# Top PDF An involution on bicubic maps and β(0, 1)-trees

### An involution on bicubic maps and β(0, 1)-trees

The smallest bicubic map has two vertices and three edges joining them. It is well-known that the faces of a bicubic map can be colored using three colors so that adjacent faces have distinct colors, say, colors 1, 2 and 3, in a counterclockwise order around white vertices. We will assume that the root vertex is black and the root face has color 3. There are exactly three different bicubic maps with 6 edges and they are given in Figure 1. The number of

### Gray coding cubic planar maps

Letting a = 0 and b = 1 in Definition 1 we will obtain a definition of a β(0, 1)- tree. Note that the label of the root of a β(0, 1)-tree is defined uniquely from the labels of its children, which allows us to modify this definition suit better to our purposes. In this paper, we will consider two modifications of the definition. First, we will re-define the root label to be one more than the sum of its children (as was done in [1] for a better description of statistics preserved under the bijection with bicubic maps to be described below), and then we will let the root label be ∗ (to allow two β(0, 1)-trees having the same shape to differ just in one label). Thus, no matter which definition we use, we still have a class of trees in one-to-one correspondence with the originally defined β(0, 1)-trees, and slightly abusing the notation, which will not cause any confusion, we will refer to all of the “modified β (0, 1)-trees” as β(0, 1)-trees.

### Enumeration of fixed points of an involution on β(1, 0)-trees

As mentioned in the introduction, there is a bijective correspondence be- tween β(1, 0)-trees and rooted non-separable maps. Under this bijection (de- scribed in detail in Section 5), trees with n nodes are mapped to maps with n edges, and, moreover, the label of the root of the tree plus one corresponds to the degree of the root face of the map. We use now expressions for B(x) and B(x, y) that were found in the map enumeration context. Brown [2] gave the following parametric expression for the series ˜ B (x) = B(x) − x:

### On Regular Elements in an Incline

Just for sake of completeness we will introduce g-inverses of an element in an incline. Definition 3.1. a ∈ R is said to be regular if there exists an element x ∈ R such that axa a. Then x is called a generalized inverse, in short g-inverse or 1-inverse of a and is denoted as a − . Let a{1} denotes the set of all 1-inverses of a.

### Some common fixed point theorems for various types of compatible mappings in intuitionistic fuzzy metric spaces

Definition 2.9. [14] A pair (A, S) of self mappings of an intuitionistic fuzzy metric space (X, M, N, *, ◊) is said to be commuting if 𝑀(𝐴𝑆𝑥, 𝑆𝐴𝑥, 𝑡) = 1 𝑎𝑛𝑑 𝑁(𝐴𝑆𝑥, 𝑆𝐴𝑥, 𝑡) = 0𝑓𝑜𝑟 𝑎𝑙𝑙 𝑥 ∈ 𝑋. Definition 2.10. [14] A pair (A, S) of self mappings of an intuitionistic fuzzy metric space (X, M, N, *, ◊) is said to be weakly commuting if 𝑀(𝐴𝑆𝑥, 𝑆𝐴𝑥, 𝑡) ≥

### The Complementary Hankel Type Transformations Of Arbitrary Order

Remark 5. Note that the definitions of the generalized operators introduces in (ii) are consistent with the rules of distributional calculus, in particular, with the definitions of multiplication by an infinitely differentiable function, differentiation of distribution which does not occur in [1], [5] and [10].

### Eurostatistics: data for short-term analysis 1992.10.

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### Image Super Resolution on the Basis of DWT and Bicubic Interpolation

Interpolation is estimation of the value of the discrete function at unknown positions based on the given and known surrounding samples. The goal of image interpolation is to produce acceptable images at different resolutions from a single low-resolution image [10]. The actual resolution of an image is defined as the number of pixels, but the effective resolution is a much harder quantity to define as it depends on subjective human judgment and perception. Image interpolation is used for several different purposes such as image resolution enhancement, multi-resolution pyramidal compressing, and position computing for rotated image pixels etc. In the past years, many linear and nonlinear image interpolation techniques have been proposed. In the linear methods, the nearest- neighbor, bilinear, and bicubic interpolation methods are widely used to increase resolution of images.

