Abstract: The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk D to the complex plane. In particular, we obtain necessary conditions for a function f to be normal.

Abstract: Conceptual properties norming studies (CPNs) ask participants to produce properties that describe concepts. From that data, different metrics may be computed (e.g., semantic richness, similarity measures), which are then used in studying concepts and as a source of carefully controlled stimuli for experimentation. Notwithstanding those metrics' demonstrated usefulness, researchers have customarily overlooked that they are only point estimates of the true unknown population values, and therefore, only rough approximations. Thus, though research based on CPN data may produce reliable results, those results are likely to be general and coarse-grained. In contrast, we suggest viewing CPNs as parameter estimation procedures, where researchers obtain only estimates of the unknown population parameters. Thus, more specific and fine-grained analyses must consider those parameters' variability. To this end, we introduce a probabilistic model from the field of ecology. Its related statistical expressions can be applied to compute estimates of CPNs' parameters and their corresponding variances. Furthermore, those expressions can be used to guide the sampling process. The traditional practice in CPN studies is to use the same number of participants across concepts, intuitively believing that practice will render the computed metrics comparable across concepts and CPNs. In contrast, the current work shows why an equal number of participants per concept is generally not desirable. Using CPN data, we show how to use the equations and discuss how they may allow more reasonable analyses and comparisons of parameter values among different concepts in a CPN, and across different CPNs.

Abstract: To study linguistically coded concepts, researchers often resort to the Property Listing Task (PLT). In a PLT, participants are asked to list properties that describe a concept (e.g., for DOG, subjects may list �is a pet�, �has four legs�, etc.). When PLT data is collected for many concepts, researchers obtain Conceptual Properties Norms (CPNs), which are used to study semantic content and as a source of control variables. Though the PLT and CPNs are widely used across psychology, only recently a model that describes the listing course of a PLT has been developed and validated. That original model describes the listing course using order of production of properties. Here we go a step beyond and validate the model using response times (RT), i.e., the time from cue onset to property listing. Our results show that RT data exhibits the same regularities observed in the previous model, but now we can also analyze the time course, i.e., dynamics of the PLT. As such, the RT validated model may be applied to study several similar memory retrieval tasks, such as the Free Listing Task, Verbal Fluidity Task, and to examine related cognitive processes. To illustrate those kinds of analyses, we present a brief example of the difference in PLT�s dynamics between listing properties for abstract versus concrete concepts, which shows that the model may be fruitfully applied to study concepts.

Abstract: We study classes of locally biholomorphic mappings defined in the polydisk P-n that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes.

Abstract: Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even further enlarged when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of three examples.

Abstract: Environmental temperature has profound effects on the biological performance and biogeographical distribution of ectothermic species. Variation of this abiotic factor across geographic gradients is expected to produce physiological differentiation and local adaptation of natural populations depending on their thermal tolerances and physiological sensitivities. Here, we studied geographic variation in whole-organism thermal physiology of seven populations of the porcelain crab Petrolisthes violaceus across a latitudinal gradient of 3000 km, characterized by a cline of thermal conditions. Our study found that populations of P. violaceus show no differences in the limits of their thermal performance curves and demonstrate a negative correlation of their optimal temperatures with latitude. Additionally, our findings show that high-latitude populations of P. violaceus exhibit broader thermal tolerances, which is consistent with the climatic variability hypothesis. Interestingly, under a future scenario of warming oceans, the thermal safety margins of P. violaceus indicate that lower latitude populations can physiologically tolerate the ocean-warming scenarios projected by the IPCC for the end of the twenty-first century.

Abstract: This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to

Abstract: This paper proposes a slow-moving management method for a system using of intermittent demand per unit time and lead time demand of items in service enterprise inventory models. Our method uses zero-inflated truncated normal statistical distribution, which makes it possible to model intermittent demand per unit time using mixed statistical distribution. We conducted numerical experiments based on an algorithm used to forecast intermittent demand over fixed lead time to show that our proposed distributions improved the performance of the continuous review inventory model with shortages. We evaluated multi-criteria elements (total cost, fill-rate, shortage of quantity per cycle, and the adequacy of the statistical distribution of the lead time demand) for decision analysis using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). We confirmed that our method improved the performance of the inventory model in comparison to other commonly used approaches such as simple exponential smoothing and Croston's method. We found an interesting association between the intermittency of demand per unit of time, the square root of this same parameter and reorder point decisions, that could be explained using classical multiple linear regression model. We confirmed that the parameter of variability of the zero-inflated truncated normal statistical distribution used to model intermittent demand was positively related to the decision of reorder points. Our study examined a decision analysis using illustrative example. Our suggested approach is original, valuable, and, in the case of slow-moving item management for service companies, allows for the verification of decision-making using multiple criteria.