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Analysis of the Impact of R&D on the Innovative Development of High-Tech Enterprises
No full textСтаття досліджує взаємозв’язок між інтенсивністю R&D та інноваційним розвитком високотехнологічних підприємств. У дослідженні визначено критичні пороги інвестування в R&D, які призводять до якісних змін в інноваційних результатах, і показано, що підприємства, які перевищують ці пороги, досягають вищих рівнів цифрової зрілості, технологічної адаптивності та розширення ринків. Емпіричний аналіз підтверджує, що інтенсивна діяльність у сфері R&D посилює здатність компаній генерувати нові продукти, прискорювати технологічні оновлення та впроваджувати сучасні цифрові інструментThe article examines the relationship between R&D intensity and the innovative development of high-tech enterprises, focusing on how investment in research and development shapes technological progress, knowledge creation, and long-term competitiveness. The study identifies the critical thresholds of R&D investment that lead to qualitative changes in innovation performance and demonstrates that enterprises surpassing these thresholds achieve higher levels of digital maturity, technological adaptability, and market expansion. The empirical analysis confirms that intensive R&D activities strengthen the ability of firms to generate new products, accelerate technological upgrades, and implement advanced digital tools such as machine learning, data analytics, and platform-based solutions.
The research emphasizes that the innovative development of high-tech enterprises depends on the interplay between financial investment, organisational capabilities, and knowledge absorption mechanisms. It is shown that companies with higher R&D intensity more actively integrate external knowledge, collaborate within innovation ecosystems, and demonstrate flexibility in transforming business models. In contrast, firms with insufficient R&D expenditure reveal restrained innovation dynamics and face structural limitations in technological advancement. The article also highlights the role of human capital, digital readiness, and strategic management practices in enhancing the effectiveness of R&D investments.
The results of the study contribute to understanding the systemic nature of innovative development in high-tech sectors and underline the necessity of long-term strategic approaches to managing R&D. The findings provide analytical support for improving corporate innovation policies and can serve as a foundation for designing effective models of technological development at the enterprise level. They also open new research perspectives related to modelling optimal R&D structures, evaluating the impact of digital transformation on innovation performance, and assessing the synergy between R&D activity and open innovation practices
Sustainable Development Marketing in the Pharmaceutical Market in Ukraine
No full textВ процесі дослідження було визначено основні напрями впровадження фармацевтичного маркетингу сталого розвитку. Встановлено, що в Україні зростає інтерес до екологічно сертифікованих товарів, етичного бізнесу та прозорої комунікації із зацікавленими сторонами, проте існують бар’єри: низька поінформованість споживачів, обмежені інвестиційні ресурси, недостатній розвиток інституційного середовища.
Відзначено, що характерними рисами маркетингу сталого розвитку є сприяння задоволенню базових людських потреб охорони здоров’я без яких не є можливим ефективний розвиток добробуту суспільства в цілому.Відзначено, що характерними рисами маркетингу сталого розвитку є сприяння задоволенню базових людських потреб охорони здоров’я без яких не є можливим ефективний розвиток добробуту суспільства в цілому.
Ключові слова: маркетинг сталого розвитку, фармацевтичне підприємство, екологічний маркетинг, соціальна відповідольність.
Kruhlikova V. V. Sustainable Development Marketing in the Pharmaceutical Market in Ukraine.
The article reveals the essence of sustainable development marketing and analyzes the features of its application in the Ukrainian pharmaceutical market in conditions of martial law and global challenges.
Modern business models are increasingly oriented towards the principles of sustainable development, which encompass economic efficiency, social responsibility, and environmental safety. This topic is especially important for Ukraine, given the need to increase the competitiveness of pharmaceutical companies and build consumer trust.
The research used an analysis of scientific sources, statistical data, and regulatory legal acts; a generalization of international experience and a comparative analysis of Ukrainian practices were conducted.
