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In this short note, we deal with gradient k-Yamabe solitons whose Ricci curvature is non-positive in the direction of the gradient of its potential function. Firstly, assuming that the potential function has gradient converging to zero at infinity, we show that the gradient k-Yamabe soliton is trivial. Afterwards, supposing the boundedness of the gradient and Hessian of the potential function, if such a gradient k-Yamabe soliton has polynomial volume growth, we prove that it must be also trivial. Finally, for a stochastically complete gradient k-Yamabe soliton having potential function with bounded gradient, we also verify its triviality.

We investigate solitons of the spacelike mean curvature flow with respect to the timelike Killing vector field of a standard static spacetime. In this setting, we apply suitable Liouville type properties in order to establish uniqueness and nonexistence results concerning these solitons. In particular, we get that the only closed (that is, compact without boundary) spacelike mean curvature flow solitons with respect to the timelike Killing vector field of a spatially closed standard static spacetime are the totally geodesic slices. Furthermore, we obtain new Calabi–Bernstein type results for entire graphs constructed over the Riemannian base of a standard static spacetime and which are spacelike mean curvature flow solitons.

AbstractWe investigate geometric aspects of complete spacelike mean curvature flow solitons of codimension one in a generalized Robertson–Walker (GRW) spacetime $-I\times _{f}M^n$ , with base $I\subset \mathbb R$ , Riemannian fiber $M^n$ and warping function $f\in C^\infty (I)$ . For this, we apply suitable maximum principles to guarantee that such a mean curvature flow soliton is a slice of the ambient space and to obtain nonexistence results concerning these solitons. In particular, we deal with entire graphs constructed over the Riemannian fiber $M^n$ , which are spacelike mean curvature flow solitons, and we also explore the geometry of a conformal vector field to establish topological and further rigidity results for compact (without boundary) mean curvature flow solitons in a GRW spacetime. Moreover, we study the stability of spacelike mean curvature flow solitons with respect to an appropriate stability operator. Standard examples of spacelike mean curvature flow solitons in GRW spacetimes are exhibited, and applications related to these examples are given.

Medicaid expansion (ME) has contributed to transforming the United States healthcare system. However, its effect on palliative care of primary liver cancers remains unknown. This study aimed to evaluate the association between ME and the receipt of palliative treatment in advanced-stage liver cancer.

Video Abstract1_2w34gx3qKaltura

The chemiluminescence (CL) reaction of eight different 2-(4-hydroxyphenyl)-4,5-dihydrothiazole-4-carboxylate esters with an organic superbase and oxygen was investigated through a kinetic and computational study. These esters are all analogues to the luciferin substrate involved in efficient firefly bioluminescence. The kinetic data obtained from CL emission and light absorption assays were used in the context of linear free energy relationships (LFER); we obtained the Hammett reaction constant ρ = +1.62 ± 0.09 and the Brønsted constant βlg= −0.39 ± 0.04. These observations from LFER, together with activation parameters obtained from Arrhenius plots, suggest that the formation of the high-energy intermediate (HEI) 1,2-dioxetanone occurs via a concerted mechanism during the rate-determining step of the reaction. Calculations performed using density functional theory support a late transition state for HEI formation within the reaction mechanism pathway, which was described considering geometric parameters, Wiberg bond indices from natural bond order analysis, and the atomic charges derived from the electrostatic potential.

Let Mnbe an n-dimensional complete linear Weingarten spacelike submanifold immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space Lpn+pof index p, which obeys standard curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). In this setting, our purpose is to establish sufficient conditions guaranteeing that such a spacelike submanifold Mnbe either totally umbilical or isometric to an isoparametric hypersurface of a totally geodesic submanifold L1n+1↪Lpn+p, with two distinct principal curvatures, one of which is simple. Our approach is based on a suitable Simons type formula jointly with a version of the Omori–Yau’s generalized maximum principle for a Cheng–Yau’s modified operator.

In this paper, under certain conditions on the mean and scalar curvatures, we prove that there are no strongly stable linear Weingarten closed two-sided hypersurfaces immersed in a certain region determined by a geodesic sphere of the (n+1)-dimensional real projective space RPn+1. We also provide a rigidity result for these hypersurfaces.

