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Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds.

The paper opted the tensor calculus on manifolds to find the solution of the CPE.

In this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with \lambda=\tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting.

The paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds.

This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.

The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example.

We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S²ⁿ⁺¹ and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to Eⁿ⁺¹ × Sⁿ(4) in higher dimension.

All results are novel and generalizations of previously obtained results.

The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.

This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.

The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.

The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.

The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly  symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold.

The authors have used the tensorial approach to achieve the goal.

A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.

The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.

This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modeling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature.

The model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics).

The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation.

The model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts.

Evidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies.

Approaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society.

Application of the quantum-like model of Fröhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and Internet-based sources.

In this paper some characterizations for the existence of warped product pointwise semi-slant submanifolds of cosymplectic space forms are obtained. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, the equality case is also discussed. By the application of derived inequality, we compute an expression for Dirichlet energy of the involved warping function. Finally, we also proved some classifications for these warped product submanifolds in terms of Ricci solitons and Ricci curvature. A non-trivial example of these warped product submanifolds is provided.

Structural mentoring barriers are policies, practices and cultural norms that collectively disadvantage marginalized groups and perpetuate disparities in mentoring. This study aims to better understand structural mentoring barriers at the postdoctoral training stage, which has a direct impact on faculty diversity and national efforts to retain underrepresented groups in research careers.

A diverse sample of postdoctoral scholars (“postdocs”) from across the USA were asked to participate in focus groups to discuss their training experiences. The authors conducted five 90-min focus groups with 32 biomedical postdocs, including 20 (63%) women and 15 (47%) individuals from underrepresented racial/ethnic groups (URG).

A social-ecological framework was used to categorize both the upstream and downstream manifestations of structural mentoring barriers, as well as mentoring barriers, overall. Notable structural barriers included: academic politics and scientific hierarchy; inequalities resulting from mentor prestige; the (over) reliance on one mentor; the lack of formal training for academic and non-academic careers; and the lack of institutional diversity and institutional mentor training. To overcome these barriers, postdocs strongly encouraged developing a network or team of mentors and recommended institutional interventions that create more comprehensive professional development, mentorship and belonging.

For postdoctoral scientists, structural mentoring barriers can permeate down to institutional, interpersonal and individual levels, impeding a successful transition to an independent research career. This work provides strong evidence for promoting mentorship networks and cultivating a “mentoring milieu” that fosters a supportive community and a strong culture of mentorship at all levels.

The purpose of the paper is to showcase the significant achievements of Egypt's scientists in the 20th century across various fields of study such as medicine, physics, chemistry, biology, math, geology, astronomy and engineering. The paper highlights the struggles and successes of these scientists, as well as the cultural, social and political factors that influenced their lives and work. The aim is to inspire young people to pursue careers in science and make their own contributions to society by presenting these scientists as role models for hard work and dedication. Ultimately, the paper seeks to promote the importance of science and its impact on society.

The purpose of this review is to present the scientific biographies of Egypt's most distinguished scientists, primarily in the field of Natural Sciences, in a balanced and comprehensive manner. The work is objective, honest and abstract, avoiding any bias or exaggeration. The author provides a clear and concise methodology, including a brief introduction to the scientist and their field of study, an explanation of their major contributions, the impact of their work on society, any challenges or obstacles faced during their career and their lasting legacy. The aim is to showcase the important achievements of these scientists, their impact on their respective fields and to inspire future generations to pursue scientific careers.

The group of outstanding scientists in 20th century Egypt were shaped by various factors, including familial upbringing, education, society, political and cultural atmosphere and state support for scientific research. These scientists made significant contributions to various academic disciplines, including medicine, physics, chemistry, biology, mathematics and engineering. Their impact on their communities and cultures has received international acclaim, making them role models for future generations of scientists and researchers. The history of these scientists highlights the importance of educational investments and supporting scientific research to foster innovation and social progress. The encyclopedia serves as a useful tool for students, instructors and education professionals, preserving Egypt's scientific heritage and honouring the scientists' outstanding accomplishments.

The encyclopedia preserves Egypt's scientific heritage, which has been overlooked for political or other reasons. It is a useful tool for a variety of readers, including students, instructors and education professionals, and it offers insights into universally relevant scientific success factors as well as scientific research methodologies. The encyclopedia honours the outstanding scientific accomplishments of Egyptian researchers and their contributions to the world's scientific community.

The practical implications of this paper are several. First, it highlights the importance of education, family upbringing and societal support for scientific research in fostering innovation and social progress. Second, it underscores the need for continued funding and support for scientific research to maintain and build upon the accomplishments of past generations of scientists. Third, it encourages young people to pursue scientific careers and make their own contributions to society. Fourth, it preserves the scientific heritage of Egypt and honors the contributions of its outstanding scientists. Finally, it serves as a useful tool for students, instructors and education professionals seeking to understand the factors underlying scientific success and research methodologies.

The social implications of the paper include promoting national pride and cultural identity, raising awareness of the importance of education and scientific research in driving social progress, inspiring future generations of scientists and researchers, reducing socioeconomic disparities and emphasizing the role of society, politics and culture in shaping scientific researchers' personalities and interests.

The paper's originality/value lies in its comprehensive documentation of the scientific biographies of Egypt's most prominent scientists in the 20th century, providing unique insights into the factors that contributed to their development and their impact across various academic disciplines. It preserves Egypt's scientific heritage and inspires future generations of scientists and researchers through the promotion of educational investments and scientific research. The encyclopedia serves as a useful tool for education professionals seeking to understand scientific success factors and research methodologies, emphasizing the importance of supportive and inclusive environments for scientific development.

This study aims to explore possible ways to promote uptake and integration of climate-smart agriculture (CSA)-Technologies, Innovations and Management Practices (TIMPS) into policy and practice in Nigeria through the development of actionable roadmaps to facilitate the process.

Two hundred and fifty-two stakeholders for the policy discourse and survey were purposively drawn from both government and private agencies, NGOs and community-based associations from the six geo-political zones of the country. Data collection was done using a mixed method comprising questionnaire administration, in-depth interviews and panel discussion. Data collected was summarised using descriptive statistics.

The major findings were lack of existing policies on CSA, lack of farmers’ awareness of CSA-TIMPs, neglect of extension programmes that can help to enlighten farmers on the importance of CSA and insufficient extension personnel to cater for farmers’ needs. Challenges to CSA-TIMPs uptake in Nigeria were: insufficient funding and support by government in programme planning and implementation, policy inconsistencies and poor farmers’ attitude and resistance to change.

This research will facilitate CSA uptake and integration through the provision of data for informed decision and action by the responsible agencies.

Suggested actionable roadmaps across the zones were robust awareness campaign and advocacy on uptake of CSA-TIMPs through e-extension, community TV/radio in local dialects; revitalisation of policy programmes such as monthly meetings should be reintroduced and creation of CSA Departments/Stations in each state; increased budget allocation to a minimum of 10% for agriculture, revitalisation of Researchers-Extension Agents-Farmers Linkage, employment of qualified extension agents and retraining of extension agents.