Generalized punctual Hilbert schemes and 𝔤-complex structures

We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple properties with Hitchin components, and which are conjecturally homeomorphic to them. For simple complex Lie algebras, this generalizes the higher complex structure. For real Lie algebras, this should give an alternative description of the Hitchin–Kostant–Rallis section.

Structural and word-forming features of microtoponyms of Donetsk region

Problem statement. Despite the fact that microtoponyms belong to the most numerous class of onyms, so far such names of Donetsk region have been studied sporadically and superficially. It is important to identify and record such onyms, so as not to lose forever.The purpose of the article is to analyze the structural and word-forming or- ganization of microtoponyms of Donetsk region.Research methods. The method of research of structural and word-forming features of microtoponyms is based on the questionnaires and interviews (for collecting microtoponymic material) and methods: descriptive (for inventory, classification and interpretation of microtoponyms), structural (for describing structural features of simple, complex and compound onyms), quantitative anal- ysis (to establish the performance of structural types, word-forming methods and manners).The main results of the study. The simple, complex and compound names are revealed based on the analysis of the structural and word-forming organiza- tion of microtoponymy of Donetsk region. Simple names of small geographical objects are formed by lexical-semantic, morphological, basic, morphologi- cal-syntactic and lexical-syntactic methods. The most productive is the lexi- cal-semantic way of creating microtoponyms. Among the suffix derivatives, names with productive forms -ivk- (-ovk-, -evk-), -k- were found. In the micro- toponymy of Donetsk region a large number of compound names is recorded, among which we single out two-word, prepositional constructions, multicom- ponent microtoponyms and predicative constructions.Conclusions and prospects. The results of the study show that the microto- ponymy of Donetsk region is diverse in terms of structure and methods and means of forming. We see the prospect of exploration in: 1) collecting the names of micro-objects of other settlements in the Donetsk region; 2) to investigate the structural and word-forming features of microtoponyms of other cities / villages of Donetsk region; 2) to analyze the lexical and semantic features of such names of the named region.

The Efficiency Score of Small Accommodation Businesses in Non-Coastal Rural Areas in Greece

Small accommodation businesses dominate the rural hospitality industry, producing simple or complex tourist products and services in order to be sustainable and competitive. In this paper, a two-stage data envelopment analysis (DEA) model was applied in a representative sample of 151 small accommodation businesses in non-coastal areas in the region of Central Macedonia in Greece. In the first stage, DEA-bootstrapping is applied to estimate point and interval efficiency ratios of accommodation businesses and identify the benchmark accommodations. The double bootstrapping truncated procedure of Simar and Wilson is implemented in the second stage to investigate the role of five business factors in terms of efficiency. The findings suggest that small accommodation businesses, although they are based in areas where tourist resources abound, are inefficient. Moreover, the results of the truncated regression method showed that the business’s size, the operating days, and the variety of activities (simple/complex) affect business’s inefficiency. On the contrary, the business’s age and their engagement in agriculture or not do not affect business’s efficiency. The results are important for rural entrepreneurs and policy makers, and they will also be useful for the adaptation of businesses to increase their efficiency.

Fabrication of Bacterial Cellulose Nanofibers/Soy Protein Isolate Colloidal Particles for the Stabilization of High Internal Phase Pickering Emulsions by Anti-solvent Precipitation and Their Application in the Delivery of Curcumin

In this study, the anti-solvent precipitation and a simple complex method were applied for the preparation of bacterial cellulose nanofiber/soy protein isolate (BCNs/SPI) colloidal particles. Fourier transform IR (FT-IR) showed that hydrogen bonds generated in BCNs/SPI colloidal particles via the anti-solvent precipitation were stronger than those generated in BCNs/SPI colloidal particles self-assembled by a simple complex method. Meanwhile, the crystallinity, thermal stability, and contact angle of BCNs/SPI colloidal particles via the anti-solvent precipitation show an improvement in comparison with those of BCNs/SPI colloidal particles via a simple complex method. BCNs/SPI colloidal particles via the anti-solvent precipitation showed enhanced gel viscoelasticity, which was confirmed by dynamic oscillatory measurements. Furthermore, high internal phase Pickering emulsions (HIPEs) were additionally stable due to their stabilization by BCNs/SPI colloidal particles via the anti-solvent precipitation. Since then, HIPEs stabilized by BCNs/SPI colloidal particles via the anti-solvent precipitation were used for the delivery of curcumin. The curcumin-loaded HIPEs showed a good encapsulation efficiency and high 2,2-diphenyl-1-picrylhydrazyl (DPPH) removal efficiency. Additionally, the bioaccessibility of curcumin was significantly increased to 30.54% after the encapsulation using the prepared HIPEs. Therefore, it can be concluded that the anti-solvent precipitation is an effective way to assemble the polysaccharide/protein complex particles for the stabilization of HIPEs, and the prepared stable HIPEs showed a potential application in the delivery of curcumin.