We apply suitable maximum principles for the drift Laplacian to obtain several uniqueness results concerning complete two-sided hypersurfaces immersed with constant f-mean curvature in a weighted product space of form R×Mfnand such that its potential function fdoes not depend on the parameter t∈R. Among these results, we prove that the slices are the only complete two-sided f-minimal hypersurfaces lying in a half-space of R×Mfnand such that the Bakry–Émeri–Ricci tensor is bounded from below. Furthermore, we study the f-mean curvature equation related to entire graphs defined on the base Mn.

We deal with (r, s)-linear Weingarten two-sided hypersurfaces immersed in the (n+1)-dimensional real projective space RPn+1, namely, two-sided hypersurfaces of RPn+1whose higher order mean curvatures Hr+1and Hs+1are linearly related, with 0≤r≤s≤n-1. Under suitable restrictions on the geometry of these hypersurfaces, we prove the nonexistence of strongly stable (r, s)-linear Weingarten closed two-sided hypersurfaces immersed in a certain region determined by a geodesic sphere of RPn+1. We also obtain a uniqueness result for strongly stable (r, s)-linear Weingarten closed two-sided hypersurfaces of RPn+1.

Our purpose is to establish nonexistence results concerning complete noncompact mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products, under mild constraints on the warping and soliton functions. Applications to self-shrinkers in the Euclidean space, as well as to mean curvature flow solitons in other important warped product models such as the Schwarzschild and Reissner-Nordström spaces, and Robertson-Walker spacetimes such as the Einstein-de Sitter spacetime, are also given. Furthermore, we study the nonexistence of entire solutions to the mean curvature flow equation. Our approach is based on a suitable conformal change of metric jointly with a maximum principle for complete noncompact Riemannian manifolds with polynomial volume growth due to Alías et al.

Kefiran is a polysaccharide present in kefir grains that have been widely explored due to its potential health benefits. The objective of this work was to characterize and quantify the components present in the ethanolic extract of milk kefir grains; to study its pharmacokinetic and toxicological properties in silico and evaluate the acute toxicity of the kefiran in zebrafish. The prediction of pharmacokinetic properties was performed by QikProp software. In silico toxicity assessment was performed using the DEREK (deductive estimate of risk from existing knowledge) software. In the chromatographic, kefiran was identified as the major component. Results showed that the kefiran had low human oral absorption and intestinal absorption its due poor solubility profile; low logP value, indicating its lipophilicity and the low MDCK and Caco-2 cells permability, and unable to cross the blood–brain barrier. Kefiran did not present any structural warning for in silico toxicity. In zebrafish, the dose of 2,000 mg/kg of kefiran produced nonsignificant alterations in the analyzed organs. It can be said then that kefiran has an acceptable degree of safety for use in the development of drugs or functional foods. Further research such as in vivo testing to confirm its pharmacological potential is currently underway.

We deal with complete linear Weingarten hypersurfaces immersed into locally symmetric Riemannian manifolds whose sectional curvature obeys certain standard constraints. Under an assumption that such a hypersurface satisfies a suitable Okumura type inequality, we apply a version of the Omori–Yau maximum principle to prove that it must be either totally umbilical or isometric to an isoparametric hypersurface having two distinct principal curvatures. When the ambient space is Einstein, we also use a technique recently developed by Alías and Meléndez (Mediterr J Math 17(2): 61, 2020 [6]) to establish a sharp integral inequality for compact linear Weingarten hypersurfaces.

We obtain a sharp estimate to the norm of the traceless second fundamental form of complete hypersurfaces with constant scalar curvature immersed into a locally symmetric Riemannian manifold obeying standard curvature constraints (which includes, in particular, the Riemannian space forms with constant sectional curvature). When the equality holds, we prove that these hypersurfaces must be isoparametric with two distinct principal curvatures. Our approach involves a suitable Okumura type inequality which was introduced by Meléndez (Bull Braz Math Soc 45:385–404, 2014) , corresponding to a weaker hypothesis when compared with to the assumption that these hypersurfaces have a priori at most two distinct principal curvatures.