### Ecotourism, Stated Preferences, a Paradox between Environmental Awareness and Environmental Actions: The Case of Monteverde, Costa Rica

The survey was divided into three sections. Section number one inquired about demographic information in- cluding age, sex, level of education and occupation. The second section of the survey asked about the types of transportation used to arrive to the region and the third part of the survey used multi-choice questions in order to analyze the individual’s opinions and knowledge of environmental programs. Question number six inquired about the most willing to do: a) action to compensate or b) change in behavior (mitigate) for their travel related emission. To analyze the data two types of statistical methodologies where used in order to determine if a distribution of observed frequencies differs from the theoretical expected frequencies the chi-square technique. Chi-square sta- tistics allow the evaluation of categorical data, instead of using means and variances, this test uses frequencies. The value of the chi-square statistic is given by the following Formula (1):

### Theory of Neutrosophic Evolution: Degrees of Evolution, Indeterminacy, and Involution

One therefore has a Neutrosophic Theory of Evolution, Involution, and Indeterminacy (neutrality, or fluctuation between Evolution and Involution).The evolution, the involution, and the indeterminate-evolution depend not only on natural selection, but also on many other factors such as: artificial selection, friends and enemies, bad luck or good luck, weather change, environment juncture etc.

### Determining suitable locations for seed transfer under climate change: A global quantitative method

when combined with careful consideration of the taxonomic and floristic literature (Montalvo and Ellstrand 2000). Specifically, it is important that seed transfer strategies account for such life-history characteristics as mating systems, pollination vectors and seed dispersal regimes (Hufford and Mazer 2003), and for environmental generalist versus specialist status (Johnson et al. 2004). Our ecoregion similarity output would enable res- toration planners and seed source managers to refine their collection and planting strategies based on these species-specific life history traits. Flowering dogwood, for example, might be more adequately adapted to areas that are lighter gray (less environmentally similar) on our ecoregion similarity maps (Figs. 4a, 5b) because its seeds can be dispersed long distances by birds (McLemore 1990) and because it is highly outcrossed (Apsit et al. 2002); highly outcrossing taxa are less likely to represent ecotypic differentiation as a result of the homogenizing effect of gene flow (Hufford and Mazer 2003). Longleaf pine, meanwhile, might be considered adequately adapted to areas that are darker gray because its wind-dispersed seed is not as likely to move long distances (Boyer 1990).

### Modulation of β-amyloid by a single dose of GSK933776 in patients with mild Alzheimer’s disease: a phase I study

Pharmacodynamics sample collection and analysis For the first four patients who received the lowest dose (1 mg/kg), blood and CSF samples were collected at hourly intervals over a 30-hour time period from appro- ximately 11 hours predosing to 19 hours postdosing. The primary sampling time period for evaluation of baseline levels was 6 to 8 hours predosing, whereby 0 to 5 hours postdosing was considered a run-in period during which we obtained stable values. The time period from 0 to 12 hours postdosing was the focus for the postdosing assessment. This duration was initially based on plasma pharmacodynamics observed in our previous study, that is, the time of onset of lowering of free Aβ (manuscript in submission). After the first four patients completed the protocol, their Aβ levels were reviewed and the sample collection times for CSF and blood for both baseline and postdosing were adjusted as follows. CSF samples were collected hourly (3 ml per sample) from 9 hours predosing to 12 hours postdosing. Blood samples were collected hourly from 6 hours predosing to 12 hours postdosing and at follow-up: once on day 7 and once on day 56 postdosing. Total tau and phosphorylated tau 181 were measured in CSF at 5 hours predosing, at the time of dosing and at 5 hours and 12 hours postdosing. Because of the short-term exposure to GSK933776, no changes in total tau or phosphorylated tau 181 were expected.

