Automorphisms of Kronrod-Reeb graphs of Morse functions on 2-sphere

Let $M$ be a compact two-dimensional manifold and, $f \in C^{\infty}(M,\mathbb{R})$ be a Morse function, and $\Gamma_f$ be its Kronrod-Reeb graph. Denote by $\mathcal{O}_{f}=\{f \circ h \mid h \in \mathcal{D}\}$ the orbit of $f$ with respect to the natural right action of the group of diffeomorphisms $\mathcal{D}$ on $C^{\infty}(M,\mathbb{R})$, and by $\mathcal{S}(f)=\{h\in\mathcal{D} \mid f \circ h = f\}$ the corresponding stabilizer of this function. It is easy to show that each $h\in\mathcal{S}(f)$ induces a homeomorphism of $\Gamma_f$. Let also $\mathcal{D}_{\mathrm{id}}(M)$ be the identity path component of $\mathcal{D}(M)$, $\mathcal{S}'(f)= \mathcal{S}(f) \cap \mathcal{D}_{\mathrm{id}}(M)$ be group of diffeomorphisms of $M$ preserving $f$ and isotopic to identity map, and $G_f$ be the group of homeomorphisms of the graph $\Gamma_f$ induced by diffeomorphisms belonging to $\mathcal{S}'(f)$. This group is one of the key ingredients for calculating the homotopy type of the orbit $\mathcal{O}_{f}$. Recently the authors described the structure of groups $G_f$ for Morse functions on all orientable surfaces distinct from $2$-torus $T^2$ and $2$-sphere $S^2$. The present paper is devoted to the case $M=S^{2}$. In this situation $\Gamma_f$ is always a tree, and therefore all elements of the group $G_f$ have a common fixed subtree $\mathrm{Fix}(G_f)$, which may even consist of a unique vertex. Our main result calculates the groups $G_f$ for all Morse functions $f:S^{2}\to\mathbb{R}$ whose fixed subtree $\mathrm{Fix}(G_f)$ consists of more than one point.Comment: 5 page

Integration of Clothing and Footwear Manufacturers into Global Value Chains: International Practices

The article deals with studying the transformations in consumer-driven value chains, using the example of clothing and footwear manufacturers. It is noted that the production of ready-made clothes in the value chain includes several stages: pre-production, or production of fabrics and components (Original Equipment Manufacturer, or OEM); fabrication of clothes (Cut, Make and Trim, or CMT); design (Original Design Manufacturer, or ODM); supply, marketing and sales (Original Brand Manufacturer, or OBM). Each stage differs in terms of technological level and added value. The practices of Turkey, Pakistan, and Albania concerning the integration of textile enterprises, manufacturers of ready-made clothes and footwear into global value chains are analyzed. It is concluded that the entry into global value chains begins at the lowest stage (drafting, assemblage, fabrication). The process of integration into this chain is possible if the company is competitive in terms of delivery time, flexibility (the ability to produce small batches, quickly respond to market changes), and productivity. The need for state support (industry development strategy, formation of clusters and industrial parks, attraction of foreign direct investment) and participation in various international trade transactions is noted. Participating in the CMT stage in the short term is positive as regards offering jobs, and in the long term it can encourage enterprises to develop and sell final products in the domestic market. Market entry barriers are increasing with each next stage in the value chain. Moving up the stages in the value chain requires investing in technologies and human resources, establishing cooperation with educational and research institutions, building ties with enterprises of the industry they are engaged in and related ones

TOUCHLESS: Demonstrations of Contactless Haptics for Affective Touch

A set of demonstrators of contactless haptic principles is described in this work. The technologies are based on electrostatic piloerection, chemical compounds and ultrasound. Additionally, applications related to affective touch are presented, ranging from storytelling to biosignal transfer, accompanied with a simple application to edit dynamic tactile patterns in an easy way. The demonstrators are the result of the Touchless project, which is a H2020 european collaborative project that integrates 3 universities and 3 companies. These demostrators are contactless haptic experiences and thus facilitate the come-and-interact paradigm, where users can approach the demo booth and directly experience the applications without having to wear devices, making the experience fast and hygienic