Under the assumption that the second fundamental form is locally timelike, we establish new nonexistence and umbilicity results concerning n-dimensional spacelike submanifolds immersed with parallel mean curvature vector in the (n+p)-dimensional de Sitter space Sqn+pof index q, such that 1≤q≤p. Our approach is based on a Simon’s type inequality involving the norm of the total umbilicity tensor, obtained by Mariano in [17], jointly with suitable maximum principles due to Alías, Caminha and do Nascimento [6, 7] for complete noncompact Riemannian manifolds and a weak version of Omori–Yau’s maximum principle for stochastically complete Riemanian manifolds proved by Pigola, Rigoli and Setti [20, 21].

Our purpose in this paper is to study some geometric properties of spacelike hypersurfaces immersed into a pp-wave spacetime, namely, a connected Lorentzian manifold admitting a parallel lightlike vector field. Initially, by applying a new form of maximum principle for smooth functions on a complete noncompact Riemannian manifold, we obtain sufficient conditions which guarantee that a complete noncompact spacelike hypersurface with polynomial volume growth is either totally geodesic, maximal or 1-maximal. As a consequence, we establish nonexistence results concerning such spacelike hypersurfaces. Next, using a weak form of the Omori–Yau maximum principle, we get uniqueness and nonexistence results for stochastically complete spacelike hypersurface with constant mean curvature. Finally, we establish the notion of spacelike mean curvature flow soliton in pp-wave spacetimes and we provide some geometric conditions that allow us to guarantee how close a complete spacelike mean curvature flow soliton is to a totally geodesic immersion.

Background: The chemical dependency caused by recreational drug abuse is highly detrimental to humans and has direct implications for society. Cannabis sativa is still at the top ranking of most used drugs in the world, and its major chemical component is Δ9-THC. This molecule is the main cause of addiction in chronic users, and its action is measured by the CB1 receptor present in the CNS. So far, there is no approved drug for the treatment of abstinence in C. sativa. Objective: In this sense, the objective of this research is to propose analogues of stemphol (2-methyl-5-pentylbenzene-1,3-diol) molecule that can serve as treatment for withdrawal crises in C. sativa addicts, initially through in silico methods. Methods: 28 structural modifications were carried out in the molecule stemphol. These were subjected to in silico predictions of pharmacokinetics, toxicology, pharmacological activity, synthetic viability and the prediction of drug-receptor interaction through molecular docking. For this, the software and web servers PreADMET, DEREK 2.1, PASS, SEA, SYLVIA 2.4 and GOLD were used. Results: 22 analogues demonstrated good pharmacokinetic results, and 16 analogues gave no warning of hepatotoxicity, mutagenicity, nephropathies and carcinogenicity in mammals. Biological activity predictions were performed on the PASS server, resulting in 28 analogues exhibiting adenylate cyclase inhibition and/or MAP kinase stimulating activity; in SEA, the performance of the CB1 receptor was analyzed, resulting in 20 analogues with action on CB1 receptors in humans. The selected analogues 1, 4, 16, 17, 19, 24, 25 and 26 were submitted to synthetic accessibility prediction in the SYLVIA software because they presented better results in terms of their pharmacokinetic, toxicological and predictive properties. Conclusion: Of these, analogues 17 and 25 provided a very satisfactory result in the interaction with the CB1 receptor through the molecular docking method, and can be considered great proposals for future in vitro and in vivo studies, with the ability to further elucidate their actions.

