In this article we consider closed bosonic string in the presence of constant metric and Kalb‐Ramond field with one non‐zero component, Bxy=Hz, where field strength H is infinitesimal. Using Buscher T‐duality procedure we dualize along x and y directions and using generalized T‐duality procedure along z direction imposing trivial winding conditions. After first two T‐dualizations we obtain Q flux theory which is just locally well defined, while after all three T‐dualizations we obtain nonlocal R flux theory. Origin of non‐locality is variable ΔV defined as line integral, which appears as an argument of the background fields. Rewriting T‐dual transformation laws in the canonical form and using standard Poisson algebra, we obtained that Q flux theory is commutative one and the R flux theory is noncommutative and nonassociative one. Consequently, there is a correlation between non‐locality and closed string noncommutativity and nonassociativity.

The essential-oil compositions of Pinus heldreichii Christ. from Montenegro and Serbia are reported at the population level. Whitebark pine is a sub-endemic high-mountain Balkan pine relict of an anthropogenically reduced area, with large morphological diversity and insufficiently clear taxonomic position. In the pine-needle terpene profile from three populations from Montenegro, and one from Serbia, 101 compounds were detected, 72 of which could be identified (Table 3). The dominant constituents are limonene (26.3%), alpha-pinene (17.5%), germacrene D (13.5%), and beta-caryophyllene (10.4%), comprising ca. 67.7% of the essential oil. Medium-to-high contents (0.5-10%) of the following 16 additional components were found: beta-pinene, beta-myrcene, alpha-humulene, delta-cadinene, alpha-muurolene, (E)-hex-2-enal, beta-gurjunene, gamma-muurolene, isopimarol, camphene, gamma-cadinene, aromadendrene, beta-bisabolene, trans-beta-farnesene, alpha-cadinene, and (Z)-hex-3-en-1-ol. The similarity of the populations and the within-population variability was visualized by principle-component analysis (PCA) of eleven selected terpenes in 97 tree samples. Cluster and genetic analyses suggest closest connection between the two spatially most-distant populations I (Montenegro) and IV (Serbia). Based on the profile of the main sesquiterpene components, the studied populations from Montenegro and Serbia are more similar to the populations from Greece and the Central Balkan peninsula (Bosnia and Serbia-Kosovo) than to those on the furthest eastern margin of their natural range (Bulgaria).

We consider type IIB superstring theory with embedded D5-brane and choose boundary conditions which preserve half of the initial supersymmetry. In the canonical approach that we use, boundary conditions are treated as canonical constraints. The effective theory, obtained from the initial one on the solution of boundary conditions, has the form of the type I superstring theory with embedded D5-brane. We obtain the expressions for D5-brane background fields of type I theory in terms of the D5-brane background fields of type IIB theory. We show that beside known Ω even fields, they contain squares of Ω odd ones, where Ω is world-sheet parity transformation, Ω : σ → −σ. We relate result of this paper and the results of [1] using T-dualities along four directions orthogonal to D5-brane.