A-72 Neuropsychological Functioning in Primary Dystonia: A Multi-Domain Meta-Analysis

Objective Primary dystonia is conventionally seen as a motor disorder, though growing literature indicates cognitive dysfunction among persons with primary dystonia (PWD). Here, we completed a meta-analysis comparing cognition on clinical measures between PWD and normal controls. Method We searched PubMed, Embase, Cochrane Library, Scopus, and PsycINFO using a uniform search-strategy to locate original research comparing cognition between PWD and control samples. All analyses were modeled under random-effects. We used Hedge’s g as a bias-corrected estimate of effect size. Between-study heterogeneity was assessed using Cochran’s Q and I2. Results The initial search strategy yielded 866 results. Twenty studies were analyzed (PWD n = 739, control n = 865; 254 effect sizes extracted). Meta-analysis showed a significant combined effect size of primary dystonia across all studies (g = −0.55, p < 0.001), with low heterogeneity (Q = 23.60, p = 0.21, I2 = 19.49). Trim-and-fill procedure estimated 6 studies missing due to publication bias (adjusted g = −0.47, Q = 44.58). Within-domain effects of primary dystonia were: Motor/Non-Motor Speed = −0.76, Global Cognition/Orientation = −0.65, Language = −0.62, Executive Functioning = −0.50, Learning/Memory = −0.46, Visuospatial/Construction = −0.44, and Simple/Complex Attention = −0.36. Heterogeneity was generally low within domains. Effects were comparable between Speed tasks with (g = −0.85) and without (g = −0.80) a motor component. Meta-regressions indicated age, education, gender, and disease duration were not related to effect sizes. Conclusions PWD consistently demonstrated lower performances on neuropsychological tests compared to controls. Effect sizes were generally moderate in strength, with smallest effects in Simple/Complex Attention, and largest in Motor/Non-Motor Speed. Within the Speed domain, results suggested cognitive slowing beyond effects from motor symptoms. This quantitative summary indicates that PWD experience difficulties in multiple aspects of cognition, as detected by neuropsychological tests.

Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots

The secant method is a very effective numerical procedure used for solving nonlinear equations of the form f(x)=0. In a recent work (A. Sidi, Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008), we presented a generalization of the secant method that uses only one evaluation of f(x) per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer k, this method generates a sequence {xn} of approximations to a real root of f(x), where, for n≥k, xn+1=xn−f(xn)/pn,k′(xn), pn,k(x) being the polynomial of degree k that interpolates f(x) at xn,xn−1,…,xn−k, the order sk of this method satisfying 1<sk<2. Clearly, when k=1, this method reduces to the secant method with s1=(1+5)/2. In addition, s1<s2<s3<⋯, such that limk→∞sk=2. In this note, we study the application of this method to simple complex roots of a function f(z). We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples.

Study of the Growth and Development of Pterocarya pterocarpa (Michx.) Kunth ex Iljinsk. in ex situ Conditions

Results of analyzes of the growth and development of species Pterocarya pterocarpa (Michx.) Kunth ex Iljinsk. of the Pterocarya Kunth genus (Juglandaceae DC. ex Perleb) — relict plant of the Arctic flora of the III period in ex situ conditions have been shown in the paper. Degree of adaptation of wingnut in ex situ conditions, its growth characteristics were assessed both in young and old age. The biomorphological structure of P. pterocarpa seedlings, the size and number of hypocotyls and germ layer were determined in the course of the study. The formation and growth of simple complex true leaves and the life cycle of germ layer were determined as a result of observations of seedlings. The growth of seedlings of wingnut occurs intensively from the third decade of April to the second decade of June under ex situ conditions have been showed the study. The final productivity of seedlings under in situ conditions was higher than under cultivation conditions in ex situ as was found under studying the growth and development of plant. The vegetation of the species P. pterocarpa under the conditions of Absheron begins from the second decade of March to the second decade of November; the duration of the growing season is several days. P. pterocarpa grows and develops normally in cultural conditions of Absheron on based of the analysis of the research.

