Theoretical investigation into the structural, thermochemical, and electronic properties of the decathio[10]circulene

For the first time, a theoretical study has been performed on the prototypical decathio[10]circulene (C(20)S(10)) species, which is an analogue of the novel octathio[8]circulene "Sulflower" molecule (C(16)S(8)). Examinations of the singlet and triplet states of C(20)S(10) were made at the B3LYP/6-311G(d) level. Local minima of C(2) and C(s) symmetry were found for the lowest singlet and triplet states, respectively. The stability of C(20)S(10) was assessed by calculating the ΔH°(f) of C(16)S(8) and C(20)S(10) and the ΔH(o) for their decomposition into C(2)S units. Frontier molecular orbital plots show that structural adjacent steric factors along with the twist and strain orientations of C(20)S(10) do not disturb the aromatic π-delocalizing effects. In fact, C(20)S(10) maintains the same p(z) HOMO character as C(16)S(8). These similarities are further verified by density-of-states characterization. Calculated infrared spectra of C(16)S(8) and C(20)S(10) show broad similarities. Molecular electrostatic potential results reveal that eight of the peripheral sulfur atoms are the most electronegative atoms in the molecule, while the interior ten-membered ring exhibits virtually no electronegativity.     

Convergence of perturbed iterates of set-valued mappings

We continue our study of the existence of convergent iterations in the presence of computational errors for a nonexpansive setvalued mapping. In a recent paper we have shown that if for any initial point, there exists a trajectory of a nonexpansive set-valued mapping attracted by a given set, then this property is stable under small perturbations of the mapping. In particular, we have shown there that for any initial point, there exists a trajectory with a subsequence which is attracted by the attractor. In the present paper we show, under certain mild additional assumptions, that for any initial point, there exists a trajectory such that, for any given positive e\epsilon, almost all of its elements belong to an e\epsilon-neighborhood of the attractor.     

Theorems of Denjoy–Wolff type

Using the Kobayashi distance, we first establish a version of the Denjoy–Wolff theorem for a bounded and strictly convex domain in ${{\mathbb{C}}^k}$ . Next, we prove analogous results for semigroups of holomorphic mappings and the resolvents of their generators. Finally, we obtain theorems of Denjoy–Wolff type for families of holomorphic retracts of the open unit ball in a complex, reflexive, and strictly convex Banach space.     

Three Generic Results in Holomorphic Fixed Point Theory

We establish three theorems which show that most of the bounded holomorphic self-mappings of a star-shaped domain in a complex Banach space map it strictly inside itself. According to the Earle–Hamilton fixed point theorem, each such mapping has a unique fixed point.     

Optimal Pricing for Optimal Transport

Suppose that c(x, y) is the cost of transporting a unit of mass from x ∈ X to y ∈ Y and suppose that a mass distribution μ on X is transported optimally (so that the total cost of transportation is minimal) to the mass distribution ν on Y. Then, roughly speaking, the Kantorovich duality theorem asserts that there is a price f(x) for a unit of mass sold (say by the producer to the distributor) at x and a price g(y) for a unit of mass sold (say by the distributor to the end consumer) at y such that for any x ∈ X and y ∈ Y, the price difference g(y) ? f(x) is not greater than the cost of transportation c(x, y) and such that there is equality g(y) ? f(x) = c(x, y) if indeed a nonzero mass was transported (via the optimal transportation plan) from x to y. We consider the following optimal pricing problem: suppose that a new pricing policy is to be determined while keeping a part of the optimal transportation plan fixed and, in addition, some prices at the sources of this part are also kept fixed. From the producers’ side, what would then be the highest compatible pricing policy possible? From the consumers’ side, what would then be the lowest compatible pricing policy possible? We have recently introduced and studied settings in c-convexity theory which gave rise to families of c-convex c-antiderivatives, and, in particular, we established the existence of optimal c-convex c-antiderivatives and explicit constructions of these optimizers were presented. In applications, it has turned out that this is a unifying language for phenomena in analysis which used to be considered quite apart. In the present paper we employ optimal c-convex c-antiderivatives and conclude that these are natural solutions to the optimal pricing problems mentioned above. This type of problems drew attention in the past and existence results were previously established in the case where X = Y = ? ⁿ under various specifications. We solve the above problem for general spaces X, Y and real-valued, lower semicontinuous cost functions c. Furthermore, an explicit construction of solutions to the general problem is presented.     

A Denjoy–Wolff theorem for compact holomorphic mappings in reflexive Banach spaces

Using the Kobayashi distance, we establish a Denjoy–Wolff theorem for compact holomorphic self-mappings of a bounded and strictly convex domain in a complex reflexive Banach space.     

Nafion®-Separated Electrode Solutions in Isoelectric Focusing

In the present paper, we present our results from studies where the electrode solutions were separated from the carrier with the polytetrafluoroethylene-based membranes (Nafion^®). We achieved a 40-fold decrease of the average ionic strength in the gel and a twofold lowering of the current already during the first 30 min from the start of IEF, as compared to the routinely employed method. The change of these parameters made it possible to carry out the electrophoresis under conditions considerably closer to steady state, and to achieve a sharp protein separation and shortening of the duration of the process. The comparative analysis of the electrophoretic parameters in question proved that the basis for this newly developed improvement of the method is the selective restriction of the processes of migration and diffusion in the whole electrophoretic system, due to the specific properties of the semi-permeable membrane Nafion^®.

     

Multiple blocking sets in finite projective spaces and improvements to the Griesmer bound for linear codes

Belov, Logachev and Sandimirov construct linear codes of minimum distance d for roughly 1/q ^k/2 of the values of d < q ^k-1. In this article we shall prove that, for q = p prime and roughly \frac38{\frac{3}{8}}-th’s of the values of d < q ^k-1, there is no linear code meeting the Griesmer bound. This result uses Blokhuis’ theorem on the size of a t-fold blocking set in PG(2, p), p prime, which we generalise to higher dimensions. We also give more general lower bounds on the size of a t-fold blocking set in PG(δ, q), for arbitrary q and δ ≥ 3. It is known that from a linear code of dimension k with minimum distance d < q ^k-1 that meets the Griesmer bound one can construct a t-fold blocking set of PG(k−1, q). Here, we calculate explicit formulas relating t and d. Finally we show, using the generalised version of Blokhuis’ theorem, that nearly all linear codes over \mathbb F_p{{\mathbb F}_p} of dimension k with minimum distance d < q ^k-1, which meet the Griesmer bound, have codewords of weight at least d + p in subcodes, which contain codewords satisfying certain hypotheses on their supports.     

Punctured combinatorial Nullstellensätze

In this article we extend Alon’s Nullstellensatz to functions which have multiple zeros at the common zeros of some polynomials g ₁,g ₂, …, g _n , that are the product of linear factors. We then prove a punctured version which states, for simple zeros, that if f vanishes at nearly all, but not all, of the common zeros of g ₁(X ₁), …,g _n (X _n ) then every residue of f modulo the ideal generated by g ₁, …, g _n , has a large degree.     

Pycnangloside: a new cerebroside from bark of Pycnanthus angolensis

Pycnanthus anglonensis is known for its medicinal value. This paper deals with a phytochemical investigation of this species, from which pycnangloside (1), a new cerebroside has been isolated. Its structure was determined by comprehensive analyses of its 1D and 2D NMR spectroscopic, and ESI mass spectrometric data. Four known compounds were also isolated and identified as biochanin A, formonentin, beta-sitosterol, and beta-sitosterol glucopyranoside.