger measures. The effectiveness of the treatment was evaluated using ANCOVA linear trend analyses of group differences on the main outcome measures. Results - The AT group's self-reported anger scores on a number of measures were significantly lower following treatment, compared with the RC wait-list condition, and these improvements were maintained at follow-up. Limited evidence for the effectiveness of treatment was provided by staffs' ratings of patient behaviour post-treatment. Conclusions - Detained men with mild-moderate intellectual disabilities and histories of severe aggression can successfully engage in, and benefit from, an intensive individual cognitive-behavioural anger treatment that also appears to have beneficial systemic effects