Background: Alzheimers disease (AD) is a neurodegenerative condition and the most common type of dementia among the elderly. The enzymes acetylcholinesterase (AChE) and nitric oxide synthase (NOS) have a pivotal role in the pathophysiology of this disease. Objective: This study aimed to select medicinal plant-derived molecules with reported inhibition of AChE and design optimized molecules that could inhibit not only AChE, but also NOS, potentially increasing its efficacy against AD. Methods: 24 compounds were selected from the literature based on their known AChE inhibitory activity. Then, we performed molecular orbital calculations, maps of electrostatic potential, molecular docking study, identification of the pharmacophoric pattern, evaluation of pharmacokinetic and toxicological properties of these molecules. Next, ten analogs were generated for each molecule to optimize their effect where the best molecules of natural products had failed. Results: The most relevant correlation was between HOMO and GAP in the correlation matrix of the molecules descriptors. The pharmacophoric groups derivation found the following pharmacophoric features: two hydrogen bond acceptors and one aromatic ring. The studied molecules interacted with the active site of AChE through hydrophobic and hydrogen bonds and with NOS through hydrogen interactions only but in a meaningful manner. In the pharmacokinetic and toxicological prediction, the compounds showed satisfactory results. Conclusion: The design of natural products analogs demonstrated good affinities with the pharmacological targets AChE and NOS, with satisfactory pharmacokinetics and toxicology profiles. Thus, the results could identify promising molecules for treating Alzheimers disease.

In this paper, our purpose is to establish new Nomizu–Smyth type results concerning complete Riemannian immersions in the hyperbolic and de Sitter spaces. Assuming that the image of the Gauss map of such an immersion lies in a totally umbilical hypersurface and supposing the existence of a point of the immersion where the Gauss–Kronecker curvature does not vanish, we prove that the immersion must be a totally umbilical hypersurface of the ambient space.

In this paper we deal with complete linear Weingarten hypersurfaces immersed into Riemannian space forms. Assuming an Okumura type inequality on the total umbilicity tensor of such hypersurfaces, we prove that either the hypersurface is totally umbilical or it holds an estimate for the norm of the total umbilicity tensor, which is also shown be sharp in the sense that the product of space forms realize them. Our approach is based on a version of the Omori–Yau maximum principle for a suitable Cheng–Yau type operator.

We study the uniqueness and nonexistence of mean curvature flow solitons (MCFS) with respect to a nowhere zero Killing vector field Kglobally defined in a Riemannian space, via suitable Liouville type results. For this, we consider the ambient space as a warped product of the type Mn×ρR, where the base Mn, with n⩾3, is an arbitrarily fixed integral leaf of the distribution orthogonal to Kand the warping function ρ∈C∞(M)is given by ρ=|K|. In particular, assuming that Mnis closed (that is, compact without boundary), we conclude that the only closed MCFS with respect to Kare the totally geodesic slices. Furthermore, we establish new Moser–Bernstein type results concerning entire Killing graphs constructed through the flow of Kand which are complete MCFS with respect to it.

We deal with complete surfaces immersed with flat normal bundle and parallel normalized mean curvature vector field in the hyperbolic space H2+p. Supposing that such a surface M2satisfies a linear Weingarten condition of the type K=aH+bfor some appropriate real constants aand b, where Hand Kdenote the mean and Gaussian curvatures, respectively, we show that M2must be either totally umbilical or isometric to one of the following flat surfaces: S1(r)×R, S1(r)×S1(r~2-r2)or S1(r)×H1(-r~2+r2). Furthermore, we obtain a version of the classical Liebmann’s Theorem (Liebmann in Math Phys Klasse 44–55, 1899) showing that the only compact (without boundary) surfaces having positive constant Gaussian curvature, immersed with flat normal bundle in the hyperbolic space H2+p, are the totally umbilical round spheres.

We derive sharp estimates for the infimum and supremum of the scalar curvature of a hypersurface immersed with constant mean curvature in a locally symmetric space obeying standard curvature constraints. Our approach is based on the well known Omori–Yau maximum principle and on the weak version of it.

We use suitable maximum principles in order to obtain characterization results concerning n-dimensional linear Weingarten submanifolds immersed with globally flat normal bundle and parallel normalized mean curvature vector field in the $$(n+p)$$(n+p)-dimensional hyperbolic space $${\mathbb {H}}^{n+p}$$Hn+p. In particular, when $$p=2$$p=2, we present complete descriptions of these submanifolds.

Immune checkpoint inhibitors (ICIs) have recently been introduced into the treatment algorithm of patients with hepatocellular carcinoma (HCC). However, the cost effectiveness of ICIs compared with pre-existing therapies for HCC has not been assessed. We performed a meta-analysis to understand the incremental cost effectiveness of ICIs compared with sorafenib.

