On the geometry of the domain of the solution of nonlinear Cauchy problem

We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study also a variant of the inverse problem of the Cauchy problem and prove that the considered inverse problem has a solution under certain regularity condition. We illustrate the Cauchy and the inverse problems in some interesting examples such that the families of the characteristic curves have either common envelopes or singular points. In these cases the definition domain of the solution of the differential equation contains a gap.Comment: accepted for publication in the book Lie groups, differential equations and geometry in Springer Unip

A Study of U.S. Education Outcomes for Female Students from the Republic of Georgia

This qualitative study sought to understand how living and studying in the United States affected the personalities, beliefs, attitudes, and careers of a group of female students from the Republic of Georgia. The researcher traveled to Tbilisi, Georgia’s capital, to interview twenty alumni of U.S. study programs (on undergraduate and graduate study levels) individually. Jack Mezirow’s Transformational Learning Theory and David Kolb’s Experiential Learning Theory provide the theoretical framework for the study. The findings revealed that living and studying in the U.S. matured the participants personally as they got to experience the challenges that accompany living independently in an unfamiliar environment, which in turn boosted their sense of self and efficacy. Also, the study participants commonly expressed that the U.S. experience taught them to appreciate difference and diversity firsthand, and enabled them to recognize — and then dismiss — stereotypes they had held about people they had never met. They also described the experience of personal interactions with people of different nationalities as eye-opening and invaluable. Living away from their home country naturally brought about changes in the participants’ frames of reference by forcing them to critically reflect on their prior knowledge and consciously transform their attitudes and actions. Furthermore, the participants greatly attributed their successful careers to the knowledge and skills gained while studying in the U.S

European Perspective of Georgia: A Comparative Analysis of Compliance with the Copenhagen Criteria in the Case of Georgia and Albania

The increasing importance of the 29-years-old relations between Georgia and the EU, the relevance of the issue and the delayedmembership have become the key reasons for the research topic.It should be noted that joining the EU is not an easy process and contains a number of bureaucratic elements. Therefore, the paperanalyzes Georgia’s economic and political willingness to comply with the Copenhagen criteria for future integration into the EU. It also compares thepace of development and the situation in Georgia and in Albania, which has the status of “official candidate” of the EU. It is interesting to see whatchanges and reforms (different from Georgia) are being implemented by Albania, which brings it even closer to the EU. The main research questionalso serves to determine Georgia’s European perspective based on an objective analysis of 2018-2021 years data and processes and to explain themain reasons that hinder Georgia’s integration (unlike Albania) with the EU

Impressão lenticular: autostereoscopic prints for advertising

O objetivo deste projeto é demonstrar o resultado da interação da modelagem 3D com a tecnologia de impressão lenticular, e encontrar um caminho para sua aplicação prática no universo da publicidade. O projeto explora os exemplos históricos de arte imersiva e sua utilização diversa na prática, aborda os fatores que influenciam a percepção humana de profundidade e também analisa vários métodos usados para produzir impressões estereoscópicas, a própria tecnologia lenticular e técnicas de publicidade. Através do método de design surge uma solução criativa e o trabalho final é realizado na forma física de um poster de impressão lenticular, que é uma proposta da sua utilização como estratégia de comunicação.The objective of this project is to demonstrate the result of mixing 3D modeling with lenticular printing technology, and find a way for its practical application in the world of advertising. The project explores historical examples of immersive art and its diverse use in practice. It addresses the factors that influence human depth perception and also explores various methods used to produce stereoscopic prints, lenticular technology itself, and advertising techniques. Through the design method, a creative solution emerges and the final work is carried out in the physical form of a lenticular poster, which is a proposition of its use as a communication strategy

A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-space

We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).Comment: 20 pages, 13 figure

Prediction of delivery after 40 weeks by antepartum ultrasound in singleton nulliparous women: a prospective cohort study

Background: Induction of labor at 39 weeks of gestation is associated with better maternal and perinatal outcomes than expectant management. However, a policy of induction of labor implies the identification of women who will deliver after 40 weeks, who are at higher risk of adverse outcome. Objective: This study primarily aimed to elucidate the role of antepartum ultrasound in predicting the onset of spontaneous labor in a cohort of low-risk singleton pregnancies, and secondarily to compare its diagnostic performance with that of other ultrasonographic and clinical parameters. Study design: This was a prospective study including singleton nulliparous women undergoing a dedicated ultrasound assessment at 36 to 38 weeks of gestation. The primary outcome was delivery ≥40 weeks of gestation. The ultrasound parameters explored were cervical length, posterior cervical angle, angle of progression, and head-perineum distance. Multivariate logistic regression, Kaplan-Meier, and area under the curve analyses were used to test the strength of association and diagnostic performance of variables considered in predicting delivery ≥40 weeks. Results: A total of 457 women were included, and 49.2% delivered ≥40 weeks. Cervical length was longer (30 vs 19 mm; P≤.0001) and posterior cervical angle wider (105° vs 98°, P≤.0001) in women delivering ≥40 weeks than those delivering 24 mm at 36 to 37 weeks of gestation shows the optimal combination of sensitivity and specificity in predicting delivery ≥40 weeks. The findings from this study can help in identifying those women for whom elective induction of labor at 39 weeks of gestation would be beneficial in reducing the risk of adverse pregnancy outcome

Screening of Georgian grapevine germplasm for susceptibility to downy mildew (Plasmopara viticola)

Downy mildew, caused by the obligate biotrophic parasite Plasmopara viticola, is one of the most serious grapevine diseases with worldwide distribution. Resistant grapevines can be used to reduce damages caused by the pathogen, recently different levels of susceptibility to P. viticola were detected in some Georgian autochthonous varieties.  The aim of the present work was to classify additional Georgian autochthonous varieties into different groups according to their susceptibility to the downy mildew agent in the framework of COST Action FA1003 "East-West Collaboration for Grapevine Diversity Exploration and Mobilization of Adaptive Traits for Breeding". The leaf disk assay defined by the OIV 452-1 protocol was used for screening 61 native varieties of Georgia. Screened varieties showed different degree of resistance: very high – 7 accessions, high - 13, medium - 15, low – 23, and very low - 3 accessions. The results suggest that further resistant genotypes are likely to be found within more than 500 Georgian grapevine cultivars

Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation

The present work devoted to the finding explicit solution of a boundary problem with the Dirichlet-Neumann condition for elliptic equation with singular coefficients in a quarter of ball. For this aim the method of Green's function have been used. Since, found Green's function contains a hypergeometric function of Appell, we had to deal with decomposition formulas, formulas of differentiation and some adjacent relations for this hypergeometric function in order to get explicit solution of the formulated problem.Comment: 12 pages, 1 figur

Bitsadze-Samarskii type problem for the integro-differential diffusion-wave equation on the Heisenberg group

This paper deals with the fractional generalization of the integro-differential diffusion-wave equation for the Heisenberg sub-Laplacian, with homogeneous Bitsadze-Samarskii type time-nonlocal conditions. For the considered problem, we show the existence, uniqueness and the explicit representation formulae for the solution