The main directions of implementation of pharmaceutical marketing of sustainable development are determined: ecological marketing (eco-marketing), social marketing, corporate social responsibility. It is revealed that in Ukraine there is a growing interest in ecologically certified products, ethical business and transparent communication with stakeholders, however, there are barriers: low consumer awareness, limited investment resources, insufficient development of the institutional environment.
Recommendations for Ukrainian pharmaceutical companies are proposed: integrating sustainability principles into marketing strategies, strengthening information campaigns to raise consumer environmental awareness, adapting international standards of sustainable development, and using digital tools for communications and transparency.
It is noted that the characteristic features of sustainable development marketing are the promotion of meeting basic human health needs, without which effective development of the well-being of society as a whole is not possible. The practice of implementing EU sustainable development marketing approaches in the field of providing the population with medicines in Ukraine is highlighted.
It has been found that under the influence of the dynamic system of sustainable development, new types and types of marketing are being formed, such as ecological marketing, green marketing, ethical marketing, socially responsible marketing, as well as innovative marketing
Ricci-Flat Manifolds, Parallel Spinors and the Rosenberg Index
No full textEvery closed connected Riemannian spin manifold of non-zero Â-genus or non-zero Hitchin invariant with non-negative scalar curvature admits a parallel spinor, in particular is Ricci-flat. In this note, we generalize this result to closed connected spin manifolds of non-vanishing Rosenberg index. This provides a criterion for the existence of a parallel spinor on a finite covering and yields that every closed connected Ricci-flat spin manifold of dimension ≥ 2 with non-vanishing Rosenberg index has special holonomy.I thank Bernd Ammann for coming up with this interesting question and for his hospitality during my short-term visit to Regensburg at the SFB 1085 Higher Invariants. I also thank my advisor, Rudolf Zeidler, for his continuous support, as well as Thorsten Hertl and the anonymous referees for their valuable comments. Funded by the European Union (ERC Starting Grant 101116001– COMSCAL)1 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)– Project-ID 427320536– SFB1442, as well as under Germany’s Excellence Strategy EXC 2044 390685587, Mathematics M¨unster: Dynamics–Geometry–Structure
Quadratic Varieties of Small Codimension
No full textLet ⊂ ℙⁿ⁺ᶜ be a nondegenerate smooth projective variety of dimension defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that is a complete intersection provided that ≥ 2 + 1. As the extreme case, they also classified with = 2. In this paper, we classify with = 2 − 1.The author would like to express his sincere gratitude to the anonymous referees for their meticulous reading of his manuscript. Their insightful comments and suggestions have significantly improved various parts of this work. The author knew the proof of Proposition 4.13 in [25] and would like to thank them for teaching how to prove it. Additionally, the author would like to thank Professor Wahei Hara for explaining the parts of the proof that were not understood and for providing a detailed explanation. The author is partially supported by JSPS KAKENHI Grant Numbers 21K03170 and 25K06940
Bilateral Two-Parameter Mock Theta Functions and Related Applications
No full textIn this paper, we investigate new relationships for bilateral series related to two-parameter mock theta functions, which lead to many identities concerning the bilateral mock theta functions. In addition, interesting relations between the classical mock theta functions and the bilateral series are also concluded.The author would like to express sincere gratitude to the anonymous referees, whose insightful comments and constructive suggestions have significantly enhanced the quality and clarity of this paper. The work is supported by the National Natural Science Foundation of China (Grant No. 12571354), the Shanghai Rising-Star Program (Grant No 23QA1407300), and the China Scholarship Council (CSC)
Sign Convention for ∞-Operations in Bott-Morse Case
No full textWe describe the sign and orientation issue appearing in the filtered ∞-formulae in Lagrangian Floer theory using the de Rham model in the Bott-Morse setting. After defining filtered ∞-operations in a Fukaya category, we verify the filtered ∞-formulae.The author is partially supported by JSPS Grant-in-Aid for Scientific Research 19H00636, 24H00182. He is also grateful for the National Center for Theoretical Sciences, Taiwan, where a part of this work was carried out