We obtain a sharp estimate to the scalar curvature of stochastically complete hypersurfaces immersed with constant mean curvature in a locally symmetric Riemannian space obeying standard curvature constraints (which includes, in particular, a Riemannian space with constant sectional curvature). For this, we suppose that these hypersurfaces satisfy a suitable Okumura-type inequality recently introduced by Meléndez (Bull Braz Math Soc 45:385–404, 2014), which is a weaker hypothesis than to assume that they have two distinct principal curvatures. Our approach is based on the equivalence between stochastic completeness and the validity of the weak version of the Omori–Yau’s generalized maximum principle, which was established by Pigola et al. (Proc Am Math Soc 131:1283–1288, 2002; Mem Am Math Soc 174:822, 2005). Nous obtenons une estimation optimale de la courbure scalaire des hypersurfaces stochastiquement complètes immergées avec courbure moyenne constante dans un espace Riemannien localement symétrique, obéissant aux contraintes de courbure standard (qui comprend, en particulier, un espace Riemannien avec courbure sectionnelle constante). Pour cela, nous supposons que ces hypersurfaces satisfont une inégalité appropriée de type Okumura récemment introduite par Meléndez (Bull Braz Math Soc 45:385–404, 2014), ce qui est une hypothèse plus faible que de supposer qu’elles ont deux courbures principales distinctes. Notre approche est basée sur l’équivalence entre la complétude stochastique et la validité de la version faible du principe maximal généralisé de Omori–Yau, qui a été établi par Pigola et al. (Proc Am Math Soc 131:1283–1288, 2002; Mem Am Math Soc 174:822, 2005).

We extend a technique due to Romero et al. (Class Quantum Gav 30:1–13, 2013) establishing sufficient conditions to guarantee the parabolicity of a complete two-sided hypersurface immersed into a Killing warped product $$M\times _{\rho }{\mathbb {R}}$$ M×ρR , whose base $$M^n$$ Mn has parabolic universal Riemannian covering. Afterwards, we apply our parabolicity criterium in order to obtain a rigidity result concerning these hypersurfaces, whose mean curvature is not supposed a priori be constant. Finally, parametric uniqueness results are applied to obtain suitable non-parametric ones, i.e., to the case of entire Killing graphs.

In this paper, we establish a criterion of parabolicity for complete two-sided hypersurfaces immersed in a Riemannian warped product of the type $$I\times _fM^n$$ I×fMn , where $$M^{n}$$ Mn is a connected n-dimensional oriented Riemannian manifold and $$f:I\rightarrow \mathbb {R}$$ f:I→R is a positive smooth function. As applications, we obtain several uniqueness results concerning these hypersurfaces with constant mean curvature, under standard constraints on the Ricci curvature of $$M^n$$ Mn and on the warping function f. Moreover, considering the higher order mean curvatures, we also obtain estimates for the index of relative nullity.

In this paper, we study complete linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Lorentz space. By applying some generalized maximum principles to a suitable Cheng–Yau modified operator, we establish sufficient conditions which assure that such a spacelike hypersurface must be a totally umbilical hypersurface of the ambient space.

Our purpose in this paper is to study the geometry of n-dimensional complete spacelike submanifolds immersed in the $$(n+p)$$ (n+p) -dimensional anti-de Sitter space $$\mathbb {H}^{n+p}_{q}$$ Hqn+p of index q, with $$1\le q\le p$$ 1≤q≤p . Under suitable constraints on the Ricci curvature and the second fundamental form, we show that a complete maximal spacelike submanifold of $$\mathbb {H}^{n+p}_{q}$$ Hqn+p must be totally geodesic. Furthermore, we establish sufficient conditions to guarantee that a complete spacelike submanifold with nonzero parallel mean curvature vector in $$\mathbb {H}^{n+p}_{p}$$ Hpn+p must be pseudo-umbilical, which means that its mean curvature vector is an umbilical direction.

Almost one-third of patients with colorectal cancer (CRC) experience recurrence after resection. Adherence to surveillance guidelines largely dictates efficacy in early detection of recurrence. We sought to assess and compare adherence to postoperative surveillance guidelines for colonoscopy, imaging, and Carcinoembryonic Antigen (CEA).

