Let P be a lattice polytope with the $$h^{*}$$ -vector $$(1, h^*_1, \ldots , h^*_s)$$ . In this note we show that if $$h_s^* \le h_1^*$$ then Ehrhart ring $${\mathbb {k}}[P]$$ is generated in degrees at most $$s-1$$ as {k}}$$ -algebra. particular, $$s=2$$ and $$h_2^* IDP. To see this, corresponding statement for semi-standard graded Cohen–Macaulay domains over algebraically closed fields.

Endpoint results are presented for multi-valued cyclic contraction mappings on complete metric spaces (X, d). Our results extend previous results given by Nadler (1969), Daffer-Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).

prangos ferulacea is a plant found in the mediterranean and middle-east regions used as carminative, anti-flatulent, emollient and antibacterial herb. it is believed that the coumarins are responsible for some of known effects of  prangos . in this research the relaxant effects of p. ferulacea coumrin rich extract as well as osthole as its main prenylated coumarins were investigated on rat ileu...

Contraction analysis considers the distance between two adjacent trajectories. If this is contracting, then trajectories have same long-term behavior. The main advantage of that it independent solutions under consideration. Using an appropriate metric, with respect to which one can show convergence a unique equilibrium or, if attraction only occurs in certain directions, periodic orbit.Contract...

bunium persicum (boiss.) is an economically important medicinal plant growing wild in arid regions in iran. the essential oil of b. persicum (eobp) was extracted using hydrodistillation. a total of eighteen compounds, representing 96.14 % of the oil was identified by gas chromatography/mass spectrometry (gc/ms).the main compounds were cuminaldehyde (23.04 %), gamma-terpinene (14.48 %), trans-3-...

o objective: many biological studies have been done to determine the activity of medicinal plants on gastrointestinal function. since acetylcholine is the major transmitter involved in the gastrointestinal motility and there are some evidences regarding the cholinergic modulatory effect of hops extract, in the present study spasmolytic and antispasmodic action of hops(humulus lupulus) on acetyl...

In this paper,  we introduce the notion of  generalized multivalued  $F$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  Our results extend and improve the results announced by many others with less hypothesis. Also, we give some illustrative examples.