How a Brain Sees: Neural Mechanisms

Multiple paradoxical visual percepts are explained using boundary completion and surface filling-in properties, including discounting the illuminant; brightness constancy, contrast, and assimilation; the Craik-O’Brien-Cornsweet Effect; and Glass patterns. Boundaries act as both generators and barriers to filling-in using specific cooperative and competitive interactions. Oriented local contrast detectors, like cortical simple cells, create uncertainties that are resolved using networks of simple, complex, and hypercomplex cells, leading to unexpected insights such as why Roman typeface letter fonts use serifs. Further uncertainties are resolved by interactions with bipole grouping cells. These simple-complex-hypercomplex-bipole networks form a double filter and grouping network that provides unified explanations of texture segregation, hyperacuity, and illusory contour strength. Discounting the illuminant suppresses illumination contaminants so that feature contours can hierarchically induce surface filling-in. These three hierarchical resolutions of uncertainty explain neon color spreading. Why groupings do not penetrate occluding objects is explained, as are percepts of DaVinci stereopsis, the Koffka-Benussi and Kanizsa-Minguzzi rings, and pictures of graffiti artists and Mooney faces. The property of analog coherence is achieved by laminar neocortical circuits. Variations of a shared canonical laminar circuit have explained data about vision, speech, and cognition. The FACADE theory of 3D vision and figure-ground separation explains much more data than a Bayesian model can. The same cortical process that assures consistency of boundary and surface percepts, despite their complementary laws, also explains how figure-ground separation is triggered. It is also explained how cortical areas V2 and V4 regulate seeing and recognition without forcing all occluders to look transparent.

On the growth and zeros of polynomials attached to arithmetic functions

In this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g and h, where g is normalized, of moderate growth, and $$0<h(n) \le h(n+1)$$ 0 < h ( n ) ≤ h ( n + 1 ) . We put $$P_0^{g,h}(x)=1$$ P 0 g , h ( x ) = 1 and $$\begin{aligned} P_n^{g,h}(x) := \frac{x}{h(n)} \sum _{k=1}^{n} g(k) \, P_{n-k}^{g,h}(x). \end{aligned}$$ P n g , h ( x ) : = x h ( n ) ∑ k = 1 n g ( k ) P n - k g , h ( x ) . As an application we obtain the best known result on the domain of the non-vanishing of the Fourier coefficients of powers of the Dedekind $$\eta $$ η -function. Here, g is the sum of divisors and h the identity function. Kostant’s result on the representation of simple complex Lie algebras and Han’s results on the Nekrasov–Okounkov hook length formula are extended. The polynomials are related to reciprocals of Eisenstein series, Klein’s j-invariant, and Chebyshev polynomials of the second kind.

Unraveling the Effects of Task Sequencing on the Syntactic Complexity, Accuracy, Lexical Complexity, and Fluency of L2 Written Production

Although several studies have explored the effects of task sequencing on second language (L2) production, there is no established set of criteria to sequence tasks for learners in L2 writing classrooms. This study examined the effect of simple ̶ complex task sequencing manipulated along both resource-directing (± number of elements) and resource-dispersing (± planning time) factors on L2 writing compared to individual task performance using Robinson’s (2010) SSARC model of task sequencing. Upper-intermediate L2 learners (N = 90) were randomly divided into two groups: (1) Participants who performed three writing tasks in a simple–complex sequence, and (2) participants who performed either the simple, less complex, or complex task. Findings revealed that simple-complex task sequencing led to increases in syntactic complexity, accuracy, lexical complexity, and fluency, as compared to individual task performance. Results are discussed in light of the SSARC model, and theoretical and pedagogical implications are provided.