Hexagonal Circular 3-Webs with Reducible Polar Curves of Degree Three
No full textThe paper reports the progress with the classical problem, posed by Blaschke and Bol in 1938. We present new examples and new classifications of natural classes of hexagonal circular 3-webs. The main results are the classification of hexagonal circular 3-webs with reducible polar curves of degree 3 and the description of hexagonal circular 3-webs admitting a one-parameter Möbius symmetry.This research was supported by FAPESP grant # 2022/12813-5. The author thanks the anonymous referees for their valuable suggestions
Basis Partitions and Their Signature
No full textBasis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions, which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we use to explain certain parity results. We then study a special class of basis partitions, which we term complete. Finally, we discuss basis partitions and minimal basis partitions among partitions with non-repeating odd parts by representing them using 2-modular graphs.This work, which was begun in 2007, was completed only in Fall 2013 when I visited The Pennsylvania State University, at which time the results of Section 9 were established. I would like to thank George Andrews for arranging that visit and for urging me to write this manuscript, which was long overdue. But this paper remained unpublished since 2013. I thank Gaurav Bhatnagar, Frank Garvan, Christian Krattenthaler, and Michael Schlosser for including this paper in the special volume of SIGMA in honor of Steve Milne’s 75th birthday. Finally, I thank the referees for their careful reading of the manuscript and for their helpful suggestions. Research supported in part by NSA Grants MSPF-06G-150 and MSPF-08G-154
The Rogers-Ramanujan Identities and Cauchy's Identity
No full textThe Rogers-Ramanujan identities are investigated using the Cauchy identity for Schur functions.The author would like to thank the anonymous referees whose suggestions substantially improved this paper
On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
No full textThe lack of a positive-definite and conserved energy is a serious obstacle in the black hole stability problem. In this work, we will show that there exists a positive-definite and conserved Hamiltonian energy for axially symmetric linear perturbations of the exterior of Kerr black hole spacetimes. In the first part, based on the Hamiltonian dimensional reduction of 3 + 1 axially symmetric, Ricci-flat Lorentzian spacetimes to a 2 + 1 Einstein-wave map system with the negatively curved hyperbolic 2-plane target, we construct a positive-definite, spacetime gauge-invariant energy functional for linear axially symmetric perturbations in the exterior of Kerr black holes, in a manner that is also gauge-independent on the target manifold. In the construction of the positive-definite energy, various dynamical terms at the boundary of the orbit space occur critically. In the second part, after setting up the initial value problem in harmonic coordinates, we prove that the positive energy for the axially symmetric linear perturbative theory of Kerr black holes is strictly conserved in time by establishing that all the boundary terms dynamically vanish for all times. This result implies a form of dynamical linear stability of the exterior of Kerr black hole spacetimes.I acknowledge the gracious hospitality of Institut des Hautes Études Scientifiques (IHES) at Bures-sur-Yvette in Fall 2016. In a previous work [61], the coauthor Vincent Moncrief had fittingly paid tribute to A. Taub, J. Marsden, and S. Dain for their influence on him and for making fundamental contributions in this direction. I take this opportunity to pay tribute to his own outstanding contributions to general relativity and Hamiltonian methods. On an individual note, for his mentorship, encouragement, and enjoyable interactions, I am indebted to him. This project has spanned several years, and my gratitude is also due to all the colleagues who have continually supported me and to the institutions that hosted me. Special thanks are due to my host Hermann Nicolai at the Albert Einstein Institute at Golm (DFG grant no. GU 1513/2-1), where significant aspects of this work were completed. A part of this work was done while I was a Postdoc at the Department of Mathematics, Yale University, where I benefited from conducive working conditions. Finally, I thank the referees for the feedback. This work was supported by the German Research Foundation (Grant numbers GU 1513/1-1 and GU 1513/2-1)