Search Results (23)

This paper explores the geometric interplay between the Levi–Civita connection and the quarter-symmetric metric connection on doubly warped product manifolds. We analyze the behavior of Ricci solitons on such manifolds, focusing on the influence of conformal and Killing vector fields within the framework of quarter-symmetric metric connections (QSMCs). Furthermore, we examine conditions under which the manifold exhibits Einstein properties, presenting new insights into Einstein-like structures in the context of doubly warped product manifolds endowed with a quarter-symmetric metric connection. Full article

In this paper, we extend the study of contravariant Einstein-like metrics to Poisson doubly warped product manifolds (PDWPMs). We derive the necessary and sufficient conditions under which the base and fiber manifolds of a PDWPM inherit Einstein-like structures from the total space. As applications, we construct Einstein-like Poisson doubly warped product structures belonging to classes $\mathcal{A}$, $\mathcal{B}$, and $\mathcal{P}$ in various spacetime models, including generalizations of Reissner–Nordström, standard static, and Robertson–Walker spacetimes. Full article

In this paper, we introduce the concept of contravariant Einstein-like Poisson manifolds of classes $\mathcal{A}$, $\mathcal{B}$, and $\mathcal{P}$. We then prove that the fiber space of a Poisson warped product manifold inherits the contravariant Einstein-like classes of the total space, while the base space inherits these classes under certain conditions related to the warping function. We also explore applications of contravariant Einstein-like Poisson structures in various spacetime models, including generalized Robertson–Walker, Reissner–Nordström, and standard static spacetimes. Full article

This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function $\psi$ and the vector field $\zeta$ dual to $d\psi$ does not change its causal character, then P is homothetic, or $\zeta$ is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the characterization of Killing and parallel vector fields using the Ricci curvature and the Hessian of the function given by the inner product of the vector field. Full article

This work investigates the effects on the factor manifolds of a singly warped product manifold resulting from the presence of a quasi-conformally flat, quasi-conformally symmetric, or divergence-free quasi-conformal curvature tensor. Quasi-conformally flat warped product manifolds exhibit three distinct scenarios: in one scenario, the base manifold has a constant curvature, while in the other two scenarios, it is quasi-Einstein. Alternatively, the fiber manifold has a constant curvature in two scenarios and is Einstein in one scenario. Quasi-conformally symmetric warped product manifolds present three distinct cases: in the first scenario, the base manifold is Ricci-symmetric and the fiber is Einstein; in the second case, the base manifold is Cartan-symmetric and the fiber has constant curvature; and in the last case, the fiber is Cartan-symmetric, and the Ricci tensor of the base manifold is of Codazzi type. Finally, conditions are provided for singly warped product manifolds that admit a divergence-free quasi-conformal curvature tensor to ensure that the Riemann curvature tensors of the factor manifolds are harmonic. Full article

We highlight some properties of a class of distinguished vector fields associated to a $(1,1)$-tensor field and to an affine connection on a Riemannian manifold, with a special view towards the Ricci vector fields, and we characterize them with respect to statistical, almost Kähler, and locally product structures. In particular, we provide conditions for these vector fields to be closed, Killing, parallel, or semi-torse forming. In the gradient case, we give a characterization of the Euclidean sphere. Among these vector fields, the Ricci and torse-forming-like vector fields are particular cases. Full article

Over recent decades, the sustainable use of non-timber forest products (NTFPs) has offered the promise of reconciling the dilemma between forest conservation and economic development, generating income for local populations. Accordingly, since the 1990s, manifold initiatives, often supported by international donors, have been investing in developing such NTFP value chains. Specifically in the Brazilian context, initiatives have proliferated as a response to the challenges of the largest remaining tropical forest ecosystem—the Amazon region and its inhabitants. Have they worked? What do we know about their impact? To provide for the first time an adequate basis for a more systematic analysis of the impact of NTFP initiatives in the Brazilian Amazon, this article presents a mapping of current and past initiatives supporting NTFP extractivism. The mapping drew on databases of funding organizations and interviews with key informants. The analysis revealed a large number of initiatives (nearly 200) strongly clustered in some areas, like around Belém, along major roads such as the BR 364, and along the Juruá rivers, concentrated on a few products with relatively high commercial value, mostly implemented by civil society organizations and targeting traditional peoples and communities. As interventions for NTFP development, the initiatives offered capacity building, financial support, and facilitate market access. With regard to the latter, the initiatives varied considerably. The vast majority promoted products, while a much smaller number engaged in company partnerships or government procurement. Despite the large number of initiatives, there is insufficient knowledge to gauge the impacts of different strategies of local resources and their users. A clear understanding of the effects of NTFP-based development initiatives and how impacts are generated is essential to seize the potential of the bioeconomy for achieving sustainable development for the Brazilian Amazon. Full article