Under suitable constraints on the Bakry–Émery–Ricci tensor and on the norm of the gradient of the height function, we apply some maximum principles related to the drift Laplacian in weighted Riemannian manifolds to study the uniqueness of complete spacelike hypersurfaces immersed with constant f-mean curvature in a weighted Lorentzian product space of the type -R×Mfn.New Calabi–Bernstein type results concerning spacelike entire graphs defined on the Riemannian base Mnare also given.

In this paper, we establish new rigidity results concerning n-dimensional linear Weingarten (LW) submanifolds immersed in an (n+p)-dimensional Riemannian space form Qcn+pwith constant sectional curvature c∈{-1,0,1}. Under the assumption that a complete LW submanifold has polynomial volume growth, we prove that it must be isometric to an Euclidean sphere Sn(r), with radius r>0. When the ambient space is the hyperbolic space Hn+p, we suppose that the norm of the total umbilicity tensor converges to zero at infinity to show that a complete noncompact LW submanifold of Hn+pmust be isometric to a horosphere of Hn+1. Our approach is based on suitable maximum principles recently due to Alías, Caminha and do Nascimento (Alías et al. in J Math Anal Appl 474:242–247, 2019; Alías et al. in Ann Mat Pura Appl 200:1637–1650, 2021)[1, 2] related to complete noncompact Riemannian manifolds.

Our purpose in this paper is to study the geometry of complete linear Weingarten spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space, which is supposed to obey standard curvature constrains. In this setting, we apply some appropriated generalized maximum principles to a suitable Cheng-Yau modified operator in order to guarantee that such a spacelike hypersurface must be isometric to an isoparametric hypersurface of the ambient space.

Our aim in this article is to study the rigidity of complete spacelike hypersurfaces immersed in a weighted Lorentzian product space of the type $$\mathbb {R}_1\times \mathbb {P}^n_f$$ R1×Pfn , whose Bakry–Émery-Ricci tensor of the fiber $$\mathbb {P}^n$$ Pn is nonnegative and the Hessian of the weighted function fis bounded from below. In this setting, supposing that the weighted mean curvature $$H_f$$ Hf is constant and assuming appropriated constraints on the norm of the gradient of the height function, we prove that such a hypersurface must be a slice of the ambient space. Applications to entire spacelike graphs construct over $$\mathbb {P}^n$$ Pn are also given. Our approach is based on a suitable formula for the drift Laplacian of an angle function naturally attached to a spacelike hypersurface jointly with a weak version of the Omori–Yau’s generalized maximum principle.

In this article, we deal with complete hypersurfaces immersed in a semi-Riemannian warped product space, which is supposed to obey standard convergence conditions. Under appropriated constraints on the higher order mean curvatures, but without the requirement of the existence of an elliptic point, we are able to obtain sufficient conditions which guarantee that such a hypersurface must be a slice of the ambient space. Our approach is based on a suitable generalized maximum principle due to Alías et al. (Math Proc Camb Philos Soc 152:365–383, 2012) applied to the linearized operators of the higher order mean curvatures.

We investigate the umbilicity of n-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field in the de Sitter space 𝕊pn+pof index p>1. We recall that a spacelike submanifold is said to be linear Weingarten when its mean curvature function Hand its normalized scalar curvature Rsatisfy a linear relation of the type R=aH+b, for some constants a,b∈ℝ. Under suitable constraints on the values of aand b, we apply a generalized maximum principle for a modified Cheng–Yau operator ℒin order to show that such a spacelike submanifold must be either totally umbilical or isometric to a product M1×M2×⋯×Mk, where the factors Miare totally umbilical submanifolds of 𝕊pn+pwhich are mutually perpendicular along their intersections. Moreover, we also study the case in which these spacelike submanifolds are ℒ-parabolic.

We establish unicity results concerning complete spacelike hypersurfaces immersed in a Lorentzian product space, under appropriated restrictions on the norm of the gradient of the height function. Our approach is based on two analytical tools: the well known Omori–Yau generalized maximum principle, and another suitable maximum principle at the infinity due to Yau. As application of our unicity results, we study the rigidity of entire vertical graphs in such ambient spaces.