### The protective effect of longer duration of breastfeeding against pregnancy-associated triple negative breast cancer

During pregnancy, extensive expansion and morphological changes prepare the mammary gland for lactation [26]. Side-branching and alveologenesis in response to progesterone (P) alone or in combination with prolactin (PRL) [27-29] generates secretory alveoli capable of producing milk [22] (Figure 1). Moreover, oxytocin released by suckling causes contraction of the surrounding myoepithelial cells that moves milk through the ductal tree to the nipple [22]. Additionally, during lactation significant changes to the vasculature, the adipose tissue and the extracellular matrix within the mammary gland trigger terminal differentiation of the majority of mammary cells [30-32] (Figure 1). Finally, during involution (the post-lactation weaning) all terminally differentiated mammary cells are eliminated by cell death and the mammary gland undergoes a significance re-organization that returns it to pre-pregnancy quiescent state [33-35] (Figure 1).

### Eurostatistics: data for short-term analysis 1992.11.

%,T12/T0 %,T/T­12 %,SOLDE 1985 = 1 0 0 EUR 1 0 = 1 0 0 EUR 1 2 = 100 Mio Mrd Τ ΤΕΡ GWH Μ3 Β DK D GR E F IRL I L NL Ρ UK USA JAP USD ECU DTS CE Eurostat EUR 10 EUR 12 UEBL/BLEU, BL ACP SE[r]

### Key stages in mammary gland development Involution: apoptosis and tissue remodelling that convert the mammary gland from milk factory to a quiescent organ

Apoptosis in mammary gland has been studied since 1986. Most previous work focussed on apoptosis at days 2 and 3 of involution, however, as this is when the most terminal deoxynucleotidyl transferase nick end labelling (TUNEL) positive cells were seen. However, it is now clear that the initial apoptotic signals are much earlier in the involution process. LIF transcription is induced 30-fold within 12 hours of forced weaning [17] and microarray data from 2 independent studies [24,25] reveals a cluster of genes that are transcriptionally upregulated between lactation and 12 hours involution and subsequently decline by 24 hours. Some of these genes encode DR ligands such as TNF, TWEAK and FasL. Furthermore, expression of transforming growth factor (TGF)β3 is induced within 8 hours of forced weaning, and triggers phosphorylation of Stat3 [26]. Genetic evidence from TGFβ3 deficient mice further suggests that this ligand is important for initiating involution.

### Performing Farmscapes on urban streets

Many visual artists and performers have experimented with ways to address these issues as, for example, Agnes Denes’ well-known “Wheatfields—a Confrontation” in New York City in 1982 and later recreated in London (2009) and Milan (2015) or Lauren Bon’s “Not a Cornfield” (2005) in Los Angeles. More overtly theatrical productions include PeerGrouP’s The Swine House (2013) and Drenthe Bluesopera (2011), and Ministry of Turen (2007) or KMK’s Les Jardins Migrants ; the walking audio tours of Mike Pearson, Carrlands and Warplands ; and the durational community-based initiative, myvillages created by Kattrin Böhm, Wapke Feenstra, and Antje Schiffers. This essay looks at four art-based projects from three street theatre companies based in France and an artist collective in Los Angeles. These projects range from short-term performance installations to long-term participatory agriculture-art events. Le Phun’s La vengeance des semis [The Seedlings’ Revenge] and Opéra Pagaï’s La Maison sur l’eau [House on the water] propose ephemeral urban farms in unexpected city sites and challenge preconceptions about farmscapes on multiple levels from the personal and local to the global. Friches Théâtre Urbain’s Aroma-Home and Fallen Fruit’s Public Fruit Maps and The Endless Orchard create more enduring and interactive projects that combine art and growing or foraging edible crops. They attempt to restore the value and efficacy of an agricultural “commons” 3