TOUCHLESS: demonstrations of contactless haptics for affective touch

A set of demonstrators of contactless haptic principles is described in this work. The technologies are based on electrostatic piloerection, chemical compounds and ultrasound. Additionally, applications related to affective touch are presented, ranging from storytelling to biosignal transfer, accompanied with a simple application to edit dynamic tactile patterns in an easy way. The demonstrators are the result of the Touchless project, which is a H2020 european collaborative project that integrates 3 universities and 3 companies. These demostrators are contactless haptic experiences and thus facilitate the come-and-interact paradigm, where users can approach the demo booth and directly experience the applications without having to wear devices, making the experience fast and hygienic.Funded by EU Horizon 2020 research and innovation programme grant agreement No 101017746 TOUCHLESS

Молодой потребитель на рынке украинской э-коммерции

Main trends in the development of e-commerce in Ukraine based on the results of the year 2015 were reviewed. Despite the crisis and annual decrease by 20%, the Ukrainian e-commerce has predispositions for growth. It is mainly caused by the factors of legislative (passing of the national law concerning e-commerce), economic (devaluation of Ukrainian hryvnia motivating the consumers to purchase goods on-line as an alternative to traditional retail, and give their preference to national producers), and technologic character (spread of the Internet, introduction of the third generation mobile telephony). Moreover, the focus upon the improvement of the Internet service, spread of the network of logistics companies, and development of on-line payment systems – these are the tasks for the Ukrainian e-commerce in the nearest future. Attention was drawn in the article to the target e-commerce audience which is mainly represented by youth. The presented results of sociological research (conducted by the authors in 2015 among young people of 18-35 years in the Lviv region) show that the consumer preferences vary significantly depending on age groups, as well as on the location of their residence (urban or rural areas).W artykule dokonano przeglądu rynku e-commerce (e-handlu) na Ukrainie na bazie wyników z 2015 roku. Mimo kryzysu i rocznego spadku w przedziale od 20%, ukraiński e-handel ma wszelkie przesłanki do własnego wzrostu. Zależy to od wielu czynników: prawnych (przyjęcia ustawy o handlu elektronicznym), ekonomicznych (dewaluacja hrywny motywuje konsumentow do zakupu towarów w segmencie on-line jako alternatywa tradycyjnego handlu detalicznego, orientacja na krajowego producenta) oraz technologicznych (wzrost wskaźników poszerzenia sieci Internetu, rozwój szybkiego mobilnego Internetu trzeciej generacji). Ponadto, ważnym zadaniem dla ukraińskiego handlu elektronicznego są koncentracja na poprawie jakości usług on-line, rozbudowa sieci firm logistycznych oraz rozwój systemów płatności. Przedstawione wyniki badania socjologicznego (2015 rok) wśród młodych konsumentów w wieku 18-35 lat obwodu lwowskiego dają podstawy do stwierdzenia o znaczących różnicach w preferencjach e-konsumentów ze względu na różnice wiekowe oraz ze względu na miejsce zamieszkania (miasto, wieś).В статье рассмотрены основные тенденции развития электронной коммерции в Украине по итогам 2015 года. Несмотря на кризисные явления и годовой спад в пределах 20%, украинская e-commerce имеет все предпосылки для роста. Во многом это предопределяется факторами правового (принятие национального закона об электронной коммерции), экономического (девальвация гривны мотивирует потребителя к покупке товаров в сегменте on-line как альтернатива традиционному ритейлу, ориентация на национального производителя) и технологического (рост проникновения интернета, внедрение мобильной связи третьего поколения) характера. Кроме того, ориентация на улучшение интернет-сервиса, расширение сети логистических компаний и развитие платежных систем – это задачи для украинской э- ком- мерции на ближайшую перспективу. Обращено внимание на целевую аудиторию e-commerce, которую в основном представляют молодые люди. Представленные результаты социологического исследования, проведенного авторами в 2015 году среди молодых людей в возврасте 18-35 лет во Львовском регионе, дают основания утверждать, что имеются существенные различия в их потребительских предпочтениях как по возрастным группам, так и по месту жительства (город, село)