In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions $d\geq 3$.
The most recent representative of the semi-aquatic insect family Chresmodidae is described from the Lebanese Cenomanian marine lithographic limestone. Its highly specialized legs, with a high number of tarsomeres, never observed in other orders of insects, were probably adapted for water surface skating. We hypothesize the occurrence of a unique, extraordinary "antenna" mutation affecting the distal part of the legs of the Chresmodidae, maybe homeotic or affecting some genes that participate in the leg development and segmentation. The Chresmodidae had a serrate ovipositor adapted to endophytic egg laying in floating or aquatic plants. They were probably predaceous on nektonic small animals. As the Chresmodidae and the aquatic water skaters of the bug families Veliidae and Gerridae were contemporaneous during at least the Lower Cretaceous, these insects probably did not cause the extinction of this curious group.
Pseudo $\star $-autonomous lattices are non-commutative generalizations of $\star $-autonomous lattices. It is proved that the class of pseudo $\star $-autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo $\star $-autonomous lattices can be described as their normal ideals.
Angiosarcoma is a soft tissue tumour with a dismal prognosis. We present a 74 year old male presenting with a non healing ulcer on the scalp. On histopathology a diagnosis of angiosarcoma was made. An early diagnosis and tumour size play a pivotal role in the survival of the patient., Deepal J Deshpande, Chitra S Nayak, Sunil N Mishra, and Literatura 6
We prove a non-archimedean Dugundji extension theorem for the spaces $C^{\ast }(X,\mathbb {K})$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $\mathbb {K}$. Assuming that $\mathbb {K}$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T\colon C^{\ast }(Y,\mathbb {K})\rightarrow C^{\ast }(X,\mathbb {K})$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $\mathbb {K}$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular space $X$ is a retract of $X$.
Plasma corticosterone (CORT) measures are a common procedure to detect stress responses in rodents. However, the procedure is invasive and can influence CORT levels, making it less than ideal for monitoring CORT circadian rhythms. In the current paper, we examined the applicability of a non-invasive fecal CORT metabolite measure to assess the circadian rhythm. We compared fecal CORT metabolite levels to circulating CORT levels, and analyzed change in the fecal circadian rhythm following an acute stressor (i.e. blood sampling by tail veil catheter). Fecal and blood samples were collected from male adolescent rats and analyzed for CORT metabolites and circulating CORT respectively. Fecal samples were collected hourly for 24 h before and after blood draw. On average, peak fecal CORT metabolite values occurred 7-9 h after the plasma CORT peak and time-matched fecal CORT values were well correlated with plasma CORT. As a result of the rapid blood draw, fecal production and CORT levels were altered the next day. These results indicate fecal CORT metabolite measures can be used to assess conditions that disrupt the circadian CORT rhythm, and provide a method to measure long-term changes in CORT production. This can benefit research that requires long-term glucocorticoid assessment (e.g. stress mechanisms underlying health)., P. K. Thanos ... [et al.]., and Obsahuje seznam literatury
It is shown that there exist a continuous function f and a regulated function g defined on the interval [0,1] such that g vanishes everywhere except for a countable set, and the K *-integral of f with respect to g does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.
In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the obtained UNOP is solved by utilizing the NLBFGS method. In comparison to other existing methods, the NLBFGS method shows a significant improvement especially for nonlinear and ill-posed control problems.
In this paper we consider Neumann noncoercive hemivariational inequalities, focusing on nontrivial solutions. We use the critical point theory for locally Lipschitz functionals.