Let Kn = {x ∈ Rn | xi ≥ 0, 1 ≤ i ≤ n} and suppose that f : Kn → Kn is nonexpansive with respect to the l1-norm, ‖x‖1 = ∑n i=1 |xi|, and satisfies f(0) = 0. Let P3(n) denote the (finite) set of positive integers p such that there exists f as above and a periodic point ξ ∈ Kn of f of minimal period p. For each n ≥ 1 we use the concept of “admissible arrays on n symbols” to define a set of positiv...

Let g: E → F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x, ε)) ⊂ F, the image under g of the closed ball about x ∈ E with radius ε. When g(x) expresses the solution of an equation depending on x , then the elements of g(B(x, ε)) are ε-pseudosolutions. Our aim is to investigate the size of the set g(B(x, ε)). We derive upper and lower bounds of the following...

Racemates increase the chances of crystallization by allowing molecular contacts to be formed in a greater number of ways. With the advent of protein synthesis, the production of protein racemates and racemic-protein crystallography are now possible. Curiously, racemic DNA crystallography had not been investigated despite the commercial availability of L- and D-deoxyribo-oligonucleotides. Here,...

Modest antidepressant response rates of mood disorders (MD) encourage benzodiazepine (BZD) co-medication with debatable benefit. Adult hippocampal neurogenesis may underlie antidepressant responses, but diazepam co-administration impairs murine neuron maturation and survival in response to fluoxetine. We counted neural progenitor cells (NPCs), mitotic cells, and mature granule neurons post-mort...

background: despite the relative success of surgical resection followed by proton, proton/photon, or conventional radiotherapy in terms of recurrence-free survival, chordomas are still associated with a high rate of recurrence. to our knowledge there are only very few reported cases of this rare tumor detected by f-18 fdg-pet. materials and methods: in this case we show the significance of f-18...

For $1$-dimensional Legendrian submanifolds of $1$-jet spaces, we extend the functorality contact homology DG-algebra (DGA) from embedded exact Lagrangian cobordisms, as in \cite{EHK}, to a class immersed cobordisms by considering their lifts conical cobordisms. To cobordism $\Sigma$ $\Lambda_-$ $\Lambda_+$, associate an DGA map, which is diagram $$\alg(\Lambda_+) \stackrel{f}{\rightarrow} \alg...

The equivalence between dg duality and Verdier has been established for cyclic operads earlier. We propose a generalization of this correspondence from to twisted modular the Feynman transform. Specifically, each operad $$\mathcal {P}$$ (taking values in dg-vector spaces over field k characteristic 0), there is certain sheaf {F}$$ associated with it on moduli space stable metric graphs such tha...

introduction: cephalometry is an efficient tool for anthropometric studies. this study sought to assess facial dimensions and types of adults residing in qazvin (iran) and dera ghazi (dg) khan (pakistan). methods: in this cross-sectional study, a total of 300 ethnic populations of qazvin and 365 ethnic populations of dg khan aged between 18-55 years were randomly selected and evaluated. the sub...