Growth and characterization of nonlinear optical zinc hydrogen phosphate single crystal grown in silica gel

Good optical quality single crystals of zinc hydrogen phosphate (ZnHPO₄) having dimensions up to 8×2×2 mm³ have been grown with the aid of sodium meta silicate gel. Single crystal XRD studies confirm that the crystal belongs to the orthorhombic system with space group P2₁2₁2₁. The functional groups present in the crystals were confirmed using FTIR technique. Optical absorbance shows very low absorption in the entire visible region. Differential thermal and thermo gravimetric analysis confirmed that the crystal is stable up to 193°C. Photoconductivity study reveals positive photoconductivity in the presence of photo active centers formed by trap energy levels. The NLO activity of the crystal was confirmed by Kurtz powder technique. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lattice Shrinkage by Incorporation of Recombinant Starmaker-Like Protein within Bioinspired Calcium Carbonate Crystals

The biological mediation of mineral formation (biomineralization) is realized through diverse organic macromolecules that guide this process in a spatial and temporal manner. Although the role of these molecules in biomineralization is being gradually revealed, the molecular basis of their regulatory function is still poorly understood. In this study, the incorporation and distribution of the model intrinsically disordered starmaker-like (Stm-l) protein, which is active in fish otoliths biomineralization, within calcium carbonate crystals, is revealed. Stm-l promotes crystal nucleation and anisotropic tailoring of crystal morphology. Intracrystalline incorporation of Stm-l protein unexpectedly results in shrinkage (and not expansion, as commonly described in biomineral and bioinspired crystals) of the crystal lattice volume, which is described herein, for the first time, for bioinspired mineralization. A ring pattern was observed in crystals grown for 48 h; this was composed of a protein-enriched region flanked by protein-depleted regions. It can be explained as a result of the Ostwald-like ripening process and intrinsic properties of Stm-l, and bears some analogy to the daily growth layers of the otolith.     

Acidic Monosaccharides become Incorporated into Calcite Single Crystals**

Carbohydrates, along with proteins and peptides, are known to represent a major class of biomacromolecules involved in calcium carbonate biomineralization. However, in spite of multiple physical and biochemical characterizations, the explicit role of saccharide macromolecules (long chains of carbohydrate molecules) in mineral deposition is not yet understood. In this study, we investigated the influence of two common acidic monosaccharides (MSs), the two simplest forms of acidic carbohydrates, namely glucuronic and galacturonic acids, on the formation of calcite crystals in vitro. We show here that the size, morphology, and microstructure of calcite crystals are altered when they are grown in the presence of these MSs. More importantly, these MSs were found to become incorporated into the calcite crystalline lattice and induce anisotropic lattice distortions, a phenomenon widely studied for other biomolecules related to CaCO₃ biomineralization, but never before reported in the case of single MSs. Changes in the calcite lattice induced by MSs incorporation were precisely determined by high-resolution synchrotron powder X-ray diffraction. We believe that the results of this research may deepen our understanding of the interaction of saccharide polymers with an inorganic host and shed light on the implications of carbohydrates for biomineralization processes.     

Order isomorphisms in cones and a characterization of duality for ellipsoids

We study order isomorphisms in finite-dimensional ordered vector spaces. We generalize theorems of Alexandrov, Zeeman, and Rothaus (valid for ??non-angular?? cones) to wide classes of cones, including in particular polyhedral cones, using a different and novel geometric method. We arrive at the following result: whenever the cone has more than n generic extremal vectors, an order isomorphism must be affine. In the remaining case, of precisely n extremal rays, the transform has a restricted diagonal form. To this end, we prove and use a new version of the well-known Fundamental theorem of affine geometry. We then apply our results to the cone of positive semi-definite matrices and get a characterization of its order isomorphisms. As a consequence, the polarity mapping is, up to a linear map, the only order-reversing isomorphism for ellipsoids.     

A Stochastic Competitive Research and Development Race Where “Winner Takes All” with Lower and Upper Bounds

The paper analyzes an environment in which several firms compete over the development of a project. Each firm decides how much to invest in the project while adhering to firm-specific lower and upper investment bounds. The completion time of the project by a firm has exponential distribution with rate that depends linearly on the investment of the firm. The firm that completes the project first collects all its revenues whereas the remaining firms earn nothing. The paper establishes the existence and uniqueness of both the Nash equilibrium and the globally optimal solution, provides explicit representations parametrically in the interest rate, and constructs computationally efficient methods to solve these two problems. It also examines sensitivity of Nash equilibrium to marginal changes in lower and upper bounds.     

Weak Measurement and Weak Information

Weak measurement devices resemble band pass filters: they strengthen average values in the state space or equivalently filter out some ‘frequencies’ from the conjugate Fourier transformed vector space. We thereby adjust a principle of classical communication theory for the use in quantum computation. We discuss some of the computational benefits and limitations of such an approach, including complexity analysis, some simple examples and a realistic not-so-weak approach.     

The mathematics of Ljubiša D.R. Kočinac

This note is a brief indication, from a personal perspective, of some of the contributions of Professor Ljubiša D.R. Ko?inac to mathematics, together with a list of selected publications of his.     

The topology of π···H hydrogen bonds

Abstract  

Unsaturated hydrocarbons are routinely used as proton acceptors because their π clouds possess a capacity to interact with Lewis acids and cationic species. Thus, in order to understand the formation of π hydrogen-bonded complexes, which in many cases are considered as weakly bound systems, the topological quantification of the charge density ruled by quantum mechanic theorems is very useful. Although elaborated by Richard Bader 40 years ago, the Quantum Theory of Atoms in Molecules (QTAIM) has only recently become widely known, and it has been applied in several scientific fields, allowing great insights in chemical bonding studies of intermolecular systems, in particular those formed by π···H hydrogen bonds.     

Predetermined intervals for start times of activities in?the?stochastic project scheduling problem

This paper proposes a new methodology to schedule activities in projects with stochastic activity durations. The main idea is to determine for each activity an interval in which the activity is allowed to start its processing. Deviations from these intervals result in penalty costs. We employ the Cross-Entropy methodology to set the intervals so as to minimize the sum of the expected penalty costs. The paper describes the implementation of the method, compares its results to other heuristic methods and provides some insights towards actual applications.     

A generalization of the Hall–Witt identity

Let Y → X be a finite normal cover of a wedge of n ≥ 3 circles. We prove that for any nonzero v ∈ H ₁(Y; Q) there exists a lift \(\widetilde F\) to Y of a basepoint-preserving homotopy equivalence F: X → X such that the set of iterates \(\left\{ {{{\widetilde F}^d}\left( v \right)} \right\}:d \in \mathbb{Z} \subseteq {H_1}\left( {Y,\mathbb{Q}} \right)\) is infinite. The main achievement of this paper is the use of representation theory to prove the existence of a purely topological object that seems to be inaccessible via topology.