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

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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**.

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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:

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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.

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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) ≥

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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].

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0 % %, T4/T0 %,T12/T0 1 %,T/T12 J %, BALANCE * 1985 = 1 0 0 EUR 1 0 = 1 0 0 EUR 12 = 100 MIO MRD Τ TOE GWH M3 Β DK D GR E F IRL I L NL Ρ UK USA JAP USD ECU SDR EC Eurostat EUR 10 EUR 12[r]

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parameter ρ captures the deviation from the long term private signal responsiveness due to the presence of residual uncertainty. Thus, prior to the last trading round, investors react to their private signals more aggressively than if the liquidation value were to be realized in the next period. Indeed, while residual uncertainty makes investors less confident about their signals, the presence of an additional trading round increases the opportunities to adjust suboptimal positions prior to liquidation. This, in turn, boosts investors’ reaction to private information. Residual uncertainty implies that informed investors speculate on short-term price movements based on their private information. This makes possible multiple equilibria. Indeed, faced with uncertain impending liquidation a long-term trader in period 2 is not going to use much his private signal. This makes the trader behave in the first period more like a short-term trader since he will try to unwind his first period holdings in the market at time 2, and carry little of that inventory to the liquidation date. In this case the liquidity of the second period market becomes much more important to determine the trader’s reaction to private information in the first period and multiple self- fulfilling expectational loops are possible as in the case with short-term traders. Again the possibility of multiple equilibria is linked to having a negative price impact in the second period (λ 2 < **0**) due to a large response to private information in the first period

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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.

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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**):

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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.

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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).

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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.

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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**).

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%,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]

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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**.

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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

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Schoenberg [**1**] introduced “spline functions” to the mathematical literature. In the last 60 years, splines have proved to be enormously important in different branches of mathematics such as numerical analysis, numerical treatment of differential, integral and partial differential equations, approximation theory and statistics. Also, splines play major roles in field of applications, such as CAGD, tomography, surgery, animation and manufac- turing. In this paper, we discuss on complete fractal splines that generalize the classical complete splines.

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control is still required. In this note we address the issue of using only **β**-control to stabilize a solar sail about an artificial libration point. **β** -control offers the possibility for passive control designs based on natural feedback laws such as ∂**β** = −k∂x where k is a constant parameter, ∂**β** is the change in sail lightness number and ∂x is the change in distance from the Sun. One type of passive control that would naturally induce such a feedback could materialize through a conceptual ‘solar balloon’. For example, as a balloon with a