Traditional natural products have been the focus of research to explore their medicinal properties. One such medicinally important plant is the white mulberry, Morus alba, widely distributed in the Asian subcontinent. It is one of the most cultivated species of mulberry tree and has attracted more focus from researchers because of its abundance in phytochemicals as well as multipurpose uses. The leaves, fruits and other parts of the white mulberry plant act as a source of valuable bioactive compounds like flavonoids, phenolic acids, terpenoids and alkaloids. These secondary metabolites have manifold healthy uses as they possess antioxidant, anti-inflammatory, antidiabetic, neutrotrophic, and anticancer properties. Despite the increasing scientific interest in this plant, there are very few reviews that highlight the phytochemistry and biological potential of white mulberry for biomedical research. To this end, this review elaborates the phytochemistry, biosynthetic pathways and pharmacological activities of the glycoside flavonoids of Morus alba. A comprehensive analysis of the available literature indicates that Morus alba could emerge as a promising natural agent to combat diverse conditions including diabetes, cancer, inflammation and infectious diseases. To achieve such important objectives, it is crucial to elucidate the biosynthesis and regulation mechanisms of the bioactive compounds in white mulberry as well as the multifaceted pharmacological effects attributed to this plant resource. The present review paper is intended to present a summary of existing scientific data and a guide for further research in the phytochemistry and pharmacology of white mulberry. Further, a biosynthetic pathway analysis of the glycoside flavonoid in mulberry is also given. Lastly, we discuss the pros and cons of the current research to ensure the prudent and effective therapeutic value of mulberry for promoting human and animal health. Full article

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d>2$. This solution family is equivalent to a fractal curve in complex space ${\mathbb{C}}^d$ with random steps parametrized by N Ising variables ${\sigma }_i=\pm 1$, in addition to a rational number $\frac{p}{q}$ and an integer winding number r, related by $\sum {\sigma }_i=qr$. This equivalence provides a dual theory describing a strong turbulent phase of the Navier-Stokes flow in ${\mathbb{R}}_d$ space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a quantum statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size $N\to \infty$ or its chemical potential $\mu \to 0$. The system with fixed N has different asymptotics at odd and even $N\to \infty$, but the limit $\mu \to 0$ is well defined. The energy dissipation rate is analytically calculated as a function of $\mu$ using methods of number theory. It grows as $\nu /{\mu }^2$ in the continuum limit $\mu \to 0$, leading to anomalous dissipation at $\mu \propto \sqrt{\nu }\to 0$. The same method is used to compute all the local vorticity distribution, which has no continuum limit but is renormalizable in the sense that infinities can be absorbed into the redefinition of the parameters. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as $t^{-\lambda }$, with a continuous spectrum of indexes $\lambda$ in the local limit $\mu \to 0$. The spectrum is determined by a resolvent, which is represented as an infinite product of $3\otimes 3$ matrices depending of the element of the Euler ensemble. Full article

MK-7, like other biological molecules, exists in geometric isomers, including cis and trans forms, among which only the all-trans form holds biological significance. Recent studies have drawn attention to the manifold health advantages linked to the consumption of menaquinone-7 (MK-7). Nonetheless, the scarcity of MK-7 in natural dietary sources underscores the necessity for creating dietary supplements to fulfil daily intake requisites. Obtaining MK-7 involves employing production techniques encompassing solid- or liquid-state fermentation. However, upscaling this process becomes intricate in static fermentation due to challenges in heat and mass transfer. Consequently, the bulk of research on MK-7 synthesis via fermentation has concentrated on the liquid-state approach. To this end, endeavors have been dedicated to refining MK-7 biosynthesis by exploring diverse fermentation media compositions, optimal growth conditions, and even integrating nanobiotechnology methodologies. Innovative biofilm reactors, capable of facilitating biofilm attachment on plastic composite substrates, have also emerged as a promising solution, particularly when utilizing B. subtilis cells. The biofilm reactors exhibit robust extracellular MK-7 secretion, effectively surmounting the hurdles posed by high aeration and agitation rates. However, a demonstration of the scalability of this technology to pilot and industrial scales is still pending. This work offers an outline of the latest advancements in MK-7 research, with a specific focus on the strides made in MK-7 production through fermentation techniques. The paramount importance of the all-trans form of MK-7 is underscored, accentuating its role in enhancing human well-being. The ramifications of this work hold the potential to pave the way for novel strategies to amplify MK-7 production and formulate products with an optimized MK-7 profile, thereby promising avenues for enhancing human health and nutrition. Full article

We consider a 10-dimensional gravitational model with an SO(6)Yang–Mills field, Gauss–Bonnet term, and $\Lambda$ term. We study so-called cosmological-type solutions defined on the product manifold $M=\mathbb{R}\times {\mathbb{R}}^3\times K$, where K is $6d$ a Calabi–Yau manifold. By setting the gauge field 1-form to coincide with the 1-form spin connection on K, we obtain exact cosmological solutions with exponential dependence of scale factors (upon t-variable) governed by two non-coinciding Hubble-like parameters: $H>0$ and h obeying $H+2h\ne 0$. We also present static analogs of these cosmological solutions (for $H\ne 0$, $h\ne H$, and $H+2h\ne 0$). The islands of stability for both classes of solutions are outlined. Full article

The main purpose of this paper is to investigate lightlike hypersurfaces of almost productlike semi-Riemannian manifolds. For this purpose, screen-semi-invariant, screen-invariant, radical-anti-invariant, and radical-invariant lightlike hypersurfaces of almost productlike semi-Riemannian manifolds are introduced and some examples of these classifications are presented. Furthermore, various characterizations dealing screen semi-invariant lightlike hypersurfaces are obtained. Full article

Integral formulas are powerful tools used to obtain global results in geometry and analysis. The integral formulas for almost multi-product manifolds, foliations and multiply twisted products of Riemannian, metric-affine and sub-Riemannian manifolds, to which this review paper is devoted, are useful for studying such problems as (i) the existence and characterization of foliations with a given geometric property, such as being totally geodesic, minimal or totally umbilical; (ii) prescribing the generalized mean curvatures of the leaves of a foliation; (iii) minimizing volume-like functionals defined for tensors on foliated manifolds. We start from the series of integral formulas for codimension one foliations of Riemannian and metric-affine manifolds, and then we consider integral formulas for regular and singular foliations of arbitrary codimension. In the second part of the article, we represent integral formulas with the mixed scalar curvature of an almost multi-product structure on Riemannian and metric-affine manifolds, give applications to hypersurfaces of space forms with $k=2,3$ distinct principal curvatures of constant multiplicities and then discuss integral formulas for foliations or distributions on sub-Riemannian manifolds. Full article

Reservoirs are a common way to store and retain water serving for a multitude of purposes like storage of drinking and irrigation water, recreation, flood protection, navigation, and hydropower production, and have been built since centuries. Today, few reservoirs serve only one purpose, which requires management of present demands and interests. Since each reservoir project will cause negative impacts alongside desired advantages both on a local, regional and global scale, it is even more urgent to develop a common management framework in an attempt to mitigate negative impacts, incorporate different demands and make them visible within the discourse in order to avoid conflicts from early on. The scientific publications on reservoirs are manifold, yet a comprehensive and integrative holistic tool about management of this infrastructure is not available. Therefore, a comprehensive and integrated conceptual tool was developed and proposed by the authors of this paper that can contribute to the sustainable management of existing reservoirs. The tool presented herein is based on the results from the interdisciplinary CHARM (CHAllenges of Reservoir Management) project as well as the condensed outcome of relevant literature to aid and enhance knowledge of reservoir management. The incorporated results are based on field, laboratory and empirical social research. The project CHARM focused on five different aspects related to existing reservoirs in southern Germany (Schwarzenbachtalsperre, Franconian Lake District), namely: sedimentation of reservoirs, biostabilisation of fine sediments, toxic cyanobacteria(l) (blooms), greenhouse gas emissions from reservoirs and social contestation, respectively consent. These five research foci contributed to the topics and setup of a conceptual tool, put together by the research consortium via delphi questioning, which can be found alongside this publication to provide insights for experts and laymen. Conceptualising and analysing the management in combination with quantitative and qualitative data in one descriptive tool presents a novelty for the case studies and area of research. The distribution within the scientific community and interested public will possibly make a positive contribution to the goal of sustainable water resources